TSTP Solution File: SWC015+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC015+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n014.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 : Thu Aug 31 20:55:39 EDT 2023

% Result   : Theorem 0.23s 0.46s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   33
% Syntax   : Number of formulae    :  195 (  11 unt;   0 def)
%            Number of atoms       :  867 ( 236 equ)
%            Maximal formula atoms :   38 (   4 avg)
%            Number of connectives : 1149 ( 477   ~; 487   |; 125   &)
%                                         (  18 <=>;  42  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   20 (  18 usr;  15 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-2 aty)
%            Number of variables   :  200 (; 159   !;  41   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2639,plain,
    $false,
    inference(avatar_sat_refutation,[],[f585,f602,f610,f615,f647,f660,f672,f711,f1133,f1349,f1460,f2237,f2241,f2342,f2638]) ).

fof(f2638,plain,
    ( ~ spl51_7
    | ~ spl51_11 ),
    inference(avatar_contradiction_clause,[],[f2637]) ).

fof(f2637,plain,
    ( $false
    | ~ spl51_7
    | ~ spl51_11 ),
    inference(subsumption_resolution,[],[f2635,f357]) ).

fof(f357,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax17) ).

fof(f2635,plain,
    ( ~ ssList(nil)
    | ~ spl51_7
    | ~ spl51_11 ),
    inference(resolution,[],[f2431,f575]) ).

fof(f575,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f564]) ).

fof(f564,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f509]) ).

fof(f509,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f318]) ).

fof(f318,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f199]) ).

fof(f199,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( neq(X0,X1)
          <=> X0 != X1 )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( neq(X0,X1)
          <=> X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax15) ).

fof(f2431,plain,
    ( neq(nil,nil)
    | ~ spl51_7
    | ~ spl51_11 ),
    inference(superposition,[],[f606,f720]) ).

fof(f720,plain,
    ( nil = sK1
    | ~ spl51_11 ),
    inference(avatar_component_clause,[],[f719]) ).

fof(f719,plain,
    ( spl51_11
  <=> nil = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_11])]) ).

fof(f606,plain,
    ( neq(sK1,nil)
    | ~ spl51_7 ),
    inference(avatar_component_clause,[],[f604]) ).

fof(f604,plain,
    ( spl51_7
  <=> neq(sK1,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_7])]) ).

fof(f2342,plain,
    ( spl51_11
    | ~ spl51_1
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_9
    | ~ spl51_63
    | ~ spl51_64 ),
    inference(avatar_split_clause,[],[f2341,f2232,f2228,f708,f595,f591,f579,f719]) ).

fof(f579,plain,
    ( spl51_1
  <=> ! [X4,X5] :
        ( app(cons(X4,nil),X5) != sK1
        | ~ ssItem(X4)
        | ~ ssList(X5)
        | cons(X4,nil) != sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_1])]) ).

fof(f591,plain,
    ( spl51_4
  <=> sK3 = app(sK2,tl(sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_4])]) ).

fof(f595,plain,
    ( spl51_5
  <=> ssList(tl(sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_5])]) ).

fof(f708,plain,
    ( spl51_9
  <=> hd(sK0) = hd(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_9])]) ).

fof(f2228,plain,
    ( spl51_63
  <=> sK0 = cons(hd(sK0),nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_63])]) ).

fof(f2232,plain,
    ( spl51_64
  <=> ssList(cons(hd(sK0),nil)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_64])]) ).

fof(f2341,plain,
    ( nil = sK1
    | ~ spl51_1
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_9
    | ~ spl51_63
    | ~ spl51_64 ),
    inference(subsumption_resolution,[],[f2340,f611]) ).

fof(f611,plain,
    ssList(sK1),
    inference(forward_demodulation,[],[f340,f341]) ).

fof(f341,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f228]) ).

fof(f228,plain,
    ( ( ( ~ neq(sK3,nil)
        & neq(sK1,nil) )
      | ( ! [X4] :
            ( ! [X5] :
                ( app(cons(X4,nil),X5) != sK1
                | cons(X4,nil) != sK0
                | ~ ssList(X5) )
            | ~ ssItem(X4) )
        & ! [X6] :
            ( ! [X7] :
                ( ~ neq(nil,sK3)
                | app(sK2,X7) != X6
                | tl(sK3) != X7
                | ~ ssList(X7) )
            | sK3 = X6
            | ~ ssList(X6) )
        & neq(sK1,nil) ) )
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f100,f227,f226,f225,f224]) ).

