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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ITP015_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n014.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 : Sun Sep 27 07:35:38 AM UTC 2026

% Result   : Theorem 23.88s 6.03s
% Output   : Refutation 25.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   89
% Syntax   : Number of formulae    :  180 ( 133 unt;   0 typ;   0 def)
%            Number of atoms       :  316 ( 178 equ;   0 cnn)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives : 2922 (  20   ~;  11   |;  38   &;2766   @)
%                                         (  18 <=>;  69  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   4 avg)
%            Number of types       :   18 (  17 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   93 (  91 usr;  29 con; 0-3 aty)
%            Number of variables   :  319 (   0   ^; 316   !;   3   ?; 319   :)

% Comments : 
%------------------------------------------------------------------------------
thf(u_type,type,
    u: $tType ).

thf(d_type,type,
    d: $tType ).

thf(du_type,type,
    du: $tType ).

thf(mono_2Etyop_2Emin_2Ebool_type,type,
    mono_2Etyop_2Emin_2Ebool: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: $tType ).

thf(mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_type,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).

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

thf(mono_2Etyop_2Enum_2Enum_type,type,
    mono_2Etyop_2Enum_2Enum: $tType ).

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

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

thf(tyop_2Einteger_2Eint_decl,type,
    tyop_2Einteger_2Eint: d ).

thf(tyop_2Emin_2Ebool_decl,type,
    tyop_2Emin_2Ebool: d ).

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

thf(tyop_2Enum_2Enum_decl,type,
    tyop_2Enum_2Enum: d ).

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

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

thf(p_decl,type,
    p: mono_2Etyop_2Emin_2Ebool > $o ).

thf(combin_i_2E0_decl,type,
    combin_i_2E0: u ).

thf(combin_k_2E0_decl,type,
    combin_k_2E0: u ).

thf(combin_s_2E0_decl,type,
    combin_s_2E0: u ).

thf(c_2Ebool_2E_21_2E0_decl,type,
    c_2Ebool_2E_21_2E0: u ).

thf(c_2Ebool_2E_21_2E1_decl,type,
    c_2Ebool_2E_21_2E1: du > u ).

thf(c_2Emin_2E_3D_2E0_decl,type,
    c_2Emin_2E_3D_2E0: u ).

thf(c_2Emin_2E_3D_2E2_decl,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(c_2Ebool_2E_3F_2E0_decl,type,
    c_2Ebool_2E_3F_2E0: u ).

thf(c_2Ebool_2E_3F_2E1_decl,type,
    c_2Ebool_2E_3F_2E1: du > u ).

thf(c_2Ebool_2ECOND_2E0_decl,type,
    c_2Ebool_2ECOND_2E0: u ).

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

thf(c_2Ewords_2Edimword_2E0_decl,type,
    c_2Ewords_2Edimword_2E0: u ).

thf(c_2Ewords_2Edimword_2E1_decl,type,
    c_2Ewords_2Edimword_2E1: du > u ).

thf(c_2Einteger__word_2Ei2w_2E0_decl,type,
    c_2Einteger__word_2Ei2w_2E0: u ).

thf(c_2Einteger__word_2Ei2w_2E1_decl,type,
    c_2Einteger__word_2Ei2w_2E1: du > u ).

thf(c_2Ewords_2En2w_2E0_decl,type,
    c_2Ewords_2En2w_2E0: u ).

thf(c_2Ewords_2En2w_2E1_decl,type,
    c_2Ewords_2En2w_2E1: du > u ).

thf(c_2Ebool_2Ethe__value_2E0_decl,type,
    c_2Ebool_2Ethe__value_2E0: u ).

thf(c_2Ewords_2Eword__2comp_2E0_decl,type,
    c_2Ewords_2Eword__2comp_2E0: u ).

thf(c_2Ewords_2Eword__2comp_2E1_decl,type,
    c_2Ewords_2Eword__2comp_2E1: du > u ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).

thf(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_decl,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2E_2F_5C_2E0_decl,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

thf(mono_2Ec_2Ebool_2E_2F_5C_2E2_decl,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Enum_2E0_2E0_decl,type,
    mono_2Ec_2Enum_2E0_2E0: mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Eprim__rec_2E_3C_2E0_decl,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

thf(mono_2Ec_2Eprim__rec_2E_3C_2E2_decl,type,
    mono_2Ec_2Eprim__rec_2E_3C_2E2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E_2E0_decl,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E_2E2_decl,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Ebool_2EF_2E0_decl,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Earithmetic_2EMOD_2E0_decl,type,
    mono_2Ec_2Earithmetic_2EMOD_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

thf(mono_2Ec_2Earithmetic_2EMOD_2E2_decl,type,
    mono_2Ec_2Earithmetic_2EMOD_2E2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Einteger_2ENum_2E0_decl,type,
    mono_2Ec_2Einteger_2ENum_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 ).

