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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP018^4 : 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 : n011.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 08:06:23 AM UTC 2026

% Result   : Theorem 131.66s 61.82s
% Output   : Refutation 137.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :  647
% Syntax   : Number of formulae    : 1320 ( 976 unt;   0 typ;   7 def)
%            Number of atoms       : 3187 (1769 equ;   0 cnn)
%            Maximal formula atoms :   35 (   2 avg)
%            Number of connectives : 67875 ( 225   ~; 111   |; 465   &;66484   @)
%                                         (   0 <=>; 590  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   40 (   6 avg)
%            Number of types       :  169 ( 168 usr)
%            Number of type conns  :  220 ( 220   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  193 ( 190 usr;  44 con; 0-5 aty)
%            Number of variables   : 5407 (  19   ^;5103   !; 278   ?;5407   :)
%                                         (   0  !>;   0  ?*;   0  @-;   7  @+)

% 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(tyop_2Emin_2Ebool_decl,type,
    tyop_2Emin_2Ebool: d ).

thf(tyop_2Emin_2Efun_decl,type,
    tyop_2Emin_2Efun: d > d > d ).

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

thf(app_2E2_decl,type,
    app_2E2: du > du > u ).

thf(i_mono_2Etyop_2Emin_2Ebool_decl,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(j_mono_2Etyop_2Emin_2Ebool_decl,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(tyop_2Ebool_2Eitself_decl,type,
    tyop_2Ebool_2Eitself: d > d ).

thf(c_2Ebool_2ECOND_2E3_decl,type,
    c_2Ebool_2ECOND_2E3: du > du > du > u ).

thf(c_2Ebool_2EIN_2E2_decl,type,
    c_2Ebool_2EIN_2E2: du > du > u ).

thf(c_2Ebool_2Eitself__case_2E0_decl,type,
    c_2Ebool_2Eitself__case_2E0: u ).

thf(c_2Ebool_2Eitself__case_2E2_decl,type,
    c_2Ebool_2Eitself__case_2E2: du > du > u ).

thf(c_2Ebool_2Ethe__value_2E0_decl,type,
    c_2Ebool_2Ethe__value_2E0: u ).

thf(c_2Emarker_2Estmarker_2E0_decl,type,
    c_2Emarker_2Estmarker_2E0: u ).

thf(c_2Emarker_2Estmarker_2E1_decl,type,
    c_2Emarker_2Estmarker_2E1: du > u ).

thf(c_2Emarker_2Eunint_2E0_decl,type,
    c_2Emarker_2Eunint_2E0: u ).

thf(c_2Emarker_2Eunint_2E1_decl,type,
    c_2Emarker_2Eunint_2E1: du > u ).

thf(c_2EnormalForms_2EEXT__POINT_2E2_decl,type,
    c_2EnormalForms_2EEXT__POINT_2E2: du > du > u ).

thf(c_2Ecombin_2E_3A_3E_2E2_decl,type,
    c_2Ecombin_2E_3A_3E_2E2: du > du > u ).

thf(c_2Ecombin_2EK_2E0_decl,type,
    c_2Ecombin_2EK_2E0: u ).

thf(c_2Ecombin_2EK_2E2_decl,type,
    c_2Ecombin_2EK_2E2: du > du > u ).

thf(mono_2Ec_2Enum_2E0_decl,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(c_2Erelation_2ETC_2E1_decl,type,
    c_2Erelation_2ETC_2E1: du > u ).

thf(tyop_2Esum_2Esum_decl,type,
    tyop_2Esum_2Esum: d > d > d ).

thf(tyop_2Eoption_2Eoption_decl,type,
    tyop_2Eoption_2Eoption: d > d ).

thf(tyop_2Epair_2Eprod_decl,type,
    tyop_2Epair_2Eprod: d > d > d ).

thf(c_2Epair_2E_23_23_2E3_decl,type,
    c_2Epair_2E_23_23_2E3: du > du > du > u ).

thf(c_2Epair_2E_2C_2E0_decl,type,
    c_2Epair_2E_2C_2E0: u ).

thf(c_2Epair_2E_2C_2E2_decl,type,
    c_2Epair_2E_2C_2E2: du > du > u ).

thf(c_2Epair_2EABS__prod_2E0_decl,type,
    c_2Epair_2EABS__prod_2E0: u ).

thf(c_2Epair_2EABS__prod_2E1_decl,type,
    c_2Epair_2EABS__prod_2E1: du > u ).

thf(c_2Epair_2ECURRY_2E3_decl,type,
    c_2Epair_2ECURRY_2E3: du > du > du > u ).

thf(c_2Epair_2EREP__prod_2E0_decl,type,
    c_2Epair_2EREP__prod_2E0: u ).

thf(c_2Epair_2EREP__prod_2E1_decl,type,
    c_2Epair_2EREP__prod_2E1: du > u ).

thf(c_2Epair_2ERPROD_2E0_decl,type,
    c_2Epair_2ERPROD_2E0: u ).

thf(c_2Epair_2ERPROD_2E2_decl,type,
    c_2Epair_2ERPROD_2E2: du > du > u ).

thf(c_2Epair_2EUNCURRY_2E1_decl,type,
    c_2Epair_2EUNCURRY_2E1: du > u ).

thf(c_2Epair_2EUNCURRY_2E2_decl,type,
    c_2Epair_2EUNCURRY_2E2: du > du > u ).

thf(c_2Epair_2Epair__CASE_2E0_decl,type,
    c_2Epair_2Epair__CASE_2E0: u ).

thf(c_2Epair_2Epair__CASE_2E2_decl,type,
    c_2Epair_2Epair__CASE_2E2: du > du > u ).

thf(c_2Eposet_2Ecarrier_2E0_decl,type,
    c_2Eposet_2Ecarrier_2E0: u ).

thf(c_2Eposet_2Ecarrier_2E1_decl,type,
    c_2Eposet_2Ecarrier_2E1: du > u ).

thf(c_2Eposet_2Erelation_2E0_decl,type,
    c_2Eposet_2Erelation_2E0: u ).

thf(c_2Eposet_2Erelation_2E1_decl,type,
    c_2Eposet_2Erelation_2E1: du > u ).

thf(c_2Epred__set_2EFINITE_2E1_decl,type,
    c_2Epred__set_2EFINITE_2E1: du > u ).

thf(c_2Epred__set_2EGSPEC_2E1_decl,type,
    c_2Epred__set_2EGSPEC_2E1: du > u ).

thf(c_2Epred__set_2EIMAGE_2E2_decl,type,
    c_2Epred__set_2EIMAGE_2E2: du > du > u ).

thf(c_2Epred__set_2EINTER_2E2_decl,type,
    c_2Epred__set_2EINTER_2E2: du > du > u ).

thf(c_2Epred__set_2EUNION_2E2_decl,type,
    c_2Epred__set_2EUNION_2E2: du > du > u ).

thf(tyop_2Elist_2Elist_decl,type,
    tyop_2Elist_2Elist: d > d ).

thf(c_2Eset__relation_2Efchains_2E0_decl,type,
    c_2Eset__relation_2Efchains_2E0: u ).

thf(c_2Eset__relation_2Efchains_2E1_decl,type,
    c_2Eset__relation_2Efchains_2E1: du > u ).

thf(c_2Eset__relation_2Erel__to__reln_2E1_decl,type,
    c_2Eset__relation_2Erel__to__reln_2E1: du > u ).

thf(c_2Eset__relation_2Ereln__to__rel_2E1_decl,type,
    c_2Eset__relation_2Ereln__to__rel_2E1: du > u ).

thf(c_2Eset__relation_2Etc_2E1_decl,type,
    c_2Eset__relation_2Etc_2E1: du > u ).

thf(c_2Eset__relation_2Etc_2E2_decl,type,
    c_2Eset__relation_2Etc_2E2: du > du > u ).

thf(c_2Eset__relation_2Euniv__reln_2E0_decl,type,
    c_2Eset__relation_2Euniv__reln_2E0: u ).

thf(c_2Eset__relation_2Euniv__reln_2E1_decl,type,
    c_2Eset__relation_2Euniv__reln_2E1: du > u ).

thf(c_2Estate__transformer_2EBIND_2E2_decl,type,
    c_2Estate__transformer_2EBIND_2E2: du > du > u ).

thf(c_2Estate__transformer_2EREAD_2E0_decl,type,
    c_2Estate__transformer_2EREAD_2E0: u ).

thf(c_2Estate__transformer_2EREAD_2E2_decl,type,
    c_2Estate__transformer_2EREAD_2E2: du > du > u ).

thf(c_2Estate__transformer_2EUNIT_2E0_decl,type,
    c_2Estate__transformer_2EUNIT_2E0: u ).

thf(c_2Estate__transformer_2EUNIT_2E2_decl,type,
    c_2Estate__transformer_2EUNIT_2E2: du > du > u ).

thf(tyop_2Efcp_2Ecart_decl,type,
    tyop_2Efcp_2Ecart: d > d > d ).

thf(c_2Equotient_2EQUOTIENT_2E3_decl,type,
    c_2Equotient_2EQUOTIENT_2E3: du > du > du > u ).

thf(c_2EreaderMonad_2EBIND_2E3_decl,type,
    c_2EreaderMonad_2EBIND_2E3: du > du > du > u ).

thf(c_2EreaderMonad_2EJOIN_2E2_decl,type,
    c_2EreaderMonad_2EJOIN_2E2: du > du > u ).

thf(c_2EreaderMonad_2EUNIT_2E0_decl,type,
    c_2EreaderMonad_2EUNIT_2E0: u ).

thf(c_2EreaderMonad_2EUNIT_2E2_decl,type,
    c_2EreaderMonad_2EUNIT_2E2: du > du > u ).

thf(c_2Etransfer_2EPAIR__REL_2E4_decl,type,
    c_2Etransfer_2EPAIR__REL_2E4: du > du > du > du > u ).

thf(tyop_2Epath_2Epath_decl,type,
    tyop_2Epath_2Epath: d > d > d ).

thf(c_2Epath_2Eparallel__comp_2E5_decl,type,
    c_2Epath_2Eparallel__comp_2E5: du > du > du > du > du > u ).

thf(c_2Etopology_2Eistopology_2E1_decl,type,
    c_2Etopology_2Eistopology_2E1: du > u ).

thf(tyop_2Eordinal_2Eordinal_decl,type,
    tyop_2Eordinal_2Eordinal: d > d ).

thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_decl,type,
    i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).

thf(c_2Efmapal_2EAP__SND_2E2_decl,type,
    c_2Efmapal_2EAP__SND_2E2: du > du > u ).

thf(tyop_2Erealax_2Ereal_decl,type,
    tyop_2Erealax_2Ereal: d ).

thf(mono_2Ec_2Erealax_2Ereal__add_decl,type,
    mono_2Ec_2Erealax_2Ereal__add: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Erealax_2Ereal__lt_decl,type,
    mono_2Ec_2Erealax_2Ereal__lt: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(mono_2Ec_2Erealax_2Ereal__neg_decl,type,
    mono_2Ec_2Erealax_2Ereal__neg: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Erealax_2Ereal_decl,type,
    i_mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > u ).

thf(j_mono_2Etyop_2Erealax_2Ereal_decl,type,
    j_mono_2Etyop_2Erealax_2Ereal: du > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_decl,type,
    mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $o > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Ereal_2Ereal__lte_decl,type,
    mono_2Ec_2Ereal_2Ereal__lte: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).

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_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
    mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(tyop_2Emetric_2Emetric_decl,type,
    tyop_2Emetric_2Emetric: d > d ).

thf(c_2Emetric_2EB_2E0_decl,type,
    c_2Emetric_2EB_2E0: u ).

thf(c_2Emetric_2EB_2E2_decl,type,
    c_2Emetric_2EB_2E2: du > du > u ).

thf(c_2Emetric_2EB_2E3_decl,type,
    c_2Emetric_2EB_2E3: du > du > du > u ).

thf(c_2Emetric_2Edist_2E0_decl,type,
    c_2Emetric_2Edist_2E0: u ).

thf(c_2Emetric_2Edist_2E1_decl,type,
    c_2Emetric_2Edist_2E1: du > u ).

thf(c_2Emetric_2Edist_2E2_decl,type,
    c_2Emetric_2Edist_2E2: du > du > u ).

thf(c_2Emetric_2Eismet_2E1_decl,type,
    c_2Emetric_2Eismet_2E1: du > u ).

thf(c_2Emetric_2Emetric_2E0_decl,type,
    c_2Emetric_2Emetric_2E0: u ).

thf(c_2Emetric_2Emetric_2E1_decl,type,
    c_2Emetric_2Emetric_2E1: du > u ).

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_2Emetric_2Edist_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
    mono_2Ec_2Emetric_2Edist_2Emono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Emetric_2Emetric_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
    mono_2Ec_2Emetric_2Emetric_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29: ( ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_decl,type,
    i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > u ).

thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_decl,type,
    i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > u ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29: du > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29: du > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ).

thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_decl,type,
    j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(c_2Enets_2Ebounded_2E2_decl,type,
    c_2Enets_2Ebounded_2E2: du > du > u ).

thf(c_2Enets_2Edorder_2E1_decl,type,
    c_2Enets_2Edorder_2E1: du > u ).

thf(c_2Enets_2Etendsto_2E0_decl,type,
    c_2Enets_2Etendsto_2E0: u ).

thf(c_2Enets_2Etendsto_2E1_decl,type,
    c_2Enets_2Etendsto_2E1: du > u ).

thf(c_2Enets_2Etendsto_2E3_decl,type,
    c_2Enets_2Etendsto_2E3: du > du > du > u ).

thf(mono_2Ec_2Eseq_2Econvergent_decl,type,
    mono_2Ec_2Eseq_2Econvergent: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > $o ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o ) > u ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o ).

thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal_decl,type,
    mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Elim_2Etends__real__real_decl,type,
    mono_2Ec_2Elim_2Etends__real__real: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(mono_2Ec_2Enets_2Etendsto_2Emono_2Etyop_2Erealax_2Ereal_decl,type,
    mono_2Ec_2Enets_2Etendsto_2Emono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_29: ( mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 ) > u ).

thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_decl,type,
    i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 > u ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29: du > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 ).

thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_decl,type,
    j_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 ).

thf(mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool_decl,type,
    mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Erealax_2Ereal > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Erealax_2Ereal > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ) > u ).

thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_decl,type,
    i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 > u ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29: du > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Erealax_2Ereal > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).

thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_decl,type,
    j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 ).

thf(mono_2Ec_2Epowser_2Ediffs_decl,type,
    mono_2Ec_2Epowser_2Ediffs: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ).

thf(mono_2Ec_2Etransc_2Etan_decl,type,
    mono_2Ec_2Etransc_2Etan: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > $o ) > u ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > $o ).

thf(c_2EHolSmt_2Earray__ext_2E2_decl,type,
    c_2EHolSmt_2Earray__ext_2E2: du > du > u ).

thf(tyop_2Ebinary__ieee_2Efloat_decl,type,
    tyop_2Ebinary__ieee_2Efloat: d > d > d ).

thf(tyop_2Ebinary__ieee_2Efp__op_decl,type,
    tyop_2Ebinary__ieee_2Efp__op: d > d > d ).

thf(c_2Ebinary__ieee_2Eclosest_2E0_decl,type,
    c_2Ebinary__ieee_2Eclosest_2E0: u ).

thf(c_2Ebinary__ieee_2Eclosest_2E2_decl,type,
    c_2Ebinary__ieee_2Eclosest_2E2: du > du > u ).

thf(c_2Ebinary__ieee_2Eclosest__such_2E0_decl,type,
    c_2Ebinary__ieee_2Eclosest__such_2E0: u ).

thf(c_2Ebinary__ieee_2Eclosest__such_2E1_decl,type,
    c_2Ebinary__ieee_2Eclosest__such_2E1: du > u ).

thf(c_2Ebinary__ieee_2Eclosest__such_2E3_decl,type,
    c_2Ebinary__ieee_2Eclosest__such_2E3: du > du > du > u ).

thf(c_2Ebinary__ieee_2Efloat__bottom_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__bottom_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__bottom_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__bottom_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__is__infinite_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__is__infinite_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__is__infinite_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__is__infinite_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__minus__infinity_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__minus__infinity_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__minus__infinity_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__minus__infinity_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__minus__min_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__minus__min_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__minus__min_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__minus__min_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__minus__zero_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__minus__zero_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__minus__zero_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__minus__zero_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__negate_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__negate_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__negate_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__negate_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__plus__infinity_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__plus__infinity_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__plus__infinity_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__plus__infinity_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__plus__min_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__plus__min_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__plus__min_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__plus__min_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__plus__zero_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__plus__zero_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__plus__zero_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__plus__zero_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__some__qnan_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__some__qnan_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__to__real_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__to__real_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__to__real_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__to__real_2E1: du > u ).

thf(c_2Ebinary__ieee_2Efloat__top_2E0_decl,type,
    c_2Ebinary__ieee_2Efloat__top_2E0: u ).

thf(c_2Ebinary__ieee_2Efloat__top_2E1_decl,type,
    c_2Ebinary__ieee_2Efloat__top_2E1: du > u ).

thf(c_2Ebinary__ieee_2Elargest_2E0_decl,type,
    c_2Ebinary__ieee_2Elargest_2E0: u ).

thf(c_2Ebinary__ieee_2Elargest_2E1_decl,type,
    c_2Ebinary__ieee_2Elargest_2E1: du > u ).

thf(c_2Ebinary__ieee_2Ethreshold_2E0_decl,type,
    c_2Ebinary__ieee_2Ethreshold_2E0: u ).

thf(c_2Ebinary__ieee_2Ethreshold_2E1_decl,type,
    c_2Ebinary__ieee_2Ethreshold_2E1: du > u ).

thf(c_2Ebinary__ieee_2Eulp_2E0_decl,type,
    c_2Ebinary__ieee_2Eulp_2E0: u ).

thf(c_2Ebinary__ieee_2Eulp_2E1_decl,type,
    c_2Ebinary__ieee_2Eulp_2E1: du > u ).

thf(sk1_decl,type,
    sk1: d ).

thf(sk2_decl,type,
    sk2: d ).

thf(sk3_decl,type,
    sk3: u > d > d > u ).

thf(sk4_decl,type,
    sk4: u > d > d > u ).

thf(sk5_decl,type,
    sk5: u > d > d > u ).

thf(sk6_decl,type,
    sk6: u > u > u > d > d > u ).

thf(sk7_decl,type,
    sk7: u > u > u > d > d > u ).

thf(sk1_def,definition,
    ( sk1
    = ( @+[A: d] :
          ~ ! [B: d] :
              ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
              = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(sk2_def,definition,
    ( sk2
    = ( @+[A: d] :
          ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ A ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
         != ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ A ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ A ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ A ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

thf(sk3_def,definition,
    ( sk3
    = ( ^ [A: u,B: d,C: d] :
        @+[D: u] :
          ~ ! [E: u,F: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) @ A ) @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ C @ F ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ D ) @ ( s @ C @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ).

thf(sk4_def,definition,
    ( sk4
    = ( ^ [A: u,B: d,C: d] :
        @+[D: u] :
          ~ ! [E: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) @ A ) @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ ( sk3 @ A @ B @ C ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ C @ E ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ E ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ ( sk3 @ A @ B @ C ) ) @ ( s @ C @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) ) ).

thf(sk5_def,definition,
    ( sk5
    = ( ^ [A: u,B: d,C: d] :
        @+[D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) @ A ) @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ ( sk3 @ A @ B @ C ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ A @ B @ C ) ) ) ) @ ( s @ C @ D ) ) )
         != ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ D ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ ( sk3 @ A @ B @ C ) ) @ ( s @ C @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ A @ B @ C ) ) ) ) ) ) ) ) ) ).

thf(sk6_def,definition,
    ( sk6
    = ( ^ [A: u,B: u,C: u,D: d,E: d] :
        @+[F: u] :
          ~ ! [G: u] :
              ( ( ( s @ D @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ E @ D ) @ B ) @ ( s @ E @ F ) ) )
                = ( s @ D @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ E @ D ) @ B ) @ ( s @ E @ G ) ) ) )
             => ( ( s @ E @ F )
                = ( s @ E @ G ) ) ) ) ) ).

thf(sk7_def,definition,
    ( sk7
    = ( ^ [A: u,B: u,C: u,D: d,E: d] :
        @+[F: u] :
          ~ ( ( ( s @ D @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ E @ D ) @ B ) @ ( s @ E @ ( sk6 @ A @ B @ C @ D @ E ) ) ) )
              = ( s @ D @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ E @ D ) @ B ) @ ( s @ E @ F ) ) ) )
           => ( ( s @ E @ ( sk6 @ A @ B @ C @ D @ E ) )
              = ( s @ E @ F ) ) ) ) ) ).

thf(3,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( ! [F: u,G: u] :
                ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
                  = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) )
               => ( ( s @ A @ F )
                  = ( s @ A @ G ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EFINITE__IMAGE__INJ) ).

thf(645,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( ! [F: u,G: u] :
                ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
                  = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) )
               => ( ( s @ A @ F )
                  = ( s @ A @ G ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(191,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ c_2Emarker_2Eunint_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Emarker_2Eunint_2E0_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(1322,plain,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ c_2Emarker_2Eunint_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(105,axiom,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
     => ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__ABS) ).

thf(1036,plain,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
     => ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(354,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__ADD) ).

thf(1879,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(204,axiom,
    ! [A: $o] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).

thf(1365,plain,
    ! [A: $o] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(1368,plain,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) )
    = $false ),
    inference(instance,[status(thm)],[1365]) ).

thf(1369,plain,
    ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) ),
    inference(simp,[status(thm)],[1368]) ).

thf(402,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ B @ ( c_2EreaderMonad_2EBIND_2E3 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ B ) ) @ E ) @ ( s @ C @ F ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ B ) ) @ E ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ D ) @ ( s @ C @ F ) ) ) ) ) @ ( s @ C @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EreaderMonad_2EBIND__def) ).

thf(2031,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ B @ ( c_2EreaderMonad_2EBIND_2E3 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ B ) ) @ E ) @ ( s @ C @ F ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ B ) ) @ E ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ D ) @ ( s @ C @ F ) ) ) ) ) @ ( s @ C @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(472,axiom,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Emarker_2Eunint_2E1 @ ( s @ A @ B ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ c_2Emarker_2Eunint_2E0 ) @ ( s @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Emarker_2Eunint_2E1_2Emono_2EA_27a) ).

thf(2263,plain,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Emarker_2Eunint_2E1 @ ( s @ A @ B ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ c_2Emarker_2Eunint_2E0 ) @ ( s @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(69,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27b_20mono_2EA_27a) ).

thf(893,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(607,axiom,
    ! [A: u] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ A ) ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(2787,plain,
    ! [A: u] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ A ) ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(495,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ A )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__EQ0) ).

thf(2331,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ A )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(43,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27b_29_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_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(777,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(182,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ! [D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [E: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ ( mono_2Ec_2Erealax_2Ereal__add @ E @ C ) )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ D @ E ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ D @ B ) )
     => ! [D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [E: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ E )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ D @ E ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ D @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2ESUP__LEMMA1) ).

