TSTP Solution File: ITP019^4 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP019^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:21:57 EDT 2024

% Result   : Theorem 27.55s 10.65s
% Output   : Refutation 27.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  292
% Syntax   : Number of formulae    :  389 ( 169 unt; 197 typ;   0 def)
%            Number of atoms       :  315 ( 296 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  886 (  24   ~;   8   |;  14   &; 819   @)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :  169 ( 168 usr)
%            Number of type conns  :   46 (  46   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   31 (  29 usr;   3 con; 0-3 aty)
%            Number of variables   :  347 (   0   ^ 343   !;   4   ?; 347   :)

% 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_2Ec_2Enum_2E0_type,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Enum_2EABS__num_type,type,
    mono_2Ec_2Enum_2EABS__num: mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Enum_2EZERO__REP_type,type,
    mono_2Ec_2Enum_2EZERO__REP: mono_2Etyop_2Emin_2Eind ).

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_2Ec_2EbasicSize_2Ebool__size_type,type,
    mono_2Ec_2EbasicSize_2Ebool__size: $o > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2EbasicSize_2Eone__size_type,type,
    mono_2Ec_2EbasicSize_2Eone__size: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Egcd_2Eis__gcd_type,type,
    mono_2Ec_2Egcd_2Eis__gcd: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Egcd_2Elcm_type,type,
    mono_2Ec_2Egcd_2Elcm: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Enumpair_2Encons_type,type,
    mono_2Ec_2Enumpair_2Encons: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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_2Ec_2Estring_2Echar__size_type,type,
    mono_2Ec_2Estring_2Echar__size: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ).

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_2Ec_2EPast__Temporal__Logic_2EInitPoint_type,type,
    mono_2Ec_2EPast__Temporal__Logic_2EInitPoint: mono_2Etyop_2Enum_2Enum > $o ).

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_2Ec_2EternaryComparisons_2Eordering__size_type,type,
    mono_2Ec_2EternaryComparisons_2Eordering__size: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ).

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_2Ec_2ECoder_2Eunit__coder_type,type,
    mono_2Ec_2ECoder_2Eunit__coder: ( mono_2Etyop_2Eone_2Eone > $o ) > 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 ).

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_2Ec_2EEncodeVar_2Efixed__width_2Emono_2Etyop_2Eone_2Eone_type,type,
    mono_2Ec_2EEncodeVar_2Efixed__width_2Emono_2Etyop_2Eone_2Eone: mono_2Etyop_2Enum_2Enum > 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 > $o ).

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_2Ec_2Ebitstring_2Eshiftr_type,type,
    mono_2Ec_2Ebitstring_2Eshiftr: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29 ).

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_2Ec_2Esptree_2Espt__acc_type,type,
    mono_2Ec_2Esptree_2Espt__acc: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

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_2Ec_2Ereal_2Ereal__of__num_type,type,
    mono_2Ec_2Ereal_2Ereal__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

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_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal_type,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_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_2Ec_2Ewords_2Eword__extract_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone_type,type,
    mono_2Ec_2Ewords_2Eword__extract_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 > mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29 ).

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_2Ec_2Ebinary__ieee_2Efloat__compare__size_type,type,
    mono_2Ec_2Ebinary__ieee_2Efloat__compare__size: mono_2Etyop_2Ebinary__ieee_2Efloat__compare > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebinary__ieee_2Erounding__size_type,type,
    mono_2Ec_2Ebinary__ieee_2Erounding__size: mono_2Etyop_2Ebinary__ieee_2Erounding > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ecomplex_2EIM_type,type,
    mono_2Ec_2Ecomplex_2EIM: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__add_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__add: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__div_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__div: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__inv_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__mul_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__mul: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__neg_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__neg: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__of__num_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__of__real_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__of__real: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ecomplex_2Ecomplex__sub_type,type,
    mono_2Ec_2Ecomplex_2Ecomplex__sub: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(15,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__MUL2) ).

thf(138,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1,conjecture,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).

thf(2,negated_conjecture,
    ~ ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
       => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(97,plain,
    ~ ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
       => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(14,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ C )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ C ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RADD) ).

