TSTP Solution File: SWC065+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC065+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n028.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 : Sun May  5 09:48:19 EDT 2024

% Result   : Theorem 0.62s 0.71s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  103 (  10 unt;   0 def)
%            Number of atoms       :  623 ( 200 equ)
%            Maximal formula atoms :   46 (   6 avg)
%            Number of connectives :  831 ( 311   ~; 285   |; 190   &)
%                                         (  12 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   7 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :  201 ( 142   !;  59   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1024,plain,
    $false,
    inference(avatar_sat_refutation,[],[f253,f258,f260,f317,f330,f951,f973,f1023]) ).

fof(f1023,plain,
    ( spl15_1
    | spl15_37 ),
    inference(avatar_contradiction_clause,[],[f1022]) ).

fof(f1022,plain,
    ( $false
    | spl15_1
    | spl15_37 ),
    inference(subsumption_resolution,[],[f1021,f165]) ).

fof(f165,plain,
    ssList(sK2),
    inference(cnf_transformation,[],[f139]) ).

fof(f139,plain,
    ( ( ( ! [X4] :
            ( ~ segmentP(sK0,X4)
            | ~ segmentP(sK1,X4)
            | ~ neq(X4,nil)
            | ~ ssList(X4) )
        & neq(sK1,nil) )
      | ( nil != sK0
        & nil = sK1 ) )
    & ( nil != sK2
      | nil = sK3 )
    & ! [X6] :
        ( ! [X7] :
            ( ! [X8] :
                ( app(X8,cons(X6,nil)) != sK2
                | ~ ssList(X8) )
            | app(cons(X6,nil),X7) != sK4
            | ~ ssList(X7) )
        | ~ ssItem(X6) )
    & equalelemsP(sK2)
    & sK3 = app(sK2,sK4)
    & ssList(sK4)
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f100,f138,f137,f136,f135,f134]) ).

