Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP019^4 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Sep 30 08:06:24 AM UTC 2026

% Result   : Theorem 38.01s 19.64s
% Output   : Refutation 38.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   95
% Syntax   : Number of formulae    :  192 ( 169 unt;   0 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  :    4 (   4   >;   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_2Etyop_2Eone_2Eone_type,type,
    mono_2Etyop_2Eone_2Eone: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Estring_2Echar_type,type,
    mono_2Etyop_2Estring_2Echar: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Estring_2Echar_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_type,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Estring_2Echar_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Esum_2Esum_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
    mono_2Etyop_2Esum_2Esum_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).

thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2EternaryComparisons_2Eordering_type,type,
    mono_2Etyop_2EternaryComparisons_2Eordering: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eone_2Eone_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ehrat_2Ehrat_type,type,
    mono_2Etyop_2Ehrat_2Ehrat: $tType ).

thf(mono_2Etyop_2Einteger_2Eint_type,type,
    mono_2Etyop_2Einteger_2Eint: $tType ).

thf(mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Eordinal_2Eordinal_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Esum_2Esum_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Equote_2Eindex_type,type,
    mono_2Etyop_2Equote_2Eindex: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Equote_2Eindex_29: $tType ).

thf(mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Etoto_2Enum__dt_type,type,
    mono_2Etyop_2Etoto_2Enum__dt: $tType ).

thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Estring_2Echar_29_type,type,
    mono_2Etyop_2Etoto_2Etoto_28tyop_2Estring_2Echar_29: $tType ).

thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29_type,type,
    mono_2Etyop_2Etoto_2Etoto_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_29: $tType ).

thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Etoto_2Etoto_28tyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29: $tType ).

thf(mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_type,type,
    mono_2Etyop_2Ebool_2Eitself_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Eone_2Eone_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Enum_2Enum_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Ehreal_2Ehreal_type,type,
    mono_2Etyop_2Ehreal_2Ehreal: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Epatricia_2Eptree_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Esptree_2Espt_28tyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2EDeepSyntax_2Edeep__form_type,type,
    mono_2Etyop_2EDeepSyntax_2Edeep__form: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29_type,type,
    mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Etoto_2Etoto_28tyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Eone_2Eone_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28tyop_2Estring_2Echar_29_2Ctyop_2Eone_2Eone_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Ehreal_2Ehreal_2Ctyop_2Ehreal_2Ehreal_29: $tType ).

thf(mono_2Etyop_2Erealax_2Ereal_type,type,
    mono_2Etyop_2Erealax_2Ereal: $tType ).

thf(mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2EringNorm_2Epolynom_28tyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2EringNorm_2Epolynom_28tyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Ering_2Ering_28tyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Ering_2Ering_28tyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Equote_2Evarmap_28tyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Equote_2Evarmap_28tyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Esemi__ring_2Esemi__ring_28tyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Esemi__ring_2Esemi__ring_28tyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Equote_2Evarmap_28tyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Equote_2Evarmap_28tyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_type,type,
    mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $tType ).

thf(mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_type,type,
    mono_2Etyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29: $tType ).

thf(mono_2Etyop_2Efrac_2Efrac_type,type,
    mono_2Etyop_2Efrac_2Efrac: $tType ).

thf(mono_2Etyop_2Erat_2Erat_type,type,
    mono_2Etyop_2Erat_2Erat: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Etopology_2Etopology_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29: $tType ).

thf(mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Erat_2Erat_29_type,type,
    mono_2Etyop_2Ecanonical_2Ecanonical__sum_28tyop_2Erat_2Erat_29: $tType ).

thf(mono_2Etyop_2EringNorm_2Epolynom_28tyop_2Erat_2Erat_29_type,type,
    mono_2Etyop_2EringNorm_2Epolynom_28tyop_2Erat_2Erat_29: $tType ).

thf(mono_2Etyop_2Ering_2Ering_28tyop_2Erat_2Erat_29_type,type,
    mono_2Etyop_2Ering_2Ering_28tyop_2Erat_2Erat_29: $tType ).

thf(mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Erat_2Erat_29_type,type,
    mono_2Etyop_2Ecanonical_2Espolynom_28tyop_2Erat_2Erat_29: $tType ).