fof(f224,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | ( ! [X4] :
                            ( ! [X5] :
                                ( app(cons(X4,nil),X5) != X1
                                | cons(X4,nil) != X0
                                | ~ ssList(X5) )
                            | ~ ssItem(X4) )
                        & ! [X6] :
                            ( ! [X7] :
                                ( ~ neq(nil,X3)
                                | app(X2,X7) != X6
                                | tl(X3) != X7
                                | ~ ssList(X7) )
                            | X3 = X6
                            | ~ ssList(X6) )
                        & neq(X1,nil) ) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ! [X4] :
                          ( ! [X5] :
                              ( app(cons(X4,nil),X5) != X1
                              | cons(X4,nil) != sK0
                              | ~ ssList(X5) )
                          | ~ ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( ~ neq(nil,X3)
                              | app(X2,X7) != X6
                              | tl(X3) != X7
                              | ~ ssList(X7) )
                          | X3 = X6
                          | ~ ssList(X6) )
                      & neq(X1,nil) ) )
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f225,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | ( ! [X4] :
                        ( ! [X5] :
                            ( app(cons(X4,nil),X5) != X1
                            | cons(X4,nil) != sK0
                            | ~ ssList(X5) )
                        | ~ ssItem(X4) )
                    & ! [X6] :
                        ( ! [X7] :
                            ( ~ neq(nil,X3)
                            | app(X2,X7) != X6
                            | tl(X3) != X7
                            | ~ ssList(X7) )
                        | X3 = X6
                        | ~ ssList(X6) )
                    & neq(X1,nil) ) )
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK1,nil) )
                | ( ! [X4] :
                      ( ! [X5] :
                          ( app(cons(X4,nil),X5) != sK1
                          | cons(X4,nil) != sK0
                          | ~ ssList(X5) )
                      | ~ ssItem(X4) )
                  & ! [X6] :
                      ( ! [X7] :
                          ( ~ neq(nil,X3)
                          | app(X2,X7) != X6
                          | tl(X3) != X7
                          | ~ ssList(X7) )
                      | X3 = X6
                      | ~ ssList(X6) )
                  & neq(sK1,nil) ) )
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f226,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK1,nil) )
              | ( ! [X4] :
                    ( ! [X5] :
                        ( app(cons(X4,nil),X5) != sK1
                        | cons(X4,nil) != sK0
                        | ~ ssList(X5) )
                    | ~ ssItem(X4) )
                & ! [X6] :
                    ( ! [X7] :
                        ( ~ neq(nil,X3)
                        | app(X2,X7) != X6
                        | tl(X3) != X7
                        | ~ ssList(X7) )
                    | X3 = X6
                    | ~ ssList(X6) )
                & neq(sK1,nil) ) )
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK1,nil) )
            | ( ! [X4] :
                  ( ! [X5] :
                      ( app(cons(X4,nil),X5) != sK1
                      | cons(X4,nil) != sK0
                      | ~ ssList(X5) )
                  | ~ ssItem(X4) )
              & ! [X6] :
                  ( ! [X7] :
                      ( ~ neq(nil,X3)
                      | app(sK2,X7) != X6
                      | tl(X3) != X7
                      | ~ ssList(X7) )
                  | X3 = X6
                  | ~ ssList(X6) )
              & neq(sK1,nil) ) )
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f227,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK1,nil) )
          | ( ! [X4] :
                ( ! [X5] :
                    ( app(cons(X4,nil),X5) != sK1
                    | cons(X4,nil) != sK0
                    | ~ ssList(X5) )
                | ~ ssItem(X4) )
            & ! [X6] :
                ( ! [X7] :
                    ( ~ neq(nil,X3)
                    | app(sK2,X7) != X6
                    | tl(X3) != X7
                    | ~ ssList(X7) )
                | X3 = X6
                | ~ ssList(X6) )
            & neq(sK1,nil) ) )
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK3,nil)
          & neq(sK1,nil) )
        | ( ! [X4] :
              ( ! [X5] :
                  ( app(cons(X4,nil),X5) != sK1
                  | cons(X4,nil) != sK0
                  | ~ ssList(X5) )
              | ~ ssItem(X4) )
          & ! [X6] :
              ( ! [X7] :
                  ( ~ neq(nil,sK3)
                  | app(sK2,X7) != X6
                  | tl(sK3) != X7
                  | ~ ssList(X7) )
              | sK3 = X6
              | ~ ssList(X6) )
          & neq(sK1,nil) ) )
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ! [X4] :
                          ( ! [X5] :
                              ( app(cons(X4,nil),X5) != X1
                              | cons(X4,nil) != X0
                              | ~ ssList(X5) )
                          | ~ ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( ~ neq(nil,X3)
                              | app(X2,X7) != X6
                              | tl(X3) != X7
                              | ~ ssList(X7) )
                          | X3 = X6
                          | ~ ssList(X6) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ! [X4] :
                          ( ! [X5] :
                              ( app(cons(X4,nil),X5) != X1
                              | cons(X4,nil) != X0
                              | ~ ssList(X5) )
                          | ~ ssItem(X4) )
                      & ! [X6] :
                          ( ! [X7] :
                              ( ~ neq(nil,X3)
                              | app(X2,X7) != X6
                              | tl(X3) != X7
                              | ~ ssList(X7) )
                          | X3 = X6
                          | ~ ssList(X6) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ? [X4] :
                              ( ? [X5] :
                                  ( app(cons(X4,nil),X5) = X1
                                  & cons(X4,nil) = X0
                                  & ssList(X5) )
                              & ssItem(X4) )
                          | ? [X6] :
                              ( ? [X7] :
                                  ( neq(nil,X3)
                                  & app(X2,X7) = X6
                                  & tl(X3) = X7
                                  & ssList(X7) )
                              & X3 != X6
                              & ssList(X6) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ? [X6] :
                              ( ? [X7] :
                                  ( app(cons(X6,nil),X7) = X1
                                  & cons(X6,nil) = X0
                                  & ssList(X7) )
                              & ssItem(X6) )
                          | ? [X4] :
                              ( ? [X5] :
                                  ( neq(nil,X3)
                                  & app(X2,X5) = X4
                                  & tl(X3) = X5
                                  & ssList(X5) )
                              & X3 != X4
                              & ssList(X4) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( neq(X3,nil)
                        | ~ neq(X1,nil) )
                      & ( ? [X6] :
                            ( ? [X7] :
                                ( app(cons(X6,nil),X7) = X1
                                & cons(X6,nil) = X0
                                & ssList(X7) )
                            & ssItem(X6) )
                        | ? [X4] :
                            ( ? [X5] :
                                ( neq(nil,X3)
                                & app(X2,X5) = X4
                                & tl(X3) = X5
                                & ssList(X5) )
                            & X3 != X4
                            & ssList(X4) )
                        | ~ neq(X1,nil) ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',co1) ).

