%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP023^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 : Wed Feb 25 08:54:33 AM UTC 2026
% Result : Theorem 3.25s 1.96s
% Output : Refutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 207 ( 66 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 222 ( 25 ~; 26 |; 7 &; 148 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 76 usr; 23 con; 0-3 aty)
% Number of variables : 66 ( 0 ^; 62 !; 4 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
d: $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_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_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_89,type,
sK0: mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_90,type,
sK1: mono_2Etyop_2Erealax_2Ereal ).
thf(func_def_92,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f347,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f344]) ).
thf(f344,plain,
$true != $true,
inference(superposition,[status(thm)],[f171,f341]) ).
thf(f341,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f336,f187]) ).
thf(f187,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f88]) ).
thf(f88,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f87]) ).
thf(f87,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f69]) ).
thf(f69,axiom,
! [X23: mono_2Etyop_2Erealax_2Ereal,X22: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
thf(f336,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
!= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f331]) ).
thf(f331,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
!= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1 ) ) )
= $true )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f191,f305]) ).
thf(f305,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
= $false )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f265]) ).
thf(f265,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
!= $true )
| ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
= $false )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f172,f211]) ).
thf(f211,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
inference(subsumption_resolution,[status(thm)],[f208,f171]) ).
thf(f208,plain,
! [X0: $o] :
( ( $false = X0 )
| ( $true = X0 )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f207]) ).
thf(f207,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0 ) ) )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f206]) ).
thf(f206,plain,
! [X0: $o] :
( ( $true = X0 )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0 ) ) )
= X0 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f171,f167]) ).
thf(f167,plain,
! [X0: $o,X1: $o] :
( ( $true = X1 )
| ( $true = X0 )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
thf(f158,plain,
! [X0: $o,X1: $o] :
( ( ( $true != X1 )
& ( $true = X0 ) )
| ( ( $true != X0 )
& ( $true = X1 ) )
| ( X0 = X1 ) ),
inference(flattening,[status(thm)],[f157]) ).
thf(f157,plain,
! [X0: $o,X1: $o] :
( ( X0 = X1 )
| ( ( $true != X1 )
& ( $true = X0 ) )
| ( ( $true != X0 )
& ( $true = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f96]) ).
thf(f96,plain,
! [X0: $o,X1: $o] :
( ( ( $true = X1 )
=> ( $true = X0 ) )
=> ( ( ( $true = X0 )
=> ( $true = X1 ) )
=> ( X0 = X1 ) ) ),
inference(fool_elimination,[status(thm)],[f95]) ).
thf(f95,plain,
! [X0: $o,X1: $o] :
( ( X1
=> X0 )
=> ( ( X0
=> X1 )
=> ( X0 = X1 ) ) ),
inference(rectify,[status(thm)],[f56]) ).
thf(f56,axiom,
! [X16: $o,X15: $o] :
( ( X15
=> X16 )
=> ( ( X16
=> X15 )
=> ( X15 = X16 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).
thf(f172,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
!= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
thf(f160,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
!= $true )
| ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
!= $true ) ),
inference(flattening,[status(thm)],[f159]) ).
thf(f159,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true )
| ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
!= $true )
| ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f94]) ).
thf(f94,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
= $true )
& ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
= $true ) )
=> ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f93]) ).
thf(f93,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal > $o,X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1 )
& ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X0 ) ),
inference(rectify,[status(thm)],[f68]) ).
thf(f68,axiom,
! [X24: mono_2Etyop_2Erealax_2Ereal > $o,X25: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X24 @ X25 )
& ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X25 ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X24 ) ),
file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
thf(f191,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f90]) ).
thf(f90,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f89]) ).
thf(f89,plain,
! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f67]) ).
thf(f67,axiom,
! [X23: mono_2Etyop_2Erealax_2Ereal,X22: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
thf(f171,plain,
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f162]) ).
thf(f162,plain,
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0 ) ) )
!= $true ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f156,f161]) ).
thf(f161,plain,
( ? [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
!= $true )
=> ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0 ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f156,plain,
? [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[status(thm)],[f110]) ).
thf(f110,plain,
~ ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f109]) ).
thf(f109,plain,
~ ! [X0: mono_2Etyop_2Erealax_2Ereal,X1: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f81]) ).
thf(f81,negated_conjecture,
~ ! [X23: mono_2Etyop_2Erealax_2Ereal,X22: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23 ) ) ),
inference(negated_conjecture,[status(cth)],[f80]) ).
thf(f80,conjecture,
! [X23: mono_2Etyop_2Erealax_2Ereal,X22: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP023^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n021.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:23:08 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : ITP023^1 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.28/0.46 % Domain : Interactive Theorem Proving
% 0.28/0.46 % Problem : HOL4 syntactic export of thm_2Ereal__topology_2EBOUNDED__BALL.p, bushy mode
% 0.28/0.46 % Version : [BG+19] axioms.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.28/0.46 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [BG+19]
% 0.28/0.46 % Names : thm_2Ereal__topology_2EBOUNDED__BALL.p [Gau19]
% 0.28/0.46 % : HL411001^1.p [TPAP]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0
% 0.28/0.46 % Syntax : Number of formulae : 160 ( 50 unt; 80 typ; 0 def)
% 0.28/0.46 % Number of atoms : 172 ( 57 equ; 46 cnn)
% 0.28/0.46 % Maximal formula atoms : 8 ( 2 avg)
% 0.28/0.46 % Number of connectives : 1075 ( 46 ~; 34 |; 25 &; 901 @)
% 0.28/0.46 % ( 39 <=>; 30 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 17 ( 5 avg)
% 0.28/0.46 % Number of types : 6 ( 5 usr)
% 0.28/0.46 % Number of type conns : 183 ( 183 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 77 ( 75 usr; 22 con; 0-3 aty)
% 0.28/0.46 % Number of variables : 144 ( 0 ^; 142 !; 2 ?; 144 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments :
% 0.28/0.46 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(u,type,
% 0.28/0.46 u: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(d,type,
% 0.28/0.46 d: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(du,type,
% 0.28/0.46 du: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.28/0.46 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(mono_2Etyop_2Erealax_2Ereal,type,
% 0.28/0.46 mono_2Etyop_2Erealax_2Ereal: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(tyop_2Emin_2Ebool,type,
% 0.28/0.46 tyop_2Emin_2Ebool: d ).
% 0.28/0.46
% 0.28/0.46 thf(tyop_2Emin_2Efun,type,
% 0.28/0.46 tyop_2Emin_2Efun: d > d > d ).
% 0.28/0.46
% 0.28/0.46 thf(tyop_2Epair_2Eprod,type,
% 0.28/0.46 tyop_2Epair_2Eprod: d > d > d ).
% 0.28/0.46
% 0.28/0.46 thf(tyop_2Erealax_2Ereal,type,
% 0.28/0.46 tyop_2Erealax_2Ereal: d ).
% 0.28/0.46
% 0.28/0.46 thf(s,type,
% 0.28/0.46 s: d > u > du ).
% 0.28/0.46
% 0.28/0.46 thf(app_2E2,type,
% 0.28/0.46 app_2E2: du > du > u ).
% 0.28/0.46
% 0.28/0.46 thf(combin_i_2E0,type,
% 0.28/0.46 combin_i_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(combin_k_2E0,type,
% 0.28/0.46 combin_k_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(combin_s_2E0,type,
% 0.28/0.46 combin_s_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2E_21_2E0,type,
% 0.28/0.46 c_2Ebool_2E_21_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2E_21_2E1,type,
% 0.28/0.46 c_2Ebool_2E_21_2E1: du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Epair_2E_2C_2E0,type,
% 0.28/0.46 c_2Epair_2E_2C_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Epair_2E_2C_2E2,type,
% 0.28/0.46 c_2Epair_2E_2C_2E2: du > du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 0.28/0.46 c_2Ebool_2E_2F_5C_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 0.28/0.46 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Emin_2E_3D_2E0,type,
% 0.28/0.46 c_2Emin_2E_3D_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Emin_2E_3D_2E2,type,
% 0.28/0.46 c_2Emin_2E_3D_2E2: du > du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 0.28/0.46 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 0.28/0.46 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2E_3F_2E0,type,
% 0.28/0.46 c_2Ebool_2E_3F_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2E_3F_2E1,type,
% 0.28/0.46 c_2Ebool_2E_3F_2E1: du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2EF_2E0,type,
% 0.28/0.46 c_2Ebool_2EF_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Epred__set_2ESUBSET_2E0,type,
% 0.28/0.46 c_2Epred__set_2ESUBSET_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Epred__set_2ESUBSET_2E2,type,
% 0.28/0.46 c_2Epred__set_2ESUBSET_2E2: du > du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2ET_2E0,type,
% 0.28/0.46 c_2Ebool_2ET_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 0.28/0.46 c_2Ebool_2E_5C_2F_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 0.28/0.46 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ereal__topology_2Eball_2E0,type,
% 0.28/0.46 c_2Ereal__topology_2Eball_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ereal__topology_2Eball_2E1,type,
% 0.28/0.46 c_2Ereal__topology_2Eball_2E1: du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ereal__topology_2Ebounded__def_2E0,type,
% 0.28/0.46 c_2Ereal__topology_2Ebounded__def_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ereal__topology_2Ebounded__def_2E1,type,
% 0.28/0.46 c_2Ereal__topology_2Ebounded__def_2E1: du > u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ereal__topology_2Ecball_2E0,type,
% 0.28/0.46 c_2Ereal__topology_2Ecball_2E0: u ).
