TSTP Solution File: SWC407+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC407+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 : Fri May  3 03:12:23 EDT 2024

% Result   : Theorem 4.25s 1.18s
% Output   : CNFRefutation 4.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   78 (  18 unt;   0 def)
%            Number of atoms       :  420 ( 136 equ)
%            Maximal formula atoms :   28 (   5 avg)
%            Number of connectives :  485 ( 143   ~; 150   |; 154   &)
%                                         (   4 <=>;  34  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  145 (   0 sgn  69   !;  58   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f21,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => nil != cons(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f37,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil != X2
                        | nil != X3 )
                      & ! [X5] :
                          ( ssItem(X5)
                         => ( ~ memberP(X3,X5)
                            | cons(X5,nil) != X2 ) ) )
                    | ! [X4] :
                        ( ssItem(X4)
                       => ( memberP(X1,X4)
                          | ~ memberP(X0,X4) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X5] :
                            ( ssItem(X5)
                           => ( ~ memberP(X3,X5)
                              | cons(X5,nil) != X2 ) ) )
                      | ! [X4] :
                          ( ssItem(X4)
                         => ( memberP(X1,X4)
                            | ~ memberP(X0,X4) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ~ memberP(X3,X4)
                              | cons(X4,nil) != X2 ) ) )
                      | ! [X5] :
                          ( ssItem(X5)
                         => ( memberP(X1,X5)
                            | ~ memberP(X0,X5) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( memberP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(X2,cons(X1,X3)) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f126,plain,
    ! [X0] :
      ( ! [X1] :
          ( nil != cons(X1,X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f148,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( memberP(cons(X1,X2),X0)
              <=> ( memberP(X2,X0)
                  | X0 = X1 ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ? [X5] :
                      ( ~ memberP(X1,X5)
                      & memberP(X0,X5)
                      & ssItem(X5) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ? [X5] :
                      ( ~ memberP(X1,X5)
                      & memberP(X0,X5)
                      & ssItem(X5) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f237,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(X2,cons(X1,X3)) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f100]) ).

fof(f238,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(X4,cons(X1,X5)) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f237]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(X4,cons(X1,X5)) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(sK8(X0,X1),cons(X1,X5)) = X0
            & ssList(X5) )
        & ssList(sK8(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f240,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(sK8(X0,X1),cons(X1,X5)) = X0
          & ssList(X5) )
     => ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
        & ssList(sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f241,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( memberP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(X2,cons(X1,X3)) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
                & ssList(sK9(X0,X1))
                & ssList(sK8(X0,X1)) )
              | ~ memberP(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f238,f240,f239]) ).

fof(f325,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(nnf_transformation,[],[f148]) ).

fof(f326,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( memberP(cons(X1,X2),X0)
                  | ( ~ memberP(X2,X0)
                    & X0 != X1 ) )
                & ( memberP(X2,X0)
                  | X0 = X1
                  | ~ memberP(cons(X1,X2),X0) ) )
              | ~ ssList(X2) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(flattening,[],[f325]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( memberP(X3,X4)
                          & cons(X4,nil) = X2
                          & ssItem(X4) ) )
                    & ? [X5] :
                        ( ~ memberP(X1,X5)
                        & memberP(X0,X5)
                        & ssItem(X5) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ? [X5] :
                      ( ~ memberP(X1,X5)
                      & memberP(sK53,X5)
                      & ssItem(X5) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( memberP(X3,X4)
                      & cons(X4,nil) = X2
                      & ssItem(X4) ) )
                & ? [X5] :
                    ( ~ memberP(X1,X5)
                    & memberP(sK53,X5)
                    & ssItem(X5) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | ? [X4] :
                    ( memberP(X3,X4)
                    & cons(X4,nil) = X2
                    & ssItem(X4) ) )
              & ? [X5] :
                  ( ~ memberP(sK54,X5)
                  & memberP(sK53,X5)
                  & ssItem(X5) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( memberP(X3,X4)
                  & cons(X4,nil) = X2
                  & ssItem(X4) ) )
            & ? [X5] :
                ( ~ memberP(sK54,X5)
                & memberP(sK53,X5)
                & ssItem(X5) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK55
              & nil = X3 )
            | ? [X4] :
                ( memberP(X3,X4)
                & cons(X4,nil) = sK55
                & ssItem(X4) ) )
          & ? [X5] :
              ( ~ memberP(sK54,X5)
              & memberP(sK53,X5)
              & ssItem(X5) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( ( nil = sK55
            & nil = X3 )
          | ? [X4] :
              ( memberP(X3,X4)
              & cons(X4,nil) = sK55
              & ssItem(X4) ) )
        & ? [X5] :
            ( ~ memberP(sK54,X5)
            & memberP(sK53,X5)
            & ssItem(X5) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( nil = sK55
          & nil = sK56 )
        | ? [X4] :
            ( memberP(sK56,X4)
            & cons(X4,nil) = sK55
            & ssItem(X4) ) )
      & ? [X5] :
          ( ~ memberP(sK54,X5)
          & memberP(sK53,X5)
          & ssItem(X5) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X4] :
        ( memberP(sK56,X4)
        & cons(X4,nil) = sK55
        & ssItem(X4) )
   => ( memberP(sK56,sK57)
      & sK55 = cons(sK57,nil)
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ? [X5] :
        ( ~ memberP(sK54,X5)
        & memberP(sK53,X5)
        & ssItem(X5) )
   => ( ~ memberP(sK54,sK58)
      & memberP(sK53,sK58)
      & ssItem(sK58) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ( ( nil = sK55
        & nil = sK56 )
      | ( memberP(sK56,sK57)
        & sK55 = cons(sK57,nil)
        & ssItem(sK57) ) )
    & ~ memberP(sK54,sK58)
    & memberP(sK53,sK58)
    & ssItem(sK58)
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f223,f349,f348,f347,f346,f345,f344]) ).

