TSTP Solution File: SWC389+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC389+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 : n025.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 09:50:46 EDT 2024

% Result   : Theorem 0.56s 0.75s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  112 (   8 unt;   0 def)
%            Number of atoms       :  607 ( 130 equ)
%            Maximal formula atoms :   24 (   5 avg)
%            Number of connectives :  771 ( 276   ~; 252   |; 196   &)
%                                         (  16 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   18 (  16 usr;   9 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :  188 ( 120   !;  68   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f852,plain,
    $false,
    inference(avatar_sat_refutation,[],[f302,f307,f316,f321,f358,f366,f399,f412,f545,f851]) ).

fof(f851,plain,
    ( spl17_1
    | ~ spl17_4
    | ~ spl17_12 ),
    inference(avatar_contradiction_clause,[],[f850]) ).

fof(f850,plain,
    ( $false
    | spl17_1
    | ~ spl17_4
    | ~ spl17_12 ),
    inference(subsumption_resolution,[],[f849,f311]) ).

fof(f311,plain,
    ( sP0(sK7,sK6)
    | ~ spl17_4 ),
    inference(avatar_component_clause,[],[f309]) ).

fof(f309,plain,
    ( spl17_4
  <=> sP0(sK7,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).

fof(f849,plain,
    ( ~ sP0(sK7,sK6)
    | spl17_1
    | ~ spl17_4
    | ~ spl17_12 ),
    inference(resolution,[],[f844,f195]) ).

fof(f195,plain,
    ! [X0,X1] :
      ( ssList(sK2(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( ( ! [X5] :
            ( ~ lt(X5,sK1(X0,X1))
            | ~ memberP(sK3(X0,X1),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ lt(sK1(X0,X1),X6)
            | ~ memberP(sK2(X0,X1),X6)
            | ~ ssItem(X6) )
        & app(app(sK2(X0,X1),X1),sK3(X0,X1)) = X0
        & cons(sK1(X0,X1),nil) = X1
        & ssList(sK3(X0,X1))
        & ssList(sK2(X0,X1))
        & ssItem(sK1(X0,X1)) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f153,f156,f155,f154]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ! [X5] :
                      ( ~ lt(X5,X2)
                      | ~ memberP(X4,X5)
                      | ~ ssItem(X5) )
                  & ! [X6] :
                      ( ~ lt(X2,X6)
                      | ~ memberP(X3,X6)
                      | ~ ssItem(X6) )
                  & app(app(X3,X1),X4) = X0
                  & cons(X2,nil) = X1
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
     => ( ? [X3] :
            ( ? [X4] :
                ( ! [X5] :
                    ( ~ lt(X5,sK1(X0,X1))
                    | ~ memberP(X4,X5)
                    | ~ ssItem(X5) )
                & ! [X6] :
                    ( ~ lt(sK1(X0,X1),X6)
                    | ~ memberP(X3,X6)
                    | ~ ssItem(X6) )
                & app(app(X3,X1),X4) = X0
                & cons(sK1(X0,X1),nil) = X1
                & ssList(X4) )
            & ssList(X3) )
        & ssItem(sK1(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ? [X4] :
              ( ! [X5] :
                  ( ~ lt(X5,sK1(X0,X1))
                  | ~ memberP(X4,X5)
                  | ~ ssItem(X5) )
              & ! [X6] :
                  ( ~ lt(sK1(X0,X1),X6)
                  | ~ memberP(X3,X6)
                  | ~ ssItem(X6) )
              & app(app(X3,X1),X4) = X0
              & cons(sK1(X0,X1),nil) = X1
              & ssList(X4) )
          & ssList(X3) )
     => ( ? [X4] :
            ( ! [X5] :
                ( ~ lt(X5,sK1(X0,X1))
                | ~ memberP(X4,X5)
                | ~ ssItem(X5) )
            & ! [X6] :
                ( ~ lt(sK1(X0,X1),X6)
                | ~ memberP(sK2(X0,X1),X6)
                | ~ ssItem(X6) )
            & app(app(sK2(X0,X1),X1),X4) = X0
            & cons(sK1(X0,X1),nil) = X1
            & ssList(X4) )
        & ssList(sK2(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ! [X5] :
              ( ~ lt(X5,sK1(X0,X1))
              | ~ memberP(X4,X5)
              | ~ ssItem(X5) )
          & ! [X6] :
              ( ~ lt(sK1(X0,X1),X6)
              | ~ memberP(sK2(X0,X1),X6)
              | ~ ssItem(X6) )
          & app(app(sK2(X0,X1),X1),X4) = X0
          & cons(sK1(X0,X1),nil) = X1
          & ssList(X4) )
     => ( ! [X5] :
            ( ~ lt(X5,sK1(X0,X1))
            | ~ memberP(sK3(X0,X1),X5)
            | ~ ssItem(X5) )
        & ! [X6] :
            ( ~ lt(sK1(X0,X1),X6)
            | ~ memberP(sK2(X0,X1),X6)
            | ~ ssItem(X6) )
        & app(app(sK2(X0,X1),X1),sK3(X0,X1)) = X0
        & cons(sK1(X0,X1),nil) = X1
        & ssList(sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ! [X5] :
                      ( ~ lt(X5,X2)
                      | ~ memberP(X4,X5)
                      | ~ ssItem(X5) )
                  & ! [X6] :
                      ( ~ lt(X2,X6)
                      | ~ memberP(X3,X6)
                      | ~ ssItem(X6) )
                  & app(app(X3,X1),X4) = X0
                  & cons(X2,nil) = X1
                  & ssList(X4) )
              & ssList(X3) )
          & ssItem(X2) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f152]) ).

