%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SCT115+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n032.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:22:59 EDT 2023

% Result   : Theorem 159.74s 23.23s
% Output   : Refutation 159.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   47
% Syntax   : Number of formulae    :  273 (   3 unt;   0 def)
%            Number of atoms       : 1230 ( 379 equ)
%            Maximal formula atoms :   47 (   4 avg)
%            Number of connectives : 1567 ( 610   ~; 588   |; 292   &)
%                                         (  39 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   42 (  40 usr;  37 prp; 0-3 aty)
%            Number of functors    :   15 (  15 usr;   9 con; 0-4 aty)
%            Number of variables   :  218 (; 179   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f241535,plain,
    $false,
    inference(avatar_sat_refutation,[],[f3206,f3324,f3345,f3365,f3376,f3502,f3720,f5965,f6261,f6378,f6739,f6829,f7800,f8388,f87519,f88185,f90193,f91107,f99452,f102191,f102393,f102394,f103653,f103899,f194972,f196894,f208443,f225214,f225215,f225455,f225602,f235597,f237006,f239929,f240735,f240885,f241126,f241297,f241531,f241534]) ).

fof(f241534,plain,
    ( ~ spl105_4
    | spl105_11
    | ~ spl105_14
    | spl105_15
    | spl105_1283 ),
    inference(avatar_contradiction_clause,[],[f241533]) ).

fof(f241533,plain,
    ( $false
    | ~ spl105_4
    | spl105_11
    | ~ spl105_14
    | spl105_15
    | spl105_1283 ),
    inference(subsumption_resolution,[],[f241532,f3375]) ).

fof(f3375,plain,
    ( v_y != sK7
    | spl105_15 ),
    inference(avatar_component_clause,[],[f3374]) ).

fof(f3374,plain,
    ( spl105_15
  <=> v_y = sK7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_15])]) ).

fof(f241532,plain,
    ( v_y = sK7
    | ~ spl105_4
    | spl105_11
    | ~ spl105_14
    | spl105_1283 ),
    inference(subsumption_resolution,[],[f240942,f241527]) ).

fof(f241527,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK7),v_y))
    | ~ spl105_4
    | spl105_11
    | ~ spl105_14 ),
    inference(forward_literal_rewriting,[],[f241526,f2634]) ).

fof(f2634,plain,
    ! [X2,X3,X0,X1,X4] :
      ( c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2)
      | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0)) ),
    inference(cnf_transformation,[],[f1805]) ).

fof(f1805,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0))
        | ~ c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2) )
      & ( c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2)
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0)) ) ),
    inference(nnf_transformation,[],[f1000]) ).

fof(f1000,plain,
    ! [X0,X1,X2,X3,X4] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0))
    <=> c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X9,X10,X11,X12,X4] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X12,X11),X10),X9))
    <=> c_member(tc_prod(X4,X12),c_Product__Type_OPair(X4,X12,X10,X9),X11) ),
    file('/export/starexec/sandbox2/tmp/tmp.v8om2dSjm5/Vampire---4.8_28787',fact_in__rel__def) ).

fof(f241526,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_y),v_L)
    | ~ spl105_4
    | spl105_11
    | ~ spl105_14 ),
    inference(subsumption_resolution,[],[f241525,f3080]) ).

fof(f3080,plain,
    ( sP2
    | ~ spl105_4 ),
    inference(avatar_component_clause,[],[f3079]) ).

fof(f3079,plain,
    ( spl105_4
  <=> sP2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_4])]) ).

fof(f241525,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_y),v_L)
    | ~ sP2
    | spl105_11
    | ~ spl105_14 ),
    inference(subsumption_resolution,[],[f241524,f3341]) ).

fof(f3341,plain,
    ( v_x != sK7
    | spl105_11 ),
    inference(avatar_component_clause,[],[f3340]) ).

fof(f3340,plain,
    ( spl105_11
  <=> v_x = sK7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_11])]) ).

fof(f241524,plain,
    ( v_x = sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_y),v_L)
    | ~ sP2
    | ~ spl105_14 ),
    inference(trivial_inequality_removal,[],[f241493]) ).

fof(f241493,plain,
    ( v_x != v_x
    | v_x = sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_y),v_L)
    | ~ sP2
    | ~ spl105_14 ),
    inference(superposition,[],[f1850,f240884]) ).

fof(f240884,plain,
    ( v_x = sK8
    | ~ spl105_14 ),
    inference(avatar_component_clause,[],[f3371]) ).

fof(f3371,plain,
    ( spl105_14
  <=> v_x = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_14])]) ).

fof(f1850,plain,
    ( v_x = sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_y),v_L)
    | v_x != sK8
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f1534,plain,
    ( ( ( v_x = sK7
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK7),v_L)
        | v_x != sK8 )
      & ( v_x = sK8
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,v_y),v_L)
        | v_x != sK7 )
      & ( v_x = sK7
        | v_x = sK8
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,sK7),v_L) )
      & ( v_y != sK7
        | v_x != sK8 )
      & ( v_x = sK8
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK8),v_L)
        | v_x != sK7 )
      & ( v_x = sK7
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_y),v_L)
        | v_x != sK8 )
      & ( v_x = sK8
        | v_x = sK7
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK8),v_L) )
      & ( v_y != sK8
        | v_x != sK7 )
      & sK7 != sK8 )
    | ~ sP2 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f1532,f1533]) ).

fof(f1533,plain,
    ( ? [X0,X1] :
        ( ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) )
        & ( v_y != X0
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X1),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
        & ( v_y != X1
          | v_x != X0 )
        & X0 != X1 )
   => ( ( v_x = sK7
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK7),v_L)
        | v_x != sK8 )
      & ( v_x = sK8
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,v_y),v_L)
        | v_x != sK7 )
      & ( v_x = sK7
        | v_x = sK8
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,sK7),v_L) )
      & ( v_y != sK7
        | v_x != sK8 )
      & ( v_x = sK8
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK8),v_L)
        | v_x != sK7 )
      & ( v_x = sK7
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,v_y),v_L)
        | v_x != sK8 )
      & ( v_x = sK8
        | v_x = sK7
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK8),v_L) )
      & ( v_y != sK8
        | v_x != sK7 )
      & sK7 != sK8 ) ),
    introduced(choice_axiom,[]) ).

fof(f1532,plain,
    ( ? [X0,X1] :
        ( ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) )
        & ( v_y != X0
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X1),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
        & ( v_y != X1
          | v_x != X0 )
        & X0 != X1 )
    | ~ sP2 ),
    inference(nnf_transformation,[],[f1524]) ).

fof(f1524,plain,
    ( ? [X0,X1] :
        ( ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) )
        & ( v_y != X0
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X1),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
        & ( v_y != X1
          | v_x != X0 )
        & X0 != X1 )
    | ~ sP2 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f240942,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK7),v_y))
    | v_y = sK7
    | spl105_1283 ),
    inference(resolution,[],[f240934,f2849]) ).

fof(f2849,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X1),X0))
      | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),X1))
      | X0 = X1 ),
    inference(forward_literal_rewriting,[],[f2848,f2635]) ).

fof(f2635,plain,
    ! [X2,X3,X0,X1,X4] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X4,X3,X2),X1),X0))
      | ~ c_member(tc_prod(X4,X3),c_Product__Type_OPair(X4,X3,X1,X0),X2) ),
    inference(cnf_transformation,[],[f1805]) ).

