TSTP Solution File: SWC241+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC241+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 20:45:03 EDT 2024

% Result   : Theorem 0.17s 0.37s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   52 (   7 unt;   0 def)
%            Number of atoms       :  262 (  50 equ)
%            Maximal formula atoms :   26 (   5 avg)
%            Number of connectives :  329 ( 119   ~; 117   |;  70   &)
%                                         (  11 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   16 (  14 usr;  10 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-3 aty)
%            Number of variables   :   69 (  45   !;  24   ?)

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

fof(f93,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ( lt(U,V)
          <=> ( U != V
              & leq(U,V) ) ) ) ),
    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
                  | nil = U
                  | ? [Y] :
                      ( ssItem(Y)
                      & ? [Z] :
                          ( ssList(Z)
                          & ? [X1] :
                              ( ssList(X1)
                              & app(app(Z,cons(Y,nil)),X1) = U
                              & ! [X2] :
                                  ( ~ ssItem(X2)
                                  | ~ memberP(Z,X2)
                                  | ~ memberP(X1,X2)
                                  | ~ lt(Y,X2)
                                  | leq(Y,X2) ) ) ) )
                  | ( nil != W
                    & ! [X3] :
                        ( ssItem(X3)
                       => ! [X4] :
                            ( ssList(X4)
                           => ! [X5] :
                                ( ~ ssList(X5)
                                | app(app(X4,cons(X3,nil)),X5) != W
                                | ? [X6] :
                                    ( ssItem(X6)
                                    & ~ leq(X6,X3)
                                    & memberP(X4,X6)
                                    & memberP(X5,X6)
                                    & leq(X3,X6) ) ) ) ) ) ) ) ) ),
    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
                    | nil = U
                    | ? [Y] :
                        ( ssItem(Y)
                        & ? [Z] :
                            ( ssList(Z)
                            & ? [X1] :
                                ( ssList(X1)
                                & app(app(Z,cons(Y,nil)),X1) = U
                                & ! [X2] :
                                    ( ~ ssItem(X2)
                                    | ~ memberP(Z,X2)
                                    | ~ memberP(X1,X2)
                                    | ~ lt(Y,X2)
                                    | leq(Y,X2) ) ) ) )
                    | ( nil != W
                      & ! [X3] :
                          ( ssItem(X3)
                         => ! [X4] :
                              ( ssList(X4)
                             => ! [X5] :
                                  ( ~ ssList(X5)
                                  | app(app(X4,cons(X3,nil)),X5) != W
                                  | ? [X6] :
                                      ( ssItem(X6)
                                      & ~ leq(X6,X3)
                                      & memberP(X4,X6)
                                      & memberP(X5,X6)
                                      & leq(X3,X6) ) ) ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

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

fof(f406,plain,
    ! [U] :
      ( ~ ssItem(U)
      | ! [V] :
          ( ~ ssItem(V)
          | ( lt(U,V)
          <=> ( U != V
              & leq(U,V) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f93]) ).

fof(f407,plain,
    ! [U] :
      ( ~ ssItem(U)
      | ! [V] :
          ( ~ ssItem(V)
          | ( ( ~ lt(U,V)
              | ( U != V
                & leq(U,V) ) )
            & ( lt(U,V)
              | U = V
              | ~ leq(U,V) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f406]) ).