thf(mono_2Ec_2Einteger_2ENum_2E1_decl,type,
    mono_2Ec_2Einteger_2ENum_2E1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).

thf(mono_2Ec_2Ebool_2ET_2E0_decl,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Ebool_2E_5C_2F_2E0_decl,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

thf(mono_2Ec_2Ebool_2E_5C_2F_2E2_decl,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E2: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Einteger_2Eint__lt_2E0_decl,type,
    mono_2Ec_2Einteger_2Eint__lt_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 ).

thf(mono_2Ec_2Einteger_2Eint__lt_2E2_decl,type,
    mono_2Ec_2Einteger_2Eint__lt_2E2: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Emin_2Ebool ).

thf(mono_2Ec_2Einteger_2Eint__neg_2E0_decl,type,
    mono_2Ec_2Einteger_2Eint__neg_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).

thf(mono_2Ec_2Einteger_2Eint__neg_2E1_decl,type,
    mono_2Ec_2Einteger_2Eint__neg_2E1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).

thf(mono_2Ec_2Einteger_2Eint__of__num_2E0_decl,type,
    mono_2Ec_2Einteger_2Eint__of__num_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 ).

thf(mono_2Ec_2Einteger_2Eint__of__num_2E1_decl,type,
    mono_2Ec_2Einteger_2Eint__of__num_2E1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).

thf(mono_2Ec_2Ebool_2E_7E_2E0_decl,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

thf(mono_2Ec_2Ebool_2E_7E_2E1_decl,type,
    mono_2Ec_2Ebool_2E_7E_2E1: mono_2Etyop_2Emin_2Ebool > mono_2Etyop_2Emin_2Ebool ).

thf(i_mono_2Etyop_2Emin_2Ebool_decl,type,
    i_mono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Ebool > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_decl,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > u ).

thf(i_mono_2Etyop_2Einteger_2Eint_decl,type,
    i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).

thf(i_mono_2Etyop_2Enum_2Enum_decl,type,
    i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).

thf(j_mono_2Etyop_2Emin_2Ebool_decl,type,
    j_mono_2Etyop_2Emin_2Ebool: du > mono_2Etyop_2Emin_2Ebool ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_decl,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

thf(j_mono_2Etyop_2Einteger_2Eint_decl,type,
    j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).

thf(j_mono_2Etyop_2Enum_2Enum_decl,type,
    j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).

thf(57,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Enum_2Enum) ).

thf(340,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(28,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
      = ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).

thf(225,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
      = ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(66,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29) ).

thf(371,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(19,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint] :
      ( ( A @ mono_2Ec_2Einteger_2ENum_2E1 )
      = ( A @ ( mono_2Ec_2Einteger_2ENum_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2ENum_2E1) ).

thf(181,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint] :
      ( ( A @ mono_2Ec_2Einteger_2ENum_2E1 )
      = ( A @ ( mono_2Ec_2Einteger_2ENum_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(62,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ( D @ ( B @ s ) @ ( C @ ( A @ s ) @ ( combin_k_2E0 @ ( A @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
      = ( C @ ( A @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ek__thm) ).

thf(359,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ( D @ ( B @ s ) @ ( C @ ( A @ s ) @ ( combin_k_2E0 @ ( A @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
      = ( C @ ( A @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(64,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).

thf(365,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(36,axiom,
    ! [A: d,B: u] :
      ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
      = ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a) ).

thf(249,plain,
    ! [A: d,B: u] :
      ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
      = ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( c_2Ebool_2E_21_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(31,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29) ).

thf(234,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(45,axiom,
    ! [A: d,B: u] :
      ( ( ( B @ ( A @ s ) )
        = ( B @ ( A @ s ) ) )
    <=> ( mono_2Ec_2Ebool_2ET_2E0 @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).

thf(276,plain,
    mono_2Ec_2Ebool_2ET_2E0 @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(52,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint ) @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint) ).

thf(308,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint ) @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(48,axiom,
    ! [A: d,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
      ( ( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
        = ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
    <=> ( ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ ( B @ mono_2Ec_2Earithmetic_2EMOD_2E2 ) )
        = ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ ( C @ mono_2Ec_2Earithmetic_2EMOD_2E2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__11) ).

