%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP023^4 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:26 AM UTC 2026
% Result : Theorem 41.05s 21.62s
% Output : Refutation 41.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 128
% Syntax : Number of formulae : 258 ( 103 unt; 0 typ; 0 def)
% Number of atoms : 1427 ( 294 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 2144 ( 46 ~; 6 |; 192 &;1788 @)
% ( 0 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 204 ( 203 usr)
% Number of type conns : 310 ( 310 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 1 con; 0-3 aty)
% Number of variables : 470 ( 0 ^; 446 !; 24 ?; 470 :)
% Comments :
%------------------------------------------------------------------------------
thf(u_type,type,
u: $tType ).
thf(d_type,type,
d: $tType ).
thf(du_type,type,
du: $tType ).
thf(mono_2Etyop_2Emin_2Eind_type,type,
mono_2Etyop_2Emin_2Eind: $tType ).
thf(mono_2Etyop_2Enum_2Enum_type,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Eone_2Eone_type,type,
mono_2Etyop_2Eone_2Eone: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Estring_2Echar_type,type,
mono_2Etyop_2Estring_2Echar: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Esum_2Esum_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Esum_2Esum_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2EternaryComparisons_2Eordering_type,type,
mono_2Etyop_2EternaryComparisons_2Eordering: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ehrat_2Ehrat_type,type,
mono_2Etyop_2Ehrat_2Ehrat: $tType ).
thf(mono_2Etyop_2Einteger_2Eint_type,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Equote_2Eindex_type,type,
mono_2Etyop_2Equote_2Eindex: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29: $tType ).
thf(mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Etoto_2Enum__dt_type,type,
mono_2Etyop_2Etoto_2Enum__dt: $tType ).
thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Estring_2Echar_29_type,type,
mono_2Etyop_2Etoto_2Etoto_28tyop_2Estring_2Echar_29: $tType ).
thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).
thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Etoto_2Etoto_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Ehreal_2Ehreal_type,type,
mono_2Etyop_2Ehreal_2Ehreal: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2EDeepSyntax_2Edeep__form_type,type,
mono_2Etyop_2EDeepSyntax_2Edeep__form: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29_type,type,
mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Eone_2Eone_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Eone_2Eone_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29: $tType ).
thf(mono_2Etyop_2Erealax_2Ereal_type,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2EringNorm_2Epolynom_28tyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2EringNorm_2Epolynom_28tyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Ering_2Ering_28tyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Ering_2Ering_28tyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Equote_2Evarmap_28tyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Equote_2Evarmap_28tyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Esemi__ring_2Esemi__ring_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Esemi__ring_2Esemi__ring_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Equote_2Evarmap_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Equote_2Evarmap_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Efrac_2Efrac_type,type,
mono_2Etyop_2Efrac_2Efrac: $tType ).
thf(mono_2Etyop_2Erat_2Erat_type,type,
mono_2Etyop_2Erat_2Erat: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).
thf(mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Erat_2Erat_29_type,type,
mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Erat_2Erat_29: $tType ).
thf(mono_2Etyop_2EringNorm_2Epolynom_28tyop_2Erat_2Erat_29_type,type,
mono_2Etyop_2EringNorm_2Epolynom_28tyop_2Erat_2Erat_29: $tType ).
thf(mono_2Etyop_2Ering_2Ering_28tyop_2Erat_2Erat_29_type,type,
mono_2Etyop_2Ering_2Ering_28tyop_2Erat_2Erat_29: $tType ).
thf(mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Erat_2Erat_29_type,type,
mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Erat_2Erat_29: $tType ).
thf(mono_2Etyop_2Equote_2Evarmap_28tyop_2Erat_2Erat_29_type,type,
mono_2Etyop_2Equote_2Evarmap_28tyop_2Erat_2Erat_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebinary__ieee_2Eflags_type,type,
mono_2Etyop_2Ebinary__ieee_2Eflags: $tType ).
thf(mono_2Etyop_2Ebinary__ieee_2Efloat__compare_type,type,
mono_2Etyop_2Ebinary__ieee_2Efloat__compare: $tType ).
thf(mono_2Etyop_2Ebinary__ieee_2Efloat__value_type,type,
mono_2Etyop_2Ebinary__ieee_2Efloat__value: $tType ).
thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Einteger_2Eint_29_type,type,
mono_2Etyop_2Eoption_2Eoption_28tyop_2Einteger_2Eint_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat__value_2Ctyop_2Ebinary__ieee_2Efloat__value_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat__value_2Ctyop_2Ebinary__ieee_2Efloat__value_29: $tType ).
thf(mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Ebinary__ieee_2Erounding_type,type,
mono_2Etyop_2Ebinary__ieee_2Erounding: $tType ).
thf(mono_2Etyop_2Eieee_2Eccode_type,type,
mono_2Etyop_2Eieee_2Eccode: $tType ).
thf(mono_2Etyop_2Eieee_2Efloat_type,type,
mono_2Etyop_2Eieee_2Efloat: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Eieee_2Eroundmode_type,type,
mono_2Etyop_2Eieee_2Eroundmode: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
mono_2Etyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).