fof(f409,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ lt(X0,X1)
      | leq(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f407]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & nil != U
                  & ! [Y] :
                      ( ~ ssItem(Y)
                      | ! [Z] :
                          ( ~ ssList(Z)
                          | ! [X1] :
                              ( ~ ssList(X1)
                              | app(app(Z,cons(Y,nil)),X1) != U
                              | ? [X2] :
                                  ( ssItem(X2)
                                  & memberP(Z,X2)
                                  & memberP(X1,X2)
                                  & lt(Y,X2)
                                  & ~ leq(Y,X2) ) ) ) )
                  & ( nil = W
                    | ? [X3] :
                        ( ssItem(X3)
                        & ? [X4] :
                            ( ssList(X4)
                            & ? [X5] :
                                ( ssList(X5)
                                & app(app(X4,cons(X3,nil)),X5) = W
                                & ! [X6] :
                                    ( ~ ssItem(X6)
                                    | leq(X6,X3)
                                    | ~ memberP(X4,X6)
                                    | ~ memberP(X5,X6)
                                    | ~ leq(X3,X6) ) ) ) ) ) ) ) ) ),
    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
              & nil != U
              & ! [Y] :
                  ( ~ ssItem(Y)
                  | ! [Z] :
                      ( ~ ssList(Z)
                      | ! [X1] :
                          ( ~ ssList(X1)
                          | app(app(Z,cons(Y,nil)),X1) != U
                          | ? [X2] :
                              ( ssItem(X2)
                              & memberP(Z,X2)
                              & memberP(X1,X2)
                              & lt(Y,X2)
                              & ~ leq(Y,X2) ) ) ) )
              & ( nil = W
                | ? [X3] :
                    ( ssItem(X3)
                    & ? [X4] :
                        ( ssList(X4)
                        & ? [X5] :
                            ( ssList(X5)
                            & app(app(X4,cons(X3,nil)),X5) = W
                            & ! [X6] :
                                ( ~ ssItem(X6)
                                | leq(X6,X3)
                                | ~ memberP(X4,X6)
                                | ~ memberP(X5,X6)
                                | ~ leq(X3,X6) ) ) ) ) ) ) ) ),
    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
    & nil != sk0_47
    & ! [Y] :
        ( ~ ssItem(Y)
        | ! [Z] :
            ( ~ ssList(Z)
            | ! [X1] :
                ( ~ ssList(X1)
                | app(app(Z,cons(Y,nil)),X1) != sk0_47
                | ( ssItem(sk0_51(X1,Z,Y))
                  & memberP(Z,sk0_51(X1,Z,Y))
                  & memberP(X1,sk0_51(X1,Z,Y))
                  & lt(Y,sk0_51(X1,Z,Y))
                  & ~ leq(Y,sk0_51(X1,Z,Y)) ) ) ) )
    & ( nil = sk0_49
      | ( ssItem(sk0_52)
        & ssList(sk0_53)
        & ssList(sk0_54)
        & app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_49
        & ! [X6] :
            ( ~ ssItem(X6)
            | leq(X6,sk0_52)
            | ~ memberP(sk0_53,X6)
            | ~ memberP(sk0_54,X6)
            | ~ leq(sk0_52,X6) ) ) ) ),
    inference(skolemization,[status(esa)],[f416]) ).

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

fof(f424,plain,
    nil != sk0_47,
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f425,plain,
    ! [X0,X1,X2] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | app(app(X1,cons(X0,nil)),X2) != sk0_47
      | ssItem(sk0_51(X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f428,plain,
    ! [X0,X1,X2] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | app(app(X1,cons(X0,nil)),X2) != sk0_47
      | lt(X0,sk0_51(X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f429,plain,
    ! [X0,X1,X2] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | app(app(X1,cons(X0,nil)),X2) != sk0_47
      | ~ leq(X0,sk0_51(X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f430,plain,
    ( nil = sk0_49
    | ssItem(sk0_52) ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f431,plain,
    ( nil = sk0_49
    | ssList(sk0_53) ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f432,plain,
    ( nil = sk0_49
    | ssList(sk0_54) ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f433,plain,
    ( nil = sk0_49
    | app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_49 ),
    inference(cnf_transformation,[status(esa)],[f417]) ).

fof(f435,plain,
    ( spl0_0
  <=> nil = sk0_49 ),
    introduced(split_symbol_definition) ).

fof(f436,plain,
    ( nil = sk0_49
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f435]) ).

fof(f438,plain,
    ( spl0_1
  <=> ssItem(sk0_52) ),
    introduced(split_symbol_definition) ).

fof(f441,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f430,f435,f438]) ).

fof(f442,plain,
    ( spl0_2
  <=> ssList(sk0_53) ),
    introduced(split_symbol_definition) ).

fof(f445,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f431,f435,f442]) ).

fof(f446,plain,
    ( spl0_3
  <=> ssList(sk0_54) ),
    introduced(split_symbol_definition) ).

