TSTP Solution File: SWC369+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC369+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 20:45:31 EDT 2024

% Result   : Theorem 0.15s 0.33s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   55 (  10 unt;   0 def)
%            Number of atoms       :  158 (  34 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  168 (  65   ~;  60   |;  23   &)
%                                         (   9 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   8 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   23 (  19   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
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(f57,axiom,
    ! [U] :
      ( ssList(U)
     => segmentP(U,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
                    | segmentP(V,U)
                    | ( nil != W
                      & nil = X )
                    | ( neq(X,nil)
                      & ( ~ neq(W,nil)
                        | ~ segmentP(X,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
                      | segmentP(V,U)
                      | ( nil != W
                        & nil = X )
                      | ( neq(X,nil)
                        & ( ~ neq(W,nil)
                          | ~ segmentP(X,W) ) ) ) ) ) ) ),
    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(f223,plain,
    ssList(nil),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f322,plain,
    ! [U] :
      ( ~ ssList(U)
      | segmentP(U,nil) ),
    inference(pre_NNF_transformation,[status(esa)],[f57]) ).

fof(f323,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | segmentP(X0,nil) ),
    inference(cnf_transformation,[status(esa)],[f322]) ).

fof(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ~ segmentP(V,U)
                  & ( nil = W
                    | nil != X )
                  & ( ~ neq(X,nil)
                    | ( neq(W,nil)
                      & segmentP(X,W) ) ) ) ) ) ),
    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
    & ~ segmentP(sk0_48,sk0_47)
    & ( nil = sk0_49
      | nil != sk0_50 )
    & ( ~ neq(sk0_50,nil)
      | ( neq(sk0_49,nil)
        & segmentP(sk0_50,sk0_49) ) ) ),
    inference(skolemization,[status(esa)],[f415]) ).

fof(f418,plain,
    ssList(sk0_48),
    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,
    ~ segmentP(sk0_48,sk0_47),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f424,plain,
    ( nil = sk0_49
    | nil != sk0_50 ),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f426,plain,
    ( ~ neq(sk0_50,nil)
    | segmentP(sk0_50,sk0_49) ),
    inference(cnf_transformation,[status(esa)],[f416]) ).

fof(f427,plain,
    ( spl0_0
  <=> nil = sk0_49 ),
    introduced(split_symbol_definition) ).

fof(f428,plain,
    ( nil = sk0_49
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f427]) ).

fof(f430,plain,
    ( spl0_1
  <=> nil = sk0_50 ),
    introduced(split_symbol_definition) ).

fof(f432,plain,
    ( nil != sk0_50
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f430]) ).

fof(f433,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f424,f427,f430]) ).

fof(f434,plain,
    ( spl0_2
  <=> neq(sk0_50,nil) ),
    introduced(split_symbol_definition) ).

fof(f436,plain,
    ( ~ neq(sk0_50,nil)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f434]) ).

fof(f441,plain,
    ( spl0_4
  <=> segmentP(sk0_50,sk0_49) ),
    introduced(split_symbol_definition) ).

fof(f442,plain,
    ( segmentP(sk0_50,sk0_49)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f441]) ).

fof(f444,plain,
    ( ~ spl0_2
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f426,f434,f441]) ).

fof(f477,plain,
    ( spl0_5
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f479,plain,
    ( ~ ssList(nil)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f477]) ).

fof(f487,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f479,f223]) ).

fof(f488,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f487]) ).

fof(f497,plain,
    ( nil != sk0_48
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f421,f432]) ).

fof(f498,plain,
    ( ~ neq(sk0_48,nil)
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f421,f436]) ).

fof(f499,plain,
    ( spl0_8
  <=> ssList(sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f501,plain,
    ( ~ ssList(sk0_48)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f499]) ).

fof(f502,plain,
    ( spl0_9
  <=> sk0_48 = nil ),
    introduced(split_symbol_definition) ).

fof(f503,plain,
    ( sk0_48 = nil
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f502]) ).

fof(f505,plain,
    ( ~ ssList(sk0_48)
    | ~ ssList(nil)
    | sk0_48 = nil
    | spl0_2 ),
    inference(resolution,[status(thm)],[f498,f220]) ).

fof(f506,plain,
    ( ~ spl0_8
    | ~ spl0_5
    | spl0_9
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f505,f499,f477,f502,f434]) ).

fof(f515,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f501,f418]) ).

fof(f516,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f515]) ).

fof(f518,plain,
    ( segmentP(sk0_48,sk0_49)
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f421,f442]) ).

fof(f519,plain,
    ( segmentP(sk0_48,sk0_47)
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f422,f518]) ).

fof(f520,plain,
    ( $false
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f519,f423]) ).

fof(f521,plain,
    ~ spl0_4,
    inference(contradiction_clause,[status(thm)],[f520]) ).

fof(f522,plain,
    ( $false
    | spl0_1
    | ~ spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f503,f497]) ).

fof(f523,plain,
    ( spl0_1
    | ~ spl0_9 ),
    inference(contradiction_clause,[status(thm)],[f522]) ).

fof(f526,plain,
    ( nil = sk0_47
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f422,f428]) ).

fof(f528,plain,
    ( ~ segmentP(sk0_48,nil)
    | ~ spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f526,f423]) ).

fof(f538,plain,
    ( ~ segmentP(nil,nil)
    | ~ spl0_9
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f503,f528]) ).

fof(f539,plain,
    ( ~ ssList(nil)
    | ~ spl0_9
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f538,f323]) ).

fof(f540,plain,
    ( ~ spl0_5
    | ~ spl0_9
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f539,f477,f502,f427]) ).

fof(f543,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f433,f444,f488,f506,f516,f521,f523,f540]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : SWC369+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n006.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue Apr 30 00:06:50 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.6.0
% 0.15/0.33  % Refutation found
% 0.15/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.35  % Elapsed time: 0.025212 seconds
% 0.15/0.35  % CPU time: 0.029102 seconds
% 0.15/0.35  % Total memory used: 12.493 MB
% 0.15/0.35  % Net memory used: 12.464 MB
%------------------------------------------------------------------------------