%------------------------------------------------------------------------------
% File     : Leo-III---1.7.10
% Problem  : ITP198^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  7 07:48:46 EDT 2024

% Result   : Theorem 19.78s 6.22s
% Output   : Refutation 20.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  555
% Syntax   : Number of formulae    :  897 ( 465 unt; 215 typ;   0 def)
%            Number of atoms       : 1403 ( 780 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives : 4920 ( 152   ~;   7   |;  80   &;4257   @)
%                                         (   0 <=>; 424  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :   38 (  37 usr)
%            Number of type conns  : 3966 (3966   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  181 ( 178 usr;   6 con; 0-4 aty)
%            Number of variables   : 2320 ( 291   ^1985   !;  44   ?;2320   :)

% Comments : 
%------------------------------------------------------------------------------
thf(set_Pr605909289e_real_type,type,
    set_Pr605909289e_real: $tType ).

thf(produc1014656201e_real_type,type,
    produc1014656201e_real: $tType ).

thf(set_Pr1517071815e_real_type,type,
    set_Pr1517071815e_real: $tType ).

thf(produc199503591e_real_type,type,
    produc199503591e_real: $tType ).

thf(set_Pr521705191e_real_type,type,
    set_Pr521705191e_real: $tType ).

thf(produc1416364679e_real_type,type,
    produc1416364679e_real: $tType ).

thf(set_Pr821009180r_real_type,type,
    set_Pr821009180r_real: $tType ).

thf(set_Pr397354154e_real_type,type,
    set_Pr397354154e_real: $tType ).

thf(produc2139219430r_real_type,type,
    produc2139219430r_real: $tType ).

thf(produc1993135732e_real_type,type,
    produc1993135732e_real: $tType ).

thf(set_Pr1588228599e_real_type,type,
    set_Pr1588228599e_real: $tType ).

thf(set_Pr1730352763l_real_type,type,
    set_Pr1730352763l_real: $tType ).

thf(set_Pr307567739e_real_type,type,
    set_Pr307567739e_real: $tType ).

thf(produc1120170903e_real_type,type,
    produc1120170903e_real: $tType ).

thf(produc729247771l_real_type,type,
    produc729247771l_real: $tType ).

thf(produc1020032539e_real_type,type,
    produc1020032539e_real: $tType ).

thf(set_Pr366573913real_o_type,type,
    set_Pr366573913real_o: $tType ).

thf(set_Pr268868489e_real_type,type,
    set_Pr268868489e_real: $tType ).

thf(produc1606031907real_o_type,type,
    produc1606031907real_o: $tType ).

thf(produc104944723e_real_type,type,
    produc104944723e_real: $tType ).

thf(set_Pr1919093775l_real_type,type,
    set_Pr1919093775l_real: $tType ).

thf(set_ch845833233e_real_type,type,
    set_ch845833233e_real: $tType ).

thf(produc96687023l_real_type,type,
    produc96687023l_real: $tType ).

thf(set_Pr1053253703real_o_type,type,
    set_Pr1053253703real_o: $tType ).

thf(produc2070499431real_o_type,type,
    produc2070499431real_o: $tType ).

thf(set_Pr1530225953e_real_type,type,
    set_Pr1530225953e_real: $tType ).

thf(set_Pr42335993r_real_type,type,
    set_Pr42335993r_real: $tType ).

thf(produc1863992257e_real_type,type,
    produc1863992257e_real: $tType ).

thf(produc928489369r_real_type,type,
    produc928489369r_real: $tType ).

thf(set_char_real_real_type,type,
    set_char_real_real: $tType ).

thf(set_char_real_o_type,type,
    set_char_real_o: $tType ).

thf(set_variable_real_type,type,
    set_variable_real: $tType ).

thf(set_char_real_type,type,
    set_char_real: $tType ).

thf(denotational_interp_type,type,
    denotational_interp: $tType ).

thf(variable_type,type,
    variable: $tType ).

thf(char_type,type,
    char: $tType ).

thf(real_type,type,
    real: $tType ).

thf(bNF_Gr1652860930e_real_type,type,
    bNF_Gr1652860930e_real: set_char_real_o > ( ( char > real > $o ) > char > set_variable_real > set_variable_real ) > set_Pr268868489e_real ).

thf(bNF_Gr574714974e_real_type,type,
    bNF_Gr574714974e_real: set_char_real_real > ( ( char > real > real ) > produc104944723e_real ) > set_Pr307567739e_real ).

thf(bNF_Gr2096011355e_real_type,type,
    bNF_Gr2096011355e_real: set_char_real > ( ( char > real ) > produc1020032539e_real ) > set_Pr397354154e_real ).

thf(denotational_Consts_type,type,
    denotational_Consts: denotational_interp > char > real ).

thf(denotational_Funcs_type,type,
    denotational_Funcs: denotational_interp > char > real > real ).

thf(denotational_Games_type,type,
    denotational_Games: denotational_interp > char > set_variable_real > set_variable_real ).

thf(denotational_Preds_type,type,
    denotational_Preds: denotational_interp > char > real > $o ).

thf(denota1150374853interp_type,type,
    denota1150374853interp: produc1993135732e_real > denotational_interp ).

thf(denotational_worlds_type,type,
    denotational_worlds: set_variable_real ).

thf(the_Pr1811203438real_o_type,type,
    the_Pr1811203438real_o: ( produc2070499431real_o > $o ) > produc2070499431real_o ).

thf(the_Pr429269900e_real_type,type,
    the_Pr429269900e_real: ( produc104944723e_real > $o ) > produc104944723e_real ).

thf(the_Pr1196831286l_real_type,type,
    the_Pr1196831286l_real: ( produc96687023l_real > $o ) > produc96687023l_real ).

thf(the_Pr1679925410e_real_type,type,
    the_Pr1679925410e_real: ( produc1020032539e_real > $o ) > produc1020032539e_real ).

thf(the_Pr1930357084real_o_type,type,
    the_Pr1930357084real_o: ( produc1606031907real_o > $o ) > produc1606031907real_o ).

thf(the_Pr198758430e_real_type,type,
    the_Pr198758430e_real: ( produc1120170903e_real > $o ) > produc1120170903e_real ).

thf(the_Pr1076580896r_real_type,type,
    the_Pr1076580896r_real: ( produc928489369r_real > $o ) > produc928489369r_real ).

thf(the_Pr543709229e_real_type,type,
    the_Pr543709229e_real: ( produc1993135732e_real > $o ) > produc1993135732e_real ).

thf(if_real_type,type,
    if_real: $o > real > real > real ).

thf(ord_le1113654598e_real_type,type,
    ord_le1113654598e_real: set_variable_real > set_variable_real > $o ).

thf(ord_le2056633321e_real_type,type,
    ord_le2056633321e_real: set_Pr268868489e_real > set_Pr268868489e_real > $o ).

thf(ord_le780198939e_real_type,type,
    ord_le780198939e_real: set_Pr307567739e_real > set_Pr307567739e_real > $o ).

thf(ord_le1631106314e_real_type,type,
    ord_le1631106314e_real: set_Pr397354154e_real > set_Pr397354154e_real > $o ).

thf(order_1507925822e_real_type,type,
    order_1507925822e_real: ( set_variable_real > set_variable_real ) > $o ).

thf(produc1566957527real_o_type,type,
    produc1566957527real_o: ( char > real > $o ) > ( char > real > $o ) > produc2070499431real_o ).

thf(produc2007437005e_real_type,type,
    produc2007437005e_real: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real ).

thf(produc686464615l_real_type,type,
    produc686464615l_real: ( char > real > real ) > ( char > real > real ) > produc96687023l_real ).

thf(produc141013715e_real_type,type,
    produc141013715e_real: ( char > real > real ) > produc104944723e_real > produc1020032539e_real ).

thf(produc1285468373real_o_type,type,
    produc1285468373real_o: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc1606031907real_o ).

thf(produc525232719e_real_type,type,
    produc525232719e_real: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > produc1120170903e_real ).

thf(produc700235985r_real_type,type,
    produc700235985r_real: ( char > real ) > ( char > real ) > produc928489369r_real ).

thf(produc2125489830e_real_type,type,
    produc2125489830e_real: ( char > real ) > produc1020032539e_real > produc1993135732e_real ).

thf(produc1053845203l_real_type,type,
    produc1053845203l_real: produc104944723e_real > ( char > real > real ) > produc729247771l_real ).

thf(produc1957227327e_real_type,type,
    produc1957227327e_real: produc104944723e_real > produc104944723e_real > produc1416364679e_real ).

thf(produc1317530464r_real_type,type,
    produc1317530464r_real: produc1020032539e_real > ( char > real ) > produc2139219430r_real ).

thf(produc680410711e_real_type,type,
    produc680410711e_real: produc1020032539e_real > produc1020032539e_real > produc199503591e_real ).

thf(produc638505729e_real_type,type,
    produc638505729e_real: produc1993135732e_real > produc1993135732e_real > produc1014656201e_real ).

thf(produc214490950real_o_type,type,
    produc214490950real_o: ( char > real > $o ) > ( char > real > $o ) > ( char > real > $o ) > ( char > real > $o ) > $o ).

thf(produc210225566e_real_type,type,
    produc210225566e_real: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ).

thf(produc1051282262l_real_type,type,
    produc1051282262l_real: ( char > real > real ) > ( char > real > real ) > ( char > real > real ) > ( char > real > real ) > $o ).

thf(produc619891650e_real_type,type,
    produc619891650e_real: ( char > real > real ) > produc104944723e_real > ( char > real > real ) > produc104944723e_real > $o ).

thf(produc1635740582real_o_type,type,
    produc1635740582real_o: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o ).

thf(produc1689380158e_real_type,type,
    produc1689380158e_real: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o ).

thf(produc885334464r_real_type,type,
    produc885334464r_real: ( char > real ) > ( char > real ) > ( char > real ) > ( char > real ) > $o ).

thf(produc345845751e_real_type,type,
    produc345845751e_real: ( char > real ) > produc1020032539e_real > ( char > real ) > produc1020032539e_real > $o ).

thf(produc1853244124e_real_type,type,
    produc1853244124e_real: set_char_real_o > ( ( char > real > $o ) > set_ch845833233e_real ) > set_Pr268868489e_real ).

thf(produc522711812e_real_type,type,
    produc522711812e_real: set_char_real_real > ( ( char > real > real ) > set_Pr268868489e_real ) > set_Pr307567739e_real ).

thf(produc1131275492real_o_type,type,
    produc1131275492real_o: set_ch845833233e_real > ( ( char > set_variable_real > set_variable_real ) > set_char_real_o ) > set_Pr366573913real_o ).

thf(produc34356277e_real_type,type,
    produc34356277e_real: set_char_real > ( ( char > real ) > set_Pr307567739e_real ) > set_Pr397354154e_real ).

thf(produc1435543300l_real_type,type,
    produc1435543300l_real: set_Pr268868489e_real > ( produc104944723e_real > set_char_real_real ) > set_Pr1730352763l_real ).

thf(produc1373880559r_real_type,type,
    produc1373880559r_real: set_Pr307567739e_real > ( produc1020032539e_real > set_char_real ) > set_Pr821009180r_real ).

thf(produc169502925al_o_o_type,type,
    produc169502925al_o_o: ( produc2070499431real_o > $o ) > ( char > real > $o ) > ( char > real > $o ) > $o ).

thf(produc809977789real_o_type,type,
    produc809977789real_o: ( produc104944723e_real > $o ) > ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ).

thf(produc311008957real_o_type,type,
    produc311008957real_o: ( produc96687023l_real > $o ) > ( char > real > real ) > ( char > real > real ) > $o ).

thf(produc753879889real_o_type,type,
    produc753879889real_o: ( produc1020032539e_real > $o ) > ( char > real > real ) > produc104944723e_real > $o ).

thf(produc647541685al_o_o_type,type,
    produc647541685al_o_o: ( produc1606031907real_o > $o ) > ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o ).

thf(produc1935758037real_o_type,type,
    produc1935758037real_o: ( produc1120170903e_real > $o ) > ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o ).

thf(produc1735668179real_o_type,type,
    produc1735668179real_o: ( produc928489369r_real > $o ) > ( char > real ) > ( char > real ) > $o ).

thf(produc998184740real_o_type,type,
    produc998184740real_o: ( produc1993135732e_real > $o ) > ( char > real ) > produc1020032539e_real > $o ).

thf(produc1070892532real_o_type,type,
    produc1070892532real_o: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc104944723e_real > $o ).

thf(produc584529143e_real_type,type,
    produc584529143e_real: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real ) > produc104944723e_real > produc104944723e_real ).

thf(produc677394266real_o_type,type,
    produc677394266real_o: ( ( char > real > real ) > produc104944723e_real > $o ) > produc1020032539e_real > $o ).

thf(produc1138486237e_real_type,type,
    produc1138486237e_real: ( ( char > real > real ) > produc104944723e_real > produc1020032539e_real ) > produc1020032539e_real > produc1020032539e_real ).

thf(produc1941565183e_real_type,type,
    produc1941565183e_real: ( ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc104944723e_real ) > produc1606031907real_o > produc104944723e_real ).

thf(produc355430254e_real_type,type,
    produc355430254e_real: ( ( char > real > $o ) > char > real > $o ) > ( ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real ) > produc104944723e_real > produc104944723e_real ).

thf(produc753666538e_real_type,type,
    produc753666538e_real: ( ( char > real > $o ) > char > real > real ) > ( ( char > set_variable_real > set_variable_real ) > produc104944723e_real ) > produc104944723e_real > produc1020032539e_real ).

thf(produc1251731407e_real_type,type,
    produc1251731407e_real: ( ( char > real > $o ) > char > real ) > ( ( char > set_variable_real > set_variable_real ) > produc1020032539e_real ) > produc104944723e_real > produc1993135732e_real ).

thf(produc683016410e_real_type,type,
    produc683016410e_real: ( ( char > real > real ) > char > real > $o ) > ( produc104944723e_real > char > set_variable_real > set_variable_real ) > produc1020032539e_real > produc104944723e_real ).

thf(produc2131385966e_real_type,type,
    produc2131385966e_real: ( ( char > real > real ) > char > real > real ) > ( produc104944723e_real > produc104944723e_real ) > produc1020032539e_real > produc1020032539e_real ).

thf(produc348783435e_real_type,type,
    produc348783435e_real: ( ( char > real > real ) > char > real ) > ( produc104944723e_real > produc1020032539e_real ) > produc1020032539e_real > produc1993135732e_real ).

thf(produc1797673857e_real_type,type,
    produc1797673857e_real: ( ( char > real ) > char > real > $o ) > ( produc1020032539e_real > char > set_variable_real > set_variable_real ) > produc1993135732e_real > produc104944723e_real ).

thf(produc202772275e_real_type,type,
    produc202772275e_real: ( ( char > real ) > char > real > real ) > ( produc1020032539e_real > produc104944723e_real ) > produc1993135732e_real > produc1020032539e_real ).

thf(produc552964208e_real_type,type,
    produc552964208e_real: ( ( char > real ) > char > real ) > ( produc1020032539e_real > produc1020032539e_real ) > produc1993135732e_real > produc1993135732e_real ).

thf(produc2033648741real_o_type,type,
    produc2033648741real_o: ( ( char > real > $o ) > ( char > real > $o ) > $o ) > produc2070499431real_o ).

thf(produc540070591e_real_type,type,
    produc540070591e_real: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc104944723e_real ).

thf(produc606131701l_real_type,type,
    produc606131701l_real: ( ( char > real > real ) > ( char > real > real ) > $o ) > produc96687023l_real ).

thf(produc877953633e_real_type,type,
    produc877953633e_real: ( ( char > real > real ) > produc104944723e_real > $o ) > produc1020032539e_real ).

thf(produc1965585607real_o_type,type,
    produc1965585607real_o: ( ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o ) > produc1606031907real_o ).

thf(produc1545903581e_real_type,type,
    produc1545903581e_real: ( ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc1120170903e_real ).

thf(produc1022533727r_real_type,type,
    produc1022533727r_real: ( ( char > real ) > ( char > real ) > $o ) > produc928489369r_real ).

thf(produc1448824728e_real_type,type,
    produc1448824728e_real: ( ( char > real ) > produc1020032539e_real > $o ) > produc1993135732e_real ).

thf(produc131289260al_o_o_type,type,
    produc131289260al_o_o: ( ( char > real > $o ) > ( char > real > $o ) > $o ) > produc2070499431real_o > $o ).

thf(produc1629511198real_o_type,type,
    produc1629511198real_o: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc104944723e_real > $o ).

thf(produc1906464077e_real_type,type,
    produc1906464077e_real: ( ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real ) > produc104944723e_real > produc104944723e_real ).

thf(produc1095814172real_o_type,type,
    produc1095814172real_o: ( ( char > real > real ) > ( char > real > real ) > $o ) > produc96687023l_real > $o ).

thf(produc679978160real_o_type,type,
    produc679978160real_o: ( ( char > real > real ) > produc104944723e_real > $o ) > produc1020032539e_real > $o ).

thf(produc1202665267e_real_type,type,
    produc1202665267e_real: ( ( char > real > real ) > produc104944723e_real > produc1020032539e_real ) > produc1020032539e_real > produc1020032539e_real ).

thf(produc1467075094al_o_o_type,type,
    produc1467075094al_o_o: ( ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o ) > produc1606031907real_o > $o ).

thf(produc1116016469e_real_type,type,
    produc1116016469e_real: ( ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc104944723e_real ) > produc1606031907real_o > produc104944723e_real ).

thf(produc143994420real_o_type,type,
    produc143994420real_o: ( ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o ) > produc1120170903e_real > $o ).

thf(produc1655853874real_o_type,type,
    produc1655853874real_o: ( ( char > real ) > ( char > real ) > $o ) > produc928489369r_real > $o ).

thf(produc569598981real_o_type,type,
    produc569598981real_o: ( ( char > real ) > produc1020032539e_real > $o ) > produc1993135732e_real > $o ).

thf(produc315720647e_real_type,type,
    produc315720647e_real: ( ( char > real ) > produc1020032539e_real > produc1993135732e_real ) > produc1993135732e_real > produc1993135732e_real ).

thf(produc421130416real_o_type,type,
    produc421130416real_o: ( produc104944723e_real > ( char > real > real ) > $o ) > produc729247771l_real > $o ).

thf(produc991789875e_real_type,type,
    produc991789875e_real: ( produc104944723e_real > ( char > real > real ) > produc1020032539e_real ) > produc729247771l_real > produc1020032539e_real ).

thf(produc864726913e_real_type,type,
    produc864726913e_real: ( produc1020032539e_real > ( char > real ) > produc1993135732e_real ) > produc2139219430r_real > produc1993135732e_real ).

thf(produc1486464481e_real_type,type,
    produc1486464481e_real: produc104944723e_real > char > real > $o ).

thf(produc634910399e_real_type,type,
    produc634910399e_real: produc1020032539e_real > char > real > real ).

thf(produc764495849real_o_type,type,
    produc764495849real_o: produc1606031907real_o > char > set_variable_real > set_variable_real ).

thf(produc1146879930e_real_type,type,
    produc1146879930e_real: produc1993135732e_real > char > real ).

thf(produc1547741887l_real_type,type,
    produc1547741887l_real: produc729247771l_real > produc104944723e_real ).

thf(produc338920564r_real_type,type,
    produc338920564r_real: produc2139219430r_real > produc1020032539e_real ).

thf(produc504912415e_real_type,type,
    produc504912415e_real: produc104944723e_real > char > set_variable_real > set_variable_real ).

thf(produc1179001601e_real_type,type,
    produc1179001601e_real: produc1020032539e_real > produc104944723e_real ).

thf(produc1930427431real_o_type,type,
    produc1930427431real_o: produc1606031907real_o > char > real > $o ).

thf(produc1176159992e_real_type,type,
    produc1176159992e_real: produc1993135732e_real > produc1020032539e_real ).

thf(produc2091833089l_real_type,type,
    produc2091833089l_real: produc729247771l_real > char > real > real ).

thf(produc368200626r_real_type,type,
    produc368200626r_real: produc2139219430r_real > char > real ).

thf(produc443915639real_o_type,type,
    produc443915639real_o: produc2070499431real_o > produc2070499431real_o ).

thf(produc914893101e_real_type,type,
    produc914893101e_real: produc104944723e_real > produc1606031907real_o ).

thf(produc995978247l_real_type,type,
    produc995978247l_real: produc96687023l_real > produc96687023l_real ).

thf(produc865271923e_real_type,type,
    produc865271923e_real: produc1020032539e_real > produc729247771l_real ).

thf(produc192924469real_o_type,type,
    produc192924469real_o: produc1606031907real_o > produc104944723e_real ).

thf(produc1656125423e_real_type,type,
    produc1656125423e_real: produc1120170903e_real > produc1120170903e_real ).

thf(produc1564675697r_real_type,type,
    produc1564675697r_real: produc928489369r_real > produc928489369r_real ).

thf(produc1726279942e_real_type,type,
    produc1726279942e_real: produc1993135732e_real > produc2139219430r_real ).

thf(produc1778103411l_real_type,type,
    produc1778103411l_real: produc729247771l_real > produc1020032539e_real ).

thf(produc918320576r_real_type,type,
    produc918320576r_real: produc2139219430r_real > produc1993135732e_real ).

thf(inv_im1954866834real_o_type,type,
    inv_im1954866834real_o: set_Pr1053253703real_o > ( ( char > real > $o ) > char > real > $o ) > set_Pr1053253703real_o ).

thf(inv_im576609886l_real_type,type,
    inv_im576609886l_real: set_Pr1053253703real_o > ( ( char > real > real ) > char > real > $o ) > set_Pr1919093775l_real ).

thf(inv_im255337747r_real_type,type,
    inv_im255337747r_real: set_Pr1053253703real_o > ( ( char > real ) > char > real > $o ) > set_Pr42335993r_real ).

thf(inv_im1748900174real_o_type,type,
    inv_im1748900174real_o: set_Pr1919093775l_real > ( ( char > real > $o ) > char > real > real ) > set_Pr1053253703real_o ).

thf(inv_im2119069858l_real_type,type,
    inv_im2119069858l_real: set_Pr1919093775l_real > ( ( char > real > real ) > char > real > real ) > set_Pr1919093775l_real ).

thf(inv_im854642519r_real_type,type,
    inv_im854642519r_real: set_Pr1919093775l_real > ( ( char > real ) > char > real > real ) > set_Pr42335993r_real ).

thf(inv_im710342731r_real_type,type,
    inv_im710342731r_real: set_Pr1588228599e_real > ( ( char > real ) > char > set_variable_real > set_variable_real ) > set_Pr42335993r_real ).

thf(inv_im331529689real_o_type,type,
    inv_im331529689real_o: set_Pr42335993r_real > ( ( char > real > $o ) > char > real ) > set_Pr1053253703real_o ).

thf(inv_im96827991l_real_type,type,
    inv_im96827991l_real: set_Pr42335993r_real > ( ( char > real > real ) > char > real ) > set_Pr1919093775l_real ).

thf(inv_im817616652r_real_type,type,
    inv_im817616652r_real: set_Pr42335993r_real > ( ( char > real ) > char > real ) > set_Pr42335993r_real ).

thf(collect_char_real_o_type,type,
    collect_char_real_o: ( ( char > real > $o ) > $o ) > set_char_real_o ).

thf(collec1429138108l_real_type,type,
    collec1429138108l_real: ( ( char > real > real ) > $o ) > set_char_real_real ).

thf(collec425771440e_real_type,type,
    collec425771440e_real: ( ( char > set_variable_real > set_variable_real ) > $o ) > set_ch845833233e_real ).

thf(collect_char_real_type,type,
    collect_char_real: ( ( char > real ) > $o ) > set_char_real ).

thf(collec633296133e_real_type,type,
    collec633296133e_real: ( ( variable > real ) > $o ) > set_variable_real ).

thf(image_448624581real_o_type,type,
    image_448624581real_o: ( produc2070499431real_o > produc2070499431real_o ) > set_Pr1053253703real_o > set_Pr1053253703real_o ).

thf(image_670686893e_real_type,type,
    image_670686893e_real: ( produc104944723e_real > produc104944723e_real ) > set_Pr268868489e_real > set_Pr268868489e_real ).