thf(1295,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ! [D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [E: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ ( mono_2Ec_2Erealax_2Ereal__add @ E @ C ) )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ D @ E ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ D @ B ) )
     => ! [D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [E: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ E )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ D @ E ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ D @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(375,axiom,
    ! [A: d,B: u,C: u,D: u] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2EMETRIC__POS) ).

thf(1950,plain,
    ! [A: d,B: u,C: u,D: u] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(145,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__UNION) ).

thf(1168,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(486,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27e_20mono_2EA_27f) ).

thf(2306,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(265,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29_2Ctyop_2Emin_2Ebool_29) ).

thf(1559,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(125,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__COMM) ).

thf(1105,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(523,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2E_3A_3E_2E2 @ ( s @ B @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecombin_2EAPP__DEF) ).

thf(2412,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2E_3A_3E_2E2 @ ( s @ B @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(59,axiom,
    ! [A: d,B: d,C: u,D: u,E: u,F: u] :
      ( ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) )
        & ! [G: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
           => ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ G ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ G ) ) ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__CONG) ).

thf(846,plain,
    ! [A: d,B: d,C: u,D: u,E: u,F: u] :
      ( ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) )
        & ! [G: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
           => ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ G ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ G ) ) ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(85,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EIN__ELIM__PAIR__THM) ).

thf(962,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(386,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        & ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__AND__THM) ).

thf(1982,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        & ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(154,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__ADD) ).

thf(1200,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(158,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__EQ__LADD) ).

thf(1211,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(461,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        & C )
      = ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            & C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__AND__FORALL__THM) ).

thf(2210,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        & C )
      = ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            & C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(431,axiom,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Emetric_2Edist_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Emetric_2Edist_2E2_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(2117,plain,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Emetric_2Edist_2Emono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(12,axiom,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EFINITE__UNION) ).

thf(683,plain,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(554,axiom,
    ! [A: d,B: u,C: u] :
    ? [D: u] :
    ! [E: u] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ D ) @ ( s @ A @ E ) ) )
      = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ D ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ C ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewhile_2EITERATION) ).

thf(2622,plain,
    ! [A: d,B: u,C: u] :
    ? [D: u] :
    ! [E: u] :
      ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ D ) @ ( s @ A @ E ) ) )
      = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ D ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ C ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(253,axiom,
    ! [A: $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29) ).

thf(1522,plain,
    ! [A: $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(512,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ D ) ) ) ) )
      = ( ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EFORALL__PROD) ).

thf(2381,plain,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ D ) ) ) ) )
      = ( ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(517,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(2395,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)],[517]) ).

thf(31,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ETC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ETC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ETC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erelation_2ETC__IDEM) ).

thf(741,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ETC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ETC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ETC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(156,axiom,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( ~ C
            & D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ E @ F ) ) ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er020) ).

thf(1205,plain,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( ~ C
            & D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ E @ F ) ) ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(425,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) ).

thf(2099,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(242,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er214) ).

thf(1486,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(487,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29) ).

thf(2309,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(38,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29) ).

thf(762,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(430,axiom,
    ! [A: d,B: d,C: d,D: d,E: u] :
      ( ! [F: u,G: u,H: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ G ) ) ) @ ( s @ B @ H ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ F ) @ ( s @ B @ H ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ G ) ) ) )
     => ! [F: u,G: u,H: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ H ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ H ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estate__transformer_2EBIND__ASSOC) ).

thf(2114,plain,
    ! [A: d,B: d,C: d,D: d,E: u] :
      ( ! [F: u,G: u,H: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ G ) ) ) @ ( s @ B @ H ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ F ) @ ( s @ B @ H ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ G ) ) ) )
     => ! [F: u,G: u,H: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ H ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ D @ A ) ) ) @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(175,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ C @ D ) )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__ADD2) ).

thf(1269,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ C @ D ) )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(630,axiom,
    ! [A: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Enum_2Enum] :
          ( ( A @ B @ C )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( B @ C ) ) )
     => ! [B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2Epowser_2Ediffs @ ( A @ B ) @ C )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Epowser_2Ediffs @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epowser_2EDIFFS__NEG) ).

thf(2854,plain,
    ! [A: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Enum_2Enum] :
          ( ( A @ B @ C )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( B @ C ) ) )
     => ! [B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Enum_2Enum] :
          ( ( mono_2Ec_2Epowser_2Ediffs @ ( A @ B ) @ C )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Epowser_2Ediffs @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(257,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__NEG) ).

thf(1533,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(116,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ C ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ C ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27b_29) ).

thf(1078,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ C ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ C ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(296,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NOT__LT) ).

thf(1655,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(135,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ? [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
     => ( ( ! [F: u,G: u] :
              ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
                & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) )
                  = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ G ) ) ) ) )
             => ( ( s @ A @ F )
                = ( s @ A @ G ) ) ) )
        = ( ? [F: u] :
              ( ! [G: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ F ) @ ( s @ B @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
              & ! [G: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
                 => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ F ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ G ) ) ) ) )
                    = ( s @ A @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2EINJECTIVE__LEFT__INVERSE__NONEMPTY) ).

thf(1137,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ? [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
     => ( ( ! [F: u,G: u] :
              ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
                & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) )
                  = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ G ) ) ) ) )
             => ( ( s @ A @ F )
                = ( s @ A @ G ) ) ) )
        = ( ? [F: u] :
              ( ! [G: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ F ) @ ( s @ B @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
              & ! [G: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
                 => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ F ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ G ) ) ) ) )
                    = ( s @ A @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(187,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__RADD) ).

thf(1310,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(403,axiom,
    ( ( mono_2Ec_2Etransc_2Etan @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Etransc_2ETAN__0) ).

thf(2034,plain,
    ( ( mono_2Ec_2Etransc_2Etan @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(2035,plain,
    ( ( mono_2Ec_2Etransc_2Etan @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(lifteq,[status(thm)],[2034]) ).

thf(438,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29) ).

thf(2141,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(388,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emetric_2Emetric @ A ) @ ( c_2Emetric_2Emetric_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) )
      = ( s @ ( tyop_2Emetric_2Emetric @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ A ) ) @ c_2Emetric_2Emetric_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Emetric_2Emetric_2E1_2Emono_2EA_27a) ).

thf(1988,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emetric_2Emetric @ A ) @ ( c_2Emetric_2Emetric_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) )
      = ( s @ ( tyop_2Emetric_2Emetric @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ A ) ) @ c_2Emetric_2Emetric_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(406,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EETA__AX) ).

thf(2042,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(8,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ E ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ E )
        = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EUNCURRY__ONE__ONE__THM) ).

thf(670,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ E ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ E )
        = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(456,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u] :
          ? [E: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) )
      = ( ! [D: u] :
          ? [E: u] :
            ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
            = ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ESURJECTIVE__IMAGE) ).

thf(2195,plain,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u] :
          ? [E: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ D ) ) )
      = ( ! [D: u] :
          ? [E: u] :
            ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
            = ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(313,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__TRANS) ).

thf(1705,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(143,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
     => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__FINITE) ).

thf(1164,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
     => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(46,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ! [E: u,F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ A @ F ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [E: u,F: u,G: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ F ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) )
     => ! [E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ A @ F ) ) ) )
         => ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2Eseteq__wlog) ).

thf(797,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ! [E: u,F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ A @ F ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [E: u,F: u,G: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ F ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) )
     => ! [E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ A @ F ) ) ) )
         => ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(352,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ A @ F ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ A @ G ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
       => ( ! [E: u,F: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) ) ) )
         => ! [E: u,F: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EGSPEC__AND) ).

thf(1872,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ A @ F ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ A @ G ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
       => ( ! [E: u,F: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) ) ) )
         => ! [E: u,F: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(583,axiom,
    ! [A: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ B @ C )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( B @ C ) ) )
     => ! [B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Elim_2Etends__real__real @ B @ C @ D )
          = ( mono_2Ec_2Elim_2Etends__real__real @ ( A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ C ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ELIM__NEG) ).

thf(2712,plain,
    ! [A: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ B @ C )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( B @ C ) ) )
     => ! [B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Elim_2Etends__real__real @ B @ C @ D )
          = ( mono_2Ec_2Elim_2Etends__real__real @ ( A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(48,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ? [G: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
                & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) )
                  = ( s @ B @ F ) ) ) ) )
      = ( ? [F: u] :
          ! [G: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ F ) @ ( s @ B @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
              & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ F ) @ ( s @ B @ G ) ) ) ) )
                = ( s @ B @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ESURJECTIVE__ON__RIGHT__INVERSE) ).

thf(814,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ? [G: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
                & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) )
                  = ( s @ B @ F ) ) ) ) )
      = ( ? [F: u] :
          ! [G: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ F ) @ ( s @ B @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
              & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ F ) @ ( s @ B @ G ) ) ) ) )
                = ( s @ B @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(193,axiom,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29) ).

thf(1327,plain,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(540,axiom,
    ! [A: d,B: u] :
      ( ( ? [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__itself) ).

thf(2476,plain,
    ! [A: d,B: u] :
      ( ( ? [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(447,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a) ).

thf(2168,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(172,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_2Ctyop_2Emin_2Ebool_29) ).

thf(1260,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(17,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ G ) ) ) )
            & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__REL) ).

thf(698,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ G ) ) ) )
            & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(33,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29) ).

thf(747,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(73,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__IDEMPOT) ).

thf(913,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(153,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ! [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ C )
         => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) ) )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__EPSILON) ).

thf(1196,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ! [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ C )
         => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) ) )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(324,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) ) ) )
     => ! [H: u,I: u,J: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ ( tyop_2Emin_2Efun @ B @ D ) @ I ) @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) ) ) )
         => ! [K: u,L: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ K ) @ ( s @ D @ L ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( c_2Epair_2E_23_23_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ D ) @ I ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) @ ( s @ C @ K ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) @ ( s @ D @ L ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient__pair_2ECOMMA__PRS) ).

thf(1746,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) ) ) )
     => ! [H: u,I: u,J: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ ( tyop_2Emin_2Efun @ B @ D ) @ I ) @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) ) ) )
         => ! [K: u,L: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ K ) @ ( s @ D @ L ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( c_2Epair_2E_23_23_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ D ) @ I ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) @ ( s @ C @ K ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) @ ( s @ D @ L ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(408,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ! [F: u,G: u] :
          ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ G ) ) ) )
          = ( ( s @ A @ F )
            = ( s @ A @ G ) ) )
     => ( ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
        = ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__11) ).

thf(2046,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ! [F: u,G: u] :
          ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ G ) ) ) )
          = ( ( s @ A @ F )
            = ( s @ A @ G ) ) )
     => ( ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
        = ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(530,axiom,
    ! [A: d,B: d,C: d,D: u] :
      ( ! [E: u,F: u,G: u,H: u] :
          ( ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
            = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) ) )
          = ( ( ( s @ A @ E )
              = ( s @ A @ G ) )
            & ( ( s @ B @ F )
              = ( s @ B @ H ) ) ) )
     => ? [E: u,F: u] :
        ! [G: u,H: u] :
          ( ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ E ) @ ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) ) ) )
            = ( s @ A @ G ) )
          & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ F ) @ ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) ) ) )
            = ( s @ B @ H ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eind__type_2EINJ__INVERSE2) ).

thf(2432,plain,
    ! [A: d,B: d,C: d,D: u] :
      ( ! [E: u,F: u,G: u,H: u] :
          ( ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
            = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) ) )
          = ( ( ( s @ A @ E )
              = ( s @ A @ G ) )
            & ( ( s @ B @ F )
              = ( s @ B @ H ) ) ) )
     => ? [E: u,F: u] :
        ! [G: u,H: u] :
          ( ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ E ) @ ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) ) ) )
            = ( s @ A @ G ) )
          & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ B ) @ F ) @ ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) ) ) )
            = ( s @ B @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(464,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29) ).

thf(2227,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(228,axiom,
    ! [A: d,B: u,C: u,D: $o] :
      ( ~ D
      | ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) )
        = ( s @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed020) ).

thf(1441,plain,
    ! [A: d,B: u,C: u,D: $o] :
      ( ~ D
      | ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) )
        = ( s @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(395,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2EnormalForms_2EEXT__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) ) )
        = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( c_2EnormalForms_2EEXT__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EnormalForms_2EEXT__POINT) ).

thf(2010,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2EnormalForms_2EEXT__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) ) )
        = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( c_2EnormalForms_2EEXT__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(369,axiom,
    ! [A: d,B: d] :
      ( ! [C: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EABS__prod_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EREP__prod_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) )
      & ! [C: u] :
          ( ( ? [D: u,E: u] :
              ! [F: u,G: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) )
                = ( ( ( s @ A @ F )
                    = ( s @ A @ D ) )
                  & ( ( s @ B @ G )
                    = ( s @ B @ E ) ) ) ) )
          = ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EREP__prod_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EABS__prod_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EABS__REP__prod) ).

thf(1921,plain,
    ! [A: d,B: d] :
      ( ! [C: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EABS__prod_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EREP__prod_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) )
      & ! [C: u] :
          ( ( ? [D: u,E: u] :
              ! [F: u,G: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) )
                = ( ( ( s @ A @ F )
                    = ( s @ A @ D ) )
                  & ( ( s @ B @ G )
                    = ( s @ B @ E ) ) ) ) )
          = ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EREP__prod_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EABS__prod_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(202,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ G ) ) ) ) ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ B @ E ) ) ) )
            & ( ( s @ A @ F )
              = ( s @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EPAIR__IN__GSPEC__2) ).

thf(1359,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ G ) ) ) ) ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ B @ E ) ) ) )
            & ( ( s @ A @ F )
              = ( s @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(335,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__strongind__left) ).

thf(1803,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(252,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__IMP__NE) ).

thf(1518,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(635,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__negate__negate) ).

thf(2869,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(357,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool) ).

thf(1887,plain,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(4,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
            & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) ) ) )
         => ( ( s @ A @ E )
            = ( s @ A @ F ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
        = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EFINITE__IMAGE__INJ__EQ) ).

thf(651,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
            & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) ) ) )
         => ( ( s @ A @ E )
            = ( s @ A @ F ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
        = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(545,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2491,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(132,axiom,
    ! [A: d,B: u,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
     => ( ! [D: u,E: u,F: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ A @ F ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ F ) ) ) ) ) )
       => ! [D: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Euniv__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Euniv__reln__def) ).

thf(1127,plain,
    ! [A: d,B: u,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
     => ( ! [D: u,E: u,F: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ A @ F ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ F ) ) ) ) ) )
       => ! [D: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Euniv__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(331,axiom,
    ! [A: d,B: u,C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ A @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enets_2EDORDER__TENDSTO) ).

thf(1782,plain,
    ! [A: d,B: u,C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ A @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(519,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( c_2Efmapal_2EAP__SND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ D ) @ ( s @ B @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Efmapal_2EAP__SND) ).

thf(2400,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( c_2Efmapal_2EAP__SND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ D ) @ ( s @ B @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(415,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
            | B ) )
      = ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
        | B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__FORALL__OR__THM) ).

thf(2067,plain,
    ! [A: d,B: $o,C: u] :
      ( ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
            | B ) )
      = ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
        | B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(381,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        | ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EOR__EXISTS__THM) ).

thf(1967,plain,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        | ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(164,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Erealax_2Ereal__neg @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LNEG__UNIQ) ).

thf(1228,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( A
        = ( mono_2Ec_2Erealax_2Ereal__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(285,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__NEGTOTAL) ).

thf(1623,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(170,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ A )
       != ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__NZ) ).

thf(1254,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ A )
       != ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(315,axiom,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            & D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ C ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ F @ E ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er021) ).

thf(1709,plain,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            & D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ C ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ F @ E ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(494,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27c_20mono_2EA_27d) ).

thf(2328,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(387,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal @ A ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( c_2Emarker_2Eunint_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Emarker_2Eunint_2E1_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(1985,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal @ A ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( c_2Emarker_2Eunint_2E1 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(405,axiom,
    ! [A: d,B: u,C: u] :
      ( ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
     => ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
        = ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2Eexists__eq__thm) ).

thf(2039,plain,
    ! [A: d,B: u,C: u] :
      ( ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
     => ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
        = ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(183,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__ANTISYM) ).

thf(1298,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(568,axiom,
    ! [A: d,B: u,C: u,D: u,E: u] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2EMETRIC__TRIANGLE) ).

thf(2667,plain,
    ! [A: d,B: u,C: u,D: u,E: u] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(474,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal) ).

thf(2269,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(598,axiom,
    ! [A: d,B: d] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__minus__infinity__def) ).

thf(2755,plain,
    ! [A: d,B: d] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(1323,plain,
    ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ c_2Emarker_2Eunint_2E0 ) ),
    inference(lifteq,[status(thm)],[1322]) ).

thf(188,axiom,
    ! [A: d,B: u,C: u,D: $o] :
      ( D
      | ( ( s @ A @ B )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed017) ).

thf(1313,plain,
    ! [A: d,B: u,C: u,D: $o] :
      ( D
      | ( ( s @ A @ B )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(544,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Eposet_2Erelation_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eposet_2Erelation__def) ).

thf(2488,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Eposet_2Erelation_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(518,axiom,
    ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__0) ).

thf(2398,plain,
    ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(2399,plain,
    ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
    = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(lifteq,[status(thm)],[2398]) ).

thf(1,conjecture,
    ! [A: d,B: d] :
      ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eneg__ulp) ).

thf(2,negated_conjecture,
    ~ ! [A: d,B: d] :
        ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
        = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(642,plain,
    ~ ! [A: d,B: d] :
        ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
        = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(643,plain,
    ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
   != ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[642]) ).

thf(644,plain,
    ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) )
   != ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[643]) ).

thf(2896,plain,
    ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 )
     != ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
    | ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
     != ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2399,644]) ).

thf(2897,plain,
    ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 )
     != ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
    | ( ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 )
     != ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    inference(simp,[status(thm)],[2896]) ).

thf(434,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2EreaderMonad_2EJOIN_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ A ) ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ A ) ) @ C ) @ ( s @ B @ D ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EreaderMonad_2EJOIN__def) ).

thf(2126,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2EreaderMonad_2EJOIN_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ A ) ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ A ) ) @ C ) @ ( s @ B @ D ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(110,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27d_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(1059,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(580,axiom,
    ! [A: d,B: d] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__minus__zero__def) ).

thf(2703,plain,
    ! [A: d,B: d] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(194,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ C ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ C ) ) ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29) ).

thf(1330,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ C ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ C ) ) ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(348,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ADDL) ).

thf(1860,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(250,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__SYM) ).

thf(1511,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(18,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) ).

thf(702,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eoption_2Eoption @ A ) @ C ) ) ) @ ( s @ ( tyop_2Eoption_2Eoption @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(271,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ B @ C ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__TRANS) ).

thf(1577,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ B @ C ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(233,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__TRANS) ).

thf(1455,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(82,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u] :
          ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
     => ! [D: u] :
          ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
         => ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINFINITE__IMAGE__INJ) ).

thf(949,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u] :
          ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
     => ! [D: u] :
          ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
         => ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(594,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ C )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EABS__SIMP) ).

thf(2745,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(49,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ E ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ A ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c) ).

thf(817,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ E ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ A ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(359,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LT__IADD) ).

thf(1892,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(631,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ A )
        = ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__EQ__NEG) ).

thf(2857,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ A )
        = ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(409,axiom,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Emarker_2Estmarker_2E1 @ ( s @ A @ B ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ c_2Emarker_2Estmarker_2E0 ) @ ( s @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Emarker_2Estmarker_2E1_2Emono_2EA_27a) ).

thf(2049,plain,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Emarker_2Estmarker_2E1 @ ( s @ A @ B ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ c_2Emarker_2Estmarker_2E0 ) @ ( s @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(190,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29) ).

thf(1319,plain,
    ! [A: d,B: $o,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(602,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29) ).

thf(2767,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(283,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ F ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__strongind) ).

thf(1609,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ F ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(200,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ? [B: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ B )
            & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) )
     => ? [B: mono_2Etyop_2Erealax_2Ereal] :
        ! [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [D: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ D )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__SUP__SOMEPOS) ).

thf(1347,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ? [B: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ B )
            & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) )
     => ? [B: mono_2Etyop_2Erealax_2Ereal] :
        ! [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [D: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ D )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(268,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__DOUBLE) ).

thf(1568,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(589,axiom,
    ! [A: d,B: d,C: u] :
    ? [D: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ B ) @ D ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Eitself__Axiom) ).

thf(2730,plain,
    ! [A: d,B: d,C: u] :
    ? [D: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ B ) @ D ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(291,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__ADD2) ).

thf(1641,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(203,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1362,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(261,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ? [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ C )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ A )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__DOWN2) ).

thf(1545,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ? [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ C )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ A )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(526,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29) ).

thf(2420,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(520,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29) ).

thf(2403,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(119,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27c_2CA_27d_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(1087,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(251,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
     => ( A
       != ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__POS__NZ) ).

thf(1514,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
     => ( A
       != ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(492,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EETA__THM) ).

thf(2324,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(423,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u,G: u] :
      ( ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ G )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F ) )
        & ! [H: u,I: u] :
            ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F )
              = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ H ) @ ( s @ B @ I ) ) ) )
           => ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ E ) @ ( s @ A @ H ) ) ) @ ( s @ B @ I ) ) )
              = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ H ) ) ) @ ( s @ B @ I ) ) ) ) ) )
     => ( ( s @ C @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ G ) ) )
        = ( s @ C @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EUNCURRY__CONG) ).

thf(2090,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u,G: u] :
      ( ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ G )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F ) )
        & ! [H: u,I: u] :
            ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F )
              = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ H ) @ ( s @ B @ I ) ) ) )
           => ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ E ) @ ( s @ A @ H ) ) ) @ ( s @ B @ I ) ) )
              = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ H ) ) ) @ ( s @ B @ I ) ) ) ) ) )
     => ( ( s @ C @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ G ) ) )
        = ( s @ C @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(206,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ C ) @ ( s @ A @ C ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2ECOND__CLAUSES__ID) ).

thf(1373,plain,
    ! [A: d,B: $o,C: u] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ C ) @ ( s @ A @ C ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(288,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ B ) @ A )
      = ( mono_2Ec_2Erealax_2Ereal__add @ C @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er217) ).

thf(1632,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ B ) @ A )
      = ( mono_2Ec_2Erealax_2Ereal__add @ C @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(305,axiom,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
     => ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__GSPEC__IFF) ).

thf(1682,plain,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
     => ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(341,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__IMP__LE) ).

thf(1828,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(417,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D )
              = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
      = ( ! [D: u,E: u] :
            ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
           => ( ( s @ A @ D )
              = ( s @ A @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINJECTIVE__IMAGE) ).

thf(2073,plain,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D )
              = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
      = ( ! [D: u,E: u] :
            ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
           => ( ( s @ A @ D )
              = ( s @ A @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(243,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2Eismet_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) )
      = ( ! [C: u,D: u] :
            ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) )
              = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
            = ( ( s @ A @ C )
              = ( s @ A @ D ) ) )
        & ! [C: u,D: u,E: u] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2Eismet) ).

thf(1489,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2Eismet_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) )
      = ( ! [C: u,D: u] :
            ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) )
              = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
            = ( ( s @ A @ C )
              = ( s @ A @ D ) ) )
        & ! [C: u,D: u,E: u] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) ) ) ) @ ( mono_2Ec_2Erealax_2Ereal__add @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(467,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u] :
            ( ( ( s @ A @ C )
              = ( s @ A @ D ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EUNWIND__FORALL__THM1) ).