% 0.28/0.46
% 0.28/0.46 thf(c_2Ereal__topology_2Ecball_2E1,type,
% 0.28/0.46 c_2Ereal__topology_2Ecball_2E1: du > u ).
% 0.28/0.47
% 0.28/0.47 thf(c_2Ebool_2E_7E_2E0,type,
% 0.28/0.47 c_2Ebool_2E_7E_2E0: u ).
% 0.28/0.47
% 0.28/0.47 thf(c_2Ebool_2E_7E_2E1,type,
% 0.28/0.47 c_2Ebool_2E_7E_2E1: du > u ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 0.28/0.47 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.28/0.47 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(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,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 0.28/0.47 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 0.28/0.47 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Ebool_2EF,type,
% 0.28/0.47 mono_2Ec_2Ebool_2EF: $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,type,
% 0.28/0.47 mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Ebool_2ET,type,
% 0.28/0.47 mono_2Ec_2Ebool_2ET: $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 0.28/0.47 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Ereal__topology_2Eball,type,
% 0.28/0.47 mono_2Ec_2Ereal__topology_2Eball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Ereal__topology_2Ebounded__def,type,
% 0.28/0.47 mono_2Ec_2Ereal__topology_2Ebounded__def: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Ereal__topology_2Ecball,type,
% 0.28/0.47 mono_2Ec_2Ereal__topology_2Ecball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
% 0.28/0.47
% 0.28/0.47 thf(mono_2Ec_2Ebool_2E_7E,type,
% 0.28/0.47 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 0.28/0.47 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 0.28/0.47
% 0.28/0.47 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.28/0.47 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 0.28/0.47
% 0.28/0.47 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.28/0.47 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 0.28/0.47
% 0.28/0.47 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(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,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(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,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
% 0.28/0.47 i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
% 0.28/0.47
% 0.28/0.47 thf(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,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.28/0.47 i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
% 0.28/0.47
% 0.28/0.47 thf(i_mono_2Etyop_2Erealax_2Ereal,type,
% 0.28/0.47 i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
% 0.28/0.47
% 0.28/0.47 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 0.28/0.47 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 0.28/0.47
% 0.28/0.47 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 0.28/0.47 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 0.28/0.47 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 0.28/0.47
% 0.28/0.47 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(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,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(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,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
% 0.28/0.47 j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o ).
% 0.28/0.47
% 0.28/0.47 thf(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,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 0.28/0.47 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 ).
% 0.28/0.47
% 0.28/0.47 thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 0.28/0.47 j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 0.28/0.47
% 0.28/0.47 thf(j_mono_2Etyop_2Erealax_2Ereal,type,
% 0.28/0.47 j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Eho_2Eeq__ext,axiom,
% 0.28/0.47 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 0.28/0.47 ( ! [V2x_2E0: u] :
% 0.28/0.47 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.28/0.47 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 0.28/0.47 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Eho_2Ei__thm,axiom,
% 0.28/0.47 ! [A_27a: d,V0x_2E0: u] :
% 0.28/0.47 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 0.28/0.47 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Eho_2Ek__thm,axiom,
% 0.28/0.47 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 0.28/0.47 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 0.28/0.47 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Eho_2Es__thm,axiom,
% 0.28/0.47 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 0.28/0.47 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 0.28/0.47 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 0.28/0.47 ! [V0: $o,V1: $o] :
% 0.28/0.47 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 0.28/0.47 <=> ( V0
% 0.28/0.47 & V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 0.28/0.47 ! [V0: $o,V1: $o] :
% 0.28/0.47 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 0.28/0.47 <=> ( V0
% 0.28/0.47 | V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Elogic_2E_7E,axiom,
% 0.28/0.47 ! [V0: $o] :
% 0.28/0.47 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 0.28/0.47 <=> ( (~) @ V0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 0.28/0.47 ! [V0: $o,V1: $o] :
% 0.28/0.47 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 0.28/0.47 <=> ( V0
% 0.28/0.47 => V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Elogic_2E_3D,axiom,
% 0.28/0.47 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 0.28/0.47 <=> ( ( s @ A_27a @ V0_2E0 )
% 0.28/0.47 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Equant_2E_21,axiom,
% 0.28/0.47 ! [A_27a: d,V0f_2E0: u] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.28/0.47 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(reserved_2Equant_2E_3F,axiom,
% 0.28/0.47 ! [A_27a: d,V0f_2E0: u] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 0.28/0.47 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_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,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( 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 @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( 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 @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( 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 @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ij_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 0.28/0.47 ! [V0_2E0: u] :
% 0.28/0.47 ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ) )
% 0.28/0.47 = ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 0.28/0.47 ! [V0: $o] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0: $o > $o] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.28/0.47 ! [V0: $o > $o > $o] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_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,axiom,
% 0.28/0.47 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o] :
% 0.28/0.47 ( ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( 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 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o] :
% 0.28/0.47 ( ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( 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 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal > $o] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.28/0.47 ( ( 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 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( 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 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(ji_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
% 0.28/0.47 = V0 ) ).
% 0.28/0.47
% 0.28/0.47 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 0.28/0.47 ! [A_27a: d,X0_2E0: u] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.28/0.47 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 0.28/0.47 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 0.28/0.47 ( ( ( s @ A_27a @ X0_2E0 )
% 0.28/0.47 = ( s @ A_27a @ X1_2E0 ) )
% 0.28/0.47 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 0.28/0.47 ! [A_27a: d,X0_2E0: u] :
% 0.28/0.47 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 0.28/0.47 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.28/0.47 ! [V0: $o > $o,V1: $o] :
% 0.28/0.47 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0: $o > $o > $o,V1: $o] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.28/0.47 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 0.28/0.47 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Eapp_2E2_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,axiom,
% 0.28/0.47 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( 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 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( 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 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( 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 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