fof(f340,plain,
    ssList(sK3),
    inference(cnf_transformation,[],[f228]) ).

fof(f2340,plain,
    ( nil = sK1
    | ~ ssList(sK1)
    | ~ spl51_1
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_9
    | ~ spl51_63
    | ~ spl51_64 ),
    inference(subsumption_resolution,[],[f1611,f2334]) ).

fof(f2334,plain,
    ( ~ ssItem(hd(sK0))
    | ~ spl51_1
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_63
    | ~ spl51_64 ),
    inference(subsumption_resolution,[],[f2333,f1237]) ).

fof(f1237,plain,
    ( ~ singletonP(sK0)
    | ~ spl51_1
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(subsumption_resolution,[],[f1236,f612]) ).

fof(f612,plain,
    ssList(sK0),
    inference(forward_demodulation,[],[f339,f342]) ).

fof(f342,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f228]) ).

fof(f339,plain,
    ssList(sK2),
    inference(cnf_transformation,[],[f228]) ).

fof(f1236,plain,
    ( ~ singletonP(sK0)
    | ~ ssList(sK0)
    | ~ spl51_1
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(subsumption_resolution,[],[f1208,f662]) ).

fof(f662,plain,
    ( ssList(tl(sK1))
    | ~ spl51_5 ),
    inference(forward_demodulation,[],[f596,f341]) ).

fof(f596,plain,
    ( ssList(tl(sK3))
    | ~ spl51_5 ),
    inference(avatar_component_clause,[],[f595]) ).

fof(f1208,plain,
    ( ~ ssList(tl(sK1))
    | ~ singletonP(sK0)
    | ~ ssList(sK0)
    | ~ spl51_1
    | ~ spl51_4 ),
    inference(trivial_inequality_removal,[],[f1199]) ).

fof(f1199,plain,
    ( sK1 != sK1
    | ~ ssList(tl(sK1))
    | sK0 != sK0
    | ~ singletonP(sK0)
    | ~ ssList(sK0)
    | ~ spl51_1
    | ~ spl51_4 ),
    inference(superposition,[],[f634,f675]) ).

fof(f675,plain,
    ( sK1 = app(sK0,tl(sK1))
    | ~ spl51_4 ),
    inference(forward_demodulation,[],[f674,f342]) ).

fof(f674,plain,
    ( sK1 = app(sK2,tl(sK1))
    | ~ spl51_4 ),
    inference(forward_demodulation,[],[f593,f341]) ).

fof(f593,plain,
    ( sK3 = app(sK2,tl(sK3))
    | ~ spl51_4 ),
    inference(avatar_component_clause,[],[f591]) ).