fof(f134,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ! [X4] :
                            ( ~ segmentP(X0,X4)
                            | ~ segmentP(X1,X4)
                            | ~ neq(X4,nil)
                            | ~ ssList(X4) )
                        & neq(X1,nil) )
                      | ( nil != X0
                        & nil = X1 ) )
                    & ( nil != X2
                      | nil = X3 )
                    & ? [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ! [X8] :
                                    ( app(X8,cons(X6,nil)) != X2
                                    | ~ ssList(X8) )
                                | app(cons(X6,nil),X7) != X5
                                | ~ ssList(X7) )
                            | ~ ssItem(X6) )
                        & equalelemsP(X2)
                        & app(X2,X5) = X3
                        & ssList(X5) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ~ segmentP(sK0,X4)
                          | ~ segmentP(X1,X4)
                          | ~ neq(X4,nil)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != sK0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( app(X8,cons(X6,nil)) != X2
                                  | ~ ssList(X8) )
                              | app(cons(X6,nil),X7) != X5
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & equalelemsP(X2)
                      & app(X2,X5) = X3
                      & ssList(X5) )
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ! [X4] :
                        ( ~ segmentP(sK0,X4)
                        | ~ segmentP(X1,X4)
                        | ~ neq(X4,nil)
                        | ~ ssList(X4) )
                    & neq(X1,nil) )
                  | ( nil != sK0
                    & nil = X1 ) )
                & ( nil != X2
                  | nil = X3 )
                & ? [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ! [X8] :
                                ( app(X8,cons(X6,nil)) != X2
                                | ~ ssList(X8) )
                            | app(cons(X6,nil),X7) != X5
                            | ~ ssList(X7) )
                        | ~ ssItem(X6) )
                    & equalelemsP(X2)
                    & app(X2,X5) = X3
                    & ssList(X5) )
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ! [X4] :
                      ( ~ segmentP(sK0,X4)
                      | ~ segmentP(sK1,X4)
                      | ~ neq(X4,nil)
                      | ~ ssList(X4) )
                  & neq(sK1,nil) )
                | ( nil != sK0
                  & nil = sK1 ) )
              & ( nil != X2
                | nil = X3 )
              & ? [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ! [X8] :
                              ( app(X8,cons(X6,nil)) != X2
                              | ~ ssList(X8) )
                          | app(cons(X6,nil),X7) != X5
                          | ~ ssList(X7) )
                      | ~ ssItem(X6) )
                  & equalelemsP(X2)
                  & app(X2,X5) = X3
                  & ssList(X5) )
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ! [X4] :
                    ( ~ segmentP(sK0,X4)
                    | ~ segmentP(sK1,X4)
                    | ~ neq(X4,nil)
                    | ~ ssList(X4) )
                & neq(sK1,nil) )
              | ( nil != sK0
                & nil = sK1 ) )
            & ( nil != X2
              | nil = X3 )
            & ? [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ! [X8] :
                            ( app(X8,cons(X6,nil)) != X2
                            | ~ ssList(X8) )
                        | app(cons(X6,nil),X7) != X5
                        | ~ ssList(X7) )
                    | ~ ssItem(X6) )
                & equalelemsP(X2)
                & app(X2,X5) = X3
                & ssList(X5) )
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ! [X4] :
                  ( ~ segmentP(sK0,X4)
                  | ~ segmentP(sK1,X4)
                  | ~ neq(X4,nil)
                  | ~ ssList(X4) )
              & neq(sK1,nil) )
            | ( nil != sK0
              & nil = sK1 ) )
          & ( nil != sK2
            | nil = X3 )
          & ? [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ! [X8] :
                          ( app(X8,cons(X6,nil)) != sK2
                          | ~ ssList(X8) )
                      | app(cons(X6,nil),X7) != X5
                      | ~ ssList(X7) )
                  | ~ ssItem(X6) )
              & equalelemsP(sK2)
              & app(sK2,X5) = X3
              & ssList(X5) )
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ( ? [X3] :
        ( ( ( ! [X4] :
                ( ~ segmentP(sK0,X4)
                | ~ segmentP(sK1,X4)
                | ~ neq(X4,nil)
                | ~ ssList(X4) )
            & neq(sK1,nil) )
          | ( nil != sK0
            & nil = sK1 ) )
        & ( nil != sK2
          | nil = X3 )
        & ? [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ! [X8] :
                        ( app(X8,cons(X6,nil)) != sK2
                        | ~ ssList(X8) )
                    | app(cons(X6,nil),X7) != X5
                    | ~ ssList(X7) )
                | ~ ssItem(X6) )
            & equalelemsP(sK2)
            & app(sK2,X5) = X3
            & ssList(X5) )
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ( ! [X4] :
              ( ~ segmentP(sK0,X4)
              | ~ segmentP(sK1,X4)
              | ~ neq(X4,nil)
              | ~ ssList(X4) )
          & neq(sK1,nil) )
        | ( nil != sK0
          & nil = sK1 ) )
      & ( nil != sK2
        | nil = sK3 )
      & ? [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ! [X8] :
                      ( app(X8,cons(X6,nil)) != sK2
                      | ~ ssList(X8) )
                  | app(cons(X6,nil),X7) != X5
                  | ~ ssList(X7) )
              | ~ ssItem(X6) )
          & equalelemsP(sK2)
          & app(sK2,X5) = sK3
          & ssList(X5) )
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ( ? [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ! [X8] :
                    ( app(X8,cons(X6,nil)) != sK2
                    | ~ ssList(X8) )
                | app(cons(X6,nil),X7) != X5
                | ~ ssList(X7) )
            | ~ ssItem(X6) )
        & equalelemsP(sK2)
        & app(sK2,X5) = sK3
        & ssList(X5) )
   => ( ! [X6] :
          ( ! [X7] :
              ( ! [X8] :
                  ( app(X8,cons(X6,nil)) != sK2
                  | ~ ssList(X8) )
              | app(cons(X6,nil),X7) != sK4
              | ~ ssList(X7) )
          | ~ ssItem(X6) )
      & equalelemsP(sK2)
      & sK3 = app(sK2,sK4)
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ~ segmentP(X0,X4)
                          | ~ segmentP(X1,X4)
                          | ~ neq(X4,nil)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( app(X8,cons(X6,nil)) != X2
                                  | ~ ssList(X8) )
                              | app(cons(X6,nil),X7) != X5
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & equalelemsP(X2)
                      & app(X2,X5) = X3
                      & ssList(X5) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ! [X4] :
                          ( ~ segmentP(X0,X4)
                          | ~ segmentP(X1,X4)
                          | ~ neq(X4,nil)
                          | ~ ssList(X4) )
                      & neq(X1,nil) )
                    | ( nil != X0
                      & nil = X1 ) )
                  & ( nil != X2
                    | nil = X3 )
                  & ? [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ! [X8] :
                                  ( app(X8,cons(X6,nil)) != X2
                                  | ~ ssList(X8) )
                              | app(cons(X6,nil),X7) != X5
                              | ~ ssList(X7) )
                          | ~ ssItem(X6) )
                      & equalelemsP(X2)
                      & app(X2,X5) = X3
                      & ssList(X5) )
                  & 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)
                   => ( ( ( ? [X4] :
                              ( segmentP(X0,X4)
                              & segmentP(X1,X4)
                              & neq(X4,nil)
                              & ssList(X4) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X5] :
                          ( ssList(X5)
                         => ( ? [X6] :
                                ( ? [X7] :
                                    ( ? [X8] :
                                        ( app(X8,cons(X6,nil)) = X2
                                        & ssList(X8) )
                                    & app(cons(X6,nil),X7) = X5
                                    & ssList(X7) )
                                & ssItem(X6) )
                            | ~ equalelemsP(X2)
                            | app(X2,X5) != X3 ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( ? [X8] :
                              ( segmentP(X0,X8)
                              & segmentP(X1,X8)
                              & neq(X8,nil)
                              & ssList(X8) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ( nil = X2
                        & nil != X3 )
                      | ! [X4] :
                          ( ssList(X4)
                         => ( ? [X5] :
                                ( ? [X6] :
                                    ( ? [X7] :
                                        ( app(X7,cons(X5,nil)) = X2
                                        & ssList(X7) )
                                    & app(cons(X5,nil),X6) = X4
                                    & ssList(X6) )
                                & ssItem(X5) )
                            | ~ equalelemsP(X2)
                            | app(X2,X4) != X3 ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ? [X8] :
                            ( segmentP(X0,X8)
                            & segmentP(X1,X8)
                            & neq(X8,nil)
                            & ssList(X8) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ( nil = X2
                      & nil != X3 )
                    | ! [X4] :
                        ( ssList(X4)
                       => ( ? [X5] :
                              ( ? [X6] :
                                  ( ? [X7] :
                                      ( app(X7,cons(X5,nil)) = X2
                                      & ssList(X7) )
                                  & app(cons(X5,nil),X6) = X4
                                  & ssList(X6) )
                              & ssItem(X5) )
                          | ~ equalelemsP(X2)
                          | app(X2,X4) != X3 ) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.klNSTchxfW/Vampire---4.8_26381',co1) ).