fof(f2848,plain,
    ! [X0,X1] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X1),X0))
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
      | X0 = X1 ),
    inference(forward_literal_rewriting,[],[f1888,f2635]) ).

fof(f1888,plain,
    ! [X0,X1] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f1043]) ).

fof(f1043,plain,
    ( ! [X0,X1] :
        ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
        | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
        | X0 = X1 )
    & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
    & ! [X3,X4] :
        ( ! [X5] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X5),v_L)
            | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L) )
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) ),
    inference(flattening,[],[f1042]) ).

fof(f1042,plain,
    ( ! [X0,X1] :
        ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
        | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
        | X0 = X1 )
    & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
    & ! [X3,X4] :
        ( ! [X5] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X5),v_L)
            | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L) )
        | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) ),
    inference(ennf_transformation,[],[f531]) ).

fof(f531,plain,
    ( ! [X0,X1] :
        ( X0 != X1
       => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L)
          | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) ) )
    & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
    & ! [X3,X4] :
        ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L)
       => ! [X5] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
           => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X5),v_L) ) ) ),
    inference(rectify,[],[f527]) ).

fof(f527,axiom,
    ( ! [X2,X35] :
        ( X2 != X35
       => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,X2),v_L)
          | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X35),v_L) ) )
    & ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L)
    & ! [X2,X35] :
        ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X35),v_L)
       => ! [X34] :
            ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,X34),v_L)
           => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X34),v_L) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.v8om2dSjm5/Vampire---4.8_28787',conj_1) ).

fof(f240934,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK7))
    | spl105_1283 ),
    inference(avatar_component_clause,[],[f240933]) ).

fof(f240933,plain,
    ( spl105_1283
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_1283])]) ).

fof(f241531,plain,
    ( ~ spl105_14
    | spl105_11
    | ~ spl105_1283
    | ~ spl105_4 ),
    inference(avatar_split_clause,[],[f3320,f3079,f240933,f3340,f3371]) ).

fof(f3320,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK7))
    | v_x = sK7
    | v_x != sK8
    | ~ spl105_4 ),
    inference(forward_literal_rewriting,[],[f3314,f2634]) ).

fof(f3314,plain,
    ( v_x = sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK7),v_L)
    | v_x != sK8
    | ~ spl105_4 ),
    inference(resolution,[],[f3080,f1855]) ).

fof(f1855,plain,
    ( v_x = sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK7),v_L)
    | v_x != sK8
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f241297,plain,
    ( ~ spl105_4
    | ~ spl105_11
    | spl105_14
    | ~ spl105_1273 ),
    inference(avatar_contradiction_clause,[],[f241296]) ).

fof(f241296,plain,
    ( $false
    | ~ spl105_4
    | ~ spl105_11
    | spl105_14
    | ~ spl105_1273 ),
    inference(subsumption_resolution,[],[f3372,f241135]) ).

fof(f241135,plain,
    ( v_x = sK8
    | ~ spl105_4
    | ~ spl105_11
    | ~ spl105_1273 ),
    inference(subsumption_resolution,[],[f241134,f239928]) ).

fof(f239928,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),v_y))
    | ~ spl105_1273 ),
    inference(avatar_component_clause,[],[f238425]) ).

fof(f238425,plain,
    ( spl105_1273
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),v_y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_1273])]) ).

fof(f241134,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),v_y))
    | v_x = sK8
    | ~ spl105_4
    | ~ spl105_11 ),
    inference(forward_literal_rewriting,[],[f241133,f2634]) ).

fof(f241133,plain,
    ( v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,v_y),v_L)
    | ~ spl105_4
    | ~ spl105_11 ),
    inference(subsumption_resolution,[],[f241025,f3080]) ).

fof(f241025,plain,
    ( v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,v_y),v_L)
    | ~ sP2
    | ~ spl105_11 ),
    inference(trivial_inequality_removal,[],[f238389]) ).

fof(f238389,plain,
    ( v_x != v_x
    | v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,v_y),v_L)
    | ~ sP2
    | ~ spl105_11 ),
    inference(superposition,[],[f1854,f238381]) ).

fof(f238381,plain,
    ( v_x = sK7
    | ~ spl105_11 ),
    inference(avatar_component_clause,[],[f3340]) ).

fof(f1854,plain,
    ( v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,v_y),v_L)
    | v_x != sK7
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f3372,plain,
    ( v_x != sK8
    | spl105_14 ),
    inference(avatar_component_clause,[],[f3371]) ).

fof(f241126,plain,
    ( spl105_10
    | ~ spl105_11
    | ~ spl105_14 ),
    inference(avatar_contradiction_clause,[],[f241125]) ).

fof(f241125,plain,
    ( $false
    | spl105_10
    | ~ spl105_11
    | ~ spl105_14 ),
    inference(subsumption_resolution,[],[f238381,f240895]) ).

fof(f240895,plain,
    ( v_x != sK7
    | spl105_10
    | ~ spl105_14 ),
    inference(superposition,[],[f3327,f240884]) ).

fof(f3327,plain,
    ( sK7 != sK8
    | spl105_10 ),
    inference(avatar_component_clause,[],[f3326]) ).

fof(f3326,plain,
    ( spl105_10
  <=> sK7 = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_10])]) ).

fof(f240885,plain,
    ( spl105_14
    | ~ spl105_4
    | spl105_11
    | ~ spl105_17 ),
    inference(avatar_split_clause,[],[f240834,f3504,f3340,f3079,f3371]) ).

fof(f3504,plain,
    ( spl105_17
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),sK7)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_17])]) ).

fof(f240834,plain,
    ( v_x = sK8
    | ~ spl105_4
    | spl105_11
    | ~ spl105_17 ),
    inference(subsumption_resolution,[],[f240833,f6738]) ).

fof(f6738,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),sK7))
    | ~ spl105_17 ),
    inference(avatar_component_clause,[],[f3504]) ).

fof(f240833,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),sK7))
    | v_x = sK8
    | ~ spl105_4
    | spl105_11 ),
    inference(forward_literal_rewriting,[],[f240832,f2634]) ).

fof(f240832,plain,
    ( v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,sK7),v_L)
    | ~ spl105_4
    | spl105_11 ),
    inference(subsumption_resolution,[],[f240779,f3080]) ).

fof(f240779,plain,
    ( v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,sK7),v_L)
    | ~ sP2
    | spl105_11 ),
    inference(trivial_inequality_removal,[],[f3348]) ).

fof(f3348,plain,
    ( v_x != v_x
    | v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,sK7),v_L)
    | ~ sP2
    | spl105_11 ),
    inference(superposition,[],[f3341,f1853]) ).

fof(f1853,plain,
    ( v_x = sK7
    | v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK8,sK7),v_L)
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f240735,plain,
    ( ~ spl105_11
    | ~ spl105_1272
    | ~ spl105_4
    | spl105_10 ),
    inference(avatar_split_clause,[],[f3336,f3326,f3079,f238420,f3340]) ).

fof(f238420,plain,
    ( spl105_1272
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_1272])]) ).

fof(f3336,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK8))
    | v_x != sK7
    | ~ spl105_4
    | spl105_10 ),
    inference(forward_literal_rewriting,[],[f3335,f2634]) ).