thf(mono_2Etyop_2Equote_2Evarmap_28tyop_2Erat_2Erat_29_type,type,
    mono_2Etyop_2Equote_2Evarmap_28tyop_2Erat_2Erat_29: $tType ).

thf(mono_2Etyop_2Elist_2Elist_28tyop_2Erealax_2Ereal_29_type,type,
    mono_2Etyop_2Elist_2Elist_28tyop_2Erealax_2Ereal_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Erealax_2Ereal_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Efcp_2Ebit1_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29_type,type,
    mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2Ctyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Efcp_2Ebit0_28tyop_2Eone_2Eone_29_29_29_29: $tType ).

thf(mono_2Etyop_2Ebinary__ieee_2Eflags_type,type,
    mono_2Etyop_2Ebinary__ieee_2Eflags: $tType ).

thf(mono_2Etyop_2Ebinary__ieee_2Efloat__compare_type,type,
    mono_2Etyop_2Ebinary__ieee_2Efloat__compare: $tType ).

thf(mono_2Etyop_2Ebinary__ieee_2Efloat__value_type,type,
    mono_2Etyop_2Ebinary__ieee_2Efloat__value: $tType ).

thf(mono_2Etyop_2Eoption_2Eoption_28tyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat__value_2Ctyop_2Ebinary__ieee_2Efloat__value_29_type,type,
    mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat__value_2Ctyop_2Ebinary__ieee_2Efloat__value_29: $tType ).

thf(mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29_29_type,type,
    mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29_29_29_29: $tType ).

thf(mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Erealax_2Ereal_29_type,type,
    mono_2Etyop_2Eind__type_2Erecspace_28tyop_2Erealax_2Ereal_29: $tType ).

thf(mono_2Etyop_2Ebinary__ieee_2Erounding_type,type,
    mono_2Etyop_2Ebinary__ieee_2Erounding: $tType ).

thf(mono_2Ec_2Enum_2E0_decl,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Enum_2EABS__num_decl,type,
    mono_2Ec_2Enum_2EABS__num: mono_2Etyop_2Emin_2Eind > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Enum_2EZERO__REP_decl,type,
    mono_2Ec_2Enum_2EZERO__REP: mono_2Etyop_2Emin_2Eind ).

thf(mono_2Ec_2EbasicSize_2Ebool__size_decl,type,
    mono_2Ec_2EbasicSize_2Ebool__size: $o > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2EbasicSize_2Eone__size_decl,type,
    mono_2Ec_2EbasicSize_2Eone__size: mono_2Etyop_2Eone_2Eone > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Egcd_2Eis__gcd_decl,type,
    mono_2Ec_2Egcd_2Eis__gcd: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2Egcd_2Elcm_decl,type,
    mono_2Ec_2Egcd_2Elcm: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Enumpair_2Encons_decl,type,
    mono_2Ec_2Enumpair_2Encons: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Estring_2Echar__size_decl,type,
    mono_2Ec_2Estring_2Echar__size: mono_2Etyop_2Estring_2Echar > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2EPast__Temporal__Logic_2EInitPoint_decl,type,
    mono_2Ec_2EPast__Temporal__Logic_2EInitPoint: mono_2Etyop_2Enum_2Enum > $o ).

thf(mono_2Ec_2EternaryComparisons_2Eordering__size_decl,type,
    mono_2Ec_2EternaryComparisons_2Eordering__size: mono_2Etyop_2EternaryComparisons_2Eordering > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2ECoder_2Eunit__coder_decl,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_2Ec_2EEncodeVar_2Efixed__width_2Emono_2Etyop_2Eone_2Eone_decl,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_2Ec_2Ebitstring_2Eshiftr_decl,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_2Ec_2Esptree_2Espt__acc_decl,type,
    mono_2Ec_2Esptree_2Espt__acc: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ereal_2Ereal__of__num_decl,type,
    mono_2Ec_2Ereal_2Ereal__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal_decl,type,
    mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Ewords_2Eword__extract_2Emono_2Etyop_2Eone_2Eone_20mono_2Etyop_2Eone_2Eone_decl,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_2Ec_2Ebinary__ieee_2Efloat__compare__size_decl,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_decl,type,
    mono_2Ec_2Ebinary__ieee_2Erounding__size: mono_2Etyop_2Ebinary__ieee_2Erounding > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ecomplex_2EIM_decl,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_decl,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_decl,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_decl,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_decl,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_decl,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_decl,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_decl,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_decl,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__RNEG__UNIQ) ).