thf(288,plain,
    ! [A: d,B: mono_2Etyop_2Enum_2Enum,C: mono_2Etyop_2Enum_2Enum] :
      ( ( ( ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ ( B @ mono_2Ec_2Earithmetic_2EMOD_2E2 ) )
          = ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ ( C @ mono_2Ec_2Earithmetic_2EMOD_2E2 ) ) )
       => ( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
          = ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ) )
      & ( ( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
          = ( C @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) )
       => ( ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ ( B @ mono_2Ec_2Earithmetic_2EMOD_2E2 ) )
          = ( c_2Ebool_2Ethe__value_2E0 @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ ( C @ mono_2Ec_2Earithmetic_2EMOD_2E2 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(56,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) )
        = mono_2Ec_2Ebool_2EF_2E0 )
      & ( ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) @ p )
      <=> ( ( B != mono_2Ec_2Enum_2E0_2E0 )
          | ( A != mono_2Ec_2Enum_2E0_2E0 ) ) )
      & ( ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) )
        = ( A @ ( B @ mono_2Ec_2Eprim__rec_2E_3C_2E2 ) ) )
      & ( ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) )
        = ( B @ ( A @ mono_2Ec_2Eprim__rec_2E_3C_2E2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE) ).

thf(320,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) )
        = mono_2Ec_2Ebool_2EF_2E0 )
      & ( ( ( B != mono_2Ec_2Enum_2E0_2E0 )
          | ( A != mono_2Ec_2Enum_2E0_2E0 ) )
       => ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) @ p ) )
      & ( ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) @ p )
       => ( ( B != mono_2Ec_2Enum_2E0_2E0 )
          | ( A != mono_2Ec_2Enum_2E0_2E0 ) ) )
      & ( ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) )
        = ( A @ ( B @ mono_2Ec_2Eprim__rec_2E_3C_2E2 ) ) )
      & ( ( B @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) )
        = ( B @ ( A @ mono_2Ec_2Eprim__rec_2E_3C_2E2 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(85,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).

thf(436,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(18,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( B @ ( A @ mono_2Ec_2Ebool_2E_2F_5C_2E2 ) @ p )
    <=> ( ( B @ p )
        & ( A @ p ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_2F_5C) ).

thf(174,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( B @ p )
          & ( A @ p ) )
       => ( B @ ( A @ mono_2Ec_2Ebool_2E_2F_5C_2E2 ) @ p ) )
      & ( ( B @ ( A @ mono_2Ec_2Ebool_2E_2F_5C_2E2 ) @ p )
       => ( ( B @ p )
          & ( A @ p ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(77,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) ).

thf(404,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(72,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29) ).

thf(389,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(20,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Ec_2Eprim__rec_2E_3C_2E2 ) )
      = ( B @ ( A @ ( mono_2Ec_2Eprim__rec_2E_3C_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Eprim__rec_2E_3C_2E2) ).

thf(184,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Ec_2Eprim__rec_2E_3C_2E2 ) )
      = ( B @ ( A @ ( mono_2Ec_2Eprim__rec_2E_3C_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(9,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( B @ ( A @ mono_2Ec_2Ebool_2E_5C_2F_2E2 ) @ p )
    <=> ( ( B @ p )
        | ( A @ p ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_5C_2F) ).

thf(125,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( B @ p )
          | ( A @ p ) )
       => ( B @ ( A @ mono_2Ec_2Ebool_2E_5C_2F_2E2 ) @ p ) )
      & ( ( B @ ( A @ mono_2Ec_2Ebool_2E_5C_2F_2E2 ) @ p )
       => ( ( B @ p )
          | ( A @ p ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(14,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
    <=> ~ ( A @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_7E) ).

thf(152,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ~ ( A @ p )
       => ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p ) )
      & ( ( A @ mono_2Ec_2Ebool_2E_7E_2E1 @ p )
       => ~ ( A @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(29,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum) ).

thf(228,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(40,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29) ).

thf(261,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(25,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( B @ ( A @ s ) )
        = ( C @ ( A @ s ) ) )
    <=> ( ( C @ ( A @ s ) )
        = ( B @ ( A @ s ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__SYM__EQ) ).

thf(211,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( ( C @ ( A @ s ) )
          = ( B @ ( A @ s ) ) )
       => ( ( B @ ( A @ s ) )
          = ( C @ ( A @ s ) ) ) )
      & ( ( ( B @ ( A @ s ) )
          = ( C @ ( A @ s ) ) )
       => ( ( C @ ( A @ s ) )
          = ( B @ ( A @ s ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(6,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ~ ( A @ p )
    <=> ( A @ ( mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_7E_2E1) ).

thf(106,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( A @ ( mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p )
       => ~ ( A @ p ) )
      & ( ~ ( A @ p )
       => ( A @ ( mono_2Ec_2Ebool_2E_7E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(87,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29) ).

thf(453,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(10,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( mono_2Ec_2Ebool_2EF_2E0 @ p )
     => ( A @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY) ).

thf(133,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( mono_2Ec_2Ebool_2EF_2E0 @ p )
     => ( A @ p ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(34,axiom,
    ! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: u,D: u] :
      ( ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
      = ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a) ).