thf(mono_2Etyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Ebool_2Eitself_28tyop_2Epair_2Eprod_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_2Ctyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Eflags_2Ctyop_2Ebinary__ieee_2Efloat_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).
thf(mono_2Etyop_2Eextreal_2Eextreal_type,type,
mono_2Etyop_2Eextreal_2Eextreal: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Eextreal_2Eextreal_2Ctyop_2Eextreal_2Eextreal_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Eextreal_2Eextreal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).
thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_type,type,
mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: $tType ).
thf(mono_2Etyop_2Ereal__topology_2Enet_28tyop_2Enum_2Enum_29_type,type,
mono_2Etyop_2Ereal__topology_2Enet_28tyop_2Enum_2Enum_29: $tType ).
thf(mono_2Etyop_2Ereal__topology_2Enet_28tyop_2Erealax_2Ereal_29_type,type,
mono_2Etyop_2Ereal__topology_2Enet_28tyop_2Erealax_2Ereal_29: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_type,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).
thf(mono_2Ec_2Ereal_2Emax_decl,type,
mono_2Ec_2Ereal_2Emax: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ereal_2Emin_decl,type,
mono_2Ec_2Ereal_2Emin: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal_decl,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(mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(mono_2Ec_2Eintegral_2Eintegrable_decl,type,
mono_2Ec_2Eintegral_2Eintegrable: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > $o ).
thf(mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal__topology_2EClosed_decl,type,
mono_2Ec_2Ereal__topology_2EClosed: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal__topology_2EOpen_decl,type,
mono_2Ec_2Ereal__topology_2EOpen: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(mono_2Ec_2Ereal__topology_2Eball_decl,type,
mono_2Ec_2Ereal__topology_2Eball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal__topology_2Ebetween_decl,type,
mono_2Ec_2Ereal__topology_2Ebetween: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o ).
thf(mono_2Ec_2Ereal__topology_2Ebounded__def_decl,type,
mono_2Ec_2Ereal__topology_2Ebounded__def: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(mono_2Ec_2Ereal__topology_2Ecball_decl,type,
mono_2Ec_2Ereal__topology_2Ecball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal__topology_2Eclosure_decl,type,
mono_2Ec_2Ereal__topology_2Eclosure: ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal__topology_2Econnected_decl,type,
mono_2Ec_2Ereal__topology_2Econnected: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(mono_2Ec_2Ereal__topology_2Efrontier_decl,type,
mono_2Ec_2Ereal__topology_2Efrontier: ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal__topology_2Einterior_decl,type,
mono_2Ec_2Ereal__topology_2Einterior: ( mono_2Etyop_2Erealax_2Ereal > $o ) > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(mono_2Ec_2Ereal__topology_2Emidpoint_decl,type,
mono_2Ec_2Ereal__topology_2Emidpoint: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).
thf(mono_2Ec_2Ereal__topology_2Esphere_decl,type,
mono_2Ec_2Ereal__topology_2Esphere: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(80,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( A = mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__EQ__EMPTY) ).
thf(365,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( A = mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(122,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ A )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CLOSURE) ).
thf(518,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ A )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(38,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
& ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ( mono_2Ec_2Ereal__topology_2Econnected @ C )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ B @ A ) ) )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__DIFF__OPEN__FROM__CLOSED) ).
thf(234,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
& ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ( mono_2Ec_2Ereal__topology_2Econnected @ C )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ B @ A ) ) )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(75,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EUNION__INTERIOR__SUBSET) ).
thf(352,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(124,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__BALL) ).
thf(523,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(44,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ C @ A ) )
=> ? [D: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ D )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ D @ A )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ D )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__IFF__CONNECTABLE__POINTS) ).
thf(247,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ C @ A ) )
=> ? [D: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ D )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ D @ A )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ D )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(51,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Ereal__topology_2Econnected @ B )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__UNION) ).
thf(269,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Ereal__topology_2Econnected @ B )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(99,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( B != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ? [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ C )
& ( C != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ C @ B )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ C @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ENOWHERE__DENSE) ).
thf(440,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( B != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ? [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ C )
& ( C != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ C @ B )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ C @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(119,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EMIDPOINT__SYM) ).
thf(511,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(87,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__CLOSURE) ).
thf(385,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(128,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ D @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__TRANS__2) ).
thf(533,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ D @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(117,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ B @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__REFL) ).
thf(500,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ B @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(16,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__DIFF) ).
thf(174,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(47,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Efrontier @ A )
= ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2Efrontier) ).
thf(257,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Efrontier @ A )
= ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(20,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) )
= ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESET__DIFF__FRONTIER) ).
thf(184,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) )
= ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__INTERIOR) ).
thf(357,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(35,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__CLOSURE) ).
thf(228,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(58,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= A )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) )
= B ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EREGULAR__OPEN__INTER) ).
thf(289,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= A )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) )
= B ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(18,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) )
= ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__FRONTIER__FRONTIER) ).
