TSTP Solution File: SWC050+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC050+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 12:39:02 EDT 2023

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   62 (   9 unt;   0 def)
%            Number of atoms       :  231 (  21 equ)
%            Maximal formula atoms :   17 (   3 avg)
%            Number of connectives :  280 ( 111   ~;  98   |;  50   &)
%                                         (   8 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   7 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-4 aty)
%            Number of variables   :   86 (;  73   !;  13   ?)

% 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(f96,conjecture,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( V != X
                    | U != W
                    | ( ( ~ neq(V,nil)
                        | ? [Y] :
                            ( ssList(Y)
                            & neq(Y,nil)
                            & rearsegP(V,Y)
                            & rearsegP(U,Y) )
                        | ! [Z] :
                            ( ssList(Z)
                           => ( ~ neq(Z,nil)
                              | ~ rearsegP(X,Z)
                              | ~ rearsegP(W,Z) ) ) )
                      & ( ~ neq(V,nil)
                        | neq(X,nil) ) ) ) ) ) ) ),
    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)
                          | ? [Y] :
                              ( ssList(Y)
                              & neq(Y,nil)
                              & rearsegP(V,Y)
                              & rearsegP(U,Y) )
                          | ! [Z] :
                              ( ssList(Z)
                             => ( ~ neq(Z,nil)
                                | ~ rearsegP(X,Z)
                                | ~ rearsegP(W,Z) ) ) )
                        & ( ~ neq(V,nil)
                          | neq(X,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(f219,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ neq(X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f218]) ).

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(f415,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ( ( neq(V,nil)
                      & ! [Y] :
                          ( ~ ssList(Y)
                          | ~ neq(Y,nil)
                          | ~ rearsegP(V,Y)
                          | ~ rearsegP(U,Y) )
                      & ? [Z] :
                          ( ssList(Z)
                          & neq(Z,nil)
                          & rearsegP(X,Z)
                          & rearsegP(W,Z) ) )
                    | ( neq(V,nil)
                      & ~ neq(X,nil) ) ) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f97]) ).

fof(f416,plain,
    ! [U,V,W,X] :
      ( pd0_0(X,W,V,U)
     => ( neq(V,nil)
        & ! [Y] :
            ( ~ ssList(Y)
            | ~ neq(Y,nil)
            | ~ rearsegP(V,Y)
            | ~ rearsegP(U,Y) )
        & ? [Z] :
            ( ssList(Z)
            & neq(Z,nil)
            & rearsegP(X,Z)
            & rearsegP(W,Z) ) ) ),
    introduced(predicate_definition,[f415]) ).

fof(f417,plain,
    ? [U] :
      ( ssList(U)
      & ? [V] :
          ( ssList(V)
          & ? [W] :
              ( ssList(W)
              & ? [X] :
                  ( ssList(X)
                  & V = X
                  & U = W
                  & ( pd0_0(X,W,V,U)
                    | ( neq(V,nil)
                      & ~ neq(X,nil) ) ) ) ) ) ),
    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
    & ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
      | ( neq(sk0_48,nil)
        & ~ neq(sk0_50,nil) ) ) ),
    inference(skolemization,[status(esa)],[f417]) ).

fof(f420,plain,
    ssList(sk0_48),
    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,
    ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
    | neq(sk0_48,nil) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f426,plain,
    ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
    | ~ neq(sk0_50,nil) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

fof(f427,plain,
    ! [U,V,W,X] :
      ( ~ pd0_0(X,W,V,U)
      | ( neq(V,nil)
        & ! [Y] :
            ( ~ ssList(Y)
            | ~ neq(Y,nil)
            | ~ rearsegP(V,Y)
            | ~ rearsegP(U,Y) )
        & ? [Z] :
            ( ssList(Z)
            & neq(Z,nil)
            & rearsegP(X,Z)
            & rearsegP(W,Z) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f416]) ).

fof(f428,plain,
    ! [U,V,W,X] :
      ( ~ pd0_0(X,W,V,U)
      | ( neq(V,nil)
        & ! [Y] :
            ( ~ ssList(Y)
            | ~ neq(Y,nil)
            | ~ rearsegP(V,Y)
            | ~ rearsegP(U,Y) )
        & ssList(sk0_51(X,W,V,U))
        & neq(sk0_51(X,W,V,U),nil)
        & rearsegP(X,sk0_51(X,W,V,U))
        & rearsegP(W,sk0_51(X,W,V,U)) ) ),
    inference(skolemization,[status(esa)],[f427]) ).

