TSTP Solution File: ITP305_1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP305_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:26:35 EDT 2024
% Result : Theorem 21.82s 5.91s
% Output : Refutation 22.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 884
% Syntax : Number of formulae : 1365 ( 191 unt; 405 typ; 0 def)
% Number of atoms : 3219 ( 798 equ; 0 cnn)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 17945 ( 28 ~; 0 |;1227 &;15658 @)
% ( 56 <=>; 976 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 94 ( 93 usr)
% Number of type conns : 486 ( 486 >; 0 *; 0 +; 0 <<)
% Number of symbols : 315 ( 312 usr; 31 con; 0-7 aty)
% Number of variables : 2887 ( 0 ^2838 !; 49 ?;2887 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'B_ZF_fun_set$\'_type',type,
'\'B_ZF_fun_set$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'': $tType ).
thf('\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'_type',type,
'\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'': $tType ).
thf('\'ZF_set$\'_type',type,
'\'ZF_set$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'': $tType ).
thf('\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'_type',type,
'\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'': $tType ).
thf('\'Unit_unit_fun$\'_type',type,
'\'Unit_unit_fun$\'': $tType ).
thf('\'A_b_b_c_LSCategory_ext_Category_ext$\'_type',type,
'\'A_b_b_c_LSCategory_ext_Category_ext$\'': $tType ).
thf('\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$\'_type',type,
'\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$\'': $tType ).
thf('\'ZF_ZF_prod_set$\'_type',type,
'\'ZF_ZF_prod_set$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'': $tType ).
thf('\'ZF_set_ZF_set_fun$\'_type',type,
'\'ZF_set_ZF_set_fun$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'': $tType ).
thf('\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'_type',type,
'\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'': $tType ).
thf('\'A_b_fun_set$\'_type',type,
'\'A_b_fun_set$\'': $tType ).
thf('\'ZF_ZF_prod_ZF_fun$\'_type',type,
'\'ZF_ZF_prod_ZF_fun$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'': $tType ).
thf('\'B_c_LSCategory_ext$\'_type',type,
'\'B_c_LSCategory_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_set$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_set$\'': $tType ).
thf('\'B_b_fun$\'_type',type,
'\'B_b_fun$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'_type',type,
'\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_a_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_a_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'': $tType ).
thf('\'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'_type',type,
'\'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'': $tType ).
thf('\'ZF_ZF_prod$\'_type',type,
'\'ZF_ZF_prod$\'': $tType ).
thf('\'B_b_prod_set$\'_type',type,
'\'B_b_prod_set$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'': $tType ).
thf('\'B$\'_type',type,
'\'B$\'': $tType ).
thf('\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext_ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_fun_fun$\'_type',type,
'\'ZF_ZF_ZF_fun_fun$\'': $tType ).
thf('\'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$\'_type',type,
'\'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$\'': $tType ).
thf('\'C$\'_type',type,
'\'C$\'': $tType ).
thf('\'B_ZF_fun_b_ZF_fun_fun$\'_type',type,
'\'B_ZF_fun_b_ZF_fun_fun$\'': $tType ).
thf('\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'_type',type,
'\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'': $tType ).
thf('\'Nat$\'_type',type,
'\'Nat$\'': $tType ).
thf('\'B_b_prod_bool_fun$\'_type',type,
'\'B_b_prod_bool_fun$\'': $tType ).
thf('\'ZF_ZF_prod_ZF_fun_set$\'_type',type,
'\'ZF_ZF_prod_ZF_fun_set$\'': $tType ).
thf('\'ZF_ZF_fun$\'_type',type,
'\'ZF_ZF_fun$\'': $tType ).
thf('\'ZF_ZF_prod_bool_fun$\'_type',type,
'\'ZF_ZF_prod_bool_fun$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'': $tType ).
thf('\'ZF_ZF_fun_set$\'_type',type,
'\'ZF_ZF_fun_set$\'': $tType ).
thf('\'B_b_prod_b_fun_set$\'_type',type,
'\'B_b_prod_b_fun_set$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'': $tType ).
thf('\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'B_a_fun$\'_type',type,
'\'B_a_fun$\'': $tType ).
thf('\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'_type',type,
'\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'': $tType ).
thf('\'B_b_prod$\'_type',type,
'\'B_b_prod$\'': $tType ).
thf('\'ZF_ZF_fun_ZF_ZF_fun_fun$\'_type',type,
'\'ZF_ZF_fun_ZF_ZF_fun_fun$\'': $tType ).
thf('\'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'A_bool_fun$\'_type',type,
'\'A_bool_fun$\'': $tType ).
thf('\'A_set$\'_type',type,
'\'A_set$\'': $tType ).
thf('\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'_type',type,
'\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'': $tType ).
thf('\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'A_b_fun$\'_type',type,
'\'A_b_fun$\'': $tType ).
thf('\'B_set$\'_type',type,
'\'B_set$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$\'': $tType ).
thf('\'A_b_fun_bool_fun$\'_type',type,
'\'A_b_fun_bool_fun$\'': $tType ).
thf('\'A$\'_type',type,
'\'A$\'': $tType ).
thf('\'ZF_ZF_unit_Category_ext$\'_type',type,
'\'ZF_ZF_unit_Category_ext$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'B_b_prod_b_fun$\'_type',type,
'\'B_b_prod_b_fun$\'': $tType ).
thf('\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'_type',type,
'\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'': $tType ).
thf('\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_set$\'_type',type,
'\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_set$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$\'': $tType ).
thf('\'ZF_bool_fun$\'_type',type,
'\'ZF_bool_fun$\'': $tType ).
thf('\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'_type',type,
'\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'': $tType ).
thf('\'B_b_b_fun_fun$\'_type',type,
'\'B_b_b_fun_fun$\'': $tType ).
thf('\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'_type',type,
'\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$\'_type',type,
'\'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$\'': $tType ).
thf('\'A_ZF_fun$\'_type',type,
'\'A_ZF_fun$\'': $tType ).
thf('\'A_set_a_set_fun$\'_type',type,
'\'A_set_a_set_fun$\'': $tType ).
thf('\'Unit$\'_type',type,
'\'Unit$\'': $tType ).
thf('\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext_a_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext_a_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_a_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_a_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext_unit_Category_ext$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_a_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_a_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext_unit_Category_ext$\'': $tType ).
thf('\'ZF$\'_type',type,
'\'ZF$\'': $tType ).
thf('\'B_ZF_fun$\'_type',type,
'\'B_ZF_fun$\'': $tType ).
thf('\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_set$\'_type',type,
'\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_set$\'': $tType ).
thf('\'B_a_fun_set$\'_type',type,
'\'B_a_fun_set$\'': $tType ).
thf('\'Nat_ZF_fun$\'_type',type,
'\'Nat_ZF_fun$\'': $tType ).
thf('\'B_a_fun_bool_fun$\'_type',type,
'\'B_a_fun_bool_fun$\'': $tType ).
thf('\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$\'_type',type,
'\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$\'': $tType ).
thf('\'B_bool_fun$\'_type',type,
'\'B_bool_fun$\'': $tType ).
thf('\'B_ZF_fun_bool_fun$\'_type',type,
'\'B_ZF_fun_bool_fun$\'': $tType ).
thf('\'uu$\'_type',type,
'\'uu$\'': '\'A_set$\'' > '\'A_bool_fun$\'' ).
thf('\'catDom$\'_type',type,
'\'catDom$\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'more$b\'_type',type,
'\'more$b\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'Unit$\'' ).
thf('\'functorComp$a\'_type',type,
'\'functorComp$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'collect$e\'_type',type,
'\'collect$e\'': '\'B_ZF_fun_bool_fun$\'' > '\'B_ZF_fun_set$\'' ).
thf('\'functor$e\'_type',type,
'\'functor$e\'': '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'collect$i\'_type',type,
'\'collect$i\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$\'' ).
thf('\'oppositeCategory$\'_type',type,
'\'oppositeCategory$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'functor_comp_def$h\'_type',type,
'\'functor_comp_def$h\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'constFunctor$j\'_type',type,
'\'constFunctor$j\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' ).
thf('\'comp$b\'_type',type,
'\'comp$b\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'c$\'_type',type,
'\'c$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'fun_app$u\'_type',type,
'\'fun_app$u\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'fun_app$s\'_type',type,
'\'fun_app$s\'': '\'B_ZF_fun_b_ZF_fun_fun$\'' > '\'B_ZF_fun$\'' > '\'B_ZF_fun$\'' ).
thf('\'nTCatCod$a\'_type',type,
'\'nTCatCod$a\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'functorM$d\'_type',type,
'\'functorM$d\'': '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'fun_app$b\'_type',type,
'\'fun_app$b\'': '\'ZF_bool_fun$\'' > '\'ZF$\'' > $o ).
thf('\'natTransP$b\'_type',type,
'\'natTransP$b\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > $o ).
thf('\'fun_app$f\'_type',type,
'\'fun_app$f\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'x$\'_type',type,
'\'x$\'': '\'A$\'' ).
thf('\'preFunctor$c\'_type',type,
'\'preFunctor$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'mapsTo$\'_type',type,
'\'mapsTo$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B$\'' > '\'A$\'' > '\'A_bool_fun$\'' ).
thf('\'the$b\'_type',type,
'\'the$b\'': '\'B_bool_fun$\'' > '\'B$\'' ).
thf('\'makeFtor$\'_type',type,
'\'makeFtor$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'nTDom$b\'_type',type,
'\'nTDom$b\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'lSCategory$\'_type',type,
'\'lSCategory$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > $o ).
thf('\'natTrans$\'_type',type,
'\'natTrans$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' ).
thf('\'uua$\'_type',type,
'\'uua$\'': '\'ZF_set$\'' > '\'ZF_bool_fun$\'' ).
thf('\'idNatTrans$\'_type',type,
'\'idNatTrans$\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' ).
thf('\'member$\'_type',type,
'\'member$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$\'' > $o ).
thf('\'constFunctor$i\'_type',type,
'\'constFunctor$i\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' ).
thf('\'yMapInv$\'_type',type,
'\'yMapInv$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'constFunctor$a\'_type',type,
'\'constFunctor$a\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'restrict$b\'_type',type,
'\'restrict$b\'': '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'B_set$\'' > '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' ).
thf('\'uud$\'_type',type,
'\'uud$\'': '\'B_ZF_fun_set$\'' > '\'B_ZF_fun_bool_fun$\'' ).
thf('\'isomorphism$b\'_type',type,
'\'isomorphism$b\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_bool_fun$\'' ).
thf('\'isomorphism$a\'_type',type,
'\'isomorphism$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' ).
thf('\'natTransP$\'_type',type,
'\'natTransP$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' ).
thf('\'fun_app$x\'_type',type,
'\'fun_app$x\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' ).
thf('\'nTCod$b\'_type',type,
'\'nTCod$b\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'functor$a\'_type',type,
'\'functor$a\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > $o ).
thf('\'extensional$\'_type',type,
'\'extensional$\'': '\'B_set$\'' > '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_set$\'' ).
thf('\'functor_abbrev$f\'_type',type,
'\'functor_abbrev$f\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > $o ).
thf('\'functor_comp_def$e\'_type',type,
'\'functor_comp_def$e\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'category$a\'_type',type,
'\'category$a\'': '\'ZF_ZF_unit_Category_ext$\'' > $o ).
thf('\'fun_app$r\'_type',type,
'\'fun_app$r\'': '\'A_b_fun$\'' > '\'A$\'' > '\'B$\'' ).
thf('\'functor_comp_def$c\'_type',type,
'\'functor_comp_def$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > $o ).
thf('\'functor_comp_def$b\'_type',type,
'\'functor_comp_def$b\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'uus$\'_type',type,
'\'uus$\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' ).
thf('\'makeCat$a\'_type',type,
'\'makeCat$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'functor_abbrev$c\'_type',type,
'\'functor_abbrev$c\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > $o ).
thf('\'nt_abbrev$d\'_type',type,
'\'nt_abbrev$d\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'preFunctor$d\'_type',type,
'\'preFunctor$d\'': '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'collect$d\'_type',type,
'\'collect$d\'': '\'B_bool_fun$\'' > '\'B_set$\'' ).
thf('\'functorComp$d\'_type',type,
'\'functorComp$d\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'objIso$b\'_type',type,
'\'objIso$b\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_bool_fun$\'' ).
thf('\'equivalence_axioms$\'_type',type,
'\'equivalence_axioms$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'mapM$f\'_type',type,
'\'mapM$f\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'B$\'' > '\'B$\'' ).
thf('\'constFunctor$\'_type',type,
'\'constFunctor$\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' ).
thf('\'idNatTrans$d\'_type',type,
'\'idNatTrans$d\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'nTCatDom$d\'_type',type,
'\'nTCatDom$d\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'uur$\'_type',type,
'\'uur$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF$\'' > '\'A_ZF_fun$\'' ).
thf('\'uuk$\'_type',type,
'\'uuk$\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_ZF_fun_fun$\'' ).
thf('\'seqSum$\'_type',type,
'\'seqSum$\'': '\'Nat_ZF_fun$\'' > '\'ZF$\'' ).
thf('\'idNatTrans$g\'_type',type,
'\'idNatTrans$g\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' ).
thf('\'collect$h\'_type',type,
'\'collect$h\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'' ).
thf('\'fun_app$h\'_type',type,
'\'fun_app$h\'': '\'B_ZF_fun_bool_fun$\'' > '\'B_ZF_fun$\'' > $o ).
thf('\'uun$\'_type',type,
'\'uun$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' ).
thf('\'nTCatDom$b\'_type',type,
'\'nTCatDom$b\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'functorM_axioms$c\'_type',type,
'\'functorM_axioms$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'fun_app$d\'_type',type,
'\'fun_app$d\'': '\'A_ZF_fun$\'' > '\'A$\'' > '\'ZF$\'' ).
thf('\'the$a\'_type',type,
'\'the$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'set$\'_type',type,
'\'set$\'': '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'functorM$c\'_type',type,
'\'functorM$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'natTransMap$d\'_type',type,
'\'natTransMap$d\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'uul$\'_type',type,
'\'uul$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_ZF_ZF_fun_fun$\'' ).
thf('\'mapO$f\'_type',type,
'\'mapO$f\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A$\'' > '\'A$\'' ).
thf('\'catDom$b\'_type',type,
'\'catDom$b\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'member$d\'_type',type,
'\'member$d\'': '\'ZF$\'' > '\'ZF_set$\'' > $o ).
thf('\'mapsTo$b\'_type',type,
'\'mapsTo$b\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF$\'' > '\'ZF$\'' > '\'ZF_bool_fun$\'' ).
thf('\'natTransComp$a\'_type',type,
'\'natTransComp$a\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' ).
thf('\'unity$\'_type',type,
'\'unity$\'': '\'Unit$\'' ).
thf('\'identityFunctor$f\'_type',type,
'\'identityFunctor$f\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'nTCompDefined$a\'_type',type,
'\'nTCompDefined$a\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > $o ).
thf('\'natTrans$a\'_type',type,
'\'natTrans$a\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > $o ).
thf('\'catCod$d\'_type',type,
'\'catCod$d\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'functorComp$c\'_type',type,
'\'functorComp$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'idNatTrans$b\'_type',type,
'\'idNatTrans$b\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'' ).
thf('\'fun_app$l\'_type',type,
'\'fun_app$l\'': '\'A_bool_fun$\'' > '\'A$\'' > $o ).
thf('\'functor_abbrev$a\'_type',type,
'\'functor_abbrev$a\'': '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > $o ).
thf('\'nTCod$c\'_type',type,
'\'nTCod$c\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$\'' ).
thf('\'functorComp$h\'_type',type,
'\'functorComp$h\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'nTCod$d\'_type',type,
'\'nTCod$d\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' ).
thf('\'mor2ZF$\'_type',type,
'\'mor2ZF$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_ZF_fun$\'' ).
thf('\'catCod$c\'_type',type,
'\'catCod$c\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'nTCod$a\'_type',type,
'\'nTCod$a\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'obj$\'_type',type,
'\'obj$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'' ).
thf('\'nTDom$a\'_type',type,
'\'nTDom$a\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'natTrans_ext$a\'_type',type,
'\'natTrans_ext$a\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'Unit$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'constFunctor$s\'_type',type,
'\'constFunctor$s\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' ).
thf('\'nt_abbrev$c\'_type',type,
'\'nt_abbrev$c\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > $o ).
thf('\'catDom$e\'_type',type,
'\'catDom$e\'': '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'zFfun$\'_type',type,
'\'zFfun$\'': '\'ZF$\'' > '\'ZF$\'' > '\'ZF_ZF_fun$\'' > '\'ZF$\'' ).
thf('\'makeFtor$e\'_type',type,
'\'makeFtor$e\'': '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' ).
thf('\'nTCompDefined$\'_type',type,
'\'nTCompDefined$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' ).
thf('\'inverse_rel$\'_type',type,
'\'inverse_rel$\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF$\'' > '\'ZF_bool_fun$\'' ).
thf('\'idNatTrans$a\'_type',type,
'\'idNatTrans$a\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'' ).
thf('\'objIso$\'_type',type,
'\'objIso$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'obj$a\'_type',type,
'\'obj$a\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_set$\'' ).
thf('\'constFunctor$c\'_type',type,
'\'constFunctor$c\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'nTCatCod$\'_type',type,
'\'nTCatCod$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'functor_abbrev$d\'_type',type,
'\'functor_abbrev$d\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > $o ).
thf('\'lSCategory_axioms$\'_type',type,
'\'lSCategory_axioms$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > $o ).
thf('\'yMapInv$a\'_type',type,
'\'yMapInv$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'zFfunCod$\'_type',type,
'\'zFfunCod$\'': '\'ZF_ZF_fun$\'' ).
thf('\'oppositeCategory$b\'_type',type,
'\'oppositeCategory$b\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'more$a\'_type',type,
'\'more$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_c_LSCategory_ext$\'' ).
thf('\'catDom$a\'_type',type,
'\'catDom$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'homFtor$\'_type',type,
'\'homFtor$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'category_ext$\'_type',type,
'\'category_ext$\'': '\'A_set$\'' > '\'B_set$\'' > '\'B_a_fun$\'' > '\'B_a_fun$\'' > '\'A_b_fun$\'' > '\'B_b_b_fun_fun$\'' > '\'B_c_LSCategory_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'functorComp$g\'_type',type,
'\'functorComp$g\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'comp$c\'_type',type,
'\'comp$c\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' ).
thf('\'mor2ZF_update$\'_type',type,
'\'mor2ZF_update$\'': '\'B_ZF_fun_b_ZF_fun_fun$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'category$c\'_type',type,
'\'category$c\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > $o ).
thf('\'cod$\'_type',type,
'\'cod$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_a_fun$\'' ).
thf('\'functor_comp_def$a\'_type',type,
'\'functor_comp_def$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'restrict$c\'_type',type,
'\'restrict$c\'': '\'B_a_fun$\'' > '\'B_set$\'' > '\'B_a_fun$\'' ).
thf('\'set$a\'_type',type,
'\'set$a\'': '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'nTDom$d\'_type',type,
'\'nTDom$d\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' ).
thf('\'compDefined$\'_type',type,
'\'compDefined$\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF$\'' > '\'ZF_bool_fun$\'' ).
thf('\'uut$\'_type',type,
'\'uut$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_fun$\'' ).
thf('\'functorComp$b\'_type',type,
'\'functorComp$b\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' ).
thf('\'nTDom$c\'_type',type,
'\'nTDom$c\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$\'' ).
thf('\'more$c\'_type',type,
'\'more$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'Unit$\'' ).
thf('\'compDefined$b\'_type',type,
'\'compDefined$b\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' ).
thf('\'compDefined$c\'_type',type,
'\'compDefined$c\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > $o ).
thf('\'natTransMap$c\'_type',type,
'\'natTransMap$c\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'ZF$\'' > '\'B$\'' ).
thf('\'nTCatDom$a\'_type',type,
'\'nTCatDom$a\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'fun_app$o\'_type',type,
'\'fun_app$o\'': '\'B_b_b_fun_fun$\'' > '\'B$\'' > '\'B_b_fun$\'' ).
thf('\'restrict$e\'_type',type,
'\'restrict$e\'': '\'ZF_ZF_fun$\'' > '\'ZF_set$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'functor_ext$a\'_type',type,
'\'functor_ext$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'B_ZF_fun$\'' > '\'Unit$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'category_axioms$\'_type',type,
'\'category_axioms$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > $o ).
thf('\'dom$b\'_type',type,
'\'dom$b\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'functor_comp_def$f\'_type',type,
'\'functor_comp_def$f\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'mapO$g\'_type',type,
'\'mapO$g\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF$\'' ).
thf('\'functor_abbrev$\'_type',type,
'\'functor_abbrev$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > $o ).
thf('\'nTCatCod$c\'_type',type,
'\'nTCatCod$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' ).
thf('\'member$m\'_type',type,
'\'member$m\'': '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_set$\'' > $o ).
thf('\'uuy$\'_type',type,
'\'uuy$\'': '\'ZF_bool_fun$\'' ).
thf('\'oppositeCategory$a\'_type',type,
'\'oppositeCategory$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' ).
thf('\'yMap$\'_type',type,
'\'yMap$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'ZF$\'' ).
thf('\'homFtorContra$a\'_type',type,
'\'homFtorContra$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'homFtorContra$\'_type',type,
'\'homFtorContra$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'member$a\'_type',type,
'\'member$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'' > $o ).
thf('\'uuu$\'_type',type,
'\'uuu$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A$\'' > '\'ZF_bool_fun$\'' ).
thf('\'mapM$d\'_type',type,
'\'mapM$d\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'mapM$e\'_type',type,
'\'mapM$e\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'ZF$\'' > '\'B$\'' ).
thf('\'uve$\'_type',type,
'\'uve$\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_ZF_fun_fun$\'' ).
thf('\'cod$b\'_type',type,
'\'cod$b\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'natTransComp$\'_type',type,
'\'natTransComp$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$\'' ).
thf('\'obj$b\'_type',type,
'\'obj$b\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_set$\'' ).
thf('\'zFfunComp$\'_type',type,
'\'zFfunComp$\'': '\'ZF_ZF_ZF_fun_fun$\'' ).
thf('\'compDefined$a\'_type',type,
'\'compDefined$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B$\'' > '\'B_bool_fun$\'' ).
thf('\'inverse_rel$a\'_type',type,
'\'inverse_rel$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B$\'' > '\'B_bool_fun$\'' ).
thf('\'the$\'_type',type,
'\'the$\'': '\'ZF_bool_fun$\'' > '\'ZF$\'' ).
thf('\'functorM_axioms$d\'_type',type,
'\'functorM_axioms$d\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'natTransMap$\'_type',type,
'\'natTransMap$\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'constFunctor$b\'_type',type,
'\'constFunctor$b\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'natTransP$d\'_type',type,
'\'natTransP$d\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > $o ).
thf('\'functorComp$\'_type',type,
'\'functorComp$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'mapM$\'_type',type,
'\'mapM$\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' ).
thf('\'fun_app$v\'_type',type,
'\'fun_app$v\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'restrict$d\'_type',type,
'\'restrict$d\'': '\'A_b_fun$\'' > '\'A_set$\'' > '\'A_b_fun$\'' ).
thf('\'implode$\'_type',type,
'\'implode$\'': '\'ZF_set$\'' > '\'ZF$\'' ).
thf('\'uuz$\'_type',type,
'\'uuz$\'': '\'ZF_ZF_fun$\'' ).
thf('\'mapO$c\'_type',type,
'\'mapO$c\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A$\'' ).
thf('\'identityFunctor$g\'_type',type,
'\'identityFunctor$g\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' ).
thf('\'mapO$a\'_type',type,
'\'mapO$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A$\'' > '\'ZF$\'' ).
thf('\'nTCod$\'_type',type,
'\'nTCod$\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'constFunctor$l\'_type',type,
'\'constFunctor$l\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'uuc$\'_type',type,
'\'uuc$\'': '\'B_set$\'' > '\'B_bool_fun$\'' ).
thf('\'catCod$e\'_type',type,
'\'catCod$e\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'lSCategory_ext$\'_type',type,
'\'lSCategory_ext$\'': '\'B_ZF_fun$\'' > '\'C$\'' > '\'B_c_LSCategory_ext$\'' ).
thf('\'catCod$b\'_type',type,
'\'catCod$b\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'collect$b\'_type',type,
'\'collect$b\'': '\'A_bool_fun$\'' > '\'A_set$\'' ).
thf('\'natTransMap$a\'_type',type,
'\'natTransMap$a\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'A_b_fun$\'' ).
thf('\'equivalence$\'_type',type,
'\'equivalence$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'homSet$\'_type',type,
'\'homSet$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A$\'' > '\'ZF$\'' ).
thf('\'fun_app$e\'_type',type,
'\'fun_app$e\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > $o ).
thf('\'mapM$a\'_type',type,
'\'mapM$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'B_ZF_fun$\'' ).
thf('\'functor_abbrev$e\'_type',type,
'\'functor_abbrev$e\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > $o ).
thf('\'y$\'_type',type,
'\'y$\'': '\'A$\'' ).
thf('\'uux$\'_type',type,
'\'uux$\'': '\'ZF_ZF_fun$\'' ).
thf('\'catDom$c\'_type',type,
'\'catDom$c\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'functor$b\'_type',type,
'\'functor$b\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'functor$\'_type',type,
'\'functor$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'extensional$a\'_type',type,
'\'extensional$a\'': '\'B_set$\'' > '\'B_ZF_fun_set$\'' ).
thf('\'fun_app$k\'_type',type,
'\'fun_app$k\'': '\'B_bool_fun$\'' > '\'B$\'' > $o ).
thf('\'natTrans$b\'_type',type,
'\'natTrans$b\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > $o ).
thf('\'eta$\'_type',type,
'\'eta$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'homFtorMapContra$\'_type',type,
'\'homFtorMapContra$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B$\'' > '\'A$\'' > '\'ZF$\'' ).
thf('\'fun_app$n\'_type',type,
'\'fun_app$n\'': '\'B_b_fun$\'' > '\'B$\'' > '\'B$\'' ).
