TSTP Solution File: SWC210+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWC210+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.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 12:39:41 EDT 2023

% Result   : Theorem 0.14s 0.32s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   66 (  12 unt;   0 def)
%            Number of atoms       :  193 (  24 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  211 (  84   ~;  76   |;  30   &)
%                                         (  10 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   9 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   40 (;  32   !;   8   ?)

% 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(f39,axiom,
    ~ singletonP(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(W)
                        | neq(U,nil) )
                      & ( ~ 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)
                          | ~ singletonP(W)
                          | neq(U,nil) )
                        & ( ~ 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(f280,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[status(esa)],[f39]) ).

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

fof(f416,plain,
    ! [U,V,W] :
      ( pd0_0(W,V,U)
     => ( neq(V,nil)
        & singletonP(W)
        & ~ neq(U,nil) ) ),
    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(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_49,sk0_48,sk0_47)
      | ( neq(sk0_48,nil)
        & ~ neq(sk0_50,nil) ) ) ),
    inference(skolemization,[status(esa)],[f417]) ).

fof(f419,plain,
    ssList(sk0_47),
    inference(cnf_transformation,[status(esa)],[f418]) ).

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_49,sk0_48,sk0_47)
    | neq(sk0_48,nil) ),
    inference(cnf_transformation,[status(esa)],[f418]) ).

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

fof(f427,plain,
    ! [U,V,W] :
      ( ~ pd0_0(W,V,U)
      | ( neq(V,nil)
        & singletonP(W)
        & ~ neq(U,nil) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f416]) ).

fof(f429,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | singletonP(X0) ),
    inference(cnf_transformation,[status(esa)],[f427]) ).

fof(f430,plain,
    ! [X0,X1,X2] :
      ( ~ pd0_0(X0,X1,X2)
      | ~ neq(X2,nil) ),
    inference(cnf_transformation,[status(esa)],[f427]) ).

fof(f431,plain,
    ( spl0_0
  <=> pd0_0(sk0_49,sk0_48,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f432,plain,
    ( pd0_0(sk0_49,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f431]) ).

fof(f434,plain,
    ( spl0_1
  <=> neq(sk0_48,nil) ),
    introduced(split_symbol_definition) ).

fof(f435,plain,
    ( neq(sk0_48,nil)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f434]) ).

fof(f437,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f425,f431,f434]) ).

fof(f438,plain,
    ( spl0_2
  <=> neq(sk0_50,nil) ),
    introduced(split_symbol_definition) ).

fof(f440,plain,
    ( ~ neq(sk0_50,nil)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f438]) ).

fof(f441,plain,
    ( spl0_0
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f426,f431,f438]) ).

fof(f457,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ~ ssList(X1)
      | ~ neq(X1,X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f219]) ).

fof(f458,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ neq(X0,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f457]) ).

fof(f474,plain,
    ( ~ neq(sk0_48,nil)
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f423,f440]) ).

fof(f475,plain,
    ( spl0_3
  <=> ssList(sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f477,plain,
    ( ~ ssList(sk0_48)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f475]) ).

fof(f478,plain,
    ( spl0_4
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f480,plain,
    ( ~ ssList(nil)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f478]) ).

fof(f481,plain,
    ( spl0_5
  <=> sk0_48 = nil ),
    introduced(split_symbol_definition) ).

fof(f482,plain,
    ( sk0_48 = nil
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f481]) ).

fof(f484,plain,
    ( ~ ssList(sk0_48)
    | ~ ssList(nil)
    | sk0_48 = nil
    | spl0_2 ),
    inference(resolution,[status(thm)],[f474,f220]) ).

fof(f485,plain,
    ( ~ spl0_3
    | ~ spl0_4
    | spl0_5
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f484,f475,f478,f481,f438]) ).

fof(f494,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f480,f223]) ).

fof(f495,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f494]) ).

fof(f496,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f477,f420]) ).

fof(f497,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f496]) ).

fof(f500,plain,
    ( pd0_0(sk0_47,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f424,f432]) ).

fof(f505,plain,
    ( spl0_8
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f507,plain,
    ( ~ ssList(sk0_47)
    | spl0_8 ),
    inference(component_clause,[status(thm)],[f505]) ).

fof(f508,plain,
    ( spl0_9
  <=> sk0_47 = nil ),
    introduced(split_symbol_definition) ).

fof(f509,plain,
    ( sk0_47 = nil
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f508]) ).

fof(f518,plain,
    ( $false
    | spl0_8 ),
    inference(forward_subsumption_resolution,[status(thm)],[f507,f419]) ).

fof(f519,plain,
    spl0_8,
    inference(contradiction_clause,[status(thm)],[f518]) ).

fof(f522,plain,
    ( pd0_0(nil,sk0_48,sk0_47)
    | ~ spl0_9
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f509,f500]) ).

fof(f523,plain,
    ( pd0_0(nil,sk0_48,nil)
    | ~ spl0_9
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f509,f522]) ).

fof(f526,plain,
    ( singletonP(nil)
    | ~ spl0_9
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f523,f429]) ).

fof(f527,plain,
    ( $false
    | ~ spl0_9
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f526,f280]) ).

fof(f528,plain,
    ( ~ spl0_9
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f527]) ).

fof(f529,plain,
    ( ~ neq(sk0_47,nil)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f500,f430]) ).

fof(f532,plain,
    ( ~ ssList(sk0_47)
    | ~ ssList(nil)
    | sk0_47 = nil
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f529,f220]) ).

fof(f533,plain,
    ( ~ spl0_8
    | ~ spl0_4
    | spl0_9
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f532,f505,f478,f508,f431]) ).

fof(f536,plain,
    ( neq(nil,nil)
    | ~ spl0_5
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f482,f435]) ).

fof(f537,plain,
    ( ~ ssList(nil)
    | ~ spl0_5
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f536,f458]) ).

fof(f538,plain,
    ( ~ spl0_4
    | ~ spl0_5
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f537,f478,f481,f434]) ).

fof(f540,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f437,f441,f485,f495,f497,f519,f528,f533,f538]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : SWC210+1 : TPTP v8.1.2. Released v2.4.0.
% 0.05/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30  % Computer : n002.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Tue May 30 11:37:13 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.14/0.31  % Drodi V3.5.1
% 0.14/0.32  % Refutation found
% 0.14/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54  % Elapsed time: 0.018053 seconds
% 0.15/0.54  % CPU time: 0.018114 seconds
% 0.15/0.54  % Memory used: 4.085 MB
%------------------------------------------------------------------------------