thf(135,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ C )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ C ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(81,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Esptree_2Espt__acc @ mono_2Ec_2Enum_2E0 @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Esptree_2Espt__acc__0) ).

thf(336,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Esptree_2Espt__acc @ mono_2Ec_2Enum_2E0 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(60,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__INV) ).

thf(276,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(9,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__DIFFSQ) ).

thf(120,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(58,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__INV) ).

thf(269,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(96,axiom,
    ! [A: $o] :
      ( ( mono_2Ec_2EbasicSize_2Ebool__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Ebool__size__def) ).

thf(385,plain,
    ! [A: $o] :
      ( ( mono_2Ec_2EbasicSize_2Ebool__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(20,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LDISTRIB) ).

thf(153,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(27,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__RMUL) ).

thf(174,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(69,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__0) ).

thf(301,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(32,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ A )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__INJ) ).

thf(189,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ A )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(63,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__LNEG__UNIQ) ).

thf(284,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(77,axiom,
    ! [A: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( mono_2Ec_2EternaryComparisons_2Eordering__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EternaryComparisons_2Eordering__size__def) ).

thf(325,plain,
    ! [A: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( mono_2Ec_2EternaryComparisons_2Eordering__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(45,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ C )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RDISTRIB) ).

thf(228,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ C )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(74,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        & ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ A )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ C @ A ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RMUL__IMP) ).

thf(316,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        & ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ A )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ C @ A ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(55,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ mono_2Ec_2Enum_2E0 @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0L) ).

thf(261,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ mono_2Ec_2Enum_2E0 @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(41,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) @ C )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RDISTRIB) ).

thf(216,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) @ C )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(52,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ A @ mono_2Ec_2Enum_2E0 @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0R) ).

thf(253,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ A @ mono_2Ec_2Enum_2E0 @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(85,axiom,
    ( mono_2Ec_2Enum_2E0
    = ( mono_2Ec_2Enum_2EABS__num @ mono_2Ec_2Enum_2EZERO__REP ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enum_2EZERO__DEF) ).

thf(348,plain,
    ( mono_2Ec_2Enum_2E0
    = ( mono_2Ec_2Enum_2EABS__num @ mono_2Ec_2Enum_2EZERO__REP ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(87,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RID) ).

thf(353,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(18,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__ADD) ).

thf(147,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(66,axiom,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__0) ).

thf(293,plain,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(13,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__NEG) ).

thf(132,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(50,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Egcd_2Elcm @ mono_2Ec_2Enum_2E0 @ A )
        = mono_2Ec_2Enum_2E0 )
      & ( ( mono_2Ec_2Egcd_2Elcm @ A @ mono_2Ec_2Enum_2E0 )
        = mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__0) ).

thf(243,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Egcd_2Elcm @ mono_2Ec_2Enum_2E0 @ A )
        = mono_2Ec_2Enum_2E0 )
      & ( ( mono_2Ec_2Egcd_2Elcm @ A @ mono_2Ec_2Enum_2E0 )
        = mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(71,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__div @ A @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__div) ).

thf(307,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__div @ A @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(47,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A )
        = B )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__EQ) ).

thf(233,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A )
        = B )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(36,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__ASSOC) ).

thf(201,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(3,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__NEG2) ).

thf(102,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(94,axiom,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__0) ).

thf(380,plain,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(8,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__SUB) ).

thf(117,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(80,axiom,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__0) ).

thf(334,plain,
    ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 )
    = ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(33,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__ASSOC) ).

thf(192,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(24,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__TRIANGLE) ).

thf(165,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(21,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,D: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ C @ D ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ C ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD2__SUB2) ).

thf(156,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,D: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ C @ D ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ C ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(88,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        & ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL__IMP) ).

thf(356,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        & ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(16,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum,D: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Egcd_2Eis__gcd @ A @ B @ C )
        & ( mono_2Ec_2Egcd_2Eis__gcd @ A @ B @ D ) )
     => ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__UNIQUE) ).

thf(141,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum,D: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Egcd_2Eis__gcd @ A @ B @ C )
        & ( mono_2Ec_2Egcd_2Eis__gcd @ A @ B @ D ) )
     => ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(78,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__REFL) ).

thf(328,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(44,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__ADD) ).

