TSTP Solution File: SWC200+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC200+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 12:39:39 EDT 2023

% Result   : Theorem 0.14s 0.52s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   58 (  10 unt;   0 def)
%            Number of atoms       :  200 (  37 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  232 (  90   ~;  90   |;  28   &)
%                                         (   9 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   6 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   55 (;  45   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [U] :
      ( ssList(U)
     => ( singletonP(U)
      <=> ? [V] :
            ( ssItem(V)
            & cons(V,nil) = U ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f38,axiom,
    ! [U] :
      ( ssItem(U)
     => ~ memberP(nil,U) ),
    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
                    | ~ singletonP(W)
                    | ? [Y] :
                        ( ssItem(Y)
                        & ! [Z] :
                            ( ssItem(Z)
                           => ( ~ memberP(U,Z)
                              | Y = Z ) ) ) ) ) ) ) ),
    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
                      | ~ singletonP(W)
                      | ? [Y] :
                          ( ssItem(Y)
                          & ! [Z] :
                              ( ssItem(Z)
                             => ( ~ memberP(U,Z)
                                | Y = Z ) ) ) ) ) ) ) ),
    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(f116,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ singletonP(X0)
      | ssItem(sk0_4(X0)) ),
    inference(cnf_transformation,[status(esa)],[f115]) ).

fof(f117,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ singletonP(X0)
      | cons(sk0_4(X0),nil) = X0 ),
    inference(cnf_transformation,[status(esa)],[f115]) ).

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

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(f275,plain,
    ! [X0,X1,X2] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | ~ ssList(X2)
      | ~ memberP(cons(X1,X2),X0)
      | X0 = X1
      | memberP(X2,X0) ),
    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)
                  & V = X
                  & U = W
                  & singletonP(W)
                  & ! [Y] :
                      ( ~ ssItem(Y)
                      | ? [Z] :
                          ( ssItem(Z)
                          & memberP(U,Z)
                          & Y != Z ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

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

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

fof(f422,plain,
    sk0_47 = sk0_49,
    inference(cnf_transformation,[status(esa)],[f416]) ).

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

fof(f424,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ssItem(sk0_51(X0)) ),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f425,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | memberP(sk0_47,sk0_51(X0)) ),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f426,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | X0 != sk0_51(X0) ),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f459,plain,
    singletonP(sk0_47),
    inference(forward_demodulation,[status(thm)],[f422,f423]) ).

fof(f728,plain,
    ( spl0_18
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f730,plain,
    ( ~ ssList(sk0_47)
    | spl0_18 ),
    inference(component_clause,[status(thm)],[f728]) ).

fof(f731,plain,
    ( spl0_19
  <=> cons(sk0_4(sk0_47),nil) = sk0_47 ),
    introduced(split_symbol_definition) ).

fof(f732,plain,
    ( cons(sk0_4(sk0_47),nil) = sk0_47
    | ~ spl0_19 ),
    inference(component_clause,[status(thm)],[f731]) ).

fof(f734,plain,
    ( ~ ssList(sk0_47)
    | cons(sk0_4(sk0_47),nil) = sk0_47 ),
    inference(resolution,[status(thm)],[f117,f459]) ).

fof(f735,plain,
    ( ~ spl0_18
    | spl0_19 ),
    inference(split_clause,[status(thm)],[f734,f728,f731]) ).

fof(f736,plain,
    ( $false
    | spl0_18 ),
    inference(forward_subsumption_resolution,[status(thm)],[f730,f417]) ).

fof(f737,plain,
    spl0_18,
    inference(contradiction_clause,[status(thm)],[f736]) ).

fof(f756,plain,
    ( spl0_20
  <=> ssItem(sk0_4(sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f757,plain,
    ( ssItem(sk0_4(sk0_47))
    | ~ spl0_20 ),
    inference(component_clause,[status(thm)],[f756]) ).

fof(f758,plain,
    ( ~ ssItem(sk0_4(sk0_47))
    | spl0_20 ),
    inference(component_clause,[status(thm)],[f756]) ).

fof(f767,plain,
    ( spl0_23
  <=> singletonP(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f769,plain,
    ( ~ singletonP(sk0_47)
    | spl0_23 ),
    inference(component_clause,[status(thm)],[f767]) ).

