TSTP Solution File: SWC213+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC213+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n001.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 12:39:41 EDT 2023

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   45 (  10 unt;   0 def)
%            Number of atoms       :  206 (  64 equ)
%            Maximal formula atoms :   24 (   4 avg)
%            Number of connectives :  250 (  89   ~;  79   |;  61   &)
%                                         (   7 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   6 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   66 (;  42   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> U != V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( V != X
                    | U != W
                    | ~ neq(V,nil)
                    | ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ssList(Z)
                           => ( app(app(Y,W),Z) != X
                              | ~ equalelemsP(W)
                              | ? [X1] :
                                  ( ssItem(X1)
                                  & ? [X2] :
                                      ( ssList(X2)
                                      & app(X2,cons(X1,nil)) = Y
                                      & ? [X3] :
                                          ( ssList(X3)
                                          & app(cons(X1,nil),X3) = W ) ) )
                              | ? [X4] :
                                  ( ssItem(X4)
                                  & ? [X5] :
                                      ( ssList(X5)
                                      & app(cons(X4,nil),X5) = Z
                                      & ? [X6] :
                                          ( ssList(X6)
                                          & app(X6,cons(X4,nil)) = W ) ) ) ) ) )
                    | neq(U,nil)
                    | ( nil != X
                      & nil = W ) ) ) ) ) ),
    file('/export/starexec/sandbox/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] :
                          ( ssList(Y)
                         => ! [Z] :
                              ( ssList(Z)
                             => ( app(app(Y,W),Z) != X
                                | ~ equalelemsP(W)
                                | ? [X1] :
                                    ( ssItem(X1)
                                    & ? [X2] :
                                        ( ssList(X2)
                                        & app(X2,cons(X1,nil)) = Y
                                        & ? [X3] :
                                            ( ssList(X3)
                                            & app(cons(X1,nil),X3) = W ) ) )
                                | ? [X4] :
                                    ( ssItem(X4)
                                    & ? [X5] :
                                        ( ssList(X5)
                                        & app(cons(X4,nil),X5) = Z
                                        & ? [X6] :
                                            ( ssList(X6)
                                            & app(X6,cons(X4,nil)) = W ) ) ) ) ) )
                      | neq(U,nil)
                      | ( nil != X
                        & nil = W ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f217,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( neq(U,V)
          <=> U != V ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f218,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ neq(U,V)
              | U != V )
            & ( neq(U,V)
              | U = V ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f217]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ neq(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f218]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | neq(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f218]) ).

fof(f223,plain,
    ssList(nil),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & neq(V,nil)
                  & ? [Y] :
                      ( ssList(Y)
                      & ? [Z] :
                          ( ssList(Z)
                          & app(app(Y,W),Z) = X
                          & equalelemsP(W)
                          & ! [X1] :
                              ( ~ ssItem(X1)
                              | ! [X2] :
                                  ( ~ ssList(X2)
                                  | app(X2,cons(X1,nil)) != Y
                                  | ! [X3] :
                                      ( ~ ssList(X3)
                                      | app(cons(X1,nil),X3) != W ) ) )
                          & ! [X4] :
                              ( ~ ssItem(X4)
                              | ! [X5] :
                                  ( ~ ssList(X5)
                                  | app(cons(X4,nil),X5) != Z
                                  | ! [X6] :
                                      ( ~ ssList(X6)
                                      | app(X6,cons(X4,nil)) != W ) ) ) ) )
                  & ~ neq(U,nil)
                  & ( nil = X
                    | nil != W ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & neq(V,nil)
                  & ? [Y] :
                      ( ssList(Y)
                      & ? [Z] :
                          ( ssList(Z)
                          & app(app(Y,W),Z) = X
                          & equalelemsP(W)
                          & ! [X1] :
                              ( ~ ssItem(X1)
                              | ! [X2] :
                                  ( ~ ssList(X2)
                                  | app(X2,cons(X1,nil)) != Y )
                              | ! [X3] :
                                  ( ~ ssList(X3)
                                  | app(cons(X1,nil),X3) != W ) )
                          & ! [X4] :
                              ( ~ ssItem(X4)
                              | ! [X5] :
                                  ( ~ ssList(X5)
                                  | app(cons(X4,nil),X5) != Z )
                              | ! [X6] :
                                  ( ~ ssList(X6)
                                  | app(X6,cons(X4,nil)) != W ) ) ) )
                  & ~ neq(U,nil)
                  & ( nil = X
                    | nil != W ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f415]) ).