fof(f634,plain,
    ( ! [X0,X1] :
        ( app(X0,X1) != sK1
        | ~ ssList(X1)
        | sK0 != X0
        | ~ singletonP(X0)
        | ~ ssList(X0) )
    | ~ spl51_1 ),
    inference(subsumption_resolution,[],[f627,f425]) ).

fof(f425,plain,
    ! [X0] :
      ( ssItem(sK8(X0))
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK8(X0),nil) = X0
            & ssItem(sK8(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f252,f253]) ).

fof(f253,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK8(X0),nil) = X0
        & ssItem(sK8(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f251]) ).

fof(f251,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f161]) ).

fof(f161,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax4) ).

fof(f627,plain,
    ( ! [X0,X1] :
        ( app(X0,X1) != sK1
        | ~ ssItem(sK8(X0))
        | ~ ssList(X1)
        | sK0 != X0
        | ~ singletonP(X0)
        | ~ ssList(X0) )
    | ~ spl51_1 ),
    inference(superposition,[],[f580,f426]) ).

fof(f426,plain,
    ! [X0] :
      ( cons(sK8(X0),nil) = X0
      | ~ singletonP(X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f580,plain,
    ( ! [X4,X5] :
        ( app(cons(X4,nil),X5) != sK1
        | ~ ssItem(X4)
        | ~ ssList(X5)
        | cons(X4,nil) != sK0 )
    | ~ spl51_1 ),
    inference(avatar_component_clause,[],[f579]) ).

fof(f2333,plain,
    ( singletonP(sK0)
    | ~ ssItem(hd(sK0))
    | ~ spl51_63
    | ~ spl51_64 ),
    inference(forward_demodulation,[],[f2242,f2230]) ).

fof(f2230,plain,
    ( sK0 = cons(hd(sK0),nil)
    | ~ spl51_63 ),
    inference(avatar_component_clause,[],[f2228]) ).

fof(f2242,plain,
    ( ~ ssItem(hd(sK0))
    | singletonP(cons(hd(sK0),nil))
    | ~ spl51_64 ),
    inference(resolution,[],[f2233,f551]) ).

fof(f551,plain,
    ! [X1] :
      ( ~ ssList(cons(X1,nil))
      | ~ ssItem(X1)
      | singletonP(cons(X1,nil)) ),
    inference(equality_resolution,[],[f427]) ).

fof(f427,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f254]) ).

fof(f2233,plain,
    ( ssList(cons(hd(sK0),nil))
    | ~ spl51_64 ),
    inference(avatar_component_clause,[],[f2232]) ).

fof(f1611,plain,
    ( ssItem(hd(sK0))
    | nil = sK1
    | ~ ssList(sK1)
    | ~ spl51_9 ),
    inference(superposition,[],[f418,f710]) ).

fof(f710,plain,
    ( hd(sK0) = hd(sK1)
    | ~ spl51_9 ),
    inference(avatar_component_clause,[],[f708]) ).

fof(f418,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f152,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ssItem(hd(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssItem(hd(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax22) ).

fof(f2241,plain,
    ( ~ spl51_9
    | ~ spl51_24
    | spl51_64 ),
    inference(avatar_contradiction_clause,[],[f2240]) ).

fof(f2240,plain,
    ( $false
    | ~ spl51_9
    | ~ spl51_24
    | spl51_64 ),
    inference(subsumption_resolution,[],[f2239,f357]) ).

fof(f2239,plain,
    ( ~ ssList(nil)
    | ~ spl51_9
    | ~ spl51_24
    | spl51_64 ),
    inference(subsumption_resolution,[],[f2238,f1609]) ).

fof(f1609,plain,
    ( ssItem(hd(sK0))
    | ~ spl51_9
    | ~ spl51_24 ),
    inference(superposition,[],[f1327,f710]) ).

fof(f1327,plain,
    ( ssItem(hd(sK1))
    | ~ spl51_24 ),
    inference(avatar_component_clause,[],[f1326]) ).

fof(f1326,plain,
    ( spl51_24
  <=> ssItem(hd(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_24])]) ).

fof(f2238,plain,
    ( ~ ssItem(hd(sK0))
    | ~ ssList(nil)
    | spl51_64 ),
    inference(resolution,[],[f2234,f492]) ).

fof(f492,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax16) ).

fof(f2234,plain,
    ( ~ ssList(cons(hd(sK0),nil))
    | spl51_64 ),
    inference(avatar_component_clause,[],[f2232]) ).