fof(f152,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( ! [X7] :
                      ( ~ lt(X7,X4)
                      | ~ memberP(X6,X7)
                      | ~ ssItem(X7) )
                  & ! [X8] :
                      ( ~ lt(X4,X8)
                      | ~ memberP(X5,X8)
                      | ~ ssItem(X8) )
                  & app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2
                  & ssList(X6) )
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    inference(nnf_transformation,[],[f150]) ).

fof(f150,plain,
    ! [X3,X2] :
      ( ? [X4] :
          ( ? [X5] :
              ( ? [X6] :
                  ( ! [X7] :
                      ( ~ lt(X7,X4)
                      | ~ memberP(X6,X7)
                      | ~ ssItem(X7) )
                  & ! [X8] :
                      ( ~ lt(X4,X8)
                      | ~ memberP(X5,X8)
                      | ~ ssItem(X8) )
                  & app(app(X5,X2),X6) = X3
                  & cons(X4,nil) = X2
                  & ssList(X6) )
              & ssList(X5) )
          & ssItem(X4) )
      | ~ sP0(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f844,plain,
    ( ~ ssList(sK2(sK7,sK6))
    | spl17_1
    | ~ spl17_4
    | ~ spl17_12 ),
    inference(subsumption_resolution,[],[f843,f297]) ).

fof(f297,plain,
    ( ~ segmentP(sK7,sK6)
    | spl17_1 ),
    inference(avatar_component_clause,[],[f295]) ).

fof(f295,plain,
    ( spl17_1
  <=> segmentP(sK7,sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).

fof(f843,plain,
    ( ~ ssList(sK2(sK7,sK6))
    | segmentP(sK7,sK6)
    | ~ spl17_4
    | ~ spl17_12 ),
    inference(subsumption_resolution,[],[f842,f203]) ).

fof(f203,plain,
    ssList(sK6),
    inference(cnf_transformation,[],[f162]) ).

fof(f162,plain,
    ( ( ( ~ singletonP(sK4)
        & neq(sK5,nil) )
      | ~ segmentP(sK5,sK4) )
    & ( ( nil = sK6
        & nil = sK7 )
      | sP0(sK7,sK6) )
    & sK4 = sK6
    & sK5 = sK7
    & ssList(sK7)
    & ssList(sK6)
    & ssList(sK5)
    & ssList(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f151,f161,f160,f159,f158]) ).