thf(257,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LINV) ).

thf(289,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__MUL2) ).

thf(139,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(84,axiom,
    ! [A: mono_2Etyop_2Estring_2Echar] :
      ( ( mono_2Ec_2Estring_2Echar__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estring_2Echar__size__def) ).

thf(347,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(79,axiom,
    ! [A: mono_2Etyop_2Ebinary__ieee_2Efloat__compare] :
      ( ( mono_2Ec_2Ebinary__ieee_2Efloat__compare__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__compare__size__def) ).

thf(333,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__EQ) ).

thf(234,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LZERO) ).

thf(352,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__LMUL) ).

thf(115,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RDISTRIB) ).

thf(217,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__ASSOC) ).

thf(202,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LID__UNIQ) ).

thf(385,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__UNIQUE) ).

thf(142,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LDISTRIB) ).

thf(184,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(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/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er253) ).

thf(344,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__COMM) ).

thf(196,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD2__SUB2) ).

thf(157,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__RZERO) ).

thf(321,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__SYM) ).

thf(211,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__COMM) ).

thf(106,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__DIFFSQ) ).

thf(121,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__NEG) ).

thf(133,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__LZERO) ).

thf(265,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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RID__UNIQ) ).

thf(312,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RZERO) ).

thf(292,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LID) ).

thf(380,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LADD) ).

thf(220,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(54,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2EPast__Temporal__Logic_2EInitPoint @ A )
      = ( A = mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EPast__Temporal__Logic_2EInitPoint) ).

thf(260,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__RNEG) ).

thf(160,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__EQ0) ).

thf(297,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RDISTRIB) ).

thf(229,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NEG) ).

thf(252,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__MUL) ).

thf(361,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(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/sandbox2/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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RMUL) ).

thf(324,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(96,axiom,
    ! [A: $o] :
      ( ( mono_2Ec_2EbasicSize_2Ebool__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EbasicSize_2Ebool__size__def) ).

thf(388,plain,
    ! [A: $o] :
      ( ( mono_2Ec_2EbasicSize_2Ebool__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__sub) ).

thf(169,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2EIM__COMPLEX__OF__REAL) ).

thf(109,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__SUB__LADD) ).

thf(124,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__ASSOC) ).

thf(193,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RINV) ).

thf(237,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__0) ).

thf(244,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__SUB) ).

thf(205,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__TRIANGLE) ).

thf(166,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__ADD) ).

thf(148,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__LNEG__UNIQ) ).

thf(286,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__SUB) ).

thf(118,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(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/sandbox2/benchmark/theBenchmark.p',thm_2EEncodeVar_2Efixed__width__unit) ).

thf(281,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/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2ELCM__COMM) ).

thf(181,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(85,axiom,
    ( mono_2Ec_2Enum_2E0
    = ( mono_2Ec_2Enum_2EABS__num @ mono_2Ec_2Enum_2EZERO__REP ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enum_2EZERO__DEF) ).

thf(350,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__RNEG) ).

thf(187,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__MUL__LNEG) ).

thf(172,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__not__nnil) ).

thf(274,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(92,axiom,
    ! [A: mono_2Etyop_2Ebinary__ieee_2Erounding] :
      ( ( mono_2Ec_2Ebinary__ieee_2Erounding__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Erounding__size__def) ).

thf(377,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RMUL__IMP) ).

thf(318,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__0) ).

thf(303,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__INV) ).

thf(271,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__SUB2) ).

thf(208,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__NEG2) ).

thf(103,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL2) ).

thf(240,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__REFL) ).

thf(330,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEGNEG) ).

thf(130,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__INV) ).

thf(278,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__SUB2) ).

thf(223,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(70,axiom,
    ! [A: mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29] :
      ( ( mono_2Ec_2Ebitstring_2Eshiftr @ A @ mono_2Ec_2Enum_2E0 )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebitstring_2Eshiftr__0) ).

thf(306,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__ADD) ).

thf(226,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ENTIRE) ).

thf(374,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(52,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ A @ mono_2Ec_2Enum_2E0 @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0R) ).