fof(f775,plain,
    ( spl0_25
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f777,plain,
    ( ~ ssList(nil)
    | spl0_25 ),
    inference(component_clause,[status(thm)],[f775]) ).

fof(f780,plain,
    ( ~ ssList(sk0_47)
    | ~ singletonP(sk0_47)
    | spl0_20 ),
    inference(resolution,[status(thm)],[f758,f116]) ).

fof(f781,plain,
    ( ~ spl0_18
    | ~ spl0_23
    | spl0_20 ),
    inference(split_clause,[status(thm)],[f780,f728,f767,f756]) ).

fof(f782,plain,
    ( $false
    | spl0_23 ),
    inference(forward_subsumption_resolution,[status(thm)],[f769,f459]) ).

fof(f783,plain,
    spl0_23,
    inference(contradiction_clause,[status(thm)],[f782]) ).

fof(f784,plain,
    ( $false
    | spl0_25 ),
    inference(forward_subsumption_resolution,[status(thm)],[f777,f223]) ).

fof(f785,plain,
    spl0_25,
    inference(contradiction_clause,[status(thm)],[f784]) ).

fof(f793,plain,
    ( sk0_4(sk0_47) != sk0_51(sk0_4(sk0_47))
    | ~ spl0_20 ),
    inference(resolution,[status(thm)],[f757,f426]) ).

fof(f939,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssList(X1)
      | ~ memberP(cons(sk0_4(sk0_47),X1),X0)
      | X0 = sk0_4(sk0_47)
      | memberP(X1,X0)
      | ~ spl0_20 ),
    inference(resolution,[status(thm)],[f275,f757]) ).

fof(f1138,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(cons(sk0_4(sk0_47),nil),X0)
      | X0 = sk0_4(sk0_47)
      | memberP(nil,X0)
      | ~ spl0_20 ),
    inference(resolution,[status(thm)],[f939,f223]) ).

fof(f1139,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(sk0_47,X0)
      | X0 = sk0_4(sk0_47)
      | memberP(nil,X0)
      | ~ spl0_19
      | ~ spl0_20 ),
    inference(forward_demodulation,[status(thm)],[f732,f1138]) ).

fof(f1140,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | ~ memberP(sk0_47,X0)
      | X0 = sk0_4(sk0_47)
      | ~ spl0_19
      | ~ spl0_20 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1139,f279]) ).

fof(f1152,plain,
    ! [X0] :
      ( ~ ssItem(sk0_51(X0))
      | sk0_51(X0) = sk0_4(sk0_47)
      | ~ ssItem(X0)
      | ~ spl0_19
      | ~ spl0_20 ),
    inference(resolution,[status(thm)],[f1140,f425]) ).

fof(f1153,plain,
    ! [X0] :
      ( sk0_51(X0) = sk0_4(sk0_47)
      | ~ ssItem(X0)
      | ~ spl0_19
      | ~ spl0_20 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1152,f424]) ).

fof(f1162,plain,
    ( sk0_51(sk0_4(sk0_47)) = sk0_4(sk0_47)
    | ~ spl0_19
    | ~ spl0_20 ),
    inference(resolution,[status(thm)],[f1153,f757]) ).

fof(f1163,plain,
    ( $false
    | ~ spl0_19
    | ~ spl0_20 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1162,f793]) ).

fof(f1164,plain,
    ( ~ spl0_19
    | ~ spl0_20 ),
    inference(contradiction_clause,[status(thm)],[f1163]) ).

fof(f1165,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f735,f737,f781,f783,f785,f1164]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12  % Problem  : SWC200+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33  % Computer : n028.cluster.edu
% 0.09/0.33  % Model    : x86_64 x86_64
% 0.09/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33  % Memory   : 8042.1875MB
% 0.09/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33  % CPULimit : 300
% 0.09/0.33  % WCLimit  : 300
% 0.09/0.33  % DateTime : Tue May 30 11:36:47 EDT 2023
% 0.09/0.33  % CPUTime  : 
% 0.09/0.34  % Drodi V3.5.1
% 0.14/0.52  % Refutation found
% 0.14/0.52  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.52  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.93/0.54  % Elapsed time: 0.208377 seconds
% 0.93/0.54  % CPU time: 1.023656 seconds
% 0.93/0.54  % Memory used: 72.649 MB
%------------------------------------------------------------------------------