thf(243,plain,
    ! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: u,D: u] :
      ( ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
      = ( D @ ( A @ s ) @ ( C @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(69,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) ).

thf(380,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(86,axiom,
    ! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,D: u,E: u,F: u,G: u] :
      ( ( ( ~ ( C @ p )
         => ( ( F @ ( A @ s ) )
            = ( G @ ( A @ s ) ) ) )
        & ( ( C @ p )
         => ( ( D @ ( A @ s ) )
            = ( E @ ( A @ s ) ) ) )
        & ( B = C ) )
     => ( ( F @ ( A @ s ) @ ( D @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
        = ( G @ ( A @ s ) @ ( E @ ( A @ s ) @ ( C @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).

thf(439,plain,
    ! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool,D: u,E: u,F: u,G: u] :
      ( ( ( ~ ( C @ p )
         => ( ( F @ ( A @ s ) )
            = ( G @ ( A @ s ) ) ) )
        & ( ( C @ p )
         => ( ( D @ ( A @ s ) )
            = ( E @ ( A @ s ) ) ) )
        & ( B = C ) )
     => ( ( F @ ( A @ s ) @ ( D @ ( A @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
        = ( G @ ( A @ s ) @ ( E @ ( A @ s ) @ ( C @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(43,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) ).

thf(270,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(4,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( A @ ( mono_2Ec_2Einteger_2Eint__lt_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Einteger_2Eint__lt_2E2) ).

thf(102,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) )
      = ( B @ ( A @ ( mono_2Ec_2Einteger_2Eint__lt_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(50,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29) ).

thf(302,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(73,axiom,
    ! [A: d] :
      ( ( mono_2Ec_2Enum_2E0_2E0 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( mono_2Ec_2Enum_2E0_2E0 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0) ).

thf(392,plain,
    ! [A: d] :
      ( ( mono_2Ec_2Enum_2E0_2E0 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( mono_2Ec_2Enum_2E0_2E0 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(81,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum) ).

thf(424,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum ) @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(78,axiom,
    ! [A: d] :
      ( ! [B: u,C: u] :
          ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( mono_2Ec_2Ebool_2EF_2E0 @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
          = ( C @ ( A @ s ) ) )
      & ! [B: u,C: u] :
          ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( mono_2Ec_2Ebool_2ET_2E0 @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
          = ( B @ ( A @ s ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).

thf(407,plain,
    ! [A: d] :
      ( ! [B: u,C: u] :
          ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( mono_2Ec_2Ebool_2EF_2E0 @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
          = ( C @ ( A @ s ) ) )
      & ! [B: u,C: u] :
          ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( mono_2Ec_2Ebool_2ET_2E0 @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ s ) )
          = ( B @ ( A @ s ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(16,axiom,
    ~ ( mono_2Ec_2Ebool_2EF_2E0 @ p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).

thf(165,plain,
    ~ ( mono_2Ec_2Ebool_2EF_2E0 @ p ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(37,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 )
      = ( A @ ( mono_2Ec_2Einteger_2Eint__of__num_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__of__num_2E1) ).

thf(252,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 )
      = ( A @ ( mono_2Ec_2Einteger_2Eint__of__num_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(88,axiom,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u] :
          ( ( E @ ( A @ s ) @ ( C @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) )
          = ( E @ ( A @ s ) @ ( D @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) ) )
     => ( ( C @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) )
        = ( D @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eeq__ext) ).

thf(456,plain,
    ! [A: d,B: d,C: u,D: u] :
      ( ! [E: u] :
          ( ( E @ ( A @ s ) @ ( C @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) )
          = ( E @ ( A @ s ) @ ( D @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) ) )
     => ( ( C @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) )
        = ( D @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(47,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Ebool) ).

thf(285,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(55,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29) ).

thf(317,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 ) @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(61,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint ) @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint) ).

thf(356,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint ) @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Einteger_2Eint @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(5,axiom,
    mono_2Ec_2Ebool_2ET_2E0 @ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).

thf(105,plain,
    mono_2Ec_2Ebool_2ET_2E0 @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(53,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29) ).

thf(311,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(75,axiom,
    ! [A: d,B: u] :
      ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
      = ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( c_2Ebool_2E_3F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a) ).

thf(398,plain,
    ! [A: d,B: u] :
      ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool )
      = ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( c_2Ebool_2E_3F_2E0 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(58,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) ).

thf(343,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(32,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool) ).

thf(237,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(83,axiom,
    ! [A: d,B: u] :
      ( ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__2comp_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a) ).

