TSTP Solution File: SWC349+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWC349+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 05:13:23 EDT 2024

% Result   : Theorem 0.22s 0.39s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   51
% Syntax   : Number of formulae    :  155 (  61 unt;   0 def)
%            Number of atoms       :  404 (  74 equ)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives :  368 ( 119   ~;  95   |; 104   &)
%                                         (  27 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   46 (  44 usr;  26 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  116 (  92   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f810,plain,
    $false,
    inference(avatar_sat_refutation,[],[f700,f705,f710,f715,f720,f725,f730,f735,f740,f745,f750,f755,f759,f763,f767,f771,f775,f779,f784,f788,f792,f796,f800,f804,f808,f809]) ).

fof(f809,plain,
    ( ~ spl69_2
    | spl69_11
    | ~ spl69_18 ),
    inference(avatar_split_clause,[],[f780,f777,f747,f702]) ).

fof(f702,plain,
    ( spl69_2
  <=> ssList(sK21) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_2])]) ).

fof(f747,plain,
    ( spl69_11
  <=> frontsegP(sK21,sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_11])]) ).

fof(f777,plain,
    ( spl69_18
  <=> ! [X0] :
        ( frontsegP(X0,sK20)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_18])]) ).

fof(f780,plain,
    ( ~ ssList(sK21)
    | spl69_11
    | ~ spl69_18 ),
    inference(resolution,[],[f778,f749]) ).

fof(f749,plain,
    ( ~ frontsegP(sK21,sK20)
    | spl69_11 ),
    inference(avatar_component_clause,[],[f747]) ).

fof(f778,plain,
    ( ! [X0] :
        ( frontsegP(X0,sK20)
        | ~ ssList(X0) )
    | ~ spl69_18 ),
    inference(avatar_component_clause,[],[f777]) ).

fof(f808,plain,
    spl69_25,
    inference(avatar_split_clause,[],[f620,f806]) ).

fof(f806,plain,
    ( spl69_25
  <=> ! [X0] :
        ( totalorderedP(cons(X0,sK20))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_25])]) ).

fof(f620,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,sK20))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f402,f378]) ).

fof(f378,plain,
    nil = sK20,
    inference(cnf_transformation,[],[f254]) ).

fof(f254,plain,
    ( ~ frontsegP(sK19,sK18)
    & neq(sK19,nil)
    & sK18 = sK20
    & sK19 = sK21
    & nil = sK20
    & ssList(sK21)
    & ssList(sK20)
    & ssList(sK19)
    & ssList(sK18) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f99,f253,f252,f251,f250]) ).

fof(f250,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ~ frontsegP(X1,X0)
                    & neq(X1,nil)
                    & X0 = X2
                    & X1 = X3
                    & nil = X2
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ frontsegP(X1,sK18)
                  & neq(X1,nil)
                  & sK18 = X2
                  & X1 = X3
                  & nil = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f251,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ~ frontsegP(X1,sK18)
                & neq(X1,nil)
                & sK18 = X2
                & X1 = X3
                & nil = X2
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ~ frontsegP(sK19,sK18)
              & neq(sK19,nil)
              & sK18 = X2
              & sK19 = X3
              & nil = X2
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f252,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ~ frontsegP(sK19,sK18)
            & neq(sK19,nil)
            & sK18 = X2
            & sK19 = X3
            & nil = X2
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ~ frontsegP(sK19,sK18)
          & neq(sK19,nil)
          & sK18 = sK20
          & sK19 = X3
          & nil = sK20
          & ssList(X3) )
      & ssList(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f253,plain,
    ( ? [X3] :
        ( ~ frontsegP(sK19,sK18)
        & neq(sK19,nil)
        & sK18 = sK20
        & sK19 = X3
        & nil = sK20
        & ssList(X3) )
   => ( ~ frontsegP(sK19,sK18)
      & neq(sK19,nil)
      & sK18 = sK20
      & sK19 = sK21
      & nil = sK20
      & ssList(sK21) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ frontsegP(X1,X0)
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & nil = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ~ frontsegP(X1,X0)
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & nil = X2
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( frontsegP(X1,X0)
                      | ~ neq(X1,nil)
                      | X0 != X2
                      | X1 != X3
                      | nil != X2 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( frontsegP(X1,X0)
                    | ~ neq(X1,nil)
                    | X0 != X2
                    | X1 != X3
                    | nil != X2 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f402,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( totalorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f65]) ).

fof(f65,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).

fof(f804,plain,
    spl69_24,
    inference(avatar_split_clause,[],[f619,f802]) ).

