TSTP Solution File: SWC322+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC322+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 12:40:03 EDT 2023

% Result   : Theorem 0.20s 0.38s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   47 (   5 unt;   0 def)
%            Number of atoms       :  183 (  79 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  210 (  74   ~;  69   |;  49   &)
%                                         (   5 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   6 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :   70 (;  53   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( V != X
                    | U != W
                    | ? [Y] :
                        ( ssItem(Y)
                        & ? [Z] :
                            ( ssList(Z)
                            & app(cons(Y,nil),Z) != W
                            & app(Z,cons(Y,nil)) = X ) )
                    | ( nil != W
                      & nil = X )
                    | ( ! [X1] :
                          ( ssItem(X1)
                         => ! [X2] :
                              ( ssList(X2)
                             => ( app(X2,cons(X1,nil)) != V
                                | app(cons(X1,nil),X2) = U ) ) )
                      & ( nil != V
                        | nil = U ) ) ) ) ) ) ),
    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
                      | ? [Y] :
                          ( ssItem(Y)
                          & ? [Z] :
                              ( ssList(Z)
                              & app(cons(Y,nil),Z) != W
                              & app(Z,cons(Y,nil)) = X ) )
                      | ( nil != W
                        & nil = X )
                      | ( ! [X1] :
                            ( ssItem(X1)
                           => ! [X2] :
                                ( ssList(X2)
                               => ( app(X2,cons(X1,nil)) != V
                                  | app(cons(X1,nil),X2) = U ) ) )
                        & ( nil != V
                          | nil = U ) ) ) ) ) ) ),
    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
                  & ! [Y] :
                      ( ~ ssItem(Y)
                      | ! [Z] :
                          ( ~ ssList(Z)
                          | app(cons(Y,nil),Z) = W
                          | app(Z,cons(Y,nil)) != X ) )
                  & ( nil = W
                    | nil != X )
                  & ( ? [X1] :
                        ( ssItem(X1)
                        & ? [X2] :
                            ( ssList(X2)
                            & app(X2,cons(X1,nil)) = V
                            & app(cons(X1,nil),X2) != U ) )
                    | ( nil = V
                      & nil != U ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ! [U,V,X1] :
      ( pd0_0(X1,V,U)
     => ( ssItem(X1)
        & ? [X2] :
            ( ssList(X2)
            & app(X2,cons(X1,nil)) = V
            & app(cons(X1,nil),X2) != U ) ) ),
    introduced(predicate_definition,[f415]) ).

fof(f417,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ! [Y] :
                      ( ~ ssItem(Y)
                      | ! [Z] :
                          ( ~ ssList(Z)
                          | app(cons(Y,nil),Z) = W
                          | app(Z,cons(Y,nil)) != X ) )
                  & ( nil = W
                    | nil != X )
                  & ( ? [X1] : pd0_0(X1,V,U)
                    | ( nil = V
                      & nil != U ) ) ) ) ) ),
    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
    & ! [Y] :
        ( ~ ssItem(Y)
        | ! [Z] :
            ( ~ ssList(Z)
            | app(cons(Y,nil),Z) = sk0_49
            | app(Z,cons(Y,nil)) != sk0_50 ) )
    & ( nil = sk0_49
      | nil != sk0_50 )
    & ( pd0_0(sk0_51,sk0_48,sk0_47)
      | ( nil = sk0_48
        & nil != sk0_47 ) ) ),
    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,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | app(cons(X0,nil),X1) = sk0_49
      | app(X1,cons(X0,nil)) != sk0_50 ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f426,plain,
    ( nil = sk0_49
    | nil != sk0_50 ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f427,plain,
    ( pd0_0(sk0_51,sk0_48,sk0_47)
    | nil = sk0_48 ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f428,plain,
    ( pd0_0(sk0_51,sk0_48,sk0_47)
    | nil != sk0_47 ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f429,plain,
    ! [U,V,X1] :
      ( ~ pd0_0(X1,V,U)
      | ( ssItem(X1)
        & ? [X2] :
            ( ssList(X2)
            & app(X2,cons(X1,nil)) = V
            & app(cons(X1,nil),X2) != U ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f416]) ).

fof(f430,plain,
    ! [U,V,X1] :
      ( ~ pd0_0(X1,V,U)
      | ( ssItem(X1)
        & ssList(sk0_52(X1,V,U))
        & app(sk0_52(X1,V,U),cons(X1,nil)) = V
        & app(cons(X1,nil),sk0_52(X1,V,U)) != U ) ),
    inference(skolemization,[status(esa)],[f429]) ).