thf(image_1739334977e_real_type,type,
    image_1739334977e_real: ( produc104944723e_real > produc1020032539e_real ) > set_Pr268868489e_real > set_Pr307567739e_real ).

thf(image_24290429real_o_type,type,
    image_24290429real_o: ( produc104944723e_real > produc1606031907real_o ) > set_Pr268868489e_real > set_Pr366573913real_o ).

thf(image_300296654e_real_type,type,
    image_300296654e_real: ( produc104944723e_real > produc1993135732e_real ) > set_Pr268868489e_real > set_Pr397354154e_real ).

thf(image_1347499973l_real_type,type,
    image_1347499973l_real: ( produc96687023l_real > produc96687023l_real ) > set_Pr1919093775l_real > set_Pr1919093775l_real ).

thf(image_450993193e_real_type,type,
    image_450993193e_real: ( produc1020032539e_real > produc104944723e_real ) > set_Pr307567739e_real > set_Pr268868489e_real ).

thf(image_1823533253e_real_type,type,
    image_1823533253e_real: ( produc1020032539e_real > produc1020032539e_real ) > set_Pr307567739e_real > set_Pr307567739e_real ).

thf(image_1698073930e_real_type,type,
    image_1698073930e_real: ( produc1020032539e_real > produc1993135732e_real ) > set_Pr307567739e_real > set_Pr397354154e_real ).

thf(image_1532748485l_real_type,type,
    image_1532748485l_real: ( produc1020032539e_real > produc729247771l_real ) > set_Pr307567739e_real > set_Pr1730352763l_real ).

thf(image_2028344445e_real_type,type,
    image_2028344445e_real: ( produc1606031907real_o > produc104944723e_real ) > set_Pr366573913real_o > set_Pr268868489e_real ).

thf(image_1495813573e_real_type,type,
    image_1495813573e_real: ( produc1120170903e_real > produc1120170903e_real ) > set_Pr1588228599e_real > set_Pr1588228599e_real ).

thf(image_1523756869r_real_type,type,
    image_1523756869r_real: ( produc928489369r_real > produc928489369r_real ) > set_Pr42335993r_real > set_Pr42335993r_real ).

thf(image_426244814e_real_type,type,
    image_426244814e_real: ( produc1993135732e_real > produc104944723e_real ) > set_Pr397354154e_real > set_Pr268868489e_real ).

thf(image_479987936e_real_type,type,
    image_479987936e_real: ( produc1993135732e_real > produc1020032539e_real ) > set_Pr397354154e_real > set_Pr307567739e_real ).

thf(image_866442351e_real_type,type,
    image_866442351e_real: ( produc1993135732e_real > produc1993135732e_real ) > set_Pr397354154e_real > set_Pr397354154e_real ).

thf(image_1012526049r_real_type,type,
    image_1012526049r_real: ( produc1993135732e_real > produc2139219430r_real ) > set_Pr397354154e_real > set_Pr821009180r_real ).

thf(image_711552709e_real_type,type,
    image_711552709e_real: ( produc729247771l_real > produc1020032539e_real ) > set_Pr1730352763l_real > set_Pr307567739e_real ).

thf(image_152725217e_real_type,type,
    image_152725217e_real: ( produc2139219430r_real > produc1993135732e_real ) > set_Pr821009180r_real > set_Pr397354154e_real ).

thf(uSubst1505767257e_repc_type,type,
    uSubst1505767257e_repc: denotational_interp > char > real > denotational_interp ).

thf(lex_pr2056840373e_real_type,type,
    lex_pr2056840373e_real: set_Pr1053253703real_o > set_Pr1588228599e_real > set_Pr521705191e_real ).

thf(lex_pr592421611e_real_type,type,
    lex_pr592421611e_real: set_Pr1919093775l_real > set_Pr521705191e_real > set_Pr1517071815e_real ).

thf(lex_pr1793499278e_real_type,type,
    lex_pr1793499278e_real: set_Pr42335993r_real > set_Pr1517071815e_real > set_Pr605909289e_real ).

thf(same_f1185518776e_real_type,type,
    same_f1185518776e_real: ( ( char > real > $o ) > $o ) > ( ( char > real > $o ) > set_Pr1588228599e_real ) > set_Pr521705191e_real ).

thf(same_f1243548200e_real_type,type,
    same_f1243548200e_real: ( ( char > real > real ) > $o ) > ( ( char > real > real ) > set_Pr521705191e_real ) > set_Pr1517071815e_real ).

thf(same_f764716049e_real_type,type,
    same_f764716049e_real: ( ( char > real ) > $o ) > ( ( char > real ) > set_Pr1517071815e_real ) > set_Pr605909289e_real ).

thf(member_char_real_o_type,type,
    member_char_real_o: ( char > real > $o ) > set_char_real_o > $o ).

thf(member312374654l_real_type,type,
    member312374654l_real: ( char > real > real ) > set_char_real_real > $o ).

thf(member2042895986e_real_type,type,
    member2042895986e_real: ( char > set_variable_real > set_variable_real ) > set_ch845833233e_real > $o ).

thf(member_char_real_type,type,
    member_char_real: ( char > real ) > set_char_real > $o ).

thf(member1795186320real_o_type,type,
    member1795186320real_o: produc2070499431real_o > set_Pr1053253703real_o > $o ).

thf(member1871517162e_real_type,type,
    member1871517162e_real: produc104944723e_real > set_Pr268868489e_real > $o ).

thf(member1801875544l_real_type,type,
    member1801875544l_real: produc96687023l_real > set_Pr1919093775l_real > $o ).

thf(member544802500e_real_type,type,
    member544802500e_real: produc1020032539e_real > set_Pr307567739e_real > $o ).

thf(member1225120698real_o_type,type,
    member1225120698real_o: produc1606031907real_o > set_Pr366573913real_o > $o ).

thf(member625963584e_real_type,type,
    member625963584e_real: produc1120170903e_real > set_Pr1588228599e_real > $o ).

thf(member1086859330r_real_type,type,
    member1086859330r_real: produc928489369r_real > set_Pr42335993r_real > $o ).

thf(member1491807627e_real_type,type,
    member1491807627e_real: produc1993135732e_real > set_Pr397354154e_real > $o ).

thf(member254017732l_real_type,type,
    member254017732l_real: produc729247771l_real > set_Pr1730352763l_real > $o ).

thf(member2016544560e_real_type,type,
    member2016544560e_real: produc1416364679e_real > set_Pr521705191e_real > $o ).

thf(member1637891325r_real_type,type,
    member1637891325r_real: produc2139219430r_real > set_Pr821009180r_real > $o ).

thf(member1778419728e_real_type,type,
    member1778419728e_real: produc199503591e_real > set_Pr1517071815e_real > $o ).

thf(member1966130802e_real_type,type,
    member1966130802e_real: produc1014656201e_real > set_Pr605909289e_real > $o ).

thf(i_type,type,
    i: denotational_interp ).

thf(d_type,type,
    d: real ).

thf(f_type,type,
    f: char ).

thf(236,axiom,
    ! [A: produc1020032539e_real,B: char > real] :
      ( ( produc918320576r_real @ ( produc1317530464r_real @ A @ B ) )
      = ( produc2125489830e_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_swap__simp) ).

thf(1105,plain,
    ! [A: produc1020032539e_real,B: char > real] :
      ( ( produc918320576r_real @ ( produc1317530464r_real @ A @ B ) )
      = ( produc2125489830e_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(4,axiom,
    ! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
      ( ! [C: variable > real] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collec633296133e_real @ A )
        = ( collec633296133e_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Collect__cong) ).

thf(347,plain,
    ! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
      ( ! [C: variable > real] :
          ( ( A @ C )
          = ( B @ C ) )
     => ( ( collec633296133e_real @ A )
        = ( collec633296133e_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(95,axiom,
    ! [A: produc2070499431real_o > $o,B: char > real > $o,C: char > real > $o] :
      ( ( produc169502925al_o_o @ A @ B @ C )
     => ( A @ ( produc1566957527real_o @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_curryE) ).

thf(628,plain,
    ! [A: produc2070499431real_o > $o,B: char > real > $o,C: char > real > $o] :
      ( ( produc169502925al_o_o @ A @ B @ C )
     => ( A @ ( produc1566957527real_o @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(51,axiom,
    ! [A: $o] :
      ( ( produc998184740real_o
        @ ^ [B: produc1993135732e_real] : A )
      = ( ^ [B: char > real,C: produc1020032539e_real] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_curry__K) ).

thf(481,plain,
    ! [A: $o] :
      ( ( produc998184740real_o
        @ ^ [B: produc1993135732e_real] : A )
      = ( ^ [B: char > real,C: produc1020032539e_real] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(142,axiom,
    ! [A: produc1993135732e_real > $o,B: produc1993135732e_real] :
      ( ! [C: char > real,D: produc1020032539e_real] : ( A @ ( produc2125489830e_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_prod__cases) ).

thf(777,plain,
    ! [A: produc1993135732e_real > $o,B: produc1993135732e_real] :
      ( ! [C: char > real,D: produc1020032539e_real] : ( A @ ( produc2125489830e_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(75,axiom,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr42335993r_real,D: ( char > real > $o ) > char > real] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ ( inv_im331529689real_o @ C @ D ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_in__inv__image) ).

thf(555,plain,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr42335993r_real,D: ( char > real > $o ) > char > real] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ ( inv_im331529689real_o @ C @ D ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(267,axiom,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1146879930e_real @ ( produc2125489830e_real @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_fst__pair) ).

thf(1200,plain,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1146879930e_real @ ( produc2125489830e_real @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(270,axiom,
    ! [A: produc1020032539e_real] :
    ? [B: char > real > real,C: produc104944723e_real] :
      ( A
      = ( produc141013715e_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_surj__pair) ).

thf(1211,plain,
    ! [A: produc1020032539e_real] :
    ? [B: char > real > real,C: produc104944723e_real] :
      ( A
      = ( produc141013715e_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(333,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr821009180r_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( image_152725217e_real @ produc918320576r_real @ C ) )
      = ( member1637891325r_real @ ( produc1317530464r_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_pair__in__swap__image) ).

thf(1401,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr821009180r_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( image_152725217e_real @ produc918320576r_real @ C ) )
      = ( member1637891325r_real @ ( produc1317530464r_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(340,axiom,
    ! [A: produc1020032539e_real,B: char > real,C: set_Pr397354154e_real] :
      ( ( member1637891325r_real @ ( produc1317530464r_real @ A @ B ) @ ( image_1012526049r_real @ produc1726279942e_real @ C ) )
      = ( member1491807627e_real @ ( produc2125489830e_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_pair__in__swap__image) ).

thf(1422,plain,
    ! [A: produc1020032539e_real,B: char > real,C: set_Pr397354154e_real] :
      ( ( member1637891325r_real @ ( produc1317530464r_real @ A @ B ) @ ( image_1012526049r_real @ produc1726279942e_real @ C ) )
      = ( member1491807627e_real @ ( produc2125489830e_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(227,axiom,
    ! [A: ( char > real > real ) > char > real > $o,B: produc104944723e_real > char > set_variable_real > set_variable_real,C: char > real > real,D: produc104944723e_real] :
      ( ( produc683016410e_real @ A @ B @ ( produc141013715e_real @ C @ D ) )
      = ( produc2007437005e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_map__prod__simp) ).

thf(1073,plain,
    ! [A: ( char > real > real ) > char > real > $o,B: produc104944723e_real > char > set_variable_real > set_variable_real,C: char > real > real,D: produc104944723e_real] :
      ( ( produc683016410e_real @ A @ B @ ( produc141013715e_real @ C @ D ) )
      = ( produc2007437005e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(288,axiom,
    ! [A: produc104944723e_real,B: set_char_real_o,C: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ A @ ( produc1853244124e_real @ B @ C ) )
     => ~ ! [D: char > real > $o] :
            ( ( member_char_real_o @ D @ B )
           => ! [E: char > set_variable_real > set_variable_real] :
                ( ( member2042895986e_real @ E @ ( C @ D ) )
               => ( A
                 != ( produc2007437005e_real @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_SigmaE) ).

thf(1269,plain,
    ! [A: produc104944723e_real,B: set_char_real_o,C: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ A @ ( produc1853244124e_real @ B @ C ) )
     => ~ ! [D: char > real > $o] :
            ( ( member_char_real_o @ D @ B )
           => ! [E: char > set_variable_real > set_variable_real] :
                ( ( member2042895986e_real @ E @ ( C @ D ) )
               => ( A
                 != ( produc2007437005e_real @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(105,axiom,
    ! [A: produc1120170903e_real > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( A @ ( produc525232719e_real @ B @ C ) )
     => ( produc1935758037real_o @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_curryI) ).

thf(655,plain,
    ! [A: produc1120170903e_real > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( A @ ( produc525232719e_real @ B @ C ) )
     => ( produc1935758037real_o @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(86,axiom,
    ! [A: ( char > real ) > ( char > real ) > $o,B: char > real,C: char > real] :
      ( ( A @ B @ C )
     => ( produc1655853874real_o @ A @ ( produc700235985r_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_case__prodI) ).

thf(597,plain,
    ! [A: ( char > real ) > ( char > real ) > $o,B: char > real,C: char > real] :
      ( ( A @ B @ C )
     => ( produc1655853874real_o @ A @ ( produc700235985r_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(218,axiom,
    ! [A: set_Pr268868489e_real,B: set_Pr268868489e_real] :
      ( ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] :
          ( ( member1871517162e_real @ ( produc2007437005e_real @ C @ D ) @ A )
         => ( member1871517162e_real @ ( produc2007437005e_real @ C @ D ) @ B ) )
     => ( ord_le2056633321e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_subrelI) ).

thf(1041,plain,
    ! [A: set_Pr268868489e_real,B: set_Pr268868489e_real] :
      ( ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] :
          ( ( member1871517162e_real @ ( produc2007437005e_real @ C @ D ) @ A )
         => ( member1871517162e_real @ ( produc2007437005e_real @ C @ D ) @ B ) )
     => ( ord_le2056633321e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(258,axiom,
    ! [A: produc1993135732e_real] :
      ( A
      = ( produc2125489830e_real @ ( produc1146879930e_real @ A ) @ ( produc1176159992e_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_surjective__pairing) ).

thf(1173,plain,
    ! [A: produc1993135732e_real] :
      ( A
      = ( produc2125489830e_real @ ( produc1146879930e_real @ A ) @ ( produc1176159992e_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(229,axiom,
    ! [A: ( char > real > real ) > $o,B: char > real > real,C: produc104944723e_real > $o,D: produc104944723e_real] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc634910399e_real @ ( produc141013715e_real @ B @ D ) ) )
          & ( C @ ( produc1179001601e_real @ ( produc141013715e_real @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_conjI__realizer) ).

thf(1078,plain,
    ! [A: ( char > real > real ) > $o,B: char > real > real,C: produc104944723e_real > $o,D: produc104944723e_real] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc634910399e_real @ ( produc141013715e_real @ B @ D ) ) )
          & ( C @ ( produc1179001601e_real @ ( produc141013715e_real @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(17,axiom,
    ! [A: set_Pr1053253703real_o,B: set_Pr1053253703real_o] :
      ( ( ( ^ [C: char > real > $o,D: char > real > $o] : ( member1795186320real_o @ ( produc1566957527real_o @ C @ D ) @ A ) )
        = ( ^ [C: char > real > $o,D: char > real > $o] : ( member1795186320real_o @ ( produc1566957527real_o @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_pred__equals__eq2) ).

thf(384,plain,
    ! [A: set_Pr1053253703real_o,B: set_Pr1053253703real_o] :
      ( ( ( ^ [C: char > real > $o,D: char > real > $o] : ( member1795186320real_o @ ( produc1566957527real_o @ C @ D ) @ A ) )
        = ( ^ [C: char > real > $o,D: char > real > $o] : ( member1795186320real_o @ ( produc1566957527real_o @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(69,axiom,
    ! [A: produc2070499431real_o,B: ( char > real > $o ) > ( char > real > $o ) > $o] :
      ( ! [C: char > real > $o,D: char > real > $o] :
          ( ( A
            = ( produc1566957527real_o @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc131289260al_o_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_case__prodI2) ).

thf(533,plain,
    ! [A: produc2070499431real_o,B: ( char > real > $o ) > ( char > real > $o ) > $o] :
      ( ! [C: char > real > $o,D: char > real > $o] :
          ( ( A
            = ( produc1566957527real_o @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc131289260al_o_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(73,axiom,
    ! [A: set_Pr366573913real_o,B: set_Pr366573913real_o] :
      ( ( ( ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( member1225120698real_o @ ( produc1285468373real_o @ C @ D ) @ A ) )
        = ( ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( member1225120698real_o @ ( produc1285468373real_o @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_pred__equals__eq2) ).

thf(550,plain,
    ! [A: set_Pr366573913real_o,B: set_Pr366573913real_o] :
      ( ( ( ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( member1225120698real_o @ ( produc1285468373real_o @ C @ D ) @ A ) )
        = ( ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( member1225120698real_o @ ( produc1285468373real_o @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(57,axiom,
    ( produc1566957527real_o
    = ( ^ [A: char > real > $o,B: char > real > $o] : ( produc2033648741real_o @ ( produc214490950real_o @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Pair__def) ).

thf(500,plain,
    ( produc1566957527real_o
    = ( ^ [A: char > real > $o,B: char > real > $o] : ( produc2033648741real_o @ ( produc214490950real_o @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(255,axiom,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc865271923e_real @ ( produc141013715e_real @ A @ B ) )
      = ( produc1053845203l_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_swap__simp) ).

thf(1164,plain,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc865271923e_real @ ( produc141013715e_real @ A @ B ) )
      = ( produc1053845203l_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(278,axiom,
    ! [A: produc1993135732e_real,B: char > real,C: produc1020032539e_real] :
      ( ( A
        = ( produc2125489830e_real @ B @ C ) )
     => ( ( produc1146879930e_real @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_fstI) ).

thf(1233,plain,
    ! [A: produc1993135732e_real,B: char > real,C: produc1020032539e_real] :
      ( ( A
        = ( produc2125489830e_real @ B @ C ) )
     => ( ( produc1146879930e_real @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(285,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr1730352763l_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( image_711552709e_real @ produc1778103411l_real @ C ) )
      = ( member254017732l_real @ ( produc1053845203l_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_pair__in__swap__image) ).

thf(1260,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr1730352763l_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( image_711552709e_real @ produc1778103411l_real @ C ) )
      = ( member254017732l_real @ ( produc1053845203l_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(313,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( produc522711812e_real @ C @ D ) )
     => ~ ( ( member312374654l_real @ A @ C )
         => ~ ( member1871517162e_real @ B @ ( D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_SigmaE2) ).

thf(1342,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( produc522711812e_real @ C @ D ) )
     => ~ ( ( member312374654l_real @ A @ C )
         => ~ ( member1871517162e_real @ B @ ( D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(178,axiom,
    ( produc2125489830e_real
    = ( ^ [A: char > real,B: produc1020032539e_real] : ( produc1448824728e_real @ ( produc345845751e_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Pair__def) ).

thf(913,plain,
    ( produc2125489830e_real
    = ( ^ [A: char > real,B: produc1020032539e_real] : ( produc1448824728e_real @ ( produc345845751e_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(233,axiom,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( A @ B @ C )
     => ( produc679978160real_o @ A @ ( produc141013715e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_case__prodI) ).

thf(1095,plain,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( A @ B @ C )
     => ( produc679978160real_o @ A @ ( produc141013715e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(173,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: produc104944723e_real] :
      ( ( ( produc1179001601e_real @ ( produc141013715e_real @ A @ B ) )
        = C )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_snd__eqD) ).

thf(898,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: produc104944723e_real] :
      ( ( ( produc1179001601e_real @ ( produc141013715e_real @ A @ B ) )
        = C )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(243,axiom,
    ! [A: char > real,B: produc1993135732e_real] :
      ( ( A
        = ( produc1146879930e_real @ B ) )
      = ( ? [C: produc1020032539e_real] :
            ( B
            = ( produc2125489830e_real @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_eq__fst__iff) ).

thf(1127,plain,
    ! [A: char > real,B: produc1993135732e_real] :
      ( ( A
        = ( produc1146879930e_real @ B ) )
      = ( ? [C: produc1020032539e_real] :
            ( B
            = ( produc2125489830e_real @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(169,axiom,
    ! [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( produc753879889real_o @ A @ B @ C )
     => ( A @ ( produc141013715e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_curryD) ).

thf(885,plain,
    ! [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( produc753879889real_o @ A @ B @ C )
     => ( A @ ( produc141013715e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(319,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( produc522711812e_real @ C @ D ) )
      = ( ( member312374654l_real @ A @ C )
        & ( member1871517162e_real @ B @ ( D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_mem__Sigma__iff) ).

thf(1359,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( produc522711812e_real @ C @ D ) )
      = ( ( member312374654l_real @ A @ C )
        & ( member1871517162e_real @ B @ ( D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(35,axiom,
    ! [A: produc1120170903e_real] :
    ? [B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( A
      = ( produc525232719e_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_surj__pair) ).

thf(436,plain,
    ! [A: produc1120170903e_real] :
    ? [B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( A
      = ( produc525232719e_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(157,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc34356277e_real @ C @ D ) )
     => ( member_char_real @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_SigmaD1) ).

thf(841,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc34356277e_real @ C @ D ) )
     => ( member_char_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(28,axiom,
    ! [A: produc1993135732e_real] :
      ( ( produc918320576r_real @ ( produc1726279942e_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_swap__swap) ).

thf(417,plain,
    ! [A: produc1993135732e_real] :
      ( ( produc918320576r_real @ ( produc1726279942e_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(78,axiom,
    ! [A: produc104944723e_real > ( char > real > real ) > $o,B: produc729247771l_real] :
      ( ( produc679978160real_o
        @ ^ [C: char > real > real,D: produc104944723e_real] : ( A @ D @ C )
        @ ( produc1778103411l_real @ B ) )
      = ( produc421130416real_o @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_case__swap) ).

thf(565,plain,
    ! [A: produc104944723e_real > ( char > real > real ) > $o,B: produc729247771l_real] :
      ( ( produc679978160real_o
        @ ^ [C: char > real > real,D: produc104944723e_real] : ( A @ D @ C )
        @ ( produc1778103411l_real @ B ) )
      = ( produc421130416real_o @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(321,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc34356277e_real @ C @ D ) )
     => ( member544802500e_real @ B @ ( D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_SigmaD2) ).

thf(1366,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc34356277e_real @ C @ D ) )
     => ( member544802500e_real @ B @ ( D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(276,axiom,
    ! [A: produc104944723e_real > $o,B: produc104944723e_real] :
      ( ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( A @ ( produc2007437005e_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_old_Oprod_Oinducts) ).

thf(1228,plain,
    ! [A: produc104944723e_real > $o,B: produc104944723e_real] :
      ( ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( A @ ( produc2007437005e_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(283,axiom,
    ! [A: produc1020032539e_real,B: produc1993135732e_real] :
      ( ( A
        = ( produc1176159992e_real @ B ) )
      = ( ? [C: char > real] :
            ( B
            = ( produc2125489830e_real @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_eq__snd__iff) ).

thf(1254,plain,
    ! [A: produc1020032539e_real,B: produc1993135732e_real] :
      ( ( A
        = ( produc1176159992e_real @ B ) )
      = ( ? [C: char > real] :
            ( B
            = ( produc2125489830e_real @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(130,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] :
      ( ( the_Pr198758430e_real
        @ ( produc143994420real_o
          @ ^ [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc525232719e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_The__split__eq) ).

thf(724,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] :
      ( ( the_Pr198758430e_real
        @ ( produc143994420real_o
          @ ^ [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc525232719e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(128,axiom,
    ! [A: produc2070499431real_o > $o,B: char > real > $o,C: char > real > $o] :
      ( ( produc169502925al_o_o @ A @ B @ C )
     => ( A @ ( produc1566957527real_o @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_curryD) ).

thf(719,plain,
    ! [A: produc2070499431real_o > $o,B: char > real > $o,C: char > real > $o] :
      ( ( produc169502925al_o_o @ A @ B @ C )
     => ( A @ ( produc1566957527real_o @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(144,axiom,
    ! [A: produc1020032539e_real,B: ( char > real ) > char > real > real,C: produc1020032539e_real > produc104944723e_real,D: set_Pr397354154e_real] :
      ( ( member544802500e_real @ A @ ( image_479987936e_real @ ( produc202772275e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real,F: produc1020032539e_real] :
            ( ( A
              = ( produc141013715e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_prod__fun__imageE) ).