fof(f3335,plain,
    ( v_x != sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK8),v_L)
    | ~ spl105_4
    | spl105_10 ),
    inference(subsumption_resolution,[],[f3334,f3080]) ).

fof(f3334,plain,
    ( v_x != sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK8),v_L)
    | ~ sP2
    | spl105_10 ),
    inference(duplicate_literal_removal,[],[f3330]) ).

fof(f3330,plain,
    ( v_x != sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK8),v_L)
    | v_x != sK7
    | ~ sP2
    | spl105_10 ),
    inference(superposition,[],[f3327,f1851]) ).

fof(f1851,plain,
    ( v_x = sK8
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK8),v_L)
    | v_x != sK7
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f239929,plain,
    ( spl105_1273
    | spl105_12
    | spl105_1272 ),
    inference(avatar_split_clause,[],[f239458,f238420,f3343,f238425]) ).

fof(f3343,plain,
    ( spl105_12
  <=> v_y = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_12])]) ).

fof(f239458,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),v_y))
    | spl105_12
    | spl105_1272 ),
    inference(subsumption_resolution,[],[f238430,f3344]) ).

fof(f3344,plain,
    ( v_y != sK8
    | spl105_12 ),
    inference(avatar_component_clause,[],[f3343]) ).

fof(f238430,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),v_y))
    | v_y = sK8
    | spl105_1272 ),
    inference(resolution,[],[f238421,f2849]) ).

fof(f238421,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK8))
    | spl105_1272 ),
    inference(avatar_component_clause,[],[f238420]) ).

fof(f237006,plain,
    ( spl105_34
    | ~ spl105_436
    | ~ spl105_1266 ),
    inference(avatar_split_clause,[],[f236739,f235595,f103651,f4988]) ).

fof(f4988,plain,
    ( spl105_34
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_34])]) ).

fof(f103651,plain,
    ( spl105_436
  <=> ! [X0] : c_member(X0,v_y,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK9(sK12))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_436])]) ).

fof(f235595,plain,
    ( spl105_1266
  <=> ! [X2,X1] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),X1))
        | ~ c_member(X2,X1,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK9(sK12))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_1266])]) ).

fof(f236739,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | ~ spl105_436
    | ~ spl105_1266 ),
    inference(resolution,[],[f235596,f103652]) ).

fof(f103652,plain,
    ( ! [X0] : c_member(X0,v_y,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK9(sK12)))
    | ~ spl105_436 ),
    inference(avatar_component_clause,[],[f103651]) ).

fof(f235596,plain,
    ( ! [X2,X1] :
        ( ~ c_member(X2,X1,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK9(sK12)))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),X1)) )
    | ~ spl105_1266 ),
    inference(avatar_component_clause,[],[f235595]) ).

fof(f235597,plain,
    ( spl105_1266
    | ~ spl105_278 ),
    inference(avatar_split_clause,[],[f90447,f90327,f235595]) ).

fof(f90327,plain,
    ( spl105_278
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK9(sK12))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_278])]) ).

fof(f90447,plain,
    ( ! [X2,X1] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),X1))
        | ~ c_member(X2,X1,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK9(sK12))) )
    | ~ spl105_278 ),
    inference(resolution,[],[f90328,f3995]) ).

fof(f3995,plain,
    ! [X90,X88,X89,X87] :
      ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X87),X88))
      | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X87),X89))
      | ~ c_member(X90,X89,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X88)) ),
    inference(resolution,[],[f2853,f2230]) ).

fof(f2230,plain,
    ! [X2,X0,X1] :
      ( hBOOL(hAPP(X0,X1))
      | ~ c_member(X2,X1,X0) ),
    inference(cnf_transformation,[],[f1651]) ).

fof(f1651,plain,
    ! [X0,X1,X2] :
      ( ( c_member(X2,X1,X0)
        | ~ hBOOL(hAPP(X0,X1)) )
      & ( hBOOL(hAPP(X0,X1))
        | ~ c_member(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f775]) ).

fof(f775,plain,
    ! [X0,X1,X2] :
      ( c_member(X2,X1,X0)
    <=> hBOOL(hAPP(X0,X1)) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X6,X10,X4] :
      ( c_member(X4,X10,X6)
    <=> hBOOL(hAPP(X6,X10)) ),
    file('/export/starexec/sandbox2/tmp/tmp.v8om2dSjm5/Vampire---4.8_28787',fact_mem__def) ).

fof(f2853,plain,
    ! [X3,X4,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X4),X5))
      | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),X4))
      | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),X5)) ),
    inference(forward_literal_rewriting,[],[f2852,f2634]) ).

fof(f2852,plain,
    ! [X3,X4,X5] :
      ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X4),X5))
      | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),X5))
      | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ),
    inference(forward_literal_rewriting,[],[f2851,f2634]) ).

fof(f2851,plain,
    ! [X3,X4,X5] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),X5))
      | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
      | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ),
    inference(forward_literal_rewriting,[],[f1886,f2635]) ).

fof(f1886,plain,
    ! [X3,X4,X5] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X5),v_L)
      | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X4,X5),v_L)
      | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ),
    inference(cnf_transformation,[],[f1043]) ).

fof(f90328,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK9(sK12)))
    | ~ spl105_278 ),
    inference(avatar_component_clause,[],[f90327]) ).

fof(f225602,plain,
    ( spl105_34
    | ~ spl105_280
    | ~ spl105_3 ),
    inference(avatar_split_clause,[],[f3305,f3076,f90382,f4988]) ).

fof(f90382,plain,
    ( spl105_280
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK9(sK12))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_280])]) ).

fof(f3076,plain,
    ( spl105_3
  <=> sP1(sK12,sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_3])]) ).

fof(f3305,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK9(sK12)))
    | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | ~ spl105_3 ),
    inference(forward_literal_rewriting,[],[f3304,f2634]) ).

fof(f3304,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK9(sK12)),v_L)
    | ~ spl105_3 ),
    inference(forward_literal_rewriting,[],[f3294,f2635]) ).

fof(f3294,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,v_y),v_L)
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK9(sK12)),v_L)
    | ~ spl105_3 ),
    inference(resolution,[],[f3077,f1866]) ).

fof(f1866,plain,
    ! [X0,X1] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
      | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK9(X0)),v_L)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1538]) ).

fof(f1538,plain,
    ! [X0,X1] :
      ( ( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
            & v_x = sK9(X0) )
          | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK9(X0)),v_L)
            & v_y != sK9(X0)
            & v_x != sK9(X0)
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK9(X0)),v_L) ) )
        & v_x != X0
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
        & v_x = X1 )
      | ~ sP1(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f1536,f1537]) ).

fof(f1537,plain,
    ! [X0] :
      ( ? [X2] :
          ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
            & v_x = X2 )
          | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X2),v_L)
            & v_y != X2
            & v_x != X2
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) ) )
     => ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          & v_x = sK9(X0) )
        | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK9(X0)),v_L)
          & v_y != sK9(X0)
          & v_x != sK9(X0)
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK9(X0)),v_L) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1536,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
              & v_x = X2 )
            | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X2),v_L)
              & v_y != X2
              & v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L) ) )
        & v_x != X0
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
        & v_x = X1 )
      | ~ sP1(X0,X1) ),
    inference(rectify,[],[f1535]) ).