fof(f431,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | ssItem(X0) ),
    inference(cnf_transformation,[status(esa)],[f430]) ).

fof(f432,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | ssList(sk0_52(X0,X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f430]) ).

fof(f433,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | app(sk0_52(X0,X1,X2),cons(X0,nil)) = X1 ),
    inference(cnf_transformation,[status(esa)],[f430]) ).

fof(f434,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | app(cons(X0,nil),sk0_52(X0,X1,X2)) != X2 ),
    inference(cnf_transformation,[status(esa)],[f430]) ).

fof(f435,plain,
    ( spl0_0
  <=> nil = sk0_49 ),
    introduced(split_symbol_definition) ).

fof(f436,plain,
    ( nil = sk0_49
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f435]) ).

fof(f438,plain,
    ( spl0_1
  <=> nil = sk0_50 ),
    introduced(split_symbol_definition) ).

fof(f440,plain,
    ( nil != sk0_50
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f438]) ).

fof(f441,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f426,f435,f438]) ).

fof(f442,plain,
    ( spl0_2
  <=> pd0_0(sk0_51,sk0_48,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f443,plain,
    ( pd0_0(sk0_51,sk0_48,sk0_47)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f442]) ).

fof(f445,plain,
    ( spl0_3
  <=> nil = sk0_48 ),
    introduced(split_symbol_definition) ).

fof(f446,plain,
    ( nil = sk0_48
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f445]) ).

fof(f448,plain,
    ( spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f427,f442,f445]) ).

fof(f449,plain,
    ( spl0_4
  <=> nil = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f451,plain,
    ( nil != sk0_47
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f449]) ).

fof(f452,plain,
    ( spl0_2
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f428,f442,f449]) ).

fof(f502,plain,
    ( nil != sk0_48
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f423,f440]) ).

fof(f507,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | app(cons(X0,nil),X1) = sk0_47
      | app(X1,cons(X0,nil)) != sk0_50 ),
    inference(forward_demodulation,[status(thm)],[f424,f425]) ).

fof(f508,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | app(cons(X0,nil),X1) = sk0_47
      | app(X1,cons(X0,nil)) != sk0_48 ),
    inference(forward_demodulation,[status(thm)],[f423,f507]) ).

fof(f509,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,sk0_48,X1)
      | ~ ssItem(X0)
      | ~ ssList(sk0_52(X0,sk0_48,X1))
      | app(cons(X0,nil),sk0_52(X0,sk0_48,X1)) = sk0_47 ),
    inference(resolution,[status(thm)],[f433,f508]) ).

fof(f510,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,sk0_48,X1)
      | ~ ssList(sk0_52(X0,sk0_48,X1))
      | app(cons(X0,nil),sk0_52(X0,sk0_48,X1)) = sk0_47 ),
    inference(forward_subsumption_resolution,[status(thm)],[f509,f431]) ).

fof(f511,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,sk0_48,X1)
      | app(cons(X0,nil),sk0_52(X0,sk0_48,X1)) = sk0_47 ),
    inference(forward_subsumption_resolution,[status(thm)],[f510,f432]) ).

fof(f512,plain,
    ! [X0] :
      ( ~ pd0_0(X0,sk0_48,sk0_47)
      | ~ pd0_0(X0,sk0_48,sk0_47) ),
    inference(resolution,[status(thm)],[f511,f434]) ).

fof(f513,plain,
    ! [X0] : ~ pd0_0(X0,sk0_48,sk0_47),
    inference(duplicate_literals_removal,[status(esa)],[f512]) ).

fof(f514,plain,
    ( $false
    | ~ spl0_2 ),
    inference(backward_subsumption_resolution,[status(thm)],[f443,f513]) ).

fof(f515,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f514]) ).

fof(f516,plain,
    ( $false
    | spl0_1
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f446,f502]) ).

fof(f517,plain,
    ( spl0_1
    | ~ spl0_3 ),
    inference(contradiction_clause,[status(thm)],[f516]) ).

fof(f518,plain,
    ( nil = sk0_47
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f424,f436]) ).

fof(f519,plain,
    ( $false
    | spl0_4
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f518,f451]) ).

fof(f520,plain,
    ( spl0_4
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f519]) ).

fof(f521,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f441,f448,f452,f515,f517,f520]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC322+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n018.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 11:30:10 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.36  % Drodi V3.5.1
% 0.20/0.38  % Refutation found
% 0.20/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.64  % Elapsed time: 0.073715 seconds
% 0.22/0.64  % CPU time: 0.036828 seconds
% 0.22/0.64  % Memory used: 4.091 MB
%------------------------------------------------------------------------------