TSTP Solution File: ITP012^4 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP012^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:21:36 EDT 2024

% Result   : Theorem 21.37s 6.38s
% Output   : Refutation 21.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  103
% Syntax   : Number of formulae    :  151 (  75 unt;  57 typ;   0 def)
%            Number of atoms       :  169 ( 111 equ;   0 cnn)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  587 (   2   ~;   0   |;   6   &; 564   @)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :   53 (  52 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :  225 (   0   ^ 223   !;   2   ?; 225   :)

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

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

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

thf(mono_2Etyop_2Emin_2Eind_type,type,
    mono_2Etyop_2Emin_2Eind: $tType ).

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

thf(mono_2Etyop_2Eone_2Eone_type,type,
    mono_2Etyop_2Eone_2Eone: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(mono_2Ec_2Einteger_2Eint__add_type,type,
    mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).

thf(mono_2Ec_2Einteger_2Eint__divides_type,type,
    mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).

thf(mono_2Ec_2Einteger_2Eint__mul_type,type,
    mono_2Ec_2Einteger_2Eint__mul: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).

thf(mono_2Ec_2Einteger_2Eint__neg_type,type,
    mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).

thf(mono_2Ec_2Einteger_2Eint__sub_type,type,
    mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).

thf(19,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__mul @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__RMUL) ).

thf(101,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__mul @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(45,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__TRIANGLE) ).

thf(185,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(22,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__neg @ A )
        = B )
      = ( A
        = ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__EQ) ).

thf(110,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__neg @ A )
        = B )
      = ( A
        = ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(43,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RMUL) ).

thf(179,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(11,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__neg @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB2) ).

thf(77,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__neg @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(28,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB2) ).

thf(129,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(35,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD) ).

thf(155,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(12,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ B @ A )
      = ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SYM) ).

thf(80,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ B @ A )
      = ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(33,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LMUL) ).

thf(145,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(20,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
      = ( mono_2Ec_2Einteger_2Eint__add @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).

thf(104,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
      = ( mono_2Ec_2Einteger_2Eint__add @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(25,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LDISTRIB) ).

thf(119,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(4,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__LMUL) ).

thf(56,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(32,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ C )
      = ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RDISTRIB) ).

thf(142,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ C )
      = ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(29,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).

thf(132,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(15,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__add @ A @ C )
        = ( mono_2Ec_2Einteger_2Eint__add @ B @ C ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__RADD) ).

thf(89,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__add @ A @ C )
        = ( mono_2Ec_2Einteger_2Eint__add @ B @ C ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(24,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__MUL2) ).

thf(116,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(10,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__RNEG) ).

thf(74,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(16,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ C @ ( mono_2Ec_2Einteger_2Eint__add @ B @ A ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__ASSOC) ).

thf(92,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ C @ ( mono_2Ec_2Einteger_2Eint__add @ B @ A ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(7,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ B @ A )
      = ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__COMM) ).

thf(65,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ B @ A )
      = ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(46,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__SUB) ).

thf(188,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(3,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ B @ A )
      = ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD__COMM) ).

thf(53,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ B @ A )
      = ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(40,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__SUB) ).

thf(169,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(39,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__NEG2) ).

thf(166,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(34,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) )
      & ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).

thf(148,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) )
      & ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(37,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
        & ( mono_2Ec_2Einteger_2Eint__divides @ B @ C ) )
     => ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__TRANS) ).

thf(161,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
        & ( mono_2Ec_2Einteger_2Eint__divides @ B @ C ) )
     => ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(47,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ B @ C ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LADD) ).

thf(191,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ B @ C ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(5,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ C )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__RDISTRIB) ).

thf(59,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ C )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(9,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
      = ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__LNEG) ).

thf(71,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
      = ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(14,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__add @ A @ B )
        = ( mono_2Ec_2Einteger_2Eint__add @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__LADD) ).

thf(86,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__add @ A @ B )
        = ( mono_2Ec_2Einteger_2Eint__add @ A @ C ) )
      = ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(41,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
      & ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__MUL) ).

thf(172,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) )
      & ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(23,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ A ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIFFSQ) ).

thf(113,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ A @ A ) @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(18,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__ADD) ).

thf(98,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(1,conjecture,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).

thf(2,negated_conjecture,
    ~ ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
        ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
       => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
          = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(48,plain,
    ~ ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
        ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
       => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
          = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(17,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEGNEG) ).

thf(95,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(42,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__divides @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__REFL) ).

thf(177,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__divides @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(44,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
        = C )
      = ( A
        = ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__RADD) ).

thf(182,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
        = C )
      = ( A
        = ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(36,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ A )
      = ( mono_2Ec_2Einteger_2Eint__neg @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__SUB) ).

thf(158,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) @ A )
      = ( mono_2Ec_2Einteger_2Eint__neg @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(31,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( A
        = ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
      = ( ( mono_2Ec_2Einteger_2Eint__add @ A @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__SUB__LADD) ).

thf(139,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( A
        = ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
      = ( ( mono_2Ec_2Einteger_2Eint__add @ A @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(21,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__neg @ A )
        = ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__EQ__NEG) ).

thf(107,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( ( mono_2Ec_2Einteger_2Eint__neg @ A )
        = ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(27,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
      = ( ? [C: mono_2Etyop_2Einteger_2Eint] :
            ( ( mono_2Ec_2Einteger_2Eint__mul @ C @ A )
            = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES) ).

thf(126,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
      = ( ? [C: mono_2Etyop_2Einteger_2Eint] :
            ( ( mono_2Ec_2Einteger_2Eint__mul @ C @ A )
            = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(30,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ B @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__SUB__ADD2) ).