fof(f1021,plain,
    ( ~ ssList(sK2)
    | spl15_1
    | spl15_37 ),
    inference(subsumption_resolution,[],[f1020,f204]) ).

fof(f204,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.klNSTchxfW/Vampire---4.8_26381',ax17) ).

fof(f1020,plain,
    ( ~ ssList(nil)
    | ~ ssList(sK2)
    | spl15_1
    | spl15_37 ),
    inference(subsumption_resolution,[],[f1009,f244]) ).

fof(f244,plain,
    ( nil != sK2
    | spl15_1 ),
    inference(avatar_component_clause,[],[f242]) ).

fof(f242,plain,
    ( spl15_1
  <=> nil = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).

fof(f1009,plain,
    ( nil = sK2
    | ~ ssList(nil)
    | ~ ssList(sK2)
    | spl15_37 ),
    inference(resolution,[],[f950,f201]) ).

fof(f201,plain,
    ! [X0,X1] :
      ( neq(X0,X1)
      | X0 = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f148,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f119,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.klNSTchxfW/Vampire---4.8_26381',ax15) ).

fof(f950,plain,
    ( ~ neq(sK2,nil)
    | spl15_37 ),
    inference(avatar_component_clause,[],[f948]) ).

fof(f948,plain,
    ( spl15_37
  <=> neq(sK2,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_37])]) ).

fof(f973,plain,
    spl15_36,
    inference(avatar_contradiction_clause,[],[f972]) ).

fof(f972,plain,
    ( $false
    | spl15_36 ),
    inference(subsumption_resolution,[],[f971,f165]) ).

fof(f971,plain,
    ( ~ ssList(sK2)
    | spl15_36 ),
    inference(resolution,[],[f946,f209]) ).

fof(f209,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.klNSTchxfW/Vampire---4.8_26381',ax55) ).

fof(f946,plain,
    ( ~ segmentP(sK2,sK2)
    | spl15_36 ),
    inference(avatar_component_clause,[],[f944]) ).

fof(f944,plain,
    ( spl15_36
  <=> segmentP(sK2,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).

