TSTP Solution File: ITP023^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP023^1 : 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 : 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 : Mon May 20 22:47:18 EDT 2024

% Result   : Theorem 0.15s 0.41s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :  122
% Syntax   : Number of formulae    :  145 (  18 unt; 117 typ;   0 def)
%            Number of atoms       :  273 (  31 equ;   0 cnn)
%            Maximal formula atoms :    3 (   9 avg)
%            Number of connectives :   37 (  20   ~;  10   |;   3   &;   0   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  221 ( 220   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  111 ( 108 usr;  25 con; 0-6 aty)
%            Number of variables   :   57 (   0   ^  46   !;   4   ?;  57   :)
%                                         (   7  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    d: $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

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

thf(type_def_8,type,
    du: $tType ).

thf(type_def_9,type,
    mono_2Etyop_2Erealax_2Ereal: $tType ).

thf(type_def_10,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).

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

thf(func_def_1,type,
    d: $tType ).

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

thf(func_def_3,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).

thf(func_def_4,type,
    mono_2Etyop_2Erealax_2Ereal: $tType ).

thf(func_def_5,type,
    tyop_2Emin_2Ebool: d ).

thf(func_def_6,type,
    tyop_2Emin_2Efun: d > d > d ).

thf(func_def_7,type,
    tyop_2Epair_2Eprod: d > d > d ).

thf(func_def_8,type,
    tyop_2Erealax_2Ereal: d ).

thf(func_def_9,type,
    s: d > u > du ).

thf(func_def_10,type,
    app_2E2: du > du > u ).

thf(func_def_11,type,
    combin_i_2E0: u ).

thf(func_def_12,type,
    combin_k_2E0: u ).

thf(func_def_13,type,
    combin_s_2E0: u ).

thf(func_def_14,type,
    c_2Ebool_2E_21_2E0: u ).

thf(func_def_15,type,
    c_2Ebool_2E_21_2E1: du > u ).

thf(func_def_16,type,
    c_2Epair_2E_2C_2E0: u ).

thf(func_def_17,type,
    c_2Epair_2E_2C_2E2: du > du > u ).

thf(func_def_18,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

thf(func_def_19,type,
    c_2Ebool_2E_2F_5C_2E2: du > du > u ).

thf(func_def_20,type,
    c_2Emin_2E_3D_2E0: u ).

thf(func_def_21,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(func_def_22,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

thf(func_def_23,type,
    c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).

thf(func_def_24,type,
    c_2Ebool_2E_3F_2E0: u ).

thf(func_def_25,type,
    c_2Ebool_2E_3F_2E1: du > u ).

thf(func_def_26,type,
    c_2Ebool_2EF_2E0: u ).

thf(func_def_27,type,
    c_2Epred__set_2ESUBSET_2E0: u ).

thf(func_def_28,type,
    c_2Epred__set_2ESUBSET_2E2: du > du > u ).

thf(func_def_29,type,
    c_2Ebool_2ET_2E0: u ).

thf(func_def_30,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

thf(func_def_31,type,
    c_2Ebool_2E_5C_2F_2E2: du > du > u ).

thf(func_def_32,type,
    c_2Ereal__topology_2Eball_2E0: u ).

thf(func_def_33,type,
    c_2Ereal__topology_2Eball_2E1: du > u ).

thf(func_def_34,type,
    c_2Ereal__topology_2Ebounded__def_2E0: u ).

thf(func_def_35,type,
    c_2Ereal__topology_2Ebounded__def_2E1: du > u ).

thf(func_def_36,type,
    c_2Ereal__topology_2Ecball_2E0: u ).

thf(func_def_37,type,
    c_2Ereal__topology_2Ecball_2E1: du > u ).

thf(func_def_38,type,
    c_2Ebool_2E_7E_2E0: u ).

thf(func_def_39,type,
    c_2Ebool_2E_7E_2E1: du > u ).

thf(func_def_40,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).

thf(func_def_41,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).

thf(func_def_42,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).

thf(func_def_43,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).

thf(func_def_44,type,
    mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(func_def_45,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_46,type,
    mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_47,type,
    mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_48,type,
    mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(func_def_49,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(func_def_50,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(func_def_51,type,
    mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).