thf('\'uuw$\'_type',type,
'\'uuw$\'': '\'ZF$\'' > '\'ZF_ZF_ZF_fun_fun$\'' ).
thf('\'functorExt$d\'_type',type,
'\'functorExt$d\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'member$h\'_type',type,
'\'member$h\'': '\'B$\'' > '\'B_set$\'' > $o ).
thf('\'functorComp$f\'_type',type,
'\'functorComp$f\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'functorComp$e\'_type',type,
'\'functorComp$e\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' ).
thf('\'functor_comp_def$d\'_type',type,
'\'functor_comp_def$d\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'member$i\'_type',type,
'\'member$i\'': '\'A$\'' > '\'A_set$\'' > $o ).
thf('\'category_ext$a\'_type',type,
'\'category_ext$a\'': '\'ZF_set$\'' > '\'ZF_set$\'' > '\'ZF_ZF_fun$\'' > '\'ZF_ZF_fun$\'' > '\'ZF_ZF_fun$\'' > '\'ZF_ZF_ZF_fun_fun$\'' > '\'Unit$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'id$b\'_type',type,
'\'id$b\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_b_fun$\'' ).
thf('\'homFtorMap$\'_type',type,
'\'homFtorMap$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'B_ZF_fun$\'' ).
thf('\'uuq$\'_type',type,
'\'uuq$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'inverse$\'_type',type,
'\'inverse$\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'mapM$g\'_type',type,
'\'mapM$g\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'ZF$\'' ).
thf('\'functorExt$a\'_type',type,
'\'functorExt$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'natTransP$c\'_type',type,
'\'natTransP$c\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > $o ).
thf('\'zF2mor$\'_type',type,
'\'zF2mor$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF$\'' > '\'B$\'' ).
thf('\'uuo$\'_type',type,
'\'uuo$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'uvc$\'_type',type,
'\'uvc$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_b_b_fun_fun$\'' ).
thf('\'category_ext$b\'_type',type,
'\'category_ext$b\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$\'' > '\'Unit$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' ).
thf('\'mapM$b\'_type',type,
'\'mapM$b\'': '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > '\'ZF$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'nt_abbrev$a\'_type',type,
'\'nt_abbrev$a\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'mapO$\'_type',type,
'\'mapO$\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'dom$\'_type',type,
'\'dom$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_a_fun$\'' ).
thf('\'zFfunDom$\'_type',type,
'\'zFfunDom$\'': '\'ZF_ZF_fun$\'' ).
thf('\'fun_app$w\'_type',type,
'\'fun_app$w\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'mapO$d\'_type',type,
'\'mapO$d\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'zFfunApp$\'_type',type,
'\'zFfunApp$\'': '\'ZF_ZF_ZF_fun_fun$\'' ).
thf('\'collect$c\'_type',type,
'\'collect$c\'': '\'ZF_bool_fun$\'' > '\'ZF_set$\'' ).
thf('\'fun_app$q\'_type',type,
'\'fun_app$q\'': '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'B$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'equivalence_axioms$a\'_type',type,
'\'equivalence_axioms$a\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'category_axioms$a\'_type',type,
'\'category_axioms$a\'': '\'ZF_ZF_unit_Category_ext$\'' > $o ).
thf('\'cod$a\'_type',type,
'\'cod$a\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'functorComp$i\'_type',type,
'\'functorComp$i\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'functor_comp_def$i\'_type',type,
'\'functor_comp_def$i\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'catCod$a\'_type',type,
'\'catCod$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'hOMCollection$\'_type',type,
'\'hOMCollection$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A$\'' > '\'ZF_set$\'' ).
thf('\'uup$\'_type',type,
'\'uup$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'B_ZF_fun$\'' ).
thf('\'mapO$h\'_type',type,
'\'mapO$h\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'objIso$a\'_type',type,
'\'objIso$a\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF$\'' > '\'ZF_bool_fun$\'' ).
thf('\'comp$\'_type',type,
'\'comp$\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_ZF_fun_fun$\'' ).
thf('\'nTDom$\'_type',type,
'\'nTDom$\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' ).
thf('\'isomorphism$\'_type',type,
'\'isomorphism$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_bool_fun$\'' ).
thf('\'makeNT$\'_type',type,
'\'makeNT$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'idNatTrans$c\'_type',type,
'\'idNatTrans$c\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'mapM$c\'_type',type,
'\'mapM$c\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'B$\'' ).
thf('\'fun_app$z\'_type',type,
'\'fun_app$z\'': '\'Nat_ZF_fun$\'' > '\'Nat$\'' > '\'ZF$\'' ).
thf('\'preFunctor$a\'_type',type,
'\'preFunctor$a\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'natTransP$a\'_type',type,
'\'natTransP$a\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > $o ).
thf('\'catExp$l\'_type',type,
'\'catExp$l\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' ).
thf('\'makeFtor$d\'_type',type,
'\'makeFtor$d\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'idNatTrans$f\'_type',type,
'\'idNatTrans$f\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' ).
thf('\'natTrans_ext$\'_type',type,
'\'natTrans_ext$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_fun$\'' > '\'Unit$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'functor_ext$\'_type',type,
'\'functor_ext$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'Unit$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'elem$\'_type',type,
'\'elem$\'': '\'ZF$\'' > '\'ZF_bool_fun$\'' ).
thf('\'mapsTo$a\'_type',type,
'\'mapsTo$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'functorM$\'_type',type,
'\'functorM$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'comp$a\'_type',type,
'\'comp$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_b_b_fun_fun$\'' ).
thf('\'fun_app$m\'_type',type,
'\'fun_app$m\'': '\'ZF_ZF_ZF_fun_fun$\'' > '\'ZF$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'nTCatCod$d\'_type',type,
'\'nTCatCod$d\'': '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'idNatTrans$e\'_type',type,
'\'idNatTrans$e\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'catExp$b\'_type',type,
'\'catExp$b\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$\'' ).
thf('\'functor_abbrev$b\'_type',type,
'\'functor_abbrev$b\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > $o ).
thf('\'fun_app$\'_type',type,
'\'fun_app$\'': '\'ZF_ZF_fun$\'' > '\'ZF$\'' > '\'ZF$\'' ).
thf('\'makeNT$b\'_type',type,
'\'makeNT$b\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'uuv$\'_type',type,
'\'uuv$\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'comp$d\'_type',type,
'\'comp$d\'': '\'ZF_ZF_fun$\'' > '\'ZF_ZF_fun_ZF_ZF_fun_fun$\'' ).
thf('\'makeCat$\'_type',type,
'\'makeCat$\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'catExp$\'_type',type,
'\'catExp$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' ).
thf('\'yFtorNT$a\'_type',type,
'\'yFtorNT$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' ).
thf('\'fun_app$p\'_type',type,
'\'fun_app$p\'': '\'B_ZF_fun$\'' > '\'B$\'' > '\'ZF$\'' ).
thf('\'fun_app$aa\'_type',type,
'\'fun_app$aa\'': '\'ZF_ZF_fun_ZF_ZF_fun_fun$\'' > '\'ZF_ZF_fun$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'catDom$d\'_type',type,
'\'catDom$d\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' ).
thf('\'mor$a\'_type',type,
'\'mor$a\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$\'' ).
thf('\'catCod$f\'_type',type,
'\'catCod$f\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'uvf$\'_type',type,
'\'uvf$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A$\'' > '\'ZF_bool_fun$\'' ).
thf('\'mapO$e\'_type',type,
'\'mapO$e\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'ZF$\'' > '\'A$\'' ).
thf('\'id$a\'_type',type,
'\'id$a\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'uuj$\'_type',type,
'\'uuj$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_b_b_fun_fun$\'' ).
thf('\'yFtor$\'_type',type,
'\'yFtor$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'homFtor$a\'_type',type,
'\'homFtor$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'functor_comp_def$\'_type',type,
'\'functor_comp_def$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > $o ).
thf('\'preFunctor$\'_type',type,
'\'preFunctor$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'uva$\'_type',type,
'\'uva$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF$\'' > '\'B_bool_fun$\'' ).
thf('\'functor$d\'_type',type,
'\'functor$d\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'natTransExt$\'_type',type,
'\'natTransExt$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'' ).
thf('\'category$\'_type',type,
'\'category$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > $o ).
thf('\'uuh$\'_type',type,
'\'uuh$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'more$\'_type',type,
'\'more$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'C$\'' ).
thf('\'fun_app$t\'_type',type,
'\'fun_app$t\'': '\'B_a_fun$\'' > '\'B$\'' > '\'A$\'' ).
thf('\'yFtorNT$\'_type',type,
'\'yFtorNT$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' ).
thf('\'fun_app$c\'_type',type,
'\'fun_app$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'' > '\'A$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'functor$c\'_type',type,
'\'functor$c\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'' > $o ).
thf('\'natTransMap$b\'_type',type,
'\'natTransMap$b\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A$\'' > '\'ZF$\'' ).
thf('\'equivalence$a\'_type',type,
'\'equivalence$a\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > $o ).
thf('\'mapO$b\'_type',type,
'\'mapO$b\'': '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > '\'ZF$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'nTCatDom$c\'_type',type,
'\'nTCatDom$c\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'nTCatDom$\'_type',type,
'\'nTCatDom$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'isZFfun$\'_type',type,
'\'isZFfun$\'': '\'ZF_bool_fun$\'' ).
thf('\'functor_comp_def$g\'_type',type,
'\'functor_comp_def$g\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'' > $o ).
thf('\'catCod$\'_type',type,
'\'catCod$\'': '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' ).
thf('\'mor$b\'_type',type,
'\'mor$b\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_set$\'' ).
thf('\'uum$\'_type',type,
'\'uum$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'ZF_ZF_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'nTCatCod$b\'_type',type,
'\'nTCatCod$b\'': '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'A_b_b_c_LSCategory_ext_Category_ext$\'' ).
thf('\'dom$a\'_type',type,
'\'dom$a\'': '\'ZF_ZF_unit_Category_ext$\'' > '\'ZF_ZF_fun$\'' ).
thf('\'nt_abbrev$b\'_type',type,
'\'nt_abbrev$b\'': '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'' > $o ).
thf('\'yFtor$a\'_type',type,
'\'yFtor$a\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' ).
thf('\'nt_abbrev$\'_type',type,
'\'nt_abbrev$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'' ).
thf('\'id$\'_type',type,
'\'id$\'': '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'' > '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'' ).
thf('\'member$e\'_type',type,
'\'member$e\'': '\'B_ZF_fun$\'' > '\'B_ZF_fun_set$\'' > $o ).
thf('\'mor$\'_type',type,
'\'mor$\'': '\'A_b_b_c_LSCategory_ext_Category_ext$\'' > '\'B_set$\'' ).
thf(158,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom410) ).
thf(1036,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(222,axiom,
! [A: '\'B$\'',B: '\'B_bool_fun$\''] :
( ( '\'member$h\'' @ A @ ( '\'collect$d\'' @ B ) )
<=> ( '\'fun_app$k\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).
thf(1337,plain,
! [A: '\'B$\'',B: '\'B_bool_fun$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'collect$d\'' @ B ) )
=> ( '\'fun_app$k\'' @ B @ A ) )
& ( ( '\'fun_app$k\'' @ B @ A )
=> ( '\'member$h\'' @ A @ ( '\'collect$d\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(43,axiom,
! [A: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ '\'uux$\'' ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom580) ).
thf(629,plain,
! [A: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ '\'uux$\'' ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(187,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).
thf(1190,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(89,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'obj$a\'' @ ( '\'makeCat$\'' @ A ) )
= ( '\'obj$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).
thf(760,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'obj$a\'' @ ( '\'makeCat$\'' @ A ) )
= ( '\'obj$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(368,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'preFunctor$c\'' @ ( '\'yFtor$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom338) ).
thf(1995,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'preFunctor$c\'' @ ( '\'yFtor$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(263,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'natTransP$b\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D ) )
=> ( ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) @ ( '\'natTransMap$\'' @ A @ D ) )
= ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom529) ).
thf(1559,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'natTransP$b\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D ) )
=> ( ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) @ ( '\'natTransMap$\'' @ A @ D ) )
= ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(130,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'oppositeCategory$\'' @ ( '\'oppositeCategory$\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).
thf(941,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'oppositeCategory$\'' @ ( '\'oppositeCategory$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(183,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'idNatTrans$c\'' @ A )
= ( '\'natTrans_ext$\'' @ A @ A @ ( '\'uut$\'' @ A ) @ '\'unity$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom560) ).
thf(1179,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'idNatTrans$c\'' @ A )
= ( '\'natTrans_ext$\'' @ A @ A @ ( '\'uut$\'' @ A ) @ '\'unity$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(18,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',C: '\'ZF$\''] :
( ( ( '\'nTCompDefined$a\'' @ A @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom539) ).
thf(555,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',C: '\'ZF$\''] :
( ( ( '\'nTCompDefined$a\'' @ A @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
( ( '\'yMapInv$\'' @ '\'c$\'' @ '\'x$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ '\'c$\'' ) @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) ) )
= ( '\'yMapInv$\'' @ '\'c$\'' @ '\'x$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture34) ).
thf(2,negated_conjecture,
( ( '\'yMapInv$\'' @ '\'c$\'' @ '\'x$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ '\'c$\'' ) @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) ) )
!= ( '\'yMapInv$\'' @ '\'c$\'' @ '\'x$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(481,plain,
( ( '\'yMapInv$\'' @ '\'c$\'' @ '\'x$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ '\'c$\'' ) @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) ) )
!= ( '\'yMapInv$\'' @ '\'c$\'' @ '\'x$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(126,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'obj$b\'' @ ( '\'oppositeCategory$\'' @ A ) )
= ( '\'obj$b\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom58) ).
thf(909,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'obj$b\'' @ ( '\'oppositeCategory$\'' @ A ) )
= ( '\'obj$b\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(156,axiom,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',D: '\'ZF$\''] :
( ( ( '\'nt_abbrev$c\'' @ A @ B @ C )
& ( '\'member$d\'' @ D @ ( '\'obj$a\'' @ ( '\'catDom$d\'' @ B ) ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catCod$b\'' @ C ) @ ( '\'natTransMap$c\'' @ A @ D ) @ ( '\'mapO$e\'' @ B @ D ) ) @ ( '\'mapO$e\'' @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom457) ).
thf(1031,plain,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',D: '\'ZF$\''] :
( ( ( '\'nt_abbrev$c\'' @ A @ B @ C )
& ( '\'member$d\'' @ D @ ( '\'obj$a\'' @ ( '\'catDom$d\'' @ B ) ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catCod$b\'' @ C ) @ ( '\'natTransMap$c\'' @ A @ D ) @ ( '\'mapO$e\'' @ B @ D ) ) @ ( '\'mapO$e\'' @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(357,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).
thf(1956,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(260,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'isomorphism$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
=> ( '\'fun_app$e\'' @ ( '\'isomorphism$a\'' @ ( '\'catCod$\'' @ A ) ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom476) ).
thf(1549,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'isomorphism$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
=> ( '\'fun_app$e\'' @ ( '\'isomorphism$a\'' @ ( '\'catCod$\'' @ A ) ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(194,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\''] :
( ( '\'member$a\'' @ A @ ( '\'collect$h\'' @ B ) )
<=> ( '\'fun_app$f\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).
thf(1211,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\''] :
( ( ( '\'member$a\'' @ A @ ( '\'collect$h\'' @ B ) )
=> ( '\'fun_app$f\'' @ B @ A ) )
& ( ( '\'fun_app$f\'' @ B @ A )
=> ( '\'member$a\'' @ A @ ( '\'collect$h\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(146,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).
thf(1005,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(78,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorM$c\'' @ A )
=> ( '\'functorM_axioms$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom223) ).
thf(730,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorM$c\'' @ A )
=> ( '\'functorM_axioms$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(254,axiom,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\''] :
( ( ( '\'functor$c\'' @ ( '\'nTDom$a\'' @ A ) )
& ( '\'functor$c\'' @ ( '\'nTCod$a\'' @ A ) )
& ( ( '\'nTCatDom$b\'' @ A )
= ( '\'catDom$d\'' @ ( '\'nTCod$a\'' @ A ) ) )
& ( ( '\'nTCatCod$b\'' @ A )
= ( '\'catCod$b\'' @ ( '\'nTDom$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$b\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$b\'' @ A ) @ ( '\'natTransMap$c\'' @ A @ B ) @ ( '\'mapO$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'mapO$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$b\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'mapM$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'natTransMap$c\'' @ A @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'natTransMap$c\'' @ A @ C ) ) @ ( '\'mapM$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) ) ) )
=> ( '\'natTransP$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom518) ).
thf(1522,plain,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\''] :
( ( ( '\'functor$c\'' @ ( '\'nTDom$a\'' @ A ) )
& ( '\'functor$c\'' @ ( '\'nTCod$a\'' @ A ) )
& ( ( '\'nTCatDom$b\'' @ A )
= ( '\'catDom$d\'' @ ( '\'nTCod$a\'' @ A ) ) )
& ( ( '\'nTCatCod$b\'' @ A )
= ( '\'catCod$b\'' @ ( '\'nTDom$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$b\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$b\'' @ A ) @ ( '\'natTransMap$c\'' @ A @ B ) @ ( '\'mapO$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'mapO$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$b\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'mapM$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'natTransMap$c\'' @ A @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'natTransMap$c\'' @ A @ C ) ) @ ( '\'mapM$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) ) ) )
=> ( '\'natTransP$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(82,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom500) ).
thf(741,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(310,axiom,
! [A: '\'A_bool_fun$\'',B: '\'A_bool_fun$\''] :
( ! [C: '\'A$\''] :
( ( '\'fun_app$l\'' @ A @ C )
<=> ( '\'fun_app$l\'' @ B @ C ) )
=> ( ( '\'collect$b\'' @ A )
= ( '\'collect$b\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom117) ).
thf(1728,plain,
! [A: '\'A_bool_fun$\'',B: '\'A_bool_fun$\''] :
( ! [C: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ A @ C )
=> ( '\'fun_app$l\'' @ B @ C ) )
& ( ( '\'fun_app$l\'' @ B @ C )
=> ( '\'fun_app$l\'' @ A @ C ) ) )
=> ( ( '\'collect$b\'' @ A )
= ( '\'collect$b\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(399,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtorContra$\'' @ A @ B )
= ( '\'homFtor$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).
thf(2099,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtorContra$\'' @ A @ B )
= ( '\'homFtor$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(171,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'mapO$a\'' @ B @ C ) ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ ( '\'yMapInv$\'' @ A @ C @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).
thf(1142,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'mapO$a\'' @ B @ C ) ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ ( '\'yMapInv$\'' @ A @ C @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(52,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) @ ( '\'mor$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom494) ).
thf(655,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) @ ( '\'mor$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(60,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category$a\'' @ A )
=> ( '\'category_axioms$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom447) ).
thf(677,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category$a\'' @ A )
=> ( '\'category_axioms$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(218,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom488) ).
thf(1305,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(301,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'makeFtor$d\'' @ A )
= ( '\'functor_ext$\'' @ ( '\'catDom$\'' @ A ) @ ( '\'catCod$\'' @ A ) @ ( '\'restrict$b\'' @ ( '\'mapM$\'' @ A ) @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) @ ( '\'more$c\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom487) ).
thf(1705,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'makeFtor$d\'' @ A )
= ( '\'functor_ext$\'' @ ( '\'catDom$\'' @ A ) @ ( '\'catCod$\'' @ A ) @ ( '\'restrict$b\'' @ ( '\'mapM$\'' @ A ) @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) @ ( '\'more$c\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(295,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A$\''] :
( ( ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ A @ B ) @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ B ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ C ) @ ( '\'natTransMap$b\'' @ A @ D ) @ ( '\'mapO$a\'' @ B @ D ) ) @ ( '\'mapO$a\'' @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom456) ).
thf(1671,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A$\''] :
( ( ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ A @ B ) @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ B ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ C ) @ ( '\'natTransMap$b\'' @ A @ D ) @ ( '\'mapO$a\'' @ B @ D ) ) @ ( '\'mapO$a\'' @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(380,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B )
= ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ C ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom309) ).
thf(2035,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B )
= ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ C ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(6,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom154) ).
thf(500,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(104,axiom,
! [A: '\'A_set$\''] :
( ( '\'collect$b\'' @ ( '\'uu$\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom107) ).
thf(797,plain,
! [A: '\'A_set$\''] :
( ( '\'collect$b\'' @ ( '\'uu$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(199,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).
thf(1233,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(412,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( A
= ( '\'category_ext$\'' @ ( '\'obj$b\'' @ A ) @ ( '\'mor$\'' @ A ) @ ( '\'dom$\'' @ A ) @ ( '\'cod$\'' @ A ) @ ( '\'id$b\'' @ A ) @ ( '\'comp$a\'' @ A ) @ ( '\'lSCategory_ext$\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'more$\'' @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).
thf(2168,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( A
= ( '\'category_ext$\'' @ ( '\'obj$b\'' @ A ) @ ( '\'mor$\'' @ A ) @ ( '\'dom$\'' @ A ) @ ( '\'cod$\'' @ A ) @ ( '\'id$b\'' @ A ) @ ( '\'comp$a\'' @ A ) @ ( '\'lSCategory_ext$\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'more$\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(349,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$\'' @ A )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$a\'' @ C @ ( '\'obj$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).
thf(1919,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$\'' @ A )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$a\'' @ C @ ( '\'obj$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(12,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom566) ).
thf(538,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(325,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'functorM$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ C ) ) @ ( '\'mapO$\'' @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).
thf(1788,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'functorM$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ C ) ) @ ( '\'mapO$\'' @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(243,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ ( '\'homFtorMapContra$\'' @ A @ C @ B ) @ ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) @ B ) ) @ ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom320) ).
thf(1426,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ ( '\'homFtorMapContra$\'' @ A @ C @ B ) @ ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) @ B ) ) @ ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(317,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ C )
& ! [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ D ) @ B )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ D ) @ B )
= D ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).
thf(1756,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ C )
& ! [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ D ) @ B )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ D ) @ B )
= D ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(220,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
<=> ( ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) )
& ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) )
& ( ( '\'nTCatDom$\'' @ A )
= ( '\'catDom$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) )
& ( ( '\'nTCatCod$\'' @ A )
= ( '\'catCod$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ B ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) @ B ) ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom515) ).
thf(1310,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
=> ( ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) )
& ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) )
& ( ( '\'nTCatDom$\'' @ A )
= ( '\'catDom$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) )
& ( ( '\'nTCatCod$\'' @ A )
= ( '\'catCod$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ B ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) @ B ) ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ) ) ) )
& ( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) )
& ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) )
& ( ( '\'nTCatDom$\'' @ A )
= ( '\'catDom$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) )
& ( ( '\'nTCatCod$\'' @ A )
= ( '\'catCod$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ B ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) @ B ) ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(10,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ ( '\'constFunctor$l\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).
thf(533,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ ( '\'constFunctor$l\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(318,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom323) ).
thf(1761,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(223,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
<=> ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom416) ).
thf(1342,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
=> ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ C ) ) ) )
& ( ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ C ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(189,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'makeCat$a\'' @ A )
= ( '\'category_ext$\'' @ ( '\'obj$b\'' @ A ) @ ( '\'mor$\'' @ A ) @ ( '\'restrict$c\'' @ ( '\'dom$\'' @ A ) @ ( '\'mor$\'' @ A ) ) @ ( '\'restrict$c\'' @ ( '\'cod$\'' @ A ) @ ( '\'mor$\'' @ A ) ) @ ( '\'restrict$d\'' @ ( '\'id$b\'' @ A ) @ ( '\'obj$b\'' @ A ) ) @ ( '\'uvc$\'' @ A ) @ ( '\'more$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom582) ).
thf(1196,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'makeCat$a\'' @ A )
= ( '\'category_ext$\'' @ ( '\'obj$b\'' @ A ) @ ( '\'mor$\'' @ A ) @ ( '\'restrict$c\'' @ ( '\'dom$\'' @ A ) @ ( '\'mor$\'' @ A ) ) @ ( '\'restrict$c\'' @ ( '\'cod$\'' @ A ) @ ( '\'mor$\'' @ A ) ) @ ( '\'restrict$d\'' @ ( '\'id$b\'' @ A ) @ ( '\'obj$b\'' @ A ) ) @ ( '\'uvc$\'' @ A ) @ ( '\'more$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(313,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ E ) @ C ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom335) ).
thf(1746,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ E ) @ C ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(431,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B )
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ C ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).
thf(2216,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B )
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ C ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(231,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ ( '\'catCod$a\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) )
= ( '\'mapO$a\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom359) ).
thf(1391,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ ( '\'catCod$a\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) )
= ( '\'mapO$a\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(353,axiom,
! [A: '\'B_ZF_fun$\'',B: '\'B_ZF_fun_bool_fun$\''] :
( ( '\'member$e\'' @ A @ ( '\'collect$e\'' @ B ) )
<=> ( '\'fun_app$h\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).
thf(1935,plain,
! [A: '\'B_ZF_fun$\'',B: '\'B_ZF_fun_bool_fun$\''] :
( ( ( '\'member$e\'' @ A @ ( '\'collect$e\'' @ B ) )
=> ( '\'fun_app$h\'' @ B @ A ) )
& ( ( '\'fun_app$h\'' @ B @ A )
=> ( '\'member$e\'' @ A @ ( '\'collect$e\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(22,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'natTrans$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom536) ).
thf(565,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'natTrans$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(480,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'uvf$\'' @ A @ B @ C ) @ D )
<=> ? [E: '\'B$\''] :
( ( D
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ E ) )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom30) ).
thf(2400,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'uvf$\'' @ A @ B @ C ) @ D )
=> ? [E: '\'B$\''] :
( ( D
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ E ) )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ B ) @ C ) ) )
& ( ? [E: '\'B$\''] :
( ( D
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ E ) )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'uvf$\'' @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(207,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ C )
& ! [D: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ D ) @ B )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ D ) @ B )
= D ) ) )
=> ( ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).
thf(1265,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ C )
& ! [D: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ D ) @ B )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ D ) @ B )
= D ) ) )
=> ( ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(50,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).
thf(651,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(237,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B )
= ( '\'makeNT$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom129) ).