% 0.28/0.47 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( 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_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ c_2Epair_2E_2C_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
% 0.28/0.47 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 0.28/0.47 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal ) )
% 0.28/0.47 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 0.28/0.47 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ V0 @ V1 ) ) )
% 0.28/0.47 = ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.28/0.47 ! [V0: $o > $o,V1: $o] :
% 0.28/0.47 ( ( V0 @ V1 )
% 0.28/0.47 = ( V0 @ V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0: $o > $o > $o,V1: $o] :
% 0.28/0.47 ( ( V0 @ V1 )
% 0.28/0.47 = ( V0 @ V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
% 0.28/0.47 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 0.28/0.47 ( ( V0 @ V1 )
% 0.28/0.47 = ( V0 @ V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoapp_2Emono_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,axiom,
% 0.28/0.47 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 0.28/0.47 ( ( V0 @ V1 )
% 0.28/0.47 = ( V0 @ V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 0.28/0.47 ( ( V0 @ V1 )
% 0.28/0.47 = ( V0 @ V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
% 0.28/0.47 ( ( V0 @ V1 )
% 0.28/0.47 = ( V0 @ V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 0.28/0.47 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
% 0.28/0.47 ( ( V0 @ V1 )
% 0.28/0.47 = ( V0 @ V1 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2ETRUTH,axiom,
% 0.28/0.47 mono_2Ec_2Ebool_2ET ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 0.28/0.47 ! [V0t1: $o,V1t2: $o] :
% 0.28/0.47 ( ( V0t1
% 0.28/0.47 => V1t2 )
% 0.28/0.47 => ( ( V1t2
% 0.28/0.47 => V0t1 )
% 0.28/0.47 => ( V0t1 = V1t2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EIMP__F,axiom,
% 0.28/0.47 ! [V0t: $o] :
% 0.28/0.47 ( ( V0t
% 0.28/0.47 => mono_2Ec_2Ebool_2EF )
% 0.28/0.47 => ( (~) @ V0t ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EF__IMP,axiom,
% 0.28/0.47 ! [V0t: $o] :
% 0.28/0.47 ( ( (~) @ V0t )
% 0.28/0.47 => ( V0t
% 0.28/0.47 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.28/0.47 ! [V0t: $o] :
% 0.28/0.47 ( ( ( mono_2Ec_2Ebool_2ET
% 0.28/0.47 => V0t )
% 0.28/0.47 <=> V0t )
% 0.28/0.47 & ( ( V0t
% 0.28/0.47 => mono_2Ec_2Ebool_2ET )
% 0.28/0.47 <=> mono_2Ec_2Ebool_2ET )
% 0.28/0.47 & ( ( mono_2Ec_2Ebool_2EF
% 0.28/0.47 => V0t )
% 0.28/0.47 <=> mono_2Ec_2Ebool_2ET )
% 0.28/0.47 & ( ( V0t
% 0.28/0.47 => V0t )
% 0.28/0.47 <=> mono_2Ec_2Ebool_2ET )
% 0.28/0.47 & ( ( V0t
% 0.28/0.47 => mono_2Ec_2Ebool_2EF )
% 0.28/0.47 <=> ( (~) @ V0t ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.28/0.47 ( ! [V0t: $o] :
% 0.28/0.47 ( ( (~) @ ( (~) @ V0t ) )
% 0.28/0.47 <=> V0t )
% 0.28/0.47 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 0.28/0.47 <=> mono_2Ec_2Ebool_2EF )
% 0.28/0.47 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 0.28/0.47 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.28/0.47 ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
% 0.28/0.47 ( ( ( s @ A_27a @ V0x_2E0 )
% 0.28/0.47 = ( s @ A_27a @ V1y_2E0 ) )
% 0.28/0.47 <=> ( ( s @ A_27a @ V1y_2E0 )
% 0.28/0.47 = ( s @ A_27a @ V0x_2E0 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.28/0.47 ! [V0t: $o] :
% 0.28/0.47 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 0.28/0.47 <=> V0t )
% 0.28/0.47 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 0.28/0.47 <=> V0t )
% 0.28/0.47 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 0.28/0.47 <=> ( (~) @ V0t ) )
% 0.28/0.47 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 0.28/0.47 <=> ( (~) @ V0t ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2ENOT__FORALL__THM,axiom,
% 0.28/0.47 ! [A_27a: d,V0P_2E0: u] :
% 0.28/0.47 ( ( (~)
% 0.28/0.47 @ ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
% 0.28/0.47 <=> ? [V2x_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EDISJ__ASSOC,axiom,
% 0.28/0.47 ! [V0A: $o,V1B: $o,V2C: $o] :
% 0.28/0.47 ( ( V0A
% 0.28/0.47 | V1B
% 0.28/0.47 | V2C )
% 0.28/0.47 <=> ( V0A
% 0.28/0.47 | V1B
% 0.28/0.47 | V2C ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EDISJ__SYM,axiom,
% 0.28/0.47 ! [V0A: $o,V1B: $o] :
% 0.28/0.47 ( ( V0A
% 0.28/0.47 | V1B )
% 0.28/0.47 <=> ( V1B
% 0.28/0.47 | V0A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ebool_2EDE__MORGAN__THM,axiom,
% 0.28/0.47 ! [V0A: $o,V1B: $o] :
% 0.28/0.47 ( ( ( (~)
% 0.28/0.47 @ ( V0A
% 0.28/0.47 & V1B ) )
% 0.28/0.47 <=> ( ( (~) @ V0A )
% 0.28/0.47 | ( (~) @ V1B ) ) )
% 0.28/0.47 & ( ( (~)
% 0.28/0.47 @ ( V0A
% 0.28/0.47 | V1B ) )
% 0.28/0.47 <=> ( ( (~) @ V0A )
% 0.28/0.47 & ( (~) @ V1B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
% 0.28/0.47 ! [V0x: mono_2Etyop_2Erealax_2Ereal,V1e: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ V1e ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ V1e ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
% 0.28/0.47 ! [V0s: mono_2Etyop_2Erealax_2Ereal > $o,V1t: mono_2Etyop_2Erealax_2Ereal > $o] :
% 0.28/0.47 ( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ V1t )
% 0.28/0.47 & ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ V0s @ V1t ) )
% 0.28/0.47 => ( mono_2Ec_2Ereal__topology_2Ebounded__def @ V0s ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
% 0.28/0.47 ! [V0x: mono_2Etyop_2Erealax_2Ereal,V1e: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ V1e ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2ENOT__NOT,axiom,
% 0.28/0.47 ! [V0t: $o] :
% 0.28/0.47 ( ( (~) @ ( (~) @ V0t ) )
% 0.28/0.47 <=> V0t ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 0.28/0.47 ! [V0A: $o] :
% 0.28/0.47 ( V0A
% 0.28/0.47 => ( ( (~) @ V0A )
% 0.28/0.47 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 0.28/0.47 ! [V0B: $o,V1A: $o] :
% 0.28/0.47 ( ( ( (~)
% 0.28/0.47 @ ( V1A
% 0.28/0.47 | V0B ) )
% 0.28/0.47 => mono_2Ec_2Ebool_2EF )
% 0.28/0.47 <=> ( ( V1A
% 0.28/0.47 => mono_2Ec_2Ebool_2EF )
% 0.28/0.47 => ( ( (~) @ V0B )
% 0.28/0.47 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 0.28/0.47 ! [V0B: $o,V1A: $o] :
% 0.28/0.47 ( ( ( (~)
% 0.28/0.47 @ ( ( (~) @ V1A )
% 0.28/0.47 | V0B ) )
% 0.28/0.47 => mono_2Ec_2Ebool_2EF )
% 0.28/0.47 <=> ( V1A
% 0.28/0.47 => ( ( (~) @ V0B )
% 0.28/0.47 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2EAND__INV2,axiom,
% 0.28/0.47 ! [V0A: $o] :
% 0.28/0.47 ( ( ( (~) @ V0A )
% 0.28/0.47 => mono_2Ec_2Ebool_2EF )
% 0.28/0.47 => ( ( V0A
% 0.28/0.47 => mono_2Ec_2Ebool_2EF )
% 0.28/0.47 => mono_2Ec_2Ebool_2EF ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2Edc__eq,axiom,
% 0.28/0.47 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.28/0.47 ( ( V2p
% 0.28/0.47 <=> ( V1q = V0r ) )
% 0.28/0.47 <=> ( ( V2p
% 0.28/0.47 | V1q
% 0.28/0.47 | V0r )
% 0.28/0.47 & ( V2p
% 0.28/0.47 | ( (~) @ V0r )
% 0.28/0.47 | ( (~) @ V1q ) )
% 0.28/0.47 & ( V1q
% 0.28/0.47 | ( (~) @ V0r )
% 0.28/0.47 | ( (~) @ V2p ) )
% 0.28/0.47 & ( V0r
% 0.28/0.47 | ( (~) @ V1q )
% 0.28/0.47 | ( (~) @ V2p ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2Edc__conj,axiom,
% 0.28/0.47 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.28/0.47 ( ( V2p
% 0.28/0.47 <=> ( V1q
% 0.28/0.47 & V0r ) )
% 0.28/0.47 <=> ( ( V2p
% 0.28/0.47 | ( (~) @ V1q )
% 0.28/0.47 | ( (~) @ V0r ) )
% 0.28/0.47 & ( V1q
% 0.28/0.47 | ( (~) @ V2p ) )
% 0.28/0.47 & ( V0r
% 0.28/0.47 | ( (~) @ V2p ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2Edc__disj,axiom,
% 0.28/0.47 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.28/0.47 ( ( V2p
% 0.28/0.47 <=> ( V1q
% 0.28/0.47 | V0r ) )
% 0.28/0.47 <=> ( ( V2p
% 0.28/0.47 | ( (~) @ V1q ) )
% 0.28/0.47 & ( V2p
% 0.28/0.47 | ( (~) @ V0r ) )
% 0.28/0.47 & ( V1q
% 0.28/0.47 | V0r
% 0.28/0.47 | ( (~) @ V2p ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2Edc__imp,axiom,
% 0.28/0.47 ! [V0r: $o,V1q: $o,V2p: $o] :
% 0.28/0.47 ( ( V2p
% 0.28/0.47 <=> ( V1q
% 0.28/0.47 => V0r ) )
% 0.28/0.47 <=> ( ( V2p
% 0.28/0.47 | V1q )
% 0.28/0.47 & ( V2p
% 0.28/0.47 | ( (~) @ V0r ) )
% 0.28/0.47 & ( ( (~) @ V1q )
% 0.28/0.47 | V0r
% 0.28/0.47 | ( (~) @ V2p ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Esat_2Edc__neg,axiom,
% 0.28/0.47 ! [V0q: $o,V1p: $o] :
% 0.28/0.47 ( ( V1p
% 0.28/0.47 <=> ( (~) @ V0q ) )
% 0.28/0.47 <=> ( ( V1p
% 0.28/0.47 | V0q )
% 0.28/0.47 & ( ( (~) @ V0q )
% 0.28/0.47 | ( (~) @ V1p ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
% 0.28/0.47 ! [V0x: mono_2Etyop_2Erealax_2Ereal,V1e: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ V1e ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 3.06/1.88 ---- Embedded in THF ---
% 3.06/1.88 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.06/1.88 %%% Generated on Tue Feb 24 08:23:10 EST 2026
% 3.06/1.88 %%% using '$$dhol' embedding, version 1.3.0.
% 3.06/1.88 %%% Logic specification used:
% 3.06/1.88 %%% thf(spec, logic, $$dhol).
% 3.06/1.88
% 3.06/1.88 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2DTF3858.p
% See solution above
% 3.06/1.89 ------------------------
% 3.25/1.91 ---- Cleaned THF ---
% 3.25/1.91 thf(u,type,
% 3.25/1.91 u: $tType ).
% 3.25/1.91
% 3.25/1.91 thf(d,type,
% 3.25/1.91 d: $tType ).