thf(2237,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u] :
            ( ( ( s @ A @ C )
              = ( s @ A @ D ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(552,axiom,
    ! [A: d,B: d,C: u,D: u,E: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ E ) ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ c_2Ebinary__ieee_2Eclosest__such_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2616,plain,
    ! [A: d,B: d,C: u,D: u,E: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ E ) ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ c_2Ebinary__ieee_2Eclosest__such_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(235,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29) ).

thf(1465,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(36,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29) ).

thf(756,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(299,axiom,
    ! [A: d,B: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2Eismet_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Edist_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2EMETRIC__ISMET) ).

thf(1664,plain,
    ! [A: d,B: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2Eismet_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Edist_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(610,axiom,
    ! [A: d,B: d,C: u] :
    ? [D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EABS__PAIR__THM) ).

thf(2794,plain,
    ! [A: d,B: d,C: u] :
    ? [D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(427,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d) ).

thf(2105,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(231,axiom,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1450,plain,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(139,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29) ).

thf(1151,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(78,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      = ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EEXTENSION) ).

thf(937,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      = ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(481,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).

thf(2291,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(100,axiom,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
     => ! [C: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EGSPEC__ID) ).

thf(1020,plain,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
     => ! [C: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(90,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINTER__ACI) ).

thf(981,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(412,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Eposet_2Ecarrier_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eposet_2Ecarrier__def) ).

thf(2058,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Eposet_2Ecarrier_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(230,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27c_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1447,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(114,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27c_2CA_27d_29_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_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(1072,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(217,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ mono_2Ec_2Emetric_2Emetric_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Emetric_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Emetric_2Emetric_2E0_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(1405,plain,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ mono_2Ec_2Emetric_2Emetric_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Emetric_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(280,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Erel__to__reln__def) ).

thf(1600,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(585,axiom,
    ! [A: d,B: u] :
    ? [C: u] :
      ( ( s @ A @ C )
      = ( s @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__REFL) ).

thf(2718,plain,
    ! [A: d,B: u] :
    ? [C: u] :
      ( ( s @ A @ C )
      = ( s @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(623,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Estate__transformer_2EUNIT_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estate__transformer_2EUNIT__DEF) ).

thf(2833,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Estate__transformer_2EUNIT_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(478,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ! [E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ E ) ) ) )
          | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ E ) ) ) ) )
     => ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ B ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) ) )
        & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EDISJ__IMP__INTRO) ).

thf(2281,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ! [E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ E ) ) ) )
          | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ E ) ) ) ) )
     => ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ B ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) ) )
        & ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(65,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27c_2CA_27d_29_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_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(877,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(15,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29) ).

thf(692,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(42,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28A_27c_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(774,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(509,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ! [D: u] :
            ( ( ( s @ A @ D )
             != ( s @ A @ B ) )
           => ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EUNWIND__EXISTS__THM) ).

thf(2371,plain,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ! [D: u] :
            ( ( ( s @ A @ D )
             != ( s @ A @ B ) )
           => ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(92,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
     => ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__FINITE) ).

thf(998,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
     => ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(615,axiom,
    ! [A: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29) ).

thf(2809,plain,
    ! [A: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(516,axiom,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
          = ( ! [E: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ E ) ) ) )
               => ? [F: mono_2Etyop_2Erealax_2Ereal] :
                    ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ F )
                    & ! [G: u] :
                        ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ) ) @ F )
                       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) ) )
     => ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etopology_2Eistopology_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2Emtop__istopology) ).

thf(2392,plain,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
          = ( ! [E: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ E ) ) ) )
               => ? [F: mono_2Etyop_2Erealax_2Ereal] :
                    ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ F )
                    & ! [G: u] :
                        ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ) ) @ F )
                       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) ) )
     => ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etopology_2Eistopology_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(1519,plain,
    ! [B: mono_2Etyop_2Erealax_2Ereal,A: mono_2Etyop_2Erealax_2Ereal] :
      ( ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      | ( A != B ) ),
    inference(cnf,[status(esa)],[1518]) ).

thf(1520,plain,
    ! [B: mono_2Etyop_2Erealax_2Ereal,A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A != B )
      | ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B ) ),
    inference(lifteq,[status(thm)],[1519]) ).

thf(1521,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ A ),
    inference(simp,[status(thm)],[1520]) ).

thf(310,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29) ).

thf(1696,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(640,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__minus__min_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2884,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__minus__min_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(349,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Erel__to__reln__swap) ).

thf(1863,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(459,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( B
       => ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ? [D: u] :
            ( B
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ERIGHT__IMP__EXISTS__THM) ).

thf(2204,plain,
    ! [A: d,B: $o,C: u] :
      ( ( B
       => ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ? [D: u] :
            ( B
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(539,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) )
      | ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( c_2EHolSmt_2Earray__ext_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) ) ) )
       != ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2EHolSmt_2Earray__ext_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Et005) ).

thf(2473,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) )
      | ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( c_2EHolSmt_2Earray__ext_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) ) ) )
       != ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2EHolSmt_2Earray__ext_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(308,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LT__REFL) ).

thf(1691,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(506,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EBETA__THM) ).

thf(2364,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(367,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__LT0) ).

thf(1915,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(22,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(714,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(227,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29) ).

thf(1438,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(5,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__ASSOC) ).

thf(661,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(3248,plain,
    ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ c_2Emarker_2Eunint_2E0 ) ) )
     != ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
    | ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal ) )
     != ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1323,644]) ).

thf(3265,plain,
    ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ c_2Emarker_2Eunint_2E0 ) ) )
     != ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ) ) )
    | ( ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal )
     != tyop_2Erealax_2Ereal )
    | ( ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal ) ) ),
    inference(simp,[status(thm)],[3248]) ).

thf(562,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u,G: u] :
      ( ( ( ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E )
          = ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ F ) )
        & ! [H: u,I: u] :
            ( ( ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ F )
              = ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ H ) @ ( s @ C @ I ) ) ) )
           => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ G ) @ ( s @ B @ H ) ) ) @ ( s @ C @ I ) ) )
              = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ D ) @ ( s @ B @ H ) ) ) @ ( s @ C @ I ) ) ) ) ) )
     => ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ G ) ) )
        = ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__case__cong) ).

thf(2646,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u,G: u] :
      ( ( ( ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E )
          = ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ F ) )
        & ! [H: u,I: u] :
            ( ( ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ F )
              = ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ H ) @ ( s @ C @ I ) ) ) )
           => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ G ) @ ( s @ B @ H ) ) ) @ ( s @ C @ I ) ) )
              = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ D ) @ ( s @ B @ H ) ) ) @ ( s @ C @ I ) ) ) ) ) )
     => ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ G ) ) )
        = ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(113,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: $o,G: $o,H: u,I: u,J: u,K: u] :
          ( ( ( F = G )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ H ) ) ) @ ( s @ A @ I ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ J ) ) ) @ ( s @ A @ K ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ H ) @ ( s @ A @ J ) ) ) ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ G ) ) @ ( s @ A @ I ) @ ( s @ A @ K ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2ECOND__RSP) ).

thf(1067,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: $o,G: $o,H: u,I: u,J: u,K: u] :
          ( ( ( F = G )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ H ) ) ) @ ( s @ A @ I ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ J ) ) ) @ ( s @ A @ K ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ H ) @ ( s @ A @ J ) ) ) ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ G ) ) @ ( s @ A @ I ) @ ( s @ A @ K ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(608,axiom,
    ! [A: d,B: u] :
      ( ( s @ A @ B )
      = ( s @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__REFL) ).

thf(2790,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(413,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2EreaderMonad_2EUNIT_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ c_2EreaderMonad_2EUNIT_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2EreaderMonad_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2061,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2EreaderMonad_2EUNIT_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ c_2EreaderMonad_2EUNIT_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(604,axiom,
    ! [A: d,B: d] :
      ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      & ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Ezero__to__real) ).

thf(2773,plain,
    ! [A: d,B: d] :
      ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      & ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(392,axiom,
    ! [A: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > $o,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( A @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ A ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(2000,plain,
    ! [A: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > $o,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( A @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ A ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(177,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ F ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__strongind__right) ).

thf(1274,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ F ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(522,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Estate__transformer_2EREAD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ D ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estate__transformer_2EREAD__def) ).

thf(2409,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Estate__transformer_2EREAD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ D ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(162,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LT__TRANS) ).

thf(1223,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(471,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 ) )
      & ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) )
          = ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) )
        = ( ( A = mono_2Ec_2Enum_2E0 )
          & ( B = mono_2Ec_2Enum_2E0 ) ) )
      & ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ A )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) ) )
        = ( ( A = mono_2Ec_2Enum_2E0 )
          & ( B = mono_2Ec_2Enum_2E0 ) ) )
      & ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) ) )
        = ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2Eeq__ints) ).

thf(2249,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 ) )
      & ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) )
          = ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) )
        = ( ( A = mono_2Ec_2Enum_2E0 )
          & ( B = mono_2Ec_2Enum_2E0 ) ) )
      & ( ( ( mono_2Ec_2Ereal_2Ereal__of__num @ A )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) ) )
        = ( ( A = mono_2Ec_2Enum_2E0 )
          & ( B = mono_2Ec_2Enum_2E0 ) ) )
      & ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) ) )
        = ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(147,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__SYM) ).

thf(1174,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(300,axiom,
    ! [A: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).

thf(1666,plain,
    ! [A: u] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ A ) ) ) )
      = ( s @ tyop_2Emin_2Ebool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(211,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool) ).

thf(1387,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(362,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ C @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er220) ).

thf(1900,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ C @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(318,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1723,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(590,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
        & ( ( s @ A @ C )
          = ( s @ A @ D ) ) )
     => ( ( s @ A @ B )
        = ( s @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__TRANS) ).

thf(2733,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
        & ( ( s @ A @ C )
          = ( s @ A @ D ) ) )
     => ( ( s @ A @ B )
        = ( s @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(52,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__REP__REFL) ).

thf(825,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(160,axiom,
    ! [A: d,B: d,C: d,D: d,E: d,F: u,G: u,H: u,I: u,J: u,K: u,L: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eparallel__comp_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) ) ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ D @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ E @ tyop_2Emin_2Ebool ) ) ) @ G ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ D ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ H ) @ ( s @ D @ I ) ) ) @ ( s @ B @ J ) @ ( s @ ( tyop_2Epair_2Eprod @ C @ E ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ K ) @ ( s @ E @ L ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) ) ) @ F ) @ ( s @ A @ H ) ) ) @ ( s @ B @ J ) ) ) @ ( s @ C @ K ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ E @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ E @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ D @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ E @ tyop_2Emin_2Ebool ) ) ) @ G ) @ ( s @ D @ I ) ) ) @ ( s @ B @ J ) ) ) @ ( s @ E @ L ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epath_2Eparallel__comp__def) ).

thf(1217,plain,
    ! [A: d,B: d,C: d,D: d,E: d,F: u,G: u,H: u,I: u,J: u,K: u,L: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epath_2Eparallel__comp_2E5 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) ) ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ D @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ E @ tyop_2Emin_2Ebool ) ) ) @ G ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ D ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ H ) @ ( s @ D @ I ) ) ) @ ( s @ B @ J ) @ ( s @ ( tyop_2Epair_2Eprod @ C @ E ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ K ) @ ( s @ E @ L ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) ) ) @ F ) @ ( s @ A @ H ) ) ) @ ( s @ B @ J ) ) ) @ ( s @ C @ K ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ E @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ E @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ D @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ E @ tyop_2Emin_2Ebool ) ) ) @ G ) @ ( s @ D @ I ) ) ) @ ( s @ B @ J ) ) ) @ ( s @ E @ L ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(440,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ C @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29) ).

thf(2147,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ C @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(247,axiom,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            | D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ D ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ F @ E ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er024) ).

thf(1502,plain,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            | D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ D ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ F @ E ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(50,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(820,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(441,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__idemp) ).

thf(2150,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(205,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__infinite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__infinite_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__infinite_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(1370,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__infinite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__infinite_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(436,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ! [E: mono_2Etyop_2Erealax_2Ereal] :
          ( ( E != D )
         => ( ( A @ E )
            = ( B @ E ) ) )
     => ( ( mono_2Ec_2Elim_2Etends__real__real @ A @ C @ D )
        = ( mono_2Ec_2Elim_2Etends__real__real @ B @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ELIM__EQUAL) ).

thf(2132,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ! [E: mono_2Etyop_2Erealax_2Ereal] :
          ( ( E != D )
         => ( ( A @ E )
            = ( B @ E ) ) )
     => ( ( mono_2Ec_2Elim_2Etends__real__real @ A @ C @ D )
        = ( mono_2Ec_2Elim_2Etends__real__real @ B @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(27,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2EA_27c) ).

thf(729,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(74,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ! [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ E ) ) ) ) ) )
      = ( ! [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ E ) ) ) ) )
        & ! [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EFORALL__IN__UNION) ).

thf(916,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ! [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ E ) ) ) ) ) )
      = ( ! [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ E ) ) ) ) )
        & ! [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(60,axiom,
    ! [A: d,B: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__FINITE) ).

thf(852,plain,
    ! [A: d,B: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(636,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ A )
        = B )
      = ( A
        = ( mono_2Ec_2Erealax_2Ereal__neg @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__EQ) ).

thf(2872,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__neg @ A )
        = B )
      = ( A
        = ( mono_2Ec_2Erealax_2Ereal__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(234,axiom,
    ! [A: d] :
      ( ! [B: u] :
          ( ( s @ ( tyop_2Emetric_2Emetric @ A ) @ ( c_2Emetric_2Emetric_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Edist_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) ) )
          = ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) )
      & ! [B: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2Eismet_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) )
          = ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Edist_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ ( c_2Emetric_2Emetric_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2Emetric__tybij) ).

thf(1457,plain,
    ! [A: d] :
      ( ! [B: u] :
          ( ( s @ ( tyop_2Emetric_2Emetric @ A ) @ ( c_2Emetric_2Emetric_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Edist_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) ) )
          = ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) )
      & ! [B: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2Eismet_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) )
          = ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Edist_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ ( c_2Emetric_2Emetric_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(338,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ C ) @ ( s @ A @ C ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__ID) ).

thf(1819,plain,
    ! [A: d,B: $o,C: u] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ C ) @ ( s @ A @ C ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(54,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27a_20mono_2EA_27c) ).

thf(830,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(218,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = A )
      = ( B
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__RID__UNIQ) ).

thf(1407,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = A )
      = ( B
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(322,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ANTISYM) ).

thf(1740,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(97,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2Etyop_2Elist_2Elist_28A_27e_29) ).

thf(1012,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(536,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a) ).

thf(2464,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(599,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2EreaderMonad_2EUNIT_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EreaderMonad_2EUNIT__def) ).

thf(2758,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2EreaderMonad_2EUNIT_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(556,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_29) ).

thf(2628,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(102,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27c_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(1027,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(462,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ( C
         => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
        = ( ! [D: u] :
              ( C
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) )
      & ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
          & C )
        = ( ! [D: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
              & C ) ) )
      & ( ( C
          & ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
        = ( ! [D: u] :
              ( C
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EPULL__FORALL) ).

thf(2213,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ( C
         => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
        = ( ! [D: u] :
              ( C
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) )
      & ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
          & C )
        = ( ! [D: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
              & C ) ) )
      & ( ( C
          & ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
        = ( ! [D: u] :
              ( C
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(216,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__LID) ).

thf(1402,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(166,axiom,
    ! [A: $o,B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ A @ B @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) ).

thf(1234,plain,
    ! [A: $o,B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ A @ B @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ A ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(64,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29) ).

thf(874,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(345,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Estate__transformer_2EUNIT_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estate__transformer_2EUNIT__UNCURRY) ).

thf(1851,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Estate__transformer_2EUNIT_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(130,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2EA_27b) ).

thf(1121,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(95,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ! [E: u,F: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
              & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
                = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) ) ) )
           => ( ( s @ A @ E )
              = ( s @ A @ F ) ) ) )
      = ( ? [E: u] :
          ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
           => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) ) ) )
              = ( s @ A @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINJECTIVE__ON__LEFT__INVERSE) ).

thf(1006,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ! [E: u,F: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
              & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
                = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) ) ) )
           => ( ( s @ A @ E )
              = ( s @ A @ F ) ) ) )
      = ( ? [E: u] :
          ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
           => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) ) ) )
              = ( s @ A @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(557,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b2) ).

thf(2631,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(587,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) ).

thf(2724,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(327,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ! [B: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ B )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) )
     => ? [B: mono_2Etyop_2Erealax_2Ereal] :
        ! [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [D: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ D )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__SUP__ALLPOS) ).

thf(1755,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ! [B: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ B )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) )
     => ? [B: mono_2Etyop_2Erealax_2Ereal] :
        ! [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [D: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ D )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(62,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__UNION) ).

thf(857,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(277,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1592,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(484,axiom,
    ! [A: d,B: u] :
      ( ! [C: u,D: u,E: u] :
          ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
          = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) ) ) @ ( s @ A @ E ) ) ) )
     => ( ! [C: u,D: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) )
            = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ C ) ) ) )
       => ! [C: u,D: u,E: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
            = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELCOMM__THM) ).

thf(2300,plain,
    ! [A: d,B: u] :
      ( ! [C: u,D: u,E: u] :
          ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
          = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) ) ) @ ( s @ A @ E ) ) ) )
     => ( ! [C: u,D: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) )
            = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ C ) ) ) )
       => ! [C: u,D: u,E: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
            = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(511,axiom,
    ! [A: d,B: u,C: u] :
      ( ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
     => ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
       => ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__EXISTS) ).

thf(2377,plain,
    ! [A: d,B: u,C: u] :
      ( ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
     => ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
       => ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(646,plain,
    ! [E: u,D: u,C: u,B: d,A: d] :
      ( ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) )
         != ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( sk5 @ C @ B @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) ) ) )
        | ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( sk6 @ E @ D @ C @ B @ A ) ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( sk7 @ E @ D @ C @ B @ A ) ) ) ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) )
      & ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) )
         != ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( sk5 @ C @ B @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) ) ) )
        | ( ( s @ A @ ( sk6 @ E @ D @ C @ B @ A ) )
         != ( s @ A @ ( sk7 @ E @ D @ C @ B @ A ) ) )
        | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[645]) ).

thf(648,plain,
    ! [E: u,D: u,C: u,B: d,A: d] :
      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) )
       != ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( sk5 @ C @ B @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) ) ) )
      | ( ( s @ A @ ( sk6 @ E @ D @ C @ B @ A ) )
       != ( s @ A @ ( sk7 @ E @ D @ C @ B @ A ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ),
    inference(cnfConj,[status(thm)],[646]) ).

thf(650,plain,
    ! [E: u,D: u,C: u,B: d,A: d] :
      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( sk5 @ C @ B @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) ) )
       != ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) ) )
      | ( ( s @ A @ ( sk7 @ E @ D @ C @ B @ A ) )
       != ( s @ A @ ( sk6 @ E @ D @ C @ B @ A ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[648]) ).

thf(382,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
           => C ) )
      = ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__EXISTS__IMP__THM) ).

thf(1970,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
           => C ) )
      = ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(127,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28A_27c_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(1111,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(582,axiom,
    ! [A: d,B: d] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__bottom__def) ).

thf(2709,plain,
    ! [A: d,B: d] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(246,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
     => ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__DOWN) ).

thf(1498,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
     => ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(275,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      | ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__NEGTOTAL) ).

thf(1587,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      | ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(122,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
     => ! [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__IN) ).

thf(1096,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
     => ! [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(302,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__NEG) ).

thf(1672,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(142,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
         => ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__REL__ABS) ).

thf(1160,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
         => ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(380,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etendsto_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Enets_2Etendsto_2E1_2Emono_2EA_27a) ).

thf(1964,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etendsto_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(35,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ B ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27b) ).

thf(753,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ B ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(468,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c) ).

thf(2240,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(551,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29) ).

thf(2613,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(428,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27g_20mono_2EA_27h) ).

thf(2108,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(358,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29) ).

thf(1889,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(106,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u,H: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ H ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ G ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ H ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u,H: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ A @ H ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ H ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ H ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ G ) ) ) ) ) )
       => ! [E: u,F: u,G: u] :
            ( ( ! [H: u,I: u] :
                  ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ H ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ I ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
                    & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ H ) ) )
                      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ I ) ) ) ) )
                 => ( ( s @ A @ H )
                    = ( s @ A @ I ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EFINITE__IMAGE__INJ__GENERAL) ).

thf(1039,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u,H: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ H ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ G ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ H ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u,H: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ A @ H ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ H ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ H ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ G ) ) ) ) ) )
       => ! [E: u,F: u,G: u] :
            ( ( ! [H: u,I: u] :
                  ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ H ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ I ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
                    & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ H ) ) )
                      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ I ) ) ) ) )
                 => ( ( s @ A @ H )
                    = ( s @ A @ I ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(181,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2EB_2E3 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ C ) @ ( s @ A @ D ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Emetric_2EB_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ C ) ) ) @ ( s @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Emetric_2EB_2E3_2Emono_2EA_27a) ).

thf(1292,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2EB_2E3 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ C ) @ ( s @ A @ D ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Emetric_2EB_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ C ) ) ) @ ( s @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(77,axiom,
    ! [A: d,B: u,C: u] :
      ( ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__implication) ).

thf(933,plain,
    ! [A: d,B: u,C: u] :
      ( ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(622,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29) ).

thf(2830,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(150,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Ereln__to__rel__inv) ).

thf(1182,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(13,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29) ).

thf(686,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(115,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29) ).

thf(1075,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(224,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ A @ G ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ A @ G ) ) ) ) ) ) ) )
     => ( ! [E: u,F: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ B @ F ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ B @ F ) ) ) ) ) )
       => ! [E: u] :
            ( ( ! [F: u] :
                ? [G: u] :
                  ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ G ) ) )
                  = ( s @ B @ F ) ) )
            = ( ! [F: u] :
                  ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) ) ) ) )
                  = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ESURJECTIVE__IMAGE__THM) ).

thf(1424,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ A @ G ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ A @ G ) ) ) ) ) ) ) )
     => ( ! [E: u,F: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ B @ F ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ B @ F ) ) ) ) ) )
       => ! [E: u] :
            ( ( ! [F: u] :
                ? [G: u] :
                  ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ G ) ) )
                  = ( s @ B @ F ) ) )
            = ( ! [F: u] :
                  ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) ) ) ) )
                  = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(488,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Eposet_2Erelation_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Eposet_2Erelation_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eposet_2Erelation_2E1_2Emono_2EA_27a) ).

thf(2312,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Eposet_2Erelation_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Eposet_2Erelation_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(159,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ B ) @ A )
      = ( mono_2Ec_2Erealax_2Ereal__add @ C @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er218) ).

thf(1214,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ B ) @ A )
      = ( mono_2Ec_2Erealax_2Ereal__add @ C @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(501,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
      = ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ B ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EOmega__Automata_2EEQUALITY__THM) ).

thf(2349,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
      = ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ B ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(605,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2781,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Eulp_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(222,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ C @ D ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__ADD2) ).

thf(1419,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ C @ D ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(56,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27c_2CA_27d_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(837,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ C @ D ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(573,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a) ).