thf(179,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) )
= ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(100,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= A )
= ( mono_2Ec_2Ereal__topology_2EOpen @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__EQ) ).
thf(443,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= A )
= ( mono_2Ec_2Ereal__topology_2EOpen @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(46,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Ereal__topology_2Econnected @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__FROM__CLOSED__UNION__AND__INTER) ).
thf(253,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Ereal__topology_2Econnected @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(120,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: 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 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CBALL) ).
thf(514,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: 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 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(55,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( mono_2Ec_2Ereal__topology_2EOpen @ C )
& ( B != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( C != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
= A )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__OPEN__SET) ).
thf(280,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( mono_2Ec_2Ereal__topology_2EOpen @ C )
& ( B != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( C != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
= A )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(32,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__CLOSED) ).
thf(221,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__DIFF__BALL) ).
thf(132,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__MINIMAL) ).
thf(243,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(96,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebetween @ ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__MIDPOINT) ).
thf(428,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebetween @ ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(126,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ B )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__SUBSET) ).
thf(527,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ B )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(29,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
=> ? [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ C )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__SUB__OPEN) ).
thf(206,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
=> ? [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ C )
& ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(64,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__INTER__SUBSET) ).
thf(307,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(59,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESPHERE__SUBSET__CBALL) ).
thf(292,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(103,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) )
= A )
& ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) )
= B ) )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EREGULAR__CLOSED__UNION) ).
thf(452,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) )
= A )
& ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) )
= B ) )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(27,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ A )
= ( mono_2Ec_2Ereal__topology_2EClosed @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__SUBSET__EQ) ).
thf(201,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ A )
= ( mono_2Ec_2Ereal__topology_2EClosed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(85,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__SUBSET) ).
thf(381,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(61,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ) )
= ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__INTERIOR__IDEMP) ).
thf(297,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ) )
= ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(94,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__INTER__SUBSET__INTER) ).
thf(424,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(93,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal_2Emin @ A @ B )
= ( mono_2Ec_2Ereal_2Emin @ B @ A ) )
& ( ( mono_2Ec_2Ereal_2Emin @ ( mono_2Ec_2Ereal_2Emin @ A @ B ) @ C )
= ( mono_2Ec_2Ereal_2Emin @ A @ ( mono_2Ec_2Ereal_2Emin @ B @ C ) ) )
& ( ( mono_2Ec_2Ereal_2Emin @ A @ ( mono_2Ec_2Ereal_2Emin @ B @ C ) )
= ( mono_2Ec_2Ereal_2Emin @ B @ ( mono_2Ec_2Ereal_2Emin @ A @ C ) ) )
& ( ( mono_2Ec_2Ereal_2Emin @ A @ A )
= A )
& ( ( mono_2Ec_2Ereal_2Emin @ A @ ( mono_2Ec_2Ereal_2Emin @ A @ B ) )
= ( mono_2Ec_2Ereal_2Emin @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__ACI) ).
thf(407,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal_2Emin @ A @ B )
= ( mono_2Ec_2Ereal_2Emin @ B @ A ) )
& ( ( mono_2Ec_2Ereal_2Emin @ ( mono_2Ec_2Ereal_2Emin @ A @ B ) @ C )
= ( mono_2Ec_2Ereal_2Emin @ A @ ( mono_2Ec_2Ereal_2Emin @ B @ C ) ) )
& ( ( mono_2Ec_2Ereal_2Emin @ A @ ( mono_2Ec_2Ereal_2Emin @ B @ C ) )
= ( mono_2Ec_2Ereal_2Emin @ B @ ( mono_2Ec_2Ereal_2Emin @ A @ C ) ) )
& ( ( mono_2Ec_2Ereal_2Emin @ A @ A )
= A )
& ( ( mono_2Ec_2Ereal_2Emin @ A @ ( mono_2Ec_2Ereal_2Emin @ A @ B ) )
= ( mono_2Ec_2Ereal_2Emin @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(53,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__UNION) ).
thf(275,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(48,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ B )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CLOSED__UNION__EMPTY__INTERIOR) ).
thf(260,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ B )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(74,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) )
= ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__INTERIOR) ).
thf(349,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) )
= ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(109,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__INTER__SUBSET) ).
thf(467,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(112,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebetween @ C @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Ereal__topology_2Ebetween @ C @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__SYM) ).
thf(484,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebetween @ C @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Ereal__topology_2Ebetween @ C @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(25,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__FRONTIER__SUBSET) ).
thf(197,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(106,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__MAXIMAL) ).
thf(461,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(115,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ B @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__ANTISYM) ).
thf(493,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ B @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(68,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: 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 @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__SUBSET__CBALL) ).
thf(317,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: 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 @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(9,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EDIFF__CLOSURE__SUBSET) ).
thf(156,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ A )
= ( mono_2Ec_2Ereal__topology_2EClosed @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__SUBSET__EQ) ).
thf(225,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ A )
= ( mono_2Ec_2Ereal__topology_2EClosed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__SUBSET__CLOSED) ).
thf(193,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(90,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ! [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ C @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ C ) )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ C @ B ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__UNIQUE) ).