thf(136,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__add @ B @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(38,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint,D: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__add @ C @ D ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__ADD2__SUB2) ).

thf(163,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint,D: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ A @ B ) @ ( mono_2Ec_2Einteger_2Eint__add @ C @ D ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ A @ C ) @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(8,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ C @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ A ) )
      = ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__ASSOC) ).

thf(68,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ C @ ( mono_2Ec_2Einteger_2Eint__mul @ B @ A ) )
      = ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(6,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ B @ A )
      = ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__MUL__SYM) ).

thf(62,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ B @ A )
      = ( mono_2Ec_2Einteger_2Eint__mul @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(26,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__LSUB) ).

thf(122,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
     => ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ B @ C ) )
        = ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(13,axiom,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ C @ ( mono_2Ec_2Einteger_2Eint__add @ B @ A ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LDISTRIB) ).

thf(83,plain,
    ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
      ( ( mono_2Ec_2Einteger_2Eint__mul @ C @ ( mono_2Ec_2Einteger_2Eint__add @ B @ A ) )
      = ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ B ) @ ( mono_2Ec_2Einteger_2Eint__mul @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(195,plain,
    $false,
    inference(e,[status(thm)],[101,185,110,179,77,129,155,80,145,104,119,56,142,132,89,116,74,92,65,188,53,169,166,148,161,191,59,71,86,172,113,98,48,95,177,182,158,139,107,126,136,163,68,62,122,83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP012^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.07/0.16  % Command  : run_Leo-III %s %d
% 0.17/0.37  % Computer : n004.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37  % CPULimit : 300
% 0.17/0.37  % WCLimit  : 300
% 0.17/0.37  % DateTime : Sat May 18 15:58:40 EDT 2024
% 0.17/0.37  % CPUTime  : 
% 0.95/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 7.32/3.38  % [INFO] 	 Parsing done (2502ms). 
% 7.32/3.40  % [INFO] 	 Running in sequential loop mode. 
% 8.62/3.72  % [INFO] 	 eprover registered as external prover. 
% 8.62/3.72  % [INFO] 	 cvc4 registered as external prover. 
% 8.62/3.72  % [INFO] 	 Scanning for conjecture ... 
% 12.21/4.73  % [INFO] 	 Found a conjecture (or negated_conjecture) and 18501 axioms. Running axiom selection ... 
% 12.83/4.89  % [INFO] 	 Axiom selection finished. Selected 45 axioms (removed 18456 axioms). 
% 12.83/4.93  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 13.01/4.93  % [INFO] 	 Type checking passed. 
% 13.01/4.94  % [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 ... 
% 21.37/6.37  % External prover 'e' found a proof!
% 21.37/6.37  % [INFO] 	 Killing All external provers ... 
% 21.37/6.38  % Time passed: 5839ms (effective reasoning time: 2975ms)
% 21.37/6.38  % 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)>
% 21.37/6.38  % Axioms used in derivation (45): thm_2Einteger_2EINT__NEG__RMUL, thm_2Einteger_2EINT__ADD__ASSOC, thm_2Einteger_2EINT__NEG__SUB, thm_2Einteger_2EINT__EQ__NEG, thm_2Einteger_2EINT__SUB__NEG2, thm_2Einteger_2EINT__DIVIDES__RADD, thm_2Einteger_2EINT__DIVIDES__RMUL, thm_2Einteger_2EINT__DIVIDES__NEG, thm_2Einteger_2EINT__NEGNEG, thm_2Einteger_2EINT__RDISTRIB, thm_2Einteger_2EINT__SUB__LNEG, thm_2Einteger_2EINT__ADD__SYM, thm_2Einteger_2EINT__SUB__SUB, thm_2Einteger_2EINT__EQ__LADD, thm_2Einteger_2EINT__DIVIDES__MUL, thm_2Einteger_2Eint__sub, thm_2Einteger_2EINT__DIVIDES__LSUB, thm_2Einteger_2EINT__DIVIDES__REFL, thm_2Einteger_2EINT__SUB__TRIANGLE, thm_2Einteger_2EINT__MUL__SYM, thm_2Einteger_2EINT__SUB__SUB2, thm_2Einteger_2EINT__ADD__SUB2, thm_2Einteger_2EINT__DIVIDES, thm_2Einteger_2EINT__MUL__COMM, thm_2Einteger_2EINT__SUB__RNEG, thm_2Einteger_2EINT__DIVIDES__LMUL, thm_2Einteger_2EINT__NEG__EQ, thm_2Einteger_2EINT__DIVIDES__LADD, thm_2Einteger_2EINT__ADD__COMM, thm_2Einteger_2EINT__DIVIDES__TRANS, thm_2Einteger_2EINT__ADD2__SUB2, thm_2Einteger_2EINT__NEG__MUL2, thm_2Einteger_2EINT__SUB__RDISTRIB, thm_2Einteger_2EINT__LDISTRIB, thm_2Einteger_2EINT__SUB__LDISTRIB, thm_2Einteger_2EINT__MUL__ASSOC, thm_2Einteger_2EINT__SUB__ADD, thm_2Einteger_2EINT__EQ__RADD, thm_2Einteger_2EINT__NEG__LMUL, thm_2Einteger_2EINT__NEG__ADD, thm_2Einteger_2EINT__EQ__SUB__RADD, thm_2Einteger_2EINT__EQ__SUB__LADD, thm_2Einteger_2EINT__ADD__SUB, thm_2Einteger_2EINT__DIFFSQ, thm_2Einteger_2EINT__SUB__ADD2
% 21.37/6.38  % No. of inferences in proof: 94
% 21.37/6.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5839 ms resp. 2975 ms w/o parsing
% 21.37/6.43  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.37/6.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------