fof(f158,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ singletonP(X0)
                        & neq(X1,nil) )
                      | ~ segmentP(X1,X0) )
                    & ( ( nil = X2
                        & nil = X3 )
                      | sP0(X3,X2) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ singletonP(sK4)
                      & neq(X1,nil) )
                    | ~ segmentP(X1,sK4) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP0(X3,X2) )
                  & sK4 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ singletonP(sK4)
                    & neq(X1,nil) )
                  | ~ segmentP(X1,sK4) )
                & ( ( nil = X2
                    & nil = X3 )
                  | sP0(X3,X2) )
                & sK4 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ singletonP(sK4)
                  & neq(sK5,nil) )
                | ~ segmentP(sK5,sK4) )
              & ( ( nil = X2
                  & nil = X3 )
                | sP0(X3,X2) )
              & sK4 = X2
              & sK5 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f160,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ singletonP(sK4)
                & neq(sK5,nil) )
              | ~ segmentP(sK5,sK4) )
            & ( ( nil = X2
                & nil = X3 )
              | sP0(X3,X2) )
            & sK4 = X2
            & sK5 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ singletonP(sK4)
              & neq(sK5,nil) )
            | ~ segmentP(sK5,sK4) )
          & ( ( nil = sK6
              & nil = X3 )
            | sP0(X3,sK6) )
          & sK4 = sK6
          & sK5 = X3
          & ssList(X3) )
      & ssList(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f161,plain,
    ( ? [X3] :
        ( ( ( ~ singletonP(sK4)
            & neq(sK5,nil) )
          | ~ segmentP(sK5,sK4) )
        & ( ( nil = sK6
            & nil = X3 )
          | sP0(X3,sK6) )
        & sK4 = sK6
        & sK5 = X3
        & ssList(X3) )
   => ( ( ( ~ singletonP(sK4)
          & neq(sK5,nil) )
        | ~ segmentP(sK5,sK4) )
      & ( ( nil = sK6
          & nil = sK7 )
        | sP0(sK7,sK6) )
      & sK4 = sK6
      & sK5 = sK7
      & ssList(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f151,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ singletonP(X0)
                      & neq(X1,nil) )
                    | ~ segmentP(X1,X0) )
                  & ( ( nil = X2
                      & nil = X3 )
                    | sP0(X3,X2) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f99,f150]) ).

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

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

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ( ( singletonP(X0)
                      | ~ neq(X1,nil) )
                    & segmentP(X1,X0) )
                  | ( ( nil != X2
                      | nil != X3 )
                    & ! [X4] :
                        ( ssItem(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ! [X6] :
                                ( ? [X8] :
                                    ( lt(X8,X4)
                                    & memberP(X6,X8)
                                    & ssItem(X8) )
                                | ? [X7] :
                                    ( lt(X4,X7)
                                    & memberP(X5,X7)
                                    & ssItem(X7) )
                                | app(app(X5,X2),X6) != X3
                                | cons(X4,nil) != X2
                                | ~ ssList(X6) ) ) ) )
                  | X0 != X2
                  | X1 != X3
                  | ~ ssList(X3) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.1vMMamTyaB/Vampire---4.8_32300',co1) ).

fof(f842,plain,
    ( ~ ssList(sK2(sK7,sK6))
    | ~ ssList(sK6)
    | segmentP(sK7,sK6)
    | ~ spl17_4
    | ~ spl17_12 ),
    inference(subsumption_resolution,[],[f841,f522]) ).

fof(f522,plain,
    ( ssList(sK3(sK7,sK6))
    | ~ spl17_12 ),
    inference(avatar_component_clause,[],[f521]) ).

fof(f521,plain,
    ( spl17_12
  <=> ssList(sK3(sK7,sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).

fof(f841,plain,
    ( ~ ssList(sK3(sK7,sK6))
    | ~ ssList(sK2(sK7,sK6))
    | ~ ssList(sK6)
    | segmentP(sK7,sK6)
    | ~ spl17_4 ),
    inference(subsumption_resolution,[],[f825,f204]) ).

fof(f204,plain,
    ssList(sK7),
    inference(cnf_transformation,[],[f162]) ).

fof(f825,plain,
    ( ~ ssList(sK7)
    | ~ ssList(sK3(sK7,sK6))
    | ~ ssList(sK2(sK7,sK6))
    | ~ ssList(sK6)
    | segmentP(sK7,sK6)
    | ~ spl17_4 ),
    inference(superposition,[],[f287,f494]) ).

fof(f494,plain,
    ( sK7 = app(app(sK2(sK7,sK6),sK6),sK3(sK7,sK6))
    | ~ spl17_4 ),
    inference(resolution,[],[f198,f311]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | app(app(sK2(X0,X1),X1),sK3(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f157]) ).

fof(f287,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,[],[f263]) ).

fof(f263,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,[],[f191]) ).