thf(393,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ! [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ C @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ C ) )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ C @ B ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(82,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__UNION__SPHERE) ).
thf(371,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(72,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Ereal__topology_2Econnected @ B )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ B )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__UNION__STRONG) ).
thf(343,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Ereal__topology_2Econnected @ B )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ B )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(50,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( mono_2Ec_2Ereal__topology_2EOpen @ C )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ C @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2Econnected) ).
thf(266,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( mono_2Ec_2Ereal__topology_2EOpen @ C )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ C @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(118,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__BALL) ).
thf(508,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(66,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__INTER) ).
thf(311,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(127,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebetween @ B @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ A ) )
= ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__REFL__EQ) ).
thf(530,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ebetween @ B @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ A ) )
= ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(13,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__DIFF) ).
thf(166,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__INTER) ).
thf(161,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(57,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__INTER__CLOSURE__SUBSET) ).
thf(286,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(28,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__INTERMEDIATE__CLOSURE) ).
thf(204,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) )
=> ( mono_2Ec_2Ereal__topology_2Econnected @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(108,axiom,
mono_2Ec_2Ereal__topology_2EOpen @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__EMPTY) ).
thf(466,plain,
mono_2Ec_2Ereal__topology_2EOpen @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(39,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__CLOSED) ).
thf(236,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(21,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__DIFF__SPHERE) ).
thf(187,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
mono_2Ec_2Ereal__topology_2Econnected @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__EMPTY) ).
thf(230,plain,
mono_2Ec_2Ereal__topology_2Econnected @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(79,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ A ) )
=> ( B = mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__EQ__EMPTY) ).
thf(362,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ A ) )
=> ( B = mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(43,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__INTERIOR__SUBSET) ).
thf(245,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(97,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CBALL) ).
thf(434,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(63,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Ereal__topology_2Econnected @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__FROM__OPEN__UNION__AND__INTER) ).
thf(303,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
& ( mono_2Ec_2Ereal__topology_2Econnected @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( mono_2Ec_2Ereal__topology_2Econnected @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(88,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESPHERE__UNION__BALL) ).
thf(387,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(129,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= ( mono_2Ec_2Ereal__topology_2Ebounded__def @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__CLOSURE__EQ) ).
thf(535,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= ( mono_2Ec_2Ereal__topology_2Ebounded__def @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(70,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CLOSURE__INTER__OPEN) ).
thf(323,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(111,axiom,
mono_2Ec_2Ereal__topology_2Ebounded__def @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__EMPTY) ).
thf(483,plain,
mono_2Ec_2Ereal__topology_2Ebounded__def @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(123,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Emin @ B @ C ) ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__MIN__INTER) ).
thf(520,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Emin @ B @ C ) ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(41,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__UNION__FRONTIER) ).
thf(240,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1,conjecture,
! [A: mono_2Etyop_2Erealax_2Ereal,B: 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 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__BALL) ).
thf(2,negated_conjecture,
~ ! [A: mono_2Etyop_2Erealax_2Ereal,B: 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 @ A @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(130,plain,
~ ! [A: mono_2Etyop_2Erealax_2Ereal,B: 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 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(104,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__OPEN__INTER__SUPERSET) ).
thf(455,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(33,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__DIFF) ).
thf(223,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ! [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ C )
& ( mono_2Ec_2Ereal__topology_2EClosed @ C ) )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__UNIQUE) ).
thf(135,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ! [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ C )
& ( mono_2Ec_2Ereal__topology_2EClosed @ C ) )
=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) ) )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(114,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
( ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( A @ B @ C )
= B )
=> ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Eintegral_2Eintegrable @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) @ ( A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eintegral_2EINTEGRABLE__CONST) ).
thf(490,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
( ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( A @ B @ C )
= B )
=> ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Eintegral_2Eintegrable @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) @ ( A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(95,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__SUBSET) ).
thf(426,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(83,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) )
= ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__MAXIMAL__EQ) ).
thf(374,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) )
= ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(121,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ A )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBOUNDED__INTERIOR) ).
thf(516,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ A )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(105,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) )
= ( mono_2Ec_2Ereal__topology_2EOpen @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ESUBSET__INTERIOR__EQ) ).
thf(458,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) )
= ( mono_2Ec_2Ereal__topology_2EOpen @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(6,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
| ( mono_2Ec_2Ereal__topology_2EClosed @ A ) )
=> ( ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) )
= ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__FRONTIER) ).
thf(145,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
| ( mono_2Ec_2Ereal__topology_2EClosed @ A ) )
=> ( ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) )
= ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
| ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ B )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__UNION__EQ__EMPTY) ).
thf(209,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
| ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ B )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(113,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EMIDPOINT__REFL) ).
thf(487,plain,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(125,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ D @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) )
=> ( mono_2Ec_2Ereal__topology_2Ebetween @ D @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBETWEEN__TRANS) ).
thf(525,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal__topology_2Ebetween @ A @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( mono_2Ec_2Ereal__topology_2Ebetween @ D @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) )
=> ( mono_2Ec_2Ereal__topology_2Ebetween @ D @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(49,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
= ( ? [B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( A
= ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CLOSED__EQ__EMPTY__AS__FRONTIER) ).