fof(f1535,plain,
    ! [X3,X2] :
      ( ( ? [X4] :
            ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
              & v_x = X4 )
            | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X4),v_L)
              & v_y != X4
              & v_x != X4
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) )
        & v_x != X3
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X3),v_L)
        & v_x = X2 )
      | ~ sP1(X3,X2) ),
    inference(nnf_transformation,[],[f1523]) ).

fof(f1523,plain,
    ! [X3,X2] :
      ( ( ? [X4] :
            ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
              & v_x = X4 )
            | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X4),v_L)
              & v_y != X4
              & v_x != X4
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) )
        & v_x != X3
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X3),v_L)
        & v_x = X2 )
      | ~ sP1(X3,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f3077,plain,
    ( sP1(sK12,sK11)
    | ~ spl105_3 ),
    inference(avatar_component_clause,[],[f3076]) ).

fof(f225455,plain,
    ( spl105_34
    | spl105_278
    | ~ spl105_3 ),
    inference(avatar_split_clause,[],[f3301,f3076,f90327,f4988]) ).

fof(f3301,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK9(sK12)))
    | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | ~ spl105_3 ),
    inference(forward_literal_rewriting,[],[f3300,f2635]) ).

fof(f3300,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK9(sK12)),v_L)
    | ~ spl105_3 ),
    inference(forward_literal_rewriting,[],[f3291,f2635]) ).

fof(f3291,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,v_y),v_L)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK9(sK12)),v_L)
    | ~ spl105_3 ),
    inference(resolution,[],[f3077,f1863]) ).

fof(f1863,plain,
    ! [X0,X1] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK9(X0)),v_L)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1538]) ).

fof(f225215,plain,
    ( spl105_63
    | ~ spl105_45
    | ~ spl105_231 ),
    inference(avatar_split_clause,[],[f88631,f87002,f5963,f8098]) ).

fof(f8098,plain,
    ( spl105_63
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_63])]) ).

fof(f5963,plain,
    ( spl105_45
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_45])]) ).

fof(f87002,plain,
    ( spl105_231
  <=> ! [X0] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK11))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_231])]) ).

fof(f88631,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK12))
    | ~ spl105_45
    | ~ spl105_231 ),
    inference(resolution,[],[f87003,f5964]) ).

fof(f5964,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK11))
    | ~ spl105_45 ),
    inference(avatar_component_clause,[],[f5963]) ).

fof(f87003,plain,
    ( ! [X0] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK11))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK12)) )
    | ~ spl105_231 ),
    inference(avatar_component_clause,[],[f87002]) ).

fof(f225214,plain,
    ( ~ spl105_276
    | spl105_34
    | ~ spl105_3 ),
    inference(avatar_split_clause,[],[f3303,f3076,f4988,f90317]) ).

fof(f90317,plain,
    ( spl105_276
  <=> v_y = sK9(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_276])]) ).

fof(f3303,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | v_y != sK9(sK12)
    | ~ spl105_3 ),
    inference(forward_literal_rewriting,[],[f3293,f2635]) ).

fof(f3293,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,v_y),v_L)
    | v_y != sK9(sK12)
    | ~ spl105_3 ),
    inference(resolution,[],[f3077,f1865]) ).

fof(f1865,plain,
    ! [X0,X1] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
      | v_y != sK9(X0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1538]) ).

fof(f208443,plain,
    ( spl105_22
    | ~ spl105_3 ),
    inference(avatar_split_clause,[],[f199250,f3076,f4112]) ).

fof(f4112,plain,
    ( spl105_22
  <=> sP1(sK12,v_x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_22])]) ).

fof(f199250,plain,
    ( sP1(sK12,v_x)
    | ~ spl105_3 ),
    inference(forward_demodulation,[],[f3077,f3286]) ).

fof(f3286,plain,
    ( v_x = sK11
    | ~ spl105_3 ),
    inference(resolution,[],[f3077,f1856]) ).

fof(f1856,plain,
    ! [X0,X1] :
      ( v_x = X1
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1538]) ).

fof(f196894,plain,
    ( spl105_37
    | ~ spl105_263
    | ~ spl105_442 ),
    inference(avatar_contradiction_clause,[],[f196893]) ).

fof(f196893,plain,
    ( $false
    | spl105_37
    | ~ spl105_263
    | ~ spl105_442 ),
    inference(subsumption_resolution,[],[f196658,f5200]) ).

fof(f5200,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK10(sK11,sK12)))
    | spl105_37 ),
    inference(avatar_component_clause,[],[f5199]) ).

fof(f5199,plain,
    ( spl105_37
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK10(sK11,sK12))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_37])]) ).

fof(f196658,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK10(sK11,sK12)))
    | ~ spl105_263
    | ~ spl105_442 ),
    inference(resolution,[],[f88184,f103898]) ).

fof(f103898,plain,
    ( ! [X4] : c_member(X4,sK10(sK11,sK12),hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12))
    | ~ spl105_442 ),
    inference(avatar_component_clause,[],[f103897]) ).

fof(f103897,plain,
    ( spl105_442
  <=> ! [X4] : c_member(X4,sK10(sK11,sK12),hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_442])]) ).

fof(f88184,plain,
    ( ! [X91,X92] :
        ( ~ c_member(X92,X91,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),X91)) )
    | ~ spl105_263 ),
    inference(avatar_component_clause,[],[f88183]) ).

fof(f88183,plain,
    ( spl105_263
  <=> ! [X91,X92] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),X91))
        | ~ c_member(X92,X91,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_263])]) ).

fof(f194972,plain,
    ( spl105_231
    | ~ spl105_21 ),
    inference(avatar_split_clause,[],[f4144,f4103,f87002]) ).

fof(f4103,plain,
    ( spl105_21
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK12)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_21])]) ).

fof(f4144,plain,
    ( ! [X0] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK11))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK12)) )
    | ~ spl105_21 ),
    inference(resolution,[],[f4104,f2853]) ).

fof(f4104,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK12))
    | ~ spl105_21 ),
    inference(avatar_component_clause,[],[f4103]) ).

fof(f103899,plain,
    ( spl105_442
    | ~ spl105_24 ),
    inference(avatar_split_clause,[],[f87778,f4226,f103897]) ).

fof(f4226,plain,
    ( spl105_24
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK10(sK11,sK12))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_24])]) ).

fof(f87778,plain,
    ( ! [X4] : c_member(X4,sK10(sK11,sK12),hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12))
    | ~ spl105_24 ),
    inference(resolution,[],[f4227,f2231]) ).

fof(f2231,plain,
    ! [X2,X0,X1] :
      ( c_member(X2,X1,X0)
      | ~ hBOOL(hAPP(X0,X1)) ),
    inference(cnf_transformation,[],[f1651]) ).

fof(f4227,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK10(sK11,sK12)))
    | ~ spl105_24 ),
    inference(avatar_component_clause,[],[f4226]) ).

fof(f103653,plain,
    ( spl105_436
    | spl105_276
    | spl105_280 ),
    inference(avatar_split_clause,[],[f90601,f90382,f90317,f103651]) ).

fof(f90601,plain,
    ( ! [X0] : c_member(X0,v_y,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK9(sK12)))
    | spl105_276
    | spl105_280 ),
    inference(subsumption_resolution,[],[f90555,f90318]) ).

fof(f90318,plain,
    ( v_y != sK9(sK12)
    | spl105_276 ),
    inference(avatar_component_clause,[],[f90317]) ).

