TSTP Solution File: SWC106+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SWC106+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 20:44:33 EDT 2024

% Result   : Theorem 0.14s 0.32s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  118 (  15 unt;   0 def)
%            Number of atoms       :  360 (  63 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  397 ( 155   ~; 149   |;  52   &)
%                                         (  20 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   23 (  21 usr;  17 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-4 aty)
%            Number of variables   :   98 (  81   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( rearsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & app(W,V) = U ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

fof(f18,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => cons(V,U) != U ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [U] :
      ( ssList(U)
     => app(nil,U) = 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
                    | ( ( ~ neq(V,nil)
                        | ! [Y] :
                            ( ssItem(Y)
                           => ! [Z] :
                                ( ssList(Z)
                               => ( cons(Y,nil) != W
                                  | app(Z,cons(Y,nil)) != X ) ) )
                        | ( neq(U,nil)
                          & rearsegP(V,U) ) )
                      & ( ~ neq(V,nil)
                        | neq(X,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
                      | ( ( ~ neq(V,nil)
                          | ! [Y] :
                              ( ssItem(Y)
                             => ! [Z] :
                                  ( ssList(Z)
                                 => ( cons(Y,nil) != W
                                    | app(Z,cons(Y,nil)) != X ) ) )
                          | ( neq(U,nil)
                            & rearsegP(V,U) ) )
                        & ( ~ neq(V,nil)
                          | neq(X,nil) ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f125,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( rearsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & app(W,V) = U ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f126,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ rearsegP(U,V)
              | ? [W] :
                  ( ssList(W)
                  & app(W,V) = U ) )
            & ( rearsegP(U,V)
              | ! [W] :
                  ( ~ ssList(W)
                  | app(W,V) != U ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f125]) ).

fof(f127,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssList(V)
          | ( ( ~ rearsegP(U,V)
              | ( ssList(sk0_6(V,U))
                & app(sk0_6(V,U),V) = U ) )
            & ( rearsegP(U,V)
              | ! [W] :
                  ( ~ ssList(W)
                  | app(W,V) != U ) ) ) ) ),
    inference(skolemization,[status(esa)],[f126]) ).

fof(f130,plain,
    ! [X0,X1,X2] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | rearsegP(X0,X1)
      | ~ ssList(X2)
      | app(X2,X1) != X0 ),
    inference(cnf_transformation,[status(esa)],[f127]) ).

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(f224,plain,
    ! [U] :
      ( ~ ssList(U)
      | ! [V] :
          ( ~ ssItem(V)
          | cons(V,U) != U ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f225,plain,
    ! [X0,X1] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | cons(X1,X0) != X0 ),
    inference(cnf_transformation,[status(esa)],[f224]) ).

fof(f248,plain,
    ! [U] :
      ( ~ ssList(U)
      | app(nil,U) = U ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f249,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(nil,X0) = X0 ),
    inference(cnf_transformation,[status(esa)],[f248]) ).

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
                  & ( ( neq(V,nil)
                      & ? [Y] :
                          ( ssItem(Y)
                          & ? [Z] :
                              ( ssList(Z)
                              & cons(Y,nil) = W
                              & app(Z,cons(Y,nil)) = X ) )
                      & ( ~ neq(U,nil)
                        | ~ rearsegP(V,U) ) )
                    | ( 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] :
            ( ssItem(Y)
            & ? [Z] :
                ( ssList(Z)
                & cons(Y,nil) = W
                & app(Z,cons(Y,nil)) = X ) )
        & ( ~ neq(U,nil)
          | ~ rearsegP(V,U) ) ) ),
    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(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_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] :
            ( ssItem(Y)
            & ? [Z] :
                ( ssList(Z)
                & cons(Y,nil) = W
                & app(Z,cons(Y,nil)) = X ) )
        & ( ~ neq(U,nil)
          | ~ rearsegP(V,U) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f416]) ).