thf(263,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
= ( ? [B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( A
= ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(26,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__CLOSURE) ).
thf(199,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(107,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__CLOSURE) ).
thf(463,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(78,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__UNION) ).
thf(359,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(17,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__UNION) ).
thf(177,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
( ( mono_2Ec_2Ereal__topology_2Efrontier @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__EMPTY) ).
thf(182,plain,
( ( mono_2Ec_2Ereal__topology_2Efrontier @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__CBALL) ).
thf(154,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2EClosed @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(67,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ) )
= ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__CLOSURE__IDEMP) ).
thf(314,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ) )
= ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(101,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__OPEN__INTER__CLOSURE) ).
thf(446,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(5,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__UNION__SUBSET) ).
thf(143,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(116,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Emax @ B @ C ) ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EBALL__MAX__UNION) ).
thf(497,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Emax @ B @ C ) ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(102,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__INTERIOR) ).
thf(450,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(81,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Emax @ B @ C ) ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__MAX__UNION) ).
thf(368,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Emax @ B @ C ) ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(45,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ B )
=> ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ B )
= ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__MINIMAL__EQ) ).
thf(250,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ B )
=> ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ B )
= ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(37,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) )
= ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__FRONTIER) ).
thf(231,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) )
= ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(69,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__INTER__CLOSURE__EQ__EMPTY) ).
thf(319,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(10,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= A )
= ( mono_2Ec_2Ereal__topology_2EClosed @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__EQ) ).
thf(158,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Eclosure @ A )
= A )
= ( mono_2Ec_2Ereal__topology_2EClosed @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(89,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ENOWHERE__DENSE__UNION) ).
thf(390,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(91,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) )
= ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__SUBSET__INTERIOR) ).
thf(401,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) )
= ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(15,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ( mono_2Ec_2Ereal__topology_2EClosed @ C )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ C @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__CLOSED) ).
thf(171,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ( mono_2Ec_2Ereal__topology_2EClosed @ C )
& ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ C ) @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ C @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(84,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Emin @ B @ C ) ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECBALL__MIN__INTER) ).
thf(378,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Emin @ B @ C ) ) )
= ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(52,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( B != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__EQ__EMPTY__ALT) ).
thf(272,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( ! [B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ B )
& ( B != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ B @ A )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(86,axiom,
( ( mono_2Ec_2Ereal__topology_2Einterior @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__EMPTY) ).
thf(383,plain,
( ( mono_2Ec_2Ereal__topology_2Einterior @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(73,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Emax @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MAX__REFL) ).
thf(346,plain,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Emax @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(7,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__INTER__FRONTIER) ).
thf(151,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EDIFF_2Emono_2Etyop_2Erealax_2Ereal @ A @ B )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) )
=> ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(62,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= ( ! [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
& ( mono_2Ec_2Ereal__topology_2EOpen @ C ) )
=> ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ C )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__NONEMPTY__OPEN__INTER) ).
thf(300,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) )
= ( ! [C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ebool_2EIN_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
& ( mono_2Ec_2Ereal__topology_2EOpen @ C ) )
=> ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ C )
!= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(14,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ) @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EUNION__FRONTIER) ).
thf(168,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ) @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(92,axiom,
( ( mono_2Ec_2Ereal__topology_2Eclosure @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__EMPTY) ).
thf(405,plain,
( ( mono_2Ec_2Ereal__topology_2Eclosure @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(22,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ( mono_2Ec_2Ereal__topology_2EClosed @ C )
& ( B != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( C != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
= A )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECONNECTED__CLOSED__SET) ).
thf(190,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Econnected @ A )
= ( ~ ? [B: mono_2Etyop_2Erealax_2Ereal > $o,C: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EClosed @ B )
& ( mono_2Ec_2Ereal__topology_2EClosed @ C )
& ( B != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( C != mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
& ( ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
= A )
& ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ B @ C )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(71,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal_2Emax @ A @ B )
= ( mono_2Ec_2Ereal_2Emax @ B @ A ) )
& ( ( mono_2Ec_2Ereal_2Emax @ ( mono_2Ec_2Ereal_2Emax @ A @ B ) @ C )
= ( mono_2Ec_2Ereal_2Emax @ A @ ( mono_2Ec_2Ereal_2Emax @ B @ C ) ) )
& ( ( mono_2Ec_2Ereal_2Emax @ A @ ( mono_2Ec_2Ereal_2Emax @ B @ C ) )
= ( mono_2Ec_2Ereal_2Emax @ B @ ( mono_2Ec_2Ereal_2Emax @ A @ C ) ) )
& ( ( mono_2Ec_2Ereal_2Emax @ A @ A )
= A )
& ( ( mono_2Ec_2Ereal_2Emax @ A @ ( mono_2Ec_2Ereal_2Emax @ A @ B ) )
= ( mono_2Ec_2Ereal_2Emax @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MAX__ACI) ).