% 3.25/1.91
% 3.25/1.91 thf(du,type,
% 3.25/1.91 du: $tType ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 3.25/1.91 mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Etyop_2Erealax_2Ereal,type,
% 3.25/1.91 mono_2Etyop_2Erealax_2Ereal: $tType ).
% 3.25/1.91
% 3.25/1.91 thf(tyop_2Emin_2Ebool,type,
% 3.25/1.91 tyop_2Emin_2Ebool: d ).
% 3.25/1.91
% 3.25/1.91 thf(tyop_2Emin_2Efun,type,
% 3.25/1.91 tyop_2Emin_2Efun: d > d > d ).
% 3.25/1.91
% 3.25/1.91 thf(tyop_2Epair_2Eprod,type,
% 3.25/1.91 tyop_2Epair_2Eprod: d > d > d ).
% 3.25/1.91
% 3.25/1.91 thf(tyop_2Erealax_2Ereal,type,
% 3.25/1.91 tyop_2Erealax_2Ereal: d ).
% 3.25/1.91
% 3.25/1.91 thf(s,type,
% 3.25/1.91 s: d > u > du ).
% 3.25/1.91
% 3.25/1.91 thf(app_2E2,type,
% 3.25/1.91 app_2E2: du > du > u ).
% 3.25/1.91
% 3.25/1.91 thf(combin_i_2E0,type,
% 3.25/1.91 combin_i_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(combin_k_2E0,type,
% 3.25/1.91 combin_k_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(combin_s_2E0,type,
% 3.25/1.91 combin_s_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_21_2E0,type,
% 3.25/1.91 c_2Ebool_2E_21_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_21_2E1,type,
% 3.25/1.91 c_2Ebool_2E_21_2E1: du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Epair_2E_2C_2E0,type,
% 3.25/1.91 c_2Epair_2E_2C_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Epair_2E_2C_2E2,type,
% 3.25/1.91 c_2Epair_2E_2C_2E2: du > du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_2F_5C_2E0,type,
% 3.25/1.91 c_2Ebool_2E_2F_5C_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_2F_5C_2E2,type,
% 3.25/1.91 c_2Ebool_2E_2F_5C_2E2: du > du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Emin_2E_3D_2E0,type,
% 3.25/1.91 c_2Emin_2E_3D_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Emin_2E_3D_2E2,type,
% 3.25/1.91 c_2Emin_2E_3D_2E2: du > du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Emin_2E_3D_3D_3E_2E0,type,
% 3.25/1.91 c_2Emin_2E_3D_3D_3E_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Emin_2E_3D_3D_3E_2E2,type,
% 3.25/1.91 c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_3F_2E0,type,
% 3.25/1.91 c_2Ebool_2E_3F_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_3F_2E1,type,
% 3.25/1.91 c_2Ebool_2E_3F_2E1: du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2EF_2E0,type,
% 3.25/1.91 c_2Ebool_2EF_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Epred__set_2ESUBSET_2E0,type,
% 3.25/1.91 c_2Epred__set_2ESUBSET_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Epred__set_2ESUBSET_2E2,type,
% 3.25/1.91 c_2Epred__set_2ESUBSET_2E2: du > du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2ET_2E0,type,
% 3.25/1.91 c_2Ebool_2ET_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_5C_2F_2E0,type,
% 3.25/1.91 c_2Ebool_2E_5C_2F_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_5C_2F_2E2,type,
% 3.25/1.91 c_2Ebool_2E_5C_2F_2E2: du > du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ereal__topology_2Eball_2E0,type,
% 3.25/1.91 c_2Ereal__topology_2Eball_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ereal__topology_2Eball_2E1,type,
% 3.25/1.91 c_2Ereal__topology_2Eball_2E1: du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ereal__topology_2Ebounded__def_2E0,type,
% 3.25/1.91 c_2Ereal__topology_2Ebounded__def_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ereal__topology_2Ebounded__def_2E1,type,
% 3.25/1.91 c_2Ereal__topology_2Ebounded__def_2E1: du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ereal__topology_2Ecball_2E0,type,
% 3.25/1.91 c_2Ereal__topology_2Ecball_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ereal__topology_2Ecball_2E1,type,
% 3.25/1.91 c_2Ereal__topology_2Ecball_2E1: du > u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_7E_2E0,type,
% 3.25/1.91 c_2Ebool_2E_7E_2E0: u ).
% 3.25/1.91
% 3.25/1.91 thf(c_2Ebool_2E_7E_2E1,type,
% 3.25/1.91 c_2Ebool_2E_7E_2E1: du > u ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
% 3.25/1.91 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 3.25/1.91 mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(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,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Ebool_2E_2F_5C,type,
% 3.25/1.91 mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
% 3.25/1.91 mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Ebool_2EF,type,
% 3.25/1.91 mono_2Ec_2Ebool_2EF: $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,type,
% 3.25/1.91 mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Ebool_2ET,type,
% 3.25/1.91 mono_2Ec_2Ebool_2ET: $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Ebool_2E_5C_2F,type,
% 3.25/1.91 mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Ereal__topology_2Eball,type,
% 3.25/1.91 mono_2Ec_2Ereal__topology_2Eball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Ereal__topology_2Ebounded__def,type,
% 3.25/1.91 mono_2Ec_2Ereal__topology_2Ebounded__def: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Ereal__topology_2Ecball,type,
% 3.25/1.91 mono_2Ec_2Ereal__topology_2Ecball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
% 3.25/1.91
% 3.25/1.91 thf(mono_2Ec_2Ebool_2E_7E,type,
% 3.25/1.91 mono_2Ec_2Ebool_2E_7E: $o > $o ).
% 3.25/1.91
% 3.25/1.91 thf(i_mono_2Etyop_2Emin_2Ebool,type,
% 3.25/1.91 i_mono_2Etyop_2Emin_2Ebool: $o > u ).
% 3.25/1.91
% 3.25/1.91 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 3.25/1.91 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
% 3.25/1.91
% 3.25/1.91 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 3.25/1.91 i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
% 3.25/1.91
% 3.25/1.91 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(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,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(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,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
% 3.25/1.91 i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Erealax_2Ereal > $o ) > u ).
% 3.25/1.91
% 3.25/1.91 thf(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,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 3.25/1.91 i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).
% 3.25/1.91
% 3.25/1.91 thf(i_mono_2Etyop_2Erealax_2Ereal,type,
% 3.25/1.91 i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).
% 3.25/1.91
% 3.25/1.91 thf(j_mono_2Etyop_2Emin_2Ebool,type,
% 3.25/1.91 j_mono_2Etyop_2Emin_2Ebool: du > $o ).
% 3.25/1.91
% 3.25/1.91 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
% 3.25/1.91 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
% 3.25/1.91
% 3.25/1.91 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
% 3.25/1.91 j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
% 3.25/1.91
% 3.25/1.91 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(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,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(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,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,type,
% 3.25/1.91 j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o ).
% 3.25/1.91
% 3.25/1.91 thf(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,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,type,
% 3.25/1.91 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 ).
% 3.25/1.91
% 3.25/1.91 thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
% 3.25/1.91 j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
% 3.25/1.91
% 3.25/1.91 thf(j_mono_2Etyop_2Erealax_2Ereal,type,
% 3.25/1.91 j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Eho_2Eeq__ext,axiom,
% 3.25/1.91 ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
% 3.25/1.91 ( ! [V2x_2E0: u] :
% 3.25/1.91 ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 3.25/1.91 = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
% 3.25/1.91 => ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Eho_2Ei__thm,axiom,
% 3.25/1.91 ! [A_27a: d,V0x_2E0: u] :
% 3.25/1.91 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
% 3.25/1.91 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Eho_2Ek__thm,axiom,
% 3.25/1.91 ! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
% 3.25/1.91 ( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
% 3.25/1.91 = ( s @ A_27a @ V0x_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Eho_2Es__thm,axiom,
% 3.25/1.91 ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
% 3.25/1.91 ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
% 3.25/1.91 = ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Elogic_2E_2F_5C,axiom,
% 3.25/1.91 ! [V0: $o,V1: $o] :
% 3.25/1.91 ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
% 3.25/1.91 <=> ( V0
% 3.25/1.91 & V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Elogic_2E_5C_2F,axiom,
% 3.25/1.91 ! [V0: $o,V1: $o] :
% 3.25/1.91 ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
% 3.25/1.91 <=> ( V0
% 3.25/1.91 | V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Elogic_2E_7E,axiom,
% 3.25/1.91 ! [V0: $o] :
% 3.25/1.91 ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
% 3.25/1.91 <=> ( (~) @ V0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
% 3.25/1.91 ! [V0: $o,V1: $o] :
% 3.25/1.91 ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
% 3.25/1.91 <=> ( V0
% 3.25/1.91 => V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Elogic_2E_3D,axiom,
% 3.25/1.91 ! [A_27a: d,V0_2E0: u,V1_2E0: u] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
% 3.25/1.91 <=> ( ( s @ A_27a @ V0_2E0 )
% 3.25/1.91 = ( s @ A_27a @ V1_2E0 ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Equant_2E_21,axiom,
% 3.25/1.91 ! [A_27a: d,V0f_2E0: u] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 3.25/1.91 <=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(reserved_2Equant_2E_3F,axiom,
% 3.25/1.91 ! [A_27a: d,V0f_2E0: u] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
% 3.25/1.91 <=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_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,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( 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 @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( 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 @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( 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 @ ( 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 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ij_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 3.25/1.91 ! [V0_2E0: u] :
% 3.25/1.91 ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ) )
% 3.25/1.91 = ( s @ tyop_2Erealax_2Ereal @ V0_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
% 3.25/1.91 ! [V0: $o] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0: $o > $o] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 3.25/1.91 ! [V0: $o > $o > $o] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_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,axiom,
% 3.25/1.91 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o] :
% 3.25/1.91 ( ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( 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 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o] :
% 3.25/1.91 ( ( 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 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( 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 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal > $o] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 3.25/1.91 ( ( 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 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( 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 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(ji_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) )
% 3.25/1.91 = V0 ) ).