fof(f428,plain,
    ! [U,V,W,X] :
      ( ~ pd0_0(X,W,V,U)
      | ( neq(V,nil)
        & ssItem(sk0_51(X,W,V,U))
        & ssList(sk0_52(X,W,V,U))
        & cons(sk0_51(X,W,V,U),nil) = W
        & app(sk0_52(X,W,V,U),cons(sk0_51(X,W,V,U),nil)) = X
        & ( ~ neq(U,nil)
          | ~ rearsegP(V,U) ) ) ),
    inference(skolemization,[status(esa)],[f427]) ).

fof(f430,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ssItem(sk0_51(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f431,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ssList(sk0_52(X0,X1,X2,X3)) ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

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

fof(f433,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | app(sk0_52(X0,X1,X2,X3),cons(sk0_51(X0,X1,X2,X3),nil)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f428]) ).

fof(f434,plain,
    ! [X0,X1,X2,X3] :
      ( ~ pd0_0(X0,X1,X2,X3)
      | ~ neq(X3,nil)
      | ~ rearsegP(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(f451,plain,
    ! [X0,X1] :
      ( ~ ssList(app(X0,X1))
      | ~ ssList(X1)
      | rearsegP(app(X0,X1),X1)
      | ~ ssList(X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f130]) ).

fof(f491,plain,
    ( ~ neq(sk0_48,nil)
    | spl0_2 ),
    inference(forward_demodulation,[status(thm)],[f423,f444]) ).

fof(f492,plain,
    ( pd0_0(sk0_48,sk0_49,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f423,f436]) ).

fof(f493,plain,
    ( pd0_0(sk0_48,sk0_47,sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f424,f492]) ).

fof(f497,plain,
    ( $false
    | spl0_2
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f439,f491]) ).

fof(f498,plain,
    ( spl0_2
    | ~ spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f497]) ).

fof(f500,plain,
    ( ssItem(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f430,f493]) ).

fof(f531,plain,
    ( ssList(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f431,f493]) ).

fof(f535,plain,
    ( spl0_9
  <=> neq(sk0_47,nil) ),
    introduced(split_symbol_definition) ).

fof(f538,plain,
    ( spl0_10
  <=> rearsegP(sk0_48,sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f540,plain,
    ( ~ rearsegP(sk0_48,sk0_47)
    | spl0_10 ),
    inference(component_clause,[status(thm)],[f538]) ).

fof(f541,plain,
    ( ~ neq(sk0_47,nil)
    | ~ rearsegP(sk0_48,sk0_47)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f434,f493]) ).

fof(f542,plain,
    ( ~ spl0_9
    | ~ spl0_10
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f541,f535,f538,f435]) ).

fof(f543,plain,
    ( cons(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47),nil) = sk0_47
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f432,f493]) ).

fof(f544,plain,
    ( app(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47),cons(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47),nil)) = sk0_48
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f433,f493]) ).

fof(f545,plain,
    ( app(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47),sk0_47) = sk0_48
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f543,f544]) ).

fof(f546,plain,
    ( spl0_11
  <=> ssList(sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f548,plain,
    ( ~ ssList(sk0_48)
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f546]) ).

fof(f549,plain,
    ( spl0_12
  <=> ssList(sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f551,plain,
    ( ~ ssList(sk0_47)
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f549]) ).

fof(f552,plain,
    ( spl0_13
  <=> rearsegP(app(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47),sk0_47),sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f553,plain,
    ( rearsegP(app(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47),sk0_47),sk0_47)
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f552]) ).

fof(f555,plain,
    ( spl0_14
  <=> ssList(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47)) ),
    introduced(split_symbol_definition) ).

fof(f557,plain,
    ( ~ ssList(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47))
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f555]) ).

fof(f558,plain,
    ( ~ ssList(sk0_48)
    | ~ ssList(sk0_47)
    | rearsegP(app(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47),sk0_47),sk0_47)
    | ~ ssList(sk0_52(sk0_48,sk0_47,sk0_48,sk0_47))
    | ~ spl0_0 ),
    inference(paramodulation,[status(thm)],[f545,f451]) ).