fof(f2237,plain,
    ( ~ spl51_64
    | spl51_63
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_9
    | spl51_11
    | ~ spl51_24 ),
    inference(avatar_split_clause,[],[f2236,f1326,f719,f708,f595,f591,f2228,f2232]) ).

fof(f2236,plain,
    ( sK0 = cons(hd(sK0),nil)
    | ~ ssList(cons(hd(sK0),nil))
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_9
    | spl51_11
    | ~ spl51_24 ),
    inference(subsumption_resolution,[],[f2220,f1609]) ).

fof(f2220,plain,
    ( sK0 = cons(hd(sK0),nil)
    | ~ ssList(cons(hd(sK0),nil))
    | ~ ssItem(hd(sK0))
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_9
    | spl51_11 ),
    inference(trivial_inequality_removal,[],[f2219]) ).

fof(f2219,plain,
    ( sK1 != sK1
    | sK0 = cons(hd(sK0),nil)
    | ~ ssList(cons(hd(sK0),nil))
    | ~ ssItem(hd(sK0))
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_9
    | spl51_11 ),
    inference(superposition,[],[f920,f1615]) ).

fof(f1615,plain,
    ( sK1 = cons(hd(sK0),tl(sK1))
    | ~ spl51_9
    | spl51_11 ),
    inference(subsumption_resolution,[],[f1614,f611]) ).

fof(f1614,plain,
    ( sK1 = cons(hd(sK0),tl(sK1))
    | ~ ssList(sK1)
    | ~ spl51_9
    | spl51_11 ),
    inference(subsumption_resolution,[],[f1610,f721]) ).

fof(f721,plain,
    ( nil != sK1
    | spl51_11 ),
    inference(avatar_component_clause,[],[f719]) ).

fof(f1610,plain,
    ( sK1 = cons(hd(sK0),tl(sK1))
    | nil = sK1
    | ~ ssList(sK1)
    | ~ spl51_9 ),
    inference(superposition,[],[f420,f710]) ).

fof(f420,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f156]) ).

fof(f156,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f155]) ).

fof(f155,plain,
    ! [X0] :
      ( cons(hd(X0),tl(X0)) = X0
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f78]) ).

fof(f78,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => cons(hd(X0),tl(X0)) = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax78) ).

fof(f920,plain,
    ( ! [X0] :
        ( sK1 != cons(X0,tl(sK1))
        | cons(X0,nil) = sK0
        | ~ ssList(cons(X0,nil))
        | ~ ssItem(X0) )
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(subsumption_resolution,[],[f913,f662]) ).

fof(f913,plain,
    ( ! [X0] :
        ( sK1 != cons(X0,tl(sK1))
        | cons(X0,nil) = sK0
        | ~ ssList(cons(X0,nil))
        | ~ ssItem(X0)
        | ~ ssList(tl(sK1)) )
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(superposition,[],[f733,f497]) ).

fof(f497,plain,
    ! [X0,X1] :
      ( cons(X1,X0) = app(cons(X1,nil),X0)
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f184]) ).

fof(f184,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) = app(cons(X1,nil),X0)
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f81]) ).

fof(f81,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) = app(cons(X1,nil),X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax81) ).

fof(f733,plain,
    ( ! [X6] :
        ( sK1 != app(X6,tl(sK1))
        | sK0 = X6
        | ~ ssList(X6) )
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(subsumption_resolution,[],[f732,f662]) ).

fof(f732,plain,
    ( ! [X6] :
        ( sK1 != app(X6,tl(sK1))
        | sK0 = X6
        | ~ ssList(tl(sK1))
        | ~ ssList(X6) )
    | ~ spl51_4 ),
    inference(subsumption_resolution,[],[f687,f612]) ).

fof(f687,plain,
    ( ! [X6] :
        ( sK1 != app(X6,tl(sK1))
        | sK0 = X6
        | ~ ssList(sK0)
        | ~ ssList(tl(sK1))
        | ~ ssList(X6) )
    | ~ spl51_4 ),
    inference(superposition,[],[f530,f675]) ).

fof(f530,plain,
    ! [X2,X0,X1] :
      ( app(X2,X1) != app(X0,X1)
      | X0 = X2
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f213]) ).

fof(f213,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( X0 = X2
              | app(X2,X1) != app(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f212]) ).

fof(f212,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( X0 = X2
              | app(X2,X1) != app(X0,X1)
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f79]) ).

fof(f79,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ( app(X2,X1) = app(X0,X1)
               => X0 = X2 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax79) ).

fof(f1460,plain,
    ( spl51_11
    | spl51_24 ),
    inference(avatar_split_clause,[],[f1459,f1326,f719]) ).

