TSTP Solution File: SWC011+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC011+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:44:08 EDT 2024

% Result   : Theorem 0.16s 0.36s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   41 (   4 unt;   0 def)
%            Number of atoms       :  190 (  43 equ)
%            Maximal formula atoms :   19 (   4 avg)
%            Number of connectives :  236 (  87   ~;  76   |;  55   &)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   8 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   4 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-4 aty)
%            Number of variables   :  129 ( 106   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( V != X
                    | U != W
                    | ( ( ~ neq(V,nil)
                        | ? [Y] :
                            ( ssItem(Y)
                            & ? [Z] :
                                ( ssList(Z)
                                & ? [X1] :
                                    ( ssList(X1)
                                    & app(app(Z,cons(Y,nil)),X1) = V
                                    & app(Z,X1) = U ) ) )
                        | ! [X2] :
                            ( ssItem(X2)
                           => ! [X3] :
                                ( ssList(X3)
                               => ! [X4] :
                                    ( ssList(X4)
                                   => ( app(app(X3,cons(X2,nil)),X4) != X
                                      | app(X3,X4) != W ) ) ) ) )
                      & ( ~ neq(V,nil)
                        | neq(X,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f97,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( V != X
                      | U != W
                      | ( ( ~ neq(V,nil)
                          | ? [Y] :
                              ( ssItem(Y)
                              & ? [Z] :
                                  ( ssList(Z)
                                  & ? [X1] :
                                      ( ssList(X1)
                                      & app(app(Z,cons(Y,nil)),X1) = V
                                      & app(Z,X1) = U ) ) )
                          | ! [X2] :
                              ( ssItem(X2)
                             => ! [X3] :
                                  ( ssList(X3)
                                 => ! [X4] :
                                      ( ssList(X4)
                                     => ( app(app(X3,cons(X2,nil)),X4) != X
                                        | app(X3,X4) != W ) ) ) ) )
                        & ( ~ neq(V,nil)
                          | neq(X,nil) ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ( ( neq(V,nil)
                      & ! [Y] :
                          ( ~ ssItem(Y)
                          | ! [Z] :
                              ( ~ ssList(Z)
                              | ! [X1] :
                                  ( ~ ssList(X1)
                                  | app(app(Z,cons(Y,nil)),X1) != V
                                  | app(Z,X1) != U ) ) )
                      & ? [X2] :
                          ( ssItem(X2)
                          & ? [X3] :
                              ( ssList(X3)
                              & ? [X4] :
                                  ( ssList(X4)
                                  & app(app(X3,cons(X2,nil)),X4) = X
                                  & app(X3,X4) = W ) ) ) )
                    | ( neq(V,nil)
                      & ~ neq(X,nil) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ! [U,V,W,X] :
      ( pd0_0(X,W,V,U)
     => ( neq(V,nil)
        & ! [Y] :
            ( ~ ssItem(Y)
            | ! [Z] :
                ( ~ ssList(Z)
                | ! [X1] :
                    ( ~ ssList(X1)
                    | app(app(Z,cons(Y,nil)),X1) != V
                    | app(Z,X1) != U ) ) )
        & ? [X2] :
            ( ssItem(X2)
            & ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,cons(X2,nil)),X4) = X
                    & app(X3,X4) = W ) ) ) ) ),
    introduced(predicate_definition,[f415]) ).

fof(f417,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ( pd0_0(X,W,V,U)
                    | ( neq(V,nil)
                      & ~ neq(X,nil) ) ) ) ) ) ),
    inference(formula_renaming,[status(thm)],[f415,f416]) ).

fof(f418,plain,
    ( ssList(sk0_47)
    & ssList(sk0_48)
    & ssList(sk0_49)
    & ssList(sk0_50)
    & sk0_48 = sk0_50
    & sk0_47 = sk0_49
    & ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
      | ( neq(sk0_48,nil)
        & ~ neq(sk0_50,nil) ) ) ),
    inference(skolemization,[status(esa)],[f417]) ).

fof(f423,plain,
    sk0_48 = sk0_50,
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f424,plain,
    sk0_47 = sk0_49,
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f425,plain,
    ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
    | neq(sk0_48,nil) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f426,plain,
    ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
    | ~ neq(sk0_50,nil) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f427,plain,
    ! [U,V,W,X] :
      ( ~ pd0_0(X,W,V,U)
      | ( neq(V,nil)
        & ! [Y] :
            ( ~ ssItem(Y)
            | ! [Z] :
                ( ~ ssList(Z)
                | ! [X1] :
                    ( ~ ssList(X1)
                    | app(app(Z,cons(Y,nil)),X1) != V
                    | app(Z,X1) != U ) ) )
        & ? [X2] :
            ( ssItem(X2)
            & ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,cons(X2,nil)),X4) = X
                    & app(X3,X4) = W ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f416]) ).