thf(785,plain,
    ! [A: produc1020032539e_real,B: ( char > real ) > char > real > real,C: produc1020032539e_real > produc104944723e_real,D: set_Pr397354154e_real] :
      ( ( member544802500e_real @ A @ ( image_479987936e_real @ ( produc202772275e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real,F: produc1020032539e_real] :
            ( ( A
              = ( produc141013715e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(13,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] :
      ( ( produc1656125423e_real @ ( produc525232719e_real @ A @ B ) )
      = ( produc525232719e_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_swap__simp) ).

thf(372,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] :
      ( ( produc1656125423e_real @ ( produc525232719e_real @ A @ B ) )
      = ( produc525232719e_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(59,axiom,
    ! [A: ( char > real > real ) > produc104944723e_real > produc1020032539e_real,B: produc1020032539e_real] :
      ( ( produc991789875e_real
        @ ^ [C: produc104944723e_real,D: char > real > real] : ( A @ D @ C )
        @ ( produc865271923e_real @ B ) )
      = ( produc1202665267e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_case__swap) ).

thf(504,plain,
    ! [A: ( char > real > real ) > produc104944723e_real > produc1020032539e_real,B: produc1020032539e_real] :
      ( ( produc991789875e_real
        @ ^ [C: produc104944723e_real,D: char > real > real] : ( A @ D @ C )
        @ ( produc865271923e_real @ B ) )
      = ( produc1202665267e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(264,axiom,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc1179001601e_real @ ( produc141013715e_real @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_snd__pair) ).

thf(1191,plain,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc1179001601e_real @ ( produc141013715e_real @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(223,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( bNF_Gr1652860930e_real @ C @ D ) )
     => ( member_char_real_o @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_GrD1) ).

thf(1059,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( bNF_Gr1652860930e_real @ C @ D ) )
     => ( member_char_real_o @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(189,axiom,
    ! [A: char > real,B: char > real > real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( denotational_Funcs @ ( denota1150374853interp @ ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ ( produc2007437005e_real @ C @ D ) ) ) ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_Funcs__mkinterp) ).

thf(949,plain,
    ! [A: char > real,B: char > real > real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( denotational_Funcs @ ( denota1150374853interp @ ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ ( produc2007437005e_real @ C @ D ) ) ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(43,axiom,
    ! [A: produc1120170903e_real > $o,B: produc1120170903e_real] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] : ( A @ ( produc525232719e_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_old_Oprod_Oinducts) ).

thf(460,plain,
    ! [A: produc1120170903e_real > $o,B: produc1120170903e_real] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] : ( A @ ( produc525232719e_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(306,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: set_Pr268868489e_real] :
      ( ( member1225120698real_o @ ( produc1285468373real_o @ A @ B ) @ ( image_24290429real_o @ produc914893101e_real @ C ) )
      = ( member1871517162e_real @ ( produc2007437005e_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_pair__in__swap__image) ).

thf(1323,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: set_Pr268868489e_real] :
      ( ( member1225120698real_o @ ( produc1285468373real_o @ A @ B ) @ ( image_24290429real_o @ produc914893101e_real @ C ) )
      = ( member1871517162e_real @ ( produc2007437005e_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(156,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: produc104944723e_real] :
      ( ( A
        = ( produc504912415e_real @ B ) )
      = ( ? [C: char > real > $o] :
            ( B
            = ( produc2007437005e_real @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_eq__snd__iff) ).

thf(838,plain,
    ! [A: char > set_variable_real > set_variable_real,B: produc104944723e_real] :
      ( ( A
        = ( produc504912415e_real @ B ) )
      = ( ? [C: char > real > $o] :
            ( B
            = ( produc2007437005e_real @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(122,axiom,
    ! [A: set_ch845833233e_real] :
      ( ( collec425771440e_real
        @ ^ [B: char > set_variable_real > set_variable_real] : ( member2042895986e_real @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_Collect__mem__eq) ).

thf(702,plain,
    ! [A: set_ch845833233e_real] :
      ( ( collec425771440e_real
        @ ^ [B: char > set_variable_real > set_variable_real] : ( member2042895986e_real @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(137,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ A @ B )
        = ( produc525232719e_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_Pair__inject) ).

thf(751,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ A @ B )
        = ( produc525232719e_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(148,axiom,
    ! [A: char,B: char,C: denotational_interp,D: real] :
      ( ( ( A = B )
       => ( ( denotational_Consts @ ( uSubst1505767257e_repc @ C @ B @ D ) @ A )
          = D ) )
      & ( ( A != B )
       => ( ( denotational_Consts @ ( uSubst1505767257e_repc @ C @ B @ D ) @ A )
          = ( denotational_Consts @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_repc__consts) ).

thf(802,plain,
    ! [A: char,B: char,C: denotational_interp,D: real] :
      ( ( ( A = B )
       => ( ( denotational_Consts @ ( uSubst1505767257e_repc @ C @ B @ D ) @ A )
          = D ) )
      & ( ( A != B )
       => ( ( denotational_Consts @ ( uSubst1505767257e_repc @ C @ B @ D ) @ A )
          = ( denotational_Consts @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(3,axiom,
    ! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
      ( ( ord_le1113654598e_real @ ( collec633296133e_real @ A ) @ ( collec633296133e_real @ B ) )
      = ( ! [C: variable > real] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_Collect__mono__iff) ).

thf(344,plain,
    ! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
      ( ( ord_le1113654598e_real @ ( collec633296133e_real @ A ) @ ( collec633296133e_real @ B ) )
      = ( ! [C: variable > real] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(174,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr268868489e_real,D: ( char > real > $o ) > char > real,E: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ C )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_300296654e_real @ ( produc1251731407e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_map__prod__imageI) ).

thf(902,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr268868489e_real,D: ( char > real > $o ) > char > real,E: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ C )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_300296654e_real @ ( produc1251731407e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(281,axiom,
    ! [A: produc1993135732e_real] :
      ~ ! [B: char > real,C: char > real > real,D: produc104944723e_real] :
          ( A
         != ( produc2125489830e_real @ B @ ( produc141013715e_real @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_prod__cases3) ).

thf(1247,plain,
    ! [A: produc1993135732e_real] :
      ~ ! [B: char > real,C: char > real > real,D: produc104944723e_real] :
          ( A
         != ( produc2125489830e_real @ B @ ( produc141013715e_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(209,axiom,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: produc104944723e_real] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc2007437005e_real @ B @ C ) )
       => ( A @ ( produc1486464481e_real @ D ) @ ( produc504912415e_real @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_BNF__Greatest__Fixpoint_Osubst__Pair) ).

thf(1013,plain,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: produc104944723e_real] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc2007437005e_real @ B @ C ) )
       => ( A @ ( produc1486464481e_real @ D ) @ ( produc504912415e_real @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(320,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > real,C: char > real > real,D: char > real > $o] :
      ( ! [E: char] : ( order_1507925822e_real @ ( A @ E ) )
     => ( ( denotational_Games @ ( denota1150374853interp @ ( produc2125489830e_real @ B @ ( produc141013715e_real @ C @ ( produc2007437005e_real @ D @ A ) ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_Games__mkinterp) ).

thf(1362,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > real,C: char > real > real,D: char > real > $o] :
      ( ! [E: char] : ( order_1507925822e_real @ ( A @ E ) )
     => ( ( denotational_Games @ ( denota1150374853interp @ ( produc2125489830e_real @ B @ ( produc141013715e_real @ C @ ( produc2007437005e_real @ D @ A ) ) ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(196,axiom,
    ! [A: ( char > real > $o ) > char > real > real,B: ( char > set_variable_real > set_variable_real ) > produc104944723e_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( produc753666538e_real @ A @ B @ ( produc2007437005e_real @ C @ D ) )
      = ( produc141013715e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_map__prod__simp) ).

thf(969,plain,
    ! [A: ( char > real > $o ) > char > real > real,B: ( char > set_variable_real > set_variable_real ) > produc104944723e_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( produc753666538e_real @ A @ B @ ( produc2007437005e_real @ C @ D ) )
      = ( produc141013715e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(89,axiom,
    ! [A: produc2070499431real_o] :
      ~ ! [B: char > real > $o,C: char > real > $o] :
          ( A
         != ( produc1566957527real_o @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_old_Oprod_Oexhaust) ).

thf(606,plain,
    ! [A: produc2070499431real_o] :
      ~ ! [B: char > real > $o,C: char > real > $o] :
          ( A
         != ( produc1566957527real_o @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(299,axiom,
    ! [A: produc1020032539e_real,B: ( char > real > real ) > char > real > real,C: produc104944723e_real > produc104944723e_real,D: set_Pr307567739e_real] :
      ( ( member544802500e_real @ A @ ( image_1823533253e_real @ ( produc2131385966e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > real,F: produc104944723e_real] :
            ( ( A
              = ( produc141013715e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_prod__fun__imageE) ).

thf(1302,plain,
    ! [A: produc1020032539e_real,B: ( char > real > real ) > char > real > real,C: produc104944723e_real > produc104944723e_real,D: set_Pr307567739e_real] :
      ( ( member544802500e_real @ A @ ( image_1823533253e_real @ ( produc2131385966e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > real,F: produc104944723e_real] :
            ( ( A
              = ( produc141013715e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(145,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real] :
      ( ( ( produc634910399e_real @ ( produc141013715e_real @ A @ B ) )
        = C )
     => ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_fst__eqD) ).

thf(789,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real] :
      ( ( ( produc634910399e_real @ ( produc141013715e_real @ A @ B ) )
        = C )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(84,axiom,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,B: produc1606031907real_o] :
      ( ( produc1629511198real_o
        @ ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( A @ D @ C )
        @ ( produc192924469real_o @ B ) )
      = ( produc1467075094al_o_o @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_case__swap) ).

thf(591,plain,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,B: produc1606031907real_o] :
      ( ( produc1629511198real_o
        @ ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( A @ D @ C )
        @ ( produc192924469real_o @ B ) )
      = ( produc1467075094al_o_o @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(251,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: char > real] :
      ( ( ( produc1146879930e_real @ ( produc2125489830e_real @ A @ B ) )
        = C )
     => ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_fst__eqD) ).

thf(1151,plain,
    ! [A: char > real,B: produc1020032539e_real,C: char > real] :
      ( ( ( produc1146879930e_real @ ( produc2125489830e_real @ A @ B ) )
        = C )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(6,axiom,
    produc677394266real_o = produc679978160real_o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_internal__case__prod__def) ).

thf(353,plain,
    produc677394266real_o = produc679978160real_o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(153,axiom,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1726279942e_real @ ( produc2125489830e_real @ A @ B ) )
      = ( produc1317530464r_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_swap__simp) ).

thf(821,plain,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1726279942e_real @ ( produc2125489830e_real @ A @ B ) )
      = ( produc1317530464r_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(175,axiom,
    ( produc809977789real_o
    = ( ^ [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] : ( A @ ( produc2007437005e_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_curry__conv) ).

thf(905,plain,
    ( produc809977789real_o
    = ( ^ [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] : ( A @ ( produc2007437005e_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(339,axiom,
    ! [A: produc1993135732e_real,B: ( char > real > $o ) > char > real,C: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real,D: set_Pr268868489e_real] :
      ( ( member1491807627e_real @ A @ ( image_300296654e_real @ ( produc1251731407e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > $o,F: char > set_variable_real > set_variable_real] :
            ( ( A
              = ( produc2125489830e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_prod__fun__imageE) ).

thf(1418,plain,
    ! [A: produc1993135732e_real,B: ( char > real > $o ) > char > real,C: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real,D: set_Pr268868489e_real] :
      ( ( member1491807627e_real @ A @ ( image_300296654e_real @ ( produc1251731407e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > $o,F: char > set_variable_real > set_variable_real] :
            ( ( A
              = ( produc2125489830e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(93,axiom,
    ! [A: char > real,B: char > real] :
      ( ( the_Pr1076580896r_real
        @ ( produc1655853874real_o
          @ ^ [C: char > real,D: char > real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc700235985r_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_The__split__eq) ).

thf(623,plain,
    ! [A: char > real,B: char > real] :
      ( ( the_Pr1076580896r_real
        @ ( produc1655853874real_o
          @ ^ [C: char > real,D: char > real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc700235985r_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(246,axiom,
    ! [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( produc998184740real_o @ A @ B @ C )
     => ( A @ ( produc2125489830e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_curryD) ).

thf(1136,plain,
    ! [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( produc998184740real_o @ A @ B @ C )
     => ( A @ ( produc2125489830e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(155,axiom,
    ! [A: produc1993135732e_real,B: ( char > real > real ) > char > real,C: produc104944723e_real > produc1020032539e_real,D: set_Pr307567739e_real] :
      ( ( member1491807627e_real @ A @ ( image_1698073930e_real @ ( produc348783435e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > real,F: produc104944723e_real] :
            ( ( A
              = ( produc2125489830e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_prod__fun__imageE) ).

thf(834,plain,
    ! [A: produc1993135732e_real,B: ( char > real > real ) > char > real,C: produc104944723e_real > produc1020032539e_real,D: set_Pr307567739e_real] :
      ( ( member1491807627e_real @ A @ ( image_1698073930e_real @ ( produc348783435e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > real,F: produc104944723e_real] :
            ( ( A
              = ( produc2125489830e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(327,axiom,
    ( produc998184740real_o
    = ( ^ [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] : ( A @ ( produc2125489830e_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_curry__def) ).

thf(1383,plain,
    ( produc998184740real_o
    = ( ^ [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] : ( A @ ( produc2125489830e_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(81,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: char > real > $o] :
      ( ( ( produc1285468373real_o @ A @ B )
        = ( produc1285468373real_o @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Pair__inject) ).

thf(574,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: char > real > $o] :
      ( ( ( produc1285468373real_o @ A @ B )
        = ( produc1285468373real_o @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(261,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr307567739e_real,D: ( char > real > real ) > char > real,E: produc104944723e_real > produc1020032539e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ C )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_1698073930e_real @ ( produc348783435e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_map__prod__imageI) ).

thf(1183,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr307567739e_real,D: ( char > real > real ) > char > real,E: produc104944723e_real > produc1020032539e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ C )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_1698073930e_real @ ( produc348783435e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(292,axiom,
    ! [A: produc104944723e_real,B: char > real > real,C: set_Pr307567739e_real] :
      ( ( member254017732l_real @ ( produc1053845203l_real @ A @ B ) @ ( image_1532748485l_real @ produc865271923e_real @ C ) )
      = ( member544802500e_real @ ( produc141013715e_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_pair__in__swap__image) ).

thf(1283,plain,
    ! [A: produc104944723e_real,B: char > real > real,C: set_Pr307567739e_real] :
      ( ( member254017732l_real @ ( produc1053845203l_real @ A @ B ) @ ( image_1532748485l_real @ produc865271923e_real @ C ) )
      = ( member544802500e_real @ ( produc141013715e_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(88,axiom,
    ! [A: produc1606031907real_o,B: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > real > $o] :
          ( ( A
            = ( produc1285468373real_o @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc1467075094al_o_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_case__prodI2) ).

thf(602,plain,
    ! [A: produc1606031907real_o,B: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > real > $o] :
          ( ( A
            = ( produc1285468373real_o @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc1467075094al_o_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(21,axiom,
    produc1941565183e_real = produc1116016469e_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_internal__case__prod__def) ).

thf(397,plain,
    produc1941565183e_real = produc1116016469e_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(325,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc1853244124e_real @ C @ D ) )
     => ~ ( ( member_char_real_o @ A @ C )
         => ~ ( member2042895986e_real @ B @ ( D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_SigmaE2) ).

thf(1377,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc1853244124e_real @ C @ D ) )
     => ~ ( ( member_char_real_o @ A @ C )
         => ~ ( member2042895986e_real @ B @ ( D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(98,axiom,
    ! [A: char > real > real,B: char > real > real,C: set_Pr1919093775l_real,D: ( char > real > real ) > char > real > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ ( inv_im2119069858l_real @ C @ D ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_in__inv__image) ).

thf(634,plain,
    ! [A: char > real > real,B: char > real > real,C: set_Pr1919093775l_real,D: ( char > real > real ) > char > real > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ ( inv_im2119069858l_real @ C @ D ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(164,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc1853244124e_real @ C @ D ) )
      = ( ( member_char_real_o @ A @ C )
        & ( member2042895986e_real @ B @ ( D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_mem__Sigma__iff) ).

thf(866,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc1853244124e_real @ C @ D ) )
      = ( ( member_char_real_o @ A @ C )
        & ( member2042895986e_real @ B @ ( D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(141,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr366573913real_o] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( image_2028344445e_real @ produc192924469real_o @ C ) )
      = ( member1225120698real_o @ ( produc1285468373real_o @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_pair__in__swap__image) ).

thf(774,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr366573913real_o] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( image_2028344445e_real @ produc192924469real_o @ C ) )
      = ( member1225120698real_o @ ( produc1285468373real_o @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(316,axiom,
    ( produc918320576r_real
    = ( ^ [A: produc2139219430r_real] : ( produc2125489830e_real @ ( produc368200626r_real @ A ) @ ( produc338920564r_real @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_prod_Oswap__def) ).

thf(1351,plain,
    ( produc918320576r_real
    = ( ^ [A: produc2139219430r_real] : ( produc2125489830e_real @ ( produc368200626r_real @ A ) @ ( produc338920564r_real @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(107,axiom,
    ( order_1507925822e_real
    = ( ^ [A: set_variable_real > set_variable_real] :
        ! [B: set_variable_real,C: set_variable_real] :
          ( ( ord_le1113654598e_real @ B @ C )
         => ( ord_le1113654598e_real @ ( A @ B ) @ ( A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_mon__mono) ).

thf(660,plain,
    ( order_1507925822e_real
    = ( ^ [A: set_variable_real > set_variable_real] :
        ! [B: set_variable_real,C: set_variable_real] :
          ( ( ord_le1113654598e_real @ B @ C )
         => ( ord_le1113654598e_real @ ( A @ B ) @ ( A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(204,axiom,
    ( produc141013715e_real
    = ( ^ [A: char > real > real,B: produc104944723e_real] : ( produc877953633e_real @ ( produc619891650e_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Pair__def) ).

thf(998,plain,
    ( produc141013715e_real
    = ( ^ [A: char > real > real,B: produc104944723e_real] : ( produc877953633e_real @ ( produc619891650e_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(314,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc34356277e_real @ C @ D ) )
     => ~ ( ( member_char_real @ A @ C )
         => ~ ( member544802500e_real @ B @ ( D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_SigmaE2) ).

thf(1345,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc34356277e_real @ C @ D ) )
     => ~ ( ( member_char_real @ A @ C )
         => ~ ( member544802500e_real @ B @ ( D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(280,axiom,
    ! [A: produc1020032539e_real,B: set_char_real_real,C: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ A @ ( produc522711812e_real @ B @ C ) )
     => ~ ! [D: char > real > real] :
            ( ( member312374654l_real @ D @ B )
           => ! [E: produc104944723e_real] :
                ( ( member1871517162e_real @ E @ ( C @ D ) )
               => ( A
                 != ( produc141013715e_real @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_SigmaE) ).

thf(1242,plain,
    ! [A: produc1020032539e_real,B: set_char_real_real,C: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ A @ ( produc522711812e_real @ B @ C ) )
     => ~ ! [D: char > real > real] :
            ( ( member312374654l_real @ D @ B )
           => ! [E: produc104944723e_real] :
                ( ( member1871517162e_real @ E @ ( C @ D ) )
               => ( A
                 != ( produc141013715e_real @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(60,axiom,
    ! [A: char > real > real,B: char > real > real,C: set_Pr1053253703real_o,D: ( char > real > real ) > char > real > $o] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ ( inv_im576609886l_real @ C @ D ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_in__inv__image) ).

thf(507,plain,
    ! [A: char > real > real,B: char > real > real,C: set_Pr1053253703real_o,D: ( char > real > real ) > char > real > $o] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ ( inv_im576609886l_real @ C @ D ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(40,axiom,
    ! [A: set_char_real_o] :
      ( ( collect_char_real_o
        @ ^ [B: char > real > $o] : ( member_char_real_o @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_Collect__mem__eq) ).

thf(452,plain,
    ! [A: set_char_real_o] :
      ( ( collect_char_real_o
        @ ^ [B: char > real > $o] : ( member_char_real_o @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(16,axiom,
    ! [A: produc1120170903e_real,B: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
          ( ( A
            = ( produc525232719e_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc143994420real_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_case__prodI2) ).

thf(380,plain,
    ! [A: produc1120170903e_real,B: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
          ( ( A
            = ( produc525232719e_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc143994420real_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(146,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( ( produc141013715e_real @ A @ B )
        = ( produc141013715e_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Pair__inject) ).

thf(793,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( ( produc141013715e_real @ A @ B )
        = ( produc141013715e_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(182,axiom,
    ! [A: produc1993135732e_real] :
      ~ ! [B: char > real,C: char > real > real,D: char > real > $o,E: char > set_variable_real > set_variable_real] :
          ( A
         != ( produc2125489830e_real @ B @ ( produc141013715e_real @ C @ ( produc2007437005e_real @ D @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_prod__cases4) ).

thf(925,plain,
    ! [A: produc1993135732e_real] :
      ~ ! [B: char > real,C: char > real > real,D: char > real > $o,E: char > set_variable_real > set_variable_real] :
          ( A
         != ( produc2125489830e_real @ B @ ( produc141013715e_real @ C @ ( produc2007437005e_real @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(300,axiom,
    ! [A: produc1993135732e_real > $o,B: produc1993135732e_real] :
      ( ! [C: char > real,D: char > real > real,E: char > real > $o,F: char > set_variable_real > set_variable_real] : ( A @ ( produc2125489830e_real @ C @ ( produc141013715e_real @ D @ ( produc2007437005e_real @ E @ F ) ) ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_prod__induct4) ).

thf(1306,plain,
    ! [A: produc1993135732e_real > $o,B: produc1993135732e_real] :
      ( ! [C: char > real,D: char > real > real,E: char > real > $o,F: char > set_variable_real > set_variable_real] : ( A @ ( produc2125489830e_real @ C @ ( produc141013715e_real @ D @ ( produc2007437005e_real @ E @ F ) ) ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(139,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o] :
      ( ( the_Pr1930357084real_o
        @ ( produc1467075094al_o_o
          @ ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc1285468373real_o @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_The__split__eq) ).

thf(761,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o] :
      ( ( the_Pr1930357084real_o
        @ ( produc1467075094al_o_o
          @ ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc1285468373real_o @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(149,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr268868489e_real,D: ( char > real > $o ) > char > real > real,E: ( char > set_variable_real > set_variable_real ) > produc104944723e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ C )
     => ( member544802500e_real @ ( produc141013715e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_1739334977e_real @ ( produc753666538e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_map__prod__imageI) ).

thf(810,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr268868489e_real,D: ( char > real > $o ) > char > real > real,E: ( char > set_variable_real > set_variable_real ) > produc104944723e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ C )
     => ( member544802500e_real @ ( produc141013715e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_1739334977e_real @ ( produc753666538e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(302,axiom,
    ! [A: set_ch845833233e_real,B: set_char_real_o] :
      ( ( image_2028344445e_real
        @ ( produc1116016469e_real
          @ ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( produc2007437005e_real @ D @ C ) )
        @ ( produc1131275492real_o @ A
          @ ^ [C: char > set_variable_real > set_variable_real] : B ) )
      = ( produc1853244124e_real @ B
        @ ^ [C: char > real > $o] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_swap__product) ).

thf(1311,plain,
    ! [A: set_ch845833233e_real,B: set_char_real_o] :
      ( ( image_2028344445e_real
        @ ( produc1116016469e_real
          @ ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( produc2007437005e_real @ D @ C ) )
        @ ( produc1131275492real_o @ A
          @ ^ [C: char > set_variable_real > set_variable_real] : B ) )
      = ( produc1853244124e_real @ B
        @ ^ [C: char > real > $o] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(126,axiom,
    ! [A: produc1606031907real_o > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( produc647541685al_o_o @ A @ B @ C )
     => ( A @ ( produc1285468373real_o @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_curryD) ).

