TSTP Solution File: SWC339+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC339+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 20:45:24 EDT 2024

% Result   : Theorem 0.15s 0.37s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   49 (  17 unt;   0 def)
%            Number of atoms       :  248 (  57 equ)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  302 ( 103   ~; 100   |;  77   &)
%                                         (   8 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   30 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   7 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   89 (  55   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( segmentP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ? [X] :
                    ( ssList(X)
                    & app(app(W,V),X) = 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
                    | ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ssList(Z)
                           => ( app(app(Y,W),Z) != X
                              | ~ totalorderedP(W)
                              | ? [X1] :
                                  ( ssItem(X1)
                                  & ? [X2] :
                                      ( ssList(X2)
                                      & app(X2,cons(X1,nil)) = Y
                                      & ? [X3] :
                                          ( ssItem(X3)
                                          & ? [X4] :
                                              ( ssList(X4)
                                              & app(cons(X3,nil),X4) = W
                                              & leq(X1,X3) ) ) ) )
                              | ? [X5] :
                                  ( ssItem(X5)
                                  & ? [X6] :
                                      ( ssList(X6)
                                      & app(cons(X5,nil),X6) = Z
                                      & ? [X7] :
                                          ( ssItem(X7)
                                          & ? [X8] :
                                              ( ssList(X8)
                                              & app(X8,cons(X7,nil)) = W
                                              & leq(X7,X5) ) ) ) ) ) ) )
                    | ( nil != X
                      & nil = W )
                    | ( segmentP(V,U)
                      & totalorderedP(U) ) ) ) ) ) ),
    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
                      | ! [Y] :
                          ( ssList(Y)
                         => ! [Z] :
                              ( ssList(Z)
                             => ( app(app(Y,W),Z) != X
                                | ~ totalorderedP(W)
                                | ? [X1] :
                                    ( ssItem(X1)
                                    & ? [X2] :
                                        ( ssList(X2)
                                        & app(X2,cons(X1,nil)) = Y
                                        & ? [X3] :
                                            ( ssItem(X3)
                                            & ? [X4] :
                                                ( ssList(X4)
                                                & app(cons(X3,nil),X4) = W
                                                & leq(X1,X3) ) ) ) )
                                | ? [X5] :
                                    ( ssItem(X5)
                                    & ? [X6] :
                                        ( ssList(X6)
                                        & app(cons(X5,nil),X6) = Z
                                        & ? [X7] :
                                            ( ssItem(X7)
                                            & ? [X8] :
                                                ( ssList(X8)
                                                & app(X8,cons(X7,nil)) = W
                                                & leq(X7,X5) ) ) ) ) ) ) )
                      | ( nil != X
                        & nil = W )
                      | ( segmentP(V,U)
                        & totalorderedP(U) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f131,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( segmentP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ? [X] :
                    ( ssList(X)
                    & app(app(W,V),X) = U ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f132,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ segmentP(U,V)
              | ? [W] :
                  ( ssList(W)
                  & ? [X] :
                      ( ssList(X)
                      & app(app(W,V),X) = U ) ) )
            & ( segmentP(U,V)
              | ! [W] :
                  ( ~ ssList(W)
                  | ! [X] :
                      ( ~ ssList(X)
                      | app(app(W,V),X) != U ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f131]) ).

fof(f133,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ segmentP(U,V)
              | ( ssList(sk0_7(V,U))
                & ssList(sk0_8(V,U))
                & app(app(sk0_7(V,U),V),sk0_8(V,U)) = U ) )
            & ( segmentP(U,V)
              | ! [W] :
                  ( ~ ssList(W)
                  | ! [X] :
                      ( ~ ssList(X)
                      | app(app(W,V),X) != U ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f132]) ).