fof(f802,plain,
    ( spl69_24
  <=> ! [X0] :
        ( strictorderedP(cons(X0,sK20))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_24])]) ).

fof(f619,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,sK20))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f401,f378]) ).

fof(f401,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( strictorderedP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f68]) ).

fof(f68,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderedP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).

fof(f800,plain,
    spl69_23,
    inference(avatar_split_clause,[],[f618,f798]) ).

fof(f798,plain,
    ( spl69_23
  <=> ! [X0] :
        ( strictorderP(cons(X0,sK20))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_23])]) ).

fof(f618,plain,
    ! [X0] :
      ( strictorderP(cons(X0,sK20))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f400,f378]) ).

fof(f400,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( strictorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f63]) ).

fof(f63,axiom,
    ! [X0] :
      ( ssItem(X0)
     => strictorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).

fof(f796,plain,
    spl69_22,
    inference(avatar_split_clause,[],[f617,f794]) ).

fof(f794,plain,
    ( spl69_22
  <=> ! [X0] :
        ( totalorderP(cons(X0,sK20))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_22])]) ).

fof(f617,plain,
    ! [X0] :
      ( totalorderP(cons(X0,sK20))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f399,f378]) ).

fof(f399,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ! [X0] :
      ( totalorderP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f61]) ).

fof(f61,axiom,
    ! [X0] :
      ( ssItem(X0)
     => totalorderP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).

fof(f792,plain,
    spl69_21,
    inference(avatar_split_clause,[],[f616,f790]) ).

fof(f790,plain,
    ( spl69_21
  <=> ! [X0] :
        ( cyclefreeP(cons(X0,sK20))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_21])]) ).

fof(f616,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,sK20))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f398,f378]) ).

fof(f398,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0] :
      ( cyclefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,axiom,
    ! [X0] :
      ( ssItem(X0)
     => cyclefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).

fof(f788,plain,
    spl69_20,
    inference(avatar_split_clause,[],[f615,f786]) ).

fof(f786,plain,
    ( spl69_20
  <=> ! [X0] :
        ( duplicatefreeP(cons(X0,sK20))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_20])]) ).

fof(f615,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,sK20))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f397,f378]) ).

fof(f397,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( duplicatefreeP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f71]) ).

fof(f71,axiom,
    ! [X0] :
      ( ssItem(X0)
     => duplicatefreeP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).

fof(f784,plain,
    spl69_19,
    inference(avatar_split_clause,[],[f614,f782]) ).

fof(f782,plain,
    ( spl69_19
  <=> ! [X0] :
        ( equalelemsP(cons(X0,sK20))
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_19])]) ).

fof(f614,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,sK20))
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f396,f378]) ).

fof(f396,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( equalelemsP(cons(X0,nil))
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f73]) ).

fof(f73,axiom,
    ! [X0] :
      ( ssItem(X0)
     => equalelemsP(cons(X0,nil)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).

fof(f779,plain,
    spl69_18,
    inference(avatar_split_clause,[],[f633,f777]) ).

fof(f633,plain,
    ! [X0] :
      ( frontsegP(X0,sK20)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f450,f378]) ).

fof(f450,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f143]) ).

fof(f143,plain,
    ! [X0] :
      ( frontsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0] :
      ( ssList(X0)
     => frontsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).

fof(f775,plain,
    spl69_17,
    inference(avatar_split_clause,[],[f632,f773]) ).

fof(f773,plain,
    ( spl69_17
  <=> ! [X0] :
        ( rearsegP(X0,sK20)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_17])]) ).

fof(f632,plain,
    ! [X0] :
      ( rearsegP(X0,sK20)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f448,f378]) ).

fof(f448,plain,
    ! [X0] :
      ( rearsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f141]) ).

fof(f141,plain,
    ! [X0] :
      ( rearsegP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,axiom,
    ! [X0] :
      ( ssList(X0)
     => rearsegP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).

fof(f771,plain,
    spl69_16,
    inference(avatar_split_clause,[],[f631,f769]) ).

fof(f769,plain,
    ( spl69_16
  <=> ! [X0] :
        ( segmentP(X0,sK20)
        | ~ ssList(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_16])]) ).

fof(f631,plain,
    ! [X0] :
      ( segmentP(X0,sK20)
      | ~ ssList(X0) ),
    inference(definition_unfolding,[],[f447,f378]) ).

fof(f447,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0] :
      ( segmentP(X0,nil)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f57,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).

fof(f767,plain,
    spl69_15,
    inference(avatar_split_clause,[],[f613,f765]) ).