fof(f191,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK15(X0,X1),X1),sK16(X0,X1)) = X0
                & ssList(sK16(X0,X1))
                & ssList(sK15(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f188,f190,f189]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK15(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK15(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK15(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK15(X0,X1),X1),sK16(X0,X1)) = X0
        & ssList(sK16(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f188,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,[],[f187]) ).

fof(f187,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,[],[f134]) ).

fof(f134,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.1vMMamTyaB/Vampire---4.8_32300',ax7) ).

fof(f545,plain,
    ( ~ spl17_4
    | spl17_12 ),
    inference(avatar_contradiction_clause,[],[f544]) ).

fof(f544,plain,
    ( $false
    | ~ spl17_4
    | spl17_12 ),
    inference(subsumption_resolution,[],[f543,f311]) ).

fof(f543,plain,
    ( ~ sP0(sK7,sK6)
    | spl17_12 ),
    inference(resolution,[],[f523,f196]) ).

fof(f196,plain,
    ! [X0,X1] :
      ( ssList(sK3(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f523,plain,
    ( ~ ssList(sK3(sK7,sK6))
    | spl17_12 ),
    inference(avatar_component_clause,[],[f521]) ).

fof(f412,plain,
    ( spl17_2
    | ~ spl17_4
    | ~ spl17_7 ),
    inference(avatar_split_clause,[],[f411,f339,f309,f299]) ).

fof(f299,plain,
    ( spl17_2
  <=> singletonP(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).

fof(f339,plain,
    ( spl17_7
  <=> ssItem(sK1(sK7,sK6)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).

fof(f411,plain,
    ( singletonP(sK6)
    | ~ spl17_4
    | ~ spl17_7 ),
    inference(subsumption_resolution,[],[f410,f203]) ).

fof(f410,plain,
    ( singletonP(sK6)
    | ~ ssList(sK6)
    | ~ spl17_4
    | ~ spl17_7 ),
    inference(subsumption_resolution,[],[f401,f340]) ).

fof(f340,plain,
    ( ssItem(sK1(sK7,sK6))
    | ~ spl17_7 ),
    inference(avatar_component_clause,[],[f339]) ).

fof(f401,plain,
    ( singletonP(sK6)
    | ~ ssItem(sK1(sK7,sK6))
    | ~ ssList(sK6)
    | ~ spl17_4 ),
    inference(superposition,[],[f285,f400]) ).

fof(f400,plain,
    ( sK6 = cons(sK1(sK7,sK6),nil)
    | ~ spl17_4 ),
    inference(resolution,[],[f311,f197]) ).

fof(f197,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | cons(sK1(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f157]) ).

fof(f285,plain,
    ! [X1] :
      ( singletonP(cons(X1,nil))
      | ~ ssItem(X1)
      | ~ ssList(cons(X1,nil)) ),
    inference(equality_resolution,[],[f252]) ).

fof(f252,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f185]) ).

fof(f185,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK14(X0),nil) = X0
            & ssItem(sK14(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f183,f184]) ).

fof(f184,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK14(X0),nil) = X0
        & ssItem(sK14(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f183,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f182]) ).

fof(f182,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,[],[f124]) ).

fof(f124,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.1vMMamTyaB/Vampire---4.8_32300',ax4) ).

fof(f399,plain,
    ( ~ spl17_3
    | ~ spl17_6 ),
    inference(avatar_contradiction_clause,[],[f398]) ).

fof(f398,plain,
    ( $false
    | ~ spl17_3
    | ~ spl17_6 ),
    inference(subsumption_resolution,[],[f396,f237]) ).

fof(f237,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/tmp/tmp.1vMMamTyaB/Vampire---4.8_32300',ax17) ).

fof(f396,plain,
    ( ~ ssList(nil)
    | ~ spl17_3
    | ~ spl17_6 ),
    inference(resolution,[],[f392,f292]) ).

fof(f292,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1) ),
    inference(duplicate_literal_removal,[],[f281]) ).

fof(f281,plain,
    ! [X1] :
      ( ~ neq(X1,X1)
      | ~ ssList(X1)
      | ~ ssList(X1) ),
    inference(equality_resolution,[],[f233]) ).

fof(f233,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ neq(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f171]) ).

fof(f171,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( neq(X0,X1)
              | X0 = X1 )
            & ( X0 != X1
              | ~ neq(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f118]) ).