fof(f359,plain,
    ! [X2,X3,X0,X1] :
      ( memberP(X0,X1)
      | app(X2,cons(X1,X3)) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f241]) ).

fof(f443,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f450,plain,
    ! [X0,X1] :
      ( nil != cons(X1,X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f470,plain,
    ! [X2,X0,X1] :
      ( memberP(X2,X0)
      | X0 = X1
      | ~ memberP(cons(X1,X2),X0)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f326]) ).

fof(f473,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f554,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f350]) ).

fof(f555,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f350]) ).

fof(f556,plain,
    ssItem(sK58),
    inference(cnf_transformation,[],[f350]) ).

fof(f557,plain,
    memberP(sK53,sK58),
    inference(cnf_transformation,[],[f350]) ).

fof(f558,plain,
    ~ memberP(sK54,sK58),
    inference(cnf_transformation,[],[f350]) ).

fof(f559,plain,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f560,plain,
    ( nil = sK56
    | sK55 = cons(sK57,nil) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f562,plain,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f563,plain,
    ( nil = sK55
    | sK55 = cons(sK57,nil) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f564,plain,
    ( nil = sK55
    | memberP(sK56,sK57) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f565,plain,
    ~ memberP(sK56,sK58),
    inference(definition_unfolding,[],[f558,f554]) ).

fof(f566,plain,
    memberP(sK55,sK58),
    inference(definition_unfolding,[],[f557,f555]) ).

fof(f570,plain,
    ! [X2,X3,X1] :
      ( memberP(app(X2,cons(X1,X3)),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssItem(X1)
      | ~ ssList(app(X2,cons(X1,X3))) ),
    inference(equality_resolution,[],[f359]) ).

cnf(c_54,plain,
    ( ~ ssList(app(X0,cons(X1,X2)))
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(app(X0,cons(X1,X2)),X1) ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f443]) ).

cnf(c_148,plain,
    ( cons(X0,X1) != nil
    | ~ ssItem(X0)
    | ~ ssList(X1) ),
    inference(cnf_transformation,[],[f450]) ).

cnf(c_170,plain,
    ( ~ memberP(cons(X0,X1),X2)
    | ~ ssItem(X0)
    | ~ ssItem(X2)
    | ~ ssList(X1)
    | X0 = X2
    | memberP(X1,X2) ),
    inference(cnf_transformation,[],[f470]) ).

cnf(c_171,plain,
    ( ~ memberP(nil,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f473]) ).

cnf(c_246,negated_conjecture,
    ( nil = sK55
    | memberP(sK56,sK57) ),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_247,negated_conjecture,
    ( cons(sK57,nil) = sK55
    | nil = sK55 ),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_248,negated_conjecture,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_250,negated_conjecture,
    ( cons(sK57,nil) = sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_251,negated_conjecture,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_252,negated_conjecture,
    ~ memberP(sK56,sK58),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_253,negated_conjecture,
    memberP(sK55,sK58),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_254,negated_conjecture,
    ssItem(sK58),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_11782,plain,
    ( nil != sK55
    | ~ ssItem(sK57)
    | ~ ssList(nil)
    | nil = sK56 ),
    inference(superposition,[status(thm)],[c_250,c_148]) ).

cnf(c_11851,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | ~ ssItem(sK57)
    | ~ ssList(nil)
    | X0 = sK57
    | nil = sK55
    | memberP(nil,X0) ),
    inference(superposition,[status(thm)],[c_247,c_170]) ).

cnf(c_11865,plain,
    ( ~ ssList(app(X0,cons(sK57,nil)))
    | ~ ssList(X0)
    | ~ ssItem(sK57)
    | ~ ssList(nil)
    | nil = sK55
    | memberP(app(X0,sK55),sK57) ),
    inference(superposition,[status(thm)],[c_247,c_54]) ).

cnf(c_11866,plain,
    ( ~ ssList(app(X0,cons(sK57,nil)))
    | ~ ssList(X0)
    | ~ ssItem(sK57)
    | ~ ssList(nil)
    | nil = sK56
    | memberP(app(X0,sK55),sK57) ),
    inference(superposition,[status(thm)],[c_250,c_54]) ).

cnf(c_11919,plain,
    ( nil != sK55
    | nil = sK56 ),
    inference(global_subsumption_just,[status(thm)],[c_11782,c_141,c_251,c_11782]) ).