fof(f1459,plain,
    ( nil = sK1
    | spl51_24 ),
    inference(subsumption_resolution,[],[f1455,f611]) ).

fof(f1455,plain,
    ( nil = sK1
    | ~ ssList(sK1)
    | spl51_24 ),
    inference(resolution,[],[f1328,f418]) ).

fof(f1328,plain,
    ( ~ ssItem(hd(sK1))
    | spl51_24 ),
    inference(avatar_component_clause,[],[f1326]) ).

fof(f1349,plain,
    ( ~ spl51_24
    | spl51_11
    | ~ spl51_15 ),
    inference(avatar_split_clause,[],[f1348,f772,f719,f1326]) ).

fof(f772,plain,
    ( spl51_15
  <=> sK1 = tl(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_15])]) ).

fof(f1348,plain,
    ( ~ ssItem(hd(sK1))
    | spl51_11
    | ~ spl51_15 ),
    inference(subsumption_resolution,[],[f1323,f611]) ).

fof(f1323,plain,
    ( ~ ssItem(hd(sK1))
    | ~ ssList(sK1)
    | spl51_11
    | ~ spl51_15 ),
    inference(trivial_inequality_removal,[],[f1299]) ).

fof(f1299,plain,
    ( sK1 != sK1
    | ~ ssItem(hd(sK1))
    | ~ ssList(sK1)
    | spl51_11
    | ~ spl51_15 ),
    inference(superposition,[],[f494,f1173]) ).

fof(f1173,plain,
    ( sK1 = cons(hd(sK1),sK1)
    | spl51_11
    | ~ spl51_15 ),
    inference(subsumption_resolution,[],[f1172,f611]) ).

fof(f1172,plain,
    ( sK1 = cons(hd(sK1),sK1)
    | ~ ssList(sK1)
    | spl51_11
    | ~ spl51_15 ),
    inference(subsumption_resolution,[],[f1160,f721]) ).

fof(f1160,plain,
    ( sK1 = cons(hd(sK1),sK1)
    | nil = sK1
    | ~ ssList(sK1)
    | ~ spl51_15 ),
    inference(superposition,[],[f420,f774]) ).

fof(f774,plain,
    ( sK1 = tl(sK1)
    | ~ spl51_15 ),
    inference(avatar_component_clause,[],[f772]) ).

fof(f494,plain,
    ! [X0,X1] :
      ( cons(X1,X0) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f181]) ).

fof(f181,plain,
    ! [X0] :
      ( ! [X1] :
          ( cons(X1,X0) != X0
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => cons(X1,X0) != X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax18) ).

fof(f1133,plain,
    ( spl51_15
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_8 ),
    inference(avatar_split_clause,[],[f1132,f704,f595,f591,f772]) ).

fof(f704,plain,
    ( spl51_8
  <=> nil = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_8])]) ).

fof(f1132,plain,
    ( sK1 = tl(sK1)
    | ~ spl51_4
    | ~ spl51_5
    | ~ spl51_8 ),
    inference(subsumption_resolution,[],[f1096,f662]) ).

fof(f1096,plain,
    ( sK1 = tl(sK1)
    | ~ ssList(tl(sK1))
    | ~ spl51_4
    | ~ spl51_8 ),
    inference(superposition,[],[f1020,f414]) ).

fof(f414,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax28) ).

fof(f1020,plain,
    ( sK1 = app(nil,tl(sK1))
    | ~ spl51_4
    | ~ spl51_8 ),
    inference(superposition,[],[f675,f706]) ).

fof(f706,plain,
    ( nil = sK0
    | ~ spl51_8 ),
    inference(avatar_component_clause,[],[f704]) ).

fof(f711,plain,
    ( spl51_8
    | spl51_9
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(avatar_split_clause,[],[f702,f595,f591,f708,f704]) ).

fof(f702,plain,
    ( hd(sK0) = hd(sK1)
    | nil = sK0
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(subsumption_resolution,[],[f701,f612]) ).

fof(f701,plain,
    ( hd(sK0) = hd(sK1)
    | nil = sK0
    | ~ ssList(sK0)
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(subsumption_resolution,[],[f681,f662]) ).

fof(f681,plain,
    ( hd(sK0) = hd(sK1)
    | nil = sK0
    | ~ ssList(tl(sK1))
    | ~ ssList(sK0)
    | ~ spl51_4 ),
    inference(superposition,[],[f503,f675]) ).

fof(f503,plain,
    ! [X0,X1] :
      ( hd(X0) = hd(app(X0,X1))
      | nil = X0
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f188]) ).

fof(f188,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f187]) ).

fof(f187,plain,
    ! [X0] :
      ( ! [X1] :
          ( hd(X0) = hd(app(X0,X1))
          | nil = X0
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f85]) ).

