TSTP Solution File: ITP019^3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP019^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 : Mon May 20 22:44:30 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   73
% Syntax   : Number of formulae    :  190 (  49 unt;  31 typ;   0 def)
%            Number of atoms       : 1240 ( 331 equ;   0 cnn)
%            Maximal formula atoms :   30 (   7 avg)
%            Number of connectives :  442 ( 136   ~; 141   |;  71   &;   0   @)
%                                         (  69 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   65 (  61   >;   4   *;   0   +;   0  <<)
%            Number of symbols     :   61 (  58 usr;  32 con; 0-6 aty)
%            Number of variables   :  205 (   0   ^ 183   !;  11   ?; 205   :)
%                                         (  11  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_6,type,
    tyop_2Enum_2Enum: $tType ).

thf(type_def_7,type,
    tyop_2Erealax_2Ereal: $tType ).

thf(type_def_8,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

thf(func_def_0,type,
    tyop_2Emin_2Ebool: $tType ).

thf(func_def_1,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

thf(func_def_2,type,
    tyop_2Enum_2Enum: $tType ).

thf(func_def_3,type,
    tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).

thf(func_def_4,type,
    tyop_2Erealax_2Ereal: $tType ).

thf(func_def_5,type,
    c_2Ebool_2E_21: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_6,type,
    c_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(func_def_7,type,
    c_2Enum_2E0: tyop_2Enum_2Enum ).

thf(func_def_8,type,
    c_2Emin_2E_3D: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_9,type,
    c_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(func_def_10,type,
    c_2Ebool_2E_3F: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_11,type,
    c_2Ebool_2EF: $o ).

thf(func_def_12,type,
    c_2Ebool_2ET: $o ).

thf(func_def_13,type,
    c_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(func_def_14,type,
    c_2Ecomplex_2Ecomplex__inv: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) > tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).

thf(func_def_15,type,
    c_2Ecomplex_2Ecomplex__of__num: tyop_2Enum_2Enum > tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).

thf(func_def_16,type,
    c_2Ebool_2E_7E: $o > $o ).

thf(func_def_18,type,
    vNOT: $o > $o ).

thf(func_def_21,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_22,type,
    sK0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal) ).

thf(func_def_23,type,
    sK1: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_24,type,
    sK2: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_26,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_27,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_28,type,
    vAND: $o > $o > $o ).

thf(func_def_29,type,
    vOR: $o > $o > $o ).

thf(func_def_30,type,
    vIMP: $o > $o > $o ).

thf(f388,plain,
    $false,
    inference(avatar_sat_refutation,[],[f142,f147,f152,f156,f164,f199,f203,f208,f212,f216,f236,f240,f244,f251,f255,f280,f284,f288,f294,f329,f337,f341,f375,f379,f383,f387]) ).

thf(f387,plain,
    ( spl3_1
    | ~ spl3_3
    | ~ spl3_26 ),
    inference(avatar_split_clause,[],[f386,f381,f149,f139]) ).

thf(f139,plain,
    ( spl3_1
  <=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

thf(f149,plain,
    ( spl3_3
  <=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

thf(f381,plain,
    ( spl3_26
  <=> ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
        ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 )
        | ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).

thf(f386,plain,
    ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = sK0 )
    | ~ spl3_3
    | ~ spl3_26 ),
    inference(trivial_inequality_removal,[],[f384]) ).

thf(f384,plain,
    ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
    | ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = sK0 )
    | ~ spl3_3
    | ~ spl3_26 ),
    inference(superposition,[],[f382,f151]) ).

thf(f151,plain,
    ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f149]) ).

thf(f382,plain,
    ( ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
        ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) )
        | ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 ) )
    | ~ spl3_26 ),
    inference(avatar_component_clause,[],[f381]) ).

thf(f383,plain,
    spl3_26,
    inference(avatar_split_clause,[],[f80,f381]) ).