thf(326,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
( ( ( mono_2Ec_2Ereal_2Emax @ A @ B )
= ( mono_2Ec_2Ereal_2Emax @ B @ A ) )
& ( ( mono_2Ec_2Ereal_2Emax @ ( mono_2Ec_2Ereal_2Emax @ A @ B ) @ C )
= ( mono_2Ec_2Ereal_2Emax @ A @ ( mono_2Ec_2Ereal_2Emax @ B @ C ) ) )
& ( ( mono_2Ec_2Ereal_2Emax @ A @ ( mono_2Ec_2Ereal_2Emax @ B @ C ) )
= ( mono_2Ec_2Ereal_2Emax @ B @ ( mono_2Ec_2Ereal_2Emax @ A @ C ) ) )
& ( ( mono_2Ec_2Ereal_2Emax @ A @ A )
= A )
& ( ( mono_2Ec_2Ereal_2Emax @ A @ ( mono_2Ec_2Ereal_2Emax @ A @ B ) )
= ( mono_2Ec_2Ereal_2Emax @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(40,axiom,
mono_2Ec_2Ereal__topology_2EClosed @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSED__EMPTY) ).
thf(239,plain,
mono_2Ec_2Ereal__topology_2EClosed @ mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(60,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Emin @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MIN__REFL) ).
thf(294,plain,
! [A: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal_2Emin @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(24,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__CLOSURE__SUBSET) ).
thf(195,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(98,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2ECLOSURE__INTERIOR__UNION__CLOSED) ).
thf(437,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EClosed @ A )
& ( mono_2Ec_2Ereal__topology_2EClosed @ B ) )
=> ( ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ A ) ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ ( mono_2Ec_2Ereal__topology_2Einterior @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(56,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
=> ( ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__UNION) ).
thf(283,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eclosure @ A ) @ ( mono_2Ec_2Ereal__topology_2Eclosure @ B ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
=> ( ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= ( mono_2Ec_2Epred__set_2EUNION_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ ( mono_2Ec_2Ereal__topology_2Efrontier @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(12,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__CBALL) ).
thf(163,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( mono_2Ec_2Ereal__topology_2Efrontier @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( mono_2Ec_2Ereal__topology_2Esphere @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( mono_2Ec_2Ereal__topology_2EOpen @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EFRONTIER__DISJOINT__EQ) ).
thf(277,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) @ A )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal )
= ( mono_2Ec_2Ereal__topology_2EOpen @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(110,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( ( ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= A )
= ( A = B ) )
& ( ( ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= B )
= ( A = B ) )
& ( ( A
= ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( A = B ) )
& ( ( B
= ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EMIDPOINT__EQ__ENDPOINT) ).
thf(469,plain,
! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
( ( ( ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= A )
= ( A = B ) )
& ( ( ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) )
= B )
= ( A = B ) )
& ( ( A
= ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( A = B ) )
& ( ( B
= ( mono_2Ec_2Ereal__topology_2Emidpoint @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(76,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__OPEN) ).
thf(354,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(65,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EOPEN__INTER) ).
thf(309,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
& ( mono_2Ec_2Ereal__topology_2EOpen @ B ) )
=> ( mono_2Ec_2Ereal__topology_2EOpen @ ( mono_2Ec_2Epred__set_2EINTER_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(31,axiom,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
| ( mono_2Ec_2Ereal__topology_2EClosed @ A ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal__topology_2EINTERIOR__FRONTIER__EMPTY) ).
thf(215,plain,
! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
( ( ( mono_2Ec_2Ereal__topology_2EOpen @ A )
| ( mono_2Ec_2Ereal__topology_2EClosed @ A ) )
=> ( ( mono_2Ec_2Ereal__topology_2Einterior @ ( mono_2Ec_2Ereal__topology_2Efrontier @ A ) )
= mono_2Ec_2Epred__set_2EEMPTY_2Emono_2Etyop_2Erealax_2Ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(545,plain,
$false,
inference(e,[status(thm)],[365,518,234,352,523,247,269,440,511,385,533,500,174,257,184,357,228,289,179,443,253,514,280,221,132,243,428,527,206,307,292,452,201,381,297,424,407,275,260,349,467,484,197,461,493,317,156,225,193,393,371,343,266,508,311,530,166,161,286,204,466,236,187,230,362,245,434,303,387,535,323,483,520,240,130,455,223,135,490,426,374,516,458,145,209,487,525,263,199,463,359,177,182,154,314,446,143,497,450,368,250,231,319,158,390,401,171,378,272,383,346,151,300,168,405,190,326,239,294,195,437,283,163,277,469,354,309,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP023^4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n001.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:41:39 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 22.70/13.60 % [INFO] Parsing done (12796ms).
% 22.86/13.70 % [INFO] Running in sequential loop mode.
% 23.35/14.08 % [INFO] eprover registered as external prover.
% 23.35/14.09 % [INFO] Scanning for conjecture ...
% 30.46/17.70 % [INFO] Found a conjecture (or negated_conjecture) and 43680 axioms. Running axiom selection ...
