TSTP Solution File: SWC218+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC218+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 12:39:42 EDT 2023

% Result   : Theorem 0.19s 0.36s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   95 (  18 unt;   0 def)
%            Number of atoms       :  275 (  66 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  296 ( 116   ~; 111   |;  27   &)
%                                         (  17 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   18 (  16 usr;  14 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   58 (;  51   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> U != V ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ssList(cons(V,U)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f21,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => nil != cons(V,U) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f26,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ssList(app(U,V)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f83,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( nil = app(U,V)
          <=> ( nil = V
              & nil = U ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f84,axiom,
    ! [U] :
      ( ssList(U)
     => app(U,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
                    | ! [Y] :
                        ( ssList(Y)
                       => ! [Z] :
                            ( ssList(Z)
                           => ( app(Y,Z) != X
                              | ! [X1] :
                                  ( ssItem(X1)
                                 => app(app(Y,cons(X1,nil)),Z) != W ) ) ) )
                    | neq(U,nil) ) ) ) ) ),
    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
                      | ! [Y] :
                          ( ssList(Y)
                         => ! [Z] :
                              ( ssList(Z)
                             => ( app(Y,Z) != X
                                | ! [X1] :
                                    ( ssItem(X1)
                                   => app(app(Y,cons(X1,nil)),Z) != W ) ) ) )
                      | neq(U,nil) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

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(f220,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | neq(X0,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f218]) ).

fof(f221,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssItem(V)
          | ssList(cons(V,U)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | ssList(cons(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f221]) ).

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

fof(f234,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssItem(V)
          | nil != cons(V,U) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f235,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | nil != cons(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f234]) ).

fof(f244,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ssList(app(U,V)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f26]) ).

fof(f245,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ssList(app(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f244]) ).

fof(f383,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( nil = app(U,V)
          <=> ( nil = V
              & nil = U ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f83]) ).

fof(f384,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( nil != app(U,V)
              | ( nil = V
                & nil = U ) )
            & ( nil = app(U,V)
              | nil != V
              | nil != U ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f383]) ).

fof(f385,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | nil != app(X0,X1)
      | nil = X1 ),
    inference(cnf_transformation,[status(esa)],[f384]) ).

fof(f388,plain,
    ! [U] :
      ( ~ ssList(U)
      | app(U,nil) = U ),
    inference(pre_NNF_transformation,[status(esa)],[f84]) ).

fof(f389,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[status(esa)],[f388]) ).

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(Y,Z) = X
                          & ? [X1] :
                              ( ssItem(X1)
                              & app(app(Y,cons(X1,nil)),Z) = W ) ) )
                  & ~ neq(U,nil) ) ) ) ),
    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
    & ssList(sk0_51)
    & ssList(sk0_52)
    & app(sk0_51,sk0_52) = sk0_50
    & ssItem(sk0_53)
    & app(app(sk0_51,cons(sk0_53,nil)),sk0_52) = sk0_49
    & ~ neq(sk0_47,nil) ),
    inference(skolemization,[status(esa)],[f415]) ).

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

fof(f421,plain,
    sk0_48 = sk0_50,
    inference(cnf_transformation,[status(esa)],[f416]) ).

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

fof(f423,plain,
    ssList(sk0_51),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f424,plain,
    ssList(sk0_52),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f425,plain,
    app(sk0_51,sk0_52) = sk0_50,
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f426,plain,
    ssItem(sk0_53),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f427,plain,
    app(app(sk0_51,cons(sk0_53,nil)),sk0_52) = sk0_49,
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f428,plain,
    ~ neq(sk0_47,nil),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f461,plain,
    app(sk0_51,sk0_52) = sk0_48,
    inference(forward_demodulation,[status(thm)],[f421,f425]) ).

fof(f468,plain,
    ( spl0_2
  <=> sk0_47 = nil ),
    introduced(split_symbol_definition) ).

fof(f469,plain,
    ( sk0_47 = nil
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f468]) ).

fof(f473,plain,
    ( spl0_3
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f475,plain,
    ( ~ ssList(sk0_47)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f473]) ).