thf(255,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__LNEG) ).

thf(112,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__RID) ).

thf(355,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Enumpair_2Encons__11) ).

thf(145,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__0) ).

thf(295,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(77,axiom,
    ! [A: mono_2Etyop_2EternaryComparisons_2Eordering] :
      ( ( mono_2Ec_2EternaryComparisons_2Eordering__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EternaryComparisons_2Eordering__size__def) ).

thf(327,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(55,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ mono_2Ec_2Enum_2E0 @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__0L) ).

thf(263,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__of__num) ).

thf(199,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__SUB__RADD) ).

thf(127,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(81,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( mono_2Ec_2Esptree_2Espt__acc @ mono_2Ec_2Enum_2E0 @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Esptree_2Espt__acc__0) ).

thf(338,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__0) ).

thf(336,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__LDISTRIB) ).

thf(154,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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__NEG__RMUL) ).

thf(175,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__0) ).

thf(383,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__of__real) ).

thf(214,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__ADD__SUB) ).

thf(151,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL) ).

thf(300,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(73,axiom,
    ! [A: mono_2Etyop_2Eone_2Eone] :
      ( ( mono_2Ec_2EbasicSize_2Eone__size @ A )
      = mono_2Ec_2Enum_2E0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EbasicSize_2Eone__size__def) ).

thf(315,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__INJ) ).

thf(190,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__RADD) ).

thf(136,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__cases) ).

thf(341,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INVINV) ).

thf(268,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__EQ__LMUL__IMP) ).

thf(358,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).

thf(283,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__SUB__ADD2) ).

thf(163,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__OF__NUM__EQ) ).

thf(178,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2Ecomplex__div) ).

thf(309,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(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/sandbox2/benchmark/theBenchmark.p',thm_2Enumpair_2Enlist__ind) ).

thf(364,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(46,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ A @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Egcd_2EIS__GCD__REF) ).

thf(232,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Egcd_2Eis__gcd @ A @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(393,plain,
    $false,
    inference(e,[status(thm)],[257,289,139,347,333,234,352,115,217,202,385,142,184,344,196,157,321,211,106,121,133,265,312,292,380,220,260,160,297,229,252,361,97,324,388,169,109,124,193,237,244,205,166,148,286,118,281,181,350,187,172,274,377,318,303,271,208,103,240,330,130,278,223,306,226,374,255,112,355,145,295,327,263,199,127,338,336,154,175,383,214,151,300,315,190,136,341,268,358,283,163,178,309,364,232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ITP019^4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.09  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.27  % Computer : n006.cluster.edu
% 0.11/0.27  % Model    : x86_64 x86_64
% 0.11/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27  % Memory   : 8046.5625MB
% 0.11/0.27  % OS       : Linux 6.8.0-71-generic
% 0.11/0.27  % CPULimit : 300
% 0.11/0.27  % WCLimit  : 300
% 0.11/0.27  % DateTime : Tue Sep 29 19:32:57 UTC 2026
% 0.11/0.27  % CPUTime  : 
% 0.11/0.27  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.27/1.09  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 20.01/11.24  % [INFO] 	 Parsing done (10143ms). 
% 20.17/11.31  % [INFO] 	 Running in sequential loop mode. 
% 20.59/11.70  % [INFO] 	 eprover registered as external prover. 
% 20.78/11.71  % [INFO] 	 Scanning for conjecture ... 
% 28.15/15.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 34393 axioms. Running axiom selection ... 
% 30.87/16.71  % [INFO] 	 Axiom selection finished. Selected 94 axioms (removed 34299 axioms). 
% 31.16/16.85  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 31.16/16.87  % [INFO] 	 Type checking passed. 
% 31.16/16.88  % [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 ... 
% 38.01/19.63  % External prover 'e' found a proof!
% 38.01/19.63  % [INFO] 	 Killing All external provers ... 
% 38.01/19.63  % Time passed: 19161ms (effective reasoning time: 8311ms)
% 38.01/19.63  % 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)>
% 38.01/19.64  % 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
% 38.01/19.64  % No. of inferences in proof: 192
% 38.01/19.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19161 ms resp. 8311 ms w/o parsing
% 38.73/19.85  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 38.73/19.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------