% 31.50/18.18 % [INFO] Axiom selection finished. Selected 127 axioms (removed 43553 axioms).
% 32.02/18.30 % [INFO] Problem is higher-order (TPTP THF).
% 32.02/18.31 % [INFO] Type checking passed.
% 32.02/18.32 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 41.05/21.61 % External prover 'e' found a proof!
% 41.05/21.61 % [INFO] Killing All external provers ...
% 41.05/21.61 % Time passed: 21257ms (effective reasoning time: 7901ms)
% 41.05/21.61 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 41.05/21.62 % Axioms used in derivation (127): thm_2Ereal__topology_2ENOWHERE__DENSE, thm_2Ereal__topology_2ECLOSURE__OPEN__INTER__CLOSURE, thm_2Ereal__topology_2EBOUNDED__SUBSET, thm_2Ereal__topology_2ECONNECTED__EMPTY, thm_2Ereal__topology_2EINTERIOR__EQ, thm_2Ereal__topology_2ECLOSURE__CLOSURE, thm_2Ereal__topology_2ECONNECTED__FROM__OPEN__UNION__AND__INTER, thm_2Ereal__topology_2EMIDPOINT__REFL, thm_2Ereal__topology_2EOPEN__EMPTY, thm_2Ereal__topology_2EFRONTIER__SUBSET__CLOSED, thm_2Ereal__topology_2ECLOSURE__UNION, thm_2Ereal__topology_2EOPEN__SUBSET__INTERIOR, thm_2Ereal__topology_2EINTERIOR__CLOSURE__IDEMP, thm_2Ereal__topology_2ENOWHERE__DENSE__UNION, thm_2Ereal__topology_2EBETWEEN__REFL, thm_2Ereal_2EREAL__MAX__REFL, thm_2Ereal__topology_2ECLOSURE__UNIQUE, thm_2Ereal__topology_2ECLOSURE__EQ__EMPTY, thm_2Ereal__topology_2EUNION__FRONTIER, thm_2Ereal__topology_2EINTERIOR__EMPTY, thm_2Ereal__topology_2EFRONTIER__FRONTIER__FRONTIER, thm_2Ereal__topology_2ESUBSET__CLOSURE, thm_2Ereal__topology_2ECLOSURE__MINIMAL__EQ, thm_2Ereal__topology_2ECLOSURE__INTER__SUBSET, thm_2Ereal__topology_2ECBALL__MIN__INTER, thm_2Ereal__topology_2EFRONTIER__CLOSURE__SUBSET, thm_2Ereal__topology_2EBETWEEN__SYM, thm_2Ereal__topology_2EBETWEEN__ANTISYM, thm_2Ereal__topology_2EINTERIOR__CLOSED__UNION__EMPTY__INTERIOR, thm_2Ereal__topology_2EFRONTIER__DISJOINT__EQ, thm_2Ereal__topology_2EDIFF__CLOSURE__SUBSET, thm_2Ereal__topology_2ECLOSED__EMPTY, thm_2Ereal__topology_2EREGULAR__CLOSED__UNION, thm_2Ereal__topology_2EFRONTIER__CLOSED, thm_2Ereal__topology_2EBALL__UNION__SPHERE, thm_2Ereal__topology_2Econnected, thm_2Ereal__topology_2ECONNECTED__DIFF__OPEN__FROM__CLOSED, thm_2Ereal__topology_2ECONNECTED__FROM__CLOSED__UNION__AND__INTER, thm_2Ereal__topology_2ECBALL__DIFF__SPHERE, thm_2Ereal__topology_2EFRONTIER__FRONTIER__SUBSET, thm_2Ereal__topology_2ECONNECTED__CLOSURE, thm_2Ereal__topology_2ECONNECTED__IFF__CONNECTABLE__POINTS, thm_2Ereal__topology_2EINTERIOR__FRONTIER, thm_2Ereal__topology_2ESUBSET__INTERIOR, thm_2Ereal__topology_2EBOUNDED__INTERIOR, thm_2Ereal__topology_2ECONNECTED__UNION, thm_2Ereal__topology_2ECLOSURE__UNION__FRONTIER, thm_2Ereal__topology_2EINTERIOR__CLOSURE__INTER__OPEN, thm_2Ereal__topology_2ECONNECTED__CLOSED, thm_2Ereal__topology_2EINTERIOR__FRONTIER__EMPTY, thm_2Ereal__topology_2ESUBSET__INTERIOR__EQ, thm_2Ereal_2EREAL__MIN__REFL, thm_2Ereal__topology_2EFRONTIER__SUBSET__EQ, thm_2Ereal__topology_2EINTERIOR__MAXIMAL__EQ, thm_2Ereal__topology_2ESET__DIFF__FRONTIER, thm_2Ereal__topology_2ECBALL__MAX__UNION, thm_2Ereal__topology_2ECONNECTED__CLOSED__SET, thm_2Ereal__topology_2EFRONTIER__INTERIOR__SUBSET, thm_2Ereal__topology_2ESPHERE__SUBSET__