thf(1409,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B )
= ( '\'makeNT$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(24,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'obj$a\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom393) ).
thf(570,plain,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'obj$a\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(327,axiom,
! [A: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( '\'preFunctor$d\'' @ A )
=> ( '\'preFunctor$d\'' @ ( '\'makeFtor$e\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom219) ).
thf(1792,plain,
! [A: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( '\'preFunctor$d\'' @ A )
=> ( '\'preFunctor$d\'' @ ( '\'makeFtor$e\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(343,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'oppositeCategory$b\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom89) ).
thf(1860,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'oppositeCategory$b\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(449,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'zF2mor$\'' @ A @ D ) ) @ C ) ) ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom326) ).
thf(2274,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'zF2mor$\'' @ A @ D ) ) @ C ) ) ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(106,axiom,
! [A: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) @ '\'uux$\'' ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom569) ).
thf(802,plain,
! [A: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) @ '\'uux$\'' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(334,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom484) ).
thf(1826,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(418,axiom,
! [A: '\'ZF$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ ( '\'catDom$c\'' @ ( '\'functorComp$b\'' @ B @ C ) ) ) )
& ( '\'fun_app$f\'' @ ( '\'functor_comp_def$b\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ C ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ C ) @ ( '\'mapM$e\'' @ B @ A ) ) @ ( '\'mapO$a\'' @ C @ ( '\'mapO$e\'' @ B @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ ( '\'catDom$d\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$a\'' @ C @ ( '\'mapO$e\'' @ B @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ ( '\'catDom$d\'' @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).
thf(2185,plain,
! [A: '\'ZF$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ ( '\'catDom$c\'' @ ( '\'functorComp$b\'' @ B @ C ) ) ) )
& ( '\'fun_app$f\'' @ ( '\'functor_comp_def$b\'' @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ C ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ C ) @ ( '\'mapM$e\'' @ B @ A ) ) @ ( '\'mapO$a\'' @ C @ ( '\'mapO$e\'' @ B @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ ( '\'catDom$d\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$a\'' @ C @ ( '\'mapO$e\'' @ B @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ ( '\'catDom$d\'' @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(292,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtorContra$a\'' @ A @ B )
= ( '\'functor_ext$a\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' @ ( '\'uup$\'' @ A @ B ) @ '\'unity$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom555) ).
thf(1660,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtorContra$a\'' @ A @ B )
= ( '\'functor_ext$a\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' @ ( '\'uup$\'' @ A @ B ) @ '\'unity$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(216,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorExt$d\'' @ A )
=> ( '\'member$m\'' @ ( '\'mapM$\'' @ A ) @ ( '\'extensional$\'' @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom486) ).
thf(1298,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorExt$d\'' @ A )
=> ( '\'member$m\'' @ ( '\'mapM$\'' @ A ) @ ( '\'extensional$\'' @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(46,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category$a\'' @ A )
=> ( '\'category$a\'' @ ( '\'oppositeCategory$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom191) ).
thf(638,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category$a\'' @ A )
=> ( '\'category$a\'' @ ( '\'oppositeCategory$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(227,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).
thf(1379,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(173,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom463) ).
thf(1147,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(312,axiom,
! [A: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
<=> ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ '\'set$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom577) ).
thf(1741,plain,
! [A: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
=> ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ '\'set$\'' ) ) )
& ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ '\'set$\'' ) )
=> ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(408,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'ZF$\''] :
( ( '\'yMapInv$a\'' @ A @ B @ C @ D )
= ( '\'natTrans_ext$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ B ) @ C @ ( '\'uur$\'' @ A @ B @ C @ D ) @ '\'unity$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom558) ).
thf(2158,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'ZF$\''] :
( ( '\'yMapInv$a\'' @ A @ B @ C @ D )
= ( '\'natTrans_ext$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ B ) @ C @ ( '\'uur$\'' @ A @ B @ C @ D ) @ '\'unity$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(461,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom530) ).
thf(2301,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(350,axiom,
! [A: '\'A_set$\'',B: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'uu$\'' @ A ) @ B )
<=> ( '\'member$i\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
thf(1922,plain,
! [A: '\'A_set$\'',B: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'uu$\'' @ A ) @ B )
=> ( '\'member$i\'' @ B @ A ) )
& ( ( '\'member$i\'' @ B @ A )
=> ( '\'fun_app$l\'' @ ( '\'uu$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(109,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ! [B: '\'ZF_set$\'',C: '\'ZF_set$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_fun$\'',G: '\'ZF_ZF_ZF_fun_fun$\''] :
( ( A
= ( '\'category_ext$a\'' @ B @ C @ D @ E @ F @ G @ '\'unity$\'' ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom550) ).
thf(817,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
~ ! [B: '\'ZF_set$\'',C: '\'ZF_set$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_fun$\'',G: '\'ZF_ZF_ZF_fun_fun$\''] :
( A
!= ( '\'category_ext$a\'' @ B @ C @ D @ E @ F @ G @ '\'unity$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(37,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
<=> ( ( '\'category$c\'' @ A )
& ( '\'lSCategory_axioms$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom471) ).
thf(606,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( '\'lSCategory$\'' @ A )
=> ( ( '\'category$c\'' @ A )
& ( '\'lSCategory_axioms$\'' @ A ) ) )
& ( ( ( '\'category$c\'' @ A )
& ( '\'lSCategory_axioms$\'' @ A ) )
=> ( '\'lSCategory$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(268,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom345) ).
thf(1572,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(149,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom421) ).
thf(1013,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(93,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$\'' @ B )
& ( '\'member$a\'' @ C @ ( '\'obj$\'' @ B ) ) )
=> ( '\'preFunctor$d\'' @ ( '\'constFunctor$s\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom259) ).
thf(770,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$\'' @ B )
& ( '\'member$a\'' @ C @ ( '\'obj$\'' @ B ) ) )
=> ( '\'preFunctor$d\'' @ ( '\'constFunctor$s\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(377,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'makeCat$\'' @ A ) @ B ) @ C )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'makeCat$\'' @ A ) ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).
thf(2024,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'makeCat$\'' @ A ) @ B ) @ C )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'makeCat$\'' @ A ) ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(286,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ ( '\'mor$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom315) ).
thf(1641,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ ( '\'mor$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(433,axiom,
'\'lSCategory$\'' @ '\'c$\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom35) ).
thf(2222,plain,
'\'lSCategory$\'' @ '\'c$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(356,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C )
<=> ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).
thf(1946,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C )
=> ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) ) )
& ( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(378,axiom,
! [A: '\'B_set$\'',B: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'uuc$\'' @ A ) @ B )
<=> ( '\'member$h\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
thf(2027,plain,
! [A: '\'B_set$\'',B: '\'B$\''] :
( ( ( '\'fun_app$k\'' @ ( '\'uuc$\'' @ A ) @ B )
=> ( '\'member$h\'' @ B @ A ) )
& ( ( '\'member$h\'' @ B @ A )
=> ( '\'fun_app$k\'' @ ( '\'uuc$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(401,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'yMap$\'' @ A @ B @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'natTransMap$b\'' @ C @ B ) ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom466) ).
thf(2105,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'yMap$\'' @ A @ B @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'natTransMap$b\'' @ C @ B ) ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(221,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ '\'set$\'' ) @ ( '\'homFtorMapContra$\'' @ A @ C @ B ) )
= ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).
thf(1334,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ '\'set$\'' ) @ ( '\'homFtorMapContra$\'' @ A @ C @ B ) )
= ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(113,axiom,
! [A: '\'ZF$\'',B: '\'Nat_ZF_fun$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ ( '\'seqSum$\'' @ B ) )
<=> ? [C: '\'Nat$\''] : ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ ( '\'fun_app$z\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom599) ).
thf(834,plain,
! [A: '\'ZF$\'',B: '\'Nat_ZF_fun$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ ( '\'seqSum$\'' @ B ) )
=> ? [C: '\'Nat$\''] : ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ ( '\'fun_app$z\'' @ B @ C ) ) )
& ( ? [C: '\'Nat$\''] : ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ ( '\'fun_app$z\'' @ B @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ ( '\'seqSum$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(345,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) )
=> ( '\'category_axioms$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).
thf(1864,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) )
=> ( '\'category_axioms$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(175,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'equivalence$a\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) )
=> ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom373) ).
thf(1151,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'equivalence$a\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) )
=> ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(391,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( A
= ( '\'category_ext$\'' @ ( '\'obj$b\'' @ A ) @ ( '\'mor$\'' @ A ) @ ( '\'dom$\'' @ A ) @ ( '\'cod$\'' @ A ) @ ( '\'id$b\'' @ A ) @ ( '\'comp$a\'' @ A ) @ ( '\'more$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom382) ).
thf(2073,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( A
= ( '\'category_ext$\'' @ ( '\'obj$b\'' @ A ) @ ( '\'mor$\'' @ A ) @ ( '\'dom$\'' @ A ) @ ( '\'cod$\'' @ A ) @ ( '\'id$b\'' @ A ) @ ( '\'comp$a\'' @ A ) @ ( '\'more$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(110,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C )
& ( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom450) ).
thf(821,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
~ ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C )
& ~ ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(160,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ ( '\'zFfun$\'' @ A @ B @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ '\'set$\'' ) @ ( '\'zFfun$\'' @ A @ B @ C ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom564) ).
thf(1040,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ ( '\'zFfun$\'' @ A @ B @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ '\'set$\'' ) @ ( '\'zFfun$\'' @ A @ B @ C ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(282,axiom,
! [A: '\'ZF$\''] : ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ '\'set$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).
thf(1632,plain,
! [A: '\'ZF$\''] : ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ '\'set$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(335,axiom,
! [A: '\'A$\'',B: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$b\'' @ B ) ) )
& ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'functorComp$i\'' @ B @ C ) )
& ( '\'fun_app$f\'' @ ( '\'functor_comp_def$i\'' @ B ) @ C ) )
=> ( ( '\'mapO$a\'' @ ( '\'functorComp$i\'' @ B @ C ) @ A )
= ( '\'mapO$a\'' @ C @ ( '\'mapO$f\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).
thf(1828,plain,
! [A: '\'A$\'',B: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$b\'' @ B ) ) )
& ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'functorComp$i\'' @ B @ C ) )
& ( '\'fun_app$f\'' @ ( '\'functor_comp_def$i\'' @ B ) @ C ) )
=> ( ( '\'mapO$a\'' @ ( '\'functorComp$i\'' @ B @ C ) @ A )
= ( '\'mapO$a\'' @ C @ ( '\'mapO$f\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(363,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ B ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) @ B ) ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom526) ).
thf(1978,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ B ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) @ B ) ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(457,axiom,
( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) ) @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) )
= ( '\'yMapInv$\'' @ '\'c$\'' @ '\'x$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ '\'c$\'' ) @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).
thf(2291,plain,
( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) ) @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) )
= ( '\'yMapInv$\'' @ '\'c$\'' @ '\'x$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ '\'c$\'' ) @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(152,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'makeCat$\'' @ A )
= ( '\'category_ext$a\'' @ ( '\'obj$a\'' @ A ) @ ( '\'mor$b\'' @ A ) @ ( '\'restrict$e\'' @ ( '\'dom$a\'' @ A ) @ ( '\'mor$b\'' @ A ) ) @ ( '\'restrict$e\'' @ ( '\'cod$a\'' @ A ) @ ( '\'mor$b\'' @ A ) ) @ ( '\'restrict$e\'' @ ( '\'id$a\'' @ A ) @ ( '\'obj$a\'' @ A ) ) @ ( '\'uve$\'' @ A ) @ ( '\'more$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom583) ).
thf(1020,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'makeCat$\'' @ A )
= ( '\'category_ext$a\'' @ ( '\'obj$a\'' @ A ) @ ( '\'mor$b\'' @ A ) @ ( '\'restrict$e\'' @ ( '\'dom$a\'' @ A ) @ ( '\'mor$b\'' @ A ) ) @ ( '\'restrict$e\'' @ ( '\'cod$a\'' @ A ) @ ( '\'mor$b\'' @ A ) ) @ ( '\'restrict$e\'' @ ( '\'id$a\'' @ A ) @ ( '\'obj$a\'' @ A ) ) @ ( '\'uve$\'' @ A ) @ ( '\'more$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(443,axiom,
'\'functor_abbrev$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'oppositeCategory$\'' @ '\'c$\'' ) @ '\'set$\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom43) ).
thf(2254,plain,
'\'functor_abbrev$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ ( '\'oppositeCategory$\'' @ '\'c$\'' ) @ '\'set$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(338,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom325) ).
thf(1843,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(181,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'B$\'',E: '\'B$\''] :
( ( ( '\'functor_abbrev$f\'' @ A @ B @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ B @ D ) @ E ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ B ) @ D ) @ E ) )
= ( '\'comp$b\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ D ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom417) ).
thf(1169,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'B$\'',E: '\'B$\''] :
( ( ( '\'functor_abbrev$f\'' @ A @ B @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ B @ D ) @ E ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ B ) @ D ) @ E ) )
= ( '\'comp$b\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ D ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(452,axiom,
! [A: '\'ZF$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ ( '\'catDom$e\'' @ ( '\'functorComp$e\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$e\'' @ B @ C ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ C ) @ ( '\'mapM$e\'' @ B @ A ) ) @ ( '\'mapO$\'' @ C @ ( '\'mapO$e\'' @ B @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ ( '\'catDom$d\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$\'' @ C @ ( '\'mapO$e\'' @ B @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ ( '\'catDom$d\'' @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom381) ).
thf(2281,plain,
! [A: '\'ZF$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ ( '\'catDom$e\'' @ ( '\'functorComp$e\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$e\'' @ B @ C ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ C ) @ ( '\'mapM$e\'' @ B @ A ) ) @ ( '\'mapO$\'' @ C @ ( '\'mapO$e\'' @ B @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ ( '\'catDom$d\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$\'' @ C @ ( '\'mapO$e\'' @ B @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ ( '\'catDom$d\'' @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(116,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'',D: '\'ZF$\''] :
( ( ( '\'nt_abbrev$d\'' @ A @ B @ C )
& ( '\'member$d\'' @ D @ ( '\'obj$a\'' @ ( '\'catDom$c\'' @ B ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$c\'' @ C ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ B ) @ D ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).
thf(877,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'',D: '\'ZF$\''] :
( ( ( '\'nt_abbrev$d\'' @ A @ B @ C )
& ( '\'member$d\'' @ D @ ( '\'obj$a\'' @ ( '\'catDom$c\'' @ B ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$c\'' @ C ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ B ) @ D ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(329,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'catDom$\'' @ A ) ) @ B ) @ C ) )
= ( '\'comp$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom425) ).
thf(1796,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'catDom$\'' @ A ) ) @ B ) @ C ) )
= ( '\'comp$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(232,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).
thf(1394,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(224,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'category_axioms$\'' @ A )
=> ( '\'category_axioms$\'' @ ( '\'oppositeCategory$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom448) ).
thf(1351,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'category_axioms$\'' @ A )
=> ( '\'category_axioms$\'' @ ( '\'oppositeCategory$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(140,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'dom$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).
thf(988,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'dom$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(246,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
=> ( '\'fun_app$e\'' @ '\'natTransExt$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom212) ).
thf(1433,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
=> ( '\'fun_app$e\'' @ '\'natTransExt$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(355,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ ( '\'zFfun$\'' @ A @ B @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom552) ).
thf(1943,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ ( '\'zFfun$\'' @ A @ B @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(162,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'member$a\'' @ ( '\'mapO$\'' @ A @ B ) @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom364) ).
thf(1104,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'member$a\'' @ ( '\'mapO$\'' @ A @ B ) @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(427,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom535) ).
thf(2205,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(278,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) )
=> ( ( '\'mapO$\'' @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom362) ).
thf(1622,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) )
=> ( ( '\'mapO$\'' @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(95,axiom,
( '\'set$a\''
= ( '\'category_ext$a\'' @ ( '\'collect$c\'' @ '\'uuy$\'' ) @ ( '\'collect$c\'' @ '\'isZFfun$\'' ) @ '\'zFfunDom$\'' @ '\'zFfunCod$\'' @ '\'uuz$\'' @ '\'zFfunComp$\'' @ '\'unity$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom578) ).
thf(774,plain,
( '\'set$a\''
= ( '\'category_ext$a\'' @ ( '\'collect$c\'' @ '\'uuy$\'' ) @ ( '\'collect$c\'' @ '\'isZFfun$\'' ) @ '\'zFfunDom$\'' @ '\'zFfunCod$\'' @ '\'uuz$\'' @ '\'zFfunComp$\'' @ '\'unity$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(473,axiom,
! [A: '\'A_set$\'',B: '\'B_set$\'',C: '\'B_a_fun$\'',D: '\'B_a_fun$\'',E: '\'A_b_fun$\'',F: '\'B_b_b_fun_fun$\'',G: '\'B_ZF_fun$\'',H: '\'C$\''] :
( ( '\'mor2ZF$\'' @ ( '\'category_ext$\'' @ A @ B @ C @ D @ E @ F @ ( '\'lSCategory_ext$\'' @ G @ H ) ) )
= G ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom446) ).
thf(2371,plain,
! [A: '\'A_set$\'',B: '\'B_set$\'',C: '\'B_a_fun$\'',D: '\'B_a_fun$\'',E: '\'A_b_fun$\'',F: '\'B_b_b_fun_fun$\'',G: '\'B_ZF_fun$\'',H: '\'C$\''] :
( ( '\'mor2ZF$\'' @ ( '\'category_ext$\'' @ A @ B @ C @ D @ E @ F @ ( '\'lSCategory_ext$\'' @ G @ H ) ) )
= G ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(290,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( ( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B )
= D ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom302) ).
thf(1651,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
~ ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ~ ( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(272,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ B ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ B ) )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ B ) @ C ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom386) ).
thf(1604,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ B ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ B ) )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ B ) @ C ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(373,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C ) @ D )
<=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom61) ).
thf(2011,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ D ) @ C ) )
& ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ D ) @ C )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(192,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ '\'set$\'' @ A ) @ B )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom473) ).
thf(1206,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ '\'set$\'' @ A ) @ B )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(102,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom491) ).
thf(793,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(302,axiom,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ B ) ) )
& ( '\'fun_app$e\'' @ ( '\'nTCompDefined$\'' @ B ) @ C ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'fun_app$w\'' @ ( '\'fun_app$x\'' @ '\'natTransComp$\'' @ B ) @ C ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ C ) ) @ ( '\'natTransMap$b\'' @ B @ A ) ) @ ( '\'natTransMap$b\'' @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom542) ).
thf(1708,plain,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ B ) ) )
& ( '\'fun_app$e\'' @ ( '\'nTCompDefined$\'' @ B ) @ C ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'fun_app$w\'' @ ( '\'fun_app$x\'' @ '\'natTransComp$\'' @ B ) @ C ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ C ) ) @ ( '\'natTransMap$b\'' @ B @ A ) ) @ ( '\'natTransMap$b\'' @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(323,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'category$\'' @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).
thf(1783,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'category$\'' @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(395,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'cod$a\'' @ ( '\'makeCat$\'' @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).
thf(2083,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'cod$a\'' @ ( '\'makeCat$\'' @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(248,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
<=> ( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom300) ).
thf(1438,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
=> ( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B )
= D ) ) )
& ( ( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B )
= D ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(55,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
<=> ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).
thf(661,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
=> ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) ) )
& ( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(190,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'oppositeCategory$b\'' @ A ) @ B @ C ) @ D )
<=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).
thf(1199,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'oppositeCategory$b\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ D ) @ C ) )
& ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ D ) @ C )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'oppositeCategory$b\'' @ A ) @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(410,axiom,
'\'fun_app$l\'' @ ( '\'mapsTo$\'' @ '\'c$\'' @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) @ '\'x$\'' ) @ '\'y$\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom41) ).
thf(2164,plain,
'\'fun_app$l\'' @ ( '\'mapsTo$\'' @ '\'c$\'' @ ( '\'zF2mor$\'' @ '\'c$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) @ '\'x$\'' ) @ '\'y$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(459,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ C ) @ B )
= ( '\'homSet$\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom48) ).
thf(2296,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ C ) @ B )
= ( '\'homSet$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(463,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ D @ ( '\'mapO$\'' @ A @ B ) ) @ ( '\'mapO$\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ B @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'objIso$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ C ) ) @ B ) ) ) )
=> ( '\'equivalence_axioms$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).
thf(2307,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ D @ ( '\'mapO$\'' @ A @ B ) ) @ ( '\'mapO$\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ B @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'objIso$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ C ) ) @ B ) ) ) )
=> ( '\'equivalence_axioms$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(370,axiom,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',E: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ B ) )
& ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'catExp$\'' @ B @ C ) @ D ) @ E ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'comp$b\'' @ ( '\'catExp$\'' @ B @ C ) @ D @ E ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ C ) @ ( '\'natTransMap$b\'' @ D @ A ) ) @ ( '\'natTransMap$b\'' @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom464) ).
thf(2000,plain,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',E: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ B ) )
& ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'catExp$\'' @ B @ C ) @ D ) @ E ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'comp$b\'' @ ( '\'catExp$\'' @ B @ C ) @ D @ E ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ C ) @ ( '\'natTransMap$b\'' @ D @ A ) ) @ ( '\'natTransMap$b\'' @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(284,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'homFtorMapContra$\'' @ A @ C @ B ) @ ( '\'mor$b\'' @ '\'set$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom137) ).
thf(1636,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'homFtorMapContra$\'' @ A @ C @ B ) @ ( '\'mor$b\'' @ '\'set$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(210,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ B ) @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom570) ).
thf(1274,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ B ) @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(447,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'B_ZF_fun$\'',D: '\'B_ZF_fun_b_ZF_fun_fun$\'',E: '\'B_ZF_fun_b_ZF_fun_fun$\''] :
( ( ( A = B )
& ( ( '\'mor2ZF$\'' @ B )
= C )
& ! [F: '\'B_ZF_fun$\''] :
( ( F = C )
=> ( ( '\'fun_app$s\'' @ D @ F )
= ( '\'fun_app$s\'' @ E @ F ) ) ) )
=> ( ( '\'mor2ZF_update$\'' @ D @ A )
= ( '\'mor2ZF_update$\'' @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom50) ).
thf(2264,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'B_ZF_fun$\'',D: '\'B_ZF_fun_b_ZF_fun_fun$\'',E: '\'B_ZF_fun_b_ZF_fun_fun$\''] :
( ( ( A = B )
& ( ( '\'mor2ZF$\'' @ B )
= C )
& ! [F: '\'B_ZF_fun$\''] :
( ( F = C )
=> ( ( '\'fun_app$s\'' @ D @ F )
= ( '\'fun_app$s\'' @ E @ F ) ) ) )
=> ( ( '\'mor2ZF_update$\'' @ D @ A )
= ( '\'mor2ZF_update$\'' @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(120,axiom,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ B ) )
=> ( ( '\'fun_app$r\'' @ ( '\'id$b\'' @ B ) @ A )
= ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'makeCat$a\'' @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).
thf(894,plain,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ B ) )
=> ( ( '\'fun_app$r\'' @ ( '\'id$b\'' @ B ) @ A )
= ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'makeCat$a\'' @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(84,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B )
= ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ B ) @ ( '\'fun_app$m\'' @ ( '\'uuw$\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom576) ).
thf(746,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B )
= ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ B ) @ ( '\'fun_app$m\'' @ ( '\'uuw$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(441,axiom,
! [A: '\'B$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$b\'' @ ( '\'functorComp$c\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$c\'' @ B @ C ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catCod$d\'' @ C ) @ ( '\'mapM$c\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ B ) @ A ) ) @ ( '\'mapO$c\'' @ C @ ( '\'mapO$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$c\'' @ C @ ( '\'mapO$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom379) ).
thf(2249,plain,
! [A: '\'B$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$b\'' @ ( '\'functorComp$c\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$c\'' @ B @ C ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catCod$d\'' @ C ) @ ( '\'mapM$c\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ B ) @ A ) ) @ ( '\'mapO$c\'' @ C @ ( '\'mapO$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$c\'' @ C @ ( '\'mapO$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(253,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom413) ).
thf(1519,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(226,axiom,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\''] :
( ( '\'natTransP$c\'' @ A )
<=> ( ( '\'functor$c\'' @ ( '\'nTDom$a\'' @ A ) )
& ( '\'functor$c\'' @ ( '\'nTCod$a\'' @ A ) )
& ( ( '\'nTCatDom$b\'' @ A )
= ( '\'catDom$d\'' @ ( '\'nTCod$a\'' @ A ) ) )
& ( ( '\'nTCatCod$b\'' @ A )
= ( '\'catCod$b\'' @ ( '\'nTDom$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$b\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$b\'' @ A ) @ ( '\'natTransMap$c\'' @ A @ B ) @ ( '\'mapO$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'mapO$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$b\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'mapM$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'natTransMap$c\'' @ A @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'natTransMap$c\'' @ A @ C ) ) @ ( '\'mapM$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom513) ).
thf(1355,plain,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\''] :
( ( ( '\'natTransP$c\'' @ A )
=> ( ( '\'functor$c\'' @ ( '\'nTDom$a\'' @ A ) )
& ( '\'functor$c\'' @ ( '\'nTCod$a\'' @ A ) )
& ( ( '\'nTCatDom$b\'' @ A )
= ( '\'catDom$d\'' @ ( '\'nTCod$a\'' @ A ) ) )
& ( ( '\'nTCatCod$b\'' @ A )
= ( '\'catCod$b\'' @ ( '\'nTDom$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$b\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$b\'' @ A ) @ ( '\'natTransMap$c\'' @ A @ B ) @ ( '\'mapO$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'mapO$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$b\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'mapM$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'natTransMap$c\'' @ A @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'natTransMap$c\'' @ A @ C ) ) @ ( '\'mapM$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) ) ) ) )
& ( ( ( '\'functor$c\'' @ ( '\'nTDom$a\'' @ A ) )
& ( '\'functor$c\'' @ ( '\'nTCod$a\'' @ A ) )
& ( ( '\'nTCatDom$b\'' @ A )
= ( '\'catDom$d\'' @ ( '\'nTCod$a\'' @ A ) ) )
& ( ( '\'nTCatCod$b\'' @ A )
= ( '\'catCod$b\'' @ ( '\'nTDom$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$b\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$b\'' @ A ) @ ( '\'natTransMap$c\'' @ A @ B ) @ ( '\'mapO$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'mapO$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$b\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'mapM$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'natTransMap$c\'' @ A @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$b\'' @ A ) ) @ ( '\'natTransMap$c\'' @ A @ C ) ) @ ( '\'mapM$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) ) ) )
=> ( '\'natTransP$c\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(315,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( ( '\'obj$b\'' @ A )
= ( '\'obj$b\'' @ B ) )
& ( ( '\'mor$\'' @ A )
= ( '\'mor$\'' @ B ) )
& ( ( '\'dom$\'' @ A )
= ( '\'dom$\'' @ B ) )
& ( ( '\'cod$\'' @ A )
= ( '\'cod$\'' @ B ) )
& ( ( '\'id$b\'' @ A )
= ( '\'id$b\'' @ B ) )
& ( ( '\'comp$a\'' @ A )
= ( '\'comp$a\'' @ B ) )
& ( ( '\'more$a\'' @ A )
= ( '\'more$a\'' @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).