fof(f951,plain,
    ( ~ spl15_36
    | ~ spl15_37
    | ~ spl15_2 ),
    inference(avatar_split_clause,[],[f942,f246,f948,f944]) ).

fof(f246,plain,
    ( spl15_2
  <=> ! [X4] :
        ( ~ segmentP(sK2,X4)
        | ~ ssList(X4)
        | ~ neq(X4,nil)
        | ~ segmentP(sK3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).

fof(f942,plain,
    ( ~ neq(sK2,nil)
    | ~ segmentP(sK2,sK2)
    | ~ spl15_2 ),
    inference(subsumption_resolution,[],[f937,f165]) ).

fof(f937,plain,
    ( ~ ssList(sK2)
    | ~ neq(sK2,nil)
    | ~ segmentP(sK2,sK2)
    | ~ spl15_2 ),
    inference(resolution,[],[f923,f247]) ).

fof(f247,plain,
    ( ! [X4] :
        ( ~ segmentP(sK3,X4)
        | ~ ssList(X4)
        | ~ neq(X4,nil)
        | ~ segmentP(sK2,X4) )
    | ~ spl15_2 ),
    inference(avatar_component_clause,[],[f246]) ).

fof(f923,plain,
    segmentP(sK3,sK2),
    inference(subsumption_resolution,[],[f918,f165]) ).

fof(f918,plain,
    ( segmentP(sK3,sK2)
    | ~ ssList(sK2) ),
    inference(superposition,[],[f706,f170]) ).

fof(f170,plain,
    sK3 = app(sK2,sK4),
    inference(cnf_transformation,[],[f139]) ).

fof(f706,plain,
    ! [X0] :
      ( segmentP(app(X0,sK4),X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f565,f169]) ).

fof(f169,plain,
    ssList(sK4),
    inference(cnf_transformation,[],[f139]) ).

fof(f565,plain,
    ! [X0,X1] :
      ( ~ ssList(X1)
      | ~ ssList(X0)
      | segmentP(app(X0,X1),X0) ),
    inference(subsumption_resolution,[],[f564,f199]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,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.klNSTchxfW/Vampire---4.8_26381',ax26) ).

fof(f564,plain,
    ! [X0,X1] :
      ( ~ ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0)
      | segmentP(app(X0,X1),X0) ),
    inference(subsumption_resolution,[],[f559,f204]) ).

fof(f559,plain,
    ! [X0,X1] :
      ( ~ ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(nil)
      | ~ ssList(X0)
      | segmentP(app(X0,X1),X0) ),
    inference(duplicate_literal_removal,[],[f552]) ).

fof(f552,plain,
    ! [X0,X1] :
      ( ~ ssList(app(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(nil)
      | ~ ssList(X0)
      | segmentP(app(X0,X1),X0)
      | ~ ssList(X0) ),
    inference(superposition,[],[f236,f197]) ).

fof(f197,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,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.klNSTchxfW/Vampire---4.8_26381',ax28) ).

fof(f236,plain,
    ! [X2,X3,X1] :
      ( ~ ssList(app(app(X2,X1),X3))
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | segmentP(app(app(X2,X1),X3),X1) ),
    inference(equality_resolution,[],[f215]) ).

fof(f215,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(X0,X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f155]) ).

fof(f155,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0
                & ssList(sK10(X0,X1))
                & ssList(sK9(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f152,f154,f153]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK9(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK9(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK9(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0
        & ssList(sK10(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f152,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f151]) ).

fof(f151,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.klNSTchxfW/Vampire---4.8_26381',ax7) ).

fof(f330,plain,
    ( ~ spl15_3
    | ~ spl15_4 ),
    inference(avatar_contradiction_clause,[],[f329]) ).

fof(f329,plain,
    ( $false
    | ~ spl15_3
    | ~ spl15_4 ),
    inference(subsumption_resolution,[],[f327,f204]) ).

fof(f327,plain,
    ( ~ ssList(nil)
    | ~ spl15_3
    | ~ spl15_4 ),
    inference(resolution,[],[f318,f239]) ).

fof(f239,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f233]) ).

fof(f233,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f200]) ).

fof(f200,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f318,plain,
    ( neq(nil,nil)
    | ~ spl15_3
    | ~ spl15_4 ),
    inference(forward_demodulation,[],[f257,f252]) ).

fof(f252,plain,
    ( nil = sK3
    | ~ spl15_3 ),
    inference(avatar_component_clause,[],[f250]) ).

fof(f250,plain,
    ( spl15_3
  <=> nil = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).