fof(f449,plain,
    ( spl0_0
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f432,f435,f446]) ).

fof(f450,plain,
    ( spl0_4
  <=> app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_49 ),
    introduced(split_symbol_definition) ).

fof(f451,plain,
    ( app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_49
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f450]) ).

fof(f453,plain,
    ( spl0_0
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f433,f435,f450]) ).

fof(f499,plain,
    ( nil = sk0_47
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f423,f436]) ).

fof(f500,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f499,f424]) ).

fof(f501,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f500]) ).

fof(f502,plain,
    ( app(app(sk0_53,cons(sk0_52,nil)),sk0_54) = sk0_47
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f423,f451]) ).

fof(f517,plain,
    ( spl0_11
  <=> ssItem(sk0_51(sk0_54,sk0_53,sk0_52)) ),
    introduced(split_symbol_definition) ).

fof(f520,plain,
    ( ~ ssItem(sk0_52)
    | ~ ssList(sk0_53)
    | ~ ssList(sk0_54)
    | ssItem(sk0_51(sk0_54,sk0_53,sk0_52))
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f425,f502]) ).

fof(f521,plain,
    ( ~ spl0_1
    | ~ spl0_2
    | ~ spl0_3
    | spl0_11
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f520,f438,f442,f446,f517,f450]) ).

fof(f544,plain,
    ( spl0_16
  <=> leq(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52)) ),
    introduced(split_symbol_definition) ).

fof(f549,plain,
    ( spl0_17
  <=> lt(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52)) ),
    introduced(split_symbol_definition) ).

fof(f550,plain,
    ( lt(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52))
    | ~ spl0_17 ),
    inference(component_clause,[status(thm)],[f549]) ).

fof(f552,plain,
    ( ~ ssItem(sk0_52)
    | ~ ssList(sk0_53)
    | ~ ssList(sk0_54)
    | lt(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52))
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f428,f502]) ).

fof(f553,plain,
    ( ~ spl0_1
    | ~ spl0_2
    | ~ spl0_3
    | spl0_17
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f552,f438,f442,f446,f549,f450]) ).

fof(f556,plain,
    ( ~ ssItem(sk0_52)
    | ~ ssList(sk0_53)
    | ~ ssList(sk0_54)
    | ~ leq(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52))
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f429,f502]) ).

fof(f557,plain,
    ( ~ spl0_1
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_16
    | ~ spl0_4 ),
    inference(split_clause,[status(thm)],[f556,f438,f442,f446,f544,f450]) ).

fof(f573,plain,
    ( spl0_21
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f575,plain,
    ( ~ ssList(nil)
    | spl0_21 ),
    inference(component_clause,[status(thm)],[f573]) ).

fof(f578,plain,
    ( $false
    | spl0_21 ),
    inference(forward_subsumption_resolution,[status(thm)],[f575,f223]) ).

fof(f579,plain,
    spl0_21,
    inference(contradiction_clause,[status(thm)],[f578]) ).

fof(f593,plain,
    ( ~ ssItem(sk0_52)
    | ~ ssItem(sk0_51(sk0_54,sk0_53,sk0_52))
    | leq(sk0_52,sk0_51(sk0_54,sk0_53,sk0_52))
    | ~ spl0_17 ),
    inference(resolution,[status(thm)],[f409,f550]) ).

fof(f594,plain,
    ( ~ spl0_1
    | ~ spl0_11
    | spl0_16
    | ~ spl0_17 ),
    inference(split_clause,[status(thm)],[f593,f438,f517,f544,f549]) ).

fof(f595,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f441,f445,f449,f453,f501,f521,f553,f557,f579,f594]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14  % Problem  : SWC241+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n018.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 Apr 30 00:26:58 EDT 2024
% 0.12/0.35  % CPUTime  : 
% 0.12/0.36  % Drodi V3.6.0
% 0.17/0.37  % Refutation found
% 0.17/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.38  % Elapsed time: 0.027261 seconds
% 0.17/0.38  % CPU time: 0.045486 seconds
% 0.17/0.38  % Total memory used: 14.998 MB
% 0.17/0.38  % Net memory used: 14.968 MB
%------------------------------------------------------------------------------