TSTP Solution File: SWC023+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC023+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 12:38:55 EDT 2023

% Result   : Theorem 0.10s 0.33s
% Output   : CNFRefutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   74 (   8 unt;   0 def)
%            Number of atoms       :  238 (  30 equ)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  261 (  97   ~;  99   |;  44   &)
%                                         (   9 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   15 (  13 usr;  10 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   47 (;  35   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,axiom,
    ! [U] :
      ( ssList(U)
     => frontsegP(U,nil) ),
    file('/export/starexec/sandbox2/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)
                        & neq(Y,nil)
                        & frontsegP(V,Y)
                        & frontsegP(U,Y) )
                    | ( ! [Z] :
                          ( ssList(Z)
                         => ( ~ neq(Z,nil)
                            | ~ frontsegP(X,Z)
                            | ~ frontsegP(W,Z) ) )
                      & ( nil != X
                        | nil != W ) ) ) ) ) ) ),
    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] :
                          ( ssList(Y)
                          & neq(Y,nil)
                          & frontsegP(V,Y)
                          & frontsegP(U,Y) )
                      | ( ! [Z] :
                            ( ssList(Z)
                           => ( ~ neq(Z,nil)
                              | ~ frontsegP(X,Z)
                              | ~ frontsegP(W,Z) ) )
                        & ( nil != X
                          | nil != W ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

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

fof(f294,plain,
    ! [U] :
      ( ~ ssList(U)
      | frontsegP(U,nil) ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f295,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | frontsegP(X0,nil) ),
    inference(cnf_transformation,[status(esa)],[f294]) ).

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)
                      | ~ neq(Y,nil)
                      | ~ frontsegP(V,Y)
                      | ~ frontsegP(U,Y) )
                  & ( ? [Z] :
                        ( ssList(Z)
                        & neq(Z,nil)
                        & frontsegP(X,Z)
                        & frontsegP(W,Z) )
                    | ( nil = X
                      & nil = W ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ! [W,X,Z] :
      ( pd0_0(Z,X,W)
     => ( ssList(Z)
        & neq(Z,nil)
        & frontsegP(X,Z)
        & frontsegP(W,Z) ) ),
    introduced(predicate_definition,[f415]) ).

fof(f417,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & neq(V,nil)
                  & ! [Y] :
                      ( ~ ssList(Y)
                      | ~ neq(Y,nil)
                      | ~ frontsegP(V,Y)
                      | ~ frontsegP(U,Y) )
                  & ( ? [Z] : pd0_0(Z,X,W)
                    | ( nil = X
                      & nil = W ) ) ) ) ) ),
    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
    & neq(sk0_48,nil)
    & ! [Y] :
        ( ~ ssList(Y)
        | ~ neq(Y,nil)
        | ~ frontsegP(sk0_48,Y)
        | ~ frontsegP(sk0_47,Y) )
    & ( pd0_0(sk0_51,sk0_50,sk0_49)
      | ( nil = sk0_50
        & nil = sk0_49 ) ) ),
    inference(skolemization,[status(esa)],[f417]) ).

fof(f420,plain,
    ssList(sk0_48),
    inference(cnf_transformation,[status(esa)],[f418]) ).

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,
    neq(sk0_48,nil),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f426,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ neq(X0,nil)
      | ~ frontsegP(sk0_48,X0)
      | ~ frontsegP(sk0_47,X0) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f427,plain,
    ( pd0_0(sk0_51,sk0_50,sk0_49)
    | nil = sk0_50 ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f428,plain,
    ( pd0_0(sk0_51,sk0_50,sk0_49)
    | nil = sk0_49 ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f429,plain,
    ! [W,X,Z] :
      ( ~ pd0_0(Z,X,W)
      | ( ssList(Z)
        & neq(Z,nil)
        & frontsegP(X,Z)
        & frontsegP(W,Z) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f416]) ).

fof(f430,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | ssList(X0) ),
    inference(cnf_transformation,[status(esa)],[f429]) ).

fof(f431,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | neq(X0,nil) ),
    inference(cnf_transformation,[status(esa)],[f429]) ).

fof(f432,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | frontsegP(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f429]) ).

fof(f433,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | frontsegP(X2,X0) ),
    inference(cnf_transformation,[status(esa)],[f429]) ).

fof(f434,plain,
    ( spl0_0
  <=> pd0_0(sk0_51,sk0_50,sk0_49) ),
    introduced(split_symbol_definition) ).

fof(f435,plain,
    ( pd0_0(sk0_51,sk0_50,sk0_49)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f434]) ).

fof(f437,plain,
    ( spl0_1
  <=> nil = sk0_50 ),
    introduced(split_symbol_definition) ).

fof(f438,plain,
    ( nil = sk0_50
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f437]) ).

fof(f440,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f427,f434,f437]) ).

fof(f441,plain,
    ( spl0_2
  <=> nil = sk0_49 ),
    introduced(split_symbol_definition) ).

fof(f442,plain,
    ( nil = sk0_49
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f441]) ).

fof(f444,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f428,f434,f441]) ).

fof(f481,plain,
    ( pd0_0(sk0_51,sk0_48,sk0_49)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f423,f435]) ).