thf(430,plain,
    ! [A: d,B: u] :
      ( ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( B @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( c_2Ewords_2Eword__2comp_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(12,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint] :
      ( ( A @ mono_2Ec_2Einteger_2Eint__neg_2E1 )
      = ( A @ ( mono_2Ec_2Einteger_2Eint__neg_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger_2Eint__neg_2E1) ).

thf(148,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint] :
      ( ( A @ mono_2Ec_2Einteger_2Eint__neg_2E1 )
      = ( A @ ( mono_2Ec_2Einteger_2Eint__neg_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(41,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29) ).

thf(264,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(49,axiom,
    ! [A: d,B: u] :
      ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
    <=> ? [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_3F) ).

thf(296,plain,
    ! [A: d,B: u] :
      ( ( ? [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
       => ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) )
      & ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_3F_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
       => ? [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(21,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Ec_2Earithmetic_2EMOD_2E2 ) )
      = ( B @ ( A @ ( mono_2Ec_2Earithmetic_2EMOD_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Earithmetic_2EMOD_2E2) ).

thf(187,plain,
    ! [A: mono_2Etyop_2Enum_2Enum,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ ( A @ mono_2Ec_2Earithmetic_2EMOD_2E2 ) )
      = ( B @ ( A @ ( mono_2Ec_2Earithmetic_2EMOD_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(26,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
      = ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool) ).

thf(219,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
      = ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(68,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29) ).

thf(377,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(63,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29) ).

thf(362,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(24,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29) ).

thf(208,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Enum_2Enum @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(1,conjecture,
    ! [A: d] :
      ( ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( mono_2Ec_2Enum_2E0_2E0 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0) ).

thf(2,negated_conjecture,
    ~ ! [A: d] :
        ( ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
        = ( mono_2Ec_2Enum_2E0_2E0 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(91,plain,
    ~ ! [A: d] :
        ( ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
        = ( mono_2Ec_2Enum_2E0_2E0 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(33,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29) ).

thf(240,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(90,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29) ).

thf(462,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Einteger_2Eint @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(42,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool) ).

thf(267,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ ( A @ mono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(17,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( A @ p )
       => ( B @ p ) )
    <=> ( B @ ( A @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2) ).

thf(167,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( B @ ( A @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p )
       => ( ( A @ p )
         => ( B @ p ) ) )
      & ( ( ( A @ p )
         => ( B @ p ) )
       => ( B @ ( A @ ( mono_2Ec_2Emin_2E_3D_3D_3E_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(67,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ~ ( mono_2Ec_2Enum_2E0_2E0 @ ( A @ mono_2Ec_2Eprim__rec_2E_3C_2E2 ) @ p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0) ).

thf(374,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ~ ( mono_2Ec_2Enum_2E0_2E0 @ ( A @ mono_2Ec_2Eprim__rec_2E_3C_2E2 ) @ p ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(38,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
      = ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Enum_2Enum) ).

thf(255,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) )
      = ( A @ ( tyop_2Enum_2Enum @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(7,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( A @ p )
      <=> ( B @ p ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).

thf(112,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( B @ p )
         => ( A @ p ) )
        & ( ( A @ p )
         => ( B @ p ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(71,axiom,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29) ).

thf(386,plain,
    ! [A: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29] :
      ( ( A @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(54,axiom,
    ! [A: d,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ewords_2En2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a) ).

thf(314,plain,
    ! [A: d,B: mono_2Etyop_2Enum_2Enum] :
      ( ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( B @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ ( c_2Ewords_2En2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(30,axiom,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2ENum_2E1 )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT) ).

thf(231,plain,
    ! [A: mono_2Etyop_2Enum_2Enum] :
      ( ( A @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2ENum_2E1 )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(65,axiom,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( F @ ( A @ s ) @ ( E @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( D @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( combin_s_2E0 @ ( C @ ( A @ tyop_2Emin_2Efun ) @ ( B @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( A @ tyop_2Emin_2Efun ) @ ( B @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ s ) )
      = ( F @ ( A @ s ) @ ( E @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) @ ( F @ ( A @ s ) @ ( D @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Es__thm) ).

thf(368,plain,
    ! [A: d,B: d,C: d,D: u,E: u,F: u] :
      ( ( F @ ( A @ s ) @ ( E @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( D @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ ( combin_s_2E0 @ ( C @ ( A @ tyop_2Emin_2Efun ) @ ( B @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( A @ tyop_2Emin_2Efun ) @ ( B @ ( A @ tyop_2Emin_2Efun ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ s ) )
      = ( F @ ( A @ s ) @ ( E @ ( B @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( B @ s ) @ ( F @ ( A @ s ) @ ( D @ ( C @ ( B @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ ( B @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( C @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(39,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Einteger_2Eint @ s ) @ j_mono_2Etyop_2Einteger_2Eint @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) )
      = ( A @ ( tyop_2Einteger_2Eint @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Einteger_2Eint) ).