fof(f257,plain,
    ( neq(sK3,nil)
    | ~ spl15_4 ),
    inference(avatar_component_clause,[],[f255]) ).

fof(f255,plain,
    ( spl15_4
  <=> neq(sK3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).

fof(f317,plain,
    ( spl15_1
    | ~ spl15_3 ),
    inference(avatar_split_clause,[],[f316,f250,f242]) ).

fof(f316,plain,
    ( nil = sK2
    | ~ spl15_3 ),
    inference(subsumption_resolution,[],[f304,f165]) ).

fof(f304,plain,
    ( nil = sK2
    | ~ ssList(sK2)
    | ~ spl15_3 ),
    inference(superposition,[],[f301,f189]) ).

fof(f189,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/tmp/tmp.klNSTchxfW/Vampire---4.8_26381',ax84) ).

fof(f301,plain,
    ( nil = app(sK2,nil)
    | ~ spl15_3 ),
    inference(backward_demodulation,[],[f263,f298]) ).

fof(f298,plain,
    ( nil = sK4
    | ~ spl15_3 ),
    inference(subsumption_resolution,[],[f297,f165]) ).

fof(f297,plain,
    ( nil = sK4
    | ~ ssList(sK2)
    | ~ spl15_3 ),
    inference(subsumption_resolution,[],[f296,f169]) ).

fof(f296,plain,
    ( nil = sK4
    | ~ ssList(sK4)
    | ~ ssList(sK2)
    | ~ spl15_3 ),
    inference(trivial_inequality_removal,[],[f292]) ).

fof(f292,plain,
    ( nil != nil
    | nil = sK4
    | ~ ssList(sK4)
    | ~ ssList(sK2)
    | ~ spl15_3 ),
    inference(superposition,[],[f190,f263]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( nil != app(X0,X1)
      | nil = X1
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f147,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f146]) ).

fof(f146,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( nil = app(X0,X1)
              | nil != X0
              | nil != X1 )
            & ( ( nil = X0
                & nil = X1 )
              | nil != app(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( nil = app(X0,X1)
          <=> ( nil = X0
              & nil = X1 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.klNSTchxfW/Vampire---4.8_26381',ax83) ).

fof(f263,plain,
    ( nil = app(sK2,sK4)
    | ~ spl15_3 ),
    inference(backward_demodulation,[],[f170,f252]) ).

fof(f260,plain,
    ( spl15_3
    | ~ spl15_1 ),
    inference(avatar_split_clause,[],[f173,f242,f250]) ).

fof(f173,plain,
    ( nil != sK2
    | nil = sK3 ),
    inference(cnf_transformation,[],[f139]) ).

fof(f258,plain,
    ( ~ spl15_1
    | spl15_4 ),
    inference(avatar_split_clause,[],[f227,f255,f242]) ).

fof(f227,plain,
    ( neq(sK3,nil)
    | nil != sK2 ),
    inference(definition_unfolding,[],[f175,f167,f168]) ).

fof(f168,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f139]) ).

fof(f167,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f139]) ).

fof(f175,plain,
    ( neq(sK1,nil)
    | nil != sK0 ),
    inference(cnf_transformation,[],[f139]) ).

fof(f253,plain,
    ( spl15_3
    | spl15_2 ),
    inference(avatar_split_clause,[],[f226,f246,f250]) ).

fof(f226,plain,
    ! [X4] :
      ( ~ segmentP(sK2,X4)
      | ~ segmentP(sK3,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil = sK3 ),
    inference(definition_unfolding,[],[f176,f168,f167,f167]) ).