thf(225,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(82,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A = mono_2Ec_2Enum_2E0 )
      | ? [B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
          ( A
          = ( mono_2Ec_2Enumpair_2Encons @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__cases) ).

thf(339,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A = mono_2Ec_2Enum_2E0 )
      | ? [B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
          ( A
          = ( mono_2Ec_2Enumpair_2Encons @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(12,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEGNEG) ).

thf(129,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(91,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( ( A
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( B
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ENTIRE) ).

thf(371,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( ( A
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( B
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(4,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__COMM) ).

thf(105,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(57,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INVINV) ).

thf(266,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(68,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) )
      = ( ( A
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL) ).

thf(298,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) )
      = ( ( A
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(61,axiom,
    ! [A: mono_2Etyop_2Eone_2Eone > $o] : ( mono_2Ec_2EEncodeVar_2Efixed__width_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2ECoder_2Eunit__coder @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EEncodeVar_2Efixed__width__unit) ).

thf(279,plain,
    ! [A: mono_2Etyop_2Eone_2Eone > $o] : ( mono_2Ec_2EEncodeVar_2Efixed__width_2Emono_2Etyop_2Eone_2Eone @ mono_2Ec_2Enum_2E0 @ ( mono_2Ec_2ECoder_2Eunit__coder @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(29,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Egcd_2Elcm @ B @ A )
      = ( mono_2Ec_2Egcd_2Elcm @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__COMM) ).

thf(180,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Egcd_2Elcm @ B @ A )
      = ( mono_2Ec_2Egcd_2Elcm @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(62,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).

thf(281,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(37,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__SUB) ).

thf(204,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(95,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = B )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LID__UNIQ) ).

thf(382,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = B )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(73,axiom,
    ! [A: mono_2Etyop_2Eone_2Eone] :
      ( ( mono_2Ec_2EbasicSize_2Eone__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EbasicSize_2Eone__size__def) ).

thf(313,plain,
    ! [A: mono_2Etyop_2Eone_2Eone] :
      ( ( mono_2Ec_2EbasicSize_2Eone__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(17,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum,D: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Enumpair_2Encons @ B @ A )
        = ( mono_2Ec_2Enumpair_2Encons @ D @ C ) )
      = ( ( B = D )
        & ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__11) ).

thf(144,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum,D: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Enumpair_2Encons @ B @ A )
        = ( mono_2Ec_2Enumpair_2Encons @ D @ C ) )
      = ( ( B = D )
        & ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(48,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RINV) ).

thf(236,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(86,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LZERO) ).

thf(350,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(22,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__RNEG) ).

thf(159,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(42,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LADD) ).

thf(219,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(93,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LID) ).

thf(377,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(90,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( ( A @ mono_2Ec_2Enum_2E0 )
        & ! [B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
            ( ( A @ C )
           => ( A @ ( mono_2Ec_2Enumpair_2Encons @ B @ C ) ) ) )
     => ! [B: mono_2Etyop_2Enum_2Enum] : ( A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__ind) ).

thf(362,plain,
    ! [A: mono_2Etyop_2Enum_2Enum > $o] :
      ( ( ( A @ mono_2Ec_2Enum_2E0 )
        & ! [B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
            ( ( A @ C )
           => ( A @ ( mono_2Ec_2Enumpair_2Encons @ B @ C ) ) ) )
     => ! [B: mono_2Etyop_2Enum_2Enum] : ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(84,axiom,
    ! [A: mono_2Etyop_2Estring_2Echar] :
      ( ( mono_2Ec_2Estring_2Echar__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Estring_2Echar__size__def) ).

thf(345,plain,
    ! [A: mono_2Etyop_2Estring_2Echar] :
      ( ( mono_2Ec_2Estring_2Echar__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(40,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ A )
      = ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__of__real) ).

thf(213,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ A )
      = ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(35,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__of__num) ).

thf(198,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(5,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ecomplex_2EIM @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2EIM__COMPLEX__OF__REAL) ).

thf(108,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ecomplex_2EIM @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__real @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(23,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__ADD2) ).

thf(162,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ B @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(92,axiom,
    ! [A: mono_2Etyop_2Ebinary__ieee_2Erounding] :
      ( ( mono_2Ec_2Ebinary__ieee_2Erounding__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Erounding__size__def) ).