thf(258,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Einteger_2Eint @ s ) @ j_mono_2Etyop_2Einteger_2Eint @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) )
      = ( A @ ( tyop_2Einteger_2Eint @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(15,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( B @ p )
        | ( A @ p ) )
    <=> ( B @ ( A @ ( mono_2Ec_2Ebool_2E_5C_2F_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_5C_2F_2E2) ).

thf(158,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( B @ ( A @ ( mono_2Ec_2Ebool_2E_5C_2F_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p )
       => ( ( B @ p )
          | ( A @ p ) ) )
      & ( ( ( B @ p )
          | ( A @ p ) )
       => ( B @ ( A @ ( mono_2Ec_2Ebool_2E_5C_2F_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(76,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint] :
      ( ( A @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ j_mono_2Etyop_2Einteger_2Eint )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ji_2Emono_2Etyop_2Einteger_2Eint) ).

thf(401,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint] :
      ( ( A @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ j_mono_2Etyop_2Einteger_2Eint )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(80,axiom,
    ! [A: d,B: u] :
      ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
    <=> ! [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Equant_2E_21) ).

thf(418,plain,
    ! [A: d,B: u] :
      ( ( ! [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
       => ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) )
      & ( ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ c_2Ebool_2E_21_2E1 @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
       => ! [C: u] : ( C @ ( A @ s ) @ ( B @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(35,axiom,
    ! [A: d,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger__word_2Ei2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a) ).

thf(246,plain,
    ! [A: d,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ ( c_2Einteger__word_2Ei2w_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(84,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Ebool) ).

thf(433,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(70,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29) ).

thf(383,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Enum_2Enum @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(59,axiom,
    ! [A: d,B: u,C: u] :
      ( ( ( B @ ( A @ s ) )
        = ( C @ ( A @ s ) ) )
    <=> ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a) ).

thf(346,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
       => ( ( B @ ( A @ s ) )
          = ( C @ ( A @ s ) ) ) )
      & ( ( ( B @ ( A @ s ) )
          = ( C @ ( A @ s ) ) )
       => ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ ( c_2Emin_2E_3D_2E0 @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(13,axiom,
    mono_2Ec_2Ebool_2ET_2E0 @ p,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).

thf(151,plain,
    mono_2Ec_2Ebool_2ET_2E0 @ p,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(22,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( A @ p )
       => ( B @ p ) )
     => ( ( ( B @ p )
         => ( A @ p ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__ANTISYM__AX) ).

thf(190,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( A @ p )
       => ( B @ p ) )
     => ( ( ( B @ p )
         => ( A @ p ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(44,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29) ).

thf(273,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(51,axiom,
    ! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: u,D: u] :
      ( ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29) ).

thf(305,plain,
    ! [A: d,B: mono_2Etyop_2Emin_2Ebool,C: u,D: u] :
      ( ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( D @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( C @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ ( c_2Ebool_2ECOND_2E0 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(11,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( A @ p )
       => ( ( B @ p )
         => ( C @ p ) ) )
    <=> ( ( ( B @ p )
          & ( A @ p ) )
       => ( C @ p ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EAND__IMP__INTRO) ).

thf(136,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool,C: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( ( B @ p )
            & ( A @ p ) )
         => ( C @ p ) )
       => ( ( A @ p )
         => ( ( B @ p )
           => ( C @ p ) ) ) )
      & ( ( ( A @ p )
         => ( ( B @ p )
           => ( C @ p ) ) )
       => ( ( ( B @ p )
            & ( A @ p ) )
         => ( C @ p ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(3,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
    <=> ( ( A @ p )
       => ( B @ p ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D_3D_3E) ).

thf(94,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( ( A @ p )
         => ( B @ p ) )
       => ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p ) )
      & ( ( B @ ( A @ mono_2Ec_2Emin_2E_3D_3D_3E_2E2 ) @ p )
       => ( ( A @ p )
         => ( B @ p ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(79,axiom,
    ! [A: d,B: u] :
      ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
      = ( B @ ( A @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ei__thm) ).

thf(415,plain,
    ! [A: d,B: u] :
      ( ( B @ ( A @ s ) @ ( combin_i_2E0 @ ( A @ ( A @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( A @ s ) )
      = ( B @ ( A @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(74,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29) ).

thf(395,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(82,axiom,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29) ).

thf(427,plain,
    ! [A: u] :
      ( ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) @ j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) )
      = ( A @ ( tyop_2Emin_2Ebool @ ( tyop_2Einteger_2Eint @ tyop_2Emin_2Efun ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(89,axiom,
    ! [A: d,B: u] :
      ( ( B @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum )
      = ( B @ ( A @ tyop_2Ebool_2Eitself @ s ) @ ( c_2Ewords_2Edimword_2E0 @ ( tyop_2Enum_2Enum @ ( A @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a) ).