thf(f80,plain,
    ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
      ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 )
      | ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) ) ),
    inference(cnf_transformation,[],[f47]) ).

thf(f47,plain,
    ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
      ( ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) )
        | ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != X0 ) )
      & ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 )
        | ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) ) ) ),
    inference(nnf_transformation,[],[f38]) ).

thf(f38,plain,
    ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
      ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) )
    <=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0 ) ),
    inference(rectify,[],[f11]) ).

thf(f11,axiom,
    ! [X6: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
      ( ( vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X6) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) )
    <=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X6 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).

thf(f379,plain,
    spl3_25,
    inference(avatar_split_clause,[],[f129,f377]) ).

thf(f377,plain,
    ( spl3_25
  <=> ! [X0: $o] :
        ( ( $false = X0 )
        | ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).

thf(f129,plain,
    ! [X0: $o] :
      ( ( $false = X0 )
      | ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
    inference(not_proxy_clausification,[],[f126]) ).

thf(f126,plain,
    ! [X0: $o] :
      ( ( $true = vAPP($o,$o,vNOT,X0) )
      | ( $false = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
    inference(binary_proxy_clausification,[],[f82]) ).

thf(f82,plain,
    ! [X0: $o] : ( vAPP($o,$o,vNOT,X0) = vAPP($o,$o,c_2Ebool_2E_7E,X0) ),
    inference(cnf_transformation,[],[f21]) ).

thf(f21,plain,
    ! [X0: $o] : ( vAPP($o,$o,vNOT,X0) = vAPP($o,$o,c_2Ebool_2E_7E,X0) ),
    inference(fool_elimination,[],[f20]) ).

thf(f20,plain,
    ! [X0: $o] :
      ( vAPP($o,$o,c_2Ebool_2E_7E,X0)
    <=> vAPP($o,$o,vNOT,X0) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X1: $o] :
      ( vAPP($o,$o,c_2Ebool_2E_7E,X1)
    <=> vAPP($o,$o,vNOT,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).

thf(f375,plain,
    spl3_24,
    inference(avatar_split_clause,[],[f118,f372]) ).

thf(f372,plain,
    ( spl3_24
  <=> ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).

thf(f118,plain,
    vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),
    inference(equality_resolution,[],[f81]) ).

thf(f81,plain,
    ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
      ( ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0) )
      | ( vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != X0 ) ),
    inference(cnf_transformation,[],[f47]) ).

thf(f341,plain,
    spl3_23,
    inference(avatar_split_clause,[],[f86,f339]) ).

thf(f339,plain,
    ( spl3_23
  <=> ! [X0: $tType,X1: X0 > $o] :
        ( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK2(X0),X1)) )
        | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).

thf(f86,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK2(X0),X1)) )
      | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ),
    inference(cnf_transformation,[],[f55]) ).

thf(f55,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
        | ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
      & ( ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK2(X0),X1)) )
        | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f53,f54]) ).

thf(f54,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
     => ( $true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK2(X0),X1)) ) ),
    introduced(choice_axiom,[]) ).

thf(f53,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
        | ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
      & ( ? [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
        | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
    inference(rectify,[],[f52]) ).

thf(f52,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
        | ! [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
      & ( ? [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) )
        | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) ) ) ),
    inference(nnf_transformation,[],[f27]) ).

thf(f27,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
    <=> ? [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) ) ),
    inference(fool_elimination,[],[f26]) ).

thf(f26,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1)
    <=> ? [X2: X0] : vAPP(X0,$o,X1,X2) ),
    inference(rectify,[],[f7]) ).

thf(f7,axiom,
    ! [X0: $tType,X3: X0 > $o] :
      ( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X3)
    <=> ? [X4: X0] : vAPP(X0,$o,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).

thf(f337,plain,
    spl3_22,
    inference(avatar_split_clause,[],[f85,f335]) ).

thf(f335,plain,
    ( spl3_22
  <=> ! [X0: $tType,X1: X0 > $o] :
        ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
        | ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK1(X0),X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).