thf(func_def_52,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(func_def_53,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(func_def_54,type,
    mono_2Ec_2Ereal__topology_2Eball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(func_def_55,type,
    mono_2Ec_2Ereal__topology_2Ebounded__def: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).

thf(func_def_56,type,
    mono_2Ec_2Ereal__topology_2Ecball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(func_def_57,type,
    mono_2Ec_2Ebool_2E_7E: $o > $o ).

thf(func_def_58,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(func_def_59,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).

thf(func_def_60,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).

thf(func_def_61,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ) > u ).

thf(func_def_62,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ) > u ).

thf(func_def_63,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).

thf(func_def_64,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > $o ) > u ).

thf(func_def_65,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(func_def_66,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(func_def_67,type,
    i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).

thf(func_def_68,type,
    i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).

thf(func_def_69,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(func_def_70,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).

thf(func_def_71,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).

thf(func_def_72,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).

thf(func_def_73,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).

thf(func_def_74,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(func_def_75,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(func_def_76,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_77,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_78,type,
    j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(func_def_79,type,
    j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).

thf(func_def_81,type,
    vNOT: $o > $o ).

thf(func_def_84,type,
    vAND: $o > $o > $o ).

thf(func_def_85,type,
    vOR: $o > $o > $o ).

thf(func_def_86,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_87,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_88,type,
    sP0: $o > $o > $o ).

thf(func_def_89,type,
    sP1: $o > $o > $o ).

thf(func_def_90,type,
    sP2: $o > $o > $o ).

thf(func_def_91,type,
    sP3: $o > $o > $o > $o ).

thf(func_def_92,type,
    sP4: $o > $o > $o > $o ).

thf(func_def_93,type,
    sP5: $o > $o > $o > $o ).

thf(func_def_94,type,
    sP6: $o > $o > $o > $o ).

thf(func_def_95,type,
    sP7: $o > $o > $o > $o ).

thf(func_def_96,type,
    sP8: $o > $o > $o > $o ).

thf(func_def_97,type,
    sP9: $o > $o > $o > $o ).

thf(func_def_98,type,
    sP10: $o > $o > $o > $o ).

thf(func_def_99,type,
    sP11: $o > $o > $o > $o ).

thf(func_def_100,type,
    sP12: $o > $o > $o > $o ).

thf(func_def_101,type,
    sP13: $o > $o > $o > $o ).

thf(func_def_102,type,
    sP14: $o > $o > $o > $o ).

thf(func_def_103,type,
    sP15: $o > $o > $o > $o ).

thf(func_def_104,type,
    sK16: mono_2Etyop_2Erealax_2Ereal ).

thf(func_def_105,type,
    sK17: mono_2Etyop_2Erealax_2Ereal ).

thf(func_def_106,type,
    sK18: u > d > u ).

thf(func_def_107,type,
    sK19: u > d > u ).

thf(func_def_108,type,
    sK20: u > d > u ).

thf(func_def_109,type,
    sK21: u > u > d > d > u ).

thf(func_def_111,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_112,type,
    vIMP: $o > $o > $o ).

thf(func_def_113,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_114,type,
    sK23: u > d > u ).

thf(f5267,plain,
    $false,
    inference(equality_resolution,[],[f5166]) ).

thf(f5166,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1)) != vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17)) ),
    inference(trivial_inequality_removal,[],[f5165]) ).

thf(f5165,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( $true != $true )
      | ( vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1)) != vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17)) ) ),
    inference(constrained_superposition,[],[f321,f5162]) ).

thf(f5162,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
    inference(subsumption_resolution,[],[f5157,f454]) ).

thf(f454,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
    inference(cnf_transformation,[],[f131]) ).

thf(f131,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
    inference(fool_elimination,[],[f130]) ).

thf(f130,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),
    inference(rectify,[],[f69]) ).

thf(f69,axiom,
    ! [X22: mono_2Etyop_2Erealax_2Ereal,X23: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).

thf(f5157,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) )
      | ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ) ),
    inference(trivial_inequality_removal,[],[f5156]) ).

thf(f5156,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
      ( ( $true != $true )
      | ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) )
      | ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ) ),
    inference(superposition,[],[f407,f455]) ).

thf(f455,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
    inference(cnf_transformation,[],[f133]) ).

thf(f133,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
    inference(fool_elimination,[],[f132]) ).

thf(f132,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),
    inference(rectify,[],[f67]) ).