thf(459,plain,
    ! [A: d,B: u] :
      ( ( B @ ( A @ tyop_2Ebool_2Eitself @ s ) @ c_2Ewords_2Edimword_2E1 @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum )
      = ( B @ ( A @ tyop_2Ebool_2Eitself @ s ) @ ( c_2Ewords_2Edimword_2E0 @ ( tyop_2Enum_2Enum @ ( A @ tyop_2Ebool_2Eitself @ tyop_2Emin_2Efun ) @ s ) @ app_2E2 ) @ ( tyop_2Enum_2Enum @ s ) @ j_mono_2Etyop_2Enum_2Enum ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(23,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( B @ p )
        & ( A @ p ) )
    <=> ( B @ ( A @ ( mono_2Ec_2Ebool_2E_2F_5C_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq2_2Ec_2Ebool_2E_2F_5C_2E2) ).

thf(200,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool,B: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( B @ ( A @ ( mono_2Ec_2Ebool_2E_2F_5C_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p )
       => ( ( B @ p )
          & ( A @ p ) ) )
      & ( ( ( B @ p )
          & ( A @ p ) )
       => ( B @ ( A @ ( mono_2Ec_2Ebool_2E_2F_5C_2E0 @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ) @ mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool ) @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(46,axiom,
    ! [A: d,B: u,C: u] :
      ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
    <=> ( ( B @ ( A @ s ) )
        = ( C @ ( A @ s ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Elogic_2E_3D) ).

thf(277,plain,
    ! [A: d,B: u,C: u] :
      ( ( ( ( B @ ( A @ s ) )
          = ( C @ ( A @ s ) ) )
       => ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p ) )
      & ( ( C @ ( A @ s ) @ ( B @ ( A @ s ) @ c_2Emin_2E_3D_2E2 ) @ ( tyop_2Emin_2Ebool @ s ) @ j_mono_2Etyop_2Emin_2Ebool @ p )
       => ( ( B @ ( A @ s ) )
          = ( C @ ( A @ s ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(8,axiom,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
      | ( A = mono_2Ec_2Ebool_2ET_2E0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Ebool__cases__ax) ).

thf(122,plain,
    ! [A: mono_2Etyop_2Emin_2Ebool] :
      ( ( A = mono_2Ec_2Ebool_2EF_2E0 )
      | ( A = mono_2Ec_2Ebool_2ET_2E0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(60,axiom,
    ( ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 )
    = ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0) ).

thf(354,plain,
    ( ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ mono_2Ec_2Einteger_2Eint__neg_2E1 )
    = ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(27,axiom,
    ! [A: d,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( B @ mono_2Ec_2Einteger_2ENum_2E1 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ mono_2Ec_2Einteger_2ENum_2E1 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ ( B @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def) ).