thf(f85,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
      | ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK1(X0),X1)) ) ),
    inference(cnf_transformation,[],[f51]) ).

thf(f51,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
        | ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK1(X0),X1)) ) )
      & ( ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
        | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f49,f50]) ).

thf(f50,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) )
     => ( $true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK1(X0),X1)) ) ),
    introduced(choice_axiom,[]) ).

thf(f49,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
        | ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
      & ( ! [X3: X0] : ( $true = vAPP(X0,$o,X1,X3) )
        | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
    inference(rectify,[],[f48]) ).

thf(f48,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
        | ? [X2: X0] : ( $true != vAPP(X0,$o,X1,X2) ) )
      & ( ! [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) )
        | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
    inference(nnf_transformation,[],[f25]) ).

thf(f25,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) )
    <=> ! [X2: X0] : ( $true = vAPP(X0,$o,X1,X2) ) ),
    inference(fool_elimination,[],[f24]) ).

thf(f24,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1)
    <=> ! [X2: X0] : vAPP(X0,$o,X1,X2) ),
    inference(rectify,[],[f6]) ).

thf(f6,axiom,
    ! [X0: $tType,X3: X0 > $o] :
      ( vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X3)
    <=> ! [X4: X0] : vAPP(X0,$o,X3,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).

thf(f329,plain,
    spl3_21,
    inference(avatar_split_clause,[],[f91,f327]) ).

thf(f327,plain,
    ( spl3_21
  <=> ! [X0: $o,X1: $o] :
        ( ( $true = X1 )
        | ( $true = X0 )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).

thf(f91,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = X1 )
      | ( $true = X0 )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ),
    inference(cnf_transformation,[],[f59]) ).

thf(f59,plain,
    ! [X0: $o,X1: $o] :
      ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
        | ( ( $true != X1 )
          & ( $true != X0 ) ) )
      & ( ( $true = X1 )
        | ( $true = X0 )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
    inference(flattening,[],[f58]) ).

thf(f58,plain,
    ! [X0: $o,X1: $o] :
      ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
        | ( ( $true != X1 )
          & ( $true != X0 ) ) )
      & ( ( $true = X1 )
        | ( $true = X0 )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f31]) ).

thf(f31,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
    <=> ( ( $true = X1 )
        | ( $true = X0 ) ) ),
    inference(fool_elimination,[],[f30]) ).

thf(f30,plain,
    ! [X0: $o,X1: $o] :
      ( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1)
    <=> ( X1
        | X0 ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X1: $o,X2: $o] :
      ( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X1),X2)
    <=> ( X2
        | X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).

thf(f294,plain,
    spl3_20,
    inference(avatar_split_clause,[],[f128,f292]) ).

thf(f292,plain,
    ( spl3_20
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).

thf(f128,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
    inference(not_proxy_clausification,[],[f127]) ).

thf(f127,plain,
    ! [X0: $o] :
      ( ( $false = vAPP($o,$o,vNOT,X0) )
      | ( $true = vAPP($o,$o,c_2Ebool_2E_7E,X0) ) ),
    inference(binary_proxy_clausification,[],[f82]) ).

thf(f288,plain,
    spl3_19,
    inference(avatar_split_clause,[],[f97,f286]) ).

thf(f286,plain,
    ( spl3_19
  <=> ! [X0: $tType,X2: X0,X1: X0] :
        ( ( X1 = X2 )
        | ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).

thf(f97,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( X1 = X2 )
      | ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true ) ),
    inference(cnf_transformation,[],[f62]) ).

thf(f62,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true )
        | ( X1 != X2 ) )
      & ( ( X1 = X2 )
        | ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) != $true ) ) ),
    inference(nnf_transformation,[],[f35]) ).

thf(f35,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true )
    <=> ( X1 = X2 ) ),
    inference(fool_elimination,[],[f34]) ).