thf(1751,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( ( '\'obj$b\'' @ A )
= ( '\'obj$b\'' @ B ) )
& ( ( '\'mor$\'' @ A )
= ( '\'mor$\'' @ B ) )
& ( ( '\'dom$\'' @ A )
= ( '\'dom$\'' @ B ) )
& ( ( '\'cod$\'' @ A )
= ( '\'cod$\'' @ B ) )
& ( ( '\'id$b\'' @ A )
= ( '\'id$b\'' @ B ) )
& ( ( '\'comp$a\'' @ A )
= ( '\'comp$a\'' @ B ) )
& ( ( '\'more$a\'' @ A )
= ( '\'more$a\'' @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(294,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'oppositeCategory$a\'' @ A ) @ B @ C ) @ D )
<=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom59) ).
thf(1666,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'oppositeCategory$a\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ D ) @ C ) )
& ( ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ D ) @ C )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'oppositeCategory$a\'' @ A ) @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(67,axiom,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'',B: '\'ZF$\''] :
( ( ( '\'natTransP$c\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$b\'' @ A ) ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$b\'' @ A ) @ ( '\'natTransMap$c\'' @ A @ B ) @ ( '\'mapO$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'mapO$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom527) ).
thf(693,plain,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$\'',B: '\'ZF$\''] :
( ( ( '\'natTransP$c\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$b\'' @ A ) ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$b\'' @ A ) @ ( '\'natTransMap$c\'' @ A @ B ) @ ( '\'mapO$e\'' @ ( '\'nTDom$a\'' @ A ) @ B ) ) @ ( '\'mapO$e\'' @ ( '\'nTCod$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(201,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_fun$\'',C: '\'ZF$\''] :
( ! [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$\'' @ B @ D ) ) @ C ) )
=> ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ ( '\'zFfun$\'' @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom575) ).
thf(1238,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_fun$\'',C: '\'ZF$\''] :
( ! [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$\'' @ B @ D ) ) @ C ) )
=> ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ ( '\'zFfun$\'' @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(230,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ? [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).
thf(1387,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ? [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(308,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'lSCategory$\'' @ ( '\'oppositeCategory$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).
thf(1723,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'lSCategory$\'' @ ( '\'oppositeCategory$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(267,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'functor_abbrev$\'' @ ( '\'homFtorContra$\'' @ A @ B ) @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).
thf(1570,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'functor_abbrev$\'' @ ( '\'homFtorContra$\'' @ A @ B ) @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(297,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'yFtor$a\'' @ A )
= ( '\'functor_ext$\'' @ A @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) @ ( '\'yFtorNT$\'' @ A ) @ '\'unity$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom556) ).
thf(1676,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'yFtor$a\'' @ A )
= ( '\'functor_ext$\'' @ A @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) @ ( '\'yFtorNT$\'' @ A ) @ '\'unity$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(100,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$a\'' @ B ) )
=> ( '\'category$\'' @ ( '\'catExp$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).
thf(788,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$a\'' @ B ) )
=> ( '\'category$\'' @ ( '\'catExp$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(405,axiom,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ B ) ) )
& ( '\'preFunctor$c\'' @ ( '\'functorComp$g\'' @ B @ C ) )
& ( '\'functor_comp_def$g\'' @ B @ C ) )
=> ( ( '\'mapO$\'' @ ( '\'functorComp$g\'' @ B @ C ) @ A )
= ( '\'mapO$b\'' @ C @ ( '\'mapO$a\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom427) ).
thf(2150,plain,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ B ) ) )
& ( '\'preFunctor$c\'' @ ( '\'functorComp$g\'' @ B @ C ) )
& ( '\'functor_comp_def$g\'' @ B @ C ) )
=> ( ( '\'mapO$\'' @ ( '\'functorComp$g\'' @ B @ C ) @ A )
= ( '\'mapO$b\'' @ C @ ( '\'mapO$a\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(379,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'A$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ B ) ) )
=> ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ B ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ C ) @ ( '\'mapO$a\'' @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom285) ).
thf(2032,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'A$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ B ) ) )
=> ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ B ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ C ) @ ( '\'mapO$a\'' @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(108,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$\'' @ B )
& ( '\'member$a\'' @ C @ ( '\'obj$\'' @ B ) ) )
=> ( '\'functor$e\'' @ ( '\'constFunctor$i\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).
thf(815,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$\'' @ B )
& ( '\'member$a\'' @ C @ ( '\'obj$\'' @ B ) ) )
=> ( '\'functor$e\'' @ ( '\'constFunctor$i\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(242,axiom,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ B ) ) )
& ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'functorComp$a\'' @ B @ C ) )
& ( '\'functor_comp_def$a\'' @ B @ C ) )
=> ( ( '\'mapO$a\'' @ ( '\'functorComp$a\'' @ B @ C ) @ A )
= ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ C ) @ ( '\'mapO$a\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).
thf(1423,plain,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ B ) ) )
& ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'functorComp$a\'' @ B @ C ) )
& ( '\'functor_comp_def$a\'' @ B @ C ) )
=> ( ( '\'mapO$a\'' @ ( '\'functorComp$a\'' @ B @ C ) @ A )
= ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ C ) @ ( '\'mapO$a\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(271,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).
thf(1602,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(430,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( '\'fun_app$c\'' @ ( '\'uus$\'' @ A ) @ B )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(2213,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( '\'fun_app$c\'' @ ( '\'uus$\'' @ A ) @ B )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(283,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'lSCategory_axioms$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom474) ).
thf(1634,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'lSCategory_axioms$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(360,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( '\'member$\'' @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mor$a\'' @ ( '\'catCod$\'' @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom347) ).
thf(1968,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( '\'member$\'' @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mor$a\'' @ ( '\'catCod$\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(117,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'catDom$c\'' @ B ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ ( '\'idNatTrans$g\'' @ B ) ) @ A )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$c\'' @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom469) ).
thf(879,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'catDom$c\'' @ B ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ ( '\'idNatTrans$g\'' @ B ) ) @ A )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$c\'' @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(389,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$a\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ D ) )
= ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom435) ).
thf(2068,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$a\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ D ) )
= ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(333,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorM_axioms$c\'' @ A )
<=> ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ C ) ) @ ( '\'mapO$\'' @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom354) ).
thf(1819,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'functorM_axioms$c\'' @ A )
=> ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ C ) ) @ ( '\'mapO$\'' @ A @ D ) ) ) )
& ( ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ C ) ) @ ( '\'mapO$\'' @ A @ D ) ) )
=> ( '\'functorM_axioms$c\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(30,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF$\''] :
( ( ( '\'natTransP$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom528) ).
thf(583,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF$\''] :
( ( ( '\'natTransP$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(425,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom532) ).
thf(2200,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(62,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$c\'' @ B )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ B ) ) )
=> ( '\'functor$c\'' @ ( '\'constFunctor$a\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom226) ).
thf(682,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$c\'' @ B )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ B ) ) )
=> ( '\'functor$c\'' @ ( '\'constFunctor$a\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(429,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'mapO$a\'' @ B @ C ) ) )
=> ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ ( '\'yMapInv$\'' @ A @ C @ B @ D ) @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom68) ).
thf(2211,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'mapO$a\'' @ B @ C ) ) )
=> ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ ( '\'yMapInv$\'' @ A @ C @ B @ D ) @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(403,axiom,
! [A: '\'ZF$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'catDom$d\'' @ B ) ) )
& ( '\'preFunctor$d\'' @ ( '\'functorComp$e\'' @ B @ C ) )
& ( '\'functor_comp_def$e\'' @ B @ C ) )
=> ( ( '\'mapO$b\'' @ ( '\'functorComp$e\'' @ B @ C ) @ A )
= ( '\'mapO$\'' @ C @ ( '\'mapO$e\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom432) ).
thf(2112,plain,
! [A: '\'ZF$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'catDom$d\'' @ B ) ) )
& ( '\'preFunctor$d\'' @ ( '\'functorComp$e\'' @ B @ C ) )
& ( '\'functor_comp_def$e\'' @ B @ C ) )
=> ( ( '\'mapO$b\'' @ ( '\'functorComp$e\'' @ B @ C ) @ A )
= ( '\'mapO$\'' @ C @ ( '\'mapO$e\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(214,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ C ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom310) ).
thf(1291,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ C ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(235,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'B$\'',E: '\'B$\''] :
( ( ( '\'functor_abbrev$f\'' @ A @ B @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ B @ D ) @ E ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ D ) ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom407) ).
thf(1402,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'B$\'',E: '\'B$\''] :
( ( ( '\'functor_abbrev$f\'' @ A @ B @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ B @ D ) @ E ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ D ) ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(439,axiom,
'\'member$i\'' @ '\'x$\'' @ ( '\'obj$b\'' @ '\'c$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom36) ).
thf(2245,plain,
'\'member$i\'' @ '\'x$\'' @ ( '\'obj$b\'' @ '\'c$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(365,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_fun$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF$\''] :
( ! [E: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ E ) @ A )
=> ( ( '\'fun_app$\'' @ B @ E )
= ( '\'fun_app$\'' @ C @ E ) ) )
=> ( ( '\'zFfun$\'' @ A @ D @ B )
= ( '\'zFfun$\'' @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom551) ).
thf(1983,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_fun$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF$\''] :
( ! [E: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ E ) @ A )
=> ( ( '\'fun_app$\'' @ B @ E )
= ( '\'fun_app$\'' @ C @ E ) ) )
=> ( ( '\'zFfun$\'' @ A @ D @ B )
= ( '\'zFfun$\'' @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(39,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
& ( '\'fun_app$f\'' @ '\'functorExt$a\'' @ A ) )
=> ( '\'fun_app$f\'' @ '\'functor$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom274) ).
thf(615,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
& ( '\'fun_app$f\'' @ '\'functorExt$a\'' @ A ) )
=> ( '\'fun_app$f\'' @ '\'functor$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(166,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'functor_abbrev$\'' @ A @ B @ C )
<=> ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( ( '\'catDom$a\'' @ A )
= B )
& ( ( '\'catCod$a\'' @ A )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom343) ).
thf(1121,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
=> ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( ( '\'catDom$a\'' @ A )
= B )
& ( ( '\'catCod$a\'' @ A )
= C ) ) )
& ( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( ( '\'catDom$a\'' @ A )
= B )
& ( ( '\'catCod$a\'' @ A )
= C ) )
=> ( '\'functor_abbrev$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(76,axiom,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\''] :
( ( '\'functor$c\'' @ A )
=> ( '\'natTransP$c\'' @ ( '\'idNatTrans$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom261) ).
thf(725,plain,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\''] :
( ( '\'functor$c\'' @ A )
=> ( '\'natTransP$c\'' @ ( '\'idNatTrans$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(137,axiom,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'functor_abbrev$d\'' @ A @ B @ C )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ C @ ( '\'mapM$e\'' @ A @ D ) @ ( '\'mapO$e\'' @ A @ E ) ) @ ( '\'mapO$e\'' @ A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).
thf(980,plain,
! [A: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'functor_abbrev$d\'' @ A @ B @ C )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ C @ ( '\'mapM$e\'' @ A @ D ) @ ( '\'mapO$e\'' @ A @ E ) ) @ ( '\'mapO$e\'' @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(33,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'natTrans$b\'' @ A )
=> ( '\'natTransP$b\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom134) ).
thf(593,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'natTrans$b\'' @ A )
=> ( '\'natTransP$b\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(98,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ B ) ) )
& ( '\'nTCompDefined$a\'' @ B @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ ( '\'natTransComp$a\'' @ B @ C ) ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ B ) @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom541) ).
thf(783,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ B ) ) )
& ( '\'nTCompDefined$a\'' @ B @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ ( '\'natTransComp$a\'' @ B @ C ) ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ B ) @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(69,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category_axioms$a\'' @ A )
=> ( '\'category$a\'' @ ( '\'makeCat$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom449) ).
thf(697,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category_axioms$a\'' @ A )
=> ( '\'category$a\'' @ ( '\'makeCat$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(258,axiom,
! [A: '\'A$\'',B: '\'A_bool_fun$\''] :
( ( '\'member$i\'' @ A @ ( '\'collect$b\'' @ B ) )
<=> ( '\'fun_app$l\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).
thf(1541,plain,
! [A: '\'A$\'',B: '\'A_bool_fun$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'collect$b\'' @ B ) )
=> ( '\'fun_app$l\'' @ B @ A ) )
& ( ( '\'fun_app$l\'' @ B @ A )
=> ( '\'member$i\'' @ A @ ( '\'collect$b\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(115,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ ( '\'homFtorMapContra$\'' @ A @ C @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) @ B ) ) @ ( '\'homFtorMapContra$\'' @ A @ C @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom334) ).
thf(874,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ ( '\'homFtorMapContra$\'' @ A @ C @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) @ B ) ) @ ( '\'homFtorMapContra$\'' @ A @ C @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(404,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'equivalence_axioms$a\'' @ A )
<=> ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ D @ ( '\'mapO$\'' @ A @ B ) ) @ ( '\'mapO$\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ B @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'objIso$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom440) ).
thf(2115,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'equivalence_axioms$a\'' @ A )
=> ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ D @ ( '\'mapO$\'' @ A @ B ) ) @ ( '\'mapO$\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ B @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'objIso$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ C ) ) @ B ) ) ) ) )
& ( ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ D @ ( '\'mapO$\'' @ A @ B ) ) @ ( '\'mapO$\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ B @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'objIso$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ C ) ) @ B ) ) ) )
=> ( '\'equivalence_axioms$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(208,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorM$c\'' @ A )
=> ( '\'functor$d\'' @ ( '\'makeFtor$d\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom188) ).
thf(1270,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorM$c\'' @ A )
=> ( '\'functor$d\'' @ ( '\'makeFtor$d\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(341,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) ) @ ( '\'mapO$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom328) ).
thf(1851,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) ) @ ( '\'mapO$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(256,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'uua$\'' @ A ) @ B )
<=> ( '\'member$d\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
thf(1534,plain,
! [A: '\'ZF_set$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'uua$\'' @ A ) @ B )
=> ( '\'member$d\'' @ B @ A ) )
& ( ( '\'member$d\'' @ B @ A )
=> ( '\'fun_app$b\'' @ ( '\'uua$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(328,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functor$d\'' @ A )
=> ( '\'natTransP$b\'' @ ( '\'idNatTrans$d\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom264) ).
thf(1794,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functor$d\'' @ A )
=> ( '\'natTransP$b\'' @ ( '\'idNatTrans$d\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(151,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'homSet$\'' @ A @ B @ C )
= ( '\'implode$\'' @ ( '\'hOMCollection$\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom591) ).
thf(1017,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'homSet$\'' @ A @ B @ C )
= ( '\'implode$\'' @ ( '\'hOMCollection$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(164,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ( ( '\'obj$a\'' @ A )
= ( '\'obj$a\'' @ B ) )
& ( ( '\'mor$b\'' @ A )
= ( '\'mor$b\'' @ B ) )
& ( ( '\'dom$a\'' @ A )
= ( '\'dom$a\'' @ B ) )
& ( ( '\'cod$a\'' @ A )
= ( '\'cod$a\'' @ B ) )
& ( ( '\'id$a\'' @ A )
= ( '\'id$a\'' @ B ) )
& ( ( '\'comp$\'' @ A )
= ( '\'comp$\'' @ B ) )
& ( ( '\'more$b\'' @ A )
= ( '\'more$b\'' @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom369) ).
thf(1111,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ( ( '\'obj$a\'' @ A )
= ( '\'obj$a\'' @ B ) )
& ( ( '\'mor$b\'' @ A )
= ( '\'mor$b\'' @ B ) )
& ( ( '\'dom$a\'' @ A )
= ( '\'dom$a\'' @ B ) )
& ( ( '\'cod$a\'' @ A )
= ( '\'cod$a\'' @ B ) )
& ( ( '\'id$a\'' @ A )
= ( '\'id$a\'' @ B ) )
& ( ( '\'comp$\'' @ A )
= ( '\'comp$\'' @ B ) )
& ( ( '\'more$b\'' @ A )
= ( '\'more$b\'' @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(361,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'natTrans$b\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$\'' @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom534) ).
thf(1970,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'natTrans$b\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$\'' @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(169,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$k\'' @ ( '\'inverse_rel$a\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).
thf(1138,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$k\'' @ ( '\'inverse_rel$a\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(307,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$f\'' @ '\'equivalence$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ D @ ( '\'mapO$a\'' @ A @ B ) ) @ ( '\'mapO$a\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).
thf(1719,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$f\'' @ '\'equivalence$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ D @ ( '\'mapO$a\'' @ A @ B ) ) @ ( '\'mapO$a\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(266,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$b\'' @ ( '\'identityFunctor$f\'' @ A ) ) ) ) )
=> ( ( '\'mapO$f\'' @ ( '\'identityFunctor$f\'' @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom286) ).
thf(1567,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$b\'' @ ( '\'identityFunctor$f\'' @ A ) ) ) ) )
=> ( ( '\'mapO$f\'' @ ( '\'identityFunctor$f\'' @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(178,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ ( '\'makeNT$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom124) ).
thf(1160,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ ( '\'makeNT$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(4,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( '\'natTrans$a\'' @ A )
=> ( '\'natTransP$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom133) ).
thf(488,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( '\'natTrans$a\'' @ A )
=> ( '\'natTransP$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(184,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ '\'set$a\'' ) @ ( '\'homSet$\'' @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).
thf(1182,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ '\'set$a\'' ) @ ( '\'homSet$\'' @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(57,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ D ) )
=> ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom460) ).
thf(669,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ D ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(299,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom411) ).
thf(1700,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(466,axiom,
! [A: '\'B$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$b\'' @ ( '\'functorComp$\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$\'' @ B @ C ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catCod$b\'' @ C ) @ ( '\'mapM$e\'' @ C @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ B ) @ A ) ) @ ( '\'mapO$e\'' @ C @ ( '\'mapO$a\'' @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$a\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$e\'' @ C @ ( '\'mapO$a\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$a\'' @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).
thf(2349,plain,
! [A: '\'B$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$b\'' @ ( '\'functorComp$\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$\'' @ B @ C ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catCod$b\'' @ C ) @ ( '\'mapM$e\'' @ C @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ B ) @ A ) ) @ ( '\'mapO$e\'' @ C @ ( '\'mapO$a\'' @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$a\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$e\'' @ C @ ( '\'mapO$a\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$a\'' @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(346,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'oppositeCategory$a\'' @ A ) @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom85) ).
thf(1889,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'oppositeCategory$a\'' @ A ) @ B @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(61,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'obj$b\'' @ ( '\'makeCat$a\'' @ A ) )
= ( '\'obj$b\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).
thf(679,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'obj$b\'' @ ( '\'makeCat$a\'' @ A ) )
= ( '\'obj$b\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(15,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom495) ).
thf(547,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(123,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ C ) ) @ ( '\'mapO$a\'' @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom349) ).
thf(901,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ C ) ) @ ( '\'mapO$a\'' @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(64,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom224) ).
thf(686,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(239,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ B )
=> ~ ( '\'fun_app$b\'' @ ( '\'elem$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom598) ).
thf(1414,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ B )
=> ~ ( '\'fun_app$b\'' @ ( '\'elem$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(386,axiom,
! [A: '\'ZF$\''] :
~ ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom595) ).
thf(2053,plain,
! [A: '\'ZF$\''] :
~ ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(423,axiom,
'\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) @ ( '\'homSet$\'' @ '\'c$\'' @ '\'x$\'' @ '\'y$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).
thf(2196,plain,
'\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) @ ( '\'homSet$\'' @ '\'c$\'' @ '\'x$\'' @ '\'y$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(402,axiom,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',E: '\'ZF$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ B ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ B ) )
& ( '\'lSCategory$\'' @ B ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'yMapInv$\'' @ B @ A @ D @ E ) @ C )
= ( '\'zFfun$\'' @ ( '\'homSet$\'' @ B @ C @ A ) @ ( '\'mapO$a\'' @ D @ C ) @ ( '\'fun_app$m\'' @ ( '\'uul$\'' @ B @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom547) ).
thf(2108,plain,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',E: '\'ZF$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ B ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ B ) )
& ( '\'lSCategory$\'' @ B ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'yMapInv$\'' @ B @ A @ D @ E ) @ C )
= ( '\'zFfun$\'' @ ( '\'homSet$\'' @ B @ C @ A ) @ ( '\'mapO$a\'' @ D @ C ) @ ( '\'fun_app$m\'' @ ( '\'uul$\'' @ B @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(381,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'functorM$c\'' @ ( '\'yFtor$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).
thf(2038,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'functorM$c\'' @ ( '\'yFtor$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(165,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( ( '\'catDom$a\'' @ A )
= B )
& ( ( '\'catCod$a\'' @ A )
= C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom344) ).
thf(1114,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\''] :
~ ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ~ ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( ( '\'catDom$a\'' @ A )
= B )
& ( ( '\'catCod$a\'' @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(143,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) @ ( '\'mor$b\'' @ '\'set$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).
thf(997,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) @ ( '\'mor$b\'' @ '\'set$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(139,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ B )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ '\'set$\'' ) @ B ) ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom372) ).
thf(985,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ B )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ '\'set$\'' ) @ B ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(257,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) @ ( '\'mor$b\'' @ '\'set$a\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).
thf(1539,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$d\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) @ ( '\'mor$b\'' @ '\'set$a\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(167,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ B )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'zFfun$\'' @ B @ C @ D ) ) @ A )
= ( '\'fun_app$\'' @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom553) ).
thf(1131,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ B )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'zFfun$\'' @ B @ C @ D ) ) @ A )
= ( '\'fun_app$\'' @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(330,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ D @ ( '\'mapO$a\'' @ A @ B ) ) @ ( '\'mapO$a\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B )
= ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'mapO$a\'' @ A @ C ) ) @ B ) ) ) )
=> ( '\'fun_app$f\'' @ '\'equivalence_axioms$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).
thf(1799,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ D @ ( '\'mapO$a\'' @ A @ B ) ) @ ( '\'mapO$a\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B )
= ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'mapO$a\'' @ A @ C ) ) @ B ) ) ) )
=> ( '\'fun_app$f\'' @ '\'equivalence_axioms$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(145,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'uut$\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ ( '\'mapO$a\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(1002,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'uut$\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ ( '\'mapO$a\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(204,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ A @ B ) @ C )
& ( ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A )
= B )
& ( ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A )
= C ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom523) ).
thf(1246,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
~ ( ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ A @ B ) @ C )
& ~ ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A )
= B )
& ( ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(305,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom132) ).
thf(1715,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(97,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ! [B: '\'ZF_set$\'',C: '\'ZF_set$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_fun$\'',G: '\'ZF_ZF_ZF_fun_fun$\'',H: '\'Unit$\''] :
( ( A
= ( '\'category_ext$a\'' @ B @ C @ D @ E @ F @ G @ H ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).
thf(779,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
~ ! [B: '\'ZF_set$\'',C: '\'ZF_set$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_fun$\'',G: '\'ZF_ZF_ZF_fun_fun$\'',H: '\'Unit$\''] :
( A
!= ( '\'category_ext$a\'' @ B @ C @ D @ E @ F @ G @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(280,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).
thf(1627,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(250,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'category_axioms$\'' @ A )
<=> ( ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'B$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom443) ).
thf(1451,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( '\'category_axioms$\'' @ A )
=> ( ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'B$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) ) )
& ( ( ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'B$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) )
=> ( '\'category_axioms$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(81,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'oppositeCategory$b\'' @ ( '\'oppositeCategory$b\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).
thf(738,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'oppositeCategory$b\'' @ ( '\'oppositeCategory$b\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(462,axiom,
! [A: '\'A$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ B ) ) )
& ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'functorComp$d\'' @ B @ C ) )
& ( '\'functor_comp_def$d\'' @ B @ C ) )
=> ( ( '\'mapO$a\'' @ ( '\'functorComp$d\'' @ B @ C ) @ A )
= ( '\'mapO$g\'' @ C @ ( '\'mapO$\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).
thf(2304,plain,
! [A: '\'A$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ B ) ) )
& ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'functorComp$d\'' @ B @ C ) )
& ( '\'functor_comp_def$d\'' @ B @ C ) )
=> ( ( '\'mapO$a\'' @ ( '\'functorComp$d\'' @ B @ C ) @ A )
= ( '\'mapO$g\'' @ C @ ( '\'mapO$\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(406,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ D @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ C ) ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'yMap$\'' @ A @ C @ D ) ) @ ( '\'mapO$a\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom69) ).
thf(2153,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ D @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ C ) ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'yMap$\'' @ A @ C @ D ) ) @ ( '\'mapO$a\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(336,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ ( '\'uun$\'' @ A @ B ) @ C )
<=> ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ C )
& ( ( '\'nTCatDom$\'' @ C )
= A )
& ( ( '\'nTCatCod$\'' @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom25) ).