fof(f482,plain,
    ( pd0_0(sk0_51,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f424,f481]) ).

fof(f483,plain,
    ( frontsegP(sk0_47,sk0_51)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f482,f433]) ).

fof(f484,plain,
    ( frontsegP(sk0_48,sk0_51)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f482,f432]) ).

fof(f485,plain,
    ( ssList(sk0_51)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f482,f430]) ).

fof(f486,plain,
    ( neq(sk0_51,nil)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f431,f482]) ).

fof(f487,plain,
    ( spl0_3
  <=> ssList(sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f489,plain,
    ( ~ ssList(sk0_51)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f487]) ).

fof(f490,plain,
    ( spl0_4
  <=> frontsegP(sk0_48,sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f492,plain,
    ( ~ frontsegP(sk0_48,sk0_51)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f490]) ).

fof(f493,plain,
    ( spl0_5
  <=> frontsegP(sk0_47,sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f495,plain,
    ( ~ frontsegP(sk0_47,sk0_51)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f493]) ).

fof(f496,plain,
    ( ~ ssList(sk0_51)
    | ~ frontsegP(sk0_48,sk0_51)
    | ~ frontsegP(sk0_47,sk0_51)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f426,f486]) ).

fof(f497,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | ~ spl0_5
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f496,f487,f490,f493,f434]) ).

fof(f498,plain,
    ( spl0_6
  <=> ssList(sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f500,plain,
    ( ~ ssList(sk0_48)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f498]) ).

fof(f501,plain,
    ( spl0_7
  <=> frontsegP(sk0_48,sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f503,plain,
    ( ~ frontsegP(sk0_48,sk0_48)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f501]) ).

fof(f504,plain,
    ( spl0_8
  <=> frontsegP(sk0_47,sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f506,plain,
    ( ~ frontsegP(sk0_47,sk0_48)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f504]) ).

fof(f507,plain,
    ( ~ ssList(sk0_48)
    | ~ frontsegP(sk0_48,sk0_48)
    | ~ frontsegP(sk0_47,sk0_48) ),
    inference(resolution,[status(thm)],[f426,f425]) ).

fof(f508,plain,
    ( ~ spl0_6
    | ~ spl0_7
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f507,f498,f501,f504]) ).

fof(f509,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f500,f420]) ).

fof(f510,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f509]) ).

fof(f511,plain,
    ( $false
    | ~ spl0_0
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f495,f483]) ).

fof(f512,plain,
    ( ~ spl0_0
    | spl0_5 ),
    inference(contradiction_clause,[status(thm)],[f511]) ).

fof(f513,plain,
    ( nil = sk0_48
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f423,f438]) ).

fof(f514,plain,
    ( nil = sk0_47
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f424,f442]) ).

fof(f523,plain,
    ( ~ frontsegP(nil,sk0_48)
    | ~ spl0_1
    | spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f513,f503]) ).

fof(f524,plain,
    ( ~ frontsegP(nil,nil)
    | ~ spl0_1
    | spl0_7 ),
    inference(forward_demodulation,[status(thm)],[f513,f523]) ).

fof(f525,plain,
    ( ~ ssList(nil)
    | ~ spl0_1
    | spl0_7 ),
    inference(resolution,[status(thm)],[f524,f295]) ).

fof(f526,plain,
    ( $false
    | ~ spl0_1
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f525,f223]) ).

fof(f527,plain,
    ( ~ spl0_1
    | spl0_7 ),
    inference(contradiction_clause,[status(thm)],[f526]) ).

fof(f528,plain,
    ( $false
    | spl0_3
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f485,f489]) ).

fof(f529,plain,
    ( spl0_3
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f528]) ).

fof(f532,plain,
    ( ~ frontsegP(nil,sk0_48)
    | ~ spl0_2
    | spl0_8 ),
    inference(forward_demodulation,[status(thm)],[f514,f506]) ).

fof(f533,plain,
    ( ~ frontsegP(nil,nil)
    | ~ spl0_1
    | ~ spl0_2
    | spl0_8 ),
    inference(forward_demodulation,[status(thm)],[f513,f532]) ).

fof(f534,plain,
    ( ~ ssList(nil)
    | ~ spl0_1
    | ~ spl0_2
    | spl0_8 ),
    inference(resolution,[status(thm)],[f533,f295]) ).

fof(f535,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_2
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f534,f223]) ).

fof(f536,plain,
    ( ~ spl0_1
    | ~ spl0_2
    | spl0_8 ),
    inference(contradiction_clause,[status(thm)],[f535]) ).

fof(f537,plain,
    ( $false
    | spl0_4
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f484,f492]) ).

fof(f538,plain,
    ( spl0_4
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f537]) ).

fof(f539,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f440,f444,f497,f508,f510,f512,f527,f529,f536,f538]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem  : SWC023+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n004.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 11:16:37 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.33  % Drodi V3.5.1
% 0.10/0.33  % Refutation found
% 0.10/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.57  % Elapsed time: 0.038687 seconds
% 0.18/0.57  % CPU time: 0.020767 seconds
% 0.18/0.57  % Memory used: 4.107 MB
%------------------------------------------------------------------------------