thf(f34,plain,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2)
    <=> ( X1 = X2 ) ),
    inference(rectify,[],[f5]) ).

thf(f5,axiom,
    ! [X0: $tType,X1: X0,X2: X0] :
      ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2)
    <=> ( X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).

thf(f284,plain,
    spl3_18,
    inference(avatar_split_clause,[],[f87,f282]) ).

thf(f282,plain,
    ( spl3_18
  <=> ! [X0: $tType,X2: X0,X1: X0 > $o] :
        ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
        | ( $true != vAPP(X0,$o,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_18])]) ).

thf(f87,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( $true = vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_3F(X0),X1) )
      | ( $true != vAPP(X0,$o,X1,X2) ) ),
    inference(cnf_transformation,[],[f55]) ).

thf(f280,plain,
    spl3_17,
    inference(avatar_split_clause,[],[f84,f278]) ).

thf(f278,plain,
    ( spl3_17
  <=> ! [X0: $tType,X1: X0 > $o,X3: X0] :
        ( ( $true = vAPP(X0,$o,X1,X3) )
        | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

thf(f84,plain,
    ! [X0: $tType,X3: X0,X1: X0 > $o] :
      ( ( $true = vAPP(X0,$o,X1,X3) )
      | ( $true != vAPP(sTfun(X0,$o),$o,c_2Ebool_2E_21(X0),X1) ) ),
    inference(cnf_transformation,[],[f51]) ).

thf(f255,plain,
    spl3_16,
    inference(avatar_split_clause,[],[f124,f253]) ).

thf(f253,plain,
    ( spl3_16
  <=> ! [X1: $o] :
        ( ( $true = X1 )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,$true),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

thf(f124,plain,
    ! [X1: $o] :
      ( ( $true = X1 )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,$true),X1) ) ),
    inference(equality_resolution,[],[f94]) ).

thf(f94,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = X1 )
      | ( $true != X0 )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ),
    inference(cnf_transformation,[],[f61]) ).

thf(f61,plain,
    ! [X0: $o,X1: $o] :
      ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
        | ( ( $true != X1 )
          & ( $true = X0 ) ) )
      & ( ( $true = X1 )
        | ( $true != X0 )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ) ),
    inference(flattening,[],[f60]) ).

thf(f60,plain,
    ! [X0: $o,X1: $o] :
      ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
        | ( ( $true != X1 )
          & ( $true = X0 ) ) )
      & ( ( $true = X1 )
        | ( $true != X0 )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f42]) ).

thf(f42,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
    <=> ( ( $true = X1 )
        | ( $true != X0 ) ) ),
    inference(ennf_transformation,[],[f33]) ).

thf(f33,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
    <=> ( ( $true = X0 )
       => ( $true = X1 ) ) ),
    inference(fool_elimination,[],[f32]) ).

thf(f32,plain,
    ! [X0: $o,X1: $o] :
      ( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1)
    <=> ( X0
       => X1 ) ),
    inference(rectify,[],[f4]) ).

thf(f4,axiom,
    ! [X1: $o,X2: $o] :
      ( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X1),X2)
    <=> ( X1
       => X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).

thf(f251,plain,
    spl3_15,
    inference(avatar_split_clause,[],[f95,f249]) ).

thf(f249,plain,
    ( spl3_15
  <=> ! [X0: $o,X1: $o] :
        ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
        | ( $true = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

thf(f95,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
      | ( $true = X0 ) ),
    inference(cnf_transformation,[],[f61]) ).

thf(f244,plain,
    spl3_14,
    inference(avatar_split_clause,[],[f89,f242]) ).

thf(f242,plain,
    ( spl3_14
  <=> ! [X0: $o,X1: $o] :
        ( ( $true = X1 )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

thf(f89,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = X1 )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ),
    inference(cnf_transformation,[],[f57]) ).