fof(f476,plain,
    ( spl0_4
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f478,plain,
    ( ~ ssList(nil)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f476]) ).

fof(f479,plain,
    ( ~ ssList(sk0_47)
    | ~ ssList(nil)
    | sk0_47 = nil ),
    inference(resolution,[status(thm)],[f220,f428]) ).

fof(f480,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f479,f473,f476,f468]) ).

fof(f481,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f478,f223]) ).

fof(f482,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f481]) ).

fof(f483,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f475,f417]) ).

fof(f484,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f483]) ).

fof(f486,plain,
    ( nil = sk0_49
    | ~ spl0_2 ),
    inference(backward_demodulation,[status(thm)],[f469,f422]) ).

fof(f495,plain,
    ( app(app(sk0_51,cons(sk0_53,nil)),sk0_52) = nil
    | ~ spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f486,f427]) ).

fof(f496,plain,
    ( spl0_6
  <=> ssList(app(sk0_51,cons(sk0_53,nil))) ),
    introduced(split_symbol_definition) ).

fof(f498,plain,
    ( ~ ssList(app(sk0_51,cons(sk0_53,nil)))
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f496]) ).

fof(f499,plain,
    ( spl0_7
  <=> ssList(sk0_52) ),
    introduced(split_symbol_definition) ).

fof(f501,plain,
    ( ~ ssList(sk0_52)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f499]) ).

fof(f504,plain,
    ( spl0_8
  <=> ssList(sk0_51) ),
    introduced(split_symbol_definition) ).

fof(f506,plain,
    ( ~ ssList(sk0_51)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f504]) ).

fof(f507,plain,
    ( spl0_9
  <=> ssList(sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f512,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f506,f423]) ).

fof(f513,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f512]) ).

fof(f514,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f501,f424]) ).

fof(f515,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f514]) ).

fof(f516,plain,
    ( spl0_10
  <=> nil = sk0_52 ),
    introduced(split_symbol_definition) ).

fof(f517,plain,
    ( nil = sk0_52
    | ~ spl0_10 ),
    inference(component_clause,[status(thm)],[f516]) ).

fof(f519,plain,
    ( ~ ssList(app(sk0_51,cons(sk0_53,nil)))
    | ~ ssList(sk0_52)
    | nil = sk0_52
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f385,f495]) ).

fof(f520,plain,
    ( ~ spl0_6
    | ~ spl0_7
    | spl0_10
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f519,f496,f499,f516,f468]) ).

fof(f537,plain,
    ( spl0_13
  <=> ssList(cons(sk0_53,nil)) ),
    introduced(split_symbol_definition) ).

fof(f539,plain,
    ( ~ ssList(cons(sk0_53,nil))
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f537]) ).

fof(f540,plain,
    ( ~ ssList(sk0_51)
    | ~ ssList(cons(sk0_53,nil))
    | spl0_6 ),
    inference(resolution,[status(thm)],[f498,f245]) ).

fof(f541,plain,
    ( ~ spl0_8
    | ~ spl0_13
    | spl0_6 ),
    inference(split_clause,[status(thm)],[f540,f504,f537,f496]) ).

fof(f542,plain,
    ( spl0_14
  <=> ssItem(sk0_53) ),
    introduced(split_symbol_definition) ).

fof(f544,plain,
    ( ~ ssItem(sk0_53)
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f542]) ).

fof(f545,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sk0_53)
    | spl0_13 ),
    inference(resolution,[status(thm)],[f539,f222]) ).

fof(f546,plain,
    ( ~ spl0_4
    | ~ spl0_14
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f545,f476,f542,f537]) ).

fof(f547,plain,
    ( $false
    | spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f544,f426]) ).

fof(f548,plain,
    spl0_14,
    inference(contradiction_clause,[status(thm)],[f547]) ).

fof(f549,plain,
    ( app(app(sk0_51,cons(sk0_53,nil)),nil) = nil
    | ~ spl0_10
    | ~ spl0_2 ),
    inference(backward_demodulation,[status(thm)],[f517,f495]) ).