CBALL, thm_2Ereal__topology_2EOPEN__INTER__CLOSURE__SUBSET, thm_2Ereal__topology_2EUNION__INTERIOR__SUBSET, thm_2Ereal__topology_2EOPEN__INTER, thm_2Eintegral_2EINTEGRABLE__CONST, thm_2Ereal__topology_2ECLOSED__UNION, thm_2Ereal__topology_2EFRONTIER__CBALL, thm_2Ereal__topology_2ECONNECTED__OPEN__SET, thm_2Ereal__topology_2EOPEN__UNION, thm_2Ereal__topology_2EINTERIOR__EQ__EMPTY, thm_2Ereal__topology_2EINTERIOR__UNION__EQ__EMPTY, thm_2Ereal__topology_2EOPEN__INTER__CLOSURE__EQ__EMPTY, thm_2Ereal__topology_2ECLOSED__CBALL, thm_2Ereal__topology_2EINTERIOR__OPEN, thm_2Ereal__topology_2EINTERIOR__CBALL, thm_2Ereal_2EREAL__MAX__ACI, thm_2Ereal__topology_2EMIDPOINT__EQ__ENDPOINT, thm_2Ereal__topology_2EBOUNDED__CBALL, thm_2Ereal__topology_2EINTERIOR__INTER, thm_2Ereal__topology_2EBALL__MIN__INTER, thm_2Ereal__topology_2ECONNECTED__INTERMEDIATE__CLOSURE, thm_2Ereal__topology_2Efrontier, thm_2Ereal__topology_2EBOUNDED__EMPTY, thm_2Ereal__topology_2EINTERIOR__MAXIMAL, thm_2Ereal__topology_2EBOUNDED__CLOSURE, thm_2Ereal__topology_2EINTERIOR__INTERIOR, thm_2Ereal__topology_2EBOUNDED__CLOSURE__EQ, thm_2Ereal__topology_2EBALL__SUBSET__CBALL, thm_2Ereal__topology_2EBETWEEN__REFL__EQ, thm_2Ereal__topology_2EFRONTIER__EMPTY, thm_2Ereal__topology_2EFRONTIER__INTER__SUBSET, thm_2Ereal__topology_2ESPHERE__UNION__BALL, thm_2Ereal__topology_2ECONNECTED__INTER__FRONTIER, thm_2Ereal__topology_2EFRONTIER__UNION__SUBSET, thm_2Ereal__topology_2EBETWEEN__TRANS, thm_2Ereal__topology_2EINTERIOR__BALL, thm_2Ereal__topology_2ECLOSURE__MINIMAL, thm_2Ereal__topology_2ECLOSED__INTER, thm_2Ereal__topology_2EINTERIOR__DIFF, thm_2Ereal__topology_2EINTERIOR__CLOSED__EQ__EMPTY__AS__FRONTIER, thm_2Ereal__topology_2ECLOSED__CLOSURE, thm_2Ereal__topology_2EREGULAR__OPEN__INTER, thm_2Ereal__topology_2ECLOSURE__SUBSET__EQ, thm_2Ereal__topology_2ECONNECTED__UNION__STRONG, thm_2Ereal__topology_2EOPEN__BALL, thm_2Ereal__topology_2ECBALL__DIFF__BALL, thm_2Ereal__topology_2ECLOSURE__NONEMPTY__OPEN__INTER, thm_2Ereal__topology_2ECLOSURE__CLOSED, thm_2Ereal__topology_2EFRONTIER__FRONTIER, thm_2Ereal__topology_2ECLOSURE__INTERIOR__IDEMP, thm_2Ereal__topology_2EBALL__MAX__UNION, thm_2Ereal__topology_2EOPEN__DIFF, thm_2Ereal__topology_2ECLOSURE__EMPTY, thm_2Ereal__topology_2ECLOSURE__SUBSET, thm_2Ereal__topology_2ECLOSURE__OPEN__INTER__SUPERSET, thm_2Ereal__topology_2EMIDPOINT__SYM, thm_2Ereal__topology_2ECLOSURE__EQ, thm_2Ereal__topology_2EFRONTIER__UNION, thm_2Ereal__topology_2ECLOSURE__INTERIOR__UNION__CLOSED, thm_2Ereal__topology_2ECLOSED__DIFF, thm_2Ereal__topology_2EINTERIOR__SUBSET, thm_2Ereal__topology_2EINTERIOR__UNIQUE, thm_2Ereal__topology_2EOPEN__SUB__OPEN, thm_2Ereal__topology_2EFRONTIER__INTER__SUBSET__INTER, thm_2Ereal__topology_2EOPEN__INTERIOR, thm_2Ereal__topology_2EBETWEEN__MIDPOINT, thm_2Ereal__topology_2EINTERIOR__EQ__EMPTY__ALT, thm_2Ereal_2EREAL__MIN__ACI, thm_2Ereal__topology_2EBETWEEN__TRANS__2
% 41.05/21.62 % No. of inferences in proof: 258
% 41.05/21.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21257 ms resp. 7901 ms w/o parsing
% 41.94/21.85 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 41.94/21.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------