thf(f57,plain,
    ! [X0: $o,X1: $o] :
      ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
        | ( $true != X1 )
        | ( $true != X0 ) )
      & ( ( ( $true = X1 )
          & ( $true = X0 ) )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
    inference(flattening,[],[f56]) ).

thf(f56,plain,
    ! [X0: $o,X1: $o] :
      ( ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
        | ( $true != X1 )
        | ( $true != X0 ) )
      & ( ( ( $true = X1 )
          & ( $true = X0 ) )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
    inference(nnf_transformation,[],[f29]) ).

thf(f29,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
    <=> ( ( $true = X1 )
        & ( $true = X0 ) ) ),
    inference(fool_elimination,[],[f28]) ).

thf(f28,plain,
    ! [X0: $o,X1: $o] :
      ( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1)
    <=> ( X1
        & X0 ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X1: $o,X2: $o] :
      ( vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X1),X2)
    <=> ( X2
        & X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).

thf(f240,plain,
    spl3_13,
    inference(avatar_split_clause,[],[f88,f238]) ).

thf(f238,plain,
    ( spl3_13
  <=> ! [X0: $o,X1: $o] :
        ( ( $true = X0 )
        | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

thf(f88,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = X0 )
      | ( $true != vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) ) ),
    inference(cnf_transformation,[],[f57]) ).

thf(f236,plain,
    spl3_12,
    inference(avatar_split_clause,[],[f125,f234]) ).

thf(f234,plain,
    ( spl3_12
  <=> ! [X0: $tType,X2: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

thf(f125,plain,
    ! [X0: $tType,X2: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X2),X2) ),
    inference(equality_resolution,[],[f98]) ).

thf(f98,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),c_2Emin_2E_3D(X0),X1),X2) = $true )
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f62]) ).

thf(f216,plain,
    spl3_11,
    inference(avatar_split_clause,[],[f123,f214]) ).

thf(f214,plain,
    ( spl3_11
  <=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),$true) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

thf(f123,plain,
    ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),$true) ),
    inference(equality_resolution,[],[f96]) ).

thf(f96,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Emin_2E_3D_3D_3E,X0),X1) )
      | ( $true != X1 ) ),
    inference(cnf_transformation,[],[f61]) ).

thf(f212,plain,
    spl3_10,
    inference(avatar_split_clause,[],[f122,f210]) ).

thf(f210,plain,
    ( spl3_10
  <=> ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,$true),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

thf(f122,plain,
    ! [X1: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,$true),X1) ),
    inference(equality_resolution,[],[f92]) ).

thf(f92,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
      | ( $true != X0 ) ),
    inference(cnf_transformation,[],[f59]) ).

thf(f208,plain,
    ( spl3_9
    | ~ spl3_4
    | spl3_5 ),
    inference(avatar_split_clause,[],[f176,f158,f154,f205]) ).

thf(f205,plain,
    ( spl3_9
  <=> ( c_2Ebool_2EF = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

thf(f154,plain,
    ( spl3_4
  <=> ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

thf(f158,plain,
    ( spl3_5
  <=> ( c_2Ebool_2EF = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

thf(f176,plain,
    ( ( c_2Ebool_2EF = $false )
    | ~ spl3_4
    | spl3_5 ),
    inference(trivial_inequality_removal,[],[f174]) ).

thf(f174,plain,
    ( ( $true != $true )
    | ( c_2Ebool_2EF = $false )
    | ~ spl3_4
    | spl3_5 ),
    inference(superposition,[],[f160,f155]) ).

thf(f155,plain,
    ( ! [X0: $o] :
        ( ( $true = X0 )
        | ( $false = X0 ) )
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f154]) ).

thf(f160,plain,
    ( ( c_2Ebool_2EF != $true )
    | spl3_5 ),
    inference(avatar_component_clause,[],[f158]) ).

thf(f203,plain,
    spl3_8,
    inference(avatar_split_clause,[],[f121,f201]) ).