thf(2681,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(30,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ? [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__cases__right) ).

thf(738,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ? [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(627,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29) ).

thf(2845,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(133,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) ) ) ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) @ ( s @ A @ E ) ) ) @ ( s @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EPAIR__IN__GSPEC__IFF) ).

thf(1131,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) ) ) ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) @ ( s @ A @ E ) ) ) @ ( s @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(107,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(1050,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(374,axiom,
    ! [A: d,B: u,C: u] :
      ( ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
     => ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
        = ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EConseqConv_2Eforall__eq__thm) ).

thf(1947,plain,
    ! [A: d,B: u,C: u] :
      ( ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
     => ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
        = ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(317,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ F ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__ind__right) ).

thf(1715,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ F ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(385,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( B
       => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ! [D: u] :
            ( B
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ERIGHT__IMP__FORALL__THM) ).

thf(1979,plain,
    ! [A: d,B: $o,C: u] :
      ( ( B
       => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ! [D: u] :
            ( B
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(475,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) )
      = ( ! [E: u] :
            ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFUN__EQ__THM) ).

thf(2272,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) )
      = ( ! [E: u] :
            ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(213,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ C ) ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ADDNEG) ).

thf(1393,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ C ) ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(254,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
      | ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__TOTAL) ).

thf(1525,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
      | ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(340,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
      = ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__LT) ).

thf(1825,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
      = ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        | ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(128,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2EA_27e) ).

thf(1114,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(192,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__ANTISYM) ).

thf(1324,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(479,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27g_20mono_2EA_27h) ).

thf(2285,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(329,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ C @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er219) ).

thf(1776,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ C @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(173,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A = B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__TOTAL) ).

thf(1263,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A = B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(256,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er213) ).

thf(1530,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(259,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__ADD__SYM) ).

thf(1539,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(624,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
     => ( ( s @ A @ C )
        = ( s @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__SYM) ).

thf(2836,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
     => ( ( s @ A @ C )
        = ( s @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(174,axiom,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eset__relation_2Etc_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) )
      = ( ! [D: u] :
            ( ! [E: u] :
                ( ( ? [F: u,G: u] :
                      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ E )
                        = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ G ) ) ) )
                      & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ G ) ) ) ) ) ) )
                  | ? [F: u,G: u] :
                      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ E )
                        = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ G ) ) ) )
                      & ? [H: u] :
                          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ H ) ) ) ) ) )
                          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ H ) @ ( s @ A @ G ) ) ) ) ) ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__def) ).

thf(1266,plain,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Eset__relation_2Etc_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) )
      = ( ! [D: u] :
            ( ! [E: u] :
                ( ( ? [F: u,G: u] :
                      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ E )
                        = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ G ) ) ) )
                      & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ G ) ) ) ) ) ) )
                  | ? [F: u,G: u] :
                      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ E )
                        = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ G ) ) ) )
                      & ? [H: u] :
                          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ A @ H ) ) ) ) ) )
                          & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ H ) @ ( s @ A @ G ) ) ) ) ) ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(442,axiom,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal) ).

thf(2153,plain,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal @ A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(514,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ E ) @ ( s @ C @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) @ ( s @ B @ E ) ) ) @ ( s @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__case__def) ).

thf(2387,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ E ) @ ( s @ C @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) @ ( s @ B @ E ) ) ) @ ( s @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(165,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
      = ( ? [F: mono_2Etyop_2Erealax_2Ereal,G: u,H: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ B @ H ) ) ) @ ( s @ B @ H ) ) ) )
            & ! [I: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ B @ I ) ) ) @ ( s @ B @ H ) ) ) )
               => ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ I ) ) ) @ ( s @ A @ G ) ) ) ) ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enets_2Ebounded) ).

thf(1231,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Ebounded_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
      = ( ? [F: mono_2Etyop_2Erealax_2Ereal,G: u,H: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ B @ H ) ) ) @ ( s @ B @ H ) ) ) )
            & ! [I: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ B @ I ) ) ) @ ( s @ B @ H ) ) ) )
               => ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ I ) ) ) @ ( s @ A @ G ) ) ) ) ) ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(629,axiom,
    ! [A: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Enum_2Enum] :
          ( ( A @ B @ C )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( B @ C ) ) )
     => ! [B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Eseq_2Econvergent @ B )
          = ( mono_2Ec_2Eseq_2Econvergent @ ( A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eseq_2ESEQ__NEG__CONV) ).

thf(2851,plain,
    ! [A: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Enum_2Enum] :
          ( ( A @ B @ C )
          = ( mono_2Ec_2Erealax_2Ereal__neg @ ( B @ C ) ) )
     => ! [B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Eseq_2Econvergent @ B )
          = ( mono_2Ec_2Eseq_2Econvergent @ ( A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(469,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29) ).

thf(2243,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(503,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] :
            ( ( ( s @ A @ D )
              = ( s @ A @ C ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EUNWIND__THM2) ).

thf(2355,plain,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] :
            ( ( ( s @ A @ D )
              = ( s @ A @ C ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(371,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) )
     => ? [B: mono_2Etyop_2Erealax_2Ereal] :
        ! [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [D: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ D )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__SUP__EXISTS) ).

thf(1932,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) )
     => ? [B: mono_2Etyop_2Erealax_2Ereal] :
        ! [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ? [D: mono_2Etyop_2Erealax_2Ereal] :
                ( ( A @ D )
                & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) ) )
          = ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(394,axiom,
    ! [A: d,B: u,C: u] :
      ( ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
     => ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
       => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EMONO__ALL) ).

thf(2006,plain,
    ! [A: d,B: u,C: u] :
      ( ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
     => ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
       => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(547,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ B )
          = B )
     => ! [B: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Elim_2Etends__real__real @ A @ B @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ELIM__X) ).

thf(2497,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ B )
          = B )
     => ! [B: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Elim_2Etends__real__real @ A @ B @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(410,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27e_20mono_2EA_27f) ).

thf(2052,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(542,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ B @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a) ).

thf(2482,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ B @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(169,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__ind__left) ).

thf(1246,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(195,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__GT0) ).

thf(1333,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(389,axiom,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
     => ! [C: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EGSPEC__ETA) ).

thf(1991,plain,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
     => ! [C: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(155,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2EA_27b) ).

thf(1202,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(330,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u,H: u,I: u,J: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EPAIR__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ D @ tyop_2Emin_2Ebool ) ) @ F ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ C @ H ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ D ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ I ) @ ( s @ D @ J ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ G ) ) ) @ ( s @ B @ I ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ D @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ D @ tyop_2Emin_2Ebool ) ) @ F ) @ ( s @ C @ H ) ) ) @ ( s @ D @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Etransfer_2EPAIR__REL__def) ).

thf(1779,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u,H: u,I: u,J: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Etransfer_2EPAIR__REL_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ D @ tyop_2Emin_2Ebool ) ) @ F ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ C @ H ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ D ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ I ) @ ( s @ D @ J ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ G ) ) ) @ ( s @ B @ I ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ D @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ D @ tyop_2Emin_2Ebool ) ) @ F ) @ ( s @ C @ H ) ) ) @ ( s @ D @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(407,axiom,
    ! [A: d,B: u] :
      ( ( ? [C: u] :
          ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ C ) ) ) ) )
      = ( ? [C: u] :
            ( ! [D: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
               => ! [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ D ) ) ) ) )
            & ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EOmega__Automata_2EELGOT__LEMMA) ).

thf(2043,plain,
    ! [A: d,B: u] :
      ( ( ? [C: u] :
          ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ C ) ) ) ) )
      = ( ? [C: u] :
            ( ! [D: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) )
               => ! [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ D ) ) ) ) )
            & ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(418,axiom,
    ! [A: d,B: u] :
      ( ( ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__itself) ).

thf(2076,plain,
    ! [A: d,B: u] :
      ( ( ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(531,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27d) ).

thf(2440,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(454,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) ) )
        = ( s @ A @ D ) )
      = ( ? [G: u,H: u] :
            ( ( ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E )
              = ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ G ) @ ( s @ C @ H ) ) ) )
            & ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) @ ( s @ B @ G ) ) ) @ ( s @ C @ H ) ) )
              = ( s @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__case__eq) ).

thf(2189,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) ) )
        = ( s @ A @ D ) )
      = ( ? [G: u,H: u] :
            ( ( ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ E )
              = ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ G ) @ ( s @ C @ H ) ) ) )
            & ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) @ ( s @ B @ G ) ) ) @ ( s @ C @ H ) ) )
              = ( s @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(151,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ A )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__LINV) ).

thf(1185,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ A )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(45,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27c_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(794,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(527,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Edist_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Emetric_2Edist_2E1_2Emono_2EA_27a) ).

thf(2423,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Edist_2E1 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(558,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27state) ).

thf(2634,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(596,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecombin_2EK__THM) ).

thf(2749,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(347,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__COMM) ).

thf(1857,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
      = ( mono_2Ec_2Erealax_2Ereal__add @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(167,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u,G: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ A @ E ) ) ) )
            & ( ( s @ B @ F )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__GSPEC) ).

thf(1241,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u,G: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ A @ E ) ) ) )
            & ( ( s @ B @ F )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(600,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__top_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__top_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2761,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__top_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(39,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
      = ( ? [F: u] :
            ( ( ( s @ B @ C )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__IMAGE) ).

thf(765,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
      = ( ? [F: u] :
            ( ( ( s @ B @ C )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(316,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ B @ A )
      = ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er215) ).

thf(1712,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ B @ A )
      = ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(179,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__GE0) ).

thf(1286,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(508,axiom,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emetric_2Edist_2E2_2Emono_2EA_27a) ).

thf(2368,plain,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(439,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29) ).

thf(2144,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(364,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1906,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(476,axiom,
    ! [A: d,B: d,C: d,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) )
          = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ G ) ) ) ) ) )
     => ! [E: u,F: u] :
          ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F ) ) )
          = ( s @ C @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ELAMBDA__PROD) ).

thf(2275,plain,
    ! [A: d,B: d,C: d,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) )
          = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ G ) ) ) ) ) )
     => ! [E: u,F: u] :
          ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F ) ) )
          = ( s @ C @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(241,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Estate__transformer_2EUNIT_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Estate__transformer_2EBIND__RIGHT__UNIT) ).

thf(1483,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( c_2Estate__transformer_2EBIND_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Estate__transformer_2EUNIT_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(14,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29) ).

thf(689,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) @ E ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(1366,plain,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) )
    = $true ),
    inference(instance,[status(thm)],[1365]) ).

thf(1367,plain,
    j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ),
    inference(simp,[status(thm)],[1366]) ).

thf(2890,plain,
    ( ~ $true
    | ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) )
     != ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1367,1369]) ).

thf(2891,plain,
    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) ) )
   != ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) ) ),
    inference(simp,[status(thm)],[2890]) ).

thf(2892,plain,
    ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $false ) )
   != ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) ),
    inference(simp,[status(thm)],[2891]) ).

thf(2893,plain,
    ( ( tyop_2Emin_2Ebool != tyop_2Emin_2Ebool )
    | ( ( i_mono_2Etyop_2Emin_2Ebool @ $false )
     != ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ) ),
    inference(simp,[status(thm)],[2892]) ).

thf(2894,plain,
    ( ( i_mono_2Etyop_2Emin_2Ebool @ $false )
   != ( i_mono_2Etyop_2Emin_2Ebool @ $true ) ),
    inference(simp,[status(thm)],[2893]) ).

thf(86,axiom,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) )
      & ! [C: u,D: u] :
          ( ? [E: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__rules) ).

thf(965,plain,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) )
      & ! [C: u,D: u] :
          ( ? [E: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(34,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__ASSOC) ).

thf(750,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(401,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( ? [D: u] :
            ( B
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( B
       => ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__EXISTS__IMP__THM) ).

thf(2028,plain,
    ! [A: d,B: $o,C: u] :
      ( ( ? [D: u] :
            ( B
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( B
       => ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(184,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Erealax_2Ereal ) ) @ D ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Erealax_2Ereal ) ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Erealax_2Ereal ) ) @ tyop_2Erealax_2Ereal ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Erealax_2Ereal ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29) ).

thf(1301,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Erealax_2Ereal ) ) @ D ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Erealax_2Ereal ) ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Erealax_2Ereal ) ) @ tyop_2Erealax_2Ereal ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Erealax_2Ereal ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(278,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1595,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(140,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ? [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__cases__left) ).

thf(1154,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ? [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(88,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_20mono_2EA_27b_20mono_2EA_27a) ).

thf(975,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(588,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEGNEG) ).

thf(2727,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(332,axiom,
    ! [A: d,B: $o,C: $o,D: u,E: u,F: u,G: u] :
      ( ( ( B = C )
        & ( C
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
        & ( ~ C
         => ( ( s @ A @ F )
            = ( s @ A @ G ) ) ) )
     => ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ D ) @ ( s @ A @ F ) ) )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__CONG) ).

thf(1784,plain,
    ! [A: d,B: $o,C: $o,D: u,E: u,F: u,G: u] :
      ( ( ( B = C )
        & ( C
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
        & ( ~ C
         => ( ( s @ A @ F )
            = ( s @ A @ G ) ) ) )
     => ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ D ) @ ( s @ A @ F ) ) )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(609,axiom,
    ! [A: d,B: d,C: u,D: u,E: u,F: u] :
      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ C ) ) )
        = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ E ) ) ) )
      = ( ( ( s @ A @ D )
          = ( s @ A @ F ) )
        & ( ( s @ B @ C )
          = ( s @ B @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EPAIR__EQ) ).

thf(2791,plain,
    ! [A: d,B: d,C: u,D: u,E: u,F: u] :
      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ C ) ) )
        = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ E ) ) ) )
      = ( ( ( s @ A @ D )
          = ( s @ A @ F ) )
        & ( ( s @ B @ C )
          = ( s @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(58,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__UNION) ).

thf(843,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(326,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ C ) @ ( s @ A @ C ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__ID) ).

thf(1752,plain,
    ! [A: d,B: $o,C: u] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ C ) @ ( s @ A @ C ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(397,axiom,
    ! [A: d,B: d,C: d,D: u] :
    ? [E: u] :
    ! [F: u,G: u] :
      ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ G ) ) ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__Axiom) ).

thf(2016,plain,
    ! [A: d,B: d,C: d,D: u] :
    ? [E: u] :
    ! [F: u,G: u] :
      ( ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ G ) ) ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(21,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29) ).

thf(711,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ E ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) @ F ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ C ) @ D ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(614,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__bottom_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__bottom_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2806,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__bottom_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(84,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u,H: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ B @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ H ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ H ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u,H: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ B @ H ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ B @ H ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
       => ! [E: u,F: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EFINITE__PRODUCT) ).

thf(958,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u,H: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ B @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ H ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ G ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ H ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u,H: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ B @ H ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ B @ H ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
       => ! [E: u,F: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(131,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B )
       != ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      = ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
            = ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ENOT__EQUAL__SETS) ).

thf(1124,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B )
       != ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      = ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
            = ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(621,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__infinity_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2827,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__minus__infinity_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(28,axiom,
    ! [A: d,B: d,C: d,D: d,E: d,F: u,G: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ F ) @ ( s @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) @ G ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ F ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29_29) ).

thf(732,plain,
    ! [A: d,B: d,C: d,D: d,E: d,F: u,G: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ F ) @ ( s @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) @ G ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ B ) ) @ F ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ C @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ D ) @ E ) ) ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(356,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__RINV) ).

thf(1884,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(295,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29) ).

thf(1652,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(370,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emetric_2Emono_2Etyop_2Erealax_2Ereal @ A ) ) )
      = ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Emetric_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Emetric_2Emetric_2E1_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(1929,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ ( mono_2Ec_2Emetric_2Emetric_2Emono_2Etyop_2Erealax_2Ereal @ A ) ) )
      = ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( c_2Emetric_2Emetric_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(225,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
     => ? [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ B ) )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2ESUP__LEMMA2) ).

thf(1428,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
     => ? [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ B ) )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(301,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__DEF) ).

thf(1669,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(314,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) ) @ c_2Epair_2E_2C_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal) ).

thf(1707,plain,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) ) @ c_2Epair_2E_2C_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(176,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__LADD) ).

thf(1271,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(289,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29) ).

thf(1635,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(391,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D )
        = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Erel__to__reln__11) ).

thf(1997,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D )
        = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(411,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) ) )
      = ( ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ESWAP__FORALL__THM) ).

thf(2055,plain,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) ) )
      = ( ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(581,axiom,
    ! [A: d,B: u,C: u,D: u,E: u] :
      ( ( ( ( s @ A @ B )
          = ( s @ A @ D ) )
        & ( ( s @ A @ C )
          = ( s @ A @ E ) ) )
     => ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
       => ( ( s @ A @ D )
          = ( s @ A @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EEQUALS__IMPLIES) ).

thf(2706,plain,
    ! [A: d,B: u,C: u,D: u,E: u] :
      ( ( ( ( s @ A @ B )
          = ( s @ A @ D ) )
        & ( ( s @ A @ C )
          = ( s @ A @ E ) ) )
     => ( ( ( s @ A @ B )
          = ( s @ A @ C ) )
       => ( ( s @ A @ D )
          = ( s @ A @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(120,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__INTER) ).

thf(1090,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(290,axiom,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ D ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
     => ! [C: u,D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ D ) ) ) )
            & ( ( s @ A @ D )
              = ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EPAIR__IN__GSPEC__same) ).

thf(1638,plain,
    ! [A: d,B: u] :
      ( ! [C: u,D: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ D ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
     => ! [C: u,D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ D ) ) ) )
            & ( ( s @ A @ D )
              = ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(303,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ C ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ A @ G ) ) ) )
          = ( ( s @ B @ E )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ A @ G ) ) ) ) )
     => ( ! [E: u,F: u,G: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ D ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ A @ G ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ C ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ A @ G ) ) ) ) ) )
       => ! [E: u] :
            ( ! [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ D ) @ ( s @ B @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) ) ) ) ) )
           => ! [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
                = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE) ).

thf(1675,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ C ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ A @ G ) ) ) )
          = ( ( s @ B @ E )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) @ ( s @ A @ G ) ) ) ) )
     => ( ! [E: u,F: u,G: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ D ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ A @ G ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ C ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ F ) ) ) @ ( s @ A @ G ) ) ) ) ) )
       => ! [E: u] :
            ( ! [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ D ) @ ( s @ B @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) ) ) ) ) )
           => ! [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
                = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(361,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) ).

thf(1897,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(75,axiom,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__APP) ).

thf(919,plain,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(504,axiom,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29) ).

thf(2358,plain,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(201,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__ADD) ).

thf(1356,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(500,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29) ).

thf(2346,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(586,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__plus__zero_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2721,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__plus__zero_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(421,axiom,
    ! [A: d,B: u,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Erealax_2Ereal) ).

thf(2084,plain,
    ! [A: d,B: u,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(270,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) ) @ C )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ADDNEG2) ).

thf(1574,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) ) @ C )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(276,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29) ).

thf(1589,plain,
    ! [A: d,B: $o,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(260,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ C ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29) ).

thf(1542,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ C ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ C ) ) ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(569,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29) ).

thf(2669,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(625,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Etransc_2Etan @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Etransc_2Etan @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Etransc_2ETAN__NEG) ).

thf(2839,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Etransc_2Etan @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Etransc_2Etan @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(186,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__LE0) ).

thf(1307,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(419,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ D ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
     => ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ D ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2EULP__ind) ).

thf(2079,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ D ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
     => ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ ( tyop_2Ebool_2Eitself @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ B ) @ D ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(505,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ c_2Ebinary__ieee_2Eclosest__such_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Eclosest__such_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2361,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ c_2Ebinary__ieee_2Eclosest__such_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(524,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
     => ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Eitself__induction) ).

thf(2415,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
     => ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(360,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29) ).

thf(1894,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(559,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27b) ).

thf(2637,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(129,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u,H: u,I: u,J: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ G ) ) ) @ ( s @ B @ H ) ) ) @ ( s @ A @ I ) ) ) @ ( s @ B @ J ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ F ) ) ) @ ( s @ A @ I ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ G ) @ ( s @ B @ H ) ) ) @ ( s @ B @ J ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u,H: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) ) @ ( s @ B @ H ) ) ) ) ) )
       => ! [E: u,F: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2ERPROD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ERPROD__DEF) ).

thf(1117,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u,G: u,H: u,I: u,J: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ G ) ) ) @ ( s @ B @ H ) ) ) @ ( s @ A @ I ) ) ) @ ( s @ B @ J ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ F ) ) ) @ ( s @ A @ I ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ G ) @ ( s @ B @ H ) ) ) @ ( s @ B @ J ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u,H: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ B @ H ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) ) @ ( s @ B @ H ) ) ) ) ) )
       => ! [E: u,F: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2ERPROD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(470,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ B @ C )
          = B )
     => ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Elim_2Etends__real__real @ ( A @ B ) @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ELIM__CONST) ).

thf(2246,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ B @ C )
          = B )
     => ! [B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Elim_2Etends__real__real @ ( A @ B ) @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(244,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29) ).

thf(1492,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(281,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ B )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__LNEG) ).

thf(1603,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ B )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(66,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ! [F: u,G: u,H: u,I: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ B @ H ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ I ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ H ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ I ) @ ( s @ A @ F ) ) ) ) ) ) ) )
     => ( ! [F: u,G: u,H: u,I: u,J: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) ) ) @ ( s @ A @ I ) ) ) @ ( s @ B @ J ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ F ) @ ( s @ A @ I ) ) ) @ ( s @ B @ J ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ D ) @ ( s @ A @ I ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ B @ J ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) ) ) ) ) )
       => ! [F: u,G: u,H: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
              & ! [I: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ I ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ A @ I ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EFINITE__PRODUCT__DEPENDENT) ).

thf(880,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ! [F: u,G: u,H: u,I: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ B @ H ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ I ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ H ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ I ) @ ( s @ A @ F ) ) ) ) ) ) ) )
     => ( ! [F: u,G: u,H: u,I: u,J: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) ) ) @ ( s @ A @ I ) ) ) @ ( s @ B @ J ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ F ) @ ( s @ A @ I ) ) ) @ ( s @ B @ J ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ D ) @ ( s @ A @ I ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ B @ J ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) ) ) ) ) )
       => ! [F: u,G: u,H: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
              & ! [I: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ I ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
                 => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ A @ I ) ) ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ C @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ C @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(647,plain,
    ! [E: u,D: u,C: u,B: d,A: d] :
      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) )
       != ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( sk5 @ C @ B @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) ) ) )
      | ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( sk6 @ E @ D @ C @ B @ A ) ) ) )
        = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( sk7 @ E @ D @ C @ B @ A ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ),
    inference(cnfConj,[status(thm)],[646]) ).

thf(649,plain,
    ! [E: u,D: u,C: u,B: d,A: d] :
      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ ( sk5 @ C @ B @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) ) )
       != ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( sk3 @ C @ B @ A ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( sk4 @ C @ B @ A ) ) ) ) @ ( s @ A @ ( sk5 @ C @ B @ A ) ) ) ) )
      | ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( sk7 @ E @ D @ C @ B @ A ) ) ) )
        = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( sk6 @ E @ D @ C @ B @ A ) ) ) ) )
      | ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
      | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ),
    inference(lifteq,[status(thm)],[647]) ).