fof(f118,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.1vMMamTyaB/Vampire---4.8_32300',ax15) ).

fof(f392,plain,
    ( neq(nil,nil)
    | ~ spl17_3
    | ~ spl17_6 ),
    inference(forward_demodulation,[],[f306,f320]) ).

fof(f320,plain,
    ( nil = sK7
    | ~ spl17_6 ),
    inference(avatar_component_clause,[],[f318]) ).

fof(f318,plain,
    ( spl17_6
  <=> nil = sK7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).

fof(f306,plain,
    ( neq(sK7,nil)
    | ~ spl17_3 ),
    inference(avatar_component_clause,[],[f304]) ).

fof(f304,plain,
    ( spl17_3
  <=> neq(sK7,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).

fof(f366,plain,
    ( spl17_1
    | ~ spl17_5
    | ~ spl17_6 ),
    inference(avatar_contradiction_clause,[],[f365]) ).

fof(f365,plain,
    ( $false
    | spl17_1
    | ~ spl17_5
    | ~ spl17_6 ),
    inference(subsumption_resolution,[],[f362,f322]) ).

fof(f322,plain,
    segmentP(nil,nil),
    inference(subsumption_resolution,[],[f286,f237]) ).

fof(f286,plain,
    ( segmentP(nil,nil)
    | ~ ssList(nil) ),
    inference(equality_resolution,[],[f254]) ).

fof(f254,plain,
    ! [X0] :
      ( segmentP(nil,X0)
      | nil != X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f186]) ).

fof(f186,plain,
    ! [X0] :
      ( ( ( segmentP(nil,X0)
          | nil != X0 )
        & ( nil = X0
          | ~ segmentP(nil,X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X0] :
      ( ( segmentP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( segmentP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.1vMMamTyaB/Vampire---4.8_32300',ax58) ).

fof(f362,plain,
    ( ~ segmentP(nil,nil)
    | spl17_1
    | ~ spl17_5
    | ~ spl17_6 ),
    inference(backward_demodulation,[],[f360,f315]) ).

fof(f315,plain,
    ( nil = sK6
    | ~ spl17_5 ),
    inference(avatar_component_clause,[],[f313]) ).

fof(f313,plain,
    ( spl17_5
  <=> nil = sK6 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).

fof(f360,plain,
    ( ~ segmentP(nil,sK6)
    | spl17_1
    | ~ spl17_6 ),
    inference(backward_demodulation,[],[f297,f320]) ).

fof(f358,plain,
    ( ~ spl17_4
    | spl17_7 ),
    inference(avatar_split_clause,[],[f355,f339,f309]) ).

fof(f355,plain,
    ( ~ sP0(sK7,sK6)
    | spl17_7 ),
    inference(resolution,[],[f341,f194]) ).

fof(f194,plain,
    ! [X0,X1] :
      ( ssItem(sK1(X0,X1))
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f341,plain,
    ( ~ ssItem(sK1(sK7,sK6))
    | spl17_7 ),
    inference(avatar_component_clause,[],[f339]) ).

fof(f321,plain,
    ( spl17_4
    | spl17_6 ),
    inference(avatar_split_clause,[],[f207,f318,f309]) ).

fof(f207,plain,
    ( nil = sK7
    | sP0(sK7,sK6) ),
    inference(cnf_transformation,[],[f162]) ).

fof(f316,plain,
    ( spl17_4
    | spl17_5 ),
    inference(avatar_split_clause,[],[f208,f313,f309]) ).

fof(f208,plain,
    ( nil = sK6
    | sP0(sK7,sK6) ),
    inference(cnf_transformation,[],[f162]) ).

fof(f307,plain,
    ( ~ spl17_1
    | spl17_3 ),
    inference(avatar_split_clause,[],[f276,f304,f295]) ).

fof(f276,plain,
    ( neq(sK7,nil)
    | ~ segmentP(sK7,sK6) ),
    inference(definition_unfolding,[],[f209,f205,f205,f206]) ).

fof(f206,plain,
    sK4 = sK6,
    inference(cnf_transformation,[],[f162]) ).

fof(f205,plain,
    sK5 = sK7,
    inference(cnf_transformation,[],[f162]) ).

fof(f209,plain,
    ( neq(sK5,nil)
    | ~ segmentP(sK5,sK4) ),
    inference(cnf_transformation,[],[f162]) ).