fof(f137,plain,
    ! [X0,X1,X2,X3] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | segmentP(X0,X1)
      | ~ ssList(X2)
      | ~ ssList(X3)
      | app(app(X2,X1),X3) != X0 ),
    inference(cnf_transformation,[status(esa)],[f133]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ? [Y] :
                      ( ssList(Y)
                      & ? [Z] :
                          ( ssList(Z)
                          & app(app(Y,W),Z) = X
                          & totalorderedP(W)
                          & ! [X1] :
                              ( ~ ssItem(X1)
                              | ! [X2] :
                                  ( ~ ssList(X2)
                                  | app(X2,cons(X1,nil)) != Y
                                  | ! [X3] :
                                      ( ~ ssItem(X3)
                                      | ! [X4] :
                                          ( ~ ssList(X4)
                                          | app(cons(X3,nil),X4) != W
                                          | ~ leq(X1,X3) ) ) ) )
                          & ! [X5] :
                              ( ~ ssItem(X5)
                              | ! [X6] :
                                  ( ~ ssList(X6)
                                  | app(cons(X5,nil),X6) != Z
                                  | ! [X7] :
                                      ( ~ ssItem(X7)
                                      | ! [X8] :
                                          ( ~ ssList(X8)
                                          | app(X8,cons(X7,nil)) != W
                                          | ~ leq(X7,X5) ) ) ) ) ) )
                  & ( nil = X
                    | nil != W )
                  & ( ~ segmentP(V,U)
                    | ~ totalorderedP(U) ) ) ) ) ),
    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
                  & ? [Y] :
                      ( ssList(Y)
                      & ? [Z] :
                          ( ssList(Z)
                          & app(app(Y,W),Z) = X
                          & totalorderedP(W)
                          & ! [X1] :
                              ( ~ ssItem(X1)
                              | ! [X2] :
                                  ( ~ ssList(X2)
                                  | app(X2,cons(X1,nil)) != Y )
                              | ! [X3] :
                                  ( ~ ssItem(X3)
                                  | ! [X4] :
                                      ( ~ ssList(X4)
                                      | app(cons(X3,nil),X4) != W )
                                  | ~ leq(X1,X3) ) )
                          & ! [X5] :
                              ( ~ ssItem(X5)
                              | ! [X6] :
                                  ( ~ ssList(X6)
                                  | app(cons(X5,nil),X6) != Z )
                              | ! [X7] :
                                  ( ~ ssItem(X7)
                                  | ! [X8] :
                                      ( ~ ssList(X8)
                                      | app(X8,cons(X7,nil)) != W )
                                  | ~ leq(X7,X5) ) ) ) )
                  & ( nil = X
                    | nil != W )
                  & ( ~ segmentP(V,U)
                    | ~ totalorderedP(U) ) ) ) ) ),
    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
    & ssList(sk0_51)
    & ssList(sk0_52)
    & app(app(sk0_51,sk0_49),sk0_52) = sk0_50
    & totalorderedP(sk0_49)
    & ! [X1] :
        ( ~ ssItem(X1)
        | ! [X2] :
            ( ~ ssList(X2)
            | app(X2,cons(X1,nil)) != sk0_51 )
        | ! [X3] :
            ( ~ ssItem(X3)
            | ! [X4] :
                ( ~ ssList(X4)
                | app(cons(X3,nil),X4) != sk0_49 )
            | ~ leq(X1,X3) ) )
    & ! [X5] :
        ( ~ ssItem(X5)
        | ! [X6] :
            ( ~ ssList(X6)
            | app(cons(X5,nil),X6) != sk0_52 )
        | ! [X7] :
            ( ~ ssItem(X7)
            | ! [X8] :
                ( ~ ssList(X8)
                | app(X8,cons(X7,nil)) != sk0_49 )
            | ~ leq(X7,X5) ) )
    & ( nil = sk0_50
      | nil != sk0_49 )
    & ( ~ segmentP(sk0_48,sk0_47)
      | ~ totalorderedP(sk0_47) ) ),
    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(f424,plain,
    ssList(sk0_51),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f425,plain,
    ssList(sk0_52),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f426,plain,
    app(app(sk0_51,sk0_49),sk0_52) = sk0_50,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f427,plain,
    totalorderedP(sk0_49),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f431,plain,
    ( ~ segmentP(sk0_48,sk0_47)
    | ~ totalorderedP(sk0_47) ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f439,plain,
    ( spl0_2
  <=> segmentP(sk0_48,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f442,plain,
    ( spl0_3
  <=> totalorderedP(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f444,plain,
    ( ~ totalorderedP(sk0_47)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f442]) ).