thf(334,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__POS) ).

thf(1801,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(269,axiom,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            | D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ D ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ E @ F ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er025) ).

thf(1571,plain,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            | D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ D ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ E @ F ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(207,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Enets_2Etendsto_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etendsto_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Enets_2Etendsto_2E0_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(1376,plain,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Enets_2Etendsto_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etendsto_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(620,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__minus__zero_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2824,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__minus__zero_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(47,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27state_29_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29) ).

thf(811,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ C ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(237,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__NEGR) ).

thf(1471,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(593,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecombin_2EK__DEF) ).

thf(2742,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(197,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Ereal__lte @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__REFL) ).

thf(1339,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Ereal__lte @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(429,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( A @ B ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal) ).

thf(2111,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( A @ B ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(199,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29) ).

thf(1344,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(264,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ A )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__NEGL) ).

thf(1556,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ A )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(477,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ D ) ) ) ) )
      = ( ? [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EEXISTS__PROD) ).

thf(2278,plain,
    ! [A: d,B: d,C: u] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ D ) ) ) ) )
      = ( ? [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(535,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Estate__transformer_2EUNIT_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Estate__transformer_2EUNIT_2E0 ) @ ( s @ B @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Estate__transformer_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2461,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Estate__transformer_2EUNIT_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Estate__transformer_2EUNIT_2E0 ) @ ( s @ B @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(307,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1688,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(68,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29) ).

thf(890,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(451,axiom,
    ! [A: d,B: u] :
      ( ( ! [C: u] :
          ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ C ) ) ) ) )
      = ( ! [C: u] :
          ? [D: u,E: u] :
          ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) )
           => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ E ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EOmega__Automata_2EELGOT2__THM) ).

thf(2180,plain,
    ! [A: d,B: u] :
      ( ( ! [C: u] :
          ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ C ) ) ) ) )
      = ( ! [C: u] :
          ? [D: u,E: u] :
          ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) )
           => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ E ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(400,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            & C ) )
      = ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        & C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__EXISTS__AND__THM) ).

thf(2025,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            & C ) )
      = ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        & C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(616,axiom,
    ! [A: d,B: d] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Eulp) ).

thf(2812,plain,
    ! [A: d,B: d] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(435,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Efchains_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Efchains_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eset__relation_2Efchains_2E1_2Emono_2EA_27a) ).

thf(2129,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Efchains_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Efchains_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(499,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) ).

thf(2343,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(555,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29) ).

thf(2625,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(365,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__ASSOC) ).

thf(1909,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(26,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27b_20mono_2EA_27a) ).

thf(726,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(80,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ B @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ B ) ) @ D ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ B ) ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ B ) ) @ B ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ B ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b) ).

thf(943,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ B @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ B ) ) @ D ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ B ) ) @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ B ) ) @ B ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ B ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(567,axiom,
    ! [A: d,B: u] :
      ( ( ? [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      = ( ~ ! [C: u] :
              ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EEXISTS__NOT__FORALL__THM) ).

thf(2664,plain,
    ! [A: d,B: u] :
      ( ( ? [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      = ( ~ ! [C: u] :
              ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(148,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
      = ( ! [F: u] :
            ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) )
            = ( s @ B @ F ) )
        & ! [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) )
        & ! [F: u,G: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
            = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ F ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ G ) ) ) )
              & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
                = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__def) ).

thf(1177,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
      = ( ! [F: u] :
            ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) )
            = ( s @ B @ F ) )
        & ! [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) )
        & ! [F: u,G: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
            = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ F ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ G ) ) ) )
              & ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
                = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(209,axiom,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            & ~ D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ F @ E ) ) ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er019) ).

thf(1381,plain,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            & ~ D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ F @ E ) ) ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(626,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2842,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(376,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29) ).

thf(1952,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(146,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29) ).

thf(1171,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ C @ A ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(603,axiom,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Emarker_2Estmarker_2E1 @ ( s @ A @ B ) ) )
      = ( s @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emarker_2Estmarker__def) ).

thf(2770,plain,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Emarker_2Estmarker_2E1 @ ( s @ A @ B ) ) )
      = ( s @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(214,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ D ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) ) ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ A @ F ) ) ) )
            & ( ( s @ B @ E )
              = ( s @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EPAIR__IN__GSPEC__1) ).

thf(1396,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ D ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) ) ) )
     => ! [D: u,E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ B @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ B @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) ) ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ A @ F ) ) ) )
            & ( ( s @ B @ E )
              = ( s @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(507,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Eposet_2Ecarrier_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Eposet_2Ecarrier_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eposet_2Ecarrier_2E1_2Emono_2EA_27a) ).

thf(2365,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Eposet_2Ecarrier_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ c_2Eposet_2Ecarrier_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(238,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ B @ C ) )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__TRANS) ).

thf(1474,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ B @ C ) )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(311,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1699,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(448,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29) ).

thf(2171,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(16,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29) ).

thf(695,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(480,axiom,
    ! [A: d,B: u] :
      ( ! [C: u] :
          ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ B ) @ ( s @ A @ C ) ) )
          = ( s @ A @ C ) )
     => ! [C: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__ID) ).

thf(2288,plain,
    ! [A: d,B: u] :
      ( ! [C: u] :
          ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ B ) @ ( s @ A @ C ) ) )
          = ( s @ A @ C ) )
     => ! [C: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ A ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(611,axiom,
    ! [A: d,B: d,C: u,D: u,E: u,F: u] :
      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
        = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) )
      = ( ( ( s @ A @ C )
          = ( s @ A @ E ) )
        & ( ( s @ B @ D )
          = ( s @ B @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ECLOSED__PAIR__EQ) ).

thf(2797,plain,
    ! [A: d,B: d,C: u,D: u,E: u,F: u] :
      ( ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
        = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) )
      = ( ( ( s @ A @ C )
          = ( s @ A @ E ) )
        & ( ( s @ B @ D )
          = ( s @ B @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(399,axiom,
    ! [A: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29) ).

thf(2022,plain,
    ! [A: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(485,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
           => ( ( s @ A @ D )
              = ( s @ A @ E ) ) ) )
      = ( ? [D: u] :
          ! [E: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) ) )
            = ( s @ A @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EINJECTIVE__LEFT__INVERSE) ).

thf(2303,plain,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
           => ( ( s @ A @ D )
              = ( s @ A @ E ) ) ) )
      = ( ? [D: u] :
          ! [E: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) ) )
            = ( s @ A @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(124,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29) ).

thf(1102,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(443,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29) ).

thf(2156,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(460,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u,H: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ D ) @ ( c_2Epair_2E_23_23_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ C @ D ) @ F ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ C @ H ) ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ D ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ G ) ) ) @ ( s @ D @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ D ) @ F ) @ ( s @ C @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EPAIR__MAP__THM) ).

thf(2207,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u,H: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ D ) @ ( c_2Epair_2E_23_23_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ C @ D ) @ F ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ C @ H ) ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ D ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ G ) ) ) @ ( s @ D @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ D ) @ F ) @ ( s @ C @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(383,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Euniv__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Euniv__reln_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Eset__relation_2Euniv__reln_2E1_2Emono_2EA_27a) ).

thf(1973,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Euniv__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ c_2Eset__relation_2Euniv__reln_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(40,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_29_20mono_2EA_27a_20mono_2EA_27state) ).

thf(768,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ C ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ C ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ C ) ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(53,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__OVER__UNION) ).

thf(827,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(44,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EUNION__ACI) ).

thf(780,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) )
      & ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(292,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ADDR) ).

thf(1643,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(414,axiom,
    ! [A: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29) ).

thf(2064,plain,
    ! [A: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ A ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(98,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) ).

thf(1015,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(93,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) )
      = ( ! [C: u,D: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ C ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ D ) ) ) ) )
           => ? [E: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) ) ) )
                & ! [F: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) )
                   => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ C ) ) ) )
                      & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enets_2Edorder) ).

thf(1000,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) )
      = ( ! [C: u,D: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ C ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ D ) ) ) ) )
           => ? [E: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) ) ) )
                & ! [F: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) )
                   => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ C ) ) ) )
                      & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(597,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ A ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29) ).

thf(2752,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ A ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(226,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29) ).

thf(1435,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(319,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ? [C: mono_2Etyop_2Erealax_2Ereal] :
        ! [D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ D )
         => ( mono_2Ec_2Erealax_2Ereal__lt @ D @ C ) )
     => ? [C: mono_2Etyop_2Erealax_2Ereal] :
        ! [D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ ( mono_2Ec_2Erealax_2Ereal__add @ D @ B ) )
         => ( mono_2Ec_2Erealax_2Ereal__lt @ D @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2ESUP__LEMMA3) ).

thf(1726,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ? [C: mono_2Etyop_2Erealax_2Ereal] :
        ! [D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ D )
         => ( mono_2Ec_2Erealax_2Ereal__lt @ D @ C ) )
     => ? [C: mono_2Etyop_2Erealax_2Ereal] :
        ! [D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ ( mono_2Ec_2Erealax_2Ereal__add @ D @ B ) )
         => ( mono_2Ec_2Erealax_2Ereal__lt @ D @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(515,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ) ) )
     => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__induction) ).

thf(2390,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ) ) )
     => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(309,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__TOTAL) ).

thf(1694,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(76,axiom,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) )
     => ! [C: u,D: u] :
          ( ( ? [E: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) ) ) )
                & ! [F: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) )
                   => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) ) ) )
            & ? [E: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) ) ) )
                & ! [F: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) )
                   => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ F ) ) ) ) ) ) )
         => ? [E: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) ) ) )
              & ! [F: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) )
                 => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enets_2EDORDER__LEMMA) ).

thf(922,plain,
    ! [A: d,B: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Edorder_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) ) ) )
     => ! [C: u,D: u] :
          ( ( ? [E: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) ) ) )
                & ! [F: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) )
                   => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) ) ) )
            & ? [E: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) ) ) )
                & ! [F: u] :
                    ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) )
                   => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ F ) ) ) ) ) ) )
         => ? [E: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ E ) ) ) @ ( s @ A @ E ) ) ) )
              & ! [F: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) )
                 => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) )
                    & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(577,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2693,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Efloat__to__real_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(550,axiom,
    ! [A: d,B: d,C: d,D: d] :
      ( ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ E ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ E ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__distinct) ).

thf(2506,plain,
    ! [A: d,B: d,C: d,D: d] :
      ( ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__zero_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__top_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__bottom_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
       != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ C @ D ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ C @ D ) @ ( c_2Ebinary__ieee_2Efloat__some__qnan_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efp__op @ C @ D ) @ E ) ) ) )
      & ! [E: u] :
          ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ E ) ) )
         != ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(266,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__ANTSYM) ).

thf(1562,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(220,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__infinite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__infinite_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__infinite_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(1413,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__infinite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ c_2Ebinary__ieee_2Efloat__is__infinite_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(286,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) )
          = ( ( ( s @ A @ F )
              = ( s @ A @ D ) )
            & ( ( s @ B @ G )
              = ( s @ B @ E ) ) ) )
     => ! [D: u,E: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EABS__prod_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ECOMMA__DEF) ).

thf(1626,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) )
          = ( ( ( s @ A @ F )
              = ( s @ A @ D ) )
            & ( ( s @ B @ G )
              = ( s @ B @ E ) ) ) )
     => ! [D: u,E: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EABS__prod_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(424,axiom,
    ! [A: d,B: u] :
      ( ( ~ ? [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      = ( ! [C: u] :
            ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__EXISTS__THM) ).

thf(2096,plain,
    ! [A: d,B: u] :
      ( ( ~ ? [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      = ( ! [C: u] :
            ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(185,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1304,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(144,axiom,
    ! [A: d,B: u] :
      ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
     => ? [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINFINITE__INHAB) ).

thf(1166,plain,
    ! [A: d,B: u] :
      ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
     => ? [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(157,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A != mono_2Ec_2Enum_2E0 )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NZ__IMP__LT) ).

thf(1208,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A != mono_2Ec_2Enum_2E0 )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(563,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(2652,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)],[563]) ).

thf(134,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ B ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ B ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29) ).

thf(1134,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ B ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Eordinal_2Eordinal @ A ) @ ( tyop_2Eordinal_2Eordinal @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ B ) ) ) @ ( s @ ( tyop_2Eordinal_2Eordinal @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(117,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_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_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(1081,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(574,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
           => C ) )
      = ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__FORALL__IMP__THM) ).

thf(2684,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
           => C ) )
      = ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(1340,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal_2Ereal__lte @ A @ A ),
    inference(cnf,[status(esa)],[1339]) ).

thf(378,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__infinite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C )
          = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
        | ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C )
          = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__infinities) ).

thf(1958,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebinary__ieee_2Efloat__is__infinite_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) )
      = ( ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C )
          = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
        | ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C )
          = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(490,axiom,
    ! [A: d,B: d,C: u,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Eclosest_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ D ) ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ c_2Ebinary__ieee_2Eclosest_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebinary__ieee_2Eclosest_2E2_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2318,plain,
    ! [A: d,B: d,C: u,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Eclosest_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ D ) ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ c_2Ebinary__ieee_2Eclosest_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(606,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ A ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29) ).

thf(2784,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ A ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(11,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ G ) ) ) ) ) )
          = ( ( s @ B @ F )
            = ( s @ B @ G ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__REL__REP) ).

thf(680,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ G ) ) ) ) ) )
          = ( ( s @ B @ F )
            = ( s @ B @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(638,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__infinity_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2878,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__plus__infinity_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(549,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29) ).

thf(2503,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(137,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29) ).

thf(1145,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(99,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EREP__ABS__RSP) ).

thf(1018,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(149,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
     => ~ ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__GT) ).

thf(1180,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
     => ~ ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(1181,plain,
    ! [B: mono_2Etyop_2Erealax_2Ereal,A: mono_2Etyop_2Erealax_2Ereal] :
      ( ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      | ~ ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(cnf,[status(esa)],[1180]) ).

thf(51,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
     => ! [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__union) ).

thf(823,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
     => ! [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(333,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1798,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(94,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(1003,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(584,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29) ).

thf(2715,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(379,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool @ A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool) ).

thf(1961,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool @ A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(566,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        | ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEXISTS__OR__THM) ).

thf(2661,plain,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        | ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(19,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) ) )
              = ( s @ A @ F ) ) ) )
      = ( ! [F: u,G: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
              & ( ( s @ B @ F )
                = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) )
           => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ F ) ) )
              = ( s @ A @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewellorder_2EFLATTEN__LEMMA) ).

thf(705,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) ) )
              = ( s @ A @ F ) ) ) )
      = ( ! [F: u,G: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ G ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
              & ( ( s @ B @ F )
                = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) )
           => ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ F ) ) )
              = ( s @ A @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(87,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ F ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ G ) ) ) )
           => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
              = ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
                = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__REL__ABS__EQ) ).

thf(971,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ F ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ G ) ) ) )
           => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
              = ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) )
                = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(372,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool) ).

thf(1941,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(572,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ C @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2EUNCURRY__DEF) ).

thf(2678,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ C @ ( c_2Epair_2EUNCURRY_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ C ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(619,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ) )
      = ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__to__real__negate) ).

thf(2821,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ) )
      = ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(123,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
     => ? [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
          & ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__INFINITE__NOT__FINITE) ).

thf(1098,plain,
    ! [A: d,B: u,C: u] :
      ( ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
     => ? [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
          & ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(633,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2863,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__plus__min_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(279,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      | ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LTE__TOTAL) ).

thf(1598,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      | ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(163,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__LADD) ).

thf(1225,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(323,axiom,
    ! [A: d,B: d,C: $o,D: u,E: u,F: u] :
      ( ( s @ B @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__ABS) ).

thf(1743,plain,
    ! [A: d,B: d,C: $o,D: u,E: u,F: u] :
      ( ( s @ B @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(455,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( ( s @ A @ C )
          = ( s @ A @ D ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      = ( ( ( s @ A @ C )
          = ( s @ A @ D ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eint__arith_2ECONJ__EQ__ELIM) ).

thf(2192,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( ( s @ A @ C )
          = ( s @ A @ D ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      = ( ( ( s @ A @ C )
          = ( s @ A @ D ) )
        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(67,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) ) ) )
     => ! [H: u,I: u,J: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ ( tyop_2Emin_2Efun @ B @ D ) @ I ) @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) ) ) )
         => ! [K: u,L: u,M: u,N: u] :
              ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ K ) ) ) @ ( s @ A @ L ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ B @ M ) ) ) @ ( s @ B @ N ) ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ K ) @ ( s @ B @ M ) ) ) ) ) @ ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ L ) @ ( s @ B @ N ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EK__RSP) ).

thf(887,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) ) ) )
     => ! [H: u,I: u,J: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ ( tyop_2Emin_2Efun @ B @ D ) @ I ) @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) ) ) )
         => ! [K: u,L: u,M: u,N: u] :
              ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ K ) ) ) @ ( s @ A @ L ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ B @ M ) ) ) @ ( s @ B @ N ) ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ K ) @ ( s @ B @ M ) ) ) ) ) @ ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ L ) @ ( s @ B @ N ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(108,axiom,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIN__DEF) ).

thf(1053,plain,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(9,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( ( s @ B @ F )
            = ( s @ B @ G ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EEQUALS__PRS) ).

thf(673,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u] :
          ( ( ( s @ B @ F )
            = ( s @ B @ G ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(446,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ B @ ( c_2Ebool_2Eitself__case_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ ( tyop_2Emin_2Efun @ B @ B ) ) @ c_2Ebool_2Eitself__case_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2Eitself__case_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2165,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ B @ ( c_2Ebool_2Eitself__case_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ A ) @ ( tyop_2Emin_2Efun @ B @ B ) ) @ c_2Ebool_2Eitself__case_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(23,axiom,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) ) ) )
     => ! [H: u,I: u,J: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ ( tyop_2Emin_2Efun @ B @ D ) @ I ) @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) ) ) )
         => ! [K: u,L: u] :
              ( ( s @ C @ ( c_2Ecombin_2EK_2E2 @ ( s @ C @ K ) @ ( s @ D @ L ) ) )
              = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) @ ( s @ C @ K ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) @ ( s @ D @ L ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EK__PRS) ).

thf(717,plain,
    ! [A: d,B: d,C: d,D: d,E: u,F: u,G: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) ) ) )
     => ! [H: u,I: u,J: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ H ) @ ( s @ ( tyop_2Emin_2Efun @ B @ D ) @ I ) @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) ) ) )
         => ! [K: u,L: u] :
              ( ( s @ C @ ( c_2Ecombin_2EK_2E2 @ ( s @ C @ K ) @ ( s @ D @ L ) ) )
              = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ C ) @ F ) @ ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ G ) @ ( s @ C @ K ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ D @ B ) @ J ) @ ( s @ D @ L ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(351,axiom,
    ! [A: d,B: u,C: u,D: u,E: $o] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) ) ) )
      = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er023) ).

thf(1869,plain,
    ! [A: d,B: u,C: u,D: u,E: $o] :
      ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) ) ) )
      = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(57,axiom,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2ESPECIFICATION) ).

thf(840,plain,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(529,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29) ).

thf(2429,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ A ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(497,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2ERPROD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2ERPROD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2ERPROD_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2337,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2ERPROD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2ERPROD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(342,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A = B )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__EQ__IMP__LE) ).

thf(1830,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A = B )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(297,axiom,
    ! [A: d,B: u,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).

thf(1658,plain,
    ! [A: d,B: u,C: mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(304,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Ereal_2Ereal__lte @ C @ B ) ) )
      = ( ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2ESETOK__LE__LT) ).

thf(1679,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Ereal_2Ereal__lte @ C @ B ) ) )
      = ( ? [B: mono_2Etyop_2Erealax_2Ereal] : ( A @ B )
        & ? [B: mono_2Etyop_2Erealax_2Ereal] :
          ! [C: mono_2Etyop_2Erealax_2Ereal] :
            ( ( A @ C )
           => ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(272,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27c_29_2Ctyop_2Emin_2Ebool_29) ).

thf(1579,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Efcp_2Ecart @ tyop_2Emin_2Ebool @ A ) @ tyop_2Emin_2Ebool ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(321,axiom,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ mono_2Ec_2Emetric_2Edist_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Emetric_2Edist_2E0_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(1738,plain,
    ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ mono_2Ec_2Emetric_2Edist_2Emono_2Etyop_2Erealax_2Ereal ) )
    = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(196,axiom,
    ! [A: d,B: u,C: u,D: $o] :
      ( ~ D
      | ( ( s @ A @ C )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed018) ).

thf(1336,plain,
    ! [A: d,B: u,C: u,D: $o] :
      ( ~ D
      | ( ( s @ A @ C )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(161,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__NEG2) ).

thf(1220,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(72,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u] :
          ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
     => ! [D: u] :
          ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
         => ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EIMAGE__11__INFINITE) ).

thf(907,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u] :
          ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
     => ! [D: u] :
          ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) )
         => ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(463,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2EnormalForms_2EEXT__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) ) )
        = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( c_2EnormalForms_2EEXT__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EnormalForms_2EEXT__POINT__DEF) ).

thf(2224,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2EnormalForms_2EEXT__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) ) )
        = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( c_2EnormalForms_2EEXT__POINT_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(533,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Elim_2Etends__real__real @ A @ B @ D )
        & ( mono_2Ec_2Elim_2Etends__real__real @ A @ C @ D ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ELIM__UNIQ) ).

thf(2454,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Elim_2Etends__real__real @ A @ B @ D )
        & ( mono_2Ec_2Elim_2Etends__real__real @ A @ C @ D ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(336,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A )
      = ( ~ ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2Ereal__lt) ).

thf(1813,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A )
      = ( ~ ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(3251,plain,
    ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ c_2Emarker_2Eunint_2E0 ) ) ) ) ) )
     != ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
    | ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
     != ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1323,644]) ).

thf(3273,plain,
    ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Efloat__to__real_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ c_2Emarker_2Eunint_2E0 ) ) ) ) ) )
     != ( mono_2Ec_2Erealax_2Ereal__neg @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Eulp_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) )
    | ( ( tyop_2Ebinary__ieee_2Efloat @ sk1 @ sk2 )
     != ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) )
    | ( ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ sk1 @ sk2 ) ) @ c_2Ebool_2Ethe__value_2E0 ) )
     != ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ mono_2Ec_2Emarker_2Eunint_2Emono_2Etyop_2Erealax_2Ereal ) ) ),
    inference(simp,[status(thm)],[3251]) ).

thf(152,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ F ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__ind) ).

thf(1188,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u,E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
        & ! [D: u,E: u] :
            ( ? [F: u] :
                ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ F ) ) ) )
                & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) )
     => ! [D: u,E: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(579,axiom,
    ! [A: d,B: d] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__minus__min__def) ).

thf(2700,plain,
    ! [A: d,B: d] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__min_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(571,axiom,
    ! [A: d,B: u] :
      ( ( ? [C: u] :
          ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ C ) ) ) ) )
      = ( ? [C: u] :
          ! [D: u,E: u] :
          ? [F: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ E ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EOmega__Automata_2EELGOT1__THM) ).