% 3.25/1.91
% 3.25/1.91 thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
% 3.25/1.91 ! [A_27a: d,X0_2E0: u] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 3.25/1.91 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
% 3.25/1.91 ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
% 3.25/1.91 ( ( ( s @ A_27a @ X0_2E0 )
% 3.25/1.91 = ( s @ A_27a @ X1_2E0 ) )
% 3.25/1.91 <=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
% 3.25/1.91 ! [A_27a: d,X0_2E0: u] :
% 3.25/1.91 ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
% 3.25/1.91 = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 3.25/1.91 ! [V0: $o > $o,V1: $o] :
% 3.25/1.91 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0: $o > $o > $o,V1: $o] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
% 3.25/1.91 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 3.25/1.91 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Eapp_2E2_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,axiom,
% 3.25/1.91 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( 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 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( 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 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ ( V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( 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 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
% 3.25/1.91 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ ( 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_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) ) @ c_2Epair_2E_2C_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal,V1: mono_2Etyop_2Erealax_2Ereal] :
% 3.25/1.91 ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V0 ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E0_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 3.25/1.91 ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( 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_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal ) )
% 3.25/1.91 = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Epred__set_2ESUBSET_2E0 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoeq_2Emono_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Erealax_2Ereal,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 3.25/1.91 ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ V0 @ V1 ) ) )
% 3.25/1.91 = ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2ESUBSET_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
% 3.25/1.91 ! [V0: $o > $o,V1: $o] :
% 3.25/1.91 ( ( V0 @ V1 )
% 3.25/1.91 = ( V0 @ V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0: $o > $o > $o,V1: $o] :
% 3.25/1.91 ( ( V0 @ V1 )
% 3.25/1.91 = ( V0 @ V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
% 3.25/1.91 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 3.25/1.91 ( ( V0 @ V1 )
% 3.25/1.91 = ( V0 @ V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoapp_2Emono_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,axiom,
% 3.25/1.91 ! [V0: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o,V1: mono_2Etyop_2Erealax_2Ereal > $o] :
% 3.25/1.91 ( ( V0 @ V1 )
% 3.25/1.91 = ( V0 @ V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
% 3.25/1.91 ( ( V0 @ V1 )
% 3.25/1.91 = ( V0 @ V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
% 3.25/1.91 ( ( V0 @ V1 )
% 3.25/1.91 = ( V0 @ V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,axiom,
% 3.25/1.91 ! [V0: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,V1: mono_2Etyop_2Erealax_2Ereal] :
% 3.25/1.91 ( ( V0 @ V1 )
% 3.25/1.91 = ( V0 @ V1 ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2ETRUTH,axiom,
% 3.25/1.91 mono_2Ec_2Ebool_2ET ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EIMP__ANTISYM__AX,axiom,
% 3.25/1.91 ! [V0t1: $o,V1t2: $o] :
% 3.25/1.91 ( ( V0t1
% 3.25/1.91 => V1t2 )
% 3.25/1.91 => ( ( V1t2
% 3.25/1.91 => V0t1 )
% 3.25/1.91 => ( V0t1 = V1t2 ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EIMP__F,axiom,
% 3.25/1.91 ! [V0t: $o] :
% 3.25/1.91 ( ( V0t
% 3.25/1.91 => mono_2Ec_2Ebool_2EF )
% 3.25/1.91 => ( (~) @ V0t ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EF__IMP,axiom,
% 3.25/1.91 ! [V0t: $o] :
% 3.25/1.91 ( ( (~) @ V0t )
% 3.25/1.91 => ( V0t
% 3.25/1.91 => mono_2Ec_2Ebool_2EF ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EIMP__CLAUSES,axiom,
% 3.25/1.91 ! [V0t: $o] :
% 3.25/1.91 ( ( ( mono_2Ec_2Ebool_2ET
% 3.25/1.91 => V0t )
% 3.25/1.91 <=> V0t )
% 3.25/1.91 & ( ( V0t
% 3.25/1.91 => mono_2Ec_2Ebool_2ET )
% 3.25/1.91 <=> mono_2Ec_2Ebool_2ET )
% 3.25/1.91 & ( ( mono_2Ec_2Ebool_2EF
% 3.25/1.91 => V0t )
% 3.25/1.91 <=> mono_2Ec_2Ebool_2ET )
% 3.25/1.91 & ( ( V0t
% 3.25/1.91 => V0t )
% 3.25/1.91 <=> mono_2Ec_2Ebool_2ET )
% 3.25/1.91 & ( ( V0t
% 3.25/1.91 => mono_2Ec_2Ebool_2EF )
% 3.25/1.91 <=> ( (~) @ V0t ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
% 3.25/1.91 ( ! [V0t: $o] :
% 3.25/1.91 ( ( (~) @ ( (~) @ V0t ) )
% 3.25/1.91 <=> V0t )
% 3.25/1.91 & ( ( (~) @ mono_2Ec_2Ebool_2ET )
% 3.25/1.91 <=> mono_2Ec_2Ebool_2EF )
% 3.25/1.91 & ( ( (~) @ mono_2Ec_2Ebool_2EF )
% 3.25/1.91 <=> mono_2Ec_2Ebool_2ET ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 3.25/1.91 ! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
% 3.25/1.91 ( ( ( s @ A_27a @ V0x_2E0 )
% 3.25/1.91 = ( s @ A_27a @ V1y_2E0 ) )
% 3.25/1.91 <=> ( ( s @ A_27a @ V1y_2E0 )
% 3.25/1.91 = ( s @ A_27a @ V0x_2E0 ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EEQ__CLAUSES,axiom,
% 3.25/1.91 ! [V0t: $o] :
% 3.25/1.91 ( ( ( mono_2Ec_2Ebool_2ET = V0t )
% 3.25/1.91 <=> V0t )
% 3.25/1.91 & ( ( V0t = mono_2Ec_2Ebool_2ET )
% 3.25/1.91 <=> V0t )
% 3.25/1.91 & ( ( mono_2Ec_2Ebool_2EF = V0t )
% 3.25/1.91 <=> ( (~) @ V0t ) )
% 3.25/1.91 & ( ( V0t = mono_2Ec_2Ebool_2EF )
% 3.25/1.91 <=> ( (~) @ V0t ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2ENOT__FORALL__THM,axiom,
% 3.25/1.91 ! [A_27a: d,V0P_2E0: u] :
% 3.25/1.91 ( ( (~)
% 3.25/1.91 @ ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) )
% 3.25/1.91 <=> ? [V2x_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EDISJ__ASSOC,axiom,
% 3.25/1.91 ! [V0A: $o,V1B: $o,V2C: $o] :
% 3.25/1.91 ( ( V0A
% 3.25/1.91 | V1B
% 3.25/1.91 | V2C )
% 3.25/1.91 <=> ( V0A
% 3.25/1.91 | V1B
% 3.25/1.91 | V2C ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EDISJ__SYM,axiom,
% 3.25/1.91 ! [V0A: $o,V1B: $o] :
% 3.25/1.91 ( ( V0A
% 3.25/1.91 | V1B )
% 3.25/1.91 <=> ( V1B
% 3.25/1.91 | V0A ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ebool_2EDE__MORGAN__THM,axiom,
% 3.25/1.91 ! [V0A: $o,V1B: $o] :
% 3.25/1.91 ( ( ( (~)
% 3.25/1.91 @ ( V0A
% 3.25/1.91 & V1B ) )
% 3.25/1.91 <=> ( ( (~) @ V0A )
% 3.25/1.91 | ( (~) @ V1B ) ) )
% 3.25/1.91 & ( ( (~)
% 3.25/1.91 @ ( V0A
% 3.25/1.91 | V1B ) )
% 3.25/1.91 <=> ( ( (~) @ V0A )
% 3.25/1.91 & ( (~) @ V1B ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
% 3.25/1.91 ! [V0x: mono_2Etyop_2Erealax_2Ereal,V1e: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ V1e ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ V1e ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