fof(f765,plain,
    ( spl69_15
  <=> ! [X0] :
        ( ~ memberP(sK20,X0)
        | ~ ssItem(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_15])]) ).

fof(f613,plain,
    ! [X0] :
      ( ~ memberP(sK20,X0)
      | ~ ssItem(X0) ),
    inference(definition_unfolding,[],[f392,f378]) ).

fof(f392,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

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

fof(f763,plain,
    spl69_14,
    inference(avatar_split_clause,[],[f668,f761]) ).

fof(f761,plain,
    ( spl69_14
  <=> ! [X1] : sP2(sK20,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_14])]) ).

fof(f668,plain,
    ! [X1] : sP2(sK20,X1),
    inference(equality_resolution,[],[f627]) ).

fof(f627,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | sK20 != X0 ),
    inference(definition_unfolding,[],[f441,f378]) ).

fof(f441,plain,
    ! [X0,X1] :
      ( sP2(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f271]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( ( sP2(X0,X1)
        | ( ( ~ lt(X1,hd(X0))
            | ~ strictorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( lt(X1,hd(X0))
          & strictorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f270]) ).

fof(f270,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP2(X1,X0) ) ),
    inference(flattening,[],[f269]) ).

fof(f269,plain,
    ! [X1,X0] :
      ( ( sP2(X1,X0)
        | ( ( ~ lt(X0,hd(X1))
            | ~ strictorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP2(X1,X0) ) ),
    inference(nnf_transformation,[],[f226]) ).

fof(f226,plain,
    ! [X1,X0] :
      ( sP2(X1,X0)
    <=> ( ( lt(X0,hd(X1))
          & strictorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f759,plain,
    spl69_13,
    inference(avatar_split_clause,[],[f666,f757]) ).

fof(f757,plain,
    ( spl69_13
  <=> ! [X1] : sP0(sK20,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_13])]) ).

fof(f666,plain,
    ! [X1] : sP0(sK20,X1),
    inference(equality_resolution,[],[f622]) ).

fof(f622,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sK20 != X0 ),
    inference(definition_unfolding,[],[f433,f378]) ).

fof(f433,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | nil != X0 ),
    inference(cnf_transformation,[],[f267]) ).

fof(f267,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ leq(X1,hd(X0))
            | ~ totalorderedP(X0)
            | nil = X0 )
          & nil != X0 ) )
      & ( ( leq(X1,hd(X0))
          & totalorderedP(X0)
          & nil != X0 )
        | nil = X0
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f266]) ).

fof(f266,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ( ( ~ leq(X0,hd(X1))
            | ~ totalorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP0(X1,X0) ) ),
    inference(flattening,[],[f265]) ).

fof(f265,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ( ( ~ leq(X0,hd(X1))
            | ~ totalorderedP(X1)
            | nil = X1 )
          & nil != X1 ) )
      & ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1
        | ~ sP0(X1,X0) ) ),
    inference(nnf_transformation,[],[f223]) ).

fof(f223,plain,
    ! [X1,X0] :
      ( sP0(X1,X0)
    <=> ( ( leq(X0,hd(X1))
          & totalorderedP(X1)
          & nil != X1 )
        | nil = X1 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f755,plain,
    spl69_12,
    inference(avatar_split_clause,[],[f601,f752]) ).

fof(f752,plain,
    ( spl69_12
  <=> neq(sK21,sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_12])]) ).

fof(f601,plain,
    neq(sK21,sK20),
    inference(definition_unfolding,[],[f381,f379,f378]) ).

fof(f379,plain,
    sK19 = sK21,
    inference(cnf_transformation,[],[f254]) ).

fof(f381,plain,
    neq(sK19,nil),
    inference(cnf_transformation,[],[f254]) ).

fof(f750,plain,
    ~ spl69_11,
    inference(avatar_split_clause,[],[f600,f747]) ).

fof(f600,plain,
    ~ frontsegP(sK21,sK20),
    inference(definition_unfolding,[],[f382,f379,f380]) ).

fof(f380,plain,
    sK18 = sK20,
    inference(cnf_transformation,[],[f254]) ).

fof(f382,plain,
    ~ frontsegP(sK19,sK18),
    inference(cnf_transformation,[],[f254]) ).

fof(f745,plain,
    spl69_10,
    inference(avatar_split_clause,[],[f611,f742]) ).

fof(f742,plain,
    ( spl69_10
  <=> totalorderedP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_10])]) ).

fof(f611,plain,
    totalorderedP(sK20),
    inference(definition_unfolding,[],[f390,f378]) ).

