TSTP Solution File: SWC351+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC351+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n023.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 12:40:09 EDT 2023

% Result   : Theorem 0.15s 0.33s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   40 (  14 unt;   0 def)
%            Number of atoms       :  183 (  47 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  216 (  73   ~;  69   |;  56   &)
%                                         (   6 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   5 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   58 (;  37   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( frontsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & app(V,W) = U ) ) ) ),
    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)
                       => ( app(W,Y) != X
                          | ~ strictorderedP(W)
                          | ? [Z] :
                              ( ssItem(Z)
                              & ? [X1] :
                                  ( ssList(X1)
                                  & app(cons(Z,nil),X1) = Y
                                  & ? [X2] :
                                      ( ssItem(X2)
                                      & ? [X3] :
                                          ( ssList(X3)
                                          & app(X3,cons(X2,nil)) = W
                                          & lt(X2,Z) ) ) ) ) ) )
                    | frontsegP(V,U)
                    | ( 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)
                         => ( app(W,Y) != X
                            | ~ strictorderedP(W)
                            | ? [Z] :
                                ( ssItem(Z)
                                & ? [X1] :
                                    ( ssList(X1)
                                    & app(cons(Z,nil),X1) = Y
                                    & ? [X2] :
                                        ( ssItem(X2)
                                        & ? [X3] :
                                            ( ssList(X3)
                                            & app(X3,cons(X2,nil)) = W
                                            & lt(X2,Z) ) ) ) ) ) )
                      | frontsegP(V,U)
                      | ( nil != X
                        & nil = W ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f119,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( frontsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & app(V,W) = U ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f120,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ frontsegP(U,V)
              | ? [W] :
                  ( ssList(W)
                  & app(V,W) = U ) )
            & ( frontsegP(U,V)
              | ! [W] :
                  ( ~ ssList(W)
                  | app(V,W) != U ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f119]) ).

fof(f121,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ frontsegP(U,V)
              | ( ssList(sk0_5(V,U))
                & app(V,sk0_5(V,U)) = U ) )
            & ( frontsegP(U,V)
              | ! [W] :
                  ( ~ ssList(W)
                  | app(V,W) != U ) ) ) ) ),
    inference(skolemization,[status(esa)],[f120]) ).

fof(f124,plain,
    ! [X0,X1,X2] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | frontsegP(X0,X1)
      | ~ ssList(X2)
      | app(X1,X2) != X0 ),
    inference(cnf_transformation,[status(esa)],[f121]) ).

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)
                      & app(W,Y) = X
                      & strictorderedP(W)
                      & ! [Z] :
                          ( ~ ssItem(Z)
                          | ! [X1] :
                              ( ~ ssList(X1)
                              | app(cons(Z,nil),X1) != Y
                              | ! [X2] :
                                  ( ~ ssItem(X2)
                                  | ! [X3] :
                                      ( ~ ssList(X3)
                                      | app(X3,cons(X2,nil)) != W
                                      | ~ lt(X2,Z) ) ) ) ) )
                  & ~ frontsegP(V,U)
                  & ( 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)
                      & app(W,Y) = X
                      & strictorderedP(W)
                      & ! [Z] :
                          ( ~ ssItem(Z)
                          | ! [X1] :
                              ( ~ ssList(X1)
                              | app(cons(Z,nil),X1) != Y )
                          | ! [X2] :
                              ( ~ ssItem(X2)
                              | ! [X3] :
                                  ( ~ ssList(X3)
                                  | app(X3,cons(X2,nil)) != W )
                              | ~ lt(X2,Z) ) ) )
                  & ~ frontsegP(V,U)
                  & ( 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)
    & app(sk0_49,sk0_51) = sk0_50
    & strictorderedP(sk0_49)
    & ! [Z] :
        ( ~ ssItem(Z)
        | ! [X1] :
            ( ~ ssList(X1)
            | app(cons(Z,nil),X1) != sk0_51 )
        | ! [X2] :
            ( ~ ssItem(X2)
            | ! [X3] :
                ( ~ ssList(X3)
                | app(X3,cons(X2,nil)) != sk0_49 )
            | ~ lt(X2,Z) ) )
    & ~ frontsegP(sk0_48,sk0_47)
    & ( nil = sk0_50
      | nil != sk0_49 ) ),
    inference(skolemization,[status(esa)],[f416]) ).

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

fof(f419,plain,
    ssList(sk0_48),
    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(f425,plain,
    ssList(sk0_51),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f426,plain,
    app(sk0_49,sk0_51) = sk0_50,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f429,plain,
    ~ frontsegP(sk0_48,sk0_47),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f442,plain,
    ! [X0,X1] :
      ( ~ ssList(app(X0,X1))
      | ~ ssList(X0)
      | frontsegP(app(X0,X1),X0)
      | ~ ssList(X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f124]) ).

fof(f478,plain,
    app(sk0_47,sk0_51) = sk0_50,
    inference(forward_demodulation,[status(thm)],[f423,f426]) ).

fof(f479,plain,
    app(sk0_47,sk0_51) = sk0_48,
    inference(forward_demodulation,[status(thm)],[f422,f478]) ).

fof(f480,plain,
    ( spl0_2
  <=> ssList(sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f482,plain,
    ( ~ ssList(sk0_48)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f480]) ).

fof(f483,plain,
    ( spl0_3
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f485,plain,
    ( ~ ssList(sk0_47)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f483]) ).

fof(f486,plain,
    ( spl0_4
  <=> frontsegP(app(sk0_47,sk0_51),sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f487,plain,
    ( frontsegP(app(sk0_47,sk0_51),sk0_47)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f486]) ).

fof(f489,plain,
    ( spl0_5
  <=> ssList(sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f491,plain,
    ( ~ ssList(sk0_51)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f489]) ).

fof(f492,plain,
    ( ~ ssList(sk0_48)
    | ~ ssList(sk0_47)
    | frontsegP(app(sk0_47,sk0_51),sk0_47)
    | ~ ssList(sk0_51) ),
    inference(paramodulation,[status(thm)],[f479,f442]) ).

fof(f493,plain,
    ( ~ spl0_2
    | ~ spl0_3
    | spl0_4
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f492,f480,f483,f486,f489]) ).

fof(f494,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f491,f425]) ).

fof(f495,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f494]) ).

fof(f496,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f485,f418]) ).

fof(f497,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f496]) ).

fof(f498,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f482,f419]) ).

fof(f499,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f498]) ).

fof(f500,plain,
    ( frontsegP(sk0_48,sk0_47)
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f479,f487]) ).

fof(f501,plain,
    ( $false
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f500,f429]) ).

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

fof(f503,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f493,f495,f497,f499,f502]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SWC351+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n023.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Tue May 30 11:42:38 EDT 2023
% 0.09/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.5.1
% 0.15/0.33  % Refutation found
% 0.15/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.56  % Elapsed time: 0.042048 seconds
% 0.15/0.56  % CPU time: 0.019228 seconds
% 0.15/0.56  % Memory used: 4.070 MB
%------------------------------------------------------------------------------