thf(f201,plain,
    ( spl3_8
  <=> ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),$true) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

thf(f121,plain,
    ! [X0: $o] : ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),$true) ),
    inference(equality_resolution,[],[f93]) ).

thf(f93,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_5C_2F,X0),X1) )
      | ( $true != X1 ) ),
    inference(cnf_transformation,[],[f59]) ).

thf(f199,plain,
    spl3_7,
    inference(avatar_split_clause,[],[f120,f196]) ).

thf(f196,plain,
    ( spl3_7
  <=> ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,$true),$true) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

thf(f120,plain,
    $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,$true),$true),
    inference(equality_resolution,[],[f119]) ).

thf(f119,plain,
    ! [X0: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),$true) )
      | ( $true != X0 ) ),
    inference(equality_resolution,[],[f90]) ).

thf(f90,plain,
    ! [X0: $o,X1: $o] :
      ( ( $true = vAPP($o,$o,vAPP($o,sTfun($o,$o),c_2Ebool_2E_2F_5C,X0),X1) )
      | ( $true != X1 )
      | ( $true != X0 ) ),
    inference(cnf_transformation,[],[f57]) ).

thf(f164,plain,
    ( ~ spl3_5
    | spl3_6 ),
    inference(avatar_split_clause,[],[f130,f162,f158]) ).

thf(f162,plain,
    ( spl3_6
  <=> ! [X0: $o] : ( $true = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

thf(f130,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( c_2Ebool_2EF != $true ) ),
    inference(trivial_inequality_removal,[],[f103]) ).

thf(f103,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( c_2Ebool_2EF != $true )
      | ( $true != $true ) ),
    inference(definition_unfolding,[],[f73,f99]) ).

thf(f99,plain,
    c_2Ebool_2ET = $true,
    inference(cnf_transformation,[],[f37]) ).

thf(f37,plain,
    c_2Ebool_2ET = $true,
    inference(fool_elimination,[],[f36]) ).

thf(f36,plain,
    c_2Ebool_2ET,
    inference(rectify,[],[f8]) ).

thf(f8,axiom,
    c_2Ebool_2ET,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).

thf(f73,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( c_2Ebool_2EF != $true )
      | ( c_2Ebool_2ET != $true ) ),
    inference(cnf_transformation,[],[f46]) ).

thf(f46,plain,
    ! [X0: $o] :
      ( ( ( c_2Ebool_2EF = $true )
        | ( $true != X0 )
        | ( $true != vAPP($o,$o,vNOT,X0) ) )
      & ( ( $true = vAPP($o,$o,vNOT,X0) )
        | ( ( c_2Ebool_2EF != $true )
          & ( $true = X0 ) ) )
      & ( ( $true = X0 )
        | ( $true != X0 )
        | ( c_2Ebool_2ET != $true ) )
      & ( ( c_2Ebool_2ET = $true )
        | ( ( $true != X0 )
          & ( $true = X0 ) ) )
      & ( ( $true = X0 )
        | ( c_2Ebool_2EF != $true )
        | ( c_2Ebool_2ET != $true ) )
      & ( ( c_2Ebool_2ET = $true )
        | ( ( $true != X0 )
          & ( c_2Ebool_2EF = $true ) ) )
      & ( ( c_2Ebool_2ET = $true )
        | ( $true != X0 )
        | ( c_2Ebool_2ET != $true ) )
      & ( ( c_2Ebool_2ET = $true )
        | ( ( c_2Ebool_2ET != $true )
          & ( $true = X0 ) ) )
      & ( ( $true = X0 )
        | ( c_2Ebool_2ET != $true )
        | ( $true != X0 ) )
      & ( ( $true = X0 )
        | ( ( $true != X0 )
          & ( c_2Ebool_2ET = $true ) ) ) ),
    inference(flattening,[],[f45]) ).