thf(1831,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'uun$\'' @ A @ B ) @ C )
=> ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ C )
& ( ( '\'nTCatDom$\'' @ C )
= A )
& ( ( '\'nTCatCod$\'' @ C )
= B ) ) )
& ( ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ C )
& ( ( '\'nTCatDom$\'' @ C )
= A )
& ( ( '\'nTCatCod$\'' @ C )
= B ) )
=> ( '\'fun_app$e\'' @ ( '\'uun$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(198,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'oppositeCategory$b\'' @ A ) @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom86) ).
thf(1231,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'oppositeCategory$b\'' @ A ) @ B @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(331,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'oppositeCategory$a\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom88) ).
thf(1814,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'oppositeCategory$a\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(202,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ ( '\'makeCat$\'' @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).
thf(1241,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ ( '\'makeCat$\'' @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(321,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'mapO$a\'' @ B @ C ) ) )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ ( '\'yMapInv$a\'' @ A @ C @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).
thf(1779,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'mapO$a\'' @ B @ C ) ) )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ ( '\'yMapInv$a\'' @ A @ C @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(13,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\''] :
( ( '\'obj$\'' @ ( '\'oppositeCategory$a\'' @ A ) )
= ( '\'obj$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).
thf(541,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\''] :
( ( '\'obj$\'' @ ( '\'oppositeCategory$a\'' @ A ) )
= ( '\'obj$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(53,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom479) ).
thf(657,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(91,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom492) ).
thf(765,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(392,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',E: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',F: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'functor_abbrev$b\'' @ A @ B @ C )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ C @ ( '\'mapM$c\'' @ A @ D ) @ ( '\'mapO$c\'' @ A @ E ) ) @ ( '\'mapO$c\'' @ A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).
thf(2076,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',E: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',F: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'functor_abbrev$b\'' @ A @ B @ C )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ C @ ( '\'mapM$c\'' @ A @ D ) @ ( '\'mapO$c\'' @ A @ E ) ) @ ( '\'mapO$c\'' @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(212,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ E ) @ C ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).
thf(1286,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ E ) @ C ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(186,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\''] :
( ( '\'homFtorMapContra$\'' @ A @ B @ C )
= ( '\'zFfun$\'' @ ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ C ) @ ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ C ) @ ( '\'uuo$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom549) ).
thf(1187,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\''] :
( ( '\'homFtorMapContra$\'' @ A @ B @ C )
= ( '\'zFfun$\'' @ ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ C ) @ ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ C ) @ ( '\'uuo$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(154,axiom,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ B ) ) )
& ( '\'fun_app$e\'' @ ( '\'nTCompDefined$\'' @ B ) @ C ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'fun_app$w\'' @ ( '\'fun_app$x\'' @ '\'natTransComp$\'' @ B ) @ C ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ B ) ) @ ( '\'natTransMap$b\'' @ B @ A ) ) @ ( '\'natTransMap$b\'' @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom540) ).
thf(1026,plain,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ B ) ) )
& ( '\'fun_app$e\'' @ ( '\'nTCompDefined$\'' @ B ) @ C ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'fun_app$w\'' @ ( '\'fun_app$x\'' @ '\'natTransComp$\'' @ B ) @ C ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ B ) ) @ ( '\'natTransMap$b\'' @ B @ A ) ) @ ( '\'natTransMap$b\'' @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(420,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'functor_abbrev$f\'' @ ( '\'yFtor$\'' @ A ) @ A @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom138) ).
thf(2189,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'functor_abbrev$f\'' @ ( '\'yFtor$\'' @ A ) @ A @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(73,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom200) ).
thf(718,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(428,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'cod$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) )
= ( '\'mapO$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom357) ).
thf(2208,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'cod$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) )
= ( '\'mapO$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(107,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\''] :
( ! [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ A @ C )
<=> ( '\'fun_app$f\'' @ B @ C ) )
=> ( ( '\'collect$h\'' @ A )
= ( '\'collect$h\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).
thf(805,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$\''] :
( ! [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ A @ C )
=> ( '\'fun_app$f\'' @ B @ C ) )
& ( ( '\'fun_app$f\'' @ B @ C )
=> ( '\'fun_app$f\'' @ A @ C ) ) )
=> ( ( '\'collect$h\'' @ A )
= ( '\'collect$h\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(293,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ '\'set$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ A ) @ B ) ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom452) ).
thf(1663,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ '\'set$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ A ) @ B ) ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(397,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) ) ) @ ( '\'mapO$a\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom327) ).
thf(2089,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) ) ) @ ( '\'mapO$a\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(133,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'nTCompDefined$\'' @ A ) @ B )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'natTransMap$b\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom538) ).
thf(953,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A$\''] :
( ( ( '\'fun_app$e\'' @ ( '\'nTCompDefined$\'' @ A ) @ B )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'natTransMap$b\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(185,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).
thf(1185,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(316,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'functor_abbrev$c\'' @ A @ B @ C )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ C @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ A ) @ D ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ A ) @ E ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ A ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).
thf(1754,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'functor_abbrev$c\'' @ A @ B @ C )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ C @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ A ) @ D ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ A ) @ E ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ A ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(358,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) @ ( '\'homFtorContra$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ ( '\'homFtorContra$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom288) ).
thf(1959,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) @ ( '\'homFtorContra$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ ( '\'homFtorContra$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(196,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'makeCat$\'' @ A ) @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom308) ).
thf(1219,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'makeCat$\'' @ A ) @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(351,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ '\'set$\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) )
= ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom332) ).
thf(1927,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ '\'set$\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) )
= ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(25,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom498) ).
thf(573,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(475,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'B_ZF_fun$\'',D: '\'B_ZF_fun_b_ZF_fun_fun$\'',E: '\'B_ZF_fun_b_ZF_fun_fun$\''] :
( ( ( A = B )
& ( ( '\'mor2ZF$\'' @ B )
= C )
& ! [F: '\'B_ZF_fun$\''] :
( ( C = F )
=> ( ( '\'fun_app$s\'' @ D @ F )
= ( '\'fun_app$s\'' @ E @ F ) ) ) )
=> ( ( '\'mor2ZF_update$\'' @ D @ A )
= ( '\'mor2ZF_update$\'' @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).
thf(2376,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'B_ZF_fun$\'',D: '\'B_ZF_fun_b_ZF_fun_fun$\'',E: '\'B_ZF_fun_b_ZF_fun_fun$\''] :
( ( ( A = B )
& ( ( '\'mor2ZF$\'' @ B )
= C )
& ! [F: '\'B_ZF_fun$\''] :
( ( C = F )
=> ( ( '\'fun_app$s\'' @ D @ F )
= ( '\'fun_app$s\'' @ E @ F ) ) ) )
=> ( ( '\'mor2ZF_update$\'' @ D @ A )
= ( '\'mor2ZF_update$\'' @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(35,axiom,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\''] :
( ( '\'functor$a\'' @ A )
=> ( '\'natTransP$d\'' @ ( '\'idNatTrans$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom262) ).
thf(601,plain,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\''] :
( ( '\'functor$a\'' @ A )
=> ( '\'natTransP$d\'' @ ( '\'idNatTrans$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(436,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B )
= ( '\'yMapInv$\'' @ A @ C @ ( '\'homFtorContra$\'' @ A @ D ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).
thf(2235,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B )
= ( '\'yMapInv$\'' @ A @ C @ ( '\'homFtorContra$\'' @ A @ D ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(125,axiom,
! [A: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
=> ( A
= ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom574) ).
thf(906,plain,
! [A: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
=> ( A
= ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(168,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ C ) ) @ ( '\'mapO$\'' @ A @ D ) ) )
=> ( '\'functorM_axioms$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).
thf(1135,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'mapO$\'' @ A @ C ) ) @ ( '\'mapO$\'' @ A @ D ) ) )
=> ( '\'functorM_axioms$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(289,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'cod$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).
thf(1648,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'cod$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(176,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'B$\'',E: '\'B$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ B @ D ) @ E ) )
=> ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ B ) @ D ) @ E ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ C ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ D ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom418) ).
thf(1154,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'B$\'',E: '\'B$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ B @ D ) @ E ) )
=> ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ B ) @ D ) @ E ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ C ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ D ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(348,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom207) ).
thf(1916,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(384,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'homFtor$a\'' @ A @ B ) )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'homFtor$a\'' @ A @ B ) @ C )
= ( '\'homSet$\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).
thf(2048,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'homFtor$a\'' @ A @ B ) )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'homFtor$a\'' @ A @ B ) @ C )
= ( '\'homSet$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(79,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtorContra$\'' @ A @ B )
= ( '\'makeFtor$\'' @ ( '\'homFtorContra$a\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).
thf(732,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtorContra$\'' @ A @ B )
= ( '\'makeFtor$\'' @ ( '\'homFtorContra$a\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(275,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'oppositeCategory$b\'' @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom390) ).
thf(1615,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'oppositeCategory$b\'' @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(94,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'natTrans$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom533) ).
thf(772,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'natTrans$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(277,axiom,
! [A: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ '\'uuy$\'' @ A )
<=> $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).
thf(1620,plain,
! [A: '\'ZF$\''] : ( '\'fun_app$b\'' @ '\'uuy$\'' @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(374,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom341) ).
thf(2016,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(28,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'functorM$c\'' @ A )
& ( '\'functorExt$d\'' @ A ) )
=> ( '\'functor$d\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom277) ).
thf(579,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'functorM$c\'' @ A )
& ( '\'functorExt$d\'' @ A ) )
=> ( '\'functor$d\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(135,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( A = B )
<=> ! [C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ A )
<=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom593) ).
thf(958,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( A = B )
=> ! [C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ B ) )
& ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ A ) ) ) )
& ( ! [C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ B ) )
& ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ B )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ A ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(422,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( '\'fun_app$p\'' @ ( '\'uup$\'' @ A @ B ) @ C )
= ( '\'homFtorMapContra$\'' @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
thf(2193,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( '\'fun_app$p\'' @ ( '\'uup$\'' @ A @ B ) @ C )
= ( '\'homFtorMapContra$\'' @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(128,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ '\'set$\'' ) @ ( '\'homSet$\'' @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom312) ).
thf(936,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ '\'set$\'' ) @ ( '\'homSet$\'' @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(458,axiom,
! [A: '\'ZF$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'B$\'',D: '\'A$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ ( '\'homSet$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ B ) @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'homFtorMapContra$\'' @ B @ C @ D ) ) @ A )
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ B ) @ C ) @ ( '\'zF2mor$\'' @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom370) ).
thf(2293,plain,
! [A: '\'ZF$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'B$\'',D: '\'A$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ ( '\'homSet$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ B ) @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'homFtorMapContra$\'' @ B @ C @ D ) ) @ A )
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ B ) @ C ) @ ( '\'zF2mor$\'' @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(369,axiom,
! [A: '\'ZF$\''] :
( ( '\'fun_app$\'' @ '\'uuz$\'' @ A )
= ( '\'zFfun$\'' @ A @ A @ '\'uux$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).
thf(1997,plain,
! [A: '\'ZF$\''] :
( ( '\'fun_app$\'' @ '\'uuz$\'' @ A )
= ( '\'zFfun$\'' @ A @ A @ '\'uux$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(285,axiom,
! [A: '\'ZF$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'catDom$d\'' @ B ) ) )
& ( '\'preFunctor$a\'' @ ( '\'functorComp$b\'' @ B @ C ) )
& ( '\'fun_app$f\'' @ ( '\'functor_comp_def$b\'' @ B ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'functorComp$b\'' @ B @ C ) ) @ A )
= ( '\'mapO$a\'' @ C @ ( '\'mapO$e\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom433) ).
thf(1638,plain,
! [A: '\'ZF$\'',B: '\'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'catDom$d\'' @ B ) ) )
& ( '\'preFunctor$a\'' @ ( '\'functorComp$b\'' @ B @ C ) )
& ( '\'fun_app$f\'' @ ( '\'functor_comp_def$b\'' @ B ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'functorComp$b\'' @ B @ C ) ) @ A )
= ( '\'mapO$a\'' @ C @ ( '\'mapO$e\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(470,axiom,
! [A: '\'A$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ B ) ) )
=> ( ( '\'natTransMap$\'' @ ( '\'idNatTrans$e\'' @ B ) @ A )
= ( '\'id$\'' @ ( '\'catCod$\'' @ B ) @ ( '\'mapO$\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom467) ).
thf(2358,plain,
! [A: '\'A$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ B ) ) )
=> ( ( '\'natTransMap$\'' @ ( '\'idNatTrans$e\'' @ B ) @ A )
= ( '\'id$\'' @ ( '\'catCod$\'' @ B ) @ ( '\'mapO$\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(58,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'mor$b\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom394) ).
thf(672,plain,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'mor$b\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(244,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ '\'set$\'' ) @ ( '\'homFtorMapContra$\'' @ A @ C @ B ) )
= ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom329) ).
thf(1428,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ '\'set$\'' ) @ ( '\'homFtorMapContra$\'' @ A @ C @ B ) )
= ( '\'homSet$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(409,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'yFtor$\'' @ A )
= ( '\'makeFtor$d\'' @ ( '\'yFtor$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom339) ).
thf(2161,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'yFtor$\'' @ A )
= ( '\'makeFtor$d\'' @ ( '\'yFtor$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(465,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'mapO$\'' @ ( '\'makeFtor$d\'' @ A ) @ B )
= ( '\'mapO$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom282) ).
thf(2346,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'mapO$\'' @ ( '\'makeFtor$d\'' @ A ) @ B )
= ( '\'mapO$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(471,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'uuu$\'' @ A @ B ) @ C )
<=> ( ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).
thf(2361,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'uuu$\'' @ A @ B ) @ C )
=> ( ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ C ) ) ) )
& ( ( ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ C ) ) )
=> ( '\'fun_app$b\'' @ ( '\'uuu$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(193,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'fun_app$e\'' @ '\'natTransExt$\'' @ A ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).
thf(1209,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'fun_app$e\'' @ '\'natTransExt$\'' @ A ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(112,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).
thf(831,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(342,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= D ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).
thf(1853,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ~ ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(476,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'yFtor$\'' @ A ) ) @ B )
= ( '\'yMapInv$\'' @ A @ C @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ D ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).
thf(2383,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'yFtor$\'' @ A ) ) @ B )
= ( '\'yMapInv$\'' @ A @ C @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ D ) @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(454,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'uuo$\'' @ A @ B ) @ C )
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'zF2mor$\'' @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).
thf(2284,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'uuo$\'' @ A @ B ) @ C )
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'zF2mor$\'' @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(172,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ C ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ C ) ) ) )
=> ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom422) ).
thf(1144,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ C ) ) )
& ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ C ) ) ) )
=> ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(424,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C )
= ( '\'zFfun$\'' @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) @ ( '\'uuq$\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom557) ).
thf(2197,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C )
= ( '\'zFfun$\'' @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) @ ( '\'uuq$\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(388,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'homFtor$\'' @ A @ B ) @ C )
= ( '\'homSet$\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).
thf(2065,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'homFtor$\'' @ A @ B ) @ C )
= ( '\'homSet$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(440,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( '\'mapO$\'' @ A @ B )
= ( '\'the$a\'' @ ( '\'uuv$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom562) ).
thf(2246,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( '\'mapO$\'' @ A @ B )
= ( '\'the$a\'' @ ( '\'uuv$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(460,axiom,
! [A: '\'B$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ ( '\'functorComp$d\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$d\'' @ B @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$e\'' @ C ) @ ( '\'mapM$g\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ B ) @ A ) ) @ ( '\'mapO$g\'' @ C @ ( '\'mapO$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$g\'' @ C @ ( '\'mapO$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom380) ).
thf(2299,plain,
! [A: '\'B$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ ( '\'functorComp$d\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$d\'' @ B @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$e\'' @ C ) @ ( '\'mapM$g\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ B ) @ A ) ) @ ( '\'mapO$g\'' @ C @ ( '\'mapO$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ B ) ) @ A ) ) ) ) @ ( '\'mapO$g\'' @ C @ ( '\'mapO$\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$\'' @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(49,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorM$c\'' @ A )
=> ( '\'preFunctor$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom147) ).
thf(649,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorM$c\'' @ A )
=> ( '\'preFunctor$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(161,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category_axioms$a\'' @ A )
<=> ( ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom444) ).
thf(1043,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( ( '\'category_axioms$a\'' @ A )
=> ( ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) ) )
& ( ( ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) @ ( '\'obj$a\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) )
=> ( '\'category_axioms$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(416,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ B )
= ( '\'homFtorContra$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom44) ).
thf(2180,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ B )
= ( '\'homFtorContra$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(88,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( '\'functor$b\'' @ A )
=> ( '\'natTransP$a\'' @ ( '\'idNatTrans$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom260) ).
thf(758,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( '\'functor$b\'' @ A )
=> ( '\'natTransP$a\'' @ ( '\'idNatTrans$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(17,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\''] :
( ( '\'collect$h\'' @ ( '\'uuh$\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).
thf(552,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\''] :
( ( '\'collect$h\'' @ ( '\'uuh$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom490) ).
thf(535,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(446,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'A$\''] :
( ( ( '\'functor_abbrev$f\'' @ A @ B @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ B ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ B ) @ D ) )
= ( '\'id$\'' @ C @ ( '\'mapO$\'' @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom284) ).
thf(2261,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'A$\''] :
( ( ( '\'functor_abbrev$f\'' @ A @ B @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ B ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ B ) @ D ) )
= ( '\'id$\'' @ C @ ( '\'mapO$\'' @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(179,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).
thf(1162,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(155,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$\'' @ A )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$a\'' @ D @ ( '\'obj$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom209) ).
thf(1029,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$\'' @ A )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$a\'' @ D @ ( '\'obj$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(174,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'preFunctor$c\'' @ A )
=> ( '\'preFunctor$c\'' @ ( '\'makeFtor$d\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).
thf(1149,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'preFunctor$c\'' @ A )
=> ( '\'preFunctor$c\'' @ ( '\'makeFtor$d\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(42,axiom,
! [A: '\'B_ZF_fun_set$\''] :
( ( '\'collect$e\'' @ ( '\'uud$\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).
thf(626,plain,
! [A: '\'B_ZF_fun_set$\''] :
( ( '\'collect$e\'' @ ( '\'uud$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(451,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'mor2ZF$\'' @ ( '\'oppositeCategory$\'' @ A ) )
= ( '\'mor2ZF$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom70) ).
thf(2278,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'mor2ZF$\'' @ ( '\'oppositeCategory$\'' @ A ) )
= ( '\'mor2ZF$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(228,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'uuw$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom28) ).
thf(1381,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'uuw$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(281,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'homFtor$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).
thf(1630,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'homFtor$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(367,axiom,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'',B: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',D: '\'A$\''] :
( ( ( '\'nt_abbrev$b\'' @ A @ B @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ ( '\'catDom$b\'' @ B ) ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catCod$f\'' @ C ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ D ) @ ( '\'mapO$f\'' @ B @ D ) ) @ ( '\'mapO$f\'' @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom455) ).
thf(1993,plain,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'',B: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',D: '\'A$\''] :
( ( ( '\'nt_abbrev$b\'' @ A @ B @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ ( '\'catDom$b\'' @ B ) ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catCod$f\'' @ C ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ D ) @ ( '\'mapO$f\'' @ B @ D ) ) @ ( '\'mapO$f\'' @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(344,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$m\'' @ ( '\'mapM$\'' @ A ) @ ( '\'extensional$\'' @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( '\'functorExt$d\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom485) ).
thf(1862,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$m\'' @ ( '\'mapM$\'' @ A ) @ ( '\'extensional$\'' @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( '\'functorExt$d\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(3,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\''] :
( ( '\'member$\'' @ A @ ( '\'collect$i\'' @ B ) )
<=> ( '\'fun_app$e\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom106) ).
thf(483,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\''] :
( ( ( '\'member$\'' @ A @ ( '\'collect$i\'' @ B ) )
=> ( '\'fun_app$e\'' @ B @ A ) )
& ( ( '\'fun_app$e\'' @ B @ A )
=> ( '\'member$\'' @ A @ ( '\'collect$i\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(127,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( '\'natTransP$a\'' @ A )
<=> ( ( '\'functor$b\'' @ ( '\'nTDom$d\'' @ A ) )
& ( '\'functor$b\'' @ ( '\'nTCod$d\'' @ A ) )
& ( ( '\'nTCatDom$d\'' @ A )
= ( '\'catDom$c\'' @ ( '\'nTCod$d\'' @ A ) ) )
& ( ( '\'nTCatCod$d\'' @ A )
= ( '\'catCod$c\'' @ ( '\'nTDom$d\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom516) ).
thf(912,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'natTransP$a\'' @ A )
=> ( ( '\'functor$b\'' @ ( '\'nTDom$d\'' @ A ) )
& ( '\'functor$b\'' @ ( '\'nTCod$d\'' @ A ) )
& ( ( '\'nTCatDom$d\'' @ A )
= ( '\'catDom$c\'' @ ( '\'nTCod$d\'' @ A ) ) )
& ( ( '\'nTCatCod$d\'' @ A )
= ( '\'catCod$c\'' @ ( '\'nTDom$d\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ) ) ) )
& ( ( ( '\'functor$b\'' @ ( '\'nTDom$d\'' @ A ) )
& ( '\'functor$b\'' @ ( '\'nTCod$d\'' @ A ) )
& ( ( '\'nTCatDom$d\'' @ A )
= ( '\'catDom$c\'' @ ( '\'nTCod$d\'' @ A ) ) )
& ( ( '\'nTCatCod$d\'' @ A )
= ( '\'catCod$c\'' @ ( '\'nTDom$d\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'natTransP$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(413,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'mapO$a\'' @ B @ C ) ) )
=> ( ( '\'yMap$\'' @ A @ C @ ( '\'yMapInv$\'' @ A @ C @ B @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom67) ).
thf(2171,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'mapO$a\'' @ B @ C ) ) )
=> ( ( '\'yMap$\'' @ A @ C @ ( '\'yMapInv$\'' @ A @ C @ B @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(92,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'category$c\'' @ A )
=> ( '\'category$c\'' @ ( '\'oppositeCategory$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom192) ).
thf(768,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'category$c\'' @ A )
=> ( '\'category$c\'' @ ( '\'oppositeCategory$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(396,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$f\'' @ '\'equivalence$\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'mapO$a\'' @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom375) ).
thf(2086,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$f\'' @ '\'equivalence$\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'mapO$a\'' @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(287,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',E: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ B ) )
& ( '\'compDefined$c\'' @ ( '\'catExp$b\'' @ B @ C ) @ D @ E ) )
=> ( ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ ( '\'comp$c\'' @ ( '\'catExp$b\'' @ B @ C ) @ D @ E ) ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ C ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ D ) @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom465) ).
thf(1643,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',E: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ B ) )
& ( '\'compDefined$c\'' @ ( '\'catExp$b\'' @ B @ C ) @ D @ E ) )
=> ( ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ ( '\'comp$c\'' @ ( '\'catExp$b\'' @ B @ C ) @ D @ E ) ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ C ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ D ) @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(456,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'ZF$\''] :
( ( '\'yMapInv$\'' @ A @ B @ C @ D )
= ( '\'makeNT$\'' @ ( '\'yMapInv$a\'' @ A @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom47) ).
thf(2288,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'ZF$\''] :
( ( '\'yMapInv$\'' @ A @ B @ C @ D )
= ( '\'makeNT$\'' @ ( '\'yMapInv$a\'' @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(21,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'lSCategory_axioms$\'' @ A ) )
=> ( '\'lSCategory$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom470) ).
thf(563,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'lSCategory_axioms$\'' @ A ) )
=> ( '\'lSCategory$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(247,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ C ) ) @ ( '\'mapO$a\'' @ A @ D ) ) )
=> ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom351) ).
thf(1435,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ C ) ) @ ( '\'mapO$a\'' @ A @ D ) ) )
=> ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(376,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ ( '\'idNatTrans$c\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom263) ).
thf(2022,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ ( '\'idNatTrans$c\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(51,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'preFunctor$a\'' @ ( '\'constFunctor$j\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).
thf(653,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'preFunctor$a\'' @ ( '\'constFunctor$j\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(264,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'oppositeCategory$\'' @ A )
= ( '\'category_ext$\'' @ ( '\'obj$b\'' @ A ) @ ( '\'mor$\'' @ A ) @ ( '\'cod$\'' @ A ) @ ( '\'dom$\'' @ A ) @ ( '\'id$b\'' @ A ) @ ( '\'uuj$\'' @ A ) @ ( '\'more$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom544) ).
thf(1562,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'oppositeCategory$\'' @ A )
= ( '\'category_ext$\'' @ ( '\'obj$b\'' @ A ) @ ( '\'mor$\'' @ A ) @ ( '\'cod$\'' @ A ) @ ( '\'dom$\'' @ A ) @ ( '\'id$b\'' @ A ) @ ( '\'uuj$\'' @ A ) @ ( '\'more$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(337,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) @ ( '\'mor$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom412) ).
thf(1841,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
=> ( '\'member$d\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) @ ( '\'mor$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(233,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ '\'set$\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) )
= ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom331) ).
thf(1396,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ '\'set$\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) )
= ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(385,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ C ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom423) ).
thf(2051,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ C ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(68,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom459) ).
thf(695,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(472,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A$\''] :
( ( ( '\'nt_abbrev$a\'' @ A @ B @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ B ) ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ C ) @ ( '\'natTransMap$\'' @ A @ D ) @ ( '\'mapO$\'' @ B @ D ) ) @ ( '\'mapO$\'' @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).
thf(2369,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'A$\''] :
( ( ( '\'nt_abbrev$a\'' @ A @ B @ C )
& ( '\'member$i\'' @ D @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ B ) ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ C ) @ ( '\'natTransMap$\'' @ A @ D ) @ ( '\'mapO$\'' @ B @ D ) ) @ ( '\'mapO$\'' @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(150,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'makeFtor$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom215) ).
thf(1015,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'makeFtor$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(75,axiom,
! [A: '\'ZF$\''] :
( ( '\'fun_app$\'' @ '\'uux$\'' @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom32) ).
thf(722,plain,
! [A: '\'ZF$\''] :
( ( '\'fun_app$\'' @ '\'uux$\'' @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(241,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ ( '\'zFfun$\'' @ A @ B @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ '\'set$\'' ) @ ( '\'zFfun$\'' @ A @ B @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom581) ).