thf(714,plain,
    ! [A: produc1606031907real_o > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( produc647541685al_o_o @ A @ B @ C )
     => ( A @ ( produc1285468373real_o @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(187,axiom,
    ! [A: produc104944723e_real] :
      ~ ! [B: char > real > $o,C: char > set_variable_real > set_variable_real] :
          ( A
         != ( produc2007437005e_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_old_Oprod_Oexhaust) ).

thf(942,plain,
    ! [A: produc104944723e_real] :
      ~ ! [B: char > real > $o,C: char > set_variable_real > set_variable_real] :
          ( A
         != ( produc2007437005e_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(36,axiom,
    ! [A: produc928489369r_real > $o,B: char > real,C: char > real] :
      ( ( A @ ( produc700235985r_real @ B @ C ) )
     => ( produc1735668179real_o @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_curryI) ).

thf(439,plain,
    ! [A: produc928489369r_real > $o,B: char > real,C: char > real] :
      ( ( A @ ( produc700235985r_real @ B @ C ) )
     => ( produc1735668179real_o @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(289,axiom,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1176159992e_real @ ( produc2125489830e_real @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_snd__conv) ).

thf(1274,plain,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1176159992e_real @ ( produc2125489830e_real @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(177,axiom,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( the_Pr1679925410e_real
        @ ( produc679978160real_o
          @ ^ [C: char > real > real,D: produc104944723e_real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc141013715e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_The__split__eq) ).

thf(910,plain,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( the_Pr1679925410e_real
        @ ( produc679978160real_o
          @ ^ [C: char > real > real,D: produc104944723e_real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc141013715e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(192,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr397354154e_real,D: ( char > real ) > char > real,E: produc1020032539e_real > produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ C )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_866442351e_real @ ( produc552964208e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_map__prod__imageI) ).

thf(957,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr397354154e_real,D: ( char > real ) > char > real,E: produc1020032539e_real > produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ C )
     => ( member1491807627e_real @ ( produc2125489830e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_866442351e_real @ ( produc552964208e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(190,axiom,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1176159992e_real @ ( produc2125489830e_real @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_snd__pair) ).

thf(952,plain,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1176159992e_real @ ( produc2125489830e_real @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(19,axiom,
    ! [A: produc1606031907real_o] :
      ( ( produc914893101e_real @ ( produc192924469real_o @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_swap__swap) ).

thf(392,plain,
    ! [A: produc1606031907real_o] :
      ( ( produc914893101e_real @ ( produc192924469real_o @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(32,axiom,
    ! [A: produc1606031907real_o > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( produc647541685al_o_o @ A @ B @ C )
     => ( A @ ( produc1285468373real_o @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_curryE) ).

thf(429,plain,
    ! [A: produc1606031907real_o > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( produc647541685al_o_o @ A @ B @ C )
     => ( A @ ( produc1285468373real_o @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(279,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( ( produc1486464481e_real @ ( produc2007437005e_real @ A @ B ) )
        = C )
     => ( A = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_fst__eqD) ).

thf(1238,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( ( produc1486464481e_real @ ( produc2007437005e_real @ A @ B ) )
        = C )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(119,axiom,
    ! [A: produc1606031907real_o] :
      ~ ! [B: char > set_variable_real > set_variable_real,C: char > real > $o] :
          ( A
         != ( produc1285468373real_o @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_old_Oprod_Oexhaust) ).

thf(693,plain,
    ! [A: produc1606031907real_o] :
      ~ ! [B: char > set_variable_real > set_variable_real,C: char > real > $o] :
          ( A
         != ( produc1285468373real_o @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(96,axiom,
    ( produc1285468373real_o
    = ( ^ [A: char > set_variable_real > set_variable_real,B: char > real > $o] : ( produc1965585607real_o @ ( produc1635740582real_o @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Pair__def) ).

thf(630,plain,
    ( produc1285468373real_o
    = ( ^ [A: char > set_variable_real > set_variable_real,B: char > real > $o] : ( produc1965585607real_o @ ( produc1635740582real_o @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(167,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( ( produc141013715e_real @ A @ B )
        = ( produc141013715e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_prod_Oinject) ).

thf(879,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( ( produc141013715e_real @ A @ B )
        = ( produc141013715e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(109,axiom,
    ! [A: produc1120170903e_real > $o,B: produc1120170903e_real] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] : ( A @ ( produc525232719e_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_prod__cases) ).

thf(665,plain,
    ! [A: produc1120170903e_real > $o,B: produc1120170903e_real] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] : ( A @ ( produc525232719e_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(253,axiom,
    ! [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( produc809977789real_o @ A @ B @ C )
     => ( A @ ( produc2007437005e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_curryD) ).

thf(1159,plain,
    ! [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( produc809977789real_o @ A @ B @ C )
     => ( A @ ( produc2007437005e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(291,axiom,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( produc679978160real_o @ A @ ( produc141013715e_real @ B @ C ) )
     => ( A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_case__prodD) ).

thf(1281,plain,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( produc679978160real_o @ A @ ( produc141013715e_real @ B @ C ) )
     => ( A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(330,axiom,
    ! [A: produc1020032539e_real] :
      ~ ! [B: char > real > real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
          ( A
         != ( produc141013715e_real @ B @ ( produc2007437005e_real @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_prod__cases3) ).

thf(1392,plain,
    ! [A: produc1020032539e_real] :
      ~ ! [B: char > real > real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
          ( A
         != ( produc141013715e_real @ B @ ( produc2007437005e_real @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(115,axiom,
    ! [A: ( char > real > real ) > ( char > real > real ) > $o,B: char > real > real,C: char > real > real] :
      ( ( A @ B @ C )
     => ( produc1095814172real_o @ A @ ( produc686464615l_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_case__prodI) ).

thf(682,plain,
    ! [A: ( char > real > real ) > ( char > real > real ) > $o,B: char > real > real,C: char > real > real] :
      ( ( A @ B @ C )
     => ( produc1095814172real_o @ A @ ( produc686464615l_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(335,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc504912415e_real @ ( produc2007437005e_real @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_snd__pair) ).

thf(1407,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc504912415e_real @ ( produc2007437005e_real @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(64,axiom,
    produc584529143e_real = produc1906464077e_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_internal__case__prod__def) ).

thf(519,plain,
    produc584529143e_real = produc1906464077e_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(120,axiom,
    ! [A: produc1120170903e_real > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( produc1935758037real_o @ A @ B @ C )
     => ( A @ ( produc525232719e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_curryE) ).

thf(697,plain,
    ! [A: produc1120170903e_real > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( produc1935758037real_o @ A @ B @ C )
     => ( A @ ( produc525232719e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(103,axiom,
    ! [A: produc928489369r_real] :
    ? [B: char > real,C: char > real] :
      ( A
      = ( produc700235985r_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_surj__pair) ).

thf(650,plain,
    ! [A: produc928489369r_real] :
    ? [B: char > real,C: char > real] :
      ( A
      = ( produc700235985r_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(91,axiom,
    ! [A: produc104944723e_real] :
      ( ( produc192924469real_o @ ( produc914893101e_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_swap__swap) ).

thf(615,plain,
    ! [A: produc104944723e_real] :
      ( ( produc192924469real_o @ ( produc914893101e_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(308,axiom,
    ! [A: ( char > real > real ) > char > real > real,B: produc104944723e_real > produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( produc2131385966e_real @ A @ B @ ( produc141013715e_real @ C @ D ) )
      = ( produc141013715e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_map__prod__simp) ).

thf(1328,plain,
    ! [A: ( char > real > real ) > char > real > real,B: produc104944723e_real > produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( produc2131385966e_real @ A @ B @ ( produc141013715e_real @ C @ D ) )
      = ( produc141013715e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(238,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( the_Pr429269900e_real
        @ ( produc1629511198real_o
          @ ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc2007437005e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_The__split__eq) ).

thf(1111,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( the_Pr429269900e_real
        @ ( produc1629511198real_o
          @ ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc2007437005e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(341,axiom,
    ! [A: produc1020032539e_real,B: ( char > real > $o ) > char > real > real,C: ( char > set_variable_real > set_variable_real ) > produc104944723e_real,D: set_Pr268868489e_real] :
      ( ( member544802500e_real @ A @ ( image_1739334977e_real @ ( produc753666538e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > $o,F: char > set_variable_real > set_variable_real] :
            ( ( A
              = ( produc141013715e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_prod__fun__imageE) ).

thf(1425,plain,
    ! [A: produc1020032539e_real,B: ( char > real > $o ) > char > real > real,C: ( char > set_variable_real > set_variable_real ) > produc104944723e_real,D: set_Pr268868489e_real] :
      ( ( member544802500e_real @ A @ ( image_1739334977e_real @ ( produc753666538e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > $o,F: char > set_variable_real > set_variable_real] :
            ( ( A
              = ( produc141013715e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(207,axiom,
    ! [A: produc1020032539e_real > ( char > real ) > $o,B: produc1020032539e_real,C: char > real] :
      ( ( A @ B @ C )
     => ( A @ ( produc1176159992e_real @ ( produc2125489830e_real @ C @ B ) ) @ ( produc1146879930e_real @ ( produc2125489830e_real @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_exI__realizer) ).

thf(1006,plain,
    ! [A: produc1020032539e_real > ( char > real ) > $o,B: produc1020032539e_real,C: char > real] :
      ( ( A @ B @ C )
     => ( A @ ( produc1176159992e_real @ ( produc2125489830e_real @ C @ B ) ) @ ( produc1146879930e_real @ ( produc2125489830e_real @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(247,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( ( produc141013715e_real @ A @ B )
        = ( produc141013715e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_old_Oprod_Oinject) ).

thf(1138,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( ( produc141013715e_real @ A @ B )
        = ( produc141013715e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(165,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( bNF_Gr574714974e_real @ C @ D ) )
     => ( member312374654l_real @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_GrD1) ).

thf(869,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( bNF_Gr574714974e_real @ C @ D ) )
     => ( member312374654l_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(90,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: set_Pr366573913real_o,D: char > real > $o] :
      ( ( member1225120698real_o @ ( produc1285468373real_o @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1225120698real_o @ ( produc1285468373real_o @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_ssubst__Pair__rhs) ).

thf(610,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: set_Pr366573913real_o,D: char > real > $o] :
      ( ( member1225120698real_o @ ( produc1285468373real_o @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1225120698real_o @ ( produc1285468373real_o @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(29,axiom,
    ! [A: char > real,B: char > real,C: char > real,D: char > real] :
      ( ( ( produc700235985r_real @ A @ B )
        = ( produc700235985r_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_prod_Oinject) ).

thf(420,plain,
    ! [A: char > real,B: char > real,C: char > real,D: char > real] :
      ( ( ( produc700235985r_real @ A @ B )
        = ( produc700235985r_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(161,axiom,
    ! [A: produc104944723e_real] :
      ( A
      = ( produc2007437005e_real @ ( produc1486464481e_real @ A ) @ ( produc504912415e_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_prod_Oexhaust__sel) ).

thf(857,plain,
    ! [A: produc104944723e_real] :
      ( A
      = ( produc2007437005e_real @ ( produc1486464481e_real @ A ) @ ( produc504912415e_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(47,axiom,
    ! [A: set_Pr1588228599e_real,B: set_Pr1588228599e_real] :
      ( ( ( ^ [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] : ( member625963584e_real @ ( produc525232719e_real @ C @ D ) @ A ) )
        = ( ^ [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] : ( member625963584e_real @ ( produc525232719e_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_pred__equals__eq2) ).

thf(471,plain,
    ! [A: set_Pr1588228599e_real,B: set_Pr1588228599e_real] :
      ( ( ( ^ [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] : ( member625963584e_real @ ( produc525232719e_real @ C @ D ) @ A ) )
        = ( ^ [C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] : ( member625963584e_real @ ( produc525232719e_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(213,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( produc522711812e_real @ C @ D ) )
     => ( member1871517162e_real @ B @ ( D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_SigmaD2) ).

thf(1028,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( produc522711812e_real @ C @ D ) )
     => ( member1871517162e_real @ B @ ( D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(295,axiom,
    ! [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( produc753879889real_o @ A @ B @ C )
     => ( A @ ( produc141013715e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_curryE) ).

thf(1292,plain,
    ! [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( produc753879889real_o @ A @ B @ C )
     => ( A @ ( produc141013715e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(70,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ A @ B )
        = ( produc525232719e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_prod_Oinject) ).

thf(537,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ A @ B )
        = ( produc525232719e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(117,axiom,
    ! [A: produc928489369r_real] :
      ~ ! [B: char > real,C: char > real] :
          ( A
         != ( produc700235985r_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_old_Oprod_Oexhaust) ).

thf(686,plain,
    ! [A: produc928489369r_real] :
      ~ ! [B: char > real,C: char > real] :
          ( A
         != ( produc700235985r_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(100,axiom,
    ( produc210225566e_real
    = ( ^ [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
          ( ( C = A )
          & ( D = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_Pair__Rep__def) ).

thf(642,plain,
    ( produc210225566e_real
    = ( ^ [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
          ( ( C = A )
          & ( D = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(67,axiom,
    ! [A: produc1120170903e_real] :
      ~ ! [B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
          ( A
         != ( produc525232719e_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_old_Oprod_Oexhaust) ).

thf(526,plain,
    ! [A: produc1120170903e_real] :
      ~ ! [B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
          ( A
         != ( produc525232719e_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(99,axiom,
    ! [A: $o] :
      ( ( produc809977789real_o
        @ ^ [B: produc104944723e_real] : A )
      = ( ^ [B: char > real > $o,C: char > set_variable_real > set_variable_real] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_curry__K) ).

thf(637,plain,
    ! [A: $o] :
      ( ( produc809977789real_o
        @ ^ [B: produc104944723e_real] : A )
      = ( ^ [B: char > real > $o,C: char > set_variable_real > set_variable_real] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(53,axiom,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( A @ B @ C )
     => ( produc143994420real_o @ A @ ( produc525232719e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_case__prodI) ).

thf(489,plain,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > set_variable_real > set_variable_real ) > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( A @ B @ C )
     => ( produc143994420real_o @ A @ ( produc525232719e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(271,axiom,
    ! [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( A @ ( produc2125489830e_real @ B @ C ) )
     => ( produc998184740real_o @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_curryI) ).

thf(1214,plain,
    ! [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( A @ ( produc2125489830e_real @ B @ C ) )
     => ( produc998184740real_o @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(114,axiom,
    ! [A: char > real,B: char > real,C: set_Pr42335993r_real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( image_1523756869r_real @ produc1564675697r_real @ C ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_pair__in__swap__image) ).

thf(679,plain,
    ! [A: char > real,B: char > real,C: set_Pr42335993r_real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( image_1523756869r_real @ produc1564675697r_real @ C ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(252,axiom,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: produc104944723e_real] :
      ( ( produc1629511198real_o @ A @ B )
     => ~ ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] :
            ( ( B
              = ( produc2007437005e_real @ C @ D ) )
           => ~ ( A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_case__prodE) ).

thf(1155,plain,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: produc104944723e_real] :
      ( ( produc1629511198real_o @ A @ B )
     => ~ ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] :
            ( ( B
              = ( produc2007437005e_real @ C @ D ) )
           => ~ ( A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(239,axiom,
    ! [A: set_Pr307567739e_real,B: set_char_real] :
      ( ( image_152725217e_real
        @ ( produc864726913e_real
          @ ^ [C: produc1020032539e_real,D: char > real] : ( produc2125489830e_real @ D @ C ) )
        @ ( produc1373880559r_real @ A
          @ ^ [C: produc1020032539e_real] : B ) )
      = ( produc34356277e_real @ B
        @ ^ [C: char > real] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_swap__product) ).

thf(1114,plain,
    ! [A: set_Pr307567739e_real,B: set_char_real] :
      ( ( image_152725217e_real
        @ ( produc864726913e_real
          @ ^ [C: produc1020032539e_real,D: char > real] : ( produc2125489830e_real @ D @ C ) )
        @ ( produc1373880559r_real @ A
          @ ^ [C: produc1020032539e_real] : B ) )
      = ( produc34356277e_real @ B
        @ ^ [C: char > real] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(297,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc1853244124e_real @ C @ D ) )
     => ( member2042895986e_real @ B @ ( D @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_SigmaD2) ).

thf(1297,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc1853244124e_real @ C @ D ) )
     => ( member2042895986e_real @ B @ ( D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(134,axiom,
    ! [A: char > real > real,B: char > real > real,C: char > real > real,D: char > real > real] :
      ( ( ( produc686464615l_real @ A @ B )
        = ( produc686464615l_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_Pair__inject) ).

thf(738,plain,
    ! [A: char > real > real,B: char > real > real,C: char > real > real,D: char > real > real] :
      ( ( ( produc686464615l_real @ A @ B )
        = ( produc686464615l_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(42,axiom,
    ! [A: char > real > real,B: ( char > real > real ) > $o] :
      ( ( member312374654l_real @ A @ ( collec1429138108l_real @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_mem__Collect__eq) ).

thf(457,plain,
    ! [A: char > real > real,B: ( char > real > real ) > $o] :
      ( ( member312374654l_real @ A @ ( collec1429138108l_real @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(129,axiom,
    ! [A: produc96687023l_real > $o,B: produc96687023l_real] :
      ( ! [C: char > real > real,D: char > real > real] : ( A @ ( produc686464615l_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_prod__cases) ).

thf(721,plain,
    ! [A: produc96687023l_real > $o,B: produc96687023l_real] :
      ( ! [C: char > real > real,D: char > real > real] : ( A @ ( produc686464615l_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(102,axiom,
    ! [A: char > real > real,B: char > real > real,C: char > real > real,D: char > real > real] :
      ( ( ( produc686464615l_real @ A @ B )
        = ( produc686464615l_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_old_Oprod_Oinject) ).

thf(647,plain,
    ! [A: char > real > real,B: char > real > real,C: char > real > real,D: char > real > real] :
      ( ( ( produc686464615l_real @ A @ B )
        = ( produc686464615l_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(286,axiom,
    ! [A: produc104944723e_real] :
      ( A
      = ( produc2007437005e_real @ ( produc1486464481e_real @ A ) @ ( produc504912415e_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_surjective__pairing) ).

thf(1263,plain,
    ! [A: produc104944723e_real] :
      ( A
      = ( produc2007437005e_real @ ( produc1486464481e_real @ A ) @ ( produc504912415e_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(287,axiom,
    ! [A: produc104944723e_real] :
      ( ( produc1906464077e_real @ produc2007437005e_real @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_case__prod__Pair__iden) ).

thf(1266,plain,
    ! [A: produc104944723e_real] :
      ( ( produc1906464077e_real @ produc2007437005e_real @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(277,axiom,
    ! [A: ( char > real ) > produc1020032539e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( A @ B @ C )
     => ( produc569598981real_o @ A @ ( produc2125489830e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_case__prodI) ).

thf(1231,plain,
    ! [A: ( char > real ) > produc1020032539e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( A @ B @ C )
     => ( produc569598981real_o @ A @ ( produc2125489830e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(310,axiom,
    ! [A: char > real > $o,B: set_char_real_o,C: char > set_variable_real > set_variable_real,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member_char_real_o @ A @ B )
     => ( ( member2042895986e_real @ C @ ( D @ A ) )
       => ( member1871517162e_real @ ( produc2007437005e_real @ A @ C ) @ ( produc1853244124e_real @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_SigmaI) ).

thf(1333,plain,
    ! [A: char > real > $o,B: set_char_real_o,C: char > set_variable_real > set_variable_real,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member_char_real_o @ A @ B )
     => ( ( member2042895986e_real @ C @ ( D @ A ) )
       => ( member1871517162e_real @ ( produc2007437005e_real @ A @ C ) @ ( produc1853244124e_real @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(186,axiom,
    ! [A: ( char > real ) > produc1020032539e_real > $o,B: produc1993135732e_real] :
      ( ( produc569598981real_o @ A @ B )
     => ~ ! [C: char > real,D: produc1020032539e_real] :
            ( ( B
              = ( produc2125489830e_real @ C @ D ) )
           => ~ ( A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_case__prodE) ).

thf(938,plain,
    ! [A: ( char > real ) > produc1020032539e_real > $o,B: produc1993135732e_real] :
      ( ( produc569598981real_o @ A @ B )
     => ~ ! [C: char > real,D: produc1020032539e_real] :
            ( ( B
              = ( produc2125489830e_real @ C @ D ) )
           => ~ ( A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(9,axiom,
    ! [A: produc928489369r_real,B: ( char > real ) > ( char > real ) > $o] :
      ( ! [C: char > real,D: char > real] :
          ( ( A
            = ( produc700235985r_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc1655853874real_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_case__prodI2) ).

thf(360,plain,
    ! [A: produc928489369r_real,B: ( char > real ) > ( char > real ) > $o] :
      ( ! [C: char > real,D: char > real] :
          ( ( A
            = ( produc700235985r_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc1655853874real_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(106,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: char > real > $o] :
      ( ( ( produc1285468373real_o @ A @ B )
        = ( produc1285468373real_o @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_old_Oprod_Oinject) ).

thf(657,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: char > real > $o] :
      ( ( ( produc1285468373real_o @ A @ B )
        = ( produc1285468373real_o @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(257,axiom,
    ! [A: char > real > real,B: produc1020032539e_real] :
      ( ( A
        = ( produc634910399e_real @ B ) )
      = ( ? [C: produc104944723e_real] :
            ( B
            = ( produc141013715e_real @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_eq__fst__iff) ).

thf(1170,plain,
    ! [A: char > real > real,B: produc1020032539e_real] :
      ( ( A
        = ( produc634910399e_real @ B ) )
      = ( ? [C: produc104944723e_real] :
            ( B
            = ( produc141013715e_real @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(76,axiom,
    ! [A: produc96687023l_real,B: ( char > real > real ) > ( char > real > real ) > $o] :
      ( ! [C: char > real > real,D: char > real > real] :
          ( ( A
            = ( produc686464615l_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc1095814172real_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_case__prodI2) ).

thf(558,plain,
    ! [A: produc96687023l_real,B: ( char > real > real ) > ( char > real > real ) > $o] :
      ( ! [C: char > real > real,D: char > real > real] :
          ( ( A
            = ( produc686464615l_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc1095814172real_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(256,axiom,
    ! [A: ( char > real > $o ) > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real,E: ( char > real > $o ) > set_Pr1588228599e_real] :
      ( ( A @ B )
     => ( ( member625963584e_real @ ( produc525232719e_real @ C @ D ) @ ( E @ B ) )
       => ( member2016544560e_real @ ( produc1957227327e_real @ ( produc2007437005e_real @ B @ C ) @ ( produc2007437005e_real @ B @ D ) ) @ ( same_f1185518776e_real @ A @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_same__fstI) ).

thf(1167,plain,
    ! [A: ( char > real > $o ) > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real,E: ( char > real > $o ) > set_Pr1588228599e_real] :
      ( ( A @ B )
     => ( ( member625963584e_real @ ( produc525232719e_real @ C @ D ) @ ( E @ B ) )
       => ( member2016544560e_real @ ( produc1957227327e_real @ ( produc2007437005e_real @ B @ C ) @ ( produc2007437005e_real @ B @ D ) ) @ ( same_f1185518776e_real @ A @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(68,axiom,
    ! [A: produc2070499431real_o > $o,B: produc2070499431real_o] :
      ( ! [C: char > real > $o,D: char > real > $o] : ( A @ ( produc1566957527real_o @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_old_Oprod_Oinducts) ).

thf(530,plain,
    ! [A: produc2070499431real_o > $o,B: produc2070499431real_o] :
      ( ! [C: char > real > $o,D: char > real > $o] : ( A @ ( produc1566957527real_o @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(108,axiom,
    ! [A: char > real,B: char > real,C: set_Pr1588228599e_real,D: ( char > real ) > char > set_variable_real > set_variable_real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( inv_im710342731r_real @ C @ D ) )
      = ( member625963584e_real @ ( produc525232719e_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_in__inv__image) ).

thf(662,plain,
    ! [A: char > real,B: char > real,C: set_Pr1588228599e_real,D: ( char > real ) > char > set_variable_real > set_variable_real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( inv_im710342731r_real @ C @ D ) )
      = ( member625963584e_real @ ( produc525232719e_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(293,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc34356277e_real @ C @ D ) )
      = ( ( member_char_real @ A @ C )
        & ( member544802500e_real @ B @ ( D @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_mem__Sigma__iff) ).