fof(f176,plain,
    ! [X4] :
      ( ~ segmentP(sK0,X4)
      | ~ segmentP(sK1,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil = sK1 ),
    inference(cnf_transformation,[],[f139]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWC065+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 20:27:23 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.35  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.klNSTchxfW/Vampire---4.8_26381
% 0.47/0.69  % (26490)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.47/0.69  % (26492)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.47/0.69  % (26491)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.47/0.69  % (26495)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.47/0.69  % (26494)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.47/0.69  % (26493)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.47/0.69  % (26497)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.47/0.69  % (26496)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.47/0.70  % (26490)Instruction limit reached!
% 0.47/0.70  % (26490)------------------------------
% 0.47/0.70  % (26490)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.47/0.70  % (26490)Termination reason: Unknown
% 0.47/0.70  % (26490)Termination phase: Saturation
% 0.47/0.70  
% 0.47/0.70  % (26490)Memory used [KB]: 1400
% 0.47/0.70  % (26490)Time elapsed: 0.012 s
% 0.47/0.70  % (26490)Instructions burned: 34 (million)
% 0.47/0.70  % (26490)------------------------------
% 0.47/0.70  % (26490)------------------------------
% 0.47/0.70  % (26498)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.47/0.70  % (26494)Instruction limit reached!
% 0.47/0.70  % (26494)------------------------------
% 0.47/0.70  % (26494)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.47/0.70  % (26494)Termination reason: Unknown
% 0.47/0.70  % (26494)Termination phase: Saturation
% 0.47/0.70  
% 0.47/0.70  % (26494)Memory used [KB]: 2048
% 0.47/0.70  % (26494)Time elapsed: 0.018 s
% 0.47/0.70  % (26494)Instructions burned: 35 (million)
% 0.47/0.70  % (26494)------------------------------
% 0.47/0.70  % (26494)------------------------------
% 0.47/0.70  % (26493)Instruction limit reached!
% 0.47/0.70  % (26493)------------------------------
% 0.47/0.70  % (26493)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.47/0.70  % (26493)Termination reason: Unknown
% 0.47/0.70  % (26493)Termination phase: Saturation
% 0.47/0.70  
% 0.47/0.70  % (26493)Memory used [KB]: 1479
% 0.47/0.70  % (26493)Time elapsed: 0.019 s
% 0.47/0.70  % (26493)Instructions burned: 33 (million)
% 0.47/0.70  % (26493)------------------------------
% 0.47/0.70  % (26493)------------------------------
% 0.47/0.71  % (26500)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.47/0.71  % (26495)Instruction limit reached!
% 0.47/0.71  % (26495)------------------------------
% 0.47/0.71  % (26495)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.47/0.71  % (26495)Termination reason: Unknown
% 0.47/0.71  % (26495)Termination phase: Saturation
% 0.47/0.71  
% 0.47/0.71  % (26495)Memory used [KB]: 1539
% 0.47/0.71  % (26495)Time elapsed: 0.024 s
% 0.47/0.71  % (26495)Instructions burned: 46 (million)
% 0.47/0.71  % (26495)------------------------------
% 0.47/0.71  % (26495)------------------------------
% 0.47/0.71  % (26492)First to succeed.
% 0.47/0.71  % (26491)Instruction limit reached!
% 0.47/0.71  % (26491)------------------------------
% 0.47/0.71  % (26491)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.47/0.71  % (26491)Termination reason: Unknown
% 0.47/0.71  % (26491)Termination phase: Saturation
% 0.47/0.71  
% 0.47/0.71  % (26491)Memory used [KB]: 2019
% 0.47/0.71  % (26491)Time elapsed: 0.026 s
% 0.47/0.71  % (26491)Instructions burned: 51 (million)
% 0.47/0.71  % (26491)------------------------------
% 0.47/0.71  % (26491)------------------------------
% 0.47/0.71  % (26497)Instruction limit reached!
% 0.47/0.71  % (26497)------------------------------
% 0.47/0.71  % (26497)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.47/0.71  % (26497)Termination reason: Unknown
% 0.47/0.71  % (26497)Termination phase: Saturation
% 0.47/0.71  
% 0.47/0.71  % (26497)Memory used [KB]: 1642
% 0.47/0.71  % (26497)Time elapsed: 0.021 s
% 0.47/0.71  % (26497)Instructions burned: 59 (million)
% 0.47/0.71  % (26497)------------------------------
% 0.47/0.71  % (26497)------------------------------
% 0.47/0.71  % (26492)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26489"
% 0.62/0.71  % (26499)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.62/0.71  % (26492)Refutation found. Thanks to Tanya!
% 0.62/0.71  % SZS status Theorem for Vampire---4
% 0.62/0.71  % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.71  % (26492)------------------------------
% 0.62/0.71  % (26492)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.71  % (26492)Termination reason: Refutation
% 0.62/0.71  
% 0.62/0.71  % (26492)Memory used [KB]: 1606
% 0.62/0.71  % (26492)Time elapsed: 0.027 s
% 0.62/0.71  % (26492)Instructions burned: 51 (million)
% 0.62/0.71  % (26489)Success in time 0.357 s
% 0.62/0.71  % Vampire---4.8 exiting
%------------------------------------------------------------------------------