% 3.25/1.91 ! [V0s: mono_2Etyop_2Erealax_2Ereal > $o,V1t: mono_2Etyop_2Erealax_2Ereal > $o] :
% 3.25/1.91 ( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ V1t )
% 3.25/1.91 & ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ V0s @ V1t ) )
% 3.25/1.91 => ( mono_2Ec_2Ereal__topology_2Ebounded__def @ V0s ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
% 3.25/1.91 ! [V0x: mono_2Etyop_2Erealax_2Ereal,V1e: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ V1e ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2ENOT__NOT,axiom,
% 3.25/1.91 ! [V0t: $o] :
% 3.25/1.91 ( ( (~) @ ( (~) @ V0t ) )
% 3.25/1.91 <=> V0t ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2EAND__INV__IMP,axiom,
% 3.25/1.91 ! [V0A: $o] :
% 3.25/1.91 ( V0A
% 3.25/1.91 => ( ( (~) @ V0A )
% 3.25/1.91 => mono_2Ec_2Ebool_2EF ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2EOR__DUAL2,axiom,
% 3.25/1.91 ! [V0B: $o,V1A: $o] :
% 3.25/1.91 ( ( ( (~)
% 3.25/1.91 @ ( V1A
% 3.25/1.91 | V0B ) )
% 3.25/1.91 => mono_2Ec_2Ebool_2EF )
% 3.25/1.91 <=> ( ( V1A
% 3.25/1.91 => mono_2Ec_2Ebool_2EF )
% 3.25/1.91 => ( ( (~) @ V0B )
% 3.25/1.91 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2EOR__DUAL3,axiom,
% 3.25/1.91 ! [V0B: $o,V1A: $o] :
% 3.25/1.91 ( ( ( (~)
% 3.25/1.91 @ ( ( (~) @ V1A )
% 3.25/1.91 | V0B ) )
% 3.25/1.91 => mono_2Ec_2Ebool_2EF )
% 3.25/1.91 <=> ( V1A
% 3.25/1.91 => ( ( (~) @ V0B )
% 3.25/1.91 => mono_2Ec_2Ebool_2EF ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2EAND__INV2,axiom,
% 3.25/1.91 ! [V0A: $o] :
% 3.25/1.91 ( ( ( (~) @ V0A )
% 3.25/1.91 => mono_2Ec_2Ebool_2EF )
% 3.25/1.91 => ( ( V0A
% 3.25/1.91 => mono_2Ec_2Ebool_2EF )
% 3.25/1.91 => mono_2Ec_2Ebool_2EF ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2Edc__eq,axiom,
% 3.25/1.91 ! [V0r: $o,V1q: $o,V2p: $o] :
% 3.25/1.91 ( ( V2p
% 3.25/1.91 <=> ( V1q = V0r ) )
% 3.25/1.91 <=> ( ( V2p
% 3.25/1.91 | V1q
% 3.25/1.91 | V0r )
% 3.25/1.91 & ( V2p
% 3.25/1.91 | ( (~) @ V0r )
% 3.25/1.91 | ( (~) @ V1q ) )
% 3.25/1.91 & ( V1q
% 3.25/1.91 | ( (~) @ V0r )
% 3.25/1.91 | ( (~) @ V2p ) )
% 3.25/1.91 & ( V0r
% 3.25/1.91 | ( (~) @ V1q )
% 3.25/1.91 | ( (~) @ V2p ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2Edc__conj,axiom,
% 3.25/1.91 ! [V0r: $o,V1q: $o,V2p: $o] :
% 3.25/1.91 ( ( V2p
% 3.25/1.91 <=> ( V1q
% 3.25/1.91 & V0r ) )
% 3.25/1.91 <=> ( ( V2p
% 3.25/1.91 | ( (~) @ V1q )
% 3.25/1.91 | ( (~) @ V0r ) )
% 3.25/1.91 & ( V1q
% 3.25/1.91 | ( (~) @ V2p ) )
% 3.25/1.91 & ( V0r
% 3.25/1.91 | ( (~) @ V2p ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2Edc__disj,axiom,
% 3.25/1.91 ! [V0r: $o,V1q: $o,V2p: $o] :
% 3.25/1.91 ( ( V2p
% 3.25/1.91 <=> ( V1q
% 3.25/1.91 | V0r ) )
% 3.25/1.91 <=> ( ( V2p
% 3.25/1.91 | ( (~) @ V1q ) )
% 3.25/1.91 & ( V2p
% 3.25/1.91 | ( (~) @ V0r ) )
% 3.25/1.91 & ( V1q
% 3.25/1.91 | V0r
% 3.25/1.91 | ( (~) @ V2p ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2Edc__imp,axiom,
% 3.25/1.91 ! [V0r: $o,V1q: $o,V2p: $o] :
% 3.25/1.91 ( ( V2p
% 3.25/1.91 <=> ( V1q
% 3.25/1.91 => V0r ) )
% 3.25/1.91 <=> ( ( V2p
% 3.25/1.91 | V1q )
% 3.25/1.91 & ( V2p
% 3.25/1.91 | ( (~) @ V0r ) )
% 3.25/1.91 & ( ( (~) @ V1q )
% 3.25/1.91 | V0r
% 3.25/1.91 | ( (~) @ V2p ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Esat_2Edc__neg,axiom,
% 3.25/1.91 ! [V0q: $o,V1p: $o] :
% 3.25/1.91 ( ( V1p
% 3.25/1.91 <=> ( (~) @ V0q ) )
% 3.25/1.91 <=> ( ( V1p
% 3.25/1.91 | V0q )
% 3.25/1.91 & ( ( (~) @ V0q )
% 3.25/1.91 | ( (~) @ V1p ) ) ) ) ).
% 3.25/1.91
% 3.25/1.91 thf(thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
% 3.25/1.91 ! [V0x: mono_2Etyop_2Erealax_2Ereal,V1e: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ V0x @ V1e ) ) ) ).
% 3.25/1.91 ------------------------
% 3.25/1.95 % (4019)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3858 for (2999ds/18Mi)
% 3.25/1.95 % (4017)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3858 for (2999ds/2Mi)
% 3.25/1.95 % (4015)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_3858 for (2999ds/27Mi)
% 3.25/1.95 % (4018)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_3858 for (2999ds/275Mi)
% 3.25/1.95 % (4014)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_3858 for (2999ds/4Mi)
% 3.25/1.95 % (4013)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3858 for (2999ds/183Mi)
% 3.25/1.95 % (4016)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3858 for (2999ds/2Mi)
% 3.25/1.95 % (4016)Instruction limit reached!
% 3.25/1.95 % (4016)------------------------------
% 3.25/1.95 % (4016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.95 % (4016)Termination reason: Unknown
% 3.25/1.95 % (4016)Termination phase: shuffling
% 3.25/1.95 % (4017)Instruction limit reached!
% 3.25/1.95 % (4017)------------------------------
% 3.25/1.95 % (4017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.95
% 3.25/1.95 % (4016)Memory used [KB]: 1151
% 3.25/1.95 % (4016)Time elapsed: 0.003 s
% 3.25/1.95 % (4016)Instructions burned: 2 (million)
% 3.25/1.95 % (4016)------------------------------
% 3.25/1.95 % (4016)------------------------------
% 3.25/1.95 % (4017)Termination reason: Unknown
% 3.25/1.95 % (4017)Termination phase: shuffling
% 3.25/1.95
% 3.25/1.95 % (4017)Memory used [KB]: 1151
% 3.25/1.95 % (4017)Time elapsed: 0.003 s
% 3.25/1.95 % (4017)Instructions burned: 2 (million)
% 3.25/1.95 % (4017)------------------------------
% 3.25/1.95 % (4017)------------------------------
% 3.25/1.95 % (4014)Instruction limit reached!
% 3.25/1.95 % (4014)------------------------------
% 3.25/1.95 % (4014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.95 % (4014)Termination reason: Unknown
% 3.25/1.95 % (4014)Termination phase: shuffling
% 3.25/1.95
% 3.25/1.95 % (4014)Memory used [KB]: 1151
% 3.25/1.95 % (4014)Time elapsed: 0.004 s
% 3.25/1.95 % (4014)Instructions burned: 4 (million)
% 3.25/1.95 % (4014)------------------------------
% 3.25/1.95 % (4014)------------------------------
% 3.25/1.96 % (4019)Instruction limit reached!
% 3.25/1.96 % (4019)------------------------------
% 3.25/1.96 % (4019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.96 % (4019)Termination reason: Unknown
% 3.25/1.96 % (4019)Termination phase: Property scanning
% 3.25/1.96
% 3.25/1.96 % (4019)Memory used [KB]: 1279
% 3.25/1.96 % (4019)Time elapsed: 0.012 s
% 3.25/1.96 % (4019)Instructions burned: 19 (million)
% 3.25/1.96 % (4019)------------------------------
% 3.25/1.96 % (4019)------------------------------
% 3.25/1.96 % (4018)First to succeed.
% 3.25/1.96 % (4018)Refutation found. Thanks to Tanya!
% 3.25/1.96 % SZS status Theorem for DTF2THF_3858
% 3.25/1.96 % SZS output start Proof for DTF2THF_3858
% 3.25/1.96 thf(type_def_5, type, d: $tType).
% 3.25/1.96 thf(type_def_7, type, u: $tType).
% 3.25/1.96 thf(type_def_8, type, du: $tType).
% 3.25/1.96 thf(type_def_9, type, mono_2Etyop_2Erealax_2Ereal: $tType).
% 3.25/1.96 thf(type_def_10, type, mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType).