thf(1420,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ ( '\'zFfun$\'' @ A @ B @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ '\'set$\'' ) @ ( '\'zFfun$\'' @ A @ B @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(85,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'cod$a\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).
thf(749,plain,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'cod$a\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(129,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom316) ).
thf(939,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(261,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).
thf(1551,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(5,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\''] :
( ! [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ A @ C )
<=> ( '\'fun_app$e\'' @ B @ C ) )
=> ( ( '\'collect$i\'' @ A )
= ( '\'collect$i\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).
thf(490,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$\''] :
( ! [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'fun_app$e\'' @ A @ C )
=> ( '\'fun_app$e\'' @ B @ C ) )
& ( ( '\'fun_app$e\'' @ B @ C )
=> ( '\'fun_app$e\'' @ A @ C ) ) )
=> ( ( '\'collect$i\'' @ A )
= ( '\'collect$i\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(59,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$c\'' @ B )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ B ) ) )
=> ( '\'functor$a\'' @ ( '\'constFunctor$c\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).
thf(675,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$c\'' @ B )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ B ) ) )
=> ( '\'functor$a\'' @ ( '\'constFunctor$c\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(9,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'functor$b\'' @ ( '\'constFunctor$\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom225) ).
thf(531,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'functor$b\'' @ ( '\'constFunctor$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(131,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ C ) ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom415) ).
thf(944,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ~ ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(103,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\''] :
( ( '\'category$\'' @ A )
=> ( '\'category$\'' @ ( '\'oppositeCategory$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom189) ).
thf(795,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\''] :
( ( '\'category$\'' @ A )
=> ( '\'category$\'' @ ( '\'oppositeCategory$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(448,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'equivalence$a\'' @ A )
& ( '\'member$a\'' @ B @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'objIso$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom374) ).
thf(2271,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'equivalence$a\'' @ A )
& ( '\'member$a\'' @ B @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'objIso$\'' @ ( '\'catCod$\'' @ A ) @ ( '\'mapO$\'' @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(40,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'catExp$l\'' @ A @ B )
= ( '\'category_ext$b\'' @ ( '\'collect$h\'' @ ( '\'uum$\'' @ A @ B ) ) @ ( '\'collect$i\'' @ ( '\'uun$\'' @ A @ B ) ) @ '\'nTDom$c\'' @ '\'nTCod$c\'' @ '\'idNatTrans$f\'' @ '\'natTransComp$\'' @ '\'unity$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom548) ).
thf(617,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'catExp$l\'' @ A @ B )
= ( '\'category_ext$b\'' @ ( '\'collect$h\'' @ ( '\'uum$\'' @ A @ B ) ) @ ( '\'collect$i\'' @ ( '\'uun$\'' @ A @ B ) ) @ '\'nTDom$c\'' @ '\'nTCod$c\'' @ '\'idNatTrans$f\'' @ '\'natTransComp$\'' @ '\'unity$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(426,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( ( '\'obj$b\'' @ A )
= ( '\'obj$b\'' @ B ) )
& ( ( '\'mor$\'' @ A )
= ( '\'mor$\'' @ B ) )
& ( ( '\'dom$\'' @ A )
= ( '\'dom$\'' @ B ) )
& ( ( '\'cod$\'' @ A )
= ( '\'cod$\'' @ B ) )
& ( ( '\'id$b\'' @ A )
= ( '\'id$b\'' @ B ) )
& ( ( '\'comp$a\'' @ A )
= ( '\'comp$a\'' @ B ) )
& ( ( '\'mor2ZF$\'' @ A )
= ( '\'mor2ZF$\'' @ B ) )
& ( ( '\'more$\'' @ A )
= ( '\'more$\'' @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom365) ).
thf(2202,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( ( '\'obj$b\'' @ A )
= ( '\'obj$b\'' @ B ) )
& ( ( '\'mor$\'' @ A )
= ( '\'mor$\'' @ B ) )
& ( ( '\'dom$\'' @ A )
= ( '\'dom$\'' @ B ) )
& ( ( '\'cod$\'' @ A )
= ( '\'cod$\'' @ B ) )
& ( ( '\'id$b\'' @ A )
= ( '\'id$b\'' @ B ) )
& ( ( '\'comp$a\'' @ A )
= ( '\'comp$a\'' @ B ) )
& ( ( '\'mor2ZF$\'' @ A )
= ( '\'mor2ZF$\'' @ B ) )
& ( ( '\'more$\'' @ A )
= ( '\'more$\'' @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(339,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'uuk$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).
thf(1845,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'uuk$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(19,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ B ) ) )
& ( '\'nTCompDefined$a\'' @ B @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ ( '\'natTransComp$a\'' @ B @ C ) ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ C ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ B ) @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom543) ).
thf(557,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ B ) ) )
& ( '\'nTCompDefined$a\'' @ B @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ ( '\'natTransComp$a\'' @ B @ C ) ) @ A )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ C ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ B ) @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(479,axiom,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ ( '\'yFtor$a\'' @ B ) ) ) )
& ( '\'lSCategory$\'' @ B ) )
=> ( ( '\'mapO$\'' @ ( '\'yFtor$a\'' @ B ) @ A )
= ( '\'homFtorContra$\'' @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom333) ).
thf(2397,plain,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ ( '\'yFtor$a\'' @ B ) ) ) )
& ( '\'lSCategory$\'' @ B ) )
=> ( ( '\'mapO$\'' @ ( '\'yFtor$a\'' @ B ) @ A )
= ( '\'homFtorContra$\'' @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(71,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B )
= ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ B ) @ ( '\'fun_app$m\'' @ ( '\'uuw$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom563) ).
thf(705,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B )
= ( '\'zFfun$\'' @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) @ ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ B ) @ ( '\'fun_app$m\'' @ ( '\'uuw$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(477,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF$\'',C: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'uva$\'' @ A @ B ) @ C )
<=> ( ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ C )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).
thf(2386,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF$\'',C: '\'B$\''] :
( ( ( '\'fun_app$k\'' @ ( '\'uva$\'' @ A @ B ) @ C )
=> ( ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ C )
= B ) ) )
& ( ( ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) )
& ( ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ C )
= B ) )
=> ( '\'fun_app$k\'' @ ( '\'uva$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(255,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) )
=> ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom461) ).
thf(1531,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) )
=> ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( '\'member$d\'' @ C @ ( '\'mor$b\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(142,axiom,
! [A: '\'B$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ B ) )
& ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ B ) @ A )
= C )
& ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ B ) @ A )
= D ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ B @ A @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).
thf(993,plain,
! [A: '\'B$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ B ) )
& ( ( '\'fun_app$t\'' @ ( '\'dom$\'' @ B ) @ A )
= C )
& ( ( '\'fun_app$t\'' @ ( '\'cod$\'' @ B ) @ A )
= D ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ B @ A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(96,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'mor$b\'' @ ( '\'makeCat$\'' @ A ) )
= ( '\'mor$b\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).
thf(776,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'mor$b\'' @ ( '\'makeCat$\'' @ A ) )
= ( '\'mor$b\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(314,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'mor$\'' @ ( '\'oppositeCategory$\'' @ A ) )
= ( '\'mor$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom55) ).
thf(1748,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'mor$\'' @ ( '\'oppositeCategory$\'' @ A ) )
= ( '\'mor$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(47,axiom,
! [A: '\'B_set$\''] :
( ( '\'collect$d\'' @ ( '\'uuc$\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom110) ).
thf(640,plain,
! [A: '\'B_set$\''] :
( ( '\'collect$d\'' @ ( '\'uuc$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(359,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ! [B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'catDom$\'' @ A ) ) @ B ) @ C ) )
= ( '\'comp$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
=> ? [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) )
& ( '\'category$c\'' @ ( '\'catDom$\'' @ A ) )
& ( '\'category$\'' @ ( '\'catCod$\'' @ A ) ) )
=> ( '\'preFunctor$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom384) ).
thf(1961,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ! [B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'catDom$\'' @ A ) ) @ B ) @ C ) )
= ( '\'comp$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
=> ? [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) )
& ( '\'category$c\'' @ ( '\'catDom$\'' @ A ) )
& ( '\'category$\'' @ ( '\'catCod$\'' @ A ) ) )
=> ( '\'preFunctor$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(303,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom322) ).
thf(1711,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(326,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'B$\'',E: '\'A$\'',F: '\'A$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ C @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ D ) @ ( '\'mapO$a\'' @ A @ E ) ) @ ( '\'mapO$a\'' @ A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).
thf(1790,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'B$\'',E: '\'A$\'',F: '\'A$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ C @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ D ) @ ( '\'mapO$a\'' @ A @ E ) ) @ ( '\'mapO$a\'' @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(411,axiom,
! [A: '\'A$\'',B: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$b\'' @ B ) ) )
& ( '\'preFunctor$c\'' @ ( '\'functorComp$h\'' @ B @ C ) )
& ( '\'functor_comp_def$h\'' @ B @ C ) )
=> ( ( '\'mapO$\'' @ ( '\'functorComp$h\'' @ B @ C ) @ A )
= ( '\'mapO$\'' @ C @ ( '\'mapO$f\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom428) ).
thf(2165,plain,
! [A: '\'A$\'',B: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',C: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$b\'' @ B ) ) )
& ( '\'preFunctor$c\'' @ ( '\'functorComp$h\'' @ B @ C ) )
& ( '\'functor_comp_def$h\'' @ B @ C ) )
=> ( ( '\'mapO$\'' @ ( '\'functorComp$h\'' @ B @ C ) @ A )
= ( '\'mapO$\'' @ C @ ( '\'mapO$f\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(217,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'uum$\'' @ A @ B ) @ C )
<=> ( '\'functor_abbrev$\'' @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).
thf(1300,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ ( '\'uum$\'' @ A @ B ) @ C )
=> ( '\'functor_abbrev$\'' @ C @ A @ B ) )
& ( ( '\'functor_abbrev$\'' @ C @ A @ B )
=> ( '\'fun_app$f\'' @ ( '\'uum$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(7,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\'',H: '\'ZF_set$\'',I: '\'ZF_set$\'',J: '\'ZF_ZF_fun$\'',K: '\'ZF_ZF_fun$\'',L: '\'ZF_ZF_fun$\'',M: '\'ZF_ZF_ZF_fun_fun$\'',N: '\'Unit$\''] :
( ( ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G )
= ( '\'category_ext$a\'' @ H @ I @ J @ K @ L @ M @ N ) )
<=> ( ( A = H )
& ( B = I )
& ( C = J )
& ( D = K )
& ( E = L )
& ( F = M )
& ( G = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).
thf(502,plain,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\'',H: '\'ZF_set$\'',I: '\'ZF_set$\'',J: '\'ZF_ZF_fun$\'',K: '\'ZF_ZF_fun$\'',L: '\'ZF_ZF_fun$\'',M: '\'ZF_ZF_ZF_fun_fun$\'',N: '\'Unit$\''] :
( ( ( ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G )
= ( '\'category_ext$a\'' @ H @ I @ J @ K @ L @ M @ N ) )
=> ( ( A = H )
& ( B = I )
& ( C = J )
& ( D = K )
& ( E = L )
& ( F = M )
& ( G = N ) ) )
& ( ( ( A = H )
& ( B = I )
& ( C = J )
& ( D = K )
& ( E = L )
& ( F = M )
& ( G = N ) )
=> ( ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G )
= ( '\'category_ext$a\'' @ H @ I @ J @ K @ L @ M @ N ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(324,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'catDom$a\'' @ ( '\'homFtorContra$\'' @ A @ B ) )
= ( '\'oppositeCategory$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom311) ).
thf(1785,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'catDom$a\'' @ ( '\'homFtorContra$\'' @ A @ B ) )
= ( '\'oppositeCategory$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(319,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_fun$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF_ZF_fun$\''] :
( ! [F: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ F ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$\'' @ B @ F ) ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ ( '\'zFfun$\'' @ A @ C @ B ) ) @ ( '\'zFfun$\'' @ C @ D @ E ) )
= ( '\'zFfun$\'' @ A @ D @ ( '\'fun_app$aa\'' @ ( '\'comp$d\'' @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom601) ).
thf(1763,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_fun$\'',C: '\'ZF$\'',D: '\'ZF$\'',E: '\'ZF_ZF_fun$\''] :
( ! [F: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ F ) @ A )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$\'' @ B @ F ) ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ ( '\'zFfun$\'' @ A @ C @ B ) ) @ ( '\'zFfun$\'' @ C @ D @ E ) )
= ( '\'zFfun$\'' @ A @ D @ ( '\'fun_app$aa\'' @ ( '\'comp$d\'' @ E ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(298,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'preFunctor$c\'' @ A )
<=> ( ! [B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'catDom$\'' @ A ) ) @ B ) @ C ) )
= ( '\'comp$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
=> ? [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) )
& ( '\'category$c\'' @ ( '\'catDom$\'' @ A ) )
& ( '\'category$\'' @ ( '\'catCod$\'' @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom436) ).
thf(1679,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'preFunctor$c\'' @ A )
=> ( ! [B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'catDom$\'' @ A ) ) @ B ) @ C ) )
= ( '\'comp$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
=> ? [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) )
& ( '\'category$c\'' @ ( '\'catDom$\'' @ A ) )
& ( '\'category$\'' @ ( '\'catCod$\'' @ A ) ) ) )
& ( ( ! [B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'catDom$\'' @ A ) @ B ) @ C )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'catDom$\'' @ A ) ) @ B ) @ C ) )
= ( '\'comp$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ C ) ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
=> ? [C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) )
& ( '\'category$c\'' @ ( '\'catDom$\'' @ A ) )
& ( '\'category$\'' @ ( '\'catCod$\'' @ A ) ) )
=> ( '\'preFunctor$c\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(311,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).
thf(1738,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(48,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ A @ B ) @ C )
<=> ? [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ D @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom482) ).
thf(643,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ A @ B ) @ C )
=> ? [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ D @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ D ) ) )
& ( ? [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ D @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(14,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'id$a\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom396) ).
thf(544,plain,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'id$a\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= E ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(159,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) ) @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom409) ).
thf(1038,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) ) @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(31,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'natTransP$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom531) ).
thf(585,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'natTransP$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(206,axiom,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ B ) ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'fun_app$u\'' @ '\'idNatTrans$f\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ B ) ) @ ( '\'mapO$a\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom468) ).
thf(1262,plain,
! [A: '\'A$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ B ) ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'fun_app$u\'' @ '\'idNatTrans$f\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ B ) ) @ ( '\'mapO$a\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(200,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom499) ).
thf(1235,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(450,axiom,
! [A: '\'B$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ ( '\'functorComp$a\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$a\'' @ B @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$c\'' @ C ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ C ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ B ) @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ C ) @ ( '\'mapO$a\'' @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$a\'' @ B ) ) @ A ) ) ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ C ) @ ( '\'mapO$a\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$a\'' @ B ) ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom377) ).
thf(2276,plain,
! [A: '\'B$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ ( '\'functorComp$a\'' @ B @ C ) ) ) )
& ( '\'functor_comp_def$a\'' @ B @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$c\'' @ C ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ C ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ B ) @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ C ) @ ( '\'mapO$a\'' @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$a\'' @ B ) ) @ A ) ) ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ C ) @ ( '\'mapO$a\'' @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$a\'' @ B ) ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(432,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\''] :
( ( '\'homFtorMapContra$\'' @ A @ B @ C )
= ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ ( '\'oppositeCategory$\'' @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom220) ).
thf(2219,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\''] :
( ( '\'homFtorMapContra$\'' @ A @ B @ C )
= ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ ( '\'oppositeCategory$\'' @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(364,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'natTrans$b\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom537) ).
thf(1980,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'natTrans$b\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D ) )
=> ( '\'fun_app$e\'' @ ( '\'compDefined$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(27,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'',D: '\'Unit$\''] :
( ( '\'mapM$\'' @ ( '\'functor_ext$\'' @ A @ B @ C @ D ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom478) ).
thf(576,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$\'',D: '\'Unit$\''] :
( ( '\'mapM$\'' @ ( '\'functor_ext$\'' @ A @ B @ C @ D ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(291,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$a\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom123) ).
thf(1658,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$a\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(464,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'natTransP$b\'' @ A )
<=> ( ( '\'functor$d\'' @ ( '\'nTDom$b\'' @ A ) )
& ( '\'functor$d\'' @ ( '\'nTCod$b\'' @ A ) )
& ( ( '\'nTCatDom$c\'' @ A )
= ( '\'catDom$\'' @ ( '\'nTCod$b\'' @ A ) ) )
& ( ( '\'nTCatCod$c\'' @ A )
= ( '\'catCod$\'' @ ( '\'nTDom$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$c\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ B ) @ ( '\'mapO$\'' @ ( '\'nTDom$b\'' @ A ) @ B ) ) @ ( '\'mapO$\'' @ ( '\'nTCod$b\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) @ ( '\'natTransMap$\'' @ A @ D ) )
= ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom514) ).
thf(2322,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'natTransP$b\'' @ A )
=> ( ( '\'functor$d\'' @ ( '\'nTDom$b\'' @ A ) )
& ( '\'functor$d\'' @ ( '\'nTCod$b\'' @ A ) )
& ( ( '\'nTCatDom$c\'' @ A )
= ( '\'catDom$\'' @ ( '\'nTCod$b\'' @ A ) ) )
& ( ( '\'nTCatCod$c\'' @ A )
= ( '\'catCod$\'' @ ( '\'nTDom$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$c\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ B ) @ ( '\'mapO$\'' @ ( '\'nTDom$b\'' @ A ) @ B ) ) @ ( '\'mapO$\'' @ ( '\'nTCod$b\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) @ ( '\'natTransMap$\'' @ A @ D ) )
= ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ) ) ) )
& ( ( ( '\'functor$d\'' @ ( '\'nTDom$b\'' @ A ) )
& ( '\'functor$d\'' @ ( '\'nTCod$b\'' @ A ) )
& ( ( '\'nTCatDom$c\'' @ A )
= ( '\'catDom$\'' @ ( '\'nTCod$b\'' @ A ) ) )
& ( ( '\'nTCatCod$c\'' @ A )
= ( '\'catCod$\'' @ ( '\'nTDom$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$c\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ B ) @ ( '\'mapO$\'' @ ( '\'nTDom$b\'' @ A ) @ B ) ) @ ( '\'mapO$\'' @ ( '\'nTCod$b\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) @ ( '\'natTransMap$\'' @ A @ D ) )
= ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'natTransP$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(83,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category$a\'' @ A )
=> ( '\'preFunctor$a\'' @ ( '\'identityFunctor$g\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).
thf(744,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'category$a\'' @ A )
=> ( '\'preFunctor$a\'' @ ( '\'identityFunctor$g\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(153,axiom,
! [A: '\'B$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$\'' @ B ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'makeFtor$d\'' @ B ) ) @ A )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom318) ).
thf(1023,plain,
! [A: '\'B$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'member$h\'' @ A @ ( '\'mor$\'' @ ( '\'catDom$\'' @ B ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'makeFtor$d\'' @ B ) ) @ A )
= ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(300,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'homFtorContra$\'' @ A @ B ) @ C )
= ( '\'homSet$\'' @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).
thf(1702,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'homFtorContra$\'' @ A @ B ) @ C )
= ( '\'homSet$\'' @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(197,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ A @ B ) @ C )
<=> ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A )
= B )
& ( ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom522) ).
thf(1221,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ A @ B ) @ C )
=> ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A )
= B )
& ( ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A )
= C ) ) )
& ( ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
& ( ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A )
= B )
& ( ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A )
= C ) )
=> ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(362,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
<=> ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'fun_app$e\'' @ '\'natTransExt$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).
thf(1972,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A )
=> ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'fun_app$e\'' @ '\'natTransExt$\'' @ A ) ) )
& ( ( ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A )
& ( '\'fun_app$e\'' @ '\'natTransExt$\'' @ A ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(77,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'mor$b\'' @ ( '\'oppositeCategory$b\'' @ A ) )
= ( '\'mor$b\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).
thf(727,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'mor$b\'' @ ( '\'oppositeCategory$b\'' @ A ) )
= ( '\'mor$b\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(147,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom319) ).
thf(1008,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(306,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functor$d\'' @ A )
=> ( '\'preFunctor$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom197) ).
thf(1717,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functor$d\'' @ A )
=> ( '\'preFunctor$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(34,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ A @ B ) @ C )
=> ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A )
= B )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom572) ).
thf(595,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ A @ B ) @ C )
=> ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A )
= B )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(387,axiom,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\''] :
( ( ( '\'functor$a\'' @ ( '\'nTDom$\'' @ A ) )
& ( '\'functor$a\'' @ ( '\'nTCod$\'' @ A ) )
& ( ( '\'nTCatDom$a\'' @ A )
= ( '\'catDom$b\'' @ ( '\'nTCod$\'' @ A ) ) )
& ( ( '\'nTCatCod$a\'' @ A )
= ( '\'catCod$f\'' @ ( '\'nTDom$\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$a\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ B ) @ ( '\'mapO$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'mapO$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$a\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'mapM$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ C ) ) @ ( '\'mapM$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) ) ) )
=> ( '\'natTransP$d\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom517) ).
thf(2056,plain,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\''] :
( ( ( '\'functor$a\'' @ ( '\'nTDom$\'' @ A ) )
& ( '\'functor$a\'' @ ( '\'nTCod$\'' @ A ) )
& ( ( '\'nTCatDom$a\'' @ A )
= ( '\'catDom$b\'' @ ( '\'nTCod$\'' @ A ) ) )
& ( ( '\'nTCatCod$a\'' @ A )
= ( '\'catCod$f\'' @ ( '\'nTDom$\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$a\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ B ) @ ( '\'mapO$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'mapO$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$a\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'mapM$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ C ) ) @ ( '\'mapM$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) ) ) )
=> ( '\'natTransP$d\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(236,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'makeCat$\'' @ A ) @ B ) @ C )
<=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).
thf(1404,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'makeCat$\'' @ A ) @ B ) @ C )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C ) )
& ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ ( '\'makeCat$\'' @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(225,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$a\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom321) ).
thf(1353,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$h\'' @ C @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$a\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ C ) ) ) @ ( '\'homSet$\'' @ A @ B @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(469,axiom,
'\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ '\'eta$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'x$\'' ) ) @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).
thf(2357,plain,
'\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ '\'eta$\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'x$\'' ) ) @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(136,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'constFunctor$l\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).
thf(978,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ ( '\'constFunctor$l\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(170,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom317) ).
thf(1140,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ B ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(209,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ ( '\'homFtor$a\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom140) ).
thf(1272,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ '\'functorM$\'' @ ( '\'homFtor$a\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(38,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtorContra$a\'' @ A @ B )
= ( '\'homFtor$a\'' @ ( '\'oppositeCategory$\'' @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom130) ).
thf(612,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtorContra$a\'' @ A @ B )
= ( '\'homFtor$a\'' @ ( '\'oppositeCategory$\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(141,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ '\'set$a\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom404) ).
thf(991,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ '\'set$a\'' @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(276,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ ( '\'zFfun$\'' @ A @ B @ C ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom568) ).
thf(1617,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF_ZF_fun$\''] :
( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ ( '\'zFfun$\'' @ A @ B @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(354,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( A
= ( '\'functor_ext$\'' @ ( '\'catDom$\'' @ A ) @ ( '\'catCod$\'' @ A ) @ ( '\'mapM$\'' @ A ) @ ( '\'more$c\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom475) ).
thf(1940,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( A
= ( '\'functor_ext$\'' @ ( '\'catDom$\'' @ A ) @ ( '\'catCod$\'' @ A ) @ ( '\'mapM$\'' @ A ) @ ( '\'more$c\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(383,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom489) ).
thf(2045,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) @ B )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(262,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'objIso$b\'' @ A @ B ) @ C )
<=> ? [D: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ D @ B ) @ C )
& ( '\'fun_app$k\'' @ ( '\'isomorphism$\'' @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom481) ).
thf(1553,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'objIso$b\'' @ A @ B ) @ C )
=> ? [D: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ D @ B ) @ C )
& ( '\'fun_app$k\'' @ ( '\'isomorphism$\'' @ A ) @ D ) ) )
& ( ? [D: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ D @ B ) @ C )
& ( '\'fun_app$k\'' @ ( '\'isomorphism$\'' @ A ) @ D ) )
=> ( '\'fun_app$l\'' @ ( '\'objIso$b\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(29,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom496) ).
thf(581,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(238,axiom,
! [A: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( '\'functorM$d\'' @ A )
=> ( '\'preFunctor$d\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom148) ).
thf(1412,plain,
! [A: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( '\'functorM$d\'' @ A )
=> ( '\'preFunctor$d\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(252,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'makeCat$a\'' @ A ) @ B @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).
thf(1517,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'makeCat$a\'' @ A ) @ B @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(435,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'functor$d\'' @ ( '\'nTDom$b\'' @ A ) )
& ( '\'functor$d\'' @ ( '\'nTCod$b\'' @ A ) )
& ( ( '\'nTCatDom$c\'' @ A )
= ( '\'catDom$\'' @ ( '\'nTCod$b\'' @ A ) ) )
& ( ( '\'nTCatCod$c\'' @ A )
= ( '\'catCod$\'' @ ( '\'nTDom$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$c\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ B ) @ ( '\'mapO$\'' @ ( '\'nTDom$b\'' @ A ) @ B ) ) @ ( '\'mapO$\'' @ ( '\'nTCod$b\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) @ ( '\'natTransMap$\'' @ A @ D ) )
= ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'natTransP$b\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom519) ).
thf(2226,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'functor$d\'' @ ( '\'nTDom$b\'' @ A ) )
& ( '\'functor$d\'' @ ( '\'nTCod$b\'' @ A ) )
& ( ( '\'nTCatDom$c\'' @ A )
= ( '\'catDom$\'' @ ( '\'nTCod$b\'' @ A ) ) )
& ( ( '\'nTCatCod$c\'' @ A )
= ( '\'catCod$\'' @ ( '\'nTDom$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$c\'' @ A ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ B ) @ ( '\'mapO$\'' @ ( '\'nTDom$b\'' @ A ) @ B ) ) @ ( '\'mapO$\'' @ ( '\'nTCod$b\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$c\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTDom$b\'' @ A ) ) @ B ) @ ( '\'natTransMap$\'' @ A @ D ) )
= ( '\'comp$b\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ C ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'nTCod$b\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'natTransP$b\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(390,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$d\'' @ D @ ( '\'obj$a\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).