thf(1286,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc34356277e_real @ C @ D ) )
      = ( ( member_char_real @ A @ C )
        & ( member544802500e_real @ B @ ( D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(216,axiom,
    ! [A: produc104944723e_real,B: char > real > real] :
      ( ( produc1778103411l_real @ ( produc1053845203l_real @ A @ B ) )
      = ( produc141013715e_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_swap__simp) ).

thf(1035,plain,
    ! [A: produc104944723e_real,B: char > real > real] :
      ( ( produc1778103411l_real @ ( produc1053845203l_real @ A @ B ) )
      = ( produc141013715e_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(26,axiom,
    ! [A: produc1120170903e_real > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( produc1935758037real_o @ A @ B @ C )
     => ( A @ ( produc525232719e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_curryD) ).

thf(412,plain,
    ! [A: produc1120170903e_real > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( produc1935758037real_o @ A @ B @ C )
     => ( A @ ( produc525232719e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(62,axiom,
    ! [A: produc1606031907real_o > $o,B: produc1606031907real_o] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( A @ ( produc1285468373real_o @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_prod__cases) ).

thf(513,plain,
    ! [A: produc1606031907real_o > $o,B: produc1606031907real_o] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( A @ ( produc1285468373real_o @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(135,axiom,
    ! [A: set_char_real_real] :
      ( ( collec1429138108l_real
        @ ^ [B: char > real > real] : ( member312374654l_real @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Collect__mem__eq) ).

thf(745,plain,
    ! [A: set_char_real_real] :
      ( ( collec1429138108l_real
        @ ^ [B: char > real > real] : ( member312374654l_real @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(38,axiom,
    ! [A: produc928489369r_real > $o,B: produc928489369r_real] :
      ( ! [C: char > real,D: char > real] : ( A @ ( produc700235985r_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_old_Oprod_Oinducts) ).

thf(444,plain,
    ! [A: produc928489369r_real > $o,B: produc928489369r_real] :
      ( ! [C: char > real,D: char > real] : ( A @ ( produc700235985r_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(324,axiom,
    ! [A: denotational_interp,B: denotational_interp] :
      ( ( ( ( denotational_Consts @ A )
          = ( denotational_Consts @ B ) )
        & ( ( denotational_Funcs @ A )
          = ( denotational_Funcs @ B ) )
        & ( ( denotational_Preds @ A )
          = ( denotational_Preds @ B ) )
        & ( ( denotational_Games @ A )
          = ( denotational_Games @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_mkinterp__eq) ).

thf(1374,plain,
    ! [A: denotational_interp,B: denotational_interp] :
      ( ( ( ( denotational_Consts @ A )
          = ( denotational_Consts @ B ) )
        & ( ( denotational_Funcs @ A )
          = ( denotational_Funcs @ B ) )
        & ( ( denotational_Preds @ A )
          = ( denotational_Preds @ B ) )
        & ( ( denotational_Games @ A )
          = ( denotational_Games @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(14,axiom,
    ! [A: produc96687023l_real > $o,B: char > real > real,C: char > real > real] :
      ( ( produc311008957real_o @ A @ B @ C )
     => ( A @ ( produc686464615l_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_curryD) ).

thf(375,plain,
    ! [A: produc96687023l_real > $o,B: char > real > real,C: char > real > real] :
      ( ( produc311008957real_o @ A @ B @ C )
     => ( A @ ( produc686464615l_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(282,axiom,
    ! [A: produc1993135732e_real] :
      ( ( produc315720647e_real @ produc2125489830e_real @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_case__prod__Pair__iden) ).

thf(1251,plain,
    ! [A: produc1993135732e_real] :
      ( ( produc315720647e_real @ produc2125489830e_real @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(92,axiom,
    ! [A: $o] :
      ( ( produc753879889real_o
        @ ^ [B: produc1020032539e_real] : A )
      = ( ^ [B: char > real > real,C: produc104944723e_real] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_curry__K) ).

thf(618,plain,
    ! [A: $o] :
      ( ( produc753879889real_o
        @ ^ [B: produc1020032539e_real] : A )
      = ( ^ [B: char > real > real,C: produc104944723e_real] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(273,axiom,
    ( produc1778103411l_real
    = ( ^ [A: produc729247771l_real] : ( produc141013715e_real @ ( produc2091833089l_real @ A ) @ ( produc1547741887l_real @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_prod_Oswap__def) ).

thf(1219,plain,
    ( produc1778103411l_real
    = ( ^ [A: produc729247771l_real] : ( produc141013715e_real @ ( produc2091833089l_real @ A ) @ ( produc1547741887l_real @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(154,axiom,
    ! [A: ( char > real ) > $o,B: char > real,C: produc1020032539e_real > $o,D: produc1020032539e_real] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc1146879930e_real @ ( produc2125489830e_real @ B @ D ) ) )
          & ( C @ ( produc1176159992e_real @ ( produc2125489830e_real @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_conjI__realizer) ).

thf(824,plain,
    ! [A: ( char > real ) > $o,B: char > real,C: produc1020032539e_real > $o,D: produc1020032539e_real] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc1146879930e_real @ ( produc2125489830e_real @ B @ D ) ) )
          & ( C @ ( produc1176159992e_real @ ( produc2125489830e_real @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(83,axiom,
    ! [A: char > real,B: char > real,C: char > real,D: char > real] :
      ( ( ( produc700235985r_real @ A @ B )
        = ( produc700235985r_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_Pair__inject) ).

thf(584,plain,
    ! [A: char > real,B: char > real,C: char > real,D: char > real] :
      ( ( ( produc700235985r_real @ A @ B )
        = ( produc700235985r_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(30,axiom,
    ! [A: produc2139219430r_real] :
      ( ( produc1726279942e_real @ ( produc918320576r_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_swap__swap) ).

thf(423,plain,
    ! [A: produc2139219430r_real] :
      ( ( produc1726279942e_real @ ( produc918320576r_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(23,axiom,
    ! [A: set_Pr42335993r_real,B: set_Pr42335993r_real] :
      ( ( ( ^ [C: char > real,D: char > real] : ( member1086859330r_real @ ( produc700235985r_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real,D: char > real] : ( member1086859330r_real @ ( produc700235985r_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_pred__equals__eq2) ).

thf(402,plain,
    ! [A: set_Pr42335993r_real,B: set_Pr42335993r_real] :
      ( ( ( ^ [C: char > real,D: char > real] : ( member1086859330r_real @ ( produc700235985r_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real,D: char > real] : ( member1086859330r_real @ ( produc700235985r_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(132,axiom,
    ! [A: char > real > $o,B: char > real > $o,C: char > real > $o,D: char > real > $o] :
      ( ( ( produc1566957527real_o @ A @ B )
        = ( produc1566957527real_o @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_old_Oprod_Oinject) ).

thf(732,plain,
    ! [A: char > real > $o,B: char > real > $o,C: char > real > $o,D: char > real > $o] :
      ( ( ( produc1566957527real_o @ A @ B )
        = ( produc1566957527real_o @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(329,axiom,
    ! [A: produc1020032539e_real] :
      ( ( produc141013715e_real @ ( produc634910399e_real @ A ) @ ( produc1179001601e_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_prod_Ocollapse) ).

thf(1389,plain,
    ! [A: produc1020032539e_real] :
      ( ( produc141013715e_real @ ( produc634910399e_real @ A ) @ ( produc1179001601e_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(242,axiom,
    ( produc753879889real_o
    = ( ^ [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] : ( A @ ( produc141013715e_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_curry__conv) ).

thf(1125,plain,
    ( produc753879889real_o
    = ( ^ [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] : ( A @ ( produc141013715e_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(125,axiom,
    ! [A: char > real > real,B: char > real > real,C: set_Pr1919093775l_real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ ( image_1347499973l_real @ produc995978247l_real @ C ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_pair__in__swap__image) ).

thf(711,plain,
    ! [A: char > real > real,B: char > real > real,C: set_Pr1919093775l_real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ ( image_1347499973l_real @ produc995978247l_real @ C ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(77,axiom,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr1053253703real_o,D: ( char > real > $o ) > char > real > $o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ ( inv_im1954866834real_o @ C @ D ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_in__inv__image) ).

thf(562,plain,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr1053253703real_o,D: ( char > real > $o ) > char > real > $o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ ( inv_im1954866834real_o @ C @ D ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(198,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real,E: set_Pr42335993r_real,F: set_Pr1517071815e_real] :
      ( ( member1966130802e_real @ ( produc638505729e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc2125489830e_real @ C @ D ) ) @ ( lex_pr1793499278e_real @ E @ F ) )
      = ( ( member1086859330r_real @ ( produc700235985r_real @ A @ C ) @ E )
        | ( ( A = C )
          & ( member1778419728e_real @ ( produc680410711e_real @ B @ D ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_in__lex__prod) ).

thf(975,plain,
    ! [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real,E: set_Pr42335993r_real,F: set_Pr1517071815e_real] :
      ( ( member1966130802e_real @ ( produc638505729e_real @ ( produc2125489830e_real @ A @ B ) @ ( produc2125489830e_real @ C @ D ) ) @ ( lex_pr1793499278e_real @ E @ F ) )
      = ( ( member1086859330r_real @ ( produc700235985r_real @ A @ C ) @ E )
        | ( ( A = C )
          & ( member1778419728e_real @ ( produc680410711e_real @ B @ D ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(323,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real,E: set_Pr1053253703real_o,F: set_Pr1588228599e_real] :
      ( ( member2016544560e_real @ ( produc1957227327e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc2007437005e_real @ C @ D ) ) @ ( lex_pr2056840373e_real @ E @ F ) )
      = ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ C ) @ E )
        | ( ( A = C )
          & ( member625963584e_real @ ( produc525232719e_real @ B @ D ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_in__lex__prod) ).

thf(1371,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real,E: set_Pr1053253703real_o,F: set_Pr1588228599e_real] :
      ( ( member2016544560e_real @ ( produc1957227327e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc2007437005e_real @ C @ D ) ) @ ( lex_pr2056840373e_real @ E @ F ) )
      = ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ C ) @ E )
        | ( ( A = C )
          & ( member625963584e_real @ ( produc525232719e_real @ B @ D ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(45,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ A @ B )
        = ( produc525232719e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_old_Oprod_Oinject) ).

thf(466,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc525232719e_real @ A @ B )
        = ( produc525232719e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(231,axiom,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc1179001601e_real @ ( produc141013715e_real @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_snd__conv) ).

thf(1090,plain,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc1179001601e_real @ ( produc141013715e_real @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(275,axiom,
    ! [A: produc1993135732e_real,B: ( char > real ) > char > real,C: produc1020032539e_real > produc1020032539e_real,D: set_Pr397354154e_real] :
      ( ( member1491807627e_real @ A @ ( image_866442351e_real @ ( produc552964208e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real,F: produc1020032539e_real] :
            ( ( A
              = ( produc2125489830e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_prod__fun__imageE) ).

thf(1224,plain,
    ! [A: produc1993135732e_real,B: ( char > real ) > char > real,C: produc1020032539e_real > produc1020032539e_real,D: set_Pr397354154e_real] :
      ( ( member1491807627e_real @ A @ ( image_866442351e_real @ ( produc552964208e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real,F: produc1020032539e_real] :
            ( ( A
              = ( produc2125489830e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(318,axiom,
    ! [A: real,B: real] :
      ( ( if_real @ $true @ A @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_001t__Real__Oreal_T) ).

thf(1356,plain,
    ! [A: real,B: real] :
      ( ( if_real @ $true @ A @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(5,axiom,
    ! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
      ( ! [C: variable > real] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_le1113654598e_real @ ( collec633296133e_real @ A ) @ ( collec633296133e_real @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_Collect__mono) ).

thf(350,plain,
    ! [A: ( variable > real ) > $o,B: ( variable > real ) > $o] :
      ( ! [C: variable > real] :
          ( ( A @ C )
         => ( B @ C ) )
     => ( ord_le1113654598e_real @ ( collec633296133e_real @ A ) @ ( collec633296133e_real @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(71,axiom,
    ! [A: char > real > $o,B: char > real > $o] :
      ( ( the_Pr1811203438real_o
        @ ( produc131289260al_o_o
          @ ^ [C: char > real > $o,D: char > real > $o] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc1566957527real_o @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_The__split__eq) ).

thf(540,plain,
    ! [A: char > real > $o,B: char > real > $o] :
      ( ( the_Pr1811203438real_o
        @ ( produc131289260al_o_o
          @ ^ [C: char > real > $o,D: char > real > $o] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc1566957527real_o @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(140,axiom,
    ! [A: ( char > real > $o ) > $o,B: char > real > $o,C: ( char > set_variable_real > set_variable_real ) > $o,D: char > set_variable_real > set_variable_real] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc1486464481e_real @ ( produc2007437005e_real @ B @ D ) ) )
          & ( C @ ( produc504912415e_real @ ( produc2007437005e_real @ B @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_conjI__realizer) ).

thf(764,plain,
    ! [A: ( char > real > $o ) > $o,B: char > real > $o,C: ( char > set_variable_real > set_variable_real ) > $o,D: char > set_variable_real > set_variable_real] :
      ( ( A @ B )
     => ( ( C @ D )
       => ( ( A @ ( produc1486464481e_real @ ( produc2007437005e_real @ B @ D ) ) )
          & ( C @ ( produc504912415e_real @ ( produc2007437005e_real @ B @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(265,axiom,
    ! [A: produc1993135732e_real,B: ( char > real ) > produc1020032539e_real > $o] :
      ( ! [C: char > real,D: produc1020032539e_real] :
          ( ( A
            = ( produc2125489830e_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc569598981real_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_case__prodI2) ).

thf(1194,plain,
    ! [A: produc1993135732e_real,B: ( char > real ) > produc1020032539e_real > $o] :
      ( ! [C: char > real,D: produc1020032539e_real] :
          ( ( A
            = ( produc2125489830e_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc569598981real_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(240,axiom,
    ! [A: ( char > real ) > char > real > real,B: produc1020032539e_real > produc104944723e_real,C: char > real,D: produc1020032539e_real] :
      ( ( produc202772275e_real @ A @ B @ ( produc2125489830e_real @ C @ D ) )
      = ( produc141013715e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_map__prod__simp) ).

thf(1117,plain,
    ! [A: ( char > real ) > char > real > real,B: produc1020032539e_real > produc104944723e_real,C: char > real,D: produc1020032539e_real] :
      ( ( produc202772275e_real @ A @ B @ ( produc2125489830e_real @ C @ D ) )
      = ( produc141013715e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(15,axiom,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: produc1020032539e_real] :
      ( ( produc421130416real_o
        @ ^ [C: produc104944723e_real,D: char > real > real] : ( A @ D @ C )
        @ ( produc865271923e_real @ B ) )
      = ( produc679978160real_o @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_case__swap) ).

thf(377,plain,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: produc1020032539e_real] :
      ( ( produc421130416real_o
        @ ^ [C: produc104944723e_real,D: char > real > real] : ( A @ D @ C )
        @ ( produc865271923e_real @ B ) )
      = ( produc679978160real_o @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(249,axiom,
    ! [A: produc1993135732e_real,B: char > real,C: produc1020032539e_real] :
      ( ( A
        = ( produc2125489830e_real @ B @ C ) )
     => ( ( produc1176159992e_real @ A )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_sndI) ).

thf(1144,plain,
    ! [A: produc1993135732e_real,B: char > real,C: produc1020032539e_real] :
      ( ( A
        = ( produc2125489830e_real @ B @ C ) )
     => ( ( produc1176159992e_real @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(87,axiom,
    ! [A: char > real > real,B: char > real > real,C: set_Pr42335993r_real,D: ( char > real > real ) > char > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ ( inv_im96827991l_real @ C @ D ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_in__inv__image) ).

thf(599,plain,
    ! [A: char > real > real,B: char > real > real,C: set_Pr42335993r_real,D: ( char > real > real ) > char > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ ( inv_im96827991l_real @ C @ D ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(163,axiom,
    ! [A: ( char > real ) > char > real > $o,B: produc1020032539e_real > char > set_variable_real > set_variable_real,C: char > real,D: produc1020032539e_real] :
      ( ( produc1797673857e_real @ A @ B @ ( produc2125489830e_real @ C @ D ) )
      = ( produc2007437005e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_map__prod__simp) ).

thf(863,plain,
    ! [A: ( char > real ) > char > real > $o,B: produc1020032539e_real > char > set_variable_real > set_variable_real,C: char > real,D: produc1020032539e_real] :
      ( ( produc1797673857e_real @ A @ B @ ( produc2125489830e_real @ C @ D ) )
      = ( produc2007437005e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(49,axiom,
    ! [A: $o] :
      ( ( A = $true )
      | ( A = $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_001t__Real__Oreal_T) ).

thf(477,plain,
    $true,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(18,axiom,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr1053253703real_o,D: char > real > $o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1795186320real_o @ ( produc1566957527real_o @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_ssubst__Pair__rhs) ).

thf(387,plain,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr1053253703real_o,D: char > real > $o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1795186320real_o @ ( produc1566957527real_o @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(55,axiom,
    ( produc619891650e_real
    = ( ^ [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
          ( ( C = A )
          & ( D = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_Pair__Rep__def) ).

thf(494,plain,
    ( produc619891650e_real
    = ( ^ [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real] :
          ( ( C = A )
          & ( D = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(11,axiom,
    ( denotational_worlds
    = ( collec633296133e_real
      @ ^ [A: variable > real] : $true ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_worlds__def) ).

thf(367,plain,
    ( denotational_worlds
    = ( collec633296133e_real
      @ ^ [A: variable > real] : $true ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(151,axiom,
    ! [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( produc809977789real_o @ A @ B @ C )
     => ( A @ ( produc2007437005e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_curryE) ).

thf(816,plain,
    ! [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( produc809977789real_o @ A @ B @ C )
     => ( A @ ( produc2007437005e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(85,axiom,
    ! [A: char > real > real,B: char > real > real,C: char > real > real,D: char > real > real] :
      ( ( ( produc686464615l_real @ A @ B )
        = ( produc686464615l_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_prod_Oinject) ).

thf(594,plain,
    ! [A: char > real > real,B: char > real > real,C: char > real > real,D: char > real > real] :
      ( ( ( produc686464615l_real @ A @ B )
        = ( produc686464615l_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(172,axiom,
    ! [A: ( char > real > $o ) > char > real > $o,B: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( produc355430254e_real @ A @ B @ ( produc2007437005e_real @ C @ D ) )
      = ( produc2007437005e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_map__prod__simp) ).

thf(895,plain,
    ! [A: ( char > real > $o ) > char > real > $o,B: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( produc355430254e_real @ A @ B @ ( produc2007437005e_real @ C @ D ) )
      = ( produc2007437005e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(211,axiom,
    ! [A: produc104944723e_real] :
      ( ( produc2007437005e_real @ ( produc1486464481e_real @ A ) @ ( produc504912415e_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_prod_Ocollapse) ).

thf(1022,plain,
    ! [A: produc104944723e_real] :
      ( ( produc2007437005e_real @ ( produc1486464481e_real @ A ) @ ( produc504912415e_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(110,axiom,
    ! [A: produc96687023l_real > $o,B: produc96687023l_real] :
      ( ! [C: char > real > real,D: char > real > real] : ( A @ ( produc686464615l_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_old_Oprod_Oinducts) ).

thf(668,plain,
    ! [A: produc96687023l_real > $o,B: produc96687023l_real] :
      ( ! [C: char > real > real,D: char > real > real] : ( A @ ( produc686464615l_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(184,axiom,
    ! [A: char > real > $o,B: produc104944723e_real] :
      ( ( A
        = ( produc1486464481e_real @ B ) )
      = ( ? [C: char > set_variable_real > set_variable_real] :
            ( B
            = ( produc2007437005e_real @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_eq__fst__iff) ).

thf(932,plain,
    ! [A: char > real > $o,B: produc104944723e_real] :
      ( ( A
        = ( produc1486464481e_real @ B ) )
      = ( ? [C: char > set_variable_real > set_variable_real] :
            ( B
            = ( produc2007437005e_real @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(138,axiom,
    ! [A: produc1020032539e_real] :
      ( ( produc1778103411l_real @ ( produc865271923e_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_swap__swap) ).

thf(758,plain,
    ! [A: produc1020032539e_real] :
      ( ( produc1778103411l_real @ ( produc865271923e_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(312,axiom,
    ! [A: set_Pr307567739e_real,B: set_Pr307567739e_real] :
      ( ( ( ^ [C: char > real > real,D: produc104944723e_real] : ( member544802500e_real @ ( produc141013715e_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real > real,D: produc104944723e_real] : ( member544802500e_real @ ( produc141013715e_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_pred__equals__eq2) ).

thf(1339,plain,
    ! [A: set_Pr307567739e_real,B: set_Pr307567739e_real] :
      ( ( ( ^ [C: char > real > real,D: produc104944723e_real] : ( member544802500e_real @ ( produc141013715e_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real > real,D: produc104944723e_real] : ( member544802500e_real @ ( produc141013715e_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(94,axiom,
    ! [A: produc2070499431real_o > $o,B: char > real > $o,C: char > real > $o] :
      ( ( A @ ( produc1566957527real_o @ B @ C ) )
     => ( produc169502925al_o_o @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_curryI) ).

thf(626,plain,
    ! [A: produc2070499431real_o > $o,B: char > real > $o,C: char > real > $o] :
      ( ( A @ ( produc1566957527real_o @ B @ C ) )
     => ( produc169502925al_o_o @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(179,axiom,
    ! [A: ( char > real > $o ) > char > real,B: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( produc1251731407e_real @ A @ B @ ( produc2007437005e_real @ C @ D ) )
      = ( produc2125489830e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_map__prod__simp) ).

thf(915,plain,
    ! [A: ( char > real > $o ) > char > real,B: ( char > set_variable_real > set_variable_real ) > produc1020032539e_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( produc1251731407e_real @ A @ B @ ( produc2007437005e_real @ C @ D ) )
      = ( produc2125489830e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(65,axiom,
    ! [A: produc96687023l_real] :
    ? [B: char > real > real,C: char > real > real] :
      ( A
      = ( produc686464615l_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_surj__pair) ).

thf(521,plain,
    ! [A: produc96687023l_real] :
    ? [B: char > real > real,C: char > real > real] :
      ( A
      = ( produc686464615l_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(22,axiom,
    ! [A: char > real,B: char > real,C: set_Pr1053253703real_o,D: ( char > real ) > char > real > $o] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( inv_im255337747r_real @ C @ D ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_in__inv__image) ).

thf(399,plain,
    ! [A: char > real,B: char > real,C: set_Pr1053253703real_o,D: ( char > real ) > char > real > $o] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( inv_im255337747r_real @ C @ D ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(219,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr307567739e_real,D: produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member544802500e_real @ ( produc141013715e_real @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_ssubst__Pair__rhs) ).

thf(1044,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr307567739e_real,D: produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member544802500e_real @ ( produc141013715e_real @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(225,axiom,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc634910399e_real @ ( produc141013715e_real @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_fst__conv) ).

thf(1066,plain,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc634910399e_real @ ( produc141013715e_real @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(143,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr268868489e_real,D: char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1871517162e_real @ ( produc2007437005e_real @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_ssubst__Pair__rhs) ).

thf(780,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr268868489e_real,D: char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1871517162e_real @ ( produc2007437005e_real @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(41,axiom,
    ( produc700235985r_real
    = ( ^ [A: char > real,B: char > real] : ( produc1022533727r_real @ ( produc885334464r_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Pair__def) ).

thf(455,plain,
    ( produc700235985r_real
    = ( ^ [A: char > real,B: char > real] : ( produc1022533727r_real @ ( produc885334464r_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(259,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: produc1020032539e_real] :
      ( ( ( produc1176159992e_real @ ( produc2125489830e_real @ A @ B ) )
        = C )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_snd__eqD) ).

thf(1176,plain,
    ! [A: char > real,B: produc1020032539e_real,C: produc1020032539e_real] :
      ( ( ( produc1176159992e_real @ ( produc2125489830e_real @ A @ B ) )
        = C )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(205,axiom,
    ! [A: produc1020032539e_real] :
      ( A
      = ( produc141013715e_real @ ( produc634910399e_real @ A ) @ ( produc1179001601e_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_prod_Oexhaust__sel) ).