fof(f430,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ ssList(X4)
      | ~ neq(X4,nil)
      | ~ rearsegP(X2,X4)
      | ~ rearsegP(X3,X4) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f431,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ssList(sk0_51(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f432,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | neq(sk0_51(X0,X1,X2,X3),nil) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f433,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | rearsegP(X0,sk0_51(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f434,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | rearsegP(X1,sk0_51(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f435,plain,
    ( spl0_0
  <=> pd0_0(sk0_50,sk0_49,sk0_48,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f436,plain,
    ( pd0_0(sk0_50,sk0_49,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f435]) ).

fof(f438,plain,
    ( spl0_1
  <=> neq(sk0_48,nil) ),
    introduced(split_symbol_definition) ).

fof(f439,plain,
    ( neq(sk0_48,nil)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f438]) ).

fof(f441,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f425,f435,f438]) ).

fof(f442,plain,
    ( spl0_2
  <=> neq(sk0_50,nil) ),
    introduced(split_symbol_definition) ).

fof(f444,plain,
    ( ~ neq(sk0_50,nil)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f442]) ).

fof(f445,plain,
    ( spl0_0
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f426,f435,f442]) ).

fof(f461,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f219]) ).

fof(f462,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ neq(X0,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f461]) ).

fof(f478,plain,
    ( spl0_3
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f480,plain,
    ( ~ ssList(nil)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f478]) ).

fof(f488,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f480,f223]) ).

fof(f489,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f488]) ).

fof(f498,plain,
    ( ~ neq(sk0_48,nil)
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f423,f444]) ).

fof(f499,plain,
    ( spl0_6
  <=> ssList(sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f501,plain,
    ( ~ ssList(sk0_48)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f499]) ).

fof(f502,plain,
    ( spl0_7
  <=> sk0_48 = nil ),
    introduced(split_symbol_definition) ).

fof(f503,plain,
    ( sk0_48 = nil
    | ~ spl0_7 ),
    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_6
    | ~ spl0_3
    | spl0_7
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f505,f499,f478,f502,f442]) ).

fof(f515,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f501,f420]) ).

fof(f516,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f515]) ).

fof(f526,plain,
    ( neq(nil,nil)
    | ~ spl0_7
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f503,f439]) ).

fof(f531,plain,
    ( ~ ssList(nil)
    | ~ spl0_7
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f526,f462]) ).

fof(f532,plain,
    ( ~ spl0_3
    | ~ spl0_7
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f531,f478,f502,f438]) ).

fof(f534,plain,
    ( pd0_0(sk0_50,sk0_47,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f424,f436]) ).

fof(f536,plain,
    ( pd0_0(sk0_48,sk0_47,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f423,f534]) ).

fof(f546,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ neq(X0,nil)
      | ~ rearsegP(sk0_48,X0)
      | ~ rearsegP(sk0_47,X0)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f430,f536]) ).

fof(f549,plain,
    ! [X0,X1,X2] :
      ( ~ ssList(sk0_51(sk0_48,X0,X1,X2))
      | ~ neq(sk0_51(sk0_48,X0,X1,X2),nil)
      | ~ rearsegP(sk0_47,sk0_51(sk0_48,X0,X1,X2))
      | ~ pd0_0(sk0_48,X0,X1,X2)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f546,f433]) ).

fof(f550,plain,
    ! [X0,X1,X2] :
      ( ~ neq(sk0_51(sk0_48,X0,X1,X2),nil)
      | ~ rearsegP(sk0_47,sk0_51(sk0_48,X0,X1,X2))
      | ~ pd0_0(sk0_48,X0,X1,X2)
      | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f549,f431]) ).

fof(f822,plain,
    ! [X0,X1,X2] :
      ( ~ rearsegP(sk0_47,sk0_51(sk0_48,X0,X1,X2))
      | ~ pd0_0(sk0_48,X0,X1,X2)
      | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f550,f432]) ).

fof(f838,plain,
    ! [X0,X1] :
      ( ~ pd0_0(sk0_48,sk0_47,X0,X1)
      | ~ pd0_0(sk0_48,sk0_47,X0,X1)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f822,f434]) ).

fof(f839,plain,
    ! [X0,X1] :
      ( ~ pd0_0(sk0_48,sk0_47,X0,X1)
      | ~ spl0_0 ),
    inference(duplicate_literals_removal,[status(esa)],[f838]) ).

fof(f844,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f536,f839]) ).

fof(f845,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f844]) ).

fof(f846,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f441,f445,f489,f506,f516,f532,f845]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC050+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n016.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 May 30 11:52:14 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 0.12/0.37  % Refutation found
% 0.12/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39  % Elapsed time: 0.042652 seconds
% 0.12/0.39  % CPU time: 0.134239 seconds
% 0.12/0.39  % Memory used: 18.485 MB
%------------------------------------------------------------------------------