thf(2675,plain,
    ! [A: d,B: u] :
      ( ( ? [C: u] :
          ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ C ) ) ) ) )
      = ( ? [C: u] :
          ! [D: u,E: u] :
          ? [F: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ E ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(171,axiom,
    ! [A: d,B: d,C: u,D: $o,E: u,F: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ E ) @ ( s @ A @ F ) ) ) ) )
      = ( s @ B @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RAND) ).

thf(1257,plain,
    ! [A: d,B: d,C: u,D: $o,E: u,F: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ E ) @ ( s @ A @ F ) ) ) ) )
      = ( s @ B @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(312,axiom,
    ! [A: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ B @ C @ D )
          = ( mono_2Ec_2Erealax_2Ereal__add @ ( B @ D ) @ ( C @ D ) ) )
     => ! [B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal,E: mono_2Etyop_2Erealax_2Ereal,F: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ( mono_2Ec_2Elim_2Etends__real__real @ B @ D @ F )
            & ( mono_2Ec_2Elim_2Etends__real__real @ C @ E @ F ) )
         => ( mono_2Ec_2Elim_2Etends__real__real @ ( A @ B @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ D @ E ) @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Elim_2ELIM__ADD) ).

thf(1702,plain,
    ! [A: ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > ( mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal] :
      ( ! [B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
          ( ( A @ B @ C @ D )
          = ( mono_2Ec_2Erealax_2Ereal__add @ ( B @ D ) @ ( C @ D ) ) )
     => ! [B: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal,E: mono_2Etyop_2Erealax_2Ereal,F: mono_2Etyop_2Erealax_2Ereal] :
          ( ( ( mono_2Ec_2Elim_2Etends__real__real @ B @ D @ F )
            & ( mono_2Ec_2Elim_2Etends__real__real @ C @ E @ F ) )
         => ( mono_2Ec_2Elim_2Etends__real__real @ ( A @ B @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ D @ E ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(178,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__IADD) ).

thf(1284,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ B @ C )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(377,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b1) ).

thf(1955,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(325,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = B )
      = ( A
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__LID__UNIQ) ).

thf(1749,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = B )
      = ( A
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(632,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Ebool_2Eitself @ A ) @ B )
      = ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EITSELF__UNIQUE) ).

thf(2860,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Ebool_2Eitself @ A ) @ B )
      = ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(355,axiom,
    ! [A: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29) ).

thf(1881,plain,
    ! [A: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(628,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NEG__NEG) ).

thf(2848,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__neg @ ( mono_2Ec_2Erealax_2Ereal__neg @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(473,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u] :
          ? [E: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ E ) ) )
            = ( s @ A @ D ) ) )
      = ( ? [D: u] :
          ! [E: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) ) )
            = ( s @ A @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ESURJECTIVE__RIGHT__INVERSE) ).

thf(2266,plain,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u] :
          ? [E: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ E ) ) )
            = ( s @ A @ D ) ) )
      = ( ? [D: u] :
          ! [E: u] :
            ( ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) ) )
            = ( s @ A @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(548,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( A @ B ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal) ).

thf(2500,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ ( A @ B ) ) )
      = ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(32,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ B ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29) ).

thf(744,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ B ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(136,axiom,
    ! [A: d,B: u,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
     => ( ! [D: u,E: u,F: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
       => ! [D: u,E: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINTER__DEF) ).

thf(1141,plain,
    ! [A: d,B: u,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
     => ( ! [D: u,E: u,F: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
       => ! [D: u,E: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(528,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => C )
      = ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
           => C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ELEFT__IMP__EXISTS__THM) ).

thf(2426,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => C )
      = ( ! [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
           => C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(258,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__ANTISYM) ).

thf(1536,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ B @ A ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1802,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ A ) ),
    inference(cnf,[status(esa)],[1801]) ).

thf(101,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EFINITE__INTER) ).

thf(1023,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(274,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ B @ C )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__LADD__IMP) ).

thf(1585,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ B @ C )
     => ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(89,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) ) ) )
      = ( ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ B @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EFORALL__IN__IMAGE) ).

thf(978,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) ) ) )
      = ( ! [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ B @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(637,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ A ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29) ).

thf(2875,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ A ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(534,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27e) ).

thf(2458,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(541,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27state_2CA_27state_29) ).

thf(2479,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ B ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ B ) @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Epair_2Eprod @ B @ B ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(306,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29) ).

thf(1685,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(212,axiom,
    ! [A: d,B: u,C: u,D: $o] :
      ( D
      | ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) )
        = ( s @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Ed019) ).

thf(1390,plain,
    ! [A: d,B: u,C: u,D: $o] :
      ( D
      | ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) @ ( s @ A @ C ) @ ( s @ A @ B ) ) )
        = ( s @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(126,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ? [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__cases) ).

thf(1108,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
      = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) )
        | ? [E: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(223,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Estate__transformer_2EREAD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Estate__transformer_2EREAD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Estate__transformer_2EREAD_2E2_2Emono_2EA_27a_20mono_2EA_27state) ).

thf(1421,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Estate__transformer_2EREAD_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ A ) @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Estate__transformer_2EREAD_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(396,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( ? [D: u] :
            ( B
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( B
        & ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__EXISTS__AND__THM) ).

thf(2013,plain,
    ! [A: d,B: $o,C: u] :
      ( ( ? [D: u] :
            ( B
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( B
        & ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(368,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1918,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(189,axiom,
    ! [A: d,B: $o > $o] :
      ( ! [C: $o] :
          ( ( B @ C )
          = ( ~ C ) )
     => ! [C: u,D: u,E: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ E ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er018) ).

thf(1316,plain,
    ! [A: d,B: $o > $o] :
      ( ! [C: $o] :
          ( ( B @ C )
          = ( ~ C ) )
     => ! [C: u,D: u,E: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ E ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(294,axiom,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A @ B ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A @ B ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A @ B ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1649,plain,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epath_2Epath @ A @ B ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epath_2Epath @ A @ B ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epath_2Epath @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epath_2Epath @ A @ B ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(502,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => C )
      = ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
           => C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2ELEFT__IMP__FORALL__THM) ).

thf(2352,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => C )
      = ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
           => C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(118,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u] :
          ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
          = ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
     => ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EINJECTIVE__IMAGE__FINITE) ).

thf(1084,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u] :
          ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ D ) ) )
            = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) ) )
          = ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
     => ! [D: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) )
          = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(618,axiom,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Emarker_2Eunint_2E1 @ ( s @ A @ B ) ) )
      = ( s @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emarker_2Eunint__def) ).

thf(2818,plain,
    ! [A: d,B: u] :
      ( ( s @ A @ ( c_2Emarker_2Eunint_2E1 @ ( s @ A @ B ) ) )
      = ( s @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(578,axiom,
    ! [A: d,B: d,C: u] :
      ~ ( ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C )
          = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C )
          = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebinary__ieee_2Efloat__infinities__distinct) ).

thf(2696,plain,
    ! [A: d,B: d,C: u] :
      ~ ( ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C )
          = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__plus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C )
          = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__minus__infinity_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Ebool_2Ethe__value_2E0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(263,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ETC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Etc__to__rel__conv) ).

thf(1553,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Etc_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Erelation_2ETC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(141,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2EA_27b) ).

thf(1157,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(343,axiom,
    ! [A: d,B: $o,C: $o,D: u,E: u,F: u,G: u] :
      ( ( ( B = C )
        & ( C
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
        & ( ~ C
         => ( ( s @ A @ F )
            = ( s @ A @ G ) ) ) )
     => ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ D ) @ ( s @ A @ F ) ) )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).

thf(1834,plain,
    ! [A: d,B: $o,C: $o,D: u,E: u,F: u,G: u] :
      ( ( ( B = C )
        & ( C
         => ( ( s @ A @ D )
            = ( s @ A @ E ) ) )
        & ( ~ C
         => ( ( s @ A @ F )
            = ( s @ A @ G ) ) ) )
     => ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) @ ( s @ A @ D ) @ ( s @ A @ F ) ) )
        = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ A @ E ) @ ( s @ A @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(493,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27d_20mono_2EA_27e) ).

thf(2325,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(37,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(759,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(180,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etendsto_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ B ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etendsto_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Enets_2Etendsto_2E3_2Emono_2EA_27a) ).

thf(1289,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etendsto_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ B ) @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Enets_2Etendsto_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(232,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
    ? [B: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Erealax_2Ereal__lt @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__BIGNUM) ).

thf(1453,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
    ? [B: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Erealax_2Ereal__lt @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(561,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( ! [D: u] :
            ( B
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( B
       => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__FORALL__IMP__THM) ).

thf(2643,plain,
    ! [A: d,B: $o,C: u] :
      ( ( ! [D: u] :
            ( B
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( B
       => ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(350,axiom,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            & D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ C ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ E @ F ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er022) ).

thf(1866,plain,
    ! [A: d,B: $o > $o > $o] :
      ( ! [C: $o,D: $o] :
          ( ( B @ C @ D )
          = ( C
            & D ) )
     => ! [C: u,D: u,E: $o,F: $o] :
          ( ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ E ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) @ ( s @ A @ C ) ) )
          = ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( B @ E @ F ) ) ) @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(565,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u] :
          ? [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) ) )
      = ( ? [D: u] :
          ! [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ESKOLEM__THM) ).

thf(2658,plain,
    ! [A: d,B: d,C: u] :
      ( ( ! [D: u] :
          ? [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) ) )
      = ( ? [D: u] :
          ! [E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(320,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ A @ F ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ A @ G ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
       => ( ! [E: u,F: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) ) ) )
         => ! [E: u,F: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EGSPEC__OR) ).

thf(1734,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ! [E: u,F: u,G: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ G ) @ ( s @ A @ F ) ) ) ) ) )
     => ( ! [E: u,F: u,G: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) @ ( s @ A @ G ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ G ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ G ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
       => ( ! [E: u,F: u] :
              ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
              = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) @ ( s @ A @ F ) ) ) ) ) )
         => ! [E: u,F: u] :
              ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(41,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27a) ).

thf(771,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(81,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__COMM) ).

thf(946,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(287,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
      = ( ~ ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2Ereal__lte) ).

thf(1629,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
      = ( ~ ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(346,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ C )
        = ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__EQ__RADD) ).

thf(1854,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ C )
        = ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(91,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) )
      = ( ! [E: u,F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Erextension) ).

thf(995,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) )
      = ( ! [E: u,F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(293,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1646,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eordinal_2Eordinal @ A ) @ tyop_2Emin_2Ebool ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(532,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
         => C )
        = ( ! [D: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
             => C ) ) )
      & ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
          & C )
        = ( ? [D: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
              & C ) ) )
      & ( ( C
          & ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
        = ( ? [D: u] :
              ( C
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EPULL__EXISTS) ).

thf(2443,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
         => C )
        = ( ! [D: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
             => C ) ) )
      & ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
          & C )
        = ( ? [D: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
              & C ) ) )
      & ( ( C
          & ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) )
        = ( ? [D: u] :
              ( C
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(449,axiom,
    ! [A: d,B: u] :
      ( ( ~ ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      = ( ? [C: u] :
            ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ENOT__FORALL__THM) ).

thf(2174,plain,
    ! [A: d,B: u] :
      ( ( ~ ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) )
      = ( ? [C: u] :
            ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(239,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
     => ? [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__MEAN) ).

thf(1476,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
     => ? [C: mono_2Etyop_2Erealax_2Ereal] :
          ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ C )
          & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(198,axiom,
    ! [A: d,B: u,C: u,D: mono_2Etyop_2Erealax_2Ereal,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2EB_2E3 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ D ) ) ) ) @ ( s @ A @ E ) ) ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) ) ) ) @ D ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2Eball) ).

thf(1341,plain,
    ! [A: d,B: u,C: u,D: mono_2Etyop_2Erealax_2Ereal,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emetric_2EB_2E3 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ D ) ) ) ) @ ( s @ A @ E ) ) ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) ) ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(70,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ? [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) ) ) )
      = ( ? [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ B @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EEXISTS__IN__IMAGE) ).

thf(896,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ? [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ F ) ) ) ) ) )
      = ( ? [F: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ B @ F ) @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ E ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ D ) @ ( s @ B @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(363,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__ADDR) ).

thf(1903,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(521,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28A_27a_29_20mono_2EA_27a) ).

thf(2406,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(111,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__OVER__INTER) ).

thf(1062,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EINTER_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(249,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ~ ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__NOT__LE) ).

thf(1508,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ~ ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(168,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ADD2) ).

thf(1244,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal,D: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ C @ D ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(601,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
      = ( ( s @ A @ C )
        = ( s @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__SYM__EQ) ).

thf(2764,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ B )
        = ( s @ A @ C ) )
      = ( ( s @ A @ C )
        = ( s @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(339,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__RNEG) ).

thf(1822,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ ( mono_2Ec_2Erealax_2Ereal__neg @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(103,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29) ).

thf(1030,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(420,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29) ).

thf(2081,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(513,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2384,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ A ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(7,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a) ).

thf(667,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(457,axiom,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ C ) ) ) ) ) )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2EMETRIC__SAME) ).

thf(2198,plain,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ C ) ) ) ) ) )
      = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(445,axiom,
    ! [A: d,B: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ B ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ B ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29) ).

thf(2162,plain,
    ! [A: d,B: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ B ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ B ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(452,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( B
        | ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ? [D: u] :
            ( B
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__OR__EXISTS__THM) ).

thf(2183,plain,
    ! [A: d,B: $o,C: u] :
      ( ( B
        | ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ? [D: u] :
            ( B
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(432,axiom,
    ! [A: d,B: d,C: u] :
      ( ( ? [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) ) )
      = ( ? [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ESWAP__EXISTS__THM) ).

thf(2120,plain,
    ! [A: d,B: d,C: u] :
      ( ( ? [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ D ) ) ) @ ( s @ B @ E ) ) ) ) )
      = ( ? [D: u,E: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ E ) ) ) @ ( s @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(489,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27i_20mono_2EA_27j) ).

thf(2315,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(390,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( s @ A @ C )
       != ( s @ A @ D ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2EMETRIC__NZ) ).

thf(1994,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( s @ A @ C )
       != ( s @ A @ D ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(398,axiom,
    ! [A: d,B: u] :
      ( ( ! [C: u,D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) )
            = ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ C ) ) ) )
        & ! [C: u,D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ C ) ) ) ) )
        & ! [C: u,D: u,E: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EEQUIV__REFL__SYM__TRANS) ).

thf(2019,plain,
    ! [A: d,B: u] :
      ( ( ! [C: u,D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) )
            = ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) )
              = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( ! [C: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ C ) ) ) )
        & ! [C: u,D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ C ) ) ) ) )
        & ! [C: u,D: u,E: u] :
            ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) ) ) )
              & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ A @ E ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(71,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
         => ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) )
            = ( ( s @ A @ E )
              = ( s @ A @ F ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
        = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecardinal_2EFINITE__IMAGE__INJ_27) ).

thf(899,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u,F: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ E ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ F ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) )
         => ( ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) )
              = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) )
            = ( ( s @ A @ E )
              = ( s @ A @ F ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EIMAGE_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) )
        = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(298,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      = ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__LE) ).

thf(1661,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      = ( ( mono_2Ec_2Ereal_2Ereal__lte @ A @ B )
        & ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(465,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29) ).

thf(2230,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal > $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(482,axiom,
    ! [A: d,B: d,C: u,D: u,E: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ E ) ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ c_2Ebinary__ieee_2Eclosest__such_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2294,plain,
    ! [A: d,B: d,C: u,D: u,E: mono_2Etyop_2Erealax_2Ereal] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Eclosest__such_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ E ) ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ c_2Ebinary__ieee_2Eclosest__such_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(404,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d) ).

thf(2036,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(592,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Elargest_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Elargest_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Elargest_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2739,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Elargest_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Elargest_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(546,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( B
        & ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ! [D: u] :
            ( B
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__AND__FORALL__THM) ).

thf(2494,plain,
    ! [A: d,B: $o,C: u] :
      ( ( B
        & ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) )
      = ( ! [D: u] :
            ( B
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(229,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29) ).

thf(1444,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(393,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27state) ).

thf(2003,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(433,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ B @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b) ).

thf(2123,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ B @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(510,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2374,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(426,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29) ).

thf(2102,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(328,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LET__ADD) ).

thf(1774,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(55,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u,H: u,I: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ H ) ) ) @ ( s @ A @ I ) ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ H ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ I ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EEQUALS__RSP) ).

thf(833,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u,H: u,I: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ H ) ) ) @ ( s @ A @ I ) ) ) ) )
         => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ H ) ) ) )
            = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ I ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(466,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => ( ( s @ A @ D )
         != ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EIMP__NEG__CONTRA) ).

thf(2233,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
       => ( ( s @ A @ D )
         != ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(353,axiom,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1876,plain,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(240,axiom,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1480,plain,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(29,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(735,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(617,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ C )
        = ( s @ A @ B ) )
      = ( ( s @ A @ B )
        = ( s @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EHolSmt_2Er001) ).

thf(2815,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( s @ A @ C )
        = ( s @ A @ B ) )
      = ( ( s @ A @ B )
        = ( s @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(591,axiom,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29) ).

thf(2736,plain,
    ! [A: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(61,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29) ).

thf(854,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(255,axiom,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1527,plain,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(138,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29) ).

thf(1148,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Eoption_2Eoption @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Eoption_2Eoption @ B ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Eoption_2Eoption @ A ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(612,axiom,
    ! [A: d,B: d,C: u] :
    ? [D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__CASES) ).

thf(2800,plain,
    ! [A: d,B: d,C: u] :
    ? [D: u,E: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ B @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(458,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ? [F: u] :
            ( ! [G: u] :
                ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ B @ G ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ F ) ) ) ) ) )
      = ( ! [F: u] :
            ( ~ ! [G: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ G ) ) ) @ ( s @ B @ F ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ B @ F ) ) ) ) )
       => ? [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EMOVE__EXISTS__IMP__THM) ).

thf(2201,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( ? [F: u] :
            ( ! [G: u] :
                ( ~ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ F ) ) ) @ ( s @ B @ G ) ) ) )
               => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ B @ G ) ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ F ) ) ) ) ) )
      = ( ! [F: u] :
            ( ~ ! [G: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ E ) @ ( s @ A @ G ) ) ) @ ( s @ B @ F ) ) ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ B @ F ) ) ) ) )
       => ? [F: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ A @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(496,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( ( s @ A @ C )
        = ( s @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2EMETRIC__ZERO) ).

thf(2334,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( ( s @ A @ C )
        = ( s @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(453,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27input_20mono_2EA_27state) ).

thf(2186,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(595,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ B @ ( c_2Ebool_2Eitself__case_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ B @ C ) ) )
      = ( s @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Eitself__case__thm) ).

thf(2746,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ B @ ( c_2Ebool_2Eitself__case_2E2 @ ( s @ ( tyop_2Ebool_2Eitself @ A ) @ c_2Ebool_2Ethe__value_2E0 ) @ ( s @ B @ C ) ) )
      = ( s @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(416,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] :
            ( ( ( s @ A @ C )
              = ( s @ A @ D ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EUNWIND__THM1) ).

thf(2070,plain,
    ! [A: d,B: u,C: u] :
      ( ( ? [D: u] :
            ( ( ( s @ A @ C )
              = ( s @ A @ D ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(104,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ B ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) ).

thf(1033,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ B ) @ C ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ B ) @ C ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(83,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: $o,G: u,H: u] :
          ( ( s @ B @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ B @ G ) @ ( s @ B @ H ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ G ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ H ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2ECOND__PRS) ).

thf(955,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: $o,G: u,H: u] :
          ( ( s @ B @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ B @ G ) @ ( s @ B @ H ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ F ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ G ) ) ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ H ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(337,axiom,
    ! [A: d,B: d,C: $o,D: u,E: u,F: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
      = ( s @ B @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__RATOR) ).

thf(1816,plain,
    ! [A: d,B: d,C: $o,D: u,E: u,F: u] :
      ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) ) ) @ ( s @ A @ F ) ) )
      = ( s @ B @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ E ) @ ( s @ A @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(245,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__ADD__ASSOC) ).

thf(1495,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( mono_2Ec_2Erealax_2Ereal__add @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(219,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( mono_2Ec_2Enets_2Etendsto_2Emono_2Etyop_2Erealax_2Ereal @ A ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Ec_2Enets_2Etendsto_2E1_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(1410,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ ( mono_2Ec_2Enets_2Etendsto_2Emono_2Etyop_2Erealax_2Ereal @ A ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( c_2Enets_2Etendsto_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(525,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2417,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( c_2Ebinary__ieee_2Efloat__negate_2E1 @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) ) @ c_2Ebinary__ieee_2Efloat__negate_2E0 ) @ ( s @ ( tyop_2Ebinary__ieee_2Efloat @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(109,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(1056,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eoption_2Eoption @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Eoption_2Eoption @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(6,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29) ).

thf(664,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ B ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ C ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ ( tyop_2Eoption_2Eoption @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(553,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EREP__prod_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2EREP__prod_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Epair_2EREP__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2619,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EREP__prod_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2EREP__prod_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(112,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ F ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) ) ) ) ) @ ( s @ A @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__REP__ABS) ).

thf(1065,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ F ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ F ) ) ) ) ) ) ) @ ( s @ A @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(24,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u,H: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ H ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__TRANS) ).

thf(720,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u,G: u,H: u] :
          ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ G ) ) ) )
            & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ G ) ) ) @ ( s @ A @ H ) ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ A @ F ) ) ) @ ( s @ A @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(498,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( A @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(2340,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > $o,B: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( A @ B ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29 @ A ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(121,axiom,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__IDEMPOT) ).

thf(1093,plain,
    ! [A: d,B: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(444,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ B @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27a) ).

thf(2159,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ C ) @ ( s @ A @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ B @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ B @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ B @ C ) ) ) @ ( s @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(613,axiom,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Emetric_2EMETRIC__SYM) ).

thf(2803,plain,
    ! [A: d,B: u,C: u,D: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ D ) @ ( s @ A @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(208,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A = B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Erealax_2EREAL__LT__TOTAL) ).

thf(1378,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( A = B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B )
      | ( mono_2Ec_2Erealax_2Ereal__lt @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(273,axiom,
    ! [A: d,B: u,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etendsto_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) )
      = ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Enets_2Etendsto) ).

thf(1582,plain,
    ! [A: d,B: u,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Enets_2Etendsto_2E3 @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ A ) @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ A @ C ) ) ) @ ( s @ A @ D ) @ ( s @ A @ E ) ) ) )
      = ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) )
        & ( mono_2Ec_2Ereal_2Ereal__lte @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ D ) ) ) ) ) ) @ ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ A @ E ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(537,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u] :
            ( ( ( s @ A @ D )
              = ( s @ A @ C ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EUNWIND__FORALL__THM2) ).

thf(2467,plain,
    ! [A: d,B: u,C: u] :
      ( ( ! [D: u] :
            ( ( ( s @ A @ D )
              = ( s @ A @ C ) )
           => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(25,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29) ).

thf(723,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Elist_2Elist @ A ) @ ( tyop_2Elist_2Elist @ A ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ B ) ) ) @ ( s @ ( tyop_2Elist_2Elist @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(575,axiom,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29) ).

thf(2687,plain,
    ! [A: mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(63,axiom,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ C @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ C @ A ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27c_20mono_2EA_27a) ).