fof(f428,plain,
    ! [U,V,W,X] :
      ( ~ pd0_0(X,W,V,U)
      | ( neq(V,nil)
        & ! [Y] :
            ( ~ ssItem(Y)
            | ! [Z] :
                ( ~ ssList(Z)
                | ! [X1] :
                    ( ~ ssList(X1)
                    | app(app(Z,cons(Y,nil)),X1) != V
                    | app(Z,X1) != U ) ) )
        & ssItem(sk0_51(X,W,V,U))
        & ssList(sk0_52(X,W,V,U))
        & ssList(sk0_53(X,W,V,U))
        & app(app(sk0_52(X,W,V,U),cons(sk0_51(X,W,V,U),nil)),sk0_53(X,W,V,U)) = X
        & app(sk0_52(X,W,V,U),sk0_53(X,W,V,U)) = W ) ),
    inference(skolemization,[status(esa)],[f427]) ).

fof(f430,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ ssItem(X4)
      | ~ ssList(X5)
      | ~ ssList(X6)
      | app(app(X5,cons(X4,nil)),X6) != X2
      | app(X5,X6) != X3 ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f431,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ssItem(sk0_51(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f432,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ssList(sk0_52(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f433,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ssList(sk0_53(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f434,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | app(app(sk0_52(X0,X1,X2,X3),cons(sk0_51(X0,X1,X2,X3),nil)),sk0_53(X0,X1,X2,X3)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f435,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | app(sk0_52(X0,X1,X2,X3),sk0_53(X0,X1,X2,X3)) = X1 ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f436,plain,
    ( spl0_0
  <=> pd0_0(sk0_50,sk0_49,sk0_48,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f437,plain,
    ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f436]) ).

fof(f439,plain,
    ( spl0_1
  <=> neq(sk0_48,nil) ),
    introduced(split_symbol_definition) ).

fof(f440,plain,
    ( neq(sk0_48,nil)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f439]) ).

fof(f442,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f425,f436,f439]) ).

fof(f443,plain,
    ( spl0_2
  <=> neq(sk0_50,nil) ),
    introduced(split_symbol_definition) ).

fof(f445,plain,
    ( ~ neq(sk0_50,nil)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f443]) ).

fof(f446,plain,
    ( spl0_0
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f426,f436,f443]) ).

fof(f461,plain,
    ( ~ neq(sk0_48,nil)
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f423,f445]) ).

fof(f462,plain,
    ( pd0_0(sk0_48,sk0_49,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f423,f437]) ).

fof(f463,plain,
    ( pd0_0(sk0_48,sk0_47,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f424,f462]) ).

fof(f467,plain,
    ( $false
    | spl0_2
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f440,f461]) ).

fof(f468,plain,
    ( spl0_2
    | ~ spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f467]) ).

fof(f473,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ pd0_0(X4,X5,X0,X6)
      | ~ ssItem(sk0_51(X0,X1,X2,X3))
      | ~ ssList(sk0_52(X0,X1,X2,X3))
      | ~ ssList(sk0_53(X0,X1,X2,X3))
      | app(sk0_52(X0,X1,X2,X3),sk0_53(X0,X1,X2,X3)) != X6 ),
    inference(resolution,[status(thm)],[f434,f430]) ).

fof(f474,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ pd0_0(X4,X5,X0,X6)
      | ~ ssList(sk0_52(X0,X1,X2,X3))
      | ~ ssList(sk0_53(X0,X1,X2,X3))
      | app(sk0_52(X0,X1,X2,X3),sk0_53(X0,X1,X2,X3)) != X6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f473,f431]) ).

fof(f483,plain,
    ! [X0,X1,X2,X3,X4,X5,X6] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ pd0_0(X4,X5,X0,X6)
      | ~ ssList(sk0_53(X0,X1,X2,X3))
      | app(sk0_52(X0,X1,X2,X3),sk0_53(X0,X1,X2,X3)) != X6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f474,f432]) ).

fof(f484,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ pd0_0(X4,X5,X0,X1)
      | ~ ssList(sk0_53(X0,X1,X2,X3))
      | ~ pd0_0(X0,X1,X2,X3) ),
    inference(resolution,[status(thm)],[f483,f435]) ).

fof(f485,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ pd0_0(X4,X5,X0,X1)
      | ~ ssList(sk0_53(X0,X1,X2,X3)) ),
    inference(duplicate_literals_removal,[status(esa)],[f484]) ).

fof(f486,plain,
    ! [X0,X1,X2,X3,X4,X5] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ pd0_0(X4,X5,X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[f485,f433]) ).

fof(f493,plain,
    ! [X0,X1] :
      ( ~ pd0_0(sk0_48,sk0_47,X0,X1)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f486,f463]) ).

fof(f494,plain,
    ( $false
    | ~ spl0_0 ),
    inference(backward_subsumption_resolution,[status(thm)],[f463,f493]) ).

fof(f495,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f494]) ).

fof(f496,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f442,f446,f468,f495]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10  % Problem  : SWC011+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n005.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 : Mon Apr 29 23:58:11 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.33  % Drodi V3.6.0
% 0.16/0.36  % Refutation found
% 0.16/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.37  % Elapsed time: 0.051736 seconds
% 0.16/0.37  % CPU time: 0.244551 seconds
% 0.16/0.37  % Total memory used: 62.671 MB
% 0.16/0.37  % Net memory used: 62.551 MB
%------------------------------------------------------------------------------