fof(f417,plain,
    ( ssList(sk0_47)
    & ssList(sk0_48)
    & ssList(sk0_49)
    & ssList(sk0_50)
    & sk0_48 = sk0_50
    & sk0_47 = sk0_49
    & neq(sk0_48,nil)
    & ssList(sk0_51)
    & ssList(sk0_52)
    & app(app(sk0_51,sk0_49),sk0_52) = sk0_50
    & equalelemsP(sk0_49)
    & ! [X1] :
        ( ~ ssItem(X1)
        | ! [X2] :
            ( ~ ssList(X2)
            | app(X2,cons(X1,nil)) != sk0_51 )
        | ! [X3] :
            ( ~ ssList(X3)
            | app(cons(X1,nil),X3) != sk0_49 ) )
    & ! [X4] :
        ( ~ ssItem(X4)
        | ! [X5] :
            ( ~ ssList(X5)
            | app(cons(X4,nil),X5) != sk0_52 )
        | ! [X6] :
            ( ~ ssList(X6)
            | app(X6,cons(X4,nil)) != sk0_49 ) )
    & ~ neq(sk0_47,nil)
    & ( nil = sk0_50
      | nil != sk0_49 ) ),
    inference(skolemization,[status(esa)],[f416]) ).

fof(f418,plain,
    ssList(sk0_47),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f422,plain,
    sk0_48 = sk0_50,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f423,plain,
    sk0_47 = sk0_49,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f424,plain,
    neq(sk0_48,nil),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f431,plain,
    ~ neq(sk0_47,nil),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f432,plain,
    ( nil = sk0_50
    | nil != sk0_49 ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f433,plain,
    ( spl0_0
  <=> nil = sk0_50 ),
    introduced(split_symbol_definition) ).

fof(f434,plain,
    ( nil = sk0_50
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f433]) ).

fof(f436,plain,
    ( spl0_1
  <=> nil = sk0_49 ),
    introduced(split_symbol_definition) ).

fof(f438,plain,
    ( nil != sk0_49
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f436]) ).

fof(f439,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f432,f433,f436]) ).

fof(f455,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f219]) ).

fof(f456,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ neq(X0,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f455]) ).

fof(f479,plain,
    ( spl0_4
  <=> sk0_47 = nil ),
    introduced(split_symbol_definition) ).

fof(f480,plain,
    ( sk0_47 = nil
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f479]) ).

fof(f484,plain,
    ( nil != sk0_47
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f423,f438]) ).

fof(f489,plain,
    ( spl0_5
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f491,plain,
    ( ~ ssList(sk0_47)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f489]) ).

fof(f492,plain,
    ( spl0_6
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f494,plain,
    ( ~ ssList(nil)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f492]) ).

fof(f495,plain,
    ( ~ ssList(sk0_47)
    | ~ ssList(nil)
    | sk0_47 = nil ),
    inference(resolution,[status(thm)],[f220,f431]) ).

fof(f496,plain,
    ( ~ spl0_5
    | ~ spl0_6
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f495,f489,f492,f479]) ).

fof(f497,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f494,f223]) ).

fof(f498,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f497]) ).

fof(f499,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f491,f418]) ).

fof(f500,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f499]) ).

fof(f501,plain,
    ( $false
    | spl0_1
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f480,f484]) ).

fof(f502,plain,
    ( spl0_1
    | ~ spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f501]) ).

fof(f503,plain,
    ( nil = sk0_48
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f422,f434]) ).

fof(f506,plain,
    ( neq(nil,nil)
    | ~ spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f503,f424]) ).

fof(f515,plain,
    ( ~ ssList(nil)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f506,f456]) ).

fof(f516,plain,
    ( ~ spl0_6
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f515,f492,f433]) ).

fof(f518,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f439,f496,f498,f500,f502,f516]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWC213+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n001.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 11:53:15 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 0.12/0.36  % Refutation found
% 0.12/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38  % Elapsed time: 0.031546 seconds
% 0.12/0.38  % CPU time: 0.050595 seconds
% 0.12/0.38  % Memory used: 16.189 MB
%------------------------------------------------------------------------------