fof(f550,plain,
    ( app(sk0_51,nil) = sk0_48
    | ~ spl0_10 ),
    inference(backward_demodulation,[status(thm)],[f517,f461]) ).

fof(f552,plain,
    ( spl0_15
  <=> sk0_48 = sk0_51 ),
    introduced(split_symbol_definition) ).

fof(f553,plain,
    ( sk0_48 = sk0_51
    | ~ spl0_15 ),
    inference(component_clause,[status(thm)],[f552]) ).

fof(f555,plain,
    ( ~ ssList(sk0_51)
    | sk0_48 = sk0_51
    | ~ spl0_10 ),
    inference(paramodulation,[status(thm)],[f550,f389]) ).

fof(f556,plain,
    ( ~ spl0_8
    | spl0_15
    | ~ spl0_10 ),
    inference(split_clause,[status(thm)],[f555,f504,f552,f516]) ).

fof(f559,plain,
    ( ~ ssList(sk0_51)
    | ~ ssList(nil)
    | ssList(sk0_48)
    | ~ spl0_10 ),
    inference(paramodulation,[status(thm)],[f550,f245]) ).

fof(f560,plain,
    ( ~ spl0_8
    | ~ spl0_4
    | spl0_9
    | ~ spl0_10 ),
    inference(split_clause,[status(thm)],[f559,f504,f476,f507,f516]) ).

fof(f563,plain,
    ( spl0_16
  <=> nil = app(sk0_51,cons(sk0_53,nil)) ),
    introduced(split_symbol_definition) ).

fof(f564,plain,
    ( nil = app(sk0_51,cons(sk0_53,nil))
    | ~ spl0_16 ),
    inference(component_clause,[status(thm)],[f563]) ).

fof(f566,plain,
    ( ~ ssList(app(sk0_51,cons(sk0_53,nil)))
    | nil = app(sk0_51,cons(sk0_53,nil))
    | ~ spl0_10
    | ~ spl0_2 ),
    inference(paramodulation,[status(thm)],[f549,f389]) ).

fof(f567,plain,
    ( ~ spl0_6
    | spl0_16
    | ~ spl0_10
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f566,f496,f563,f516,f468]) ).

fof(f588,plain,
    ( nil = app(sk0_48,cons(sk0_53,nil))
    | ~ spl0_15
    | ~ spl0_16 ),
    inference(forward_demodulation,[status(thm)],[f553,f564]) ).

fof(f590,plain,
    ( spl0_18
  <=> nil = cons(sk0_53,nil) ),
    introduced(split_symbol_definition) ).

fof(f591,plain,
    ( nil = cons(sk0_53,nil)
    | ~ spl0_18 ),
    inference(component_clause,[status(thm)],[f590]) ).

fof(f593,plain,
    ( ~ ssList(sk0_48)
    | ~ ssList(cons(sk0_53,nil))
    | nil = cons(sk0_53,nil)
    | ~ spl0_15
    | ~ spl0_16 ),
    inference(resolution,[status(thm)],[f588,f385]) ).

fof(f594,plain,
    ( ~ spl0_9
    | ~ spl0_13
    | spl0_18
    | ~ spl0_15
    | ~ spl0_16 ),
    inference(split_clause,[status(thm)],[f593,f507,f537,f590,f552,f563]) ).

fof(f602,plain,
    ( ~ ssList(nil)
    | ~ ssItem(sk0_53)
    | ~ spl0_18 ),
    inference(resolution,[status(thm)],[f591,f235]) ).

fof(f603,plain,
    ( ~ spl0_4
    | ~ spl0_14
    | ~ spl0_18 ),
    inference(split_clause,[status(thm)],[f602,f476,f542,f590]) ).

fof(f612,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f480,f482,f484,f513,f515,f520,f541,f546,f548,f556,f560,f567,f594,f603]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC218+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n029.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 : Tue May 30 11:39:52 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.35  % Drodi V3.5.1
% 0.19/0.36  % Refutation found
% 0.19/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.37  % Elapsed time: 0.031075 seconds
% 0.19/0.37  % CPU time: 0.054906 seconds
% 0.19/0.37  % Memory used: 16.211 MB
%------------------------------------------------------------------------------