thf(374,plain,
    ! [A: mono_2Etyop_2Ebinary__ieee_2Erounding] :
      ( ( mono_2Ec_2Ebinary__ieee_2Erounding__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(53,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( B
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__RNEG__UNIQ) ).

thf(255,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( B
        = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(83,axiom,
    ! [A: mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29] :
      ( ( mono_2Ec_2Ewords_2Eword__extract_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone @ mono_2Ec_2Enum_2E0 @ mono_2Ec_2Enum_2E0 @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EHolSmt_2Er253) ).

thf(342,plain,
    ! [A: mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29] :
      ( ( mono_2Ec_2Ewords_2Eword__extract_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone @ mono_2Ec_2Enum_2E0 @ mono_2Ec_2Enum_2E0 @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(10,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ C ) )
      = ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__SUB__LADD) ).

thf(123,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ C ) )
      = ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(67,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__EQ0) ).

thf(295,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(19,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__SUB) ).

thf(150,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(56,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__LZERO) ).

thf(263,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(72,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = A )
      = ( B
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ) ).

thf(310,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B )
        = A )
      = ( B
        = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(28,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ A )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__OF__NUM__EQ) ).

thf(177,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ A )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(79,axiom,
    ! [A: mono_2Etyop_2Ebinary__ieee_2Efloat__compare] :
      ( ( mono_2Ec_2Ebinary__ieee_2Efloat__compare__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__compare__size__def) ).

thf(331,plain,
    ! [A: mono_2Etyop_2Ebinary__ieee_2Efloat__compare] :
      ( ( mono_2Ec_2Ebinary__ieee_2Efloat__compare__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(89,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        & ( B
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__MUL) ).

thf(359,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( A
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        & ( B
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(51,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NEG) ).

thf(250,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(46,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ A @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__REF) ).

thf(231,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ A @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(75,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__RZERO) ).

thf(319,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(70,axiom,
    ! [A: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( mono_2Ec_2Ebitstring_2Eshiftr @ A @ mono_2Ec_2Enum_2E0 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebitstring_2Eshiftr__0) ).

thf(304,plain,
    ! [A: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( mono_2Ec_2Ebitstring_2Eshiftr @ A @ mono_2Ec_2Enum_2E0 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(54,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2EPast__Temporal__Logic_2EInitPoint @ A )
      = ( A = mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2EPast__Temporal__Logic_2EInitPoint) ).

thf(258,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2EPast__Temporal__Logic_2EInitPoint @ A )
      = ( A = mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(31,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RNEG) ).

thf(186,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(7,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__LMUL) ).

thf(114,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(26,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__LNEG) ).

thf(171,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(65,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RZERO) ).

thf(290,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(38,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__SUB2) ).

thf(207,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(59,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Enumpair_2Encons @ B @ A )
     != mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__not__nnil) ).

thf(272,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Enumpair_2Encons @ B @ A )
     != mono_2Ec_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(64,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LINV) ).

thf(287,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__add @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ A )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(25,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__sub) ).

thf(168,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(30,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LDISTRIB) ).

thf(183,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ B @ C ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B ) @ ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(39,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Egcd_2Eis__gcd @ A @ B @ C )
      = ( mono_2Ec_2Egcd_2Eis__gcd @ B @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__SYM) ).

thf(210,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Egcd_2Eis__gcd @ A @ B @ C )
      = ( mono_2Ec_2Egcd_2Eis__gcd @ B @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(49,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( B = C )
        = ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL2) ).

thf(239,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( A
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( B = C )
        = ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(11,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B )
        = C )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__SUB__RADD) ).

thf(126,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ B )
        = C )
      = ( A
        = ( mono_2Ec_2Ecomplex_2Ecomplex__add @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(34,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__COMM) ).

thf(195,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(6,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LNEG) ).

thf(111,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ A ) @ B )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(76,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ C ) )
      = ( ( C
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RMUL) ).

thf(322,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ A @ C )
        = ( mono_2Ec_2Ecomplex_2Ecomplex__mul @ B @ C ) )
      = ( ( C
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(43,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__SUB2) ).