fof(f559,plain,
    ( ~ spl0_11
    | ~ spl0_12
    | spl0_13
    | ~ spl0_14
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f558,f546,f549,f552,f555,f435]) ).

fof(f560,plain,
    ( $false
    | ~ spl0_0
    | spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f557,f531]) ).

fof(f561,plain,
    ( ~ spl0_0
    | spl0_14 ),
    inference(contradiction_clause,[status(thm)],[f560]) ).

fof(f562,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f551,f419]) ).

fof(f563,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f562]) ).

fof(f564,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f548,f420]) ).

fof(f565,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f564]) ).

fof(f566,plain,
    ( rearsegP(sk0_48,sk0_47)
    | ~ spl0_0
    | ~ spl0_13 ),
    inference(forward_demodulation,[status(thm)],[f545,f553]) ).

fof(f568,plain,
    app(nil,nil) = nil,
    inference(resolution,[status(thm)],[f249,f223]) ).

fof(f569,plain,
    app(nil,sk0_48) = sk0_48,
    inference(resolution,[status(thm)],[f249,f420]) ).

fof(f570,plain,
    app(nil,sk0_47) = sk0_47,
    inference(resolution,[status(thm)],[f249,f419]) ).

fof(f574,plain,
    ( spl0_16
  <=> ssList(nil) ),
    introduced(split_symbol_definition) ).

fof(f576,plain,
    ( ~ ssList(nil)
    | spl0_16 ),
    inference(component_clause,[status(thm)],[f574]) ).

fof(f579,plain,
    ( $false
    | spl0_16 ),
    inference(forward_subsumption_resolution,[status(thm)],[f576,f223]) ).

fof(f580,plain,
    spl0_16,
    inference(contradiction_clause,[status(thm)],[f579]) ).

fof(f582,plain,
    ( spl0_17
  <=> rearsegP(app(nil,sk0_48),sk0_48) ),
    introduced(split_symbol_definition) ).

fof(f585,plain,
    ( ~ ssList(sk0_48)
    | ~ ssList(sk0_48)
    | rearsegP(app(nil,sk0_48),sk0_48)
    | ~ ssList(nil) ),
    inference(paramodulation,[status(thm)],[f569,f451]) ).

fof(f586,plain,
    ( ~ spl0_11
    | spl0_17
    | ~ spl0_16 ),
    inference(split_clause,[status(thm)],[f585,f546,f582,f574]) ).

fof(f588,plain,
    ( spl0_18
  <=> rearsegP(app(nil,sk0_47),sk0_47) ),
    introduced(split_symbol_definition) ).

fof(f591,plain,
    ( ~ ssList(sk0_47)
    | ~ ssList(sk0_47)
    | rearsegP(app(nil,sk0_47),sk0_47)
    | ~ ssList(nil) ),
    inference(paramodulation,[status(thm)],[f570,f451]) ).

fof(f592,plain,
    ( ~ spl0_12
    | spl0_18
    | ~ spl0_16 ),
    inference(split_clause,[status(thm)],[f591,f549,f588,f574]) ).

fof(f597,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | neq(sk0_47,X0)
      | sk0_47 = X0 ),
    inference(resolution,[status(thm)],[f220,f419]) ).

fof(f664,plain,
    ( spl0_34
  <=> sk0_47 = nil ),
    introduced(split_symbol_definition) ).

fof(f665,plain,
    ( sk0_47 = nil
    | ~ spl0_34 ),
    inference(component_clause,[status(thm)],[f664]) ).

fof(f667,plain,
    ( neq(sk0_47,nil)
    | sk0_47 = nil ),
    inference(resolution,[status(thm)],[f597,f223]) ).

fof(f668,plain,
    ( spl0_9
    | spl0_34 ),
    inference(split_clause,[status(thm)],[f667,f535,f664]) ).