% 3.25/1.96 thf(func_def_0, type, u: $tType).
% 3.25/1.96 thf(func_def_1, type, d: $tType).
% 3.25/1.96 thf(func_def_2, type, du: $tType).
% 3.25/1.96 thf(func_def_3, type, mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType).
% 3.25/1.96 thf(func_def_4, type, mono_2Etyop_2Erealax_2Ereal: $tType).
% 3.25/1.96 thf(func_def_5, type, tyop_2Emin_2Ebool: d).
% 3.25/1.96 thf(func_def_6, type, tyop_2Emin_2Efun: d > d > d).
% 3.25/1.96 thf(func_def_7, type, tyop_2Epair_2Eprod: d > d > d).
% 3.25/1.96 thf(func_def_8, type, tyop_2Erealax_2Ereal: d).
% 3.25/1.96 thf(func_def_9, type, s: d > u > du).
% 3.25/1.96 thf(func_def_10, type, app_2E2: du > du > u).
% 3.25/1.96 thf(func_def_11, type, combin_i_2E0: u).
% 3.25/1.96 thf(func_def_12, type, combin_k_2E0: u).
% 3.25/1.96 thf(func_def_13, type, combin_s_2E0: u).
% 3.25/1.96 thf(func_def_14, type, c_2Ebool_2E_21_2E0: u).
% 3.25/1.96 thf(func_def_15, type, c_2Ebool_2E_21_2E1: du > u).
% 3.25/1.96 thf(func_def_16, type, c_2Epair_2E_2C_2E0: u).
% 3.25/1.96 thf(func_def_17, type, c_2Epair_2E_2C_2E2: du > du > u).
% 3.25/1.96 thf(func_def_18, type, c_2Ebool_2E_2F_5C_2E0: u).
% 3.25/1.96 thf(func_def_19, type, c_2Ebool_2E_2F_5C_2E2: du > du > u).
% 3.25/1.96 thf(func_def_20, type, c_2Emin_2E_3D_2E0: u).
% 3.25/1.96 thf(func_def_21, type, c_2Emin_2E_3D_2E2: du > du > u).
% 3.25/1.96 thf(func_def_22, type, c_2Emin_2E_3D_3D_3E_2E0: u).
% 3.25/1.96 thf(func_def_23, type, c_2Emin_2E_3D_3D_3E_2E2: du > du > u).
% 3.25/1.96 thf(func_def_24, type, c_2Ebool_2E_3F_2E0: u).
% 3.25/1.96 thf(func_def_25, type, c_2Ebool_2E_3F_2E1: du > u).
% 3.25/1.96 thf(func_def_26, type, c_2Ebool_2EF_2E0: u).
% 3.25/1.96 thf(func_def_27, type, c_2Epred__set_2ESUBSET_2E0: u).
% 3.25/1.96 thf(func_def_28, type, c_2Epred__set_2ESUBSET_2E2: du > du > u).
% 3.25/1.96 thf(func_def_29, type, c_2Ebool_2ET_2E0: u).
% 3.25/1.96 thf(func_def_30, type, c_2Ebool_2E_5C_2F_2E0: u).
% 3.25/1.96 thf(func_def_31, type, c_2Ebool_2E_5C_2F_2E2: du > du > u).
% 3.25/1.96 thf(func_def_32, type, c_2Ereal__topology_2Eball_2E0: u).
% 3.25/1.96 thf(func_def_33, type, c_2Ereal__topology_2Eball_2E1: du > u).
% 3.25/1.96 thf(func_def_34, type, c_2Ereal__topology_2Ebounded__def_2E0: u).
% 3.25/1.96 thf(func_def_35, type, c_2Ereal__topology_2Ebounded__def_2E1: du > u).
% 3.25/1.96 thf(func_def_36, type, c_2Ereal__topology_2Ecball_2E0: u).
% 3.25/1.96 thf(func_def_37, type, c_2Ereal__topology_2Ecball_2E1: du > u).
% 3.25/1.96 thf(func_def_38, type, c_2Ebool_2E_7E_2E0: u).
% 3.25/1.96 thf(func_def_39, type, c_2Ebool_2E_7E_2E1: du > u).
% 3.25/1.96 thf(func_def_40, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ($o > $o) > $o > $o).
% 3.25/1.96 thf(func_def_41, type, mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o > $o) > $o > $o > $o).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 thf(func_def_48, type, mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o).
% 3.25/1.96 thf(func_def_49, type, mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o).
% 3.25/1.96 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).
% 3.25/1.96 thf(func_def_53, type, mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o).
% 3.25/1.96 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).
% 3.25/1.96 thf(func_def_55, type, mono_2Ec_2Ereal__topology_2Ebounded__def: (mono_2Etyop_2Erealax_2Ereal > $o) > $o).
% 3.25/1.96 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).
% 3.25/1.96 thf(func_def_57, type, mono_2Ec_2Ebool_2E_7E: $o > $o).
% 3.25/1.96 thf(func_def_58, type, i_mono_2Etyop_2Emin_2Ebool: $o > u).
% 3.25/1.96 thf(func_def_59, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ($o > $o) > u).
% 3.25/1.96 thf(func_def_60, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ($o > $o > $o) > u).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 thf(func_def_64, type, i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: (mono_2Etyop_2Erealax_2Ereal > $o) > u).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 thf(func_def_68, type, i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u).
% 3.25/1.96 thf(func_def_69, type, j_mono_2Etyop_2Emin_2Ebool: du > $o).
% 3.25/1.96 thf(func_def_70, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 thf(func_def_75, type, j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Erealax_2Ereal > $o).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 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).
% 3.25/1.96 thf(func_def_79, type, j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal).
% 3.25/1.96 thf(func_def_89, type, sK0: mono_2Etyop_2Erealax_2Ereal).
% 3.25/1.96 thf(func_def_90, type, sK1: mono_2Etyop_2Erealax_2Ereal).
% 3.25/1.96 thf(func_def_92, type, ph3: !>[X0: $tType]:(X0)).
% 3.25/1.96 thf(f347,plain,(
% 3.25/1.96 $false),
% 3.25/1.96 inference(trivial_inequality_removal,[status(thm)],[f344])).
% 3.25/1.96 thf(f344,plain,(
% 3.25/1.96 ($true != $true)),
% 3.25/1.96 inference(superposition,[status(thm)],[f171,f341])).
% 3.25/1.96 thf(f341,plain,(
% 3.25/1.96 ( ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : (((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1))) = $true)) )),
% 3.25/1.96 inference(subsumption_resolution,[status(thm)],[f336,f187])).
% 3.25/1.96 thf(f187,plain,(
% 3.25/1.96 ( ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : (((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0))) = $true)) )),
% 3.25/1.96 inference(cnf_transformation,[status(thm)],[f88])).
% 3.25/1.96 thf(f88,plain,(
% 3.25/1.96 ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0))) = $true)),
% 3.25/1.96 inference(fool_elimination,[status(thm)],[f87])).
% 3.25/1.96 thf(f87,plain,(
% 3.25/1.96 ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : (mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0)))),
% 3.25/1.96 inference(rectify,[status(thm)],[f69])).
% 3.25/1.96 thf(f69,axiom,(
% 3.25/1.96 ! [X23 : mono_2Etyop_2Erealax_2Ereal,X22 : mono_2Etyop_2Erealax_2Ereal] : (mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23)))),
% 3.25/1.96 file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ereal__topology_2EBOUNDED__CBALL)).
% 3.25/1.96 thf(f336,plain,(
% 3.25/1.96 ( ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : (((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1))) != $true) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1))) = $true)) )),
% 3.25/1.96 inference(trivial_inequality_removal,[status(thm)],[f331])).
% 3.25/1.96 thf(f331,plain,(
% 3.25/1.96 ( ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : (((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1))) != $true) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X0 @ X1))) = $true) | ($true = $false)) )),
% 3.25/1.96 inference(superposition,[status(thm)],[f191,f305])).
% 3.25/1.96 thf(f305,plain,(
% 3.25/1.96 ( ! [X0 : mono_2Etyop_2Erealax_2Ereal > $o,X1 : mono_2Etyop_2Erealax_2Ereal > $o] : (((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1) = $false) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ X0) = $true) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ X1) != $true)) )),
% 3.25/1.96 inference(trivial_inequality_removal,[status(thm)],[f265])).
% 3.25/1.96 thf(f265,plain,(
% 3.25/1.96 ( ! [X0 : mono_2Etyop_2Erealax_2Ereal > $o,X1 : mono_2Etyop_2Erealax_2Ereal > $o] : (((mono_2Ec_2Ereal__topology_2Ebounded__def @ X1) != $true) | ((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1) = $false) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ X0) = $true) | ($true != $true)) )),
% 3.25/1.96 inference(superposition,[status(thm)],[f172,f211])).
% 3.25/1.96 thf(f211,plain,(
% 3.25/1.96 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 3.25/1.96 inference(subsumption_resolution,[status(thm)],[f208,f171])).
% 3.25/1.96 thf(f208,plain,(
% 3.25/1.96 ( ! [X0 : $o] : (($false = X0) | ($true = X0) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0))) = $true)) )),
% 3.25/1.96 inference(binary_proxy_clausification,[status(thm)],[f207])).