thf(2071,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$d\'' @ D @ ( '\'obj$a\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(163,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'ZF$\'',E: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'uur$\'' @ A @ B @ C @ D ) @ E )
= ( '\'zFfun$\'' @ ( '\'homSet$\'' @ A @ E @ B ) @ ( '\'mapO$a\'' @ C @ E ) @ ( '\'fun_app$m\'' @ ( '\'uul$\'' @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom31) ).
thf(1108,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',D: '\'ZF$\'',E: '\'A$\''] :
( ( '\'fun_app$d\'' @ ( '\'uur$\'' @ A @ B @ C @ D ) @ E )
= ( '\'zFfun$\'' @ ( '\'homSet$\'' @ A @ E @ B ) @ ( '\'mapO$a\'' @ C @ E ) @ ( '\'fun_app$m\'' @ ( '\'uul$\'' @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(177,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom403) ).
thf(1157,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(393,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom594) ).
thf(2078,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ A ) @ B )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(65,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'dom$a\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).
thf(688,plain,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'dom$a\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(124,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'uuj$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).
thf(903,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'uuj$\'' @ A ) @ B ) @ C )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(322,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) @ ( '\'mor$a\'' @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom131) ).
thf(1781,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) @ ( '\'mor$a\'' @ ( '\'catExp$\'' @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(195,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catDom$c\'' @ ( '\'identityFunctor$g\'' @ A ) ) ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'identityFunctor$g\'' @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).
thf(1216,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catDom$c\'' @ ( '\'identityFunctor$g\'' @ A ) ) ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'identityFunctor$g\'' @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(119,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( '\'nTCatDom$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) )
= ( '\'oppositeCategory$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom506) ).
thf(891,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( '\'nTCatDom$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) )
= ( '\'oppositeCategory$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(249,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'id$a\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'makeCat$\'' @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom293) ).
thf(1448,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'member$d\'' @ A @ ( '\'obj$a\'' @ B ) )
=> ( ( '\'fun_app$\'' @ ( '\'id$a\'' @ B ) @ A )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'makeCat$\'' @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(419,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B ) ) @ ( '\'homSet$\'' @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).
thf(2187,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B ) ) @ ( '\'homSet$\'' @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(148,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'idNatTrans$d\'' @ A )
= ( '\'natTrans_ext$a\'' @ A @ A @ ( '\'uus$\'' @ A ) @ '\'unity$\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).
thf(1010,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'idNatTrans$d\'' @ A )
= ( '\'natTrans_ext$a\'' @ A @ A @ ( '\'uus$\'' @ A ) @ '\'unity$\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(269,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ ( '\'catCod$a\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) )
= ( '\'mapO$a\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).
thf(1575,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ ( '\'catCod$a\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) )
= ( '\'mapO$a\'' @ A @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(211,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
<=> ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom301) ).
thf(1276,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D )
=> ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= D ) ) )
& ( ( ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) )
& ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B )
= C )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ A ) @ B )
= D ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ A @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(288,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).
thf(1646,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(442,axiom,
! [A: '\'A$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ B ) ) )
& ( '\'preFunctor$c\'' @ ( '\'functorComp$f\'' @ B @ C ) )
& ( '\'functor_comp_def$f\'' @ B @ C ) )
=> ( ( '\'mapO$\'' @ ( '\'functorComp$f\'' @ B @ C ) @ A )
= ( '\'mapO$h\'' @ C @ ( '\'mapO$\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom426) ).
thf(2251,plain,
! [A: '\'A$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ B ) ) )
& ( '\'preFunctor$c\'' @ ( '\'functorComp$f\'' @ B @ C ) )
& ( '\'functor_comp_def$f\'' @ B @ C ) )
=> ( ( '\'mapO$\'' @ ( '\'functorComp$f\'' @ B @ C ) @ A )
= ( '\'mapO$h\'' @ C @ ( '\'mapO$\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(44,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'more$b\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= G ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).
thf(632,plain,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'more$b\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= G ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(203,axiom,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'',B: '\'A$\''] :
( ( ( '\'natTransP$d\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$a\'' @ A ) ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ B ) @ ( '\'mapO$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'mapO$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom525) ).
thf(1244,plain,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\'',B: '\'A$\''] :
( ( ( '\'natTransP$d\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$a\'' @ A ) ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ B ) @ ( '\'mapO$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'mapO$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(99,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'natTransP$b\'' @ A )
=> ( '\'natTrans$b\'' @ ( '\'makeNT$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom126) ).
thf(786,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( '\'natTransP$b\'' @ A )
=> ( '\'natTrans$b\'' @ ( '\'makeNT$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(478,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'zF2mor$\'' @ A @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom51) ).
thf(2394,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'zF2mor$\'' @ A @ ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(32,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) ) )
=> ( ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom567) ).
thf(588,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A ) ) )
=> ( ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ B ) )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(205,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'functor$b\'' @ ( '\'nTDom$d\'' @ A ) )
& ( '\'functor$b\'' @ ( '\'nTCod$d\'' @ A ) )
& ( ( '\'nTCatDom$d\'' @ A )
= ( '\'catDom$c\'' @ ( '\'nTCod$d\'' @ A ) ) )
& ( ( '\'nTCatCod$d\'' @ A )
= ( '\'catCod$c\'' @ ( '\'nTDom$d\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'natTransP$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom521) ).
thf(1253,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$\''] :
( ( ( '\'functor$b\'' @ ( '\'nTDom$d\'' @ A ) )
& ( '\'functor$b\'' @ ( '\'nTCod$d\'' @ A ) )
& ( ( '\'nTCatDom$d\'' @ A )
= ( '\'catDom$c\'' @ ( '\'nTCod$d\'' @ A ) ) )
& ( ( '\'nTCatCod$d\'' @ A )
= ( '\'catCod$c\'' @ ( '\'nTDom$d\'' @ A ) ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'nTCatDom$d\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$d\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ B ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'mapO$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) )
& ! [B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatDom$d\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTDom$d\'' @ A ) ) @ B ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$d\'' @ A ) ) @ ( '\'fun_app$\'' @ ( '\'natTransMap$d\'' @ A ) @ C ) ) @ ( '\'fun_app$\'' @ ( '\'mapM$d\'' @ ( '\'nTCod$d\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'natTransP$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(70,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ '\'set$\'' @ A ) @ B )
& ( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B ) ) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom573) ).
thf(699,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
~ ( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ '\'set$\'' @ A ) @ B )
& ~ ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(414,axiom,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'B$\''] :
( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ B ) @ C ) ) ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ B ) @ C ) @ A )
= ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom507) ).
thf(2174,plain,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'B$\''] :
( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ B ) @ C ) ) ) )
=> ( ( '\'natTransMap$b\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ B ) @ C ) @ A )
= ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(453,axiom,
'\'member$i\'' @ '\'y$\'' @ ( '\'obj$b\'' @ '\'c$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom37) ).
thf(2283,plain,
'\'member$i\'' @ '\'y$\'' @ ( '\'obj$b\'' @ '\'c$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(394,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).
thf(2081,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(23,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'constFunctor$b\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).
thf(568,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'category$a\'' @ B )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ B ) ) )
=> ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'constFunctor$b\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(219,axiom,
! [A: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( '\'functor$e\'' @ A )
=> ( '\'preFunctor$d\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom198) ).
thf(1308,plain,
! [A: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\''] :
( ( '\'functor$e\'' @ A )
=> ( '\'preFunctor$d\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(188,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'hOMCollection$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C )
= ( '\'hOMCollection$\'' @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom590) ).
thf(1193,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'hOMCollection$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C )
= ( '\'hOMCollection$\'' @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(417,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'B$\'',E: '\'A$\'',F: '\'A$\''] :
( ( ( '\'functor_abbrev$f\'' @ A @ B @ C )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ D ) @ ( '\'mapO$\'' @ A @ E ) ) @ ( '\'mapO$\'' @ A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).
thf(2183,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'B$\'',E: '\'A$\'',F: '\'A$\''] :
( ( ( '\'functor_abbrev$f\'' @ A @ B @ C )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ C @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ D ) @ ( '\'mapO$\'' @ A @ E ) ) @ ( '\'mapO$\'' @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(122,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom144) ).
thf(899,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(63,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'makeFtor$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).
thf(684,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functorM$\'' @ A )
=> ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'makeFtor$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(16,axiom,
! [A: '\'ZF_set$\''] :
( ( '\'collect$c\'' @ ( '\'uua$\'' @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).
thf(549,plain,
! [A: '\'ZF_set$\''] :
( ( '\'collect$c\'' @ ( '\'uua$\'' @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(375,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'makeFtor$\'' @ A ) @ B )
= ( '\'mapO$a\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom283) ).
thf(2019,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( ( '\'mapO$a\'' @ ( '\'makeFtor$\'' @ A ) @ B )
= ( '\'mapO$a\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(105,axiom,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( '\'functor$b\'' @ A )
=> ( '\'preFunctor$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom195) ).
thf(800,plain,
! [A: '\'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$\''] :
( ( '\'functor$b\'' @ A )
=> ( '\'preFunctor$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(56,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functor$d\'' @ A )
=> ( '\'functorM$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom203) ).
thf(667,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functor$d\'' @ A )
=> ( '\'functorM$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(215,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'equivalence$a\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ D @ ( '\'mapO$\'' @ A @ B ) ) @ ( '\'mapO$\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom367) ).
thf(1294,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'equivalence$a\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ A ) ) )
& ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'catCod$\'' @ A ) @ D @ ( '\'mapO$\'' @ A @ B ) ) @ ( '\'mapO$\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ E )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(273,axiom,
! [A: '\'A_set$\'',B: '\'B_set$\'',C: '\'B_a_fun$\'',D: '\'B_a_fun$\'',E: '\'A_b_fun$\'',F: '\'B_b_b_fun_fun$\'',G: '\'B_c_LSCategory_ext$\''] :
( ( '\'obj$b\'' @ ( '\'category_ext$\'' @ A @ B @ C @ D @ E @ F @ G ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom392) ).
thf(1607,plain,
! [A: '\'A_set$\'',B: '\'B_set$\'',C: '\'B_a_fun$\'',D: '\'B_a_fun$\'',E: '\'A_b_fun$\'',F: '\'B_b_b_fun_fun$\'',G: '\'B_c_LSCategory_ext$\''] :
( ( '\'obj$b\'' @ ( '\'category_ext$\'' @ A @ B @ C @ D @ E @ F @ G ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(90,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'category$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).
thf(763,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'category$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(371,axiom,
! [A: '\'B_ZF_fun_set$\'',B: '\'B_ZF_fun$\''] :
( ( '\'fun_app$h\'' @ ( '\'uud$\'' @ A ) @ B )
<=> ( '\'member$e\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
thf(2003,plain,
! [A: '\'B_ZF_fun_set$\'',B: '\'B_ZF_fun$\''] :
( ( ( '\'fun_app$h\'' @ ( '\'uud$\'' @ A ) @ B )
=> ( '\'member$e\'' @ B @ A ) )
& ( ( '\'member$e\'' @ B @ A )
=> ( '\'fun_app$h\'' @ ( '\'uud$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(445,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF$\''] :
( ( '\'zF2mor$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B )
= ( '\'zF2mor$\'' @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).
thf(2258,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF$\''] :
( ( '\'zF2mor$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B )
= ( '\'zF2mor$\'' @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(474,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'member$e\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'extensional$a\'' @ ( '\'mor$\'' @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom483) ).
thf(2374,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( '\'lSCategory$\'' @ A )
=> ( '\'member$e\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'extensional$a\'' @ ( '\'mor$\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(251,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorExt$d\'' @ A )
<=> ( '\'member$m\'' @ ( '\'mapM$\'' @ A ) @ ( '\'extensional$\'' @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom477) ).
thf(1512,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'functorExt$d\'' @ A )
=> ( '\'member$m\'' @ ( '\'mapM$\'' @ A ) @ ( '\'extensional$\'' @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) ) )
& ( ( '\'member$m\'' @ ( '\'mapM$\'' @ A ) @ ( '\'extensional$\'' @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( '\'functorExt$d\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(309,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( '\'mapO$a\'' @ A @ B )
= ( '\'the$\'' @ ( '\'uuu$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom561) ).
thf(1725,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( '\'mapO$a\'' @ A @ B )
= ( '\'the$\'' @ ( '\'uuu$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(270,axiom,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\''] :
( ( '\'natTransP$d\'' @ A )
<=> ( ( '\'functor$a\'' @ ( '\'nTDom$\'' @ A ) )
& ( '\'functor$a\'' @ ( '\'nTCod$\'' @ A ) )
& ( ( '\'nTCatDom$a\'' @ A )
= ( '\'catDom$b\'' @ ( '\'nTCod$\'' @ A ) ) )
& ( ( '\'nTCatCod$a\'' @ A )
= ( '\'catCod$f\'' @ ( '\'nTDom$\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$a\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ B ) @ ( '\'mapO$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'mapO$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$a\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'mapM$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ C ) ) @ ( '\'mapM$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom512) ).
thf(1578,plain,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$\''] :
( ( ( '\'natTransP$d\'' @ A )
=> ( ( '\'functor$a\'' @ ( '\'nTDom$\'' @ A ) )
& ( '\'functor$a\'' @ ( '\'nTCod$\'' @ A ) )
& ( ( '\'nTCatDom$a\'' @ A )
= ( '\'catDom$b\'' @ ( '\'nTCod$\'' @ A ) ) )
& ( ( '\'nTCatCod$a\'' @ A )
= ( '\'catCod$f\'' @ ( '\'nTDom$\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$a\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ B ) @ ( '\'mapO$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'mapO$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$a\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'mapM$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ C ) ) @ ( '\'mapM$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) ) ) ) )
& ( ( ( '\'functor$a\'' @ ( '\'nTDom$\'' @ A ) )
& ( '\'functor$a\'' @ ( '\'nTCod$\'' @ A ) )
& ( ( '\'nTCatDom$a\'' @ A )
= ( '\'catDom$b\'' @ ( '\'nTCod$\'' @ A ) ) )
& ( ( '\'nTCatCod$a\'' @ A )
= ( '\'catCod$f\'' @ ( '\'nTDom$\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$a\'' @ A ) ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatCod$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ B ) @ ( '\'mapO$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'mapO$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$a\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'mapM$f\'' @ ( '\'nTDom$\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ D ) )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ ( '\'nTCatCod$a\'' @ A ) ) @ ( '\'fun_app$r\'' @ ( '\'natTransMap$a\'' @ A ) @ C ) ) @ ( '\'mapM$f\'' @ ( '\'nTCod$\'' @ A ) @ B ) ) ) ) )
=> ( '\'natTransP$d\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(132,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'homSet$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C )
= ( '\'homSet$\'' @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom52) ).
thf(950,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'homSet$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ C )
= ( '\'homSet$\'' @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(259,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'makeCat$\'' @ A ) ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom405) ).
thf(1546,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ A @ B ) @ C )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'makeCat$\'' @ A ) ) @ B ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(279,axiom,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',D: '\'B$\'',E: '\'A$\'',F: '\'A$\''] :
( ( ( '\'functor_abbrev$e\'' @ A @ B @ C )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ C @ ( '\'mapM$f\'' @ A @ D ) @ ( '\'mapO$f\'' @ A @ E ) ) @ ( '\'mapO$f\'' @ A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).
thf(1625,plain,
! [A: '\'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',D: '\'B$\'',E: '\'A$\'',F: '\'A$\''] :
( ( ( '\'functor_abbrev$e\'' @ A @ B @ C )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ C @ ( '\'mapM$f\'' @ A @ D ) @ ( '\'mapO$f\'' @ A @ E ) ) @ ( '\'mapO$f\'' @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(372,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom206) ).
thf(2008,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D ) )
=> ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(296,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( A
= ( '\'category_ext$a\'' @ ( '\'obj$a\'' @ A ) @ ( '\'mor$b\'' @ A ) @ ( '\'dom$a\'' @ A ) @ ( '\'cod$a\'' @ A ) @ ( '\'id$a\'' @ A ) @ ( '\'comp$\'' @ A ) @ ( '\'more$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).
thf(1673,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( A
= ( '\'category_ext$a\'' @ ( '\'obj$a\'' @ A ) @ ( '\'mor$b\'' @ A ) @ ( '\'dom$a\'' @ A ) @ ( '\'cod$a\'' @ A ) @ ( '\'id$a\'' @ A ) @ ( '\'comp$\'' @ A ) @ ( '\'more$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(101,axiom,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'comp$\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= F ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom395) ).
thf(790,plain,
! [A: '\'ZF_set$\'',B: '\'ZF_set$\'',C: '\'ZF_ZF_fun$\'',D: '\'ZF_ZF_fun$\'',E: '\'ZF_ZF_fun$\'',F: '\'ZF_ZF_ZF_fun_fun$\'',G: '\'Unit$\''] :
( ( '\'comp$\'' @ ( '\'category_ext$a\'' @ A @ B @ C @ D @ E @ F @ G ) )
= F ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(36,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\''] :
( ( '\'mor$a\'' @ ( '\'oppositeCategory$a\'' @ A ) )
= ( '\'mor$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).
thf(603,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\''] :
( ( '\'mor$a\'' @ ( '\'oppositeCategory$a\'' @ A ) )
= ( '\'mor$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(80,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom480) ).
thf(735,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) )
=> ( '\'fun_app$b\'' @ ( '\'isomorphism$b\'' @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(144,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'oppositeCategory$b\'' @ A )
= ( '\'category_ext$a\'' @ ( '\'obj$a\'' @ A ) @ ( '\'mor$b\'' @ A ) @ ( '\'cod$a\'' @ A ) @ ( '\'dom$a\'' @ A ) @ ( '\'id$a\'' @ A ) @ ( '\'uuk$\'' @ A ) @ ( '\'more$b\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom545) ).
thf(999,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'oppositeCategory$b\'' @ A )
= ( '\'category_ext$a\'' @ ( '\'obj$a\'' @ A ) @ ( '\'mor$b\'' @ A ) @ ( '\'cod$a\'' @ A ) @ ( '\'dom$a\'' @ A ) @ ( '\'id$a\'' @ A ) @ ( '\'uuk$\'' @ A ) @ ( '\'more$b\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(455,axiom,
'\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) @ ( '\'mapO$a\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ '\'x$\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom42) ).
thf(2287,plain,
'\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'yMap$\'' @ '\'c$\'' @ '\'x$\'' @ '\'eta$\'' ) ) @ ( '\'mapO$a\'' @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ '\'c$\'' ) @ '\'y$\'' ) @ '\'x$\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(41,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'functorM$c\'' @ A )
<=> ( ( '\'preFunctor$c\'' @ A )
& ( '\'functorM_axioms$c\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).
thf(620,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'functorM$c\'' @ A )
=> ( ( '\'preFunctor$c\'' @ A )
& ( '\'functorM_axioms$c\'' @ A ) ) )
& ( ( ( '\'preFunctor$c\'' @ A )
& ( '\'functorM_axioms$c\'' @ A ) )
=> ( '\'functorM$c\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(400,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'yFtor$\'' @ A ) ) @ B )
= ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom84) ).
thf(2102,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'yFtor$\'' @ A ) ) @ B )
= ( '\'fun_app$q\'' @ ( '\'yFtorNT$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(86,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtor$\'' @ A @ B )
= ( '\'makeFtor$\'' @ ( '\'homFtor$a\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).
thf(752,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( '\'homFtor$\'' @ A @ B )
= ( '\'makeFtor$\'' @ ( '\'homFtor$a\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(407,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'uul$\'' @ A @ B ) @ C ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ B ) @ ( '\'zF2mor$\'' @ A @ D ) ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom29) ).
thf(2155,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'uul$\'' @ A @ B ) @ C ) @ D )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ B ) @ ( '\'zF2mor$\'' @ A @ D ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(444,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF$\''] :
( ( '\'zF2mor$\'' @ A @ B )
= ( '\'the$b\'' @ ( '\'uva$\'' @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom579) ).
thf(2255,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'ZF$\''] :
( ( '\'zF2mor$\'' @ A @ B )
= ( '\'the$b\'' @ ( '\'uva$\'' @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(366,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( ( '\'member$d\'' @ ( '\'mapO$a\'' @ A @ B ) @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ ( '\'mapO$a\'' @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom363) ).
thf(1989,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\''] :
( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) ) )
=> ( ( '\'member$d\'' @ ( '\'mapO$a\'' @ A @ B ) @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ ( '\'mapO$a\'' @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(332,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ A @ B ) @ C )
=> ( A
= ( '\'zFfun$\'' @ B @ C @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom554) ).
thf(1816,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ A @ B ) @ C )
=> ( A
= ( '\'zFfun$\'' @ B @ C @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(398,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'uuv$\'' @ A @ B ) @ C )
<=> ( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom22) ).
thf(2091,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ ( '\'uuv$\'' @ A @ B ) @ C )
=> ( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) ) )
& ( ( ( '\'member$a\'' @ C @ ( '\'obj$\'' @ ( '\'catCod$\'' @ A ) ) )
& ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ A ) ) @ B ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ A ) @ C ) ) )
=> ( '\'fun_app$f\'' @ ( '\'uuv$\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(347,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'B$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) )
=> ( '\'category_axioms$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom441) ).
thf(1891,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( '\'member$i\'' @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) @ ( '\'obj$b\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ B ) @ B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ A ) @ B ) ) ) @ B )
= B ) )
& ! [B: '\'B$\''] :
( ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ ( '\'fun_app$t\'' @ ( '\'cod$\'' @ A ) @ B ) ) )
= B ) )
& ! [B: '\'B$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ C ) ) @ D )
= ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ B ) @ E ) @ C ) @ F ) ) )
=> ( '\'category_axioms$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(111,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'member$\'' @ A @ ( '\'mor$a\'' @ ( '\'catExp$\'' @ B @ C ) ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom143) ).
thf(828,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'member$\'' @ A @ ( '\'mor$a\'' @ ( '\'catExp$\'' @ B @ C ) ) )
=> ( '\'fun_app$e\'' @ '\'natTrans$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(382,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ ( '\'uuh$\'' @ A ) @ B )
<=> ( '\'member$a\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
thf(2040,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ ( '\'uuh$\'' @ A ) @ B )
=> ( '\'member$a\'' @ B @ A ) )
& ( ( '\'member$a\'' @ B @ A )
=> ( '\'fun_app$f\'' @ ( '\'uuh$\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(134,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom346) ).
thf(955,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'member$d\'' @ B @ ( '\'mor$b\'' @ A ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'id$a\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'dom$a\'' @ A ) @ B ) ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(274,axiom,
! [A: '\'ZF$\'',B: '\'ZF_bool_fun$\''] :
( ( '\'member$d\'' @ A @ ( '\'collect$c\'' @ B ) )
<=> ( '\'fun_app$b\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).
thf(1610,plain,
! [A: '\'ZF$\'',B: '\'ZF_bool_fun$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'collect$c\'' @ B ) )
=> ( '\'fun_app$b\'' @ B @ A ) )
& ( ( '\'fun_app$b\'' @ B @ A )
=> ( '\'member$d\'' @ A @ ( '\'collect$c\'' @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(182,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A )
<=> ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ C ) ) @ ( '\'mapO$a\'' @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom353) ).
thf(1172,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A )
=> ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ C ) ) @ ( '\'mapO$a\'' @ A @ D ) ) ) )
& ( ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B ) @ ( '\'mapO$a\'' @ A @ C ) ) @ ( '\'mapO$a\'' @ A @ D ) ) )
=> ( '\'fun_app$f\'' @ '\'functorM_axioms$d\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(121,axiom,
! [A: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'functor_abbrev$a\'' @ A @ B @ C )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ C @ ( '\'mapM$b\'' @ A @ D ) @ ( '\'mapO$b\'' @ A @ E ) ) @ ( '\'mapO$b\'' @ A @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom73) ).
thf(897,plain,
! [A: '\'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',D: '\'ZF$\'',E: '\'ZF$\'',F: '\'ZF$\''] :
( ( ( '\'functor_abbrev$a\'' @ A @ B @ C )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ B @ D @ E ) @ F ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ C @ ( '\'mapM$b\'' @ A @ D ) @ ( '\'mapO$b\'' @ A @ E ) ) @ ( '\'mapO$b\'' @ A @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(157,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( ( '\'catDom$\'' @ A )
= ( '\'catDom$\'' @ B ) )
& ( ( '\'catCod$\'' @ A )
= ( '\'catCod$\'' @ B ) )
& ( ( '\'mapM$\'' @ A )
= ( '\'mapM$\'' @ B ) )
& ( ( '\'more$c\'' @ A )
= ( '\'more$c\'' @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom472) ).
thf(1033,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( ( '\'catDom$\'' @ A )
= ( '\'catDom$\'' @ B ) )
& ( ( '\'catCod$\'' @ A )
= ( '\'catCod$\'' @ B ) )
& ( ( '\'mapM$\'' @ A )
= ( '\'mapM$\'' @ B ) )
& ( ( '\'more$c\'' @ A )
= ( '\'more$c\'' @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(213,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ D ) )
= ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom434) ).
thf(1288,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'B$\'',D: '\'B$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ C ) @ D ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ '\'set$\'' ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ D ) )
= ( '\'fun_app$p\'' @ ( '\'homFtorMap$\'' @ A @ B ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(434,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'uuq$\'' @ A @ B ) @ C )
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'zF2mor$\'' @ A @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom26) ).
thf(2223,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'ZF$\''] :
( ( '\'fun_app$\'' @ ( '\'uuq$\'' @ A @ B ) @ C )
= ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'zF2mor$\'' @ A @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(45,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ C )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B ) )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ C )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ C ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom565) ).
thf(635,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ C )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B ) )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ C )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ C ) ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ C ) ) @ B )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ A ) @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunComp$\'' @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(74,axiom,
( '\'set$\''
= ( '\'makeCat$\'' @ '\'set$a\'' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom289) ).