fof(f302,plain,
    ( ~ spl17_1
    | ~ spl17_2 ),
    inference(avatar_split_clause,[],[f275,f299,f295]) ).

fof(f275,plain,
    ( ~ singletonP(sK6)
    | ~ segmentP(sK7,sK6) ),
    inference(definition_unfolding,[],[f210,f206,f205,f206]) ).

fof(f210,plain,
    ( ~ singletonP(sK4)
    | ~ segmentP(sK5,sK4) ),
    inference(cnf_transformation,[],[f162]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWC389+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.14  % 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
% 0.13/0.35  % Computer : n025.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 20:30:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35  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.1vMMamTyaB/Vampire---4.8_32300
% 0.50/0.73  % (32408)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)
% 0.50/0.73  % (32412)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)
% 0.50/0.73  % (32409)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)
% 0.50/0.73  % (32410)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.50/0.73  % (32411)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)
% 0.50/0.73  % (32413)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)
% 0.50/0.73  % (32415)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)
% 0.50/0.73  % (32414)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)
% 0.56/0.74  % (32408)Instruction limit reached!
% 0.56/0.74  % (32408)------------------------------
% 0.56/0.74  % (32408)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74  % (32408)Termination reason: Unknown
% 0.56/0.74  % (32408)Termination phase: Saturation
% 0.56/0.74  
% 0.56/0.74  % (32408)Memory used [KB]: 1508
% 0.56/0.74  % (32408)Time elapsed: 0.012 s
% 0.56/0.74  % (32408)Instructions burned: 34 (million)
% 0.56/0.74  % (32408)------------------------------
% 0.56/0.74  % (32408)------------------------------
% 0.56/0.75  % (32416)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)
% 0.56/0.75  % (32412)Instruction limit reached!
% 0.56/0.75  % (32412)------------------------------
% 0.56/0.75  % (32412)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (32412)Termination reason: Unknown
% 0.56/0.75  % (32412)Termination phase: Saturation
% 0.56/0.75  
% 0.56/0.75  % (32412)Memory used [KB]: 2116
% 0.56/0.75  % (32412)Time elapsed: 0.017 s
% 0.56/0.75  % (32412)Instructions burned: 36 (million)
% 0.56/0.75  % (32412)------------------------------
% 0.56/0.75  % (32412)------------------------------
% 0.56/0.75  % (32411)Instruction limit reached!
% 0.56/0.75  % (32411)------------------------------
% 0.56/0.75  % (32411)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (32411)Termination reason: Unknown
% 0.56/0.75  % (32411)Termination phase: Saturation
% 0.56/0.75  
% 0.56/0.75  % (32411)Memory used [KB]: 1758
% 0.56/0.75  % (32411)Time elapsed: 0.019 s
% 0.56/0.75  % (32411)Instructions burned: 34 (million)
% 0.56/0.75  % (32411)------------------------------
% 0.56/0.75  % (32411)------------------------------
% 0.56/0.75  % (32413)Instruction limit reached!
% 0.56/0.75  % (32413)------------------------------
% 0.56/0.75  % (32413)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75  % (32413)Termination reason: Unknown
% 0.56/0.75  % (32413)Termination phase: Saturation
% 0.56/0.75  
% 0.56/0.75  % (32413)Memory used [KB]: 1434
% 0.56/0.75  % (32413)Time elapsed: 0.020 s
% 0.56/0.75  % (32413)Instructions burned: 46 (million)
% 0.56/0.75  % (32413)------------------------------
% 0.56/0.75  % (32413)------------------------------
% 0.56/0.75  % (32410)First to succeed.
% 0.56/0.75  % (32410)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-32407"
% 0.56/0.75  % (32417)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)
% 0.56/0.75  % (32419)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.56/0.75  % (32410)Refutation found. Thanks to Tanya!
% 0.56/0.75  % SZS status Theorem for Vampire---4
% 0.56/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.76  % (32410)------------------------------
% 0.56/0.76  % (32410)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.76  % (32410)Termination reason: Refutation
% 0.56/0.76  
% 0.56/0.76  % (32410)Memory used [KB]: 1413
% 0.56/0.76  % (32410)Time elapsed: 0.022 s
% 0.56/0.76  % (32410)Instructions burned: 39 (million)
% 0.56/0.76  % (32407)Success in time 0.389 s
% 0.56/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------