thf(222,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( mono_2Ec_2Ecomplex_2Ecomplex__sub @ A @ ( mono_2Ec_2Ecomplex_2Ecomplex__add @ A @ B ) )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__neg @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(390,plain,
    $false,
    inference(e,[status(thm)],[138,97,135,336,276,120,269,385,153,174,301,189,284,325,228,316,261,216,253,348,353,147,293,132,243,307,233,201,102,380,117,334,192,165,156,356,141,328,225,339,129,371,105,266,298,279,180,281,204,382,313,144,236,350,159,219,377,362,345,213,198,108,162,374,255,342,123,295,150,263,310,177,331,359,250,231,319,304,258,186,114,171,290,207,272,287,168,183,210,239,126,195,111,322,222]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem  : ITP019^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n006.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Sat May 18 17:15:26 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 0.99/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 12.23/6.62  % [INFO] 	 Parsing done (5688ms). 
% 12.23/6.65  % [INFO] 	 Running in sequential loop mode. 
% 12.53/6.83  % [INFO] 	 eprover registered as external prover. 
% 12.53/6.83  % [INFO] 	 cvc4 registered as external prover. 
% 12.53/6.84  % [INFO] 	 Scanning for conjecture ... 
% 17.93/8.48  % [INFO] 	 Found a conjecture (or negated_conjecture) and 34393 axioms. Running axiom selection ... 
% 19.25/8.90  % [INFO] 	 Axiom selection finished. Selected 94 axioms (removed 34299 axioms). 
% 19.25/8.96  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 19.25/8.97  % [INFO] 	 Type checking passed. 
% 19.56/8.97  % [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 ... 
% 27.55/10.65  % External prover 'e' found a proof!
% 27.55/10.65  % [INFO] 	 Killing All external provers ... 
% 27.55/10.65  % Time passed: 10178ms (effective reasoning time: 3995ms)
% 27.55/10.65  % 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)>
% 27.55/10.65  % Axioms used in derivation (94): thm_2Egcd_2ELCM__COMM, thm_2Ecomplex_2ECOMPLEX__NEG__EQ, thm_2Ebinary__ieee_2Efloat__compare__size__def, thm_2Ecomplex_2ECOMPLEX__MUL__RNEG, thm_2Ecomplex_2ECOMPLEX__SUB__TRIANGLE, thm_2Ecomplex_2ECOMPLEX__ADD__ASSOC, thm_2Ecomplex_2ECOMPLEX__ADD__RINV, thm_2Ecomplex_2ECOMPLEX__ADD__COMM, thm_2Ecomplex_2ECOMPLEX__EQ__LMUL2, thm_2Ecomplex_2ECOMPLEX__SUB__0, thm_2Ecomplex_2ECOMPLEX__EQ__RMUL__IMP, thm_2Ecomplex_2ECOMPLEX__INV__MUL, thm_2Ecomplex_2ECOMPLEX__SUB__ADD, thm_2Enumpair_2Enlist__cases, thm_2Ecomplex_2ECOMPLEX__ADD__RDISTRIB, thm_2Egcd_2EIS__GCD__UNIQUE, thm_2Ecomplex_2ECOMPLEX__NEG__SUB, thm_2Ereal_2EREAL__OF__NUM__EQ, thm_2Ecomplex_2ECOMPLEX__MUL__RZERO, thm_2Ecomplex_2ECOMPLEX__SUB__SUB2, thm_2Ecomplex_2ECOMPLEX__EQ__RADD, thm_2Ecomplex_2ECOMPLEX__SUB__