TSTP Solution File: SWC046+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC046+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n006.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 20:44:18 EDT 2024

% Result   : Theorem 12.09s 1.94s
% Output   : CNFRefutation 12.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   65 (  11 unt;   0 def)
%            Number of atoms       :  226 (  46 equ)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  251 (  90   ~;  93   |;  44   &)
%                                         (   9 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   8 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :   59 (  44   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ? [U] :
      ( ssItem(U)
      & ? [V] :
          ( ssItem(V)
          & U != V ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [U] :
      ( ssList(U)
     => ( nil = U
        | ? [V] :
            ( ssList(V)
            & ? [W] :
                ( ssItem(W)
                & cons(W,V) = U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f37,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ! [W] :
              ( ssList(W)
             => ( memberP(cons(V,W),U)
              <=> ( U = V
                  | memberP(W,U) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f38,axiom,
    ! [U] :
      ( ssItem(U)
     => ~ memberP(nil,U) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( nil != V
                    | V != X
                    | U != W
                    | nil = U
                    | ? [Y] :
                        ( ssItem(Y)
                        & ( ( ~ memberP(W,Y)
                            & ! [Z] :
                                ( ssList(Z)
                               => ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) )
                            & memberP(X,Y) )
                          | ( memberP(W,Y)
                            & ( ~ memberP(X,Y)
                              | ? [Z] :
                                  ( ssList(Z)
                                  & segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f97,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( nil != V
                      | V != X
                      | U != W
                      | nil = U
                      | ? [Y] :
                          ( ssItem(Y)
                          & ( ( ~ memberP(W,Y)
                              & ! [Z] :
                                  ( ssList(Z)
                                 => ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) )
                              & memberP(X,Y) )
                            | ( memberP(W,Y)
                              & ( ~ memberP(X,Y)
                                | ? [Z] :
                                    ( ssList(Z)
                                    & segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ) ) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f102,plain,
    ( ssItem(sk0_0)
    & ssItem(sk0_1)
    & sk0_0 != sk0_1 ),
    inference(skolemization,[status(esa)],[f2]) ).

fof(f103,plain,
    ssItem(sk0_0),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f229,plain,
    ! [U] :
      ( ~ ssList(U)
      | nil = U
      | ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssItem(W)
              & cons(W,V) = U ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f230,plain,
    ! [U] :
      ( ~ ssList(U)
      | nil = U
      | ( ssList(sk0_43(U))
        & ssItem(sk0_44(U))
        & cons(sk0_44(U),sk0_43(U)) = U ) ),
    inference(skolemization,[status(esa)],[f229]) ).

fof(f231,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssList(sk0_43(X0)) ),
    inference(cnf_transformation,[status(esa)],[f230]) ).

fof(f232,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | ssItem(sk0_44(X0)) ),
    inference(cnf_transformation,[status(esa)],[f230]) ).

fof(f233,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | nil = X0
      | cons(sk0_44(X0),sk0_43(X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f230]) ).

fof(f273,plain,
    ! [U] :
      ( ~ ssItem(U)
      | ! [V] :
          ( ~ ssItem(V)
          | ! [W] :
              ( ~ ssList(W)
              | ( memberP(cons(V,W),U)
              <=> ( U = V
                  | memberP(W,U) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f37]) ).

fof(f274,plain,
    ! [U] :
      ( ~ ssItem(U)
      | ! [V] :
          ( ~ ssItem(V)
          | ! [W] :
              ( ~ ssList(W)
              | ( ( ~ memberP(cons(V,W),U)
                  | U = V
                  | memberP(W,U) )
                & ( memberP(cons(V,W),U)
                  | ( U != V
                    & ~ memberP(W,U) ) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f273]) ).

fof(f276,plain,
    ! [X0,X1,X2] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X0)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f274]) ).

fof(f278,plain,
    ! [U] :
      ( ~ ssItem(U)
      | ~ memberP(nil,U) ),
    inference(pre_NNF_transformation,[status(esa)],[f38]) ).