thf(1000,plain,
    ! [A: produc1020032539e_real] :
      ( A
      = ( produc141013715e_real @ ( produc634910399e_real @ A ) @ ( produc1179001601e_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(33,axiom,
    ( produc525232719e_real
    = ( ^ [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] : ( produc1545903581e_real @ ( produc1689380158e_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Pair__def) ).

thf(431,plain,
    ( produc525232719e_real
    = ( ^ [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real] : ( produc1545903581e_real @ ( produc1689380158e_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(104,axiom,
    ! [A: produc928489369r_real > $o,B: char > real,C: char > real] :
      ( ( produc1735668179real_o @ A @ B @ C )
     => ( A @ ( produc700235985r_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_curryD) ).

thf(653,plain,
    ! [A: produc928489369r_real > $o,B: char > real,C: char > real] :
      ( ( produc1735668179real_o @ A @ B @ C )
     => ( A @ ( produc700235985r_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(181,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc1486464481e_real @ ( produc2007437005e_real @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_fst__pair) ).

thf(922,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc1486464481e_real @ ( produc2007437005e_real @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(266,axiom,
    ! [A: produc104944723e_real > ( char > real > real ) > $o,B: produc104944723e_real,C: char > real > real] :
      ( ( A @ B @ C )
     => ( A @ ( produc1179001601e_real @ ( produc141013715e_real @ C @ B ) ) @ ( produc634910399e_real @ ( produc141013715e_real @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_exI__realizer) ).

thf(1198,plain,
    ! [A: produc104944723e_real > ( char > real > real ) > $o,B: produc104944723e_real,C: char > real > real] :
      ( ( A @ B @ C )
     => ( A @ ( produc1179001601e_real @ ( produc141013715e_real @ C @ B ) ) @ ( produc634910399e_real @ ( produc141013715e_real @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(331,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ A @ B )
        = ( produc2007437005e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_old_Oprod_Oinject) ).

thf(1396,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ A @ B )
        = ( produc2007437005e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(159,axiom,
    ! [A: char > real,B: set_char_real,C: produc1020032539e_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member_char_real @ A @ B )
     => ( ( member544802500e_real @ C @ ( D @ A ) )
       => ( member1491807627e_real @ ( produc2125489830e_real @ A @ C ) @ ( produc34356277e_real @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_SigmaI) ).

thf(851,plain,
    ! [A: char > real,B: set_char_real,C: produc1020032539e_real,D: ( char > real ) > set_Pr307567739e_real] :
      ( ( member_char_real @ A @ B )
     => ( ( member544802500e_real @ C @ ( D @ A ) )
       => ( member1491807627e_real @ ( produc2125489830e_real @ A @ C ) @ ( produc34356277e_real @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(235,axiom,
    ! [A: set_Pr397354154e_real,B: set_Pr397354154e_real] :
      ( ! [C: char > real,D: produc1020032539e_real] :
          ( ( member1491807627e_real @ ( produc2125489830e_real @ C @ D ) @ A )
         => ( member1491807627e_real @ ( produc2125489830e_real @ C @ D ) @ B ) )
     => ( ord_le1631106314e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_subrelI) ).

thf(1102,plain,
    ! [A: set_Pr397354154e_real,B: set_Pr397354154e_real] :
      ( ! [C: char > real,D: produc1020032539e_real] :
          ( ( member1491807627e_real @ ( produc2125489830e_real @ C @ D ) @ A )
         => ( member1491807627e_real @ ( produc2125489830e_real @ C @ D ) @ B ) )
     => ( ord_le1631106314e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(31,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: set_Pr1588228599e_real] :
      ( ( member625963584e_real @ ( produc525232719e_real @ A @ B ) @ ( image_1495813573e_real @ produc1656125423e_real @ C ) )
      = ( member625963584e_real @ ( produc525232719e_real @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_pair__in__swap__image) ).

thf(426,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: set_Pr1588228599e_real] :
      ( ( member625963584e_real @ ( produc525232719e_real @ A @ B ) @ ( image_1495813573e_real @ produc1656125423e_real @ C ) )
      = ( member625963584e_real @ ( produc525232719e_real @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(290,axiom,
    ! [A: produc104944723e_real,B: ( char > real > real ) > char > real > $o,C: produc104944723e_real > char > set_variable_real > set_variable_real,D: set_Pr307567739e_real] :
      ( ( member1871517162e_real @ A @ ( image_450993193e_real @ ( produc683016410e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > real,F: produc104944723e_real] :
            ( ( A
              = ( produc2007437005e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_prod__fun__imageE) ).

thf(1277,plain,
    ! [A: produc104944723e_real,B: ( char > real > real ) > char > real > $o,C: produc104944723e_real > char > set_variable_real > set_variable_real,D: set_Pr307567739e_real] :
      ( ( member1871517162e_real @ A @ ( image_450993193e_real @ ( produc683016410e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > real,F: produc104944723e_real] :
            ( ( A
              = ( produc2007437005e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member544802500e_real @ ( produc141013715e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(63,axiom,
    ! [A: produc729247771l_real] :
      ( ( produc865271923e_real @ ( produc1778103411l_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_swap__swap) ).

thf(516,plain,
    ! [A: produc729247771l_real] :
      ( ( produc865271923e_real @ ( produc1778103411l_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(1,conjecture,
    ( ( denotational_Preds
      @ ( denota1150374853interp
        @ ( produc2125489830e_real
          @ ^ [A: char] : ( if_real @ ( A = f ) @ d @ ( denotational_Consts @ i @ A ) )
          @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) ) )
    = ( denotational_Preds @ i ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ( ( denotational_Preds
      @ ( denota1150374853interp
        @ ( produc2125489830e_real
          @ ^ [A: char] : ( if_real @ ( A = f ) @ d @ ( denotational_Consts @ i @ A ) )
          @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) ) )
   != ( denotational_Preds @ i ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(342,plain,
    ( ( denotational_Preds
      @ ( denota1150374853interp
        @ ( produc2125489830e_real
          @ ^ [A: char] : ( if_real @ ( A = f ) @ d @ ( denotational_Consts @ i @ A ) )
          @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) ) )
   != ( denotational_Preds @ i ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(210,axiom,
    ! [A: produc1020032539e_real] :
      ~ ! [B: char > real > real,C: produc104944723e_real] :
          ( A
         != ( produc141013715e_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_old_Oprod_Oexhaust) ).

thf(1018,plain,
    ! [A: produc1020032539e_real] :
      ~ ! [B: char > real > real,C: produc104944723e_real] :
          ( A
         != ( produc141013715e_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(7,axiom,
    ! [A: set_Pr1919093775l_real,B: set_Pr1919093775l_real] :
      ( ( ( ^ [C: char > real > real,D: char > real > real] : ( member1801875544l_real @ ( produc686464615l_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real > real,D: char > real > real] : ( member1801875544l_real @ ( produc686464615l_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_pred__equals__eq2) ).

thf(355,plain,
    ! [A: set_Pr1919093775l_real,B: set_Pr1919093775l_real] :
      ( ( ( ^ [C: char > real > real,D: char > real > real] : ( member1801875544l_real @ ( produc686464615l_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real > real,D: char > real > real] : ( member1801875544l_real @ ( produc686464615l_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(74,axiom,
    ( produc686464615l_real
    = ( ^ [A: char > real > real,B: char > real > real] : ( produc606131701l_real @ ( produc1051282262l_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Pair__def) ).

thf(553,plain,
    ( produc686464615l_real
    = ( ^ [A: char > real > real,B: char > real > real] : ( produc606131701l_real @ ( produc1051282262l_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(220,axiom,
    ! [A: produc104944723e_real,B: ( char > real ) > char > real > $o,C: produc1020032539e_real > char > set_variable_real > set_variable_real,D: set_Pr397354154e_real] :
      ( ( member1871517162e_real @ A @ ( image_426244814e_real @ ( produc1797673857e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real,F: produc1020032539e_real] :
            ( ( A
              = ( produc2007437005e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_prod__fun__imageE) ).

thf(1049,plain,
    ! [A: produc104944723e_real,B: ( char > real ) > char > real > $o,C: produc1020032539e_real > char > set_variable_real > set_variable_real,D: set_Pr397354154e_real] :
      ( ( member1871517162e_real @ A @ ( image_426244814e_real @ ( produc1797673857e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real,F: produc1020032539e_real] :
            ( ( A
              = ( produc2007437005e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1491807627e_real @ ( produc2125489830e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(337,axiom,
    ! [A: produc104944723e_real > $o,B: produc104944723e_real] :
      ( ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( A @ ( produc2007437005e_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_prod__cases) ).

thf(1413,plain,
    ! [A: produc104944723e_real > $o,B: produc104944723e_real] :
      ( ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( A @ ( produc2007437005e_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(228,axiom,
    ( uSubst1505767257e_repc
    = ( ^ [A: denotational_interp,B: char,C: real] :
          ( denota1150374853interp
          @ ( produc2125489830e_real
            @ ^ [D: char] : ( if_real @ ( D = B ) @ C @ ( denotational_Consts @ A @ D ) )
            @ ( produc141013715e_real @ ( denotational_Funcs @ A ) @ ( produc2007437005e_real @ ( denotational_Preds @ A ) @ ( denotational_Games @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_repc__def) ).

thf(1076,plain,
    ( uSubst1505767257e_repc
    = ( ^ [A: denotational_interp,B: char,C: real] :
          ( denota1150374853interp
          @ ( produc2125489830e_real
            @ ^ [D: char] : ( if_real @ ( D = B ) @ C @ ( denotational_Consts @ A @ D ) )
            @ ( produc141013715e_real @ ( denotational_Funcs @ A ) @ ( produc2007437005e_real @ ( denotational_Preds @ A ) @ ( denotational_Games @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(268,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr397354154e_real,D: produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1491807627e_real @ ( produc2125489830e_real @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_ssubst__Pair__rhs) ).

thf(1203,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr397354154e_real,D: produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1491807627e_real @ ( produc2125489830e_real @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(269,axiom,
    ! [A: produc1993135732e_real > $o,B: produc1993135732e_real] :
      ( ! [C: char > real,D: char > real > real,E: produc104944723e_real] : ( A @ ( produc2125489830e_real @ C @ ( produc141013715e_real @ D @ E ) ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_prod__induct3) ).

thf(1208,plain,
    ! [A: produc1993135732e_real > $o,B: produc1993135732e_real] :
      ( ! [C: char > real,D: char > real > real,E: produc104944723e_real] : ( A @ ( produc2125489830e_real @ C @ ( produc141013715e_real @ D @ E ) ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(206,axiom,
    ! [A: real,B: real] :
      ( ( if_real @ $false @ A @ B )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_001t__Real__Oreal_T) ).

thf(1003,plain,
    ! [A: real,B: real] :
      ( ( if_real @ $false @ A @ B )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(118,axiom,
    ! [A: char > real > $o,B: char > real > $o] :
      ( ( produc443915639real_o @ ( produc1566957527real_o @ A @ B ) )
      = ( produc1566957527real_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_swap__simp) ).

thf(690,plain,
    ! [A: char > real > $o,B: char > real > $o] :
      ( ( produc443915639real_o @ ( produc1566957527real_o @ A @ B ) )
      = ( produc1566957527real_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(212,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real,E: set_Pr1919093775l_real,F: set_Pr521705191e_real] :
      ( ( member1778419728e_real @ ( produc680410711e_real @ ( produc141013715e_real @ A @ B ) @ ( produc141013715e_real @ C @ D ) ) @ ( lex_pr592421611e_real @ E @ F ) )
      = ( ( member1801875544l_real @ ( produc686464615l_real @ A @ C ) @ E )
        | ( ( A = C )
          & ( member2016544560e_real @ ( produc1957227327e_real @ B @ D ) @ F ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_in__lex__prod) ).

thf(1025,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: char > real > real,D: produc104944723e_real,E: set_Pr1919093775l_real,F: set_Pr521705191e_real] :
      ( ( member1778419728e_real @ ( produc680410711e_real @ ( produc141013715e_real @ A @ B ) @ ( produc141013715e_real @ C @ D ) ) @ ( lex_pr592421611e_real @ E @ F ) )
      = ( ( member1801875544l_real @ ( produc686464615l_real @ A @ C ) @ E )
        | ( ( A = C )
          & ( member2016544560e_real @ ( produc1957227327e_real @ B @ D ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(166,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ A @ B )
        = ( produc2007437005e_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_Pair__inject) ).

thf(872,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ A @ B )
        = ( produc2007437005e_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(123,axiom,
    ! [A: char > real > $o,B: ( char > real > $o ) > $o] :
      ( ( member_char_real_o @ A @ ( collect_char_real_o @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_mem__Collect__eq) ).

thf(705,plain,
    ! [A: char > real > $o,B: ( char > real > $o ) > $o] :
      ( ( member_char_real_o @ A @ ( collect_char_real_o @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(170,axiom,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: produc1020032539e_real] :
      ( ( produc679978160real_o @ A @ B )
     => ~ ! [C: char > real > real,D: produc104944723e_real] :
            ( ( B
              = ( produc141013715e_real @ C @ D ) )
           => ~ ( A @ C @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_case__prodE) ).

thf(887,plain,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: produc1020032539e_real] :
      ( ( produc679978160real_o @ A @ B )
     => ~ ! [C: char > real > real,D: produc104944723e_real] :
            ( ( B
              = ( produc141013715e_real @ C @ D ) )
           => ~ ( A @ C @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(27,axiom,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: produc104944723e_real] :
      ( ( produc1467075094al_o_o
        @ ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( A @ D @ C )
        @ ( produc914893101e_real @ B ) )
      = ( produc1629511198real_o @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_case__swap) ).

thf(414,plain,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: produc104944723e_real] :
      ( ( produc1467075094al_o_o
        @ ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( A @ D @ C )
        @ ( produc914893101e_real @ B ) )
      = ( produc1629511198real_o @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(322,axiom,
    ! [A: produc1020032539e_real > $o,B: produc1020032539e_real] :
      ( ! [C: char > real > real,D: char > real > $o,E: char > set_variable_real > set_variable_real] : ( A @ ( produc141013715e_real @ C @ ( produc2007437005e_real @ D @ E ) ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_prod__induct3) ).

thf(1368,plain,
    ! [A: produc1020032539e_real > $o,B: produc1020032539e_real] :
      ( ! [C: char > real > real,D: char > real > $o,E: char > set_variable_real > set_variable_real] : ( A @ ( produc141013715e_real @ C @ ( produc2007437005e_real @ D @ E ) ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(221,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ A @ B )
        = ( produc2125489830e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_old_Oprod_Oinject) ).

thf(1053,plain,
    ! [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ A @ B )
        = ( produc2125489830e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(112,axiom,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc104944723e_real,B: produc1606031907real_o] :
      ( ( produc1906464077e_real
        @ ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( A @ D @ C )
        @ ( produc192924469real_o @ B ) )
      = ( produc1116016469e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_case__swap) ).

thf(673,plain,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > produc104944723e_real,B: produc1606031907real_o] :
      ( ( produc1906464077e_real
        @ ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( A @ D @ C )
        @ ( produc192924469real_o @ B ) )
      = ( produc1116016469e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(37,axiom,
    ! [A: produc104944723e_real > ( char > real > real ) > produc1020032539e_real,B: produc729247771l_real] :
      ( ( produc1202665267e_real
        @ ^ [C: char > real > real,D: produc104944723e_real] : ( A @ D @ C )
        @ ( produc1778103411l_real @ B ) )
      = ( produc991789875e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_case__swap) ).

thf(441,plain,
    ! [A: produc104944723e_real > ( char > real > real ) > produc1020032539e_real,B: produc729247771l_real] :
      ( ( produc1202665267e_real
        @ ^ [C: char > real > real,D: produc104944723e_real] : ( A @ D @ C )
        @ ( produc1778103411l_real @ B ) )
      = ( produc991789875e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(217,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr307567739e_real,D: ( char > real > real ) > char > real > real,E: produc104944723e_real > produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ C )
     => ( member544802500e_real @ ( produc141013715e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_1823533253e_real @ ( produc2131385966e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_map__prod__imageI) ).

thf(1038,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr307567739e_real,D: ( char > real > real ) > char > real > real,E: produc104944723e_real > produc104944723e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ C )
     => ( member544802500e_real @ ( produc141013715e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_1823533253e_real @ ( produc2131385966e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(58,axiom,
    produc1138486237e_real = produc1202665267e_real,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_internal__case__prod__def) ).

thf(502,plain,
    produc1138486237e_real = produc1202665267e_real,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(44,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: char > real > $o] :
      ( ( ( produc1285468373real_o @ A @ B )
        = ( produc1285468373real_o @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_prod_Oinject) ).

thf(463,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o,C: char > set_variable_real > set_variable_real,D: char > real > $o] :
      ( ( ( produc1285468373real_o @ A @ B )
        = ( produc1285468373real_o @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(304,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr307567739e_real,D: ( char > real > real ) > char > real > $o,E: produc104944723e_real > char > set_variable_real > set_variable_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ C )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_450993193e_real @ ( produc683016410e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_map__prod__imageI) ).

thf(1317,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_Pr307567739e_real,D: ( char > real > real ) > char > real > $o,E: produc104944723e_real > char > set_variable_real > set_variable_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ C )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_450993193e_real @ ( produc683016410e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(244,axiom,
    ! [A: set_Pr268868489e_real,B: set_char_real_real] :
      ( ( image_711552709e_real
        @ ( produc991789875e_real
          @ ^ [C: produc104944723e_real,D: char > real > real] : ( produc141013715e_real @ D @ C ) )
        @ ( produc1435543300l_real @ A
          @ ^ [C: produc104944723e_real] : B ) )
      = ( produc522711812e_real @ B
        @ ^ [C: char > real > real] : A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_swap__product) ).

thf(1130,plain,
    ! [A: set_Pr268868489e_real,B: set_char_real_real] :
      ( ( image_711552709e_real
        @ ( produc991789875e_real
          @ ^ [C: produc104944723e_real,D: char > real > real] : ( produc141013715e_real @ D @ C ) )
        @ ( produc1435543300l_real @ A
          @ ^ [C: produc104944723e_real] : B ) )
      = ( produc522711812e_real @ B
        @ ^ [C: char > real > real] : A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(311,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( bNF_Gr2096011355e_real @ C @ D ) )
     => ( member_char_real @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_GrD1) ).

thf(1336,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_char_real,D: ( char > real ) > produc1020032539e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ ( bNF_Gr2096011355e_real @ C @ D ) )
     => ( member_char_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(176,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc1486464481e_real @ ( produc2007437005e_real @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_fst__conv) ).

thf(907,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc1486464481e_real @ ( produc2007437005e_real @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(263,axiom,
    ! [A: produc104944723e_real] :
    ? [B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( A
      = ( produc2007437005e_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_surj__pair) ).

thf(1188,plain,
    ! [A: produc104944723e_real] :
    ? [B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( A
      = ( produc2007437005e_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(262,axiom,
    ( produc2007437005e_real
    = ( ^ [A: char > real > $o,B: char > set_variable_real > set_variable_real] : ( produc540070591e_real @ ( produc210225566e_real @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Pair__def) ).

thf(1186,plain,
    ( produc2007437005e_real
    = ( ^ [A: char > real > $o,B: char > set_variable_real > set_variable_real] : ( produc540070591e_real @ ( produc210225566e_real @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(334,axiom,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( the_Pr543709229e_real
        @ ( produc569598981real_o
          @ ^ [C: char > real,D: produc1020032539e_real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc2125489830e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_The__split__eq) ).

thf(1404,plain,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( the_Pr543709229e_real
        @ ( produc569598981real_o
          @ ^ [C: char > real,D: produc1020032539e_real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc2125489830e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(284,axiom,
    ! [A: ( char > real ) > $o,B: char > real,C: produc1020032539e_real,D: produc1020032539e_real,E: ( char > real ) > set_Pr1517071815e_real] :
      ( ( A @ B )
     => ( ( member1778419728e_real @ ( produc680410711e_real @ C @ D ) @ ( E @ B ) )
       => ( member1966130802e_real @ ( produc638505729e_real @ ( produc2125489830e_real @ B @ C ) @ ( produc2125489830e_real @ B @ D ) ) @ ( same_f764716049e_real @ A @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_same__fstI) ).

thf(1257,plain,
    ! [A: ( char > real ) > $o,B: char > real,C: produc1020032539e_real,D: produc1020032539e_real,E: ( char > real ) > set_Pr1517071815e_real] :
      ( ( A @ B )
     => ( ( member1778419728e_real @ ( produc680410711e_real @ C @ D ) @ ( E @ B ) )
       => ( member1966130802e_real @ ( produc638505729e_real @ ( produc2125489830e_real @ B @ C ) @ ( produc2125489830e_real @ B @ D ) ) @ ( same_f764716049e_real @ A @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(248,axiom,
    ! [A: produc1020032539e_real > $o,B: produc1020032539e_real] :
      ( ! [C: char > real > real,D: produc104944723e_real] : ( A @ ( produc141013715e_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_prod__cases) ).

thf(1141,plain,
    ! [A: produc1020032539e_real > $o,B: produc1020032539e_real] :
      ( ! [C: char > real > real,D: produc104944723e_real] : ( A @ ( produc141013715e_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(274,axiom,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc634910399e_real @ ( produc141013715e_real @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_fst__pair) ).

thf(1221,plain,
    ! [A: char > real > real,B: produc104944723e_real] :
      ( ( produc634910399e_real @ ( produc141013715e_real @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(317,axiom,
    ! [A: produc1993135732e_real] :
    ? [B: char > real,C: produc1020032539e_real] :
      ( A
      = ( produc2125489830e_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_surj__pair) ).

thf(1353,plain,
    ! [A: produc1993135732e_real] :
    ? [B: char > real,C: produc1020032539e_real] :
      ( A
      = ( produc2125489830e_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(131,axiom,
    ! [A: char > real > real,B: char > real > real,C: set_Pr1919093775l_real,D: char > real > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1801875544l_real @ ( produc686464615l_real @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_ssubst__Pair__rhs) ).

thf(727,plain,
    ! [A: char > real > real,B: char > real > real,C: set_Pr1919093775l_real,D: char > real > real] :
      ( ( member1801875544l_real @ ( produc686464615l_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1801875544l_real @ ( produc686464615l_real @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(199,axiom,
    ! [A: produc104944723e_real,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( A
        = ( produc2007437005e_real @ B @ C ) )
     => ( ( produc504912415e_real @ A )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_sndI) ).

thf(978,plain,
    ! [A: produc104944723e_real,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( A
        = ( produc2007437005e_real @ B @ C ) )
     => ( ( produc504912415e_real @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(208,axiom,
    ! [A: ( char > real ) > produc1020032539e_real > $o,B: char > real,C: produc1020032539e_real,D: produc1993135732e_real] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc2125489830e_real @ B @ C ) )
       => ( A @ ( produc1146879930e_real @ D ) @ ( produc1176159992e_real @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_BNF__Greatest__Fixpoint_Osubst__Pair) ).

thf(1008,plain,
    ! [A: ( char > real ) > produc1020032539e_real > $o,B: char > real,C: produc1020032539e_real,D: produc1993135732e_real] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc2125489830e_real @ B @ C ) )
       => ( A @ ( produc1146879930e_real @ D ) @ ( produc1176159992e_real @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(80,axiom,
    ! [A: produc928489369r_real > $o,B: produc928489369r_real] :
      ( ! [C: char > real,D: char > real] : ( A @ ( produc700235985r_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_prod__cases) ).

thf(571,plain,
    ! [A: produc928489369r_real > $o,B: produc928489369r_real] :
      ( ! [C: char > real,D: char > real] : ( A @ ( produc700235985r_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(260,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr397354154e_real,D: ( char > real ) > char > real > $o,E: produc1020032539e_real > char > set_variable_real > set_variable_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ C )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_426244814e_real @ ( produc1797673857e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_map__prod__imageI) ).

thf(1180,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr397354154e_real,D: ( char > real ) > char > real > $o,E: produc1020032539e_real > char > set_variable_real > set_variable_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ C )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_426244814e_real @ ( produc1797673857e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(111,axiom,
    produc1070892532real_o = produc1629511198real_o,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_internal__case__prod__def) ).