% 3.25/1.96 thf(f207,plain,(
% 3.25/1.96 ( ! [X0 : $o] : (($true = X0) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0))) = X0)) )),
% 3.25/1.96 inference(trivial_inequality_removal,[status(thm)],[f206])).
% 3.25/1.96 thf(f206,plain,(
% 3.25/1.96 ( ! [X0 : $o] : (($true = X0) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0))) = X0) | ($true != $true)) )),
% 3.25/1.96 inference(superposition,[status(thm)],[f171,f167])).
% 3.25/1.96 thf(f167,plain,(
% 3.25/1.96 ( ! [X0 : $o,X1 : $o] : (($true = X1) | ($true = X0) | (X0 = X1)) )),
% 3.25/1.96 inference(cnf_transformation,[status(thm)],[f158])).
% 3.25/1.96 thf(f158,plain,(
% 3.25/1.96 ! [X0 : $o,X1 : $o] : ((($true != X1) & ($true = X0)) | (($true != X0) & ($true = X1)) | (X0 = X1))),
% 3.25/1.96 inference(flattening,[status(thm)],[f157])).
% 3.25/1.96 thf(f157,plain,(
% 3.25/1.96 ! [X0 : $o,X1 : $o] : (((X0 = X1) | (($true != X1) & ($true = X0))) | (($true != X0) & ($true = X1)))),
% 3.25/1.96 inference(ennf_transformation,[status(thm)],[f96])).
% 3.25/1.96 thf(f96,plain,(
% 3.25/1.96 ! [X0 : $o,X1 : $o] : ((($true = X1) => ($true = X0)) => ((($true = X0) => ($true = X1)) => (X0 = X1)))),
% 3.25/1.96 inference(fool_elimination,[status(thm)],[f95])).
% 3.25/1.96 thf(f95,plain,(
% 3.25/1.96 ! [X0 : $o,X1 : $o] : ((X1 => X0) => ((X0 => X1) => (X0 = X1)))),
% 3.25/1.96 inference(rectify,[status(thm)],[f56])).
% 3.25/1.96 thf(f56,axiom,(
% 3.25/1.96 ! [X16 : $o,X15 : $o] : ((X15 => X16) => ((X16 => X15) => (X15 = X16)))),
% 3.25/1.96 file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ebool_2EIMP__ANTISYM__AX)).
% 3.25/1.96 thf(f172,plain,(
% 3.25/1.96 ( ! [X0 : mono_2Etyop_2Erealax_2Ereal > $o,X1 : mono_2Etyop_2Erealax_2Ereal > $o] : (((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1) != $true) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ X0) = $true) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ X1) != $true)) )),
% 3.25/1.96 inference(cnf_transformation,[status(thm)],[f160])).
% 3.25/1.96 thf(f160,plain,(
% 3.25/1.96 ! [X0 : mono_2Etyop_2Erealax_2Ereal > $o,X1 : mono_2Etyop_2Erealax_2Ereal > $o] : (((mono_2Ec_2Ereal__topology_2Ebounded__def @ X0) = $true) | ((mono_2Ec_2Ereal__topology_2Ebounded__def @ X1) != $true) | ((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1) != $true))),
% 3.25/1.96 inference(flattening,[status(thm)],[f159])).
% 3.25/1.96 thf(f159,plain,(
% 3.25/1.96 ! [X0 : mono_2Etyop_2Erealax_2Ereal > $o,X1 : mono_2Etyop_2Erealax_2Ereal > $o] : (((mono_2Ec_2Ereal__topology_2Ebounded__def @ X0) = $true) | (((mono_2Ec_2Ereal__topology_2Ebounded__def @ X1) != $true) | ((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1) != $true)))),
% 3.25/1.96 inference(ennf_transformation,[status(thm)],[f94])).
% 3.25/1.96 thf(f94,plain,(
% 3.25/1.96 ! [X0 : mono_2Etyop_2Erealax_2Ereal > $o,X1 : mono_2Etyop_2Erealax_2Ereal > $o] : ((((mono_2Ec_2Ereal__topology_2Ebounded__def @ X1) = $true) & ((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1) = $true)) => ((mono_2Ec_2Ereal__topology_2Ebounded__def @ X0) = $true))),
% 3.25/1.96 inference(fool_elimination,[status(thm)],[f93])).
% 3.25/1.96 thf(f93,plain,(
% 3.25/1.96 ! [X0 : mono_2Etyop_2Erealax_2Ereal > $o,X1 : mono_2Etyop_2Erealax_2Ereal > $o] : (((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X0 @ X1) & (mono_2Ec_2Ereal__topology_2Ebounded__def @ X1)) => (mono_2Ec_2Ereal__topology_2Ebounded__def @ X0))),
% 3.25/1.96 inference(rectify,[status(thm)],[f68])).
% 3.25/1.96 thf(f68,axiom,(
% 3.25/1.96 ! [X24 : mono_2Etyop_2Erealax_2Ereal > $o,X25 : mono_2Etyop_2Erealax_2Ereal > $o] : (((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X24 @ X25) & (mono_2Ec_2Ereal__topology_2Ebounded__def @ X25)) => (mono_2Ec_2Ereal__topology_2Ebounded__def @ X24))),
% 3.25/1.96 file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ereal__topology_2EBOUNDED__SUBSET)).
% 3.25/1.96 thf(f191,plain,(
% 3.25/1.96 ( ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : (((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0)) @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0))) = $true)) )),
% 3.25/1.96 inference(cnf_transformation,[status(thm)],[f90])).
% 3.25/1.96 thf(f90,plain,(
% 3.25/1.96 ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : ((mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0)) @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0))) = $true)),
% 3.25/1.96 inference(fool_elimination,[status(thm)],[f89])).
% 3.25/1.96 thf(f89,plain,(
% 3.25/1.96 ! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : (mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0)) @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0)))),
% 3.25/1.96 inference(rectify,[status(thm)],[f67])).
% 3.25/1.96 thf(f67,axiom,(
% 3.25/1.96 ! [X23 : mono_2Etyop_2Erealax_2Ereal,X22 : mono_2Etyop_2Erealax_2Ereal] : (mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23)) @ (mono_2Ec_2Ereal__topology_2Ecball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23)))),
% 3.25/1.96 file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL)).
% 3.25/1.96 thf(f171,plain,(
% 3.25/1.96 ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0))) != $true)),
% 3.25/1.96 inference(cnf_transformation,[status(thm)],[f162])).
% 3.25/1.96 thf(f162,plain,(
% 3.25/1.96 ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0))) != $true)),
% 3.25/1.96 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f156,f161])).
% 3.25/1.96 thf(f161,plain,(
% 3.25/1.96 ? [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0))) != $true) => ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ sK1 @ sK0))) != $true)),
% 3.25/1.96 introduced(definition,[],[choice_axiom])).
% 3.25/1.96 thf(f156,plain,(
% 3.25/1.96 ? [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0))) != $true)),
% 3.25/1.96 inference(ennf_transformation,[status(thm)],[f110])).
% 3.25/1.96 thf(f110,plain,(
% 3.25/1.96 ~! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : ((mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0))) = $true)),
% 3.25/1.96 inference(fool_elimination,[status(thm)],[f109])).
% 3.25/1.96 thf(f109,plain,(
% 3.25/1.96 ~! [X0 : mono_2Etyop_2Erealax_2Ereal,X1 : mono_2Etyop_2Erealax_2Ereal] : (mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X0)))),
% 3.25/1.96 inference(rectify,[status(thm)],[f81])).
% 3.25/1.96 thf(f81,negated_conjecture,(
% 3.25/1.96 ~! [X23 : mono_2Etyop_2Erealax_2Ereal,X22 : mono_2Etyop_2Erealax_2Ereal] : (mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23)))),
% 3.25/1.96 inference(negated_conjecture,[status(cth)],[f80])).
% 3.25/1.96 thf(f80,conjecture,(
% 3.25/1.96 ! [X23 : mono_2Etyop_2Erealax_2Ereal,X22 : mono_2Etyop_2Erealax_2Ereal] : (mono_2Ec_2Ereal__topology_2Ebounded__def @ (mono_2Ec_2Ereal__topology_2Eball @ (mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X22 @ X23)))),
% 3.25/1.96 file('/export/starexec/sandbox/tmp/tmp.4xV8al8DCF/DTF2THF_3858.p',thm_2Ereal__topology_2EBOUNDED__BALL)).
% 3.25/1.96 % SZS output end Proof for DTF2THF_3858
% 3.25/1.96 % (4018)------------------------------
% 3.25/1.96 % (4018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.96 % (4018)Termination reason: Refutation
% 3.25/1.96
% 3.25/1.96 % (4018)Memory used [KB]: 5756
% 3.25/1.96 % (4018)Time elapsed: 0.014 s
% 3.25/1.96 % (4018)Instructions burned: 19 (million)
% 3.25/1.96 % (4018)------------------------------
% 3.25/1.96 % (4018)------------------------------
% 3.25/1.96 % (4012)Success in time 0.042 s
%------------------------------------------------------------------------------