thf(871,plain,
    ! [A: d,B: d,C: d,D: u,E: u] :
      ( ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ C @ A ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) )
      = ( s @ ( tyop_2Epath_2Epath @ B @ C ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ C @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ C @ A ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ C @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epath_2Epath @ B @ C ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(437,axiom,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emetric_2Edist_2E2_2Emono_2EA_27b) ).

thf(2138,plain,
    ! [A: d,B: u,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Emetric_2Edist_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ A ) @ tyop_2Erealax_2Ereal ) ) @ c_2Emetric_2Edist_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(210,axiom,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Esum_2Esum @ A @ B ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A @ B ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1384,plain,
    ! [A: d,B: d,C: u,D: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Esum_2Esum @ A @ B ) @ C ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A @ B ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Esum_2Esum @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A @ B ) @ C ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(543,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EABS__prod_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Epair_2EABS__prod_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Epair_2EABS__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b) ).

thf(2485,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2EABS__prod_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ c_2Epair_2EABS__prod_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(384,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__EXT) ).

thf(1976,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C ) @ ( s @ A @ E ) ) )
          = ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ E ) ) ) )
     => ( ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ C )
        = ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(262,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LE__ADDL) ).

thf(1550,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Ereal_2Ereal__lte @ B @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) )
      = ( mono_2Ec_2Ereal_2Ereal__lte @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(248,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Ebool) ).

thf(1505,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Eoption_2Eoption @ A ) ) @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(215,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__ADD__RID) ).

thf(1399,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(284,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__ADD) ).

thf(1621,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ A )
        & ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ B ) )
     => ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(282,axiom,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Erel__to__reln__inv) ).

thf(1606,plain,
    ! [A: d,B: d,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Eset__relation_2Erel__to__reln_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(639,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eseq_2EK__PARTIAL) ).

thf(2881,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ A @ ( c_2Ecombin_2EK_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(96,axiom,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EGSPEC__PAIR__ETA) ).

thf(1009,plain,
    ! [A: d,B: d,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) )
          = ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) @ ( s @ A @ E ) ) ) @ ( s @ B @ F ) ) ) ) ) )
     => ! [D: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2EUNCURRY_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(641,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Erealax_2Ereal) ).

thf(2887,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( i_mono_2Etyop_2Erealax_2Ereal @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(634,axiom,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Ethreshold_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27t_20mono_2EA_27w) ).

thf(2866,plain,
    ! [A: d,B: d,C: u] :
      ( ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( c_2Ebinary__ieee_2Ethreshold_2E1 @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) )
      = ( j_mono_2Etyop_2Erealax_2Ereal @ ( s @ tyop_2Erealax_2Ereal @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ tyop_2Erealax_2Ereal ) @ c_2Ebinary__ieee_2Ethreshold_2E0 ) @ ( s @ ( tyop_2Ebool_2Eitself @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(344,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Ebool) ).

thf(1848,plain,
    ! [A: d,B: u,C: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(483,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ C @ ( c_2Epair_2ECURRY_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ D ) @ ( s @ A @ E ) @ ( s @ B @ F ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2ECURRY__DEF) ).

thf(2297,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ C @ ( c_2Epair_2ECURRY_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ D ) @ ( s @ A @ E ) @ ( s @ B @ F ) ) )
      = ( s @ C @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ C ) @ D ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ E ) @ ( s @ B @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(221,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( B
        = ( mono_2Ec_2Erealax_2Ereal__neg @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__RNEG__UNIQ) ).

thf(1416,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal] :
      ( ( ( mono_2Ec_2Erealax_2Ereal__add @ A @ B )
        = ( mono_2Ec_2Ereal_2Ereal__of__num @ mono_2Ec_2Enum_2E0 ) )
      = ( B
        = ( mono_2Ec_2Erealax_2Ereal__neg @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(10,axiom,
    ! [A: d,B: u,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
     => ( ! [D: u,E: u,F: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
       => ! [D: u,E: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epred__set_2EUNION__DEF) ).

thf(676,plain,
    ! [A: d,B: u,C: u] :
      ( ! [D: u,E: u,F: u] :
          ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) )
          = ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) )
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EIN_2E2 @ ( s @ A @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ F ) ) ) ) ) )
     => ( ! [D: u,E: u,F: u] :
            ( ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) @ ( s @ A @ F ) ) )
            = ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ F ) @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) ) ) @ B ) @ ( s @ A @ F ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) )
       => ! [D: u,E: u] :
            ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EUNION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) )
            = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Epred__set_2EGSPEC_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ tyop_2Emin_2Ebool ) ) ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ E ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(422,axiom,
    ! [A: d,B: $o,C: u] :
      ( ( ! [D: u] :
            ( B
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( B
        | ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ERIGHT__FORALL__OR__THM) ).

thf(2087,plain,
    ! [A: d,B: $o,C: u] :
      ( ( ! [D: u] :
            ( B
            | ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) )
      = ( B
        | ! [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ C ) @ ( s @ A @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(570,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Emetric_2EB_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Emetric_2EB_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Emetric_2EB_2E2_2Emono_2EA_27a) ).

thf(2672,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( c_2Emetric_2EB_2E2 @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ C ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ A ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) ) @ c_2Emetric_2EB_2E0 ) @ ( s @ ( tyop_2Emetric_2Emetric @ A ) @ B ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ tyop_2Erealax_2Ereal ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(560,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ D )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eset__relation_2Ereln__to__rel__11) ).

thf(2640,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ D ) ) )
        = ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ tyop_2Emin_2Ebool ) ) @ ( c_2Eset__relation_2Ereln__to__rel_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ) )
      = ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ D )
        = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ B ) @ tyop_2Emin_2Ebool ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(491,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c) ).

thf(2321,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ C ) @ ( s @ B @ D ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ B ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Epair_2Eprod @ A @ B ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ C ) ) ) @ ( s @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(373,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__REFL) ).

thf(1944,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal] :
      ~ ( mono_2Ec_2Erealax_2Ereal__lt @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(79,axiom,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) )
          = ( s @ B @ F ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Equotient_2EQUOTIENT__ABS__REP) ).

thf(940,plain,
    ! [A: d,B: d,C: u,D: u,E: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) ) @ C ) @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) ) ) )
     => ! [F: u] :
          ( ( s @ B @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ B ) @ D ) @ ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ A ) @ E ) @ ( s @ B @ F ) ) ) ) )
          = ( s @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(576,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27state_20mono_2EA_27state) ).

thf(2690,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A @ B ) @ ( s @ A @ C ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ A @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Epair_2Eprod @ A @ A ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A @ B ) ) ) @ ( s @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(267,axiom,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ereal_2EREAL__LT__RADD) ).

thf(1565,plain,
    ! [A: mono_2Etyop_2Erealax_2Ereal,B: mono_2Etyop_2Erealax_2Ereal,C: mono_2Etyop_2Erealax_2Ereal] :
      ( ( mono_2Ec_2Erealax_2Ereal__lt @ ( mono_2Ec_2Erealax_2Ereal__add @ A @ C ) @ ( mono_2Ec_2Erealax_2Ereal__add @ B @ C ) )
      = ( mono_2Ec_2Erealax_2Ereal__lt @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(236,axiom,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_29 @ A ) ) @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29) ).

thf(1468,plain,
    ! [A: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29,B: mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emin_2Efun @ tyop_2Erealax_2Ereal @ ( tyop_2Epair_2Eprod @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29_29 @ A ) ) @ ( s @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) @ ( i_mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29 @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(538,axiom,
    ! [A: $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,B: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29) ).

thf(2470,plain,
    ! [A: $o > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29,B: $o] :
      ( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29 @ ( A @ B ) ) )
      = ( s @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29 @ A ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(20,axiom,
    ! [A: d,B: u,C: u] :
      ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ A ) ) @ C ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ A ) ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ A ) ) @ A ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29) ).

thf(708,plain,
    ! [A: d,B: u,C: u] :
      ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ A ) ) @ C ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ A ) ) @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ A ) ) @ A ) ) @ c_2Epair_2Epair__CASE_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) ) @ B ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A @ ( tyop_2Emin_2Efun @ ( tyop_2Elist_2Elist @ tyop_2Emin_2Ebool ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(366,axiom,
    ! [A: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ A ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29) ).

thf(1912,plain,
    ! [A: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal ) > mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) @ tyop_2Erealax_2Ereal ) @ ( tyop_2Emetric_2Emetric @ tyop_2Erealax_2Ereal ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29 @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(450,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ E ) @ ( s @ C @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) @ ( s @ B @ E ) ) ) @ ( s @ C @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Epair_2Epair__case__thm) ).

thf(2177,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( s @ A @ ( c_2Epair_2Epair__CASE_2E2 @ ( s @ ( tyop_2Epair_2Eprod @ B @ C ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ B @ E ) @ ( s @ C @ D ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) ) )
      = ( s @ A @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ C @ A ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ B @ ( tyop_2Emin_2Efun @ C @ A ) ) @ F ) @ ( s @ B @ E ) ) ) @ ( s @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(564,axiom,
    ! [A: d,B: u,C: $o] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        | C )
      = ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            | C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ELEFT__OR__EXISTS__THM) ).