thf(671,plain,
    produc1070892532real_o = produc1629511198real_o,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(237,axiom,
    ! [A: produc1020032539e_real] :
      ( ( produc1202665267e_real @ produc141013715e_real @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_case__prod__Pair__iden) ).

thf(1108,plain,
    ! [A: produc1020032539e_real] :
      ( ( produc1202665267e_real @ produc141013715e_real @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(66,axiom,
    ( produc345845751e_real
    = ( ^ [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
          ( ( C = A )
          & ( D = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Pair__Rep__def) ).

thf(524,plain,
    ( produc345845751e_real
    = ( ^ [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
          ( ( C = A )
          & ( D = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(82,axiom,
    ! [A: produc2070499431real_o > $o,B: produc2070499431real_o] :
      ( ! [C: char > real > $o,D: char > real > $o] : ( A @ ( produc1566957527real_o @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_prod__cases) ).

thf(581,plain,
    ! [A: produc2070499431real_o > $o,B: produc2070499431real_o] :
      ( ! [C: char > real > $o,D: char > real > $o] : ( A @ ( produc1566957527real_o @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(272,axiom,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( produc522711812e_real @ C @ D ) )
     => ( member312374654l_real @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_SigmaD1) ).

thf(1216,plain,
    ! [A: char > real > real,B: produc104944723e_real,C: set_char_real_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member544802500e_real @ ( produc141013715e_real @ A @ B ) @ ( produc522711812e_real @ C @ D ) )
     => ( member312374654l_real @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(171,axiom,
    ! [A: produc1993135732e_real] :
      ~ ! [B: char > real,C: produc1020032539e_real] :
          ( A
         != ( produc2125489830e_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_old_Oprod_Oexhaust) ).

thf(891,plain,
    ! [A: produc1993135732e_real] :
      ~ ! [B: char > real,C: produc1020032539e_real] :
          ( A
         != ( produc2125489830e_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(294,axiom,
    ! [A: char > real,B: char > real > real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( denotational_Consts @ ( denota1150374853interp @ ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ ( produc2007437005e_real @ C @ D ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Consts__mkinterp) ).

thf(1289,plain,
    ! [A: char > real,B: char > real > real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( denotational_Consts @ ( denota1150374853interp @ ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ ( produc2007437005e_real @ C @ D ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(158,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ A @ B )
        = ( produc2125489830e_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Pair__inject) ).

thf(844,plain,
    ! [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ A @ B )
        = ( produc2125489830e_real @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(307,axiom,
    ( produc998184740real_o
    = ( ^ [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] : ( A @ ( produc2125489830e_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_curry__conv) ).

thf(1326,plain,
    ( produc998184740real_o
    = ( ^ [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] : ( A @ ( produc2125489830e_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(121,axiom,
    ! [A: char > real > $o,B: char > real > $o,C: char > real > $o,D: char > real > $o] :
      ( ( ( produc1566957527real_o @ A @ B )
        = ( produc1566957527real_o @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_prod_Oinject) ).

thf(699,plain,
    ! [A: char > real > $o,B: char > real > $o,C: char > real > $o,D: char > real > $o] :
      ( ( ( produc1566957527real_o @ A @ B )
        = ( produc1566957527real_o @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(194,axiom,
    ! [A: produc104944723e_real,B: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o] :
      ( ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] :
          ( ( A
            = ( produc2007437005e_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc1629511198real_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_case__prodI2) ).

thf(963,plain,
    ! [A: produc104944723e_real,B: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o] :
      ( ! [C: char > real > $o,D: char > set_variable_real > set_variable_real] :
          ( ( A
            = ( produc2007437005e_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc1629511198real_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(136,axiom,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real,B: produc104944723e_real] :
      ( ( produc1116016469e_real
        @ ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( A @ D @ C )
        @ ( produc914893101e_real @ B ) )
      = ( produc1906464077e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_case__swap) ).

thf(748,plain,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real,B: produc104944723e_real] :
      ( ( produc1116016469e_real
        @ ^ [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( A @ D @ C )
        @ ( produc914893101e_real @ B ) )
      = ( produc1906464077e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(224,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( ( produc504912415e_real @ ( produc2007437005e_real @ A @ B ) )
        = C )
     => ( B = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_snd__eqD) ).

thf(1062,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > set_variable_real > set_variable_real] :
      ( ( ( produc504912415e_real @ ( produc2007437005e_real @ A @ B ) )
        = C )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(188,axiom,
    ! [A: ( char > real > real ) > $o,B: char > real > real,C: produc104944723e_real,D: produc104944723e_real,E: ( char > real > real ) > set_Pr521705191e_real] :
      ( ( A @ B )
     => ( ( member2016544560e_real @ ( produc1957227327e_real @ C @ D ) @ ( E @ B ) )
       => ( member1778419728e_real @ ( produc680410711e_real @ ( produc141013715e_real @ B @ C ) @ ( produc141013715e_real @ B @ D ) ) @ ( same_f1243548200e_real @ A @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_same__fstI) ).

thf(946,plain,
    ! [A: ( char > real > real ) > $o,B: char > real > real,C: produc104944723e_real,D: produc104944723e_real,E: ( char > real > real ) > set_Pr521705191e_real] :
      ( ( A @ B )
     => ( ( member2016544560e_real @ ( produc1957227327e_real @ C @ D ) @ ( E @ B ) )
       => ( member1778419728e_real @ ( produc680410711e_real @ ( produc141013715e_real @ B @ C ) @ ( produc141013715e_real @ B @ D ) ) @ ( same_f1243548200e_real @ A @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(97,axiom,
    ! [A: produc96687023l_real > $o,B: char > real > real,C: char > real > real] :
      ( ( A @ ( produc686464615l_real @ B @ C ) )
     => ( produc311008957real_o @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_curryI) ).

thf(632,plain,
    ! [A: produc96687023l_real > $o,B: char > real > real,C: char > real > real] :
      ( ( A @ ( produc686464615l_real @ B @ C ) )
     => ( produc311008957real_o @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(203,axiom,
    ! [A: produc1020032539e_real > $o,B: produc1020032539e_real] :
      ( ! [C: char > real > real,D: produc104944723e_real] : ( A @ ( produc141013715e_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_old_Oprod_Oinducts) ).

thf(995,plain,
    ! [A: produc1020032539e_real > $o,B: produc1020032539e_real] :
      ( ! [C: char > real > real,D: produc104944723e_real] : ( A @ ( produc141013715e_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(150,axiom,
    ! [A: produc1993135732e_real > $o,B: produc1993135732e_real] :
      ( ! [C: char > real,D: produc1020032539e_real] : ( A @ ( produc2125489830e_real @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_old_Oprod_Oinducts) ).

thf(813,plain,
    ! [A: produc1993135732e_real > $o,B: produc1993135732e_real] :
      ( ! [C: char > real,D: produc1020032539e_real] : ( A @ ( produc2125489830e_real @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(328,axiom,
    ! [A: produc104944723e_real,B: ( char > real > $o ) > char > real > $o,C: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real,D: set_Pr268868489e_real] :
      ( ( member1871517162e_real @ A @ ( image_670686893e_real @ ( produc355430254e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > $o,F: char > set_variable_real > set_variable_real] :
            ( ( A
              = ( produc2007437005e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ E @ F ) @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_prod__fun__imageE) ).

thf(1385,plain,
    ! [A: produc104944723e_real,B: ( char > real > $o ) > char > real > $o,C: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real,D: set_Pr268868489e_real] :
      ( ( member1871517162e_real @ A @ ( image_670686893e_real @ ( produc355430254e_real @ B @ C ) @ D ) )
     => ~ ! [E: char > real > $o,F: char > set_variable_real > set_variable_real] :
            ( ( A
              = ( produc2007437005e_real @ ( B @ E ) @ ( C @ F ) ) )
           => ~ ( member1871517162e_real @ ( produc2007437005e_real @ E @ F ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(214,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr397354154e_real,D: ( char > real ) > char > real > real,E: produc1020032539e_real > produc104944723e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ C )
     => ( member544802500e_real @ ( produc141013715e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_479987936e_real @ ( produc202772275e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_map__prod__imageI) ).

thf(1030,plain,
    ! [A: char > real,B: produc1020032539e_real,C: set_Pr397354154e_real,D: ( char > real ) > char > real > real,E: produc1020032539e_real > produc104944723e_real] :
      ( ( member1491807627e_real @ ( produc2125489830e_real @ A @ B ) @ C )
     => ( member544802500e_real @ ( produc141013715e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_479987936e_real @ ( produc202772275e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(79,axiom,
    ! [A: char > real > real,B: char > real > real] :
      ( ( the_Pr1196831286l_real
        @ ( produc1095814172real_o
          @ ^ [C: char > real > real,D: char > real > real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc686464615l_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_The__split__eq) ).

thf(568,plain,
    ! [A: char > real > real,B: char > real > real] :
      ( ( the_Pr1196831286l_real
        @ ( produc1095814172real_o
          @ ^ [C: char > real > real,D: char > real > real] :
              ( ( A = C )
              & ( B = D ) ) ) )
      = ( produc686464615l_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(296,axiom,
    ! [A: char > real,B: char > real > real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( denotational_Preds @ ( denota1150374853interp @ ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ ( produc2007437005e_real @ C @ D ) ) ) ) )
      = C ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Preds__mkinterp) ).

thf(1294,plain,
    ! [A: char > real,B: char > real > real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( denotational_Preds @ ( denota1150374853interp @ ( produc2125489830e_real @ A @ ( produc141013715e_real @ B @ ( produc2007437005e_real @ C @ D ) ) ) ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(183,axiom,
    ! [A: produc104944723e_real,B: produc1020032539e_real] :
      ( ( A
        = ( produc1179001601e_real @ B ) )
      = ( ? [C: char > real > real] :
            ( B
            = ( produc141013715e_real @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_eq__snd__iff) ).

thf(929,plain,
    ! [A: produc104944723e_real,B: produc1020032539e_real] :
      ( ( A
        = ( produc1179001601e_real @ B ) )
      = ( ? [C: char > real > real] :
            ( B
            = ( produc141013715e_real @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(50,axiom,
    ! [A: produc1606031907real_o > $o,B: produc1606031907real_o] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( A @ ( produc1285468373real_o @ C @ D ) )
     => ( A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_old_Oprod_Oinducts) ).

thf(478,plain,
    ! [A: produc1606031907real_o > $o,B: produc1606031907real_o] :
      ( ! [C: char > set_variable_real > set_variable_real,D: char > real > $o] : ( A @ ( produc1285468373real_o @ C @ D ) )
     => ( A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(116,axiom,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( A @ B @ C )
     => ( produc1467075094al_o_o @ A @ ( produc1285468373real_o @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_case__prodI) ).

thf(684,plain,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( A @ B @ C )
     => ( produc1467075094al_o_o @ A @ ( produc1285468373real_o @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(301,axiom,
    ! [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( A @ ( produc2007437005e_real @ B @ C ) )
     => ( produc809977789real_o @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_curryI) ).

thf(1309,plain,
    ! [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( A @ ( produc2007437005e_real @ B @ C ) )
     => ( produc809977789real_o @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(34,axiom,
    ! [A: char > real,B: char > real,C: set_Pr1919093775l_real,D: ( char > real ) > char > real > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( inv_im854642519r_real @ C @ D ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_in__inv__image) ).

thf(433,plain,
    ! [A: char > real,B: char > real,C: set_Pr1919093775l_real,D: ( char > real ) > char > real > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( inv_im854642519r_real @ C @ D ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(61,axiom,
    ! [A: char > real,B: char > real,C: char > real,D: char > real] :
      ( ( ( produc700235985r_real @ A @ B )
        = ( produc700235985r_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_old_Oprod_Oinject) ).

thf(510,plain,
    ! [A: char > real,B: char > real,C: char > real,D: char > real] :
      ( ( ( produc700235985r_real @ A @ B )
        = ( produc700235985r_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(127,axiom,
    ! [A: produc1606031907real_o] :
    ? [B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( A
      = ( produc1285468373real_o @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_surj__pair) ).

thf(716,plain,
    ! [A: produc1606031907real_o] :
    ? [B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( A
      = ( produc1285468373real_o @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(254,axiom,
    ! [A: set_Pr268868489e_real,B: set_Pr268868489e_real] :
      ( ( ( ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( member1871517162e_real @ ( produc2007437005e_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( member1871517162e_real @ ( produc2007437005e_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_pred__equals__eq2) ).

thf(1161,plain,
    ! [A: set_Pr268868489e_real,B: set_Pr268868489e_real] :
      ( ( ( ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( member1871517162e_real @ ( produc2007437005e_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real > $o,D: char > set_variable_real > set_variable_real] : ( member1871517162e_real @ ( produc2007437005e_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(147,axiom,
    ! [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( A @ ( produc141013715e_real @ B @ C ) )
     => ( produc753879889real_o @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_curryI) ).

thf(800,plain,
    ! [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] :
      ( ( A @ ( produc141013715e_real @ B @ C ) )
     => ( produc753879889real_o @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(245,axiom,
    ! [A: produc1993135732e_real] :
      ( ( produc2125489830e_real @ ( produc1146879930e_real @ A ) @ ( produc1176159992e_real @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_prod_Ocollapse) ).

thf(1133,plain,
    ! [A: produc1993135732e_real] :
      ( ( produc2125489830e_real @ ( produc1146879930e_real @ A ) @ ( produc1176159992e_real @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(315,axiom,
    ! [A: ( char > real ) > char > real,B: produc1020032539e_real > produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
      ( ( produc552964208e_real @ A @ B @ ( produc2125489830e_real @ C @ D ) )
      = ( produc2125489830e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_map__prod__simp) ).

thf(1348,plain,
    ! [A: ( char > real ) > char > real,B: produc1020032539e_real > produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
      ( ( produc552964208e_real @ A @ B @ ( produc2125489830e_real @ C @ D ) )
      = ( produc2125489830e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(39,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: set_Pr1588228599e_real,D: char > set_variable_real > set_variable_real] :
      ( ( member625963584e_real @ ( produc525232719e_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member625963584e_real @ ( produc525232719e_real @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ssubst__Pair__rhs) ).

thf(447,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > set_variable_real > set_variable_real,C: set_Pr1588228599e_real,D: char > set_variable_real > set_variable_real] :
      ( ( member625963584e_real @ ( produc525232719e_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member625963584e_real @ ( produc525232719e_real @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(234,axiom,
    ! [A: produc104944723e_real,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( A
        = ( produc2007437005e_real @ B @ C ) )
     => ( ( produc1486464481e_real @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_fstI) ).

thf(1097,plain,
    ! [A: produc104944723e_real,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( A
        = ( produc2007437005e_real @ B @ C ) )
     => ( ( produc1486464481e_real @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(152,axiom,
    ! [A: char > real > real,B: set_char_real_real,C: produc104944723e_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member312374654l_real @ A @ B )
     => ( ( member1871517162e_real @ C @ ( D @ A ) )
       => ( member544802500e_real @ ( produc141013715e_real @ A @ C ) @ ( produc522711812e_real @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_SigmaI) ).

thf(818,plain,
    ! [A: char > real > real,B: set_char_real_real,C: produc104944723e_real,D: ( char > real > real ) > set_Pr268868489e_real] :
      ( ( member312374654l_real @ A @ B )
     => ( ( member1871517162e_real @ C @ ( D @ A ) )
       => ( member544802500e_real @ ( produc141013715e_real @ A @ C ) @ ( produc522711812e_real @ B @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(326,axiom,
    ! [A: set_Pr397354154e_real,B: set_Pr397354154e_real] :
      ( ( ( ^ [C: char > real,D: produc1020032539e_real] : ( member1491807627e_real @ ( produc2125489830e_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real,D: produc1020032539e_real] : ( member1491807627e_real @ ( produc2125489830e_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_pred__equals__eq2) ).

thf(1380,plain,
    ! [A: set_Pr397354154e_real,B: set_Pr397354154e_real] :
      ( ( ( ^ [C: char > real,D: produc1020032539e_real] : ( member1491807627e_real @ ( produc2125489830e_real @ C @ D ) @ A ) )
        = ( ^ [C: char > real,D: produc1020032539e_real] : ( member1491807627e_real @ ( produc2125489830e_real @ C @ D ) @ B ) ) )
      = ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(24,axiom,
    ! [A: char > real,B: char > real,C: set_Pr42335993r_real,D: char > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1086859330r_real @ ( produc700235985r_real @ A @ D ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_ssubst__Pair__rhs) ).

thf(405,plain,
    ! [A: char > real,B: char > real,C: set_Pr42335993r_real,D: char > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ C )
     => ( ( D = B )
       => ( member1086859330r_real @ ( produc700235985r_real @ A @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(160,axiom,
    ! [A: denotational_interp,B: char,C: real] :
      ( ( denotational_Funcs @ ( uSubst1505767257e_repc @ A @ B @ C ) )
      = ( denotational_Funcs @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_repc__funcs) ).

thf(854,plain,
    ! [A: denotational_interp,B: char,C: real] :
      ( ( denotational_Funcs @ ( uSubst1505767257e_repc @ A @ B @ C ) )
      = ( denotational_Funcs @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(250,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc1853244124e_real @ C @ D ) )
     => ( member_char_real_o @ A @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_SigmaD1) ).

thf(1148,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_char_real_o,D: ( char > real > $o ) > set_ch845833233e_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ ( produc1853244124e_real @ C @ D ) )
     => ( member_char_real_o @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(133,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: ( char > set_variable_real > set_variable_real ) > $o] :
      ( ( member2042895986e_real @ A @ ( collec425771440e_real @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_mem__Collect__eq) ).

thf(735,plain,
    ! [A: char > set_variable_real > set_variable_real,B: ( char > set_variable_real > set_variable_real ) > $o] :
      ( ( member2042895986e_real @ A @ ( collec425771440e_real @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(25,axiom,
    ! [A: produc96687023l_real > $o,B: char > real > real,C: char > real > real] :
      ( ( produc311008957real_o @ A @ B @ C )
     => ( A @ ( produc686464615l_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_curryE) ).

thf(410,plain,
    ! [A: produc96687023l_real > $o,B: char > real > real,C: char > real > real] :
      ( ( produc311008957real_o @ A @ B @ C )
     => ( A @ ( produc686464615l_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(195,axiom,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( A @ B @ C )
     => ( A @ ( produc504912415e_real @ ( produc2007437005e_real @ C @ B ) ) @ ( produc1486464481e_real @ ( produc2007437005e_real @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_exI__realizer) ).

thf(967,plain,
    ! [A: ( char > set_variable_real > set_variable_real ) > ( char > real > $o ) > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( A @ B @ C )
     => ( A @ ( produc504912415e_real @ ( produc2007437005e_real @ C @ B ) ) @ ( produc1486464481e_real @ ( produc2007437005e_real @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(180,axiom,
    ! [A: produc1020032539e_real,B: char > real > real,C: produc104944723e_real] :
      ( ( A
        = ( produc141013715e_real @ B @ C ) )
     => ( ( produc1179001601e_real @ A )
        = C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_sndI) ).

thf(918,plain,
    ! [A: produc1020032539e_real,B: char > real > real,C: produc104944723e_real] :
      ( ( A
        = ( produc141013715e_real @ B @ C ) )
     => ( ( produc1179001601e_real @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(303,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr268868489e_real,D: ( char > real > $o ) > char > real > $o,E: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ C )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_670686893e_real @ ( produc355430254e_real @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_map__prod__imageI) ).

thf(1314,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: set_Pr268868489e_real,D: ( char > real > $o ) > char > real > $o,E: ( char > set_variable_real > set_variable_real ) > char > set_variable_real > set_variable_real] :
      ( ( member1871517162e_real @ ( produc2007437005e_real @ A @ B ) @ C )
     => ( member1871517162e_real @ ( produc2007437005e_real @ ( D @ A ) @ ( E @ B ) ) @ ( image_670686893e_real @ ( produc355430254e_real @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(8,axiom,
    ! [A: ( char > real > $o ) > ( char > real > $o ) > $o,B: char > real > $o,C: char > real > $o] :
      ( ( A @ B @ C )
     => ( produc131289260al_o_o @ A @ ( produc1566957527real_o @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_case__prodI) ).

thf(358,plain,
    ! [A: ( char > real > $o ) > ( char > real > $o ) > $o,B: char > real > $o,C: char > real > $o] :
      ( ( A @ B @ C )
     => ( produc131289260al_o_o @ A @ ( produc1566957527real_o @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(222,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc504912415e_real @ ( produc2007437005e_real @ A @ B ) )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_snd__conv) ).

thf(1056,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc504912415e_real @ ( produc2007437005e_real @ A @ B ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(215,axiom,
    ( produc809977789real_o
    = ( ^ [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] : ( A @ ( produc2007437005e_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_curry__def) ).

thf(1033,plain,
    ( produc809977789real_o
    = ( ^ [A: produc104944723e_real > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] : ( A @ ( produc2007437005e_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(193,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc914893101e_real @ ( produc2007437005e_real @ A @ B ) )
      = ( produc1285468373real_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_swap__simp) ).

thf(960,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real] :
      ( ( produc914893101e_real @ ( produc2007437005e_real @ A @ B ) )
      = ( produc1285468373real_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(191,axiom,
    ( produc192924469real_o
    = ( ^ [A: produc1606031907real_o] : ( produc2007437005e_real @ ( produc1930427431real_o @ A ) @ ( produc764495849real_o @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_prod_Oswap__def) ).

thf(955,plain,
    ( produc192924469real_o
    = ( ^ [A: produc1606031907real_o] : ( produc2007437005e_real @ ( produc1930427431real_o @ A ) @ ( produc764495849real_o @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(48,axiom,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr1919093775l_real,D: ( char > real > $o ) > char > real > real] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ ( inv_im1748900174real_o @ C @ D ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_in__inv__image) ).

thf(474,plain,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr1919093775l_real,D: ( char > real > $o ) > char > real > real] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ ( inv_im1748900174real_o @ C @ D ) )
      = ( member1801875544l_real @ ( produc686464615l_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(336,axiom,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ A @ B )
        = ( produc2007437005e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_prod_Oinject) ).

thf(1410,plain,
    ! [A: char > real > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o,D: char > set_variable_real > set_variable_real] :
      ( ( ( produc2007437005e_real @ A @ B )
        = ( produc2007437005e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(201,axiom,
    ! [A: produc1993135732e_real,B: set_char_real,C: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ A @ ( produc34356277e_real @ B @ C ) )
     => ~ ! [D: char > real] :
            ( ( member_char_real @ D @ B )
           => ! [E: produc1020032539e_real] :
                ( ( member544802500e_real @ E @ ( C @ D ) )
               => ( A
                 != ( produc2125489830e_real @ D @ E ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_SigmaE) ).

thf(987,plain,
    ! [A: produc1993135732e_real,B: set_char_real,C: ( char > real ) > set_Pr307567739e_real] :
      ( ( member1491807627e_real @ A @ ( produc34356277e_real @ B @ C ) )
     => ~ ! [D: char > real] :
            ( ( member_char_real @ D @ B )
           => ! [E: produc1020032539e_real] :
                ( ( member544802500e_real @ E @ ( C @ D ) )
               => ( A
                 != ( produc2125489830e_real @ D @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(162,axiom,
    ! [A: produc1020032539e_real] :
      ( A
      = ( produc141013715e_real @ ( produc634910399e_real @ A ) @ ( produc1179001601e_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_surjective__pairing) ).

thf(860,plain,
    ! [A: produc1020032539e_real] :
      ( A
      = ( produc141013715e_real @ ( produc634910399e_real @ A ) @ ( produc1179001601e_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(101,axiom,
    ! [A: set_char_real] :
      ( ( collect_char_real
        @ ^ [B: char > real] : ( member_char_real @ B @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Collect__mem__eq) ).

thf(644,plain,
    ! [A: set_char_real] :
      ( ( collect_char_real
        @ ^ [B: char > real] : ( member_char_real @ B @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(202,axiom,
    ! [A: set_Pr307567739e_real,B: set_Pr307567739e_real] :
      ( ! [C: char > real > real,D: produc104944723e_real] :
          ( ( member544802500e_real @ ( produc141013715e_real @ C @ D ) @ A )
         => ( member544802500e_real @ ( produc141013715e_real @ C @ D ) @ B ) )
     => ( ord_le780198939e_real @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_subrelI) ).