fof(f90555,plain,
    ( ! [X0] :
        ( v_y = sK9(sK12)
        | c_member(X0,v_y,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK9(sK12))) )
    | spl105_280 ),
    inference(resolution,[],[f90383,f3396]) ).

fof(f3396,plain,
    ! [X2,X3,X1] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X1),X2))
      | X1 = X2
      | c_member(X3,X1,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X2)) ),
    inference(resolution,[],[f2849,f2231]) ).

fof(f90383,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK9(sK12)))
    | spl105_280 ),
    inference(avatar_component_clause,[],[f90382]) ).

fof(f102394,plain,
    ( spl105_24
    | ~ spl105_1
    | ~ spl105_13 ),
    inference(avatar_split_clause,[],[f3976,f3363,f3070,f4226]) ).

fof(f3070,plain,
    ( spl105_1
  <=> sP0(sK11,sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_1])]) ).

fof(f3363,plain,
    ( spl105_13
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),v_y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_13])]) ).

fof(f3976,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK10(sK11,sK12)))
    | ~ spl105_1
    | ~ spl105_13 ),
    inference(forward_literal_rewriting,[],[f3975,f2635]) ).

fof(f3975,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK10(sK11,sK12)),v_L)
    | ~ spl105_1
    | ~ spl105_13 ),
    inference(subsumption_resolution,[],[f3974,f3364]) ).

fof(f3364,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),v_y))
    | ~ spl105_13 ),
    inference(avatar_component_clause,[],[f3363]) ).

fof(f3974,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),v_y))
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK10(sK11,sK12)),v_L)
    | ~ spl105_1 ),
    inference(forward_literal_rewriting,[],[f3963,f2634]) ).

fof(f3963,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,v_y),v_L)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK10(sK11,sK12)),v_L)
    | ~ spl105_1 ),
    inference(resolution,[],[f3071,f1876]) ).

fof(f1876,plain,
    ! [X0,X1] :
      ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,sK10(X0,X1)),v_L)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1542]) ).

fof(f1542,plain,
    ! [X0,X1] :
      ( ( ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
            & v_x = sK10(X0,X1) )
          | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK10(X0,X1)),v_L)
            & v_x != sK10(X0,X1)
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,sK10(X0,X1)),v_L) ) )
        & v_x != X1
        & v_x != X0
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f1540,f1541]) ).

fof(f1541,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
            & v_x = X2 )
          | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
            & v_x != X2
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L) ) )
     => ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
          & v_x = sK10(X0,X1) )
        | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK10(X0,X1)),v_L)
          & v_x != sK10(X0,X1)
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,sK10(X0,X1)),v_L) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f1540,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
              & v_x = X2 )
            | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
              & v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_L) ) )
        & v_x != X1
        & v_x != X0
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f1539]) ).

fof(f1539,plain,
    ! [X2,X3] :
      ( ( ? [X6] :
            ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
              & v_x = X6 )
            | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X6),v_L)
              & v_x != X6
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X6),v_L) ) )
        & v_x != X3
        & v_x != X2
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_L) )
      | ~ sP0(X2,X3) ),
    inference(nnf_transformation,[],[f1522]) ).

fof(f1522,plain,
    ! [X2,X3] :
      ( ( ? [X6] :
            ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
              & v_x = X6 )
            | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X6),v_L)
              & v_x != X6
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X6),v_L) ) )
        & v_x != X3
        & v_x != X2
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_L) )
      | ~ sP0(X2,X3) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f3071,plain,
    ( sP0(sK11,sK12)
    | ~ spl105_1 ),
    inference(avatar_component_clause,[],[f3070]) ).

fof(f102393,plain,
    ( spl105_7
    | ~ spl105_13
    | ~ spl105_409 ),
    inference(avatar_split_clause,[],[f100357,f99450,f3363,f3204]) ).

fof(f3204,plain,
    ( spl105_7
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK13)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_7])]) ).

fof(f99450,plain,
    ( spl105_409
  <=> ! [X3] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),v_y))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),sK13)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_409])]) ).

fof(f100357,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK13))
    | ~ spl105_13
    | ~ spl105_409 ),
    inference(resolution,[],[f99451,f3364]) ).

fof(f99451,plain,
    ( ! [X3] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),v_y))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),sK13)) )
    | ~ spl105_409 ),
    inference(avatar_component_clause,[],[f99450]) ).

fof(f102191,plain,
    ( spl105_21
    | ~ spl105_1 ),
    inference(avatar_split_clause,[],[f3966,f3070,f4103]) ).

fof(f3966,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK12))
    | ~ spl105_1 ),
    inference(forward_literal_rewriting,[],[f3957,f2635]) ).

fof(f3957,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK12),v_L)
    | ~ spl105_1 ),
    inference(resolution,[],[f3071,f1867]) ).

fof(f1867,plain,
    ! [X0,X1] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1542]) ).

fof(f99452,plain,
    ( spl105_409
    | ~ spl105_9 ),
    inference(avatar_split_clause,[],[f96298,f3322,f99450]) ).

fof(f3322,plain,
    ( spl105_9
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK13)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_9])]) ).

fof(f96298,plain,
    ( ! [X3] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),v_y))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X3),sK13)) )
    | ~ spl105_9 ),
    inference(resolution,[],[f3323,f2853]) ).

fof(f3323,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK13))
    | ~ spl105_9 ),
    inference(avatar_component_clause,[],[f3322]) ).

fof(f91107,plain,
    ( spl105_63
    | ~ spl105_22 ),
    inference(avatar_split_clause,[],[f90259,f4112,f8098]) ).

fof(f90259,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK12))
    | ~ spl105_22 ),
    inference(forward_literal_rewriting,[],[f90250,f2635]) ).

fof(f90250,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK12),v_L)
    | ~ spl105_22 ),
    inference(resolution,[],[f4113,f1857]) ).

fof(f1857,plain,
    ! [X0,X1] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1538]) ).

fof(f4113,plain,
    ( sP1(sK12,v_x)
    | ~ spl105_22 ),
    inference(avatar_component_clause,[],[f4112]) ).

fof(f90193,plain,
    ( ~ spl105_63
    | ~ spl105_247 ),
    inference(avatar_contradiction_clause,[],[f90192]) ).

fof(f90192,plain,
    ( $false
    | ~ spl105_63
    | ~ spl105_247 ),
    inference(subsumption_resolution,[],[f90132,f2850]) ).

fof(f2850,plain,
    ! [X2] : ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X2),X2)),
    inference(forward_literal_rewriting,[],[f1887,f2634]) ).

fof(f1887,plain,
    ! [X2] : ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X2),v_L),
    inference(cnf_transformation,[],[f1043]) ).

fof(f90132,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),v_y))
    | ~ spl105_63
    | ~ spl105_247 ),
    inference(resolution,[],[f87518,f8099]) ).

fof(f8099,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK12))
    | ~ spl105_63 ),
    inference(avatar_component_clause,[],[f8098]) ).

fof(f87518,plain,
    ( ! [X0] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK12))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),v_y)) )
    | ~ spl105_247 ),
    inference(avatar_component_clause,[],[f87517]) ).

fof(f87517,plain,
    ( spl105_247
  <=> ! [X0] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK12))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),v_y)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_247])]) ).

fof(f88185,plain,
    ( spl105_263
    | ~ spl105_21 ),
    inference(avatar_split_clause,[],[f9440,f4103,f88183]) ).