thf(720,plain,
( '\'set$\''
= ( '\'makeCat$\'' @ '\'set$a\'' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(180,axiom,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ B ) )
& ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ B ) @ A )
= C )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ B ) @ A )
= D ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ B @ A @ C ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).
thf(1165,plain,
! [A: '\'ZF$\'',B: '\'ZF_ZF_unit_Category_ext$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'member$d\'' @ A @ ( '\'mor$b\'' @ B ) )
& ( ( '\'fun_app$\'' @ ( '\'dom$a\'' @ B ) @ A )
= C )
& ( ( '\'fun_app$\'' @ ( '\'cod$a\'' @ B ) @ A )
= D ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ B @ A @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(438,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'homFtorContra$\'' @ A @ C ) ) @ B )
= ( '\'homFtorMapContra$\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom139) ).
thf(2241,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ A ) ) )
=> ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'homFtorContra$\'' @ A @ C ) ) @ B )
= ( '\'homFtorMapContra$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(26,axiom,
'\'category$a\'' @ '\'set$\'',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom279) ).
thf(575,plain,
'\'category$a\'' @ '\'set$\'',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(229,axiom,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ ( '\'yFtor$a\'' @ B ) ) ) )
& ( '\'lSCategory$\'' @ B ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'yFtor$a\'' @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ ( '\'yFtor$a\'' @ B ) ) ) @ A ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ ( '\'yFtor$a\'' @ B ) ) @ ( '\'homFtorContra$\'' @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom342) ).
thf(1384,plain,
! [A: '\'A$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\''] :
( ( ( '\'member$i\'' @ A @ ( '\'obj$b\'' @ ( '\'catDom$\'' @ ( '\'yFtor$a\'' @ B ) ) ) )
& ( '\'lSCategory$\'' @ B ) )
=> ( ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ ( '\'yFtor$a\'' @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$\'' @ ( '\'yFtor$a\'' @ B ) ) ) @ A ) )
= ( '\'id$\'' @ ( '\'catCod$\'' @ ( '\'yFtor$a\'' @ B ) ) @ ( '\'homFtorContra$\'' @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(8,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'obj$a\'' @ ( '\'oppositeCategory$b\'' @ A ) )
= ( '\'obj$a\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom57) ).
thf(528,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\''] :
( ( '\'obj$a\'' @ ( '\'oppositeCategory$b\'' @ A ) )
= ( '\'obj$a\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(304,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C )
=> ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'oppositeCategory$\'' @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom391) ).
thf(1713,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'B$\''] :
( ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ C )
=> ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ ( '\'oppositeCategory$\'' @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(66,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'functorM_axioms$c\'' @ A ) )
=> ( '\'functorM$c\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).
thf(691,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'preFunctor$c\'' @ A )
& ( '\'functorM_axioms$c\'' @ A ) )
=> ( '\'functorM$c\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(234,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) )
= ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom340) ).
thf(1399,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( ( '\'fun_app$n\'' @ ( '\'fun_app$o\'' @ ( '\'comp$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) )
= ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(352,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B ) )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ B ) )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ! [C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ B ) @ C ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom571) ).
thf(1930,plain,
! [A: '\'ZF$\'',B: '\'ZF$\''] :
( ( ( ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A )
= ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ B ) )
& ( ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ A )
= ( '\'fun_app$\'' @ '\'zFfunCod$\'' @ B ) )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ A )
& ( '\'fun_app$b\'' @ '\'isZFfun$\'' @ B )
& ! [C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ ( '\'fun_app$\'' @ '\'zFfunDom$\'' @ A ) )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ C )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ B ) @ C ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(468,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'homSet$\'' @ A @ B @ C ) ) )
=> ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'zF2mor$\'' @ A @ D ) @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'zF2mor$\'' @ A @ D ) )
= D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).
thf(2353,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ ( '\'homSet$\'' @ A @ B @ C ) ) )
=> ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ ( '\'zF2mor$\'' @ A @ D ) @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mor2ZF$\'' @ A ) @ ( '\'zF2mor$\'' @ A @ D ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(114,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( '\'fun_app$f\'' @ '\'equivalence_axioms$\'' @ A )
<=> ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ D @ ( '\'mapO$a\'' @ A @ B ) ) @ ( '\'mapO$a\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B )
= ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'mapO$a\'' @ A @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom439) ).
thf(839,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'equivalence_axioms$\'' @ A )
=> ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ D @ ( '\'mapO$a\'' @ A @ B ) ) @ ( '\'mapO$a\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B )
= ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'mapO$a\'' @ A @ C ) ) @ B ) ) ) ) )
& ( ( ! [B: '\'A$\'',C: '\'A$\'',D: '\'ZF$\''] :
( ( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'catCod$a\'' @ A ) @ D @ ( '\'mapO$a\'' @ A @ B ) ) @ ( '\'mapO$a\'' @ A @ C ) ) )
=> ? [E: '\'B$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ B ) @ C )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E )
= D ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'catDom$a\'' @ A ) @ E @ C ) @ D )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ B )
= ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) )
=> ( B = E ) )
& ! [B: '\'ZF$\''] :
( ( '\'member$d\'' @ B @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
=> ? [C: '\'A$\''] :
( ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'fun_app$b\'' @ ( '\'objIso$a\'' @ ( '\'catCod$a\'' @ A ) @ ( '\'mapO$a\'' @ A @ C ) ) @ B ) ) ) )
=> ( '\'fun_app$f\'' @ '\'equivalence_axioms$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(138,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ C ) ) )
=> ( ( '\'mapO$a\'' @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom361) ).
thf(982,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A$\'',C: '\'ZF$\''] :
( ( ( '\'fun_app$f\'' @ '\'preFunctor$\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'catDom$a\'' @ A ) ) )
& ( '\'member$d\'' @ C @ ( '\'obj$a\'' @ ( '\'catCod$a\'' @ A ) ) )
& ( ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ ( '\'catDom$a\'' @ A ) ) @ B ) )
= ( '\'fun_app$\'' @ ( '\'id$a\'' @ ( '\'catCod$a\'' @ A ) ) @ C ) ) )
=> ( ( '\'mapO$a\'' @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(245,axiom,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ D ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom371) ).
thf(1431,plain,
! [A: '\'ZF$\'',B: '\'ZF$\'',C: '\'ZF$\'',D: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ '\'set$\'' @ A @ B ) @ C )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ B ) )
=> ( '\'fun_app$b\'' @ ( '\'elem$\'' @ ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ '\'zFfunApp$\'' @ A ) @ D ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(340,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).
thf(1848,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\'',E: '\'B$\'',F: '\'A$\''] :
( ( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
& ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ E @ D ) @ F ) )
=> ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ A @ B ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(240,axiom,
! [A: '\'ZF$\'',B: '\'ZF_bool_fun$\'',C: '\'ZF$\''] :
( ( ! [D: '\'ZF$\''] :
( ( ! [E: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ E ) @ D )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ E ) @ A ) )
=> ( '\'fun_app$b\'' @ B @ E ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ A ) )
=> ( '\'fun_app$b\'' @ B @ D ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom597) ).
thf(1416,plain,
! [A: '\'ZF$\'',B: '\'ZF_bool_fun$\'',C: '\'ZF$\''] :
( ( ! [D: '\'ZF$\''] :
( ( ! [E: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ E ) @ D )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ E ) @ A ) )
=> ( '\'fun_app$b\'' @ B @ E ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ A ) )
=> ( '\'fun_app$b\'' @ B @ D ) )
& ( '\'fun_app$b\'' @ ( '\'elem$\'' @ C ) @ A ) )
=> ( '\'fun_app$b\'' @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(467,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'B$\'',E: '\'B$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ B @ D ) @ E ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ C @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ D ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom408) ).
thf(2351,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',C: '\'ZF_ZF_unit_Category_ext$\'',D: '\'B$\'',E: '\'B$\''] :
( ( ( '\'functor_abbrev$\'' @ A @ B @ C )
& ( '\'fun_app$k\'' @ ( '\'compDefined$a\'' @ B @ D ) @ E ) )
=> ( '\'fun_app$b\'' @ ( '\'compDefined$\'' @ C @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ D ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(72,axiom,
! [A: '\'ZF_bool_fun$\'',B: '\'ZF_bool_fun$\''] :
( ! [C: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ A @ C )
<=> ( '\'fun_app$b\'' @ B @ C ) )
=> ( ( '\'collect$c\'' @ A )
= ( '\'collect$c\'' @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).
thf(708,plain,
! [A: '\'ZF_bool_fun$\'',B: '\'ZF_bool_fun$\''] :
( ! [C: '\'ZF$\''] :
( ( ( '\'fun_app$b\'' @ A @ C )
=> ( '\'fun_app$b\'' @ B @ C ) )
& ( ( '\'fun_app$b\'' @ B @ C )
=> ( '\'fun_app$b\'' @ A @ C ) ) )
=> ( ( '\'collect$c\'' @ A )
= ( '\'collect$c\'' @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(54,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$\'' @ B )
& ( '\'member$a\'' @ C @ ( '\'obj$\'' @ B ) ) )
=> ( '\'functorM$d\'' @ ( '\'constFunctor$s\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom245) ).
thf(659,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$\'',C: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'category$\'' @ B )
& ( '\'member$a\'' @ C @ ( '\'obj$\'' @ B ) ) )
=> ( '\'functorM$d\'' @ ( '\'constFunctor$s\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(265,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'member$h\'' @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ ( '\'mor$\'' @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom314) ).
thf(1565,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\''] :
( ( ( '\'category$c\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ A ) ) )
=> ( '\'member$h\'' @ ( '\'fun_app$r\'' @ ( '\'id$b\'' @ A ) @ B ) @ ( '\'mor$\'' @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(437,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ D @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ C ) ) @ B ) )
=> ( ( '\'yMapInv$\'' @ A @ C @ B @ ( '\'yMap$\'' @ A @ C @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).
thf(2238,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',C: '\'A$\'',D: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'lSCategory$\'' @ A )
& ( '\'functor_abbrev$\'' @ B @ ( '\'oppositeCategory$\'' @ A ) @ '\'set$\'' )
& ( '\'member$i\'' @ C @ ( '\'obj$b\'' @ A ) )
& ( '\'fun_app$f\'' @ ( '\'nt_abbrev$\'' @ D @ ( '\'mapO$\'' @ ( '\'yFtor$\'' @ A ) @ C ) ) @ B ) )
=> ( ( '\'yMapInv$\'' @ A @ C @ B @ ( '\'yMap$\'' @ A @ C @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(20,axiom,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom493) ).
thf(560,plain,
! [A: '\'ZF_ZF_unit_Category_ext$\'',B: '\'ZF$\'',C: '\'ZF$\''] :
( ( ( '\'category$a\'' @ A )
& ( '\'fun_app$b\'' @ ( '\'inverse_rel$\'' @ A @ B ) @ C ) )
=> ( ( '\'fun_app$\'' @ ( '\'inverse$\'' @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(320,axiom,
! [A: '\'ZF_bool_fun$\'',B: '\'ZF$\''] :
( ( ? [C: '\'ZF$\''] :
! [D: '\'ZF$\''] :
( ~ ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ C )
=> ( '\'fun_app$b\'' @ A @ D ) )
& ! [C: '\'ZF$\''] :
( ! [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ C )
=> ( '\'fun_app$b\'' @ A @ D ) )
=> ( '\'fun_app$b\'' @ A @ C ) ) )
=> ( '\'fun_app$b\'' @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom596) ).
thf(1769,plain,
! [A: '\'ZF_bool_fun$\'',B: '\'ZF$\''] :
( ( ? [C: '\'ZF$\''] :
! [D: '\'ZF$\''] :
( ~ ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ C )
=> ( '\'fun_app$b\'' @ A @ D ) )
& ! [C: '\'ZF$\''] :
( ! [D: '\'ZF$\''] :
( ( '\'fun_app$b\'' @ ( '\'elem$\'' @ D ) @ C )
=> ( '\'fun_app$b\'' @ A @ D ) )
=> ( '\'fun_app$b\'' @ A @ C ) ) )
=> ( '\'fun_app$b\'' @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(87,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'hOMCollection$\'' @ A @ B @ C )
= ( '\'collect$c\'' @ ( '\'uvf$\'' @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom589) ).
thf(755,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'A$\'',C: '\'A$\''] :
( ( '\'hOMCollection$\'' @ A @ B @ C )
= ( '\'collect$c\'' @ ( '\'uvf$\'' @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(421,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A$\''] :
( ( ( '\'natTransP$b\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$c\'' @ A ) ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ B ) @ ( '\'mapO$\'' @ ( '\'nTDom$b\'' @ A ) @ B ) ) @ ( '\'mapO$\'' @ ( '\'nTCod$b\'' @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom524) ).
thf(2191,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\'',B: '\'A$\''] :
( ( ( '\'natTransP$b\'' @ A )
& ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$c\'' @ A ) ) ) )
=> ( '\'fun_app$f\'' @ ( '\'mapsTo$a\'' @ ( '\'nTCatCod$c\'' @ A ) @ ( '\'natTransMap$\'' @ A @ B ) @ ( '\'mapO$\'' @ ( '\'nTDom$b\'' @ A ) @ B ) ) @ ( '\'mapO$\'' @ ( '\'nTCod$b\'' @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(191,axiom,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom87) ).
thf(1204,plain,
! [A: '\'A_b_b_c_LSCategory_ext_Category_ext$\'',B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ A @ B @ C ) @ D )
=> ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'oppositeCategory$\'' @ A ) @ B @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(118,axiom,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) )
& ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) )
& ( ( '\'nTCatDom$\'' @ A )
= ( '\'catDom$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) )
& ( ( '\'nTCatCod$\'' @ A )
= ( '\'catCod$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ B ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) @ B ) ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom520) ).
thf(882,plain,
! [A: '\'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$\''] :
( ( ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) )
& ( '\'fun_app$f\'' @ '\'functor$\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) )
& ( ( '\'nTCatDom$\'' @ A )
= ( '\'catDom$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) )
& ( ( '\'nTCatCod$\'' @ A )
= ( '\'catCod$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) )
& ! [B: '\'A$\''] :
( ( '\'member$i\'' @ B @ ( '\'obj$b\'' @ ( '\'nTCatDom$\'' @ A ) ) )
=> ( '\'fun_app$b\'' @ ( '\'mapsTo$b\'' @ ( '\'nTCatCod$\'' @ A ) @ ( '\'natTransMap$b\'' @ A @ B ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) @ B ) ) @ ( '\'mapO$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) @ B ) ) )
& ! [B: '\'B$\'',C: '\'A$\'',D: '\'A$\''] :
( ( '\'fun_app$l\'' @ ( '\'mapsTo$\'' @ ( '\'nTCatDom$\'' @ A ) @ B @ C ) @ D )
=> ( ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTDom$c\'' @ A ) ) @ B ) ) @ ( '\'natTransMap$b\'' @ A @ D ) )
= ( '\'fun_app$\'' @ ( '\'fun_app$m\'' @ ( '\'comp$\'' @ ( '\'nTCatCod$\'' @ A ) ) @ ( '\'natTransMap$b\'' @ A @ C ) ) @ ( '\'fun_app$p\'' @ ( '\'mapM$a\'' @ ( '\'fun_app$v\'' @ '\'nTCod$c\'' @ A ) ) @ B ) ) ) ) )
=> ( '\'fun_app$e\'' @ '\'natTransP$\'' @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(415,axiom,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'dom$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) )
= ( '\'mapO$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).
thf(2177,plain,
! [A: '\'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$\'',B: '\'B$\''] :
( ( ( '\'functor$d\'' @ A )
& ( '\'member$h\'' @ B @ ( '\'mor$\'' @ ( '\'catDom$\'' @ A ) ) ) )
=> ( ( '\'dom$b\'' @ ( '\'catCod$\'' @ A ) @ ( '\'fun_app$q\'' @ ( '\'mapM$\'' @ A ) @ B ) )
= ( '\'mapO$\'' @ A @ ( '\'fun_app$t\'' @ ( '\'dom$\'' @ ( '\'catDom$\'' @ A ) ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(2466,plain,
$false,
inference(cvc4,[status(thm)],[1036,1337,629,1190,760,1995,1559,941,1179,555,481,909,1031,1956,1549,1211,1005,730,1522,741,1728,2099,1142,655,677,1305,1705,1671,2035,500,797,1233,2168,1919,538,1788,1426,1756,1310,533,1761,1342,1196,1746,2216,1391,1935,565,2400,1265,651,1409,570,1792,1860,2274,802,1826,2185,1660,1298,638,1379,1147,1741,2158,2301,1922,817,606,1572,1013,770,2024,1641,2222,1946,2027,2105,1334,834,1864,1151,2073,821,1040,1632,1828,1978,2291,1020,2254,1843,1169,2281,877,1796,1394,1351,988,1433,1943,1104,2205,1622,774,2371,1651,1604,2011,1206,793,1708,1783,2083,1438,661,1199,2164,2296,2307,2000,1636,1274,2264,894,746,2249,1519,1355,1751,1666,693,1238,1387,1723,1570,1676,788,2150,2032,815,1423,1602,2213,1634,1968,879,2068,1819,583,2200,682,2211,2112,1291,1402,2245,1983,615,1121,725,980,593,783,697,1541,874,2115,1270,1851,1534,1794,1017,1111,1970,1138,1719,1567,1160,488,1182,669,1700,2349,1889,679,547,901,686,1414,2053,2196,2108,2038,1114,997,985,1539,1131,1799,1002,1246,1715,779,1627,1451,738,2304,2153,1831,1231,1814,1241,1779,541,657,765,2076,1286,1187,1026,2189,718,2208,805,1663,2089,953,1185,1754,1959,1219,1927,573,2376,601,2235,906,1135,1648,1154,1916,2048,732,1615,772,1620,2016,579,958,2193,936,2293,1997,1638,2358,672,1428,2161,2346,2361,1209,831,1853,2383,2284,1144,2197,2065,2246,2299,649,1043,2180,758,552,535,2261,1162,1029,1149,626,2278,1381,1630,1993,1862,483,912,2171,768,2086,1643,2288,563,1435,2022,653,1562,1841,1396,2051,695,2369,1015,722,1420,749,939,1551,490,675,531,944,795,2271,617,2202,1845,557,2397,705,2386,1531,993,776,1748,640,1961,1711,1790,2165,1300,502,1785,1763,1679,1738,643,544,1038,585,1262,1235,2276,2219,1980,576,1658,2322,744,1023,1702,1221,1972,727,1008,1717,595,2056,1404,1353,2357,978,1140,1272,612,991,1617,1940,2045,1553,581,1412,1517,2226,2071,1108,1157,2078,688,903,1781,1216,891,1448,2187,1010,1575,1276,1646,2251,632,1244,786,2394,588,1253,699,2174,2283,2081,568,1308,1193,2183,899,684,549,2019,800,667,1294,1607,763,2003,2258,2374,1512,1725,1578,950,1546,1625,2008,1673,790,603,735,999,2287,620,2102,752,2155,2255,1989,1816,2091,1891,828,2040,955,1610,1172,897,1033,1288,2223,635,720,1165,2241,575,1384,528,1713,691,1399,1930,2353,839,982,1431,1848,1416,2351,708,659,1565,2238,560,1769,755,2191,1204,882,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP305_1 : TPTP v8.2.0. Released v8.0.0.
% 0.06/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n019.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sat May 18 16:47:24 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.67/1.31 % [INFO] Parsing done (436ms).
% 2.67/1.33 % [INFO] Running in sequential loop mode.
% 3.68/1.72 % [INFO] eprover registered as external prover.
% 3.68/1.72 % [INFO] cvc4 registered as external prover.
% 3.68/1.73 % [INFO] Scanning for conjecture ...
% 4.09/1.93 % [INFO] Found a conjecture (or negated_conjecture) and 623 axioms. Running axiom selection ...
% 5.13/2.14 % [INFO] Axiom selection finished. Selected 478 axioms (removed 145 axioms).
% 5.93/2.40 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.24/2.43 % [INFO] Type checking passed.
% 6.24/2.43 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 21.82/5.90 % External prover 'cvc4' found a proof!
% 21.82/5.90 % [INFO] Killing All external provers ...
% 21.82/5.90 % Time passed: 5373ms (effective reasoning time: 4574ms)
% 21.82/5.91 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 21.82/5.91 % Axioms used in derivation (478): axiom326, axiom32, axiom260, axiom315, axiom61, axiom527, axiom452, axiom491, axiom100, axiom28, axiom76, axiom564, axiom553, axiom54, axiom549, axiom480, axiom396, axiom25, axiom369, axiom404, axiom474, axiom333, axiom516, axiom295, axiom485, axiom322, axiom307, axiom496, axiom311, axiom284, axiom423, axiom65, axiom575, axiom36, axiom203, axiom531, axiom291, axiom441, axiom507, axiom430, axiom50, axiom158, axiom131, axiom386, axiom392, axiom580, axiom344, axiom138, axiom597, axiom337, axiom119, axiom210, axiom407, axiom191, axiom477, axiom401, axiom467, axiom397, axiom412, axiom460, axiom354, axiom579, axiom22, axiom445, axiom147, axiom524, axiom434, axiom341, axiom173, axiom348, axiom376, axiom172, axiom535, axiom42, axiom513, axiom300, axiom350, axiom561, axiom329, axiom372, axiom195, axiom583, axiom358, axiom161, axiom33, axiom542, axiom123, axiom383, axiom2, axiom134, axiom456, axiom87, axiom572, axiom568, axiom130, axiom557, axiom235, axiom98, axiom484, axiom225, axiom473, axiom39, axiom499, axiom330, axiom418, axiom304, axiom488, axiom520, axiom365, axiom64, axiom591, axiom59, axiom578, axiom530, axiom363, axiom283, axiom126, axiom539, axiom427, axiom48, axiom343, axiom27, axiom352, axiom411, axiom294, axiom314, axiom289, axiom437, axiom601, axiom115, axiom94, axiom83, axiom336, axiom308, axiom321, axiom35, axiom78, axiom24, axiom278, axiom272, axiom228, axiom405, axiom5, axiom101, axiom455, axiom475, axiom121, axiom132, axiom56, axiom466, axiom137, axiom563, axiom290, axiom206, axiom318, axiom60, axiom0, axiom574, axiom490, axiom13, axiom53, axiom433, axiom143, axiom359, axiom416, axiom489, axiom545, axiom108, axiom395, axiom387, axiom459, axiom400, axiom517, axiom75, axiom325, axiom448, axiom552, axiom385, axiom478, axiom90, axiom528, axiom332, axiom9, axiom303, axiom366, axiom207, axiom494, axiom538, axiom133, axiom80, axiom371, axiom252, axiom97, axiom567, axiom422, axiom472, axiom192, axiom355, axiom391, axiom263, axiom415, axiom589, axiom444, axiom82, axiom45, axiom483, axiom556, axiom541, axiom360, axiom398, axiom382, axiom426, axiom319, axiom347, axiom67, axiom534, axiom450, axiom523, axiom72, axiom461, axiom463, axiom310, axiom449, axiom224, axiom438, axiom105, axiom408, axiom89, axiom111, axiom512, axiom38, axiom419, axiom377, axiom500, axiom91, axiom218, axiom86, axiom297, axiom447, axiom52, axiom432, axiom279, axiom12, axiom390, axiom37, axiom331, axiom342, axiom212, axiom223, axiom571, axiom381, axiom79, axiom544, axiom425, axiom454, axiom573, axiom205, axiom364, axiom443, axiom96, axiom149, axiom189, axiom375, axiom394, axiom23, axiom227, axiom560, axiom93, axiom476, axiom595, axiom562, axiom41, axiom409, axiom286, axiom313, axiom118, axiom63, axiom19, axiom458, axiom8, axiom410, axiom320, axiom30, axiom370, axiom428, axiom479, axiom259, axiom74, axiom451, axiom570, axiom85, axiom566, axiom220, axiom598, axiom302, axiom367, axiom497, axiom378, axiom57, axiom599, axiom471, axiom506, axiom374, axiom440, axiom129, axiom581, axiom282, axiom594, axiom287, axiom414, axiom153, axiom324, axiom71, axiom462, axiom106, axiom533, axiom293, axiom403, axiom522, axiom436, axiom482, axiom555, axiom486, axiom346, axiom262, axiom68, axiom335, axiom26, axiom493, axiom356, axiom298, axiom46, axiom439, axiom469, axiom110, axiom49, axiom577, axiom219, axiom197, axiom421, axiom590, axiom547, axiom18, axiom338, axiom379, axiom88, axiom558, axiom389, axiom226, axiom166, axiom526, axiom559, axiom457, axiom521, axiom442, axiom327, axiom92, axiom399, axiom66, axiom345, axiom464, axiom296, axiom569, axiom357, axiom215, axiom576, axiom596, axiom274, axiom117, axiom393, axiom453, axiom44, axiom81, axiom515, axiom306, axiom323, axiom446, axiom84, axiom554, axiom495, axiom349, axiom368, axiom301, axiom550, axiom565, axiom148, axiom316, axiom285, axiom20, axiom540, axiom537, axiom211, axiom29, axiom361, axiom429, axiom532, axiom31, axiom380, axiom188, axiom264, axiom431, axiom176, axiom159, axiom487, axiom519, axiom402, axiom384, axiom551, axiom73, axiom107, axiom417, axiom339, axiom154, axiom40, axiom47, axiom518, axiom171, axiom3, axiom305, axiom424, axiom187, axiom288, axiom69, axiom317, axiom277, axiom198, axiom529, axiom144, axiom55, axiom593, axiom245, axiom536, axiom373, axiom435, axiom312, axiom95, axiom70, axiom238, axiom465, axiom543, axiom299, axiom351, axiom124, axiom261, axiom77, axiom413, axiom334, axiom160, axiom582, axiom514, axiom43, axiom481, axiom406, axiom388, axiom420, axiom62, axiom498, axiom209, axiom21, axiom139, axiom200, axiom250, axiom58, axiom292, axiom525, axiom234, axiom362, axiom51, axiom548, axiom309, axiom470, axiom468, axiom492, axiom328, axiom140, axiom340, axiom194, axiom353
% 21.82/5.91 % No. of inferences in proof: 960
% 21.82/5.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5373 ms resp. 4574 ms w/o parsing
% 22.43/6.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.43/6.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------