fof(f279,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(nil,X0) ),
    inference(cnf_transformation,[status(esa)],[f278]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & nil = V
                  & V = X
                  & U = W
                  & nil != U
                  & ! [Y] :
                      ( ~ ssItem(Y)
                      | ( ( memberP(W,Y)
                          | ? [Z] :
                              ( ssList(Z)
                              & segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) )
                          | ~ memberP(X,Y) )
                        & ( ~ memberP(W,Y)
                          | ( memberP(X,Y)
                            & ! [Z] :
                                ( ~ ssList(Z)
                                | ~ segmentP(X,app(app(cons(Y,nil),Z),cons(Y,nil))) ) ) ) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ( ssList(sk0_47)
    & ssList(sk0_48)
    & ssList(sk0_49)
    & ssList(sk0_50)
    & nil = sk0_48
    & sk0_48 = sk0_50
    & sk0_47 = sk0_49
    & nil != sk0_47
    & ! [Y] :
        ( ~ ssItem(Y)
        | ( ( memberP(sk0_49,Y)
            | ( ssList(sk0_51(Y))
              & segmentP(sk0_50,app(app(cons(Y,nil),sk0_51(Y)),cons(Y,nil))) )
            | ~ memberP(sk0_50,Y) )
          & ( ~ memberP(sk0_49,Y)
            | ( memberP(sk0_50,Y)
              & ! [Z] :
                  ( ~ ssList(Z)
                  | ~ segmentP(sk0_50,app(app(cons(Y,nil),Z),cons(Y,nil))) ) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f415]) ).

fof(f417,plain,
    ssList(sk0_47),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f421,plain,
    nil = sk0_48,
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f422,plain,
    sk0_48 = sk0_50,
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f423,plain,
    sk0_47 = sk0_49,
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f424,plain,
    nil != sk0_47,
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f427,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(sk0_49,X0)
      | memberP(sk0_50,X0) ),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f446,plain,
    ! [X1,X2] :
      ( ~ ssItem(X1)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | memberP(cons(X1,X2),X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f276]) ).

fof(f447,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | memberP(cons(X0,X1),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f446]) ).

fof(f459,plain,
    nil = sk0_50,
    inference(forward_demodulation,[status(thm)],[f421,f422]) ).

fof(f465,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(sk0_47,X0)
      | memberP(sk0_50,X0) ),
    inference(forward_demodulation,[status(thm)],[f423,f427]) ).

fof(f466,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(sk0_47,X0)
      | memberP(nil,X0) ),
    inference(forward_demodulation,[status(thm)],[f459,f465]) ).

fof(f467,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(sk0_47,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f466,f279]) ).

fof(f492,plain,
    ( spl0_3
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f494,plain,
    ( ~ ssList(sk0_47)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f492]) ).

fof(f502,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f494,f417]) ).

fof(f503,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f502]) ).

fof(f580,plain,
    ( spl0_7
  <=> nil = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f581,plain,
    ( nil = sk0_47
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f580]) ).

fof(f1178,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f581,f424]) ).

fof(f1179,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f1178]) ).

fof(f1433,plain,
    ( spl0_66
  <=> ssItem(sk0_0) ),
    introduced(split_symbol_definition) ).

fof(f1435,plain,
    ( ~ ssItem(sk0_0)
    | spl0_66 ),
    inference(component_clause,[status(thm)],[f1433]) ).

fof(f1452,plain,
    ( $false
    | spl0_66 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1435,f103]) ).

fof(f1453,plain,
    spl0_66,
    inference(contradiction_clause,[status(thm)],[f1452]) ).

fof(f2606,plain,
    ( spl0_151
  <=> cons(sk0_44(sk0_47),sk0_43(sk0_47)) = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f2607,plain,
    ( cons(sk0_44(sk0_47),sk0_43(sk0_47)) = sk0_47
    | ~ spl0_151 ),
    inference(component_clause,[status(thm)],[f2606]) ).