fof(f9440,plain,
    ( ! [X91,X92] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),X91))
        | ~ c_member(X92,X91,hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12)) )
    | ~ spl105_21 ),
    inference(resolution,[],[f3995,f4104]) ).

fof(f87519,plain,
    ( spl105_247
    | ~ spl105_34 ),
    inference(avatar_split_clause,[],[f4991,f4988,f87517]) ).

fof(f4991,plain,
    ( ! [X0] :
        ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),sK12))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),X0),v_y)) )
    | ~ spl105_34 ),
    inference(resolution,[],[f4989,f2853]) ).

fof(f4989,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | ~ spl105_34 ),
    inference(avatar_component_clause,[],[f4988]) ).

fof(f8388,plain,
    ( spl105_63
    | ~ spl105_60 ),
    inference(avatar_split_clause,[],[f7810,f7798,f8098]) ).

fof(f7798,plain,
    ( spl105_60
  <=> sP0(v_y,sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_60])]) ).

fof(f7810,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK12))
    | ~ spl105_60 ),
    inference(forward_literal_rewriting,[],[f7801,f2635]) ).

fof(f7801,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK12),v_L)
    | ~ spl105_60 ),
    inference(resolution,[],[f7799,f1867]) ).

fof(f7799,plain,
    ( sP0(v_y,sK12)
    | ~ spl105_60 ),
    inference(avatar_component_clause,[],[f7798]) ).

fof(f7800,plain,
    ( spl105_60
    | ~ spl105_1
    | ~ spl105_44 ),
    inference(avatar_split_clause,[],[f7772,f5960,f3070,f7798]) ).

fof(f5960,plain,
    ( spl105_44
  <=> v_y = sK11 ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_44])]) ).

fof(f7772,plain,
    ( sP0(v_y,sK12)
    | ~ spl105_1
    | ~ spl105_44 ),
    inference(superposition,[],[f3071,f5961]) ).

fof(f5961,plain,
    ( v_y = sK11
    | ~ spl105_44 ),
    inference(avatar_component_clause,[],[f5960]) ).

fof(f6829,plain,
    ( ~ spl105_13
    | ~ spl105_37
    | ~ spl105_1 ),
    inference(avatar_split_clause,[],[f4137,f3070,f5199,f3363]) ).

fof(f4137,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK10(sK11,sK12)))
    | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),v_y))
    | ~ spl105_1 ),
    inference(forward_literal_rewriting,[],[f4136,f2634]) ).

fof(f4136,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),v_y))
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK10(sK11,sK12)),v_L)
    | ~ spl105_1 ),
    inference(forward_literal_rewriting,[],[f4124,f2634]) ).

fof(f4124,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,v_y),v_L)
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK10(sK11,sK12)),v_L)
    | ~ spl105_1 ),
    inference(resolution,[],[f3071,f1878]) ).

fof(f1878,plain,
    ! [X0,X1] :
      ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
      | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK10(X0,X1)),v_L)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1542]) ).

fof(f6739,plain,
    ( spl105_10
    | spl105_17
    | spl105_16 ),
    inference(avatar_split_clause,[],[f3507,f3500,f3504,f3326]) ).

fof(f3500,plain,
    ( spl105_16
  <=> hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK7),sK8)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl105_16])]) ).

fof(f3507,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK8),sK7))
    | sK7 = sK8
    | spl105_16 ),
    inference(resolution,[],[f3501,f2849]) ).

fof(f3501,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK7),sK8))
    | spl105_16 ),
    inference(avatar_component_clause,[],[f3500]) ).

fof(f6378,plain,
    ( spl105_34
    | ~ spl105_37
    | ~ spl105_1 ),
    inference(avatar_split_clause,[],[f4133,f3070,f5199,f4988]) ).

fof(f4133,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK10(sK11,sK12)))
    | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | ~ spl105_1 ),
    inference(forward_literal_rewriting,[],[f4132,f2634]) ).

fof(f4132,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK10(sK11,sK12)),v_L)
    | ~ spl105_1 ),
    inference(forward_literal_rewriting,[],[f4121,f2635]) ).

fof(f4121,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,v_y),v_L)
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK10(sK11,sK12)),v_L)
    | ~ spl105_1 ),
    inference(resolution,[],[f3071,f1875]) ).

fof(f1875,plain,
    ! [X0,X1] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
      | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,sK10(X0,X1)),v_L)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1542]) ).

fof(f6261,plain,
    ( spl105_34
    | spl105_24
    | ~ spl105_1 ),
    inference(avatar_split_clause,[],[f4131,f3070,f4226,f4988]) ).

fof(f4131,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),sK10(sK11,sK12)))
    | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | ~ spl105_1 ),
    inference(forward_literal_rewriting,[],[f4130,f2635]) ).

fof(f4130,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK12),v_y))
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK10(sK11,sK12)),v_L)
    | ~ spl105_1 ),
    inference(forward_literal_rewriting,[],[f4119,f2635]) ).

fof(f4119,plain,
    ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,v_y),v_L)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK12,sK10(sK11,sK12)),v_L)
    | ~ spl105_1 ),
    inference(resolution,[],[f3071,f1873]) ).

fof(f1873,plain,
    ! [X0,X1] :
      ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
      | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,sK10(X0,X1)),v_L)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1542]) ).

fof(f5965,plain,
    ( spl105_44
    | spl105_45
    | spl105_13 ),
    inference(avatar_split_clause,[],[f4712,f3363,f5963,f5960]) ).

fof(f4712,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK11))
    | v_y = sK11
    | spl105_13 ),
    inference(resolution,[],[f4710,f2849]) ).

fof(f4710,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),v_y))
    | spl105_13 ),
    inference(avatar_component_clause,[],[f3363]) ).

fof(f3720,plain,
    ( ~ spl105_4
    | ~ spl105_10 ),
    inference(avatar_split_clause,[],[f3710,f3326,f3079]) ).

fof(f3710,plain,
    ( ~ sP2
    | ~ spl105_10 ),
    inference(trivial_inequality_removal,[],[f3692]) ).

fof(f3692,plain,
    ( sK7 != sK7
    | ~ sP2
    | ~ spl105_10 ),
    inference(superposition,[],[f1847,f3686]) ).

fof(f3686,plain,
    ( sK7 = sK8
    | ~ spl105_10 ),
    inference(avatar_component_clause,[],[f3326]) ).

fof(f1847,plain,
    ( sK7 != sK8
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f3502,plain,
    ( ~ spl105_16
    | ~ spl105_4
    | spl105_11
    | spl105_14 ),
    inference(avatar_split_clause,[],[f3387,f3371,f3340,f3079,f3500]) ).

fof(f3387,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK7),sK8))
    | ~ spl105_4
    | spl105_11
    | spl105_14 ),
    inference(forward_literal_rewriting,[],[f3386,f2634]) ).

fof(f3386,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK8),v_L)
    | ~ spl105_4
    | spl105_11
    | spl105_14 ),
    inference(subsumption_resolution,[],[f3385,f3080]) ).

fof(f3385,plain,
    ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK8),v_L)
    | ~ sP2
    | spl105_11
    | spl105_14 ),
    inference(subsumption_resolution,[],[f3384,f3341]) ).

fof(f3384,plain,
    ( v_x = sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK8),v_L)
    | ~ sP2
    | spl105_14 ),
    inference(trivial_inequality_removal,[],[f3377]) ).

