TSTP Solution File: SWC256+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC256+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 20:45:06 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   62 (  10 unt;   0 def)
%            Number of atoms       :  204 (  45 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  225 (  83   ~;  76   |;  42   &)
%                                         (  10 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   7 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   54 (  41   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [U] :
      ( ssList(U)
     => ( singletonP(U)
      <=> ? [V] :
            ( ssItem(V)
            & cons(V,nil) = U ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> U != V ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    ssList(nil),
    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)
                    | singletonP(U)
                    | ( ! [Y] :
                          ( ssItem(Y)
                         => ( cons(Y,nil) != W
                            | ~ memberP(X,Y) ) )
                      & ( 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)
                      | singletonP(U)
                      | ( ! [Y] :
                            ( ssItem(Y)
                           => ( cons(Y,nil) != W
                              | ~ memberP(X,Y) ) )
                        & ( nil != X
                          | nil != W ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f113,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( singletonP(U)
      <=> ? [V] :
            ( ssItem(V)
            & cons(V,nil) = U ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f4]) ).

fof(f114,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ singletonP(U)
          | ? [V] :
              ( ssItem(V)
              & cons(V,nil) = U ) )
        & ( singletonP(U)
          | ! [V] :
              ( ~ ssItem(V)
              | cons(V,nil) != U ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f113]) ).

fof(f115,plain,
    ! [U] :
      ( ~ ssList(U)
      | ( ( ~ singletonP(U)
          | ( ssItem(sk0_4(U))
            & cons(sk0_4(U),nil) = U ) )
        & ( singletonP(U)
          | ! [V] :
              ( ~ ssItem(V)
              | cons(V,nil) != U ) ) ) ),
    inference(skolemization,[status(esa)],[f114]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | singletonP(X0)
      | ~ ssItem(X1)
      | cons(X1,nil) != X0 ),
    inference(cnf_transformation,[status(esa)],[f115]) ).

fof(f217,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( neq(U,V)
          <=> U != V ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f218,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ neq(U,V)
              | U != V )
            & ( neq(U,V)
              | U = V ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f217]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ neq(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f218]) ).

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

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

fof(f416,plain,
    ! [W,X,Y] :
      ( pd0_0(Y,X,W)
     => ( ssItem(Y)
        & cons(Y,nil) = W
        & memberP(X,Y) ) ),
    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)
                  & ~ singletonP(U)
                  & ( ? [Y] : pd0_0(Y,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)
    & ~ singletonP(sk0_47)
    & ( pd0_0(sk0_51,sk0_50,sk0_49)
      | ( nil = sk0_50
        & nil = sk0_49 ) ) ),
    inference(skolemization,[status(esa)],[f417]) ).

fof(f419,plain,
    ssList(sk0_47),
    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,
    ~ singletonP(sk0_47),
    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(f429,plain,
    ! [W,X,Y] :
      ( ~ pd0_0(Y,X,W)
      | ( ssItem(Y)
        & cons(Y,nil) = W
        & memberP(X,Y) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f416]) ).

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

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

fof(f433,plain,
    ( spl0_0
  <=> pd0_0(sk0_51,sk0_50,sk0_49) ),
    introduced(split_symbol_definition) ).

fof(f434,plain,
    ( pd0_0(sk0_51,sk0_50,sk0_49)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f433]) ).

fof(f436,plain,
    ( spl0_1
  <=> nil = sk0_50 ),
    introduced(split_symbol_definition) ).

fof(f437,plain,
    ( nil = sk0_50
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f436]) ).

fof(f439,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f427,f433,f436]) ).

fof(f447,plain,
    ! [X0] :
      ( ~ ssList(cons(X0,nil))
      | singletonP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f118]) ).

fof(f459,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f219]) ).

fof(f460,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ neq(X0,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f459]) ).

fof(f476,plain,
    ( pd0_0(sk0_51,sk0_48,sk0_49)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f423,f434]) ).

fof(f477,plain,
    ( pd0_0(sk0_51,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f424,f476]) ).

fof(f479,plain,
    ( ssItem(sk0_51)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f477,f430]) ).

fof(f480,plain,
    ( cons(sk0_51,nil) = sk0_47
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f431,f477]) ).

fof(f484,plain,
    ( spl0_4
  <=> ssItem(sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f486,plain,
    ( ~ ssItem(sk0_51)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f484]) ).

fof(f487,plain,
    ( spl0_5
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f489,plain,
    ( ~ ssList(nil)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f487]) ).

fof(f497,plain,
    ( nil = sk0_48
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f423,f437]) ).

fof(f499,plain,
    ( neq(nil,nil)
    | ~ spl0_1 ),
    inference(backward_demodulation,[status(thm)],[f497,f425]) ).

fof(f504,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f489,f223]) ).

fof(f505,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f504]) ).

fof(f511,plain,
    ( $false
    | ~ spl0_0
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f486,f479]) ).

fof(f512,plain,
    ( ~ spl0_0
    | spl0_4 ),
    inference(contradiction_clause,[status(thm)],[f511]) ).

fof(f514,plain,
    ( ~ ssList(nil)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f499,f460]) ).

fof(f515,plain,
    ( ~ spl0_5
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f514,f487,f436]) ).

fof(f526,plain,
    ( spl0_7
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f528,plain,
    ( ~ ssList(sk0_47)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f526]) ).

fof(f529,plain,
    ( spl0_8
  <=> singletonP(cons(sk0_51,nil)) ),
    introduced(split_symbol_definition) ).

fof(f530,plain,
    ( singletonP(cons(sk0_51,nil))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f529]) ).

fof(f532,plain,
    ( ~ ssList(sk0_47)
    | singletonP(cons(sk0_51,nil))
    | ~ ssItem(sk0_51)
    | ~ spl0_0 ),
    inference(paramodulation,[status(thm)],[f480,f447]) ).

fof(f533,plain,
    ( ~ spl0_7
    | spl0_8
    | ~ spl0_4
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f532,f526,f529,f484,f433]) ).

fof(f534,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f528,f419]) ).

fof(f535,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f534]) ).

fof(f536,plain,
    ( singletonP(sk0_47)
    | ~ spl0_0
    | ~ spl0_8 ),
    inference(forward_demodulation,[status(thm)],[f480,f530]) ).

fof(f537,plain,
    ( $false
    | ~ spl0_0
    | ~ spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f536,f426]) ).

fof(f538,plain,
    ( ~ spl0_0
    | ~ spl0_8 ),
    inference(contradiction_clause,[status(thm)],[f537]) ).

fof(f539,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f439,f505,f512,f515,f533,f535,f538]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWC256+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 23:57:05 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38  % Elapsed time: 0.027503 seconds
% 0.13/0.38  % CPU time: 0.046621 seconds
% 0.13/0.38  % Total memory used: 14.668 MB
% 0.13/0.38  % Net memory used: 14.643 MB
%------------------------------------------------------------------------------