thf(2655,plain,
    ! [A: d,B: u,C: $o] :
      ( ( ? [D: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
        | C )
      = ( ? [D: u] :
            ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A @ tyop_2Emin_2Ebool ) @ B ) @ ( s @ A @ D ) ) ) )
            | C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(4422,plain,
    $false,
    inference(e,[status(thm)],[645,1322,1036,1879,1369,2031,2263,893,2787,2331,777,1295,1950,1168,2306,1559,1105,2412,846,962,1982,1200,1211,2210,2117,683,2622,1522,2381,2395,741,1205,2099,1486,2309,762,2114,1269,2854,1533,1078,1655,1137,1310,2035,2141,1988,2042,670,2195,1705,1164,797,1872,2712,814,1327,2476,2168,1260,698,747,913,1196,1746,2046,2432,2227,1441,2010,1921,1359,1803,1518,2869,1887,651,2491,1127,1782,2400,2067,1967,1228,1623,1254,1709,2328,1985,2039,1298,2667,2269,2755,1323,1313,2488,2897,2126,1059,2703,1330,1860,1511,702,1577,1455,949,2745,817,1892,2857,2049,1319,2767,1609,1347,1568,2730,1641,1362,1545,2420,2403,1087,1514,2324,2090,1373,1632,1682,1828,2034,2073,1489,2237,2616,1465,756,1664,2794,2105,1450,1151,937,2291,1020,981,2058,1447,1072,1405,1600,2718,2833,2281,877,692,774,2371,998,2809,2392,1521,1696,2884,1863,2204,2473,1691,2364,1915,714,1438,661,3265,2646,1067,2790,2061,2773,2000,1274,2409,1223,2249,1174,1666,1387,1900,1723,2733,825,1217,2147,1502,820,2150,1370,2132,729,916,852,2872,1457,1819,830,1407,1740,1012,2464,2758,1365,2628,1027,2213,1402,1234,874,1851,1121,1006,2631,2724,1755,857,1592,2300,2377,650,1970,1111,2709,1498,1587,1096,1672,1160,1964,753,642,2240,2613,2108,1889,1039,1292,933,2830,1182,686,1075,1424,2312,1214,2349,2781,1419,837,2681,738,2845,1131,1050,1947,1715,1979,2272,1393,1525,1825,1114,1324,2285,1776,1263,1530,1539,2836,1266,2153,2387,1231,2851,2243,2355,1932,2006,2497,2052,2482,1246,1333,1991,1202,1779,2043,2076,2440,2189,1185,794,2423,2634,2749,1857,1241,2761,765,1712,1286,2368,2144,1906,2275,1483,689,2894,965,750,2028,1301,1595,1154,975,2727,1784,2791,843,1752,2016,711,2806,958,2398,1124,2827,732,1884,1652,1929,1428,1669,1707,1271,1635,1997,2055,2706,1090,1638,1675,1897,919,2358,1356,2346,2721,2084,1574,1589,1542,2669,2839,1307,2079,2361,2415,1894,2637,1117,2246,1492,1603,880,649,1801,1571,1376,2824,811,1471,2742,1339,2111,1344,1556,2278,2461,1688,890,2180,2025,2812,2129,2343,2625,1909,726,943,2664,1177,1381,2842,1952,1171,2770,1396,2365,1474,1699,2171,695,2288,2797,2022,2303,1102,2156,2207,1973,768,827,780,1643,2064,1015,1000,2752,1435,1726,2390,1694,922,2693,2506,1562,1413,1626,2096,1304,1166,1208,2652,1134,1081,2684,1340,1958,2318,2784,680,2878,2503,1145,1018,1181,823,1798,1003,2715,1961,2661,705,971,1941,2678,2821,1098,2863,1598,1225,1743,2192,887,1053,673,2165,717,1869,840,2429,2337,1830,1658,1679,1579,1738,1336,1220,907,2224,2454,1813,3273,1188,2700,2675,1257,1702,1284,1955,1749,2860,2892,1881,2848,2266,2500,744,1141,2426,1536,1802,1023,1585,978,2875,2458,2479,1685,1390,1108,1421,2013,1918,1316,1649,2352,1084,2818,1180,2696,1553,1157,1834,2325,759,1289,1453,2643,1866,2658,1734,771,946,1629,1854,995,1646,2443,2174,1476,1341,896,1903,2406,1062,1508,1244,2764,1822,1030,2081,2384,2399,667,2198,2162,2183,2120,2315,1994,2019,899,1661,2230,2294,2036,2739,2494,1444,2003,2123,2374,2102,1774,833,2233,1876,1480,735,2815,2736,854,1527,1148,2800,2201,2334,2186,2746,2070,1033,955,1816,1495,1410,2417,1056,664,2619,1065,720,2340,1093,2159,2803,1378,1582,2467,723,2687,871,2138,1384,2485,1976,644,1550,1505,1399,1621,1606,2881,1009,2887,2866,1848,2297,1416,676,2087,2672,2640,2321,1944,1367,940,2690,1565,1468,2470,708,1912,2177,2655]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ITP018^4 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20  % Computer : n011.cluster.edu
% 0.10/0.20  % Model    : x86_64 x86_64
% 0.10/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20  % Memory   : 8046.5625MB
% 0.10/0.20  % OS       : Linux 6.8.0-71-generic
% 0.10/0.20  % CPULimit : 300
% 0.10/0.20  % WCLimit  : 300
% 0.10/0.20  % DateTime : Tue Sep 29 19:33:05 UTC 2026
% 0.10/0.21  % CPUTime  : 
% 0.10/0.21  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.78  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 19.11/10.68  % [INFO] 	 Parsing done (9894ms). 
% 19.26/10.76  % [INFO] 	 Running in sequential loop mode. 
% 19.90/11.13  % [INFO] 	 eprover registered as external prover. 
% 19.90/11.14  % [INFO] 	 Scanning for conjecture ... 
% 25.45/14.08  % [INFO] 	 Found a conjecture (or negated_conjecture) and 34036 axioms. Running axiom selection ... 
% 34.63/21.83  % [INFO] 	 Axiom selection finished. Selected 639 axioms (removed 33397 axioms). 
% 37.21/22.84  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 37.21/22.90  % [INFO] 	 Type checking passed. 
% 37.45/22.90  % [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 ... 
% 131.66/61.80  % External prover 'e' found a proof!
% 131.66/61.81  % [INFO] 	 Killing All external provers ... 
% 131.66/61.81  % Time passed: 61465ms (effective reasoning time: 51043ms)
% 131.66/61.81  % 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)>
% 131.66/61.82  % Axioms used in derivation (639): ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29, arityeq2_2Ec_2Emetric_2Edist_2E2_2Emono_2EA_27a, thm_2Epred__set_2EINTER__ASSOC, thm_2Epred__set_2EIN__ABS, thm_2Ereal_2EREAL__LT__NZ, thm_2Epred__set_2EIN__UNION, thm_2Ereal_2EREAL__NEG__GT0, thm_2Ereal_2EREAL__LE__NEGL, thm_2EHolSmt_2Er022, thm_2Eset__relation_2Etc__union, arityeq1_2Ec_2Eset__relation_2Efchains_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Epair_2EABS__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b, thm_2Ereal_2EREAL__RNEG__UNIQ, thm_2Ebool_2ERIGHT__AND__FORALL__THM, thm_2Eint__arith_2ECONJ__EQ__ELIM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27d_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, thm_2Efmapal_2EAP__SND, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_20mono_2EA_27b_20mono_2EA_27a, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool, thm_2Epred__set_2EIMAGE__DEF, thm_2Ereal_2EREAL__NEG__LE0, thm_2Equotient_2EQUOTIENT__REL__REP, thm_2Ebool_2ECOND__ABS, thm_2Eset__relation_2Ereln__to__rel__inv, arityeq3_2Ec_2Enets_2Etendsto_2E3_2Emono_2EA_27a, thm_2Ecardinal_2EINFINITE__IMAGE__INJ, thm_2Ebool_2ERIGHT__FORALL__IMP__THM, thm_2Ereal_2EREAL__ADD__LID, thm_2Equotient_2EQUOTIENT__ABS__REP, thm_2Ebool_2EETA__THM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_2Ctyop_2Emin_2Ebool_29, thm_2Epred__set_2EEXISTS__IN__IMAGE, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, ji_2Emono_2Etyop_2Emin_2Ebool, thm_2Epred__set_2EIMAGE__IN, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29, thm_2Ecardinal_2ELEFT__IMP__EXISTS__THM, thm_2Ebinary__ieee_2Efloat__infinities, arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq1_2Ec_2Emarker_2Estmarker_2E1_2Emono_2EA_27a, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27e_20mono_2EA_27f, thm_2EHolSmt_2Er020, thm_2Epred__set_2EIMAGE__ID, thm_2EHolSmt_2Ed020, thm_2Ecardinal_2EINJECTIVE__IMAGE, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27b_29, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29, thm_2Ebool_2ELEFT__OR__EXISTS__THM, thm_2Epred__set_2EINJECTIVE__IMAGE__FINITE, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27e, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27b, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29, thm_2Ebool_2EFORALL__AND__THM, thm_2Ereal_2EREAL__LET__ADD, thm_2Estate__transformer_2EUNIT__DEF, thm_2Emetric_2Eball, thm_2Ecombin_2EAPP__DEF, thm_2EOmega__Automata_2EELGOT2__THM, thm_2Epred__set_2EFINITE__UNION, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29, thm_2Ereal_2EREAL__ADD__RINV, thm_2Eposet_2Erelation__def, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, thm_2Ebool_2EFUN__EQ__THM, thm_2Ereal_2EREAL__LE__LT, thm_2Ereal_2EREAL__LT__TRANS, thm_2Ereal_2Ereal__lte, thm_2Eset__relation_2Etc__strongind, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29, thm_2Ecardinal_2ESURJECTIVE__IMAGE, thm_2Ebinary__ieee_2Efloat__minus__zero__def, arityeq1_2Ec_2Eposet_2Ecarrier_2E1_2Emono_2EA_27a, thm_2EHolSmt_2Er023, thm_2Ebool_2EEQ__EXT, thm_2Ereal_2EREAL__NEGNEG, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27d_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, thm_2Ereal_2EREAL__LE__EPSILON, thm_2Epred__set_2EIN__IMAGE, thm_2Epred__set_2EFORALL__IN__UNION, thm_2Ewords_2EWORD__FINITE, ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29, thm_2Emetric_2EMETRIC__SYM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27c, thm_2Ecardinal_2EUNION__ACI, monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool, arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w, thm_2Eset__relation_2Etc__ind__left, thm_2Eset__relation_2Erel__to__reln__def, thm_2Ebool_2EIN__DEF, thm_2EHolSmt_2Er021, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27c_20mono_2EA_27a, thm_2Ecardinal_2EFINITE__IMAGE__INJ__GENERAL, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29, thm_2EOmega__Automata_2EELGOT__LEMMA, thm_2Enets_2EDORDER__TENDSTO, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Ebool_2Eitself_28A_27t_29, thm_2Ebool_2Eitself__Axiom, thm_2EHolSmt_2Er219, thm_2Ereal_2ESUP__LEMMA2, thm_2Estate__transformer_2EBIND__RIGHT__UNIT, thm_2Ereal_2EREAL__NEG__NEG, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29, thm_2Emarker_2Eunint__def, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29, thm_2Ebinary__ieee_2Efloat__negate__negate, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29, thm_2Ecardinal_2EOR__EXISTS__THM, thm_2Ebool_2ECOND__RAND, thm_2Equotient_2ECOND__PRS, thm_2Ereal_2EREAL__OF__NUM__EQ, thm_2Eind__type_2EINJ__INVERSE2, arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__infinity_2E1_2Emono_2EA_27t_20mono_2EA_27w, thm_2Ereal_2ESETOK__LE__LT, thm_2Ereal_2Ereal__lt, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Emin_2Ebool, arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w, thm_2Ecardinal_2EINJECTIVE__LEFT__INVERSE, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27a_20mono_2EA_27b, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27state_2CA_27state_29, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27a_20mono_2EA_27c, thm_2Ecardinal_2ESURJECTIVE__RIGHT__INVERSE, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29, monoeq_2Emono_2Ec_2Emetric_2Emetric_2E0_2Emono_2Etyop_2Erealax_2Ereal, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28A_27a_29_20mono_2EA_27a, thm_2Ereal_2EREAL__LTE__ANTSYM, thm_2Ereal_2EREAL__LTE__ANTISYM, thm_2Epair_2Epair__case__cong, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27c_29_20mono_2Etyop_2Emin_2Ebool, thm_2Eset__relation_2Etc__cases__right, thm_2Ebool_2EEXISTS__OR__THM, thm_2Ebool_2ERIGHT__EXISTS__IMP__THM, thm_2Epair_2EPAIR__EQ, thm_2EHolSmt_2Ed018, thm_2Epred__set_2EFINITELY__INJECTIVE__IMAGE__FINITE, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29, thm_2Ereal_2EREAL__LET__TOTAL, thm_2Eset__relation_2Euniv__reln__def, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27b_29_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2ERPROD_2E2_2Emono_2EA_27a_20mono_2EA_27b, thm_2Ereal_2EREAL__LT__GT, thm_2Ewellorder_2EINJECTIVE__LEFT__INVERSE__NONEMPTY, monoeq_2Emono_2Ec_2Enets_2Etendsto_2E1_2Emono_2Etyop_2Erealax_2Ereal, thm_2Erealax_2EREAL__ADD__ASSOC, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool, thm_2Ereal_2EREAL__LET__ANTISYM, thm_2Emetric_2EMETRIC__TRIANGLE, ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29, thm_2EreaderMonad_2EUNIT__def, thm_2Ebool_2ESKOLEM__THM, arityeq1_2Ec_2Ebinary__ieee_2Efloat__to__real_2E1_2Emono_2EA_27a_20mono_2EA_27b, monoeq_2Emono_2Ec_2Enets_2Etendsto_2E0_2Emono_2Etyop_2Erealax_2Ereal, thm_2Ebinary__ieee_2Efloat__distinct, thm_2Ereal_2EREAL__LT__NEGTOTAL, thm_2Ereal_2EREAL__LE__TOTAL, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c, arityeq1_2Ec_2Ebinary__ieee_2Eulp_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool, thm_2EquantHeuristics_2EUNWIND__EXISTS__THM, thm_2EquantHeuristics_2EEXISTS__NOT__FORALL__THM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29, thm_2Ebool_2ENOT__EXISTS__THM, thm_2Epair_2EPAIR__MAP__THM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27c_2CA_27d_29_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_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, arityeq2_2Ec_2Ebinary__ieee_2Eclosest_2E2_2Emono_2EA_27t_20mono_2EA_27w, thm_2Epair_2Epair__case__thm, thm_2Ereal_2EREAL__LE__ANTISYM, thm_2EHolSmt_2Ed017, thm_2Ebool_2EPULL__FORALL, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28A_27c_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29, arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__min_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq1_2Ec_2Emarker_2Eunint_2E1_2Emono_2EA_27a, thm_2Ereal_2EREAL__SUP__SOMEPOS, arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27i_20mono_2EA_27j, thm_2Emetric_2EMETRIC__NZ, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2EA_27b, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27a, thm_2Elim_2ELIM__CONST, thm_2Epair_2ERPROD__DEF, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29, thm_2Eset__relation_2Erel__to__reln__swap, thm_2Epred__set_2EGSPEC__ETA, ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, thm_2Eset__relation_2Erel__to__reln__inv, thm_2Epred__set_2EIN__GSPEC, thm_2Epred__set_2EFINITE__INTER, thm_2Ebool_2EABS__SIMP, thm_2Equotient_2EQUOTIENT__REP__REFL, thm_2Epath_2Eparallel__comp__def, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eordinal_2Eordinal_28A_27a_29_20mono_2Etyop_2Eordinal_2Eordinal_28A_27a_29, thm_2Ereal_2EREAL__BIGNUM, thm_2EConseqConv_2Eexists__eq__thm, thm_2Emarker_2Estmarker__def, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29_29_20mono_2EA_27a_20mono_2EA_27state, thm_2Epred__set_2EUNION__OVER__INTER, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29, thm_2Equotient_2EK__PRS, thm_2Ecardinal_2EFINITE__PRODUCT, thm_2EHolSmt_2Et005, thm_2Epred__set_2EFORALL__IN__IMAGE, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool, monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal, thm_2Ecardinal_2EFINITE__IMAGE__INJ__EQ, thm_2Ebool_2ERIGHT__OR__EXISTS__THM, thm_2Epair_2EFORALL__PROD, thm_2EHolSmt_2Er215, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27d_20mono_2EA_27e, thm_2Ebool_2ESWAP__EXISTS__THM, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal, arityeq2_2Ec_2Estate__transformer_2EREAD_2E2_2Emono_2EA_27a_20mono_2EA_27state, thm_2Ereal_2EREAL__LT__ANTISYM, thm_2Ereal_2ESUP__LEMMA1, thm_2Erelation_2ETC__IDEM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27c_2CA_27d_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29, thm_2Ebool_2EUNWIND__THM1, thm_2Emetric_2Emetric__tybij, thm_2Ebool_2EBETA__THM, thm_2Epred__set_2ESPECIFICATION, arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__infinite_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool, thm_2Eset__relation_2Etc__ind, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27c_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2EA_27b, thm_2EConseqConv_2Eforall__eq__thm, thm_2Ereal_2EREAL__ADD__LINV, thm_2Ereal_2EREAL__ADD__COMM, thm_2EnormalForms_2EEXT__POINT__DEF, thm_2Ewellorder_2Eseteq__wlog, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b, thm_2Epred__set_2EPAIR__IN__GSPEC__2, thm_2Ereal_2EREAL__LE__NEG, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2EA_27c, thm_2Ebinary__ieee_2EULP__ind, arityeq3_2Ec_2Emetric_2EB_2E3_2Emono_2EA_27a, thm_2Epred__set_2EIN__GSPEC__IFF, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27input_20mono_2EA_27state, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2Etyop_2Elist_2Elist_28A_27e_29, thm_2Ebool_2ELEFT__FORALL__IMP__THM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27c_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27c_29_2Ctyop_2Emin_2Ebool_29, thm_2Equotient_2EK__RSP, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27d, arityeq3_2Ec_2Ebinary__ieee_2Eclosest__such_2E3_2Emono_2EA_27t_20mono_2EA_27w, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27b, thm_2Ereal_2EREAL__LE__RADD, thm_2Ebool_2EUNWIND__THM2, thm_2Ereal_2EREAL__LT__NEG, thm_2Ereal_2EREAL__LNEG__UNIQ, ij_2Emono_2Etyop_2Erealax_2Ereal, thm_2Ereal_2EREAL__LE__RNEG, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27d, thm_2Epred__set_2EIMAGE__CONG, thm_2Emetric_2EMETRIC__ISMET, thm_2Eset__relation_2Ereln__to__rel__11, thm_2Ebinary__ieee_2Ezero__to__real, thm_2Equotient_2EQUOTIENT__TRANS, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29, thm_2Ereal_2EREAL__LET__ADD2, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27c_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29, thm_2Ebool_2Ebool__case__CONG, thm_2Ereal_2EREAL__LE__LNEG, thm_2Ereal_2EREAL__ADD__LID__UNIQ, thm_2EHolSmt_2Er019, thm_2EHolSmt_2Er024, thm_2Ebool_2ERIGHT__EXISTS__AND__THM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool, thm_2Etransc_2ETAN__0, thm_2Ereal_2EREAL__LT__TOTAL, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_2Ctyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27x_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool, thm_2Ebool_2EFORALL__itself, thm_2Ebool_2EEQ__TRANS, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, thm_2Ebool_2EEQ__REFL, ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29, thm_2Epred__set_2EINTER__IDEMPOT, thm_2Elim_2ELIM__ADD, thm_2Equotient_2EQUOTIENT__SYM, thm_2EOmega__Automata_2EEQUALITY__THM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a, thm_2Ereal_2EREAL__DOWN, thm_2Ecardinal_2ESURJECTIVE__ON__RIGHT__INVERSE, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b1, thm_2Eseq_2EK__PARTIAL, thm_2Eposet_2Ecarrier__def, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29, thm_2Equotient_2EQUOTIENT__REP__ABS, thm_2Epred__set_2EPAIR__IN__GSPEC__same, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27state_20mono_2EA_27state, thm_2Ereal_2EREAL__LE__NEG2, thm_2Ereal_2EREAL__INJ, thm_2Epair_2Epair__case__def, thm_2Ebool_2EEXISTS__itself, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29, thm_2Equotient_2EEQUALS__RSP, thm_2Ebinary__ieee_2Efloat__minus__infinity__def, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29_20mono_2EA_27b_20mono_2EA_27a, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29, thm_2EConseqConv_2ECOND__CLAUSES__ID, thm_2Ebool_2ECOND__CONG, thm_2Ereal_2EREAL__LT__IMP__LE, thm_2Equotient_2EQUOTIENT__def, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool, arityeq1_2Ec_2Emetric_2Emetric_2E1_2Emono_2EA_27a, thm_2Ebool_2ECOND__ID, thm_2Ereal_2EREAL__ADD__RID, arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27a_20mono_2EA_27b, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27w_29_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27t_29, thm_2Ereal_2EREAL__EQ__RADD, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b, thm_2Ebinary__ieee_2Efloat__to__real__negate, thm_2Ereal_2EREAL__MEAN, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_29, thm_2Ereal_2EREAL__LTE__TRANS, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b2, ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2EA_27a, thm_2Ebool_2EPULL__EXISTS, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27c_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29, thm_2Ecardinal_2EINJECTIVE__ON__LEFT__INVERSE, arityeq1_2Ec_2Ebinary__ieee_2Efloat__top_2E1_2Emono_2EA_27t_20mono_2EA_27w, thm_2Ebinary__ieee_2Efloat__minus__min__def, thm_2Epred__set_2EUNION__COMM, thm_2EHolSmt_2Er018, thm_2Erealax_2EREAL__ADD__SYM, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29, arityeq1_2Ec_2Ebinary__ieee_2Eclosest__such_2E1_2Emono_2EA_27a_20mono_2EA_27b, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool, thm_2Equotient_2EREP__ABS__RSP, thm_2Ecardinal_2ERIGHT__IMP__FORALL__THM, monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal, ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, thm_2Ereal_2EREAL__LE__NEGR, thm_2Ecardinal_2EIN__ELIM__PAIR__THM, thm_2Ecombin_2EK__THM, thm_2Epair_2Epair__case__eq, thm_2Ereal_2EREAL__LE__ADD2, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28A_27a_29_29, thm_2EHolSmt_2Er220, thm_2Epred__set_2EGSPEC__AND, thm_2Eset__relation_2Etc__ind__right, thm_2EquantHeuristics_2EIMP__NEG__CONTRA, thm_2Ebool_2EUNWIND__FORALL__THM2, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29, thm_2Epred__set_2EGSPEC__PAIR__ETA, arityeq1_2Ec_2Epair_2EREP__prod_2E1_2Emono_2EA_27a_20mono_2EA_27b, thm_2Elim_2ELIM__X, thm_2EquantHeuristics_2EMOVE__EXISTS__IMP__THM, thm_2Epred__set_2EUNION__ASSOC, thm_2Ereal_2EREAL__POS__NZ, thm_2Epred__set_2EIN__APP, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Elist_2Elist_28A_27c_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, thm_2Ereal_2EREAL__LE__ADDR, ji_2Emono_2Etyop_2Erealax_2Ereal, thm_2Enets_2EDORDER__LEMMA, thm_2Ereal_2EREAL__LTE__TOTAL, thm_2Estate__transformer_2EBIND__ASSOC, thm_2Eset__relation_2Etc__def, thm_2EHolSmt_2Er025, thm_2Equotient_2EEQUALS__IMPLIES, thm_2Ebool_2Eitself__case__thm, thm_2Ereal_2EREAL__LT__ADD, thm_2Epair_2Epair__induction, thm_2Ereal_2EREAL__LT__IMP__NE, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a, thm_2Epair_2ELAMBDA__PROD, arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27a_20mono_2EA_27b, monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, thm_2Ebool_2EMONO__ALL, thm_2Enets_2Ebounded, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_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_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, thm_2Ereal_2EREAL__EQ__LADD, arityeq2_2Ec_2EreaderMonad_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b, thm_2Ereal_2EREAL__NEG__0, thm_2EHolSmt_2Er214, thm_2Ecardinal_2ESURJECTIVE__IMAGE__THM, thm_2Ecardinal_2EFINITE__PRODUCT__DEPENDENT, thm_2Ecardinal_2EFINITE__IMAGE__INJ_27, thm_2Epair_2Epair__CASES, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27a, thm_2Emetric_2Emtop__istopology, thm_2Ebool_2ELEFT__EXISTS__AND__THM, thm_2Erealax_2EREAL__LT__IADD, thm_2Equotient_2ECOND__RSP, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29, thm_2Ewhile_2EITERATION, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Eordinal_2Eordinal_28A_27a_29_2Ctyop_2Eordinal_2Eordinal_28A_27a_29_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29, thm_2Ereal_2EREAL__LT__ADDNEG2, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29, thm_2Epred__set_2EINTER__FINITE, thm_2Epred__set_2EGSPEC__OR, thm_2Ebool_2EITSELF__UNIQUE, thm_2Ereal_2EREAL__NEG__GE0, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_29, thm_2EreaderMonad_2EJOIN__def, arityeq1_2Ec_2Ebinary__ieee_2Elargest_2E1_2Emono_2EA_27t_20mono_2EA_27w, thm_2Ereal_2EREAL__LE__DOUBLE, thm_2Ereal_2EREAL__NOT__LT, thm_2Ereal_2EREAL__LET__TRANS, thm_2Equotient_2EQUOTIENT__REL__ABS, thm_2EHolSmt_2Er001, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27b_20mono_2EA_27a, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emetric_2Emetric_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29, thm_2Epred__set_2EPAIR__IN__GSPEC__IFF, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29, thm_2Ebool_2ELEFT__AND__FORALL__THM, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27state, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29, thm_2Ebool_2ESWAP__FORALL__THM, thm_2Ebool_2ECOND__RATOR, thm_2Eset__relation_2Etc__to__rel__conv, arityeq2_2Ec_2Estate__transformer_2EUNIT_2E2_2Emono_2EA_27a_20mono_2EA_27b, thm_2Estate__transformer_2EUNIT__UNCURRY, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29, thm_2Epred__set_2EIMAGE__11, thm_2Emetric_2EMETRIC__SAME, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27b_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29, thm_2Ebool_2EEQ__SYM, thm_2Eset__relation_2Erel__to__reln__11, thm_2Elim_2ELIM__NEG, thm_2Ebool_2Ebool__case__ID, thm_2Epred__set_2EPAIR__IN__GSPEC__1, thm_2Epred__set_2EINTER__UNION, thm_2Ewellorder_2EFLATTEN__LEMMA, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, thm_2Ereal_2EREAL__LT__REFL, thm_2Eset__relation_2Erextension, thm_2EquantHeuristics_2EDISJ__IMP__INTRO, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27c, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2EA_27e, thm_2Ebool_2ELEFT__FORALL__OR__THM, thm_2Ereal_2EREAL__ADD__RID__UNIQ, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27e_20mono_2EA_27f, thm_2Ereal_2EREAL__LT__LE, thm_2Epred__set_2EINTER__OVER__UNION, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27d, thm_2Emetric_2Eismet, thm_2EHolSmt_2Er217, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29, arityeq2_2Ec_2Ebool_2Eitself__case_2E2_2Emono_2EA_27a_20mono_2EA_27b, arityeq1_2Ec_2Ebinary__ieee_2Efloat__plus__infinity_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27c_20mono_2EA_27d, thm_2Epair_2ECOMMA__DEF, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Erealax_2Ereal, thm_2Ereal_2EREAL__LE__LADD__IMP, thm_2Etransfer_2EPAIR__REL__def, monoeq_2Emono_2Ec_2Emarker_2Eunint_2E0_2Emono_2Etyop_2Erealax_2Ereal, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_29, arityeq1_2Ec_2Emetric_2Edist_2E1_2Emono_2EA_27a, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29_2Ctyop_2Emin_2Ebool_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29, monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Emin_2Ebool, thm_2Equotient__pair_2ECOMMA__PRS, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Elist_2Elist_28A_27b_29_2Ctyop_2Elist_2Elist_28A_27c_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27state, thm_2Eset__relation_2Etc__cases, thm_2EnormalForms_2EEXT__POINT, thm_2EHolSmt_2Er213, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29, thm_2Erealax_2EREAL__LT__TOTAL, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27d_29, thm_2Epred__set_2EEXTENSION, arityeq1_2Ec_2Eset__relation_2Euniv__reln_2E1_2Emono_2EA_27a, thm_2Ereal_2EREAL__ADD__SYM, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Ebool_29, thm_2Equotient_2EEQUIV__REFL__SYM__TRANS, thm_2Ebinary__ieee_2Efloat__bottom__def, reserved_2Eho_2Eeq__ext, thm_2Epred__set_2EIMAGE__11__INFINITE, thm_2Ereal_2EREAL__LTE__ADD, thm_2Ereal_2EREAL__NEG__LT0, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27c_2CA_27d_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b, arityeq1_2Ec_2Ebinary__ieee_2Ethreshold_2E1_2Emono_2EA_27t_20mono_2EA_27w, thm_2Eset__relation_2Etc__strongind__right, thm_2Epred__set_2EIN__INFINITE__NOT__FINITE, thm_2Ereal_2EREAL__NEG__EQ, thm_2Ereal_2EREAL__POS, thm_2Ebool_2ERIGHT__FORALL__OR__THM, monoeq_2Emono_2Ec_2Emetric_2Edist_2E0_2Emono_2Etyop_2Erealax_2Ereal, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27a, thm_2Eset__relation_2Etc__rules, arityeq1_2Ec_2Ebinary__ieee_2Efloat__is__infinite_2E1_2Emono_2EA_27a_20mono_2EA_27b, thm_2Epair_2ECLOSED__PAIR__EQ, thm_2Ecardinal_2EINTER__ACI, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29, thm_2Ereal_2EREAL__NEG__ADD, thm_2Epair_2EUNCURRY__CONG, thm_2Ereal_2EREAL__NZ__IMP__LT, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28A_27b_29_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_2Eoption_2Eoption_28A_27a_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, arityeq2_2Ec_2Emetric_2Edist_2E2_2Emono_2EA_27b, thm_2Epair_2EABS__REP__prod, thm_2Ereal_2EREAL__LE__ADD, thm_2Ecombin_2EK__DEF, thm_2Erealax_2EREAL__LT__TRANS, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27b_29, thm_2Elim_2ELIM__EQUAL, thm_2Ecardinal_2ELEFT__IMP__FORALL__THM, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_29, thm_2Ereal_2EREAL__ADD__ASSOC, monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_29, arityeq1_2Ec_2Eposet_2Erelation_2E1_2Emono_2EA_27a, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29, thm_2Ecardinal_2EFINITE__IMAGE__INJ, thm_2Epair_2ECURRY__DEF, thm_2Epred__set_2EUNION__DEF, thm_2Epred__set_2EIMAGE__UNION, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29, thm_2Ereal_2EREAL__LT__RADD, thm_2Ereal_2EREAL__LE__LADD, thm_2Ereal_2EREAL__LE__ADDL, thm_2Ebool_2ELCOMM__THM, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_20mono_2EA_27a_20mono_2Etyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Emetric_2Emetric_28tyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_20mono_2Etyop_2Erealax_2Ereal, thm_2Emetric_2EMETRIC__POS, monoeq_2Emono_2Ec_2Emetric_2Edist_2E2_2Emono_2Etyop_2Erealax_2Ereal, thm_2Ebool_2EMONO__EXISTS, thm_2Erealax_2EREAL__LT__REFL, ij_2Emono_2Etyop_2Emin_2Ebool, thm_2Epair_2EUNCURRY__DEF, thm_2Ereal_2EREAL__DOWN2, thm_2Ereal_2EREAL__LE__NEGTOTAL, thm_2Ereal_2EREAL__SUP__EXISTS, thm_2Enets_2Edorder, thm_2Ereal_2EREAL__NEG__EQ0, thm_2Ecardinal_2ERIGHT__IMP__EXISTS__THM, thm_2Ebool_2EUNWIND__FORALL__THM1, thm_2Ebool_2EETA__AX, thm_2Epair_2EUNCURRY__ONE__ONE__THM, thm_2Eset__relation_2Etc__implication, thm_2Ebool_2EEXISTS__REFL, monoeq_2Emono_2Ec_2Emarker_2Eunint_2E1_2Emono_2Etyop_2Erealax_2Ereal, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29, thm_2Ebool_2ENOT__FORALL__THM, thm_2Ebool_2EEQ__SYM__EQ, thm_2Ebool_2Eitself__induction, thm_2Epred__set_2EGSPEC__ID, thm_2Ereal_2EREAL__LT__ADDNEG, thm_2Ereal_2EREAL__SUP__ALLPOS, thm_2Ereal_2EREAL__EQ__IMP__LE, thm_2EOmega__Automata_2EELGOT1__THM, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Epath_2Epath_28A_27b_2CA_27c_29_20mono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27c_2CA_27a_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29_29_29, thm_2Emetric_2EMETRIC__ZERO, thm_2Ereal_2EREAL__LTE__ADD2, arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27g_20mono_2EA_27h, thm_2Epred__set_2EINTER__DEF, thm_2Ereal_2Eeq__ints, arityeq1_2Ec_2Ebinary__ieee_2Efloat__negate_2E1_2Emono_2EA_27t_20mono_2EA_27w, monoeq_2Emono_2Ec_2Emetric_2Emetric_2E1_2Emono_2Etyop_2Erealax_2Ereal, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool, thm_2Estate__transformer_2EREAD__def, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Efun_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29_2Ctyop_2Erealax_2Ereal_29, thm_2Ereal_2ESUP__LEMMA3, thm_2EreaderMonad_2EBIND__def, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27g_20mono_2EA_27h, thm_2Epowser_2EDIFFS__NEG, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29, thm_2Enets_2Etendsto, thm_2Ereal_2EREAL__LT__IADD, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Elist_2Elist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27a_29_2Ctyop_2Epair_2Eprod_28tyop_2Elist_2Elist_28A_27d_29_2CA_27e_29_29_29, arityeq1_2Ec_2Ebinary__ieee_2Efloat__minus__zero_2E1_2Emono_2EA_27t_20mono_2EA_27w, thm_2Epred__set_2EIMAGE__FINITE, thm_2Epred__set_2EIN__INTER, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29, thm_2Epred__set_2ENOT__EQUAL__SETS, thm_2Ereal_2EREAL__EQ__NEG, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27a_2CA_27state_29_29_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29, thm_2EHolSmt_2Er218, thm_2Ebool_2ELEFT__EXISTS__IMP__THM, thm_2Epred__set_2EINFINITE__INHAB, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2Ctyop_2Eoption_2Eoption_28A_27c_29_29_20mono_2Etyop_2Emin_2Ebool, arityeq2_2Ec_2Emetric_2EB_2E2_2Emono_2EA_27a, thm_2Epair_2EABS__PAIR__THM, thm_2Epair_2EEXISTS__PROD, thm_2Elim_2ELIM__UNIQ, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2EA_27b, thm_2Epair_2Epair__Axiom, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27c_2CA_27d_29_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_2Esum_2Esum_28A_27a_2CA_27b_29_2Ctyop_2Elist_2Elist_28tyop_2Emin_2Ebool_29_29_29_29_29, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Emin_2Ebool, thm_2EHolSmt_2Ed019, thm_2Ereal_2EREAL__LT__ADD2, thm_2Eseq_2ESEQ__NEG__CONV, thm_2Ebinary__ieee_2Eulp, thm_2Epred__set_2EUNION__IDEMPOT, thm_2Equotient_2EEQUALS__PRS, thm_2Ebinary__ieee_2Efloat__infinities__distinct, thm_2Etransc_2ETAN__NEG, thm_2Ereal_2EREAL__LT__LADD, thm_2Equotient_2EQUOTIENT__REL, thm_2Ereal_2EREAL__LE__REFL, arityeq1_2Ec_2Enets_2Etendsto_2E1_2Emono_2EA_27a, thm_2Ereal_2EREAL__LT__ADDR, thm_2Eset__relation_2Etc__strongind__left, thm_2Epred__set_2EINTER__COMM, thm_2Ereal_2EREAL__LT__ADDL, thm_2Equotient_2EQUOTIENT__REL__ABS__EQ, thm_2Ereal_2EREAL__NOT__LE, thm_2Eset__relation_2Etc__idemp, arityeq1_2Ec_2Ebinary__ieee_2Efloat__bottom_2E1_2Emono_2EA_27t_20mono_2EA_27w, arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ebinary__ieee_2Efloat_28A_27t_2CA_27w_29_20mono_2Etyop_2Emin_2Ebool, thm_2Ereal_2EREAL__LE__TRANS, thm_2Eset__relation_2Etc__cases__left, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Emin_2Ebool_29
% 131.66/61.82  % No. of inferences in proof: 1313
% 131.66/61.82  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 61465 ms resp. 51043 ms w/o parsing
% 136.20/63.02  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 137.26/63.05  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------