thf(992,plain,
    ! [A: set_Pr307567739e_real,B: set_Pr307567739e_real] :
      ( ! [C: char > real > real,D: produc104944723e_real] :
          ( ( member544802500e_real @ ( produc141013715e_real @ C @ D ) @ A )
         => ( member544802500e_real @ ( produc141013715e_real @ C @ D ) @ B ) )
     => ( ord_le780198939e_real @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(200,axiom,
    ! [A: produc1020032539e_real,B: char > real > real,C: produc104944723e_real] :
      ( ( A
        = ( produc141013715e_real @ B @ C ) )
     => ( ( produc634910399e_real @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_fstI) ).

thf(982,plain,
    ! [A: produc1020032539e_real,B: char > real > real,C: produc104944723e_real] :
      ( ( A
        = ( produc141013715e_real @ B @ C ) )
     => ( ( produc634910399e_real @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(298,axiom,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1146879930e_real @ ( produc2125489830e_real @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_fst__conv) ).

thf(1299,plain,
    ! [A: char > real,B: produc1020032539e_real] :
      ( ( produc1146879930e_real @ ( produc2125489830e_real @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(332,axiom,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( produc1629511198real_o @ A @ ( produc2007437005e_real @ B @ C ) )
     => ( A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_case__prodD) ).

thf(1399,plain,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( produc1629511198real_o @ A @ ( produc2007437005e_real @ B @ C ) )
     => ( A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(241,axiom,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: char > real > real,C: produc104944723e_real,D: produc1020032539e_real] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc141013715e_real @ B @ C ) )
       => ( A @ ( produc634910399e_real @ D ) @ ( produc1179001601e_real @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_BNF__Greatest__Fixpoint_Osubst__Pair) ).

thf(1120,plain,
    ! [A: ( char > real > real ) > produc104944723e_real > $o,B: char > real > real,C: produc104944723e_real,D: produc1020032539e_real] :
      ( ( A @ B @ C )
     => ( ( D
          = ( produc141013715e_real @ B @ C ) )
       => ( A @ ( produc634910399e_real @ D ) @ ( produc1179001601e_real @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(12,axiom,
    ! [A: char > real,B: ( char > real ) > $o] :
      ( ( member_char_real @ A @ ( collect_char_real @ B ) )
      = ( B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_mem__Collect__eq) ).

thf(369,plain,
    ! [A: char > real,B: ( char > real ) > $o] :
      ( ( member_char_real @ A @ ( collect_char_real @ B ) )
      = ( B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(232,axiom,
    ! [A: ( char > real ) > produc1020032539e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( produc569598981real_o @ A @ ( produc2125489830e_real @ B @ C ) )
     => ( A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_case__prodD) ).

thf(1093,plain,
    ! [A: ( char > real ) > produc1020032539e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( produc569598981real_o @ A @ ( produc2125489830e_real @ B @ C ) )
     => ( A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(20,axiom,
    ! [A: produc1606031907real_o > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( A @ ( produc1285468373real_o @ B @ C ) )
     => ( produc647541685al_o_o @ A @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_curryI) ).

thf(395,plain,
    ! [A: produc1606031907real_o > $o,B: char > set_variable_real > set_variable_real,C: char > real > $o] :
      ( ( A @ ( produc1285468373real_o @ B @ C ) )
     => ( produc647541685al_o_o @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(309,axiom,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( A @ B @ C )
     => ( produc1629511198real_o @ A @ ( produc2007437005e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_case__prodI) ).

thf(1331,plain,
    ! [A: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > $o,B: char > real > $o,C: char > set_variable_real > set_variable_real] :
      ( ( A @ B @ C )
     => ( produc1629511198real_o @ A @ ( produc2007437005e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(52,axiom,
    ! [A: char > real > real,B: char > real > real] :
      ( ( produc995978247l_real @ ( produc686464615l_real @ A @ B ) )
      = ( produc686464615l_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_swap__simp) ).

thf(486,plain,
    ! [A: char > real > real,B: char > real > real] :
      ( ( produc995978247l_real @ ( produc686464615l_real @ A @ B ) )
      = ( produc686464615l_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(305,axiom,
    ! [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ A @ B )
        = ( produc2125489830e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_prod_Oinject) ).

thf(1320,plain,
    ! [A: char > real,B: produc1020032539e_real,C: char > real,D: produc1020032539e_real] :
      ( ( ( produc2125489830e_real @ A @ B )
        = ( produc2125489830e_real @ C @ D ) )
      = ( ( A = C )
        & ( B = D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(46,axiom,
    ! [A: produc928489369r_real > $o,B: char > real,C: char > real] :
      ( ( produc1735668179real_o @ A @ B @ C )
     => ( A @ ( produc700235985r_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_curryE) ).

thf(469,plain,
    ! [A: produc928489369r_real > $o,B: char > real,C: char > real] :
      ( ( produc1735668179real_o @ A @ B @ C )
     => ( A @ ( produc700235985r_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(185,axiom,
    ! [A: ( char > real > real ) > char > real,B: produc104944723e_real > produc1020032539e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( produc348783435e_real @ A @ B @ ( produc141013715e_real @ C @ D ) )
      = ( produc2125489830e_real @ ( A @ C ) @ ( B @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_map__prod__simp) ).

thf(935,plain,
    ! [A: ( char > real > real ) > char > real,B: produc104944723e_real > produc1020032539e_real,C: char > real > real,D: produc104944723e_real] :
      ( ( produc348783435e_real @ A @ B @ ( produc141013715e_real @ C @ D ) )
      = ( produc2125489830e_real @ ( A @ C ) @ ( B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(72,axiom,
    ! [A: char > real > $o,B: char > real > $o,C: char > real > $o,D: char > real > $o] :
      ( ( ( produc1566957527real_o @ A @ B )
        = ( produc1566957527real_o @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Pair__inject) ).

thf(543,plain,
    ! [A: char > real > $o,B: char > real > $o,C: char > real > $o,D: char > real > $o] :
      ( ( ( produc1566957527real_o @ A @ B )
        = ( produc1566957527real_o @ C @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(338,axiom,
    ( produc753879889real_o
    = ( ^ [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] : ( A @ ( produc141013715e_real @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_curry__def) ).

thf(1416,plain,
    ( produc753879889real_o
    = ( ^ [A: produc1020032539e_real > $o,B: char > real > real,C: produc104944723e_real] : ( A @ ( produc141013715e_real @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(113,axiom,
    ! [A: char > real,B: char > real,C: set_Pr42335993r_real,D: ( char > real ) > char > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( inv_im817616652r_real @ C @ D ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_in__inv__image) ).

thf(676,plain,
    ! [A: char > real,B: char > real,C: set_Pr42335993r_real,D: ( char > real ) > char > real] :
      ( ( member1086859330r_real @ ( produc700235985r_real @ A @ B ) @ ( inv_im817616652r_real @ C @ D ) )
      = ( member1086859330r_real @ ( produc700235985r_real @ ( D @ A ) @ ( D @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(10,axiom,
    ! [A: char > real,B: char > real] :
      ( ( produc1564675697r_real @ ( produc700235985r_real @ A @ B ) )
      = ( produc700235985r_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_swap__simp) ).

thf(364,plain,
    ! [A: char > real,B: char > real] :
      ( ( produc1564675697r_real @ ( produc700235985r_real @ A @ B ) )
      = ( produc700235985r_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(124,axiom,
    ! [A: produc2070499431real_o] :
    ? [B: char > real > $o,C: char > real > $o] :
      ( A
      = ( produc1566957527real_o @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_surj__pair) ).

thf(708,plain,
    ! [A: produc2070499431real_o] :
    ? [B: char > real > $o,C: char > real > $o] :
      ( A
      = ( produc1566957527real_o @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(168,axiom,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o] :
      ( ( produc192924469real_o @ ( produc1285468373real_o @ A @ B ) )
      = ( produc2007437005e_real @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_swap__simp) ).

thf(882,plain,
    ! [A: char > set_variable_real > set_variable_real,B: char > real > $o] :
      ( ( produc192924469real_o @ ( produc1285468373real_o @ A @ B ) )
      = ( produc2007437005e_real @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(197,axiom,
    ! [A: produc1993135732e_real] :
      ( A
      = ( produc2125489830e_real @ ( produc1146879930e_real @ A ) @ ( produc1176159992e_real @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_prod_Oexhaust__sel) ).

thf(972,plain,
    ! [A: produc1993135732e_real] :
      ( A
      = ( produc2125489830e_real @ ( produc1146879930e_real @ A ) @ ( produc1176159992e_real @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(54,axiom,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr1053253703real_o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ ( image_448624581real_o @ produc443915639real_o @ C ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ B @ A ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_pair__in__swap__image) ).

thf(491,plain,
    ! [A: char > real > $o,B: char > real > $o,C: set_Pr1053253703real_o] :
      ( ( member1795186320real_o @ ( produc1566957527real_o @ A @ B ) @ ( image_448624581real_o @ produc443915639real_o @ C ) )
      = ( member1795186320real_o @ ( produc1566957527real_o @ B @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(230,axiom,
    ! [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( produc998184740real_o @ A @ B @ C )
     => ( A @ ( produc2125489830e_real @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_curryE) ).

thf(1088,plain,
    ! [A: produc1993135732e_real > $o,B: char > real,C: produc1020032539e_real] :
      ( ( produc998184740real_o @ A @ B @ C )
     => ( A @ ( produc2125489830e_real @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(56,axiom,
    ! [A: produc96687023l_real] :
      ~ ! [B: char > real > real,C: char > real > real] :
          ( A
         != ( produc686464615l_real @ B @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_old_Oprod_Oexhaust) ).

thf(496,plain,
    ! [A: produc96687023l_real] :
      ~ ! [B: char > real > real,C: char > real > real] :
          ( A
         != ( produc686464615l_real @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(226,axiom,
    ! [A: produc1020032539e_real,B: ( char > real > real ) > produc104944723e_real > $o] :
      ( ! [C: char > real > real,D: produc104944723e_real] :
          ( ( A
            = ( produc141013715e_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc679978160real_o @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_case__prodI2) ).

thf(1069,plain,
    ! [A: produc1020032539e_real,B: ( char > real > real ) > produc104944723e_real > $o] :
      ( ! [C: char > real > real,D: produc104944723e_real] :
          ( ( A
            = ( produc141013715e_real @ C @ D ) )
         => ( B @ C @ D ) )
     => ( produc679978160real_o @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(1432,plain,
    $false,
    inference(e,[status(thm)],[1105,347,628,481,777,555,1200,1211,1401,1422,1073,1269,655,597,1041,1173,1078,384,533,550,500,1164,1233,1260,1342,913,1095,898,1127,885,1359,436,841,417,565,1366,1228,1254,724,719,785,372,504,1191,1059,949,460,1323,838,702,751,802,344,902,1247,1013,1362,969,606,1302,789,591,1151,353,821,905,1418,623,1136,834,1383,574,1183,1283,602,397,1377,634,866,774,1351,660,998,1345,1242,507,452,380,793,925,1306,761,810,1311,714,942,439,1274,910,957,952,392,429,1238,693,630,879,665,1159,1281,1392,682,1407,519,697,650,615,1328,1111,1425,1006,1138,869,610,420,857,471,1028,1292,537,686,642,526,637,489,1214,679,1155,1114,1297,738,457,721,647,1263,1266,1231,1333,938,360,657,1170,558,1167,530,662,1286,1035,412,513,745,444,1374,375,1251,618,1219,824,584,423,402,732,1389,1125,711,562,975,1371,466,1090,1224,1356,350,540,764,1194,1117,377,1144,599,863,477,387,494,367,816,594,895,1022,668,932,758,1339,626,915,521,399,1044,1066,780,455,1176,1000,431,653,922,1198,1396,851,1102,426,1277,516,342,1018,355,553,1049,1413,1076,1203,1208,1003,690,1025,872,705,887,414,1368,1053,673,441,1038,502,463,1317,1130,1336,907,1188,1186,1404,1257,1141,1221,1353,727,978,1008,571,1180,671,1108,524,581,1216,891,1289,844,1326,699,963,748,1062,946,632,995,813,1385,1030,568,1294,929,478,684,1309,433,510,716,1161,800,1133,1348,447,1097,818,1380,405,854,1148,735,410,967,918,1314,358,1056,1033,960,955,474,1410,987,860,644,992,982,1299,1399,1120,369,1093,395,1331,486,1320,469,935,543,1416,676,364,708,882,972,491,1088,496,1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : ITP198^1 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n006.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May  6 14:28:54 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 1.01/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.10/1.19  % [INFO] 	 Parsing done (278ms). 
% 2.10/1.20  % [INFO] 	 Running in sequential loop mode. 
% 2.82/1.41  % [INFO] 	 eprover registered as external prover. 
% 2.82/1.41  % [INFO] 	 cvc4 registered as external prover. 
% 2.82/1.41  % [INFO] 	 Scanning for conjecture ... 
% 3.09/1.52  % [INFO] 	 Found a conjecture and 357 axioms. Running axiom selection ... 
% 3.45/1.63  % [INFO] 	 Axiom selection finished. Selected 339 axioms (removed 18 axioms). 
% 4.11/1.81  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.11/1.82  % [INFO] 	 Type checking passed. 
% 4.11/1.83  % [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 ... 
% 19.78/6.21  % External prover 'e' found a proof!
% 19.78/6.22  % [INFO] 	 Killing All external provers ... 
% 19.78/6.22  % Time passed: 5694ms (effective reasoning time: 5017ms)
% 19.78/6.22  % 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)>
% 19.78/6.22  % Axioms used in derivation (339): fact_283_prod__fun__imageE, fact_89_curry__def, fact_338_eq__fst__iff, fact_198_The__split__eq, fact_318_fst__pair, fact_134_curryE, fact_333_sndI, fact_330_eq__snd__iff, fact_54_prod__cases, fact_119_swap__swap, fact_9_old_Oprod_Oinject, fact_343_mon__mono, fact_104_swap__simp, fact_140_Pair__def, fact_227_case__prod__Pair__iden, fact_183_internal__case__prod__def, fact_319_BNF__Greatest__Fixpoint_Osubst__Pair, fact_88_curry__conv, fact_92_curryI, fact_59_surj__pair, fact_125_curryD, fact_165_in__inv__image, fact_17_prod_Oinject, fact_221_case__prodD, fact_109_swap__simp, fact_274_in__lex__prod, fact_143_Pair__def, fact_87_curry__conv, fact_199_The__split__eq, fact_39_old_Oprod_Oexhaust, fact_114_swap__swap, fact_302_snd__conv, fact_266_map__prod__imageI, fact_309_snd__pair, fact_188_case__swap, fact_113_Pair__Rep__def, fact_341_subrelI, fact_20_prod_Oinject, fact_170_mem__Collect__eq, fact_269_map__prod__imageI, fact_259_map__prod__simp, fact_263_map__prod__simp, fact_270_map__prod__imageI, fact_317_fst__pair, fact_111_Pair__Rep__def, fact_254_same__fstI, fact_1_Funcs__mkinterp, fact_184_internal__case__prod__def, fact_154_pair__in__swap__image, fact_136_curryE, fact_238_SigmaD2, fact_326_exI__realizer, fact_57_surj__pair, fact_306_snd__eqD, fact_108_swap__simp, fact_67_prod__cases3, fact_310_fst__conv, fact_290_prod_Ocollapse, fact_305_snd__eqD, fact_210_case__prodI, fact_242_SigmaD1, fact_212_case__prodI, fact_135_curryE, fact_175_Collect__mem__eq, fact_251_swap__product, fact_258_map__prod__simp, fact_321_BNF__Greatest__Fixpoint_Osubst__Pair, fact_276_prod__fun__imageE, fact_106_swap__simp, fact_146_Pair__def, fact_84_ssubst__Pair__rhs, fact_86_curry__conv, fact_81_ssubst__Pair__rhs, fact_46_Pair__inject, fact_14_old_Oprod_Oinject, fact_153_pair__in__swap__image, fact_176_Collect__mem__eq, fact_144_Pair__def, fact_231_mem__Sigma__iff, fact_250_swap__product, fact_70_pred__equals__eq2, fact_160_in__inv__image, fact_33_old_Oprod_Oexhaust, fact_132_curryE, fact_277_prod__fun__imageE, fact_101_swap__simp, fact_91_curry__def, fact_34_old_Oprod_Oexhaust, fact_303_snd__conv, fact_192_case__swap, fact_152_pair__in__swap__image, fact_120_curry__K, fact_90_curry__def, fact_268_map__prod__imageI, fact_53_prod__cases, fact_315_fst__eqD, fact_278_prod__fun__imageE, fact_201_The__split__eq, fact_334_fstI, fact_173_Collect__mem__eq, fact_133_curryE, fact_18_prod_Oinject, fact_62_surj__pair, fact_56_prod__cases, fact_256_map__prod__simp, fact_169_mem__Collect__eq, fact_253_same__fstI, fact_335_fstI, fact_255_map__prod__simp, fact_300_prod_Oswap__def, fact_281_prod__fun__imageE, fact_80_ssubst__Pair__rhs, fact_129_curryD, fact_4_repc__def, fact_166_in__inv__image, fact_282_prod__fun__imageE, fact_31_old_Oprod_Oinducts, fact_195_The__split__eq, fact_93_curryI, fact_314_fst__eqD, fact_26_old_Oprod_Oinducts, fact_7_old_Oprod_Oinject, fact_116_swap__swap, fact_112_Pair__Rep__def, fact_257_map__prod__simp, fact_127_curryD, fact_292_surjective__pairing, fact_206_case__prodI2, fact_213_case__prodI, fact_324_conjI__realizer, fact_36_old_Oprod_Oexhaust, fact_121_curry__K, fact_76_pred__equals__eq2, fact_25_old_Oprod_Oinducts, fact_217_case__prodI, fact_139_Pair__def, fact_162_in__inv__image, fact_218_case__prodE, fact_145_Pair__def, fact_245_SigmaE, fact_131_curryE, fact_273_in__lex__prod, fact_96_curryI, fact_336_fstI, fact_312_fst__conv, fact_271_map__prod__imageI, fact_228_SigmaI, fact_12_old_Oprod_Oinject, fact_163_in__inv__image, fact_43_Pair__inject, fact_180_Collect__cong, fact_44_Pair__inject, fact_27_old_Oprod_Oinducts, fact_85_ssubst__Pair__rhs, fact_296_prod_Oexhaust__sel, fact_102_swap__simp, fact_239_SigmaD2, fact_328_eq__snd__iff, help_If_2_1_If_001t__Real__Oreal_T, fact_98_curryI, fact_249_swap__product, fact_2_Consts__mkinterp, fact_280_prod__fun__imageE, fact_215_case__prodI, fact_196_The__split__eq, fact_74_pred__equals__eq2, fact_190_case__swap, fact_158_in__inv__image, fact_347_Collect__mono, fact_148_pair__in__swap__image, fact_191_case__swap, fact_61_surj__pair, fact_351_GrD1, fact_137_curryE, fact_10_old_Oprod_Oinject, fact_11_old_Oprod_Oinject, fact_225_case__prod__Pair__iden, fact_295_prod_Oexhaust__sel, fact_337_eq__fst__iff, fact_82_ssubst__Pair__rhs, fact_202_case__prodI2, fact_233_mem__Sigma__iff, fact_68_prod__cases3, fact_99_curryI, fact_38_old_Oprod_Oexhaust, fact_316_fst__pair, fact_149_pair__in__swap__image, fact_232_mem__Sigma__iff, fact_97_curryI, fact_236_SigmaE2, fact_155_pair__in__swap__image, fact_47_Pair__inject, fact_208_case__prodI2, fact_342_subrelI, fact_279_prod__fun__imageE, fact_40_old_Oprod_Oexhaust, fact_189_case__swap, fact_240_SigmaD2, fact_5_prod__cases4, fact_322_conjI__realizer, fact_222_case__prodD, fact_226_case__prod__Pair__iden, fact_122_curry__K, fact_353_GrD1, fact_327_exI__realizer, fact_100_worlds__def, fact_79_ssubst__Pair__rhs, fact_42_Pair__inject, fact_64_surj__pair, fact_19_prod_Oinject, fact_313_fst__eqD, fact_107_swap__simp, fact_246_SigmaE, fact_95_curryI, fact_304_snd__eqD, fact_297_prod_Oexhaust__sel, fact_156_pair__in__swap__image, fact_181_internal__case__prod__def, fact_138_curryE, fact_167_mem__Collect__eq, fact_41_Pair__inject, fact_21_prod_Oinject, fact_329_eq__snd__iff, fact_262_map__prod__simp, fact_72_pred__equals__eq2, fact_45_Pair__inject, fact_264_map__prod__imageI, fact_118_swap__swap, fact_48_Pair__inject, fact_272_map__prod__imageI, fact_267_map__prod__imageI, fact_78_ssubst__Pair__rhs, fact_23_repc__consts, fact_142_Pair__def, fact_223_case__prodD, fact_244_SigmaE, fact_105_swap__simp, fact_331_sndI, fact_241_SigmaD1, fact_203_case__prodI2, fact_298_prod_Oswap__def, fact_151_pair__in__swap__image, fact_63_surj__pair, fact_13_old_Oprod_Oinject, fact_3_mkinterp__eq, fact_124_curryD, fact_24_repc__funcs, fact_22_prod_Oinject, fact_252_same__fstI, fact_207_case__prodI2, fact_339_eq__fst__iff, fact_261_map__prod__simp, fact_168_mem__Collect__eq, fact_16_prod_Oinject, fact_77_pred__equals__eq2, fact_126_curryD, fact_294_surjective__pairing, fact_73_pred__equals__eq2, fact_28_old_Oprod_Oinducts, fact_275_in__lex__prod, fact_58_surj__pair, fact_299_prod_Oswap__def, fact_307_snd__pair, fact_220_case__prodE, fact_15_prod_Oinject, fact_83_ssubst__Pair__rhs, fact_216_case__prodI, fact_52_prod__cases, fact_110_swap__simp, fact_55_prod__cases, fact_60_surj__pair, fact_29_old_Oprod_Oinducts, fact_214_case__prodI, fact_182_internal__case__prod__def, fact_174_Collect__mem__eq, fact_150_pair__in__swap__image, fact_348_Collect__mono__iff, fact_6_prod__induct4, fact_37_old_Oprod_Oexhaust, fact_187_case__swap, fact_311_fst__conv, fact_75_pred__equals__eq2, fact_66_prod__induct3, fact_30_old_Oprod_Oinducts, fact_332_sndI, fact_123_curryD, fact_71_pred__equals__eq2, fact_65_prod__induct3, fact_288_prod_Ocollapse, fact_323_conjI__realizer, fact_69_Games__mkinterp, fact_325_exI__realizer, fact_161_in__inv__image, fact_352_GrD1, fact_204_case__prodI2, fact_197_The__split__eq, fact_193_case__swap, fact_237_SigmaE2, fact_186_case__swap, fact_32_old_Oprod_Oinducts, fact_115_swap__swap, fact_159_in__inv__image, help_If_3_1_If_001t__Real__Oreal_T, fact_164_in__inv__image, fact_200_The__split__eq, fact_157_in__inv__image, fact_185_internal__case__prod__def, fact_128_curryD, fact_229_SigmaI, help_If_1_1_If_001t__Real__Oreal_T, fact_308_snd__pair, fact_260_map__prod__simp, fact_301_snd__conv, fact_265_map__prod__imageI, fact_50_prod__cases, fact_103_swap__simp, fact_0_Preds__mkinterp, fact_235_SigmaE2, fact_51_prod__cases, fact_141_Pair__def, fact_49_prod__cases, fact_243_SigmaD1, fact_219_case__prodE, fact_35_old_Oprod_Oexhaust, fact_194_The__split__eq, fact_284_prod__fun__imageE, fact_130_curryD, fact_209_case__prodI2, fact_205_case__prodI2, fact_117_swap__swap, fact_289_prod_Ocollapse, fact_147_pair__in__swap__image, fact_230_SigmaI, fact_94_curryI, fact_293_surjective__pairing, fact_320_BNF__Greatest__Fixpoint_Osubst__Pair, fact_211_case__prodI, fact_340_subrelI, fact_8_old_Oprod_Oinject
% 19.78/6.22  % No. of inferences in proof: 682
% 19.78/6.22  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5694 ms resp. 5017 ms w/o parsing
% 20.73/6.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 20.73/6.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------