fof(f3377,plain,
    ( v_x != v_x
    | v_x = sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK8),v_L)
    | ~ sP2
    | spl105_14 ),
    inference(superposition,[],[f3372,f1849]) ).

fof(f1849,plain,
    ( v_x = sK8
    | v_x = sK7
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK7,sK8),v_L)
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f3376,plain,
    ( ~ spl105_14
    | ~ spl105_15
    | ~ spl105_4 ),
    inference(avatar_split_clause,[],[f3311,f3079,f3374,f3371]) ).

fof(f3311,plain,
    ( v_y != sK7
    | v_x != sK8
    | ~ spl105_4 ),
    inference(resolution,[],[f3080,f1852]) ).

fof(f1852,plain,
    ( v_y != sK7
    | v_x != sK8
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f3365,plain,
    ( spl105_1
    | spl105_3
    | spl105_4
    | spl105_13 ),
    inference(avatar_split_clause,[],[f2847,f3363,f3079,f3076,f3070]) ).

fof(f2847,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),v_y))
    | sP2
    | sP1(sK12,sK11)
    | sP0(sK11,sK12) ),
    inference(forward_literal_rewriting,[],[f1880,f2635]) ).

fof(f1880,plain,
    ( sP2
    | sP1(sK12,sK11)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,v_y),v_L)
    | sP0(sK11,sK12) ),
    inference(cnf_transformation,[],[f1546]) ).

fof(f1546,plain,
    ( sP2
    | sP1(sK12,sK11)
    | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK13),v_L)
      & v_x != sK13
      & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK13),v_L)
      & v_x != sK11
      & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,v_y),v_L)
      & v_x = sK12 )
    | sP0(sK11,sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f1543,f1545,f1544]) ).

fof(f1544,plain,
    ( ? [X0,X1] :
        ( sP1(X1,X0)
        | ( ? [X2] :
              ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
              & v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X2),v_L) )
          & v_x != X0
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          & v_x = X1 )
        | sP0(X0,X1) )
   => ( sP1(sK12,sK11)
      | ( ? [X2] :
            ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,X2),v_L)
            & v_x != X2
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X2),v_L) )
        & v_x != sK11
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,v_y),v_L)
        & v_x = sK12 )
      | sP0(sK11,sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f1545,plain,
    ( ? [X2] :
        ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,X2),v_L)
        & v_x != X2
        & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X2),v_L) )
   => ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK13),v_L)
      & v_x != sK13
      & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK13),v_L) ) ),
    introduced(choice_axiom,[]) ).

fof(f1543,plain,
    ( sP2
    | ? [X0,X1] :
        ( sP1(X1,X0)
        | ( ? [X2] :
              ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X2),v_L)
              & v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X2),v_L) )
          & v_x != X0
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          & v_x = X1 )
        | sP0(X0,X1) ) ),
    inference(rectify,[],[f1525]) ).

fof(f1525,plain,
    ( sP2
    | ? [X2,X3] :
        ( sP1(X3,X2)
        | ( ? [X5] :
              ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L)
              & v_x != X5
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X5),v_L) )
          & v_x != X2
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
          & v_x = X3 )
        | sP0(X2,X3) ) ),
    inference(definition_folding,[],[f1041,f1524,f1523,f1522]) ).

fof(f1041,plain,
    ( ? [X0,X1] :
        ( ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) )
        & ( v_y != X0
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X1),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
        & ( v_y != X1
          | v_x != X0 )
        & X0 != X1 )
    | ? [X2,X3] :
        ( ( ? [X4] :
              ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
                & v_x = X4 )
              | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X4),v_L)
                & v_y != X4
                & v_x != X4
                & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) )
          & v_x != X3
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X3),v_L)
          & v_x = X2 )
        | ( ? [X5] :
              ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L)
              & v_x != X5
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X5),v_L) )
          & v_x != X2
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
          & v_x = X3 )
        | ( ? [X6] :
              ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
                & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
                & v_x = X6 )
              | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X6),v_L)
                & v_x != X6
                & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X6),v_L) ) )
          & v_x != X3
          & v_x != X2
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_L) ) ) ),
    inference(flattening,[],[f1040]) ).

fof(f1040,plain,
    ( ? [X0,X1] :
        ( ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) )
        & ( v_y != X0
          | v_x != X1 )
        & ( v_x = X1
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X1),v_L)
          | v_x != X0 )
        & ( v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
          | v_x != X1 )
        & ( v_x = X1
          | v_x = X0
          | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
        & ( v_y != X1
          | v_x != X0 )
        & X0 != X1 )
    | ? [X2,X3] :
        ( ( ? [X4] :
              ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
                & v_x = X4 )
              | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X4),v_L)
                & v_y != X4
                & v_x != X4
                & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) ) )
          & v_x != X3
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X3),v_L)
          & v_x = X2 )
        | ( ? [X5] :
              ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L)
              & v_x != X5
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X5),v_L) )
          & v_x != X2
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
          & v_x = X3 )
        | ( ? [X6] :
              ( ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
                & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
                & v_x = X6 )
              | ( ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X6),v_L)
                & v_x != X6
                & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X6),v_L) ) )
          & v_x != X3
          & v_x != X2
          & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_L) ) ) ),
    inference(ennf_transformation,[],[f530]) ).

fof(f530,plain,
    ~ ( ! [X0,X1] :
          ( X0 != X1
         => ( ( v_x != X0
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X0),v_L)
              & v_x = X1 )
            | ( v_x != X1
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_y),v_L)
              & v_x = X0 )
            | ( v_x != X0
              & v_x != X1
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X0),v_L) )
            | ( v_y = X0
              & v_x = X1 )
            | ( v_x != X1
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X1),v_L)
              & v_x = X0 )
            | ( v_x != X0
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,v_y),v_L)
              & v_x = X1 )
            | ( v_x != X1
              & v_x != X0
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X0,X1),v_L) )
            | ( v_y = X1
              & v_x = X0 ) ) )
      & ! [X2,X3] :
          ( ( ( v_x != X3
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X3),v_L)
              & v_x = X2 )
           => ! [X4] :
                ( ( v_x = X4
                 => ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L) )
                & ( ( v_x != X4
                    & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X4),v_L) )
                 => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X4),v_L)
                    | v_y = X4 ) ) ) )
          & ( ( v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
              & v_x = X3 )
           => ! [X5] :
                ( ( v_x != X5
                  & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X5),v_L) )
               => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X5),v_L) ) )
          & ( ( v_x != X3
              & v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X3),v_L) )
           => ! [X6] :
                ( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,v_y),v_L)
                    & v_x = X6 )
                 => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L) )
                & ( ( v_x != X6
                    & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X3,X6),v_L) )
                 => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X6),v_L) ) ) ) ) ),
    inference(rectify,[],[f529]) ).