thf(f45,plain,
    ! [X0: $o] :
      ( ( ( c_2Ebool_2EF = $true )
        | ( $true != X0 )
        | ( $true != vAPP($o,$o,vNOT,X0) ) )
      & ( ( $true = vAPP($o,$o,vNOT,X0) )
        | ( ( c_2Ebool_2EF != $true )
          & ( $true = X0 ) ) )
      & ( ( $true = X0 )
        | ( $true != X0 )
        | ( c_2Ebool_2ET != $true ) )
      & ( ( c_2Ebool_2ET = $true )
        | ( ( $true != X0 )
          & ( $true = X0 ) ) )
      & ( ( $true = X0 )
        | ( c_2Ebool_2EF != $true )
        | ( c_2Ebool_2ET != $true ) )
      & ( ( c_2Ebool_2ET = $true )
        | ( ( $true != X0 )
          & ( c_2Ebool_2EF = $true ) ) )
      & ( ( c_2Ebool_2ET = $true )
        | ( $true != X0 )
        | ( c_2Ebool_2ET != $true ) )
      & ( ( c_2Ebool_2ET = $true )
        | ( ( c_2Ebool_2ET != $true )
          & ( $true = X0 ) ) )
      & ( ( $true = X0 )
        | ( c_2Ebool_2ET != $true )
        | ( $true != X0 ) )
      & ( ( $true = X0 )
        | ( ( $true != X0 )
          & ( c_2Ebool_2ET = $true ) ) ) ),
    inference(nnf_transformation,[],[f41]) ).

thf(f41,plain,
    ! [X0: $o] :
      ( ( ( ( c_2Ebool_2EF = $true )
          | ( $true != X0 ) )
      <=> ( $true = vAPP($o,$o,vNOT,X0) ) )
      & ( ( ( $true = X0 )
          | ( $true != X0 ) )
      <=> ( c_2Ebool_2ET = $true ) )
      & ( ( ( $true = X0 )
          | ( c_2Ebool_2EF != $true ) )
      <=> ( c_2Ebool_2ET = $true ) )
      & ( ( ( c_2Ebool_2ET = $true )
          | ( $true != X0 ) )
      <=> ( c_2Ebool_2ET = $true ) )
      & ( ( ( $true = X0 )
          | ( c_2Ebool_2ET != $true ) )
      <=> ( $true = X0 ) ) ),
    inference(ennf_transformation,[],[f19]) ).

thf(f19,plain,
    ! [X0: $o] :
      ( ( ( ( $true = X0 )
         => ( c_2Ebool_2EF = $true ) )
      <=> ( $true = vAPP($o,$o,vNOT,X0) ) )
      & ( ( ( $true = X0 )
         => ( $true = X0 ) )
      <=> ( c_2Ebool_2ET = $true ) )
      & ( ( ( c_2Ebool_2EF = $true )
         => ( $true = X0 ) )
      <=> ( c_2Ebool_2ET = $true ) )
      & ( ( ( $true = X0 )
         => ( c_2Ebool_2ET = $true ) )
      <=> ( c_2Ebool_2ET = $true ) )
      & ( ( ( c_2Ebool_2ET = $true )
         => ( $true = X0 ) )
      <=> ( $true = X0 ) ) ),
    inference(fool_elimination,[],[f18]) ).

thf(f18,plain,
    ! [X0: $o] :
      ( ( ( X0
         => c_2Ebool_2EF )
      <=> vAPP($o,$o,vNOT,X0) )
      & ( ( X0
         => X0 )
      <=> c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
         => X0 )
      <=> c_2Ebool_2ET )
      & ( ( X0
         => c_2Ebool_2ET )
      <=> c_2Ebool_2ET )
      & ( ( c_2Ebool_2ET
         => X0 )
      <=> X0 ) ),
    inference(rectify,[],[f10]) ).