thf(222,plain,
    ! [A: d,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( B @ i_mono_2Etyop_2Einteger_2Eint @ ( tyop_2Einteger_2Eint @ s ) @ c_2Einteger__word_2Ei2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) )
      = ( B @ mono_2Ec_2Einteger_2ENum_2E1 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( B @ mono_2Ec_2Einteger_2Eint__neg_2E1 @ mono_2Ec_2Einteger_2ENum_2E1 @ i_mono_2Etyop_2Enum_2Enum @ ( tyop_2Enum_2Enum @ s ) @ c_2Ewords_2En2w_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ c_2Ewords_2Eword__2comp_2E1 @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) @ ( mono_2Ec_2Enum_2E0_2E0 @ mono_2Ec_2Einteger_2Eint__of__num_2E1 @ ( B @ mono_2Ec_2Einteger_2Eint__lt_2E2 ) @ i_mono_2Etyop_2Emin_2Ebool @ ( tyop_2Emin_2Ebool @ s ) @ c_2Ebool_2ECOND_2E3 ) ) @ ( A @ ( tyop_2Emin_2Ebool @ tyop_2Efcp_2Ecart ) @ s ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(4033,plain,
    $false,
    inference(e,[status(thm)],[340,225,371,181,359,365,249,234,276,308,288,320,436,174,404,389,184,125,152,228,261,211,106,453,133,243,380,439,270,102,302,392,424,407,165,252,456,285,317,356,105,311,398,343,237,430,148,264,296,187,219,377,362,208,91,240,462,267,167,374,255,112,386,314,231,368,258,158,401,418,246,433,383,346,151,190,273,305,136,94,415,395,427,459,200,277,122,354,222]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : ITP015_1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.37  % Computer : n014.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Fri Sep 25 17:21:17 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 0.11/0.38  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.95/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.12/1.30  % [INFO] 	 Parsing done (324ms). 
% 2.12/1.31  % [INFO] 	 Running in sequential loop mode. 
% 2.84/1.71  % [INFO] 	 eprover registered as external prover. 
% 2.84/1.72  % [INFO] 	 Scanning for conjecture ... 
% 3.21/1.91  % [INFO] 	 Found a conjecture (or negated_conjecture) and 88 axioms. Running axiom selection ... 
% 3.61/2.03  % [INFO] 	 Axiom selection finished. Selected 88 axioms (removed 0 axioms). 
% 3.96/2.19  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 4.20/2.20  % [INFO] 	 Type checking passed. 
% 4.20/2.21  % [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 ... 
% 5.07/2.57  % [INFO] 	 [Domain constraints] Detected constraint on mono_2Etyop_2Emin_2Ebool 
% 5.07/2.57  % [INFO] 	 [Domain constraints] dom(mono_2Etyop_2Emin_2Ebool) ⊆ {mono_2Ec_2Ebool_2ET_2E0,mono_2Ec_2Ebool_2EF_2E0} 
% 23.88/6.02  % External prover 'e' found a proof!
% 23.88/6.02  % [INFO] 	 Killing All external provers ... 
% 23.88/6.02  % Time passed: 5502ms (effective reasoning time: 4700ms)
% 23.88/6.02  % 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)>
% 23.88/6.03  % Axioms used in derivation (88): ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29, ji_2Emono_2Etyop_2Emin_2Ebool, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29, ij_2Emono_2Etyop_2Einteger_2Eint, arityeq1_2Ec_2Ewords_2Edimword_2E1_2Emono_2EA_27a, thm_2Eprim__rec_2ENOT__LESS__0, ij_2Emono_2Etyop_2Emin_2Ebool, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29, arityeq2_2Ec_2Eprim__rec_2E_3C_2E2, ji_2Emono_2Etyop_2Enum_2Enum, reserved_2Eho_2Enotfalse, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum, thm_2Ebool_2EREFL__CLAUSE, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29, reserved_2Equant_2E_21, thm_2Ebool_2EIMP__ANTISYM__AX, arityeq2_2Ec_2Ebool_2E_2F_5C_2E2, arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29, ji_2Emono_2Etyop_2Einteger_2Eint, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29, reserved_2Equant_2E_3F, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, reserved_2Eho_2Etruth, reserved_2Elogic_2E_2F_5C, reserved_2Eho_2Ei__thm, reserved_2Eho_2Es__thm, thm_2Ebool_2EFALSITY, reserved_2Elogic_2E_3D, arityeq1_2Ec_2Ewords_2Eword__2comp_2E1_2Emono_2EA_27a, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2EAND__IMP__INTRO, arityeq2_2Ec_2Earithmetic_2EMOD_2E2, arityeq1_2Ec_2Ewords_2En2w_2E1_2Emono_2EA_27a, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, thm_2Einteger_2EINT__NEG__0, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29, arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efcp_2Ecart_28tyop_2Emin_2Ebool_2CA_27a_29, thm_2Ebool_2ETRUTH, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool, arityeq1_2Ec_2Einteger__word_2Ei2w_2E1_2Emono_2EA_27a, reserved_2Eho_2Ek__thm, arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, reserved_2Elogic_2E_7E, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29, thm_2Einteger_2EINT__LT__CALCULATE, reserved_2Eho_2Eboolext, arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a, reserved_2Eho_2Ebool__cases__ax, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29, reserved_2Elogic_2E_3D_3D_3E, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29, arityeq1_2Ec_2Einteger_2Eint__of__num_2E1, reserved_2Eho_2Eeq__ext, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29, ij_2Emono_2Etyop_2Enum_2Enum, arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a, arityeq1_2Ec_2Ebool_2E_7E_2E1, arityeq1_2Ec_2Einteger_2ENum_2E1, arityeq2_2Ec_2Einteger_2Eint__lt_2E2, arityeq2_2Ec_2Ebool_2E_5C_2F_2E2, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29, thm_2Einteger__word_2Ei2w__def, thm_2Ebool_2EEQ__SYM__EQ, reserved_2Elogic_2E_5C_2F, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool, arityeq1_2Ec_2Einteger_2Eint__neg_2E1, thm_2Ewords_2EWORD__NEG__0, thm_2Einteger_2ENUM__OF__INT, monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29, thm_2Ewords_2En2w__11, thm_2Ebool_2Ebool__case__thm, ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29, ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29
% 23.88/6.03  % No. of inferences in proof: 180
% 23.88/6.03  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5502 ms resp. 4700 ms w/o parsing
% 25.12/6.17  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.12/6.17  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------