cnf(c_11939,plain,
    ( nil = sK55
    | X0 = sK57
    | ~ ssItem(X0)
    | ~ memberP(sK55,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_11851,c_141,c_248,c_171,c_11851]) ).

cnf(c_11940,plain,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | X0 = sK57
    | nil = sK55 ),
    inference(renaming,[status(thm)],[c_11939]) ).

cnf(c_11950,plain,
    ( ~ ssItem(sK58)
    | nil = sK55
    | sK57 = sK58 ),
    inference(superposition,[status(thm)],[c_253,c_11940]) ).

cnf(c_11953,plain,
    ( ~ ssList(app(X0,cons(sK57,nil)))
    | ~ ssList(X0)
    | nil = sK56
    | memberP(app(X0,sK55),sK57) ),
    inference(global_subsumption_just,[status(thm)],[c_11866,c_141,c_251,c_11866]) ).

cnf(c_11965,plain,
    ( ~ ssList(app(X0,sK55))
    | ~ ssList(X0)
    | nil = sK56
    | memberP(app(X0,sK55),sK57) ),
    inference(superposition,[status(thm)],[c_250,c_11953]) ).

cnf(c_11968,plain,
    ( ~ ssList(app(X0,cons(sK57,nil)))
    | ~ ssList(X0)
    | nil = sK55
    | memberP(app(X0,sK55),sK57) ),
    inference(global_subsumption_just,[status(thm)],[c_11865,c_141,c_248,c_11865]) ).

cnf(c_11979,plain,
    ( ~ ssList(app(X0,sK55))
    | ~ ssList(X0)
    | nil = sK55
    | memberP(app(X0,sK55),sK57) ),
    inference(superposition,[status(thm)],[c_247,c_11968]) ).

cnf(c_12107,plain,
    ( nil = sK55
    | sK57 = sK58 ),
    inference(global_subsumption_just,[status(thm)],[c_11950,c_254,c_11950]) ).

cnf(c_12113,plain,
    ( ~ memberP(sK56,sK57)
    | nil = sK55 ),
    inference(superposition,[status(thm)],[c_12107,c_252]) ).

cnf(c_12186,plain,
    nil = sK56,
    inference(global_subsumption_just,[status(thm)],[c_11965,c_246,c_11919,c_12113]) ).

cnf(c_12189,plain,
    ~ memberP(nil,sK58),
    inference(superposition,[status(thm)],[c_12186,c_252]) ).

cnf(c_12193,plain,
    nil = sK55,
    inference(global_subsumption_just,[status(thm)],[c_11979,c_246,c_12113]) ).

cnf(c_12198,plain,
    memberP(nil,sK58),
    inference(superposition,[status(thm)],[c_12193,c_253]) ).

cnf(c_12200,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_12198,c_12189]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWC407+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.15/0.36  % Computer : n010.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May  2 23:11:19 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.22/0.51  Running first-order theorem proving
% 0.22/0.51  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.25/1.18  % SZS status Started for theBenchmark.p
% 4.25/1.18  % SZS status Theorem for theBenchmark.p
% 4.25/1.18  
% 4.25/1.18  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.25/1.18  
% 4.25/1.18  ------  iProver source info
% 4.25/1.18  
% 4.25/1.18  git: date: 2024-05-02 19:28:25 +0000
% 4.25/1.18  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.25/1.18  git: non_committed_changes: false
% 4.25/1.18  
% 4.25/1.18  ------ Parsing...
% 4.25/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.25/1.18  
% 4.25/1.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 4.25/1.18  
% 4.25/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.25/1.18  
% 4.25/1.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.25/1.18  ------ Proving...
% 4.25/1.18  ------ Problem Properties 
% 4.25/1.18  
% 4.25/1.18  
% 4.25/1.18  clauses                                 191
% 4.25/1.18  conjectures                             11
% 4.25/1.18  EPR                                     58
% 4.25/1.18  Horn                                    117
% 4.25/1.18  unary                                   21
% 4.25/1.18  binary                                  46
% 4.25/1.18  lits                                    635
% 4.25/1.18  lits eq                                 86
% 4.25/1.18  fd_pure                                 0
% 4.25/1.18  fd_pseudo                               0
% 4.25/1.18  fd_cond                                 21
% 4.25/1.18  fd_pseudo_cond                          14
% 4.25/1.18  AC symbols                              0
% 4.25/1.18  
% 4.25/1.18  ------ Input Options Time Limit: Unbounded
% 4.25/1.18  
% 4.25/1.18  
% 4.25/1.18  ------ 
% 4.25/1.18  Current options:
% 4.25/1.18  ------ 
% 4.25/1.18  
% 4.25/1.18  
% 4.25/1.18  
% 4.25/1.18  
% 4.25/1.18  ------ Proving...
% 4.25/1.18  
% 4.25/1.18  
% 4.25/1.18  % SZS status Theorem for theBenchmark.p
% 4.25/1.18  
% 4.25/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.25/1.18  
% 4.25/1.18  
%------------------------------------------------------------------------------