RDISTRIB, thm_2Enum_2EZERO__DEF, thm_2Ecomplex_2ECOMPLEX__SUB__RZERO, thm_2Ecomplex_2ECOMPLEX__SUB__NEG2, thm_2Ecomplex_2ECOMPLEX__SUB__RNEG, thm_2Ebinary__ieee_2Erounding__size__def, thm_2Ecomplex_2ECOMPLEX__NEG__INV, thm_2Ecomplex_2ECOMPLEX__LNEG__UNIQ, thm_2Ecomplex_2ECOMPLEX__EQ__LMUL, thm_2Ecomplex_2ECOMPLEX__NEG__RMUL, thm_2EPast__Temporal__Logic_2EInitPoint, thm_2Ecomplex_2ECOMPLEX__SUB__SUB, thm_2EternaryComparisons_2Eordering__size__def, thm_2EbasicSize_2Eone__size__def, thm_2Ecomplex_2ECOMPLEX__SUB__ADD2, thm_2Ecomplex_2ECOMPLEX__ADD2__SUB2, thm_2Ecomplex_2Ecomplex__of__num, thm_2Egcd_2ELCM__0, thm_2Ecomplex_2ECOMPLEX__NEG__ADD, thm_2Ecomplex_2ECOMPLEX__INVINV, thm_2Enumpair_2Encons__not__nnil, thm_2Egcd_2EIS__GCD__REF, thm_2Ebitstring_2Eshiftr__0, thm_2Ereal_2EREAL__INJ, thm_2Ecomplex_2ECOMPLEX__NEG__0, thm_2Ecomplex_2ECOMPLEX__0, thm_2Estring_2Echar__size__def, thm_2Ecomplex_2ECOMPLEX__ADD__LID, thm_2Ecomplex_2ECOMPLEX__EQ__SUB__RADD, thm_2Ecomplex_2ECOMPLEX__ADD__SUB, thm_2Ecomplex_2ECOMPLEX__EQ__LADD, thm_2Ecomplex_2ECOMPLEX__DIFFSQ, thm_2Ecomplex_2ECOMPLEX__EQ__SUB__LADD, thm_2Ecomplex_2Ecomplex__of__real, thm_2Ecomplex_2ECOMPLEX__MUL__LZERO, thm_2EHolSmt_2Er253, thm_2Ecomplex_2ECOMPLEX__INV__EQ__0, thm_2Ecomplex_2ECOMPLEX__NEG__MUL2, thm_2Ecomplex_2ECOMPLEX__EQ__NEG, thm_2EbasicSize_2Ebool__size__def, thm_2Egcd_2EIS__GCD__SYM, thm_2Ecomplex_2ECOMPLEX__SUB__LZERO, thm_2Ecomplex_2ECOMPLEX__ADD__LDISTRIB, thm_2Ecomplex_2ECOMPLEX__SUB__LNEG, thm_2Ecomplex_2ECOMPLEX__MUL__LNEG, thm_2Ecomplex_2ECOMPLEX__ENTIRE, thm_2Enumpair_2Encons__11, thm_2Ecomplex_2ECOMPLEX__SUB__LDISTRIB, thm_2Ecomplex_2ECOMPLEX__MUL__COMM, thm_2Ecomplex_2ECOMPLEX__INV__INV, thm_2Ecomplex_2ECOMPLEX__RNEG__UNIQ, thm_2Ecomplex_2ECOMPLEX__INV__0, thm_2Ecomplex_2ECOMPLEX__ADD__RID, thm_2Ecomplex_2ECOMPLEX__NEGNEG, thm_2Ecomplex_2ECOMPLEX__EQ__LMUL__IMP, thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ, thm_2Ecomplex_2Ecomplex__div, thm_2Ecomplex_2EIM__COMPLEX__OF__REAL, thm_2Ecomplex_2ECOMPLEX__MUL__ASSOC, thm_2Ecomplex_2Ecomplex__sub, thm_2Ecomplex_2ECOMPLEX__NEG__EQ0, thm_2Ecomplex_2ECOMPLEX__EQ__RMUL, thm_2Egcd_2EIS__GCD__0R, thm_2EEncodeVar_2Efixed__width__unit, thm_2Ecomplex_2ECOMPLEX__NEG__LMUL, thm_2Ecomplex_2ECOMPLEX__SUB__REFL, thm_2Ecomplex_2ECOMPLEX__ADD__SUB2, thm_2Ecomplex_2ECOMPLEX__ADD__LINV, thm_2Enumpair_2Enlist__ind, thm_2Ecomplex_2ECOMPLEX__ADD__LID__UNIQ, thm_2Egcd_2EIS__GCD__0L, thm_2Esptree_2Espt__acc__0, thm_2Ecomplex_2ECOMPLEX__INV__NEG
% 27.55/10.65  % No. of inferences in proof: 192
% 27.55/10.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10178 ms resp. 3995 ms w/o parsing
% 27.71/10.71  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.71/10.71  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------