fof(f85,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil != X0
           => hd(X0) = hd(app(X0,X1)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax85) ).

fof(f672,plain,
    ( spl51_6
    | ~ spl51_7 ),
    inference(avatar_contradiction_clause,[],[f671]) ).

fof(f671,plain,
    ( $false
    | spl51_6
    | ~ spl51_7 ),
    inference(subsumption_resolution,[],[f669,f668]) ).

fof(f668,plain,
    ( ~ neq(nil,nil)
    | spl51_6 ),
    inference(superposition,[],[f661,f666]) ).

fof(f666,plain,
    ( nil = sK1
    | spl51_6 ),
    inference(subsumption_resolution,[],[f665,f357]) ).

fof(f665,plain,
    ( nil = sK1
    | ~ ssList(nil)
    | spl51_6 ),
    inference(subsumption_resolution,[],[f663,f611]) ).

fof(f663,plain,
    ( nil = sK1
    | ~ ssList(sK1)
    | ~ ssList(nil)
    | spl51_6 ),
    inference(resolution,[],[f661,f510]) ).

fof(f510,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f318]) ).

fof(f661,plain,
    ( ~ neq(nil,sK1)
    | spl51_6 ),
    inference(forward_demodulation,[],[f601,f341]) ).

fof(f601,plain,
    ( ~ neq(nil,sK3)
    | spl51_6 ),
    inference(avatar_component_clause,[],[f599]) ).

fof(f599,plain,
    ( spl51_6
  <=> neq(nil,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_6])]) ).

fof(f669,plain,
    ( neq(nil,nil)
    | spl51_6
    | ~ spl51_7 ),
    inference(superposition,[],[f606,f666]) ).

fof(f660,plain,
    ( spl51_5
    | ~ spl51_7 ),
    inference(avatar_contradiction_clause,[],[f659]) ).

fof(f659,plain,
    ( $false
    | spl51_5
    | ~ spl51_7 ),
    inference(subsumption_resolution,[],[f657,f357]) ).

fof(f657,plain,
    ( ~ ssList(nil)
    | spl51_5
    | ~ spl51_7 ),
    inference(resolution,[],[f654,f575]) ).

fof(f654,plain,
    ( neq(nil,nil)
    | spl51_5
    | ~ spl51_7 ),
    inference(superposition,[],[f606,f652]) ).

fof(f652,plain,
    ( nil = sK1
    | spl51_5 ),
    inference(subsumption_resolution,[],[f651,f611]) ).

fof(f651,plain,
    ( nil = sK1
    | ~ ssList(sK1)
    | spl51_5 ),
    inference(resolution,[],[f648,f419]) ).

fof(f419,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f154]) ).

fof(f154,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(flattening,[],[f153]) ).

fof(f153,plain,
    ! [X0] :
      ( ssList(tl(X0))
      | nil = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( nil != X0
       => ssList(tl(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax24) ).

fof(f648,plain,
    ( ~ ssList(tl(sK1))
    | spl51_5 ),
    inference(forward_demodulation,[],[f597,f341]) ).

fof(f597,plain,
    ( ~ ssList(tl(sK3))
    | spl51_5 ),
    inference(avatar_component_clause,[],[f595]) ).

fof(f647,plain,
    ( spl51_3
    | ~ spl51_7 ),
    inference(avatar_contradiction_clause,[],[f646]) ).

fof(f646,plain,
    ( $false
    | spl51_3
    | ~ spl51_7 ),
    inference(subsumption_resolution,[],[f644,f357]) ).

fof(f644,plain,
    ( ~ ssList(nil)
    | spl51_3
    | ~ spl51_7 ),
    inference(resolution,[],[f625,f575]) ).

fof(f625,plain,
    ( neq(nil,nil)
    | spl51_3
    | ~ spl51_7 ),
    inference(superposition,[],[f606,f622]) ).

fof(f622,plain,
    ( nil = sK1
    | spl51_3 ),
    inference(subsumption_resolution,[],[f621,f611]) ).

fof(f621,plain,
    ( nil = sK1
    | ~ ssList(sK1)
    | spl51_3 ),
    inference(resolution,[],[f620,f419]) ).

fof(f620,plain,
    ( ~ ssList(tl(sK1))
    | spl51_3 ),
    inference(subsumption_resolution,[],[f619,f612]) ).

fof(f619,plain,
    ( ~ ssList(tl(sK1))
    | ~ ssList(sK0)
    | spl51_3 ),
    inference(resolution,[],[f617,f502]) ).

fof(f502,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f186]) ).