fof(f682,plain,
    ( $false
    | ~ spl0_0
    | ~ spl0_13
    | spl0_10 ),
    inference(forward_subsumption_resolution,[status(thm)],[f540,f566]) ).

fof(f683,plain,
    ( ~ spl0_0
    | ~ spl0_13
    | spl0_10 ),
    inference(contradiction_clause,[status(thm)],[f682]) ).

fof(f684,plain,
    ( spl0_38
  <=> rearsegP(app(nil,nil),nil) ),
    introduced(split_symbol_definition) ).

fof(f687,plain,
    ( ~ ssList(nil)
    | ~ ssList(nil)
    | rearsegP(app(nil,nil),nil)
    | ~ ssList(nil) ),
    inference(paramodulation,[status(thm)],[f568,f451]) ).

fof(f688,plain,
    ( ~ spl0_16
    | spl0_38 ),
    inference(split_clause,[status(thm)],[f687,f574,f684]) ).

fof(f692,plain,
    app(sk0_48,nil) = sk0_48,
    inference(resolution,[status(thm)],[f389,f420]) ).

fof(f693,plain,
    app(sk0_47,nil) = sk0_47,
    inference(resolution,[status(thm)],[f389,f419]) ).

fof(f694,plain,
    ( spl0_39
  <=> rearsegP(app(sk0_48,nil),nil) ),
    introduced(split_symbol_definition) ).

fof(f697,plain,
    ( ~ ssList(sk0_48)
    | ~ ssList(nil)
    | rearsegP(app(sk0_48,nil),nil)
    | ~ ssList(sk0_48) ),
    inference(paramodulation,[status(thm)],[f692,f451]) ).

fof(f698,plain,
    ( ~ spl0_11
    | ~ spl0_16
    | spl0_39 ),
    inference(split_clause,[status(thm)],[f697,f546,f574,f694]) ).

fof(f700,plain,
    ( spl0_40
  <=> rearsegP(app(sk0_47,nil),nil) ),
    introduced(split_symbol_definition) ).

fof(f703,plain,
    ( ~ ssList(sk0_47)
    | ~ ssList(nil)
    | rearsegP(app(sk0_47,nil),nil)
    | ~ ssList(sk0_47) ),
    inference(paramodulation,[status(thm)],[f693,f451]) ).

fof(f704,plain,
    ( ~ spl0_12
    | ~ spl0_16
    | spl0_40 ),
    inference(split_clause,[status(thm)],[f703,f549,f574,f700]) ).

fof(f707,plain,
    ! [X0] :
      ( ~ ssItem(X0)
      | cons(X0,nil) != nil ),
    inference(resolution,[status(thm)],[f225,f223]) ).

fof(f710,plain,
    ( cons(sk0_51(sk0_48,sk0_47,sk0_48,sk0_47),nil) != nil
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f707,f500]) ).

fof(f711,plain,
    ( sk0_47 != nil
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f543,f710]) ).

fof(f845,plain,
    ( nil != nil
    | ~ spl0_34
    | ~ spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f665,f711]) ).

fof(f846,plain,
    ( $false
    | ~ spl0_34
    | ~ spl0_0 ),
    inference(trivial_equality_resolution,[status(esa)],[f845]) ).

fof(f847,plain,
    ( ~ spl0_34
    | ~ spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f846]) ).

fof(f848,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f441,f445,f498,f542,f559,f561,f563,f565,f580,f586,f592,f668,f683,f688,f698,f704,f847]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SWC106+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n031.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue Apr 30 00:36:28 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.14/0.32  % Drodi V3.6.0
% 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
% 0.14/0.34  % Elapsed time: 0.024845 seconds
% 0.14/0.34  % CPU time: 0.053495 seconds
% 0.14/0.34  % Total memory used: 17.155 MB
% 0.14/0.34  % Net memory used: 17.100 MB
%------------------------------------------------------------------------------