fof(f2609,plain,
    ( nil = sk0_47
    | cons(sk0_44(sk0_47),sk0_43(sk0_47)) = sk0_47 ),
    inference(resolution,[status(thm)],[f233,f417]) ).

fof(f2610,plain,
    ( spl0_7
    | spl0_151 ),
    inference(split_clause,[status(thm)],[f2609,f580,f2606]) ).

fof(f3175,plain,
    ( spl0_162
  <=> ssList(sk0_43(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f3176,plain,
    ( ssList(sk0_43(sk0_47))
    | ~ spl0_162 ),
    inference(component_clause,[status(thm)],[f3175]) ).

fof(f3177,plain,
    ( ~ ssList(sk0_43(sk0_47))
    | spl0_162 ),
    inference(component_clause,[status(thm)],[f3175]) ).

fof(f3178,plain,
    ( spl0_163
  <=> ssItem(sk0_44(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f3180,plain,
    ( ~ ssItem(sk0_44(sk0_47))
    | spl0_163 ),
    inference(component_clause,[status(thm)],[f3178]) ).

fof(f3202,plain,
    ( ~ ssList(sk0_47)
    | nil = sk0_47
    | spl0_163 ),
    inference(resolution,[status(thm)],[f3180,f232]) ).

fof(f3203,plain,
    ( ~ spl0_3
    | spl0_7
    | spl0_163 ),
    inference(split_clause,[status(thm)],[f3202,f492,f580,f3178]) ).

fof(f3204,plain,
    ( ~ ssList(sk0_47)
    | nil = sk0_47
    | spl0_162 ),
    inference(resolution,[status(thm)],[f3177,f231]) ).

fof(f3205,plain,
    ( ~ spl0_3
    | spl0_7
    | spl0_162 ),
    inference(split_clause,[status(thm)],[f3204,f492,f580,f3175]) ).

fof(f3322,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | memberP(cons(X0,sk0_43(sk0_47)),X0)
      | ~ spl0_162 ),
    inference(resolution,[status(thm)],[f3176,f447]) ).

fof(f3513,plain,
    ( spl0_196
  <=> memberP(sk0_47,sk0_44(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f3514,plain,
    ( memberP(sk0_47,sk0_44(sk0_47))
    | ~ spl0_196 ),
    inference(component_clause,[status(thm)],[f3513]) ).

fof(f3740,plain,
    ( ~ ssItem(sk0_44(sk0_47))
    | ~ spl0_196 ),
    inference(resolution,[status(thm)],[f3514,f467]) ).

fof(f3741,plain,
    ( ~ spl0_163
    | ~ spl0_196 ),
    inference(split_clause,[status(thm)],[f3740,f3178,f3513]) ).

fof(f3816,plain,
    ( ~ ssItem(sk0_44(sk0_47))
    | memberP(sk0_47,sk0_44(sk0_47))
    | ~ spl0_162
    | ~ spl0_151 ),
    inference(paramodulation,[status(thm)],[f2607,f3322]) ).

fof(f3817,plain,
    ( ~ spl0_163
    | spl0_196
    | ~ spl0_162
    | ~ spl0_151 ),
    inference(split_clause,[status(thm)],[f3816,f3178,f3513,f3175,f2606]) ).

fof(f3818,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f503,f1179,f1453,f2610,f3203,f3205,f3741,f3817]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SWC046+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Apr 29 23:57:05 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 12.09/1.94  % Refutation found
% 12.09/1.94  % SZS status Theorem for theBenchmark: Theorem is valid
% 12.09/1.94  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.69/1.98  % Elapsed time: 1.625811 seconds
% 12.69/1.98  % CPU time: 12.773108 seconds
% 12.69/1.98  % Total memory used: 161.255 MB
% 12.69/1.98  % Net memory used: 156.423 MB
%------------------------------------------------------------------------------