fof(f186,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(app(X0,X1))
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f26,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ssList(app(X0,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964',ax26) ).

fof(f617,plain,
    ( ~ ssList(app(sK0,tl(sK1)))
    | spl51_3 ),
    inference(forward_demodulation,[],[f616,f342]) ).

fof(f616,plain,
    ( ~ ssList(app(sK2,tl(sK1)))
    | spl51_3 ),
    inference(forward_demodulation,[],[f589,f341]) ).

fof(f589,plain,
    ( ~ ssList(app(sK2,tl(sK3)))
    | spl51_3 ),
    inference(avatar_component_clause,[],[f587]) ).

fof(f587,plain,
    ( spl51_3
  <=> ssList(app(sK2,tl(sK3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_3])]) ).

fof(f615,plain,
    ( spl51_2
    | ~ spl51_7 ),
    inference(avatar_contradiction_clause,[],[f614]) ).

fof(f614,plain,
    ( $false
    | spl51_2
    | ~ spl51_7 ),
    inference(subsumption_resolution,[],[f613,f606]) ).

fof(f613,plain,
    ( ~ neq(sK1,nil)
    | spl51_2 ),
    inference(forward_demodulation,[],[f584,f341]) ).

fof(f584,plain,
    ( ~ neq(sK3,nil)
    | spl51_2 ),
    inference(avatar_component_clause,[],[f582]) ).

fof(f582,plain,
    ( spl51_2
  <=> neq(sK3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl51_2])]) ).

fof(f610,plain,
    spl51_7,
    inference(avatar_split_clause,[],[f577,f604]) ).

fof(f577,plain,
    neq(sK1,nil),
    inference(duplicate_literal_removal,[],[f343]) ).

fof(f343,plain,
    ( neq(sK1,nil)
    | neq(sK1,nil) ),
    inference(cnf_transformation,[],[f228]) ).

fof(f602,plain,
    ( ~ spl51_3
    | spl51_4
    | ~ spl51_5
    | ~ spl51_6
    | ~ spl51_2 ),
    inference(avatar_split_clause,[],[f540,f582,f599,f595,f591,f587]) ).

fof(f540,plain,
    ( ~ neq(sK3,nil)
    | ~ neq(nil,sK3)
    | ~ ssList(tl(sK3))
    | sK3 = app(sK2,tl(sK3))
    | ~ ssList(app(sK2,tl(sK3))) ),
    inference(equality_resolution,[],[f539]) ).

fof(f539,plain,
    ! [X7] :
      ( ~ neq(sK3,nil)
      | ~ neq(nil,sK3)
      | tl(sK3) != X7
      | ~ ssList(X7)
      | app(sK2,X7) = sK3
      | ~ ssList(app(sK2,X7)) ),
    inference(equality_resolution,[],[f347]) ).

fof(f347,plain,
    ! [X6,X7] :
      ( ~ neq(sK3,nil)
      | ~ neq(nil,sK3)
      | app(sK2,X7) != X6
      | tl(sK3) != X7
      | ~ ssList(X7)
      | sK3 = X6
      | ~ ssList(X6) ),
    inference(cnf_transformation,[],[f228]) ).

fof(f585,plain,
    ( spl51_1
    | ~ spl51_2 ),
    inference(avatar_split_clause,[],[f348,f582,f579]) ).

fof(f348,plain,
    ! [X4,X5] :
      ( ~ neq(sK3,nil)
      | app(cons(X4,nil),X5) != sK1
      | cons(X4,nil) != sK0
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(cnf_transformation,[],[f228]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWC015+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36  % Computer : n014.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Mon Aug 28 14:41:46 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.23/0.37  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.difphOJxKZ/Vampire---4.8_30964
% 0.23/0.37  % (31071)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.42  % (31079)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.23/0.43  % (31074)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.23/0.43  % (31076)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.23/0.43  % (31078)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.23/0.43  % (31075)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.23/0.43  % (31077)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.23/0.43  % (31073)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.23/0.46  % (31079)First to succeed.
% 0.23/0.46  % (31079)Refutation found. Thanks to Tanya!
% 0.23/0.46  % SZS status Theorem for Vampire---4
% 0.23/0.46  % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.46  % (31079)------------------------------
% 0.23/0.46  % (31079)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.46  % (31079)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.46  % (31079)Termination reason: Refutation
% 0.23/0.46  
% 0.23/0.46  % (31079)Memory used [KB]: 6908
% 0.23/0.46  % (31079)Time elapsed: 0.033 s
% 0.23/0.46  % (31079)------------------------------
% 0.23/0.46  % (31079)------------------------------
% 0.23/0.46  % (31071)Success in time 0.09 s
% 0.23/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------