fof(f445,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f431,f439,f442]) ).

fof(f452,plain,
    ! [X0,X1,X2] :
      ( ~ ssList(app(app(X0,X1),X2))
      | ~ ssList(X1)
      | segmentP(app(app(X0,X1),X2),X1)
      | ~ ssList(X0)
      | ~ ssList(X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f137]) ).

fof(f478,plain,
    totalorderedP(sk0_47),
    inference(forward_demodulation,[status(thm)],[f423,f427]) ).

fof(f480,plain,
    app(app(sk0_51,sk0_47),sk0_52) = sk0_50,
    inference(forward_demodulation,[status(thm)],[f423,f426]) ).

fof(f481,plain,
    app(app(sk0_51,sk0_47),sk0_52) = sk0_48,
    inference(forward_demodulation,[status(thm)],[f422,f480]) ).

fof(f482,plain,
    ( spl0_4
  <=> ssList(app(app(sk0_51,sk0_47),sk0_52)) ),
    introduced(split_symbol_definition) ).

fof(f484,plain,
    ( ~ ssList(app(app(sk0_51,sk0_47),sk0_52))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f482]) ).

fof(f485,plain,
    ( spl0_5
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f487,plain,
    ( ~ ssList(sk0_47)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f485]) ).

fof(f488,plain,
    ( spl0_6
  <=> ssList(sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f490,plain,
    ( ~ ssList(sk0_51)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f488]) ).

fof(f491,plain,
    ( spl0_7
  <=> ssList(sk0_52) ),
    introduced(split_symbol_definition) ).

fof(f493,plain,
    ( ~ ssList(sk0_52)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f491]) ).

fof(f494,plain,
    ( ~ ssList(app(app(sk0_51,sk0_47),sk0_52))
    | ~ ssList(sk0_47)
    | segmentP(sk0_48,sk0_47)
    | ~ ssList(sk0_51)
    | ~ ssList(sk0_52) ),
    inference(paramodulation,[status(thm)],[f481,f452]) ).

fof(f495,plain,
    ( ~ spl0_4
    | ~ spl0_5
    | spl0_2
    | ~ spl0_6
    | ~ spl0_7 ),
    inference(split_clause,[status(thm)],[f494,f482,f485,f439,f488,f491]) ).

fof(f504,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f444,f478]) ).

fof(f505,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f504]) ).

fof(f506,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f490,f424]) ).

fof(f507,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f506]) ).

fof(f508,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f487,f418]) ).

fof(f509,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f508]) ).

fof(f510,plain,
    ( ~ ssList(sk0_48)
    | spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f481,f484]) ).

fof(f511,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f510,f419]) ).

fof(f512,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f511]) ).

fof(f513,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f493,f425]) ).

fof(f514,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f513]) ).

fof(f515,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f445,f495,f505,f507,f509,f512,f514]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SWC339+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35  % Computer : n007.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon Apr 29 23:56:02 EDT 2024
% 0.15/0.35  % CPUTime  : 
% 0.15/0.37  % Drodi V3.6.0
% 0.15/0.37  % Refutation found
% 0.15/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.38  % Elapsed time: 0.028413 seconds
% 0.15/0.38  % CPU time: 0.044358 seconds
% 0.15/0.38  % Total memory used: 14.666 MB
% 0.15/0.38  % Net memory used: 14.643 MB
%------------------------------------------------------------------------------