thf(f67,axiom,
    ! [X22: mono_2Etyop_2Erealax_2Ereal,X23: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Ecball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).

thf(f407,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) )
      | ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) )
      | ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) ) ),
    inference(cnf_transformation,[],[f205]) ).

thf(f205,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) )
      | ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) )
      | ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) ) ),
    inference(flattening,[],[f204]) ).

thf(f204,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) )
      | ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) )
      | ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) ) ),
    inference(ennf_transformation,[],[f107]) ).

thf(f107,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1) )
        & ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) ) )
     => ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) ) ),
    inference(fool_elimination,[],[f106]) ).

thf(f106,plain,
    ! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X0),X1)
        & vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X1) )
     => vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X0) ),
    inference(rectify,[],[f68]) ).

thf(f68,axiom,
    ! [X24: mono_2Etyop_2Erealax_2Ereal > $o,X25: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),sTfun(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o),mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,X24),X25)
        & vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X25) )
     => vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,X24) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).

thf(f321,plain,
    $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17))),
    inference(cnf_transformation,[],[f238]) ).

thf(f238,plain,
    $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f195,f237]) ).

thf(f237,plain,
    ( ? [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) )
   => ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,sK16),sK17))) ) ),
    introduced(choice_axiom,[]) ).

thf(f195,plain,
    ? [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true != vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
    inference(ennf_transformation,[],[f85]) ).

thf(f85,plain,
    ~ ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( $true = vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))) ),
    inference(fool_elimination,[],[f84]) ).

thf(f84,plain,
    ~ ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X0),X1))),
    inference(rectify,[],[f81]) ).

thf(f81,negated_conjecture,
    ~ ! [X22: mono_2Etyop_2Erealax_2Ereal,X23: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),
    inference(negated_conjecture,[],[f80]) ).

thf(f80,conjecture,
    ! [X22: mono_2Etyop_2Erealax_2Ereal,X23: mono_2Etyop_2Erealax_2Ereal] : vAPP(sTfun(mono_2Etyop_2Erealax_2Ereal,$o),$o,mono_2Ec_2Ereal__topology_2Ebounded__def,vAPP(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,sTfun(mono_2Etyop_2Erealax_2Ereal,$o),mono_2Ec_2Ereal__topology_2Eball,vAPP(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,vAPP(mono_2Etyop_2Erealax_2Ereal,sTfun(mono_2Etyop_2Erealax_2Ereal,mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29),mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,X22),X23))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : ITP023^1 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.00/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.30  % Computer : n032.cluster.edu
% 0.11/0.30  % Model    : x86_64 x86_64
% 0.11/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30  % Memory   : 8042.1875MB
% 0.11/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit   : 300
% 0.11/0.30  % WCLimit    : 300
% 0.11/0.30  % DateTime   : Sat May 18 17:46:22 EDT 2024
% 0.11/0.30  % CPUTime    : 
% 0.11/0.31  % (2615)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32  % (2618)WARNING: value z3 for option sas not known
% 0.15/0.33  % (2618)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)
% 0.15/0.33  % (2619)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33  % (2616)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33  % (2621)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)
% 0.15/0.33  % (2620)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)
% 0.15/0.33  % (2622)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)
% 0.15/0.33  % (2617)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33  % Exception at run slice level
% 0.15/0.33  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.34  % Exception at run slice level
% 0.15/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.34  % (2622)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.34  % Exception at run slice level
% 0.15/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.34  % (2623)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.35  % (2624)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.35  % (2623)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.35  % Exception at run slice level
% 0.15/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35  % (2624)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.36  % (2625)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.36  % (2626)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.15/0.40  % (2618)First to succeed.
% 0.15/0.40  % (2618)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2615"
% 0.15/0.41  % (2618)Refutation found. Thanks to Tanya!
% 0.15/0.41  % SZS status Theorem for theBenchmark
% 0.15/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.41  % (2618)------------------------------
% 0.15/0.41  % (2618)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.41  % (2618)Termination reason: Refutation
% 0.15/0.41  
% 0.15/0.41  % (2618)Memory used [KB]: 1815
% 0.15/0.41  % (2618)Time elapsed: 0.080 s
% 0.15/0.41  % (2618)Instructions burned: 300 (million)
% 0.15/0.41  % (2615)Success in time 0.103 s
%------------------------------------------------------------------------------