fof(f529,negated_conjecture,
    ~ ( ! [X2,X35] :
          ( X2 != X35
         => ( ( v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X2),v_L)
              & v_x = X35 )
            | ( v_x != X35
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,v_y),v_L)
              & v_x = X2 )
            | ( v_x != X2
              & v_x != X35
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,X2),v_L) )
            | ( v_y = X2
              & v_x = X35 )
            | ( v_x != X35
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X35),v_L)
              & v_x = X2 )
            | ( v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
              & v_x = X35 )
            | ( v_x != X35
              & v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X35),v_L) )
            | ( v_y = X35
              & v_x = X2 ) ) )
      & ! [X2,X35] :
          ( ( ( v_x != X35
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X35),v_L)
              & v_x = X2 )
           => ! [X34] :
                ( ( v_x = X34
                 => ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,v_y),v_L) )
                & ( ( v_x != X34
                    & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,X34),v_L) )
                 => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X34),v_L)
                    | v_y = X34 ) ) ) )
          & ( ( v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
              & v_x = X35 )
           => ! [X34] :
                ( ( v_x != X34
                  & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X34),v_L) )
               => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X34),v_L) ) )
          & ( ( v_x != X35
              & v_x != X2
              & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X35),v_L) )
           => ! [X34] :
                ( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,v_y),v_L)
                    & v_x = X34 )
                 => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L) )
                & ( ( v_x != X34
                    & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,X34),v_L) )
                 => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X34),v_L) ) ) ) ) ),
    inference(negated_conjecture,[],[f528]) ).

fof(f528,conjecture,
    ( ! [X2,X35] :
        ( X2 != X35
       => ( ( v_x != X2
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X2),v_L)
            & v_x = X35 )
          | ( v_x != X35
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,v_y),v_L)
            & v_x = X2 )
          | ( v_x != X2
            & v_x != X35
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,X2),v_L) )
          | ( v_y = X2
            & v_x = X35 )
          | ( v_x != X35
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X35),v_L)
            & v_x = X2 )
          | ( v_x != X2
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
            & v_x = X35 )
          | ( v_x != X35
            & v_x != X2
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X35),v_L) )
          | ( v_y = X35
            & v_x = X2 ) ) )
    & ! [X2,X35] :
        ( ( ( v_x != X35
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X35),v_L)
            & v_x = X2 )
         => ! [X34] :
              ( ( v_x = X34
               => ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,v_y),v_L) )
              & ( ( v_x != X34
                  & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,X34),v_L) )
               => ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X34),v_L)
                  | v_y = X34 ) ) ) )
        & ( ( v_x != X2
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L)
            & v_x = X35 )
         => ! [X34] :
              ( ( v_x != X34
                & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,X34),v_L) )
             => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X34),v_L) ) )
        & ( ( v_x != X35
            & v_x != X2
            & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X35),v_L) )
         => ! [X34] :
              ( ( ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,v_y),v_L)
                  & v_x = X34 )
               => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,v_y),v_L) )
              & ( ( v_x != X34
                  & c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X35,X34),v_L) )
               => c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X34),v_L) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.v8om2dSjm5/Vampire---4.8_28787',conj_2) ).

fof(f3345,plain,
    ( ~ spl105_11
    | ~ spl105_12
    | ~ spl105_4 ),
    inference(avatar_split_clause,[],[f3307,f3079,f3343,f3340]) ).

fof(f3307,plain,
    ( v_y != sK8
    | v_x != sK7
    | ~ spl105_4 ),
    inference(resolution,[],[f3080,f1848]) ).

fof(f1848,plain,
    ( v_y != sK8
    | v_x != sK7
    | ~ sP2 ),
    inference(cnf_transformation,[],[f1534]) ).

fof(f3324,plain,
    ( spl105_1
    | spl105_3
    | spl105_4
    | spl105_9 ),
    inference(avatar_split_clause,[],[f2846,f3322,f3079,f3076,f3070]) ).

fof(f2846,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),v_y),sK13))
    | sP2
    | sP1(sK12,sK11)
    | sP0(sK11,sK12) ),
    inference(forward_literal_rewriting,[],[f1882,f2635]) ).

fof(f1882,plain,
    ( sP2
    | sP1(sK12,sK11)
    | c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_y,sK13),v_L)
    | sP0(sK11,sK12) ),
    inference(cnf_transformation,[],[f1546]) ).

fof(f3206,plain,
    ( spl105_1
    | spl105_3
    | spl105_4
    | ~ spl105_7 ),
    inference(avatar_split_clause,[],[f2845,f3204,f3079,f3076,f3070]) ).

fof(f2845,plain,
    ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_L),sK11),sK13))
    | sP2
    | sP1(sK12,sK11)
    | sP0(sK11,sK12) ),
    inference(forward_literal_rewriting,[],[f1884,f2634]) ).

fof(f1884,plain,
    ( sP2
    | sP1(sK12,sK11)
    | ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,sK11,sK13),v_L)
    | sP0(sK11,sK12) ),
    inference(cnf_transformation,[],[f1546]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SCT115+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.33  % Computer : n032.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Thu Aug 24 15:41:42 EDT 2023
% 0.15/0.33  % CPUTime    : 
% 0.15/0.33  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.33  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.v8om2dSjm5/Vampire---4.8_28787
% 0.15/0.33  % (28942)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (28946)dis-1010_4:3_afr=on:amm=off:bsr=on:bce=on:drc=off:fsd=off:fde=unused:gs=on:gsaa=from_current:irw=on:nwc=1.3:nicw=on:sas=z3:tgt=full:urr=ec_only_619 on Vampire---4 for (619ds/0Mi)
% 0.15/0.38  % (28949)dis+1011_3:2_av=off:ep=RST:fsd=off:fde=none:gsp=on:nm=2:nwc=2.0:sos=on:sp=reverse_frequency_405 on Vampire---4 for (405ds/0Mi)
% 0.15/0.39  % (28947)lrs+1002_9_av=off:bs=on:bsr=on:bce=on:cond=on:drc=off:er=filter:flr=on:fsd=off:fsr=off:fde=unused:lcm=predicate:nm=2:nwc=1.3:sims=off:stl=62_466 on Vampire---4 for (466ds/0Mi)
% 0.15/0.39  % (28945)lrs+1010_4_aac=none:add=off:afr=on:amm=off:anc=all_dependent:bd=off:cond=on:drc=off:flr=on:fde=none:gs=on:lma=on:nm=16:nwc=1.1:sims=off:sos=all:sac=on:sp=occurrence:stl=188_669 on Vampire---4 for (669ds/0Mi)
% 0.15/0.39  % (28948)ott+10_8_br=off:cond=on:fsr=off:gsp=on:nm=16:nwc=3.0:sims=off:sp=reverse_frequency:urr=on_432 on Vampire---4 for (432ds/0Mi)
% 0.18/0.40  % (28944)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_957 on Vampire---4 for (957ds/0Mi)
% 0.18/0.40  % (28943)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_1064 on Vampire---4 for (1064ds/0Mi)
% 159.74/23.21  % (28945)First to succeed.
% 159.74/23.23  % (28945)Refutation found. Thanks to Tanya!
% 159.74/23.23  % SZS status Theorem for Vampire---4
% 159.74/23.23  % SZS output start Proof for Vampire---4
% See solution above
% 159.74/23.24  % (28945)------------------------------
% 159.74/23.24  % (28945)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 159.74/23.24  % (28945)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 159.74/23.24  % (28945)Termination reason: Refutation
% 159.74/23.24  
% 159.74/23.24  % (28945)Memory used [KB]: 172065
% 159.74/23.24  % (28945)Time elapsed: 22.839 s
% 159.74/23.24  % (28945)------------------------------
% 159.74/23.24  % (28945)------------------------------
% 159.74/23.24  % (28942)Success in time 22.815 s
% 159.74/23.24  % Vampire---4.8 exiting
%------------------------------------------------------------------------------