fof(f390,plain,
    totalorderedP(nil),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,axiom,
    totalorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).

fof(f740,plain,
    spl69_9,
    inference(avatar_split_clause,[],[f610,f737]) ).

fof(f737,plain,
    ( spl69_9
  <=> strictorderedP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_9])]) ).

fof(f610,plain,
    strictorderedP(sK20),
    inference(definition_unfolding,[],[f389,f378]) ).

fof(f389,plain,
    strictorderedP(nil),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,axiom,
    strictorderedP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).

fof(f735,plain,
    spl69_8,
    inference(avatar_split_clause,[],[f609,f732]) ).

fof(f732,plain,
    ( spl69_8
  <=> totalorderP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_8])]) ).

fof(f609,plain,
    totalorderP(sK20),
    inference(definition_unfolding,[],[f388,f378]) ).

fof(f388,plain,
    totalorderP(nil),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,axiom,
    totalorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).

fof(f730,plain,
    spl69_7,
    inference(avatar_split_clause,[],[f608,f727]) ).

fof(f727,plain,
    ( spl69_7
  <=> strictorderP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_7])]) ).

fof(f608,plain,
    strictorderP(sK20),
    inference(definition_unfolding,[],[f387,f378]) ).

fof(f387,plain,
    strictorderP(nil),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    strictorderP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).

fof(f725,plain,
    spl69_6,
    inference(avatar_split_clause,[],[f607,f722]) ).

fof(f722,plain,
    ( spl69_6
  <=> cyclefreeP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_6])]) ).

fof(f607,plain,
    cyclefreeP(sK20),
    inference(definition_unfolding,[],[f386,f378]) ).

fof(f386,plain,
    cyclefreeP(nil),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    cyclefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).

fof(f720,plain,
    spl69_5,
    inference(avatar_split_clause,[],[f606,f717]) ).

fof(f717,plain,
    ( spl69_5
  <=> duplicatefreeP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_5])]) ).

fof(f606,plain,
    duplicatefreeP(sK20),
    inference(definition_unfolding,[],[f385,f378]) ).

fof(f385,plain,
    duplicatefreeP(nil),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,axiom,
    duplicatefreeP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).

fof(f715,plain,
    spl69_4,
    inference(avatar_split_clause,[],[f605,f712]) ).

fof(f712,plain,
    ( spl69_4
  <=> equalelemsP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_4])]) ).

fof(f605,plain,
    equalelemsP(sK20),
    inference(definition_unfolding,[],[f384,f378]) ).

fof(f384,plain,
    equalelemsP(nil),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,axiom,
    equalelemsP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).

fof(f710,plain,
    ~ spl69_3,
    inference(avatar_split_clause,[],[f604,f707]) ).

fof(f707,plain,
    ( spl69_3
  <=> singletonP(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_3])]) ).

fof(f604,plain,
    ~ singletonP(sK20),
    inference(definition_unfolding,[],[f383,f378]) ).

fof(f383,plain,
    ~ singletonP(nil),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f705,plain,
    spl69_2,
    inference(avatar_split_clause,[],[f377,f702]) ).

fof(f377,plain,
    ssList(sK21),
    inference(cnf_transformation,[],[f254]) ).

fof(f700,plain,
    spl69_1,
    inference(avatar_split_clause,[],[f376,f697]) ).

fof(f697,plain,
    ( spl69_1
  <=> ssList(sK20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl69_1])]) ).

fof(f376,plain,
    ssList(sK20),
    inference(cnf_transformation,[],[f254]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWC349+1 : TPTP v8.2.0. Released v2.4.0.
% 0.04/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n003.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun May 19 03:50:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (26697)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (26700)WARNING: value z3 for option sas not known
% 0.22/0.38  % (26700)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38  % (26702)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39  % (26701)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39  % (26698)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39  % (26702)First to succeed.
% 0.22/0.39  % (26699)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39  % (26702)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26697"
% 0.22/0.39  % (26703)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.39  % (26702)Refutation found. Thanks to Tanya!
% 0.22/0.39  % SZS status Theorem for theBenchmark
% 0.22/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39  % (26702)------------------------------
% 0.22/0.39  % (26702)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.39  % (26702)Termination reason: Refutation
% 0.22/0.39  
% 0.22/0.39  % (26702)Memory used [KB]: 1263
% 0.22/0.39  % (26702)Time elapsed: 0.009 s
% 0.22/0.39  % (26702)Instructions burned: 20 (million)
% 0.22/0.39  % (26697)Success in time 0.012 s
%------------------------------------------------------------------------------