thf(f10,axiom,
    ! [X5: $o] :
      ( ( ( X5
         => c_2Ebool_2EF )
      <=> vAPP($o,$o,vNOT,X5) )
      & ( ( X5
         => X5 )
      <=> c_2Ebool_2ET )
      & ( ( c_2Ebool_2EF
         => X5 )
      <=> c_2Ebool_2ET )
      & ( ( X5
         => c_2Ebool_2ET )
      <=> c_2Ebool_2ET )
      & ( ( c_2Ebool_2ET
         => X5 )
      <=> X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).

thf(f156,plain,
    spl3_4,
    inference(avatar_split_clause,[],[f15,f154]) ).

thf(f15,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f152,plain,
    spl3_3,
    inference(avatar_split_clause,[],[f137,f149]) ).

thf(f137,plain,
    vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0),
    inference(equality_proxy_clausification,[],[f136]) ).

thf(f136,plain,
    $true = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0)),
    inference(not_proxy_clausification,[],[f64]) ).

thf(f64,plain,
    $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0))),
    inference(cnf_transformation,[],[f44]) ).

thf(f44,plain,
    ( ( $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0))) )
    & ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),sK0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f40,f43]) ).

thf(f43,plain,
    ( ? [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
        ( ( $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0))) )
        & ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),X0)) ) )
   => ( ( $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,sK0))) )
      & ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),sK0)) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f40,plain,
    ? [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
      ( ( $true != vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0))) )
      & ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),X0)) ) ),
    inference(ennf_transformation,[],[f17]) ).

thf(f17,plain,
    ~ ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
        ( ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),X0)) )
       => ( $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0))) ) ),
    inference(fool_elimination,[],[f16]) ).

thf(f16,plain,
    ~ ! [X0: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
        ( vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X0)
       => vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X0)) ),
    inference(rectify,[],[f13]) ).

thf(f13,negated_conjecture,
    ~ ! [X6: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
        ( vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X6)
       => vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X6) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ),
    inference(negated_conjecture,[],[f12]) ).

thf(f12,conjecture,
    ! [X6: tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)] :
      ( vAPP($o,$o,vNOT,vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) = X6)
     => vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__inv,X6) = vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).

thf(f147,plain,
    ~ spl3_2,
    inference(avatar_split_clause,[],[f14,f144]) ).

thf(f144,plain,
    ( spl3_2
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

thf(f14,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

thf(f142,plain,
    ~ spl3_1,
    inference(avatar_split_clause,[],[f135,f139]) ).

thf(f135,plain,
    vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0) != sK0,
    inference(equality_proxy_clausification,[],[f134]) ).

thf(f134,plain,
    $false = vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),sK0),
    inference(not_proxy_clausification,[],[f63]) ).

thf(f63,plain,
    $true = vAPP($o,$o,vNOT,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o,vAPP(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),sTfun(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),$o),vEQ(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal)),vAPP(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Ecomplex_2Ecomplex__of__num,c_2Enum_2E0)),sK0)),
    inference(cnf_transformation,[],[f44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ITP019^3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n002.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat May 18 16:17:37 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (12979)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (12980)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (12984)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38  % (12983)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (12985)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38  % (12981)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % Exception at run slice level
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs% Exception at run slice level
% 0.14/0.38  
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  % Exception at run slice level
% 0.14/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.38  % (12986)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.39  % (12986)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.39  % (12984)First to succeed.
% 0.14/0.39  % (12982)WARNING: value z3 for option sas not known
% 0.14/0.39  % (12982)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39  % (12984)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12979"
% 0.14/0.39  % (12984)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40  % (12984)------------------------------
% 0.14/0.40  % (12984)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40  % (12984)Termination reason: Refutation
% 0.14/0.40  
% 0.14/0.40  % (12984)Memory used [KB]: 938
% 0.14/0.40  % (12984)Time elapsed: 0.015 s
% 0.14/0.40  % (12984)Instructions burned: 22 (million)
% 0.14/0.40  % (12979)Success in time 0.02 s
%------------------------------------------------------------------------------