%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP305_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:37:40 AM UTC 2026
% Result : Theorem 35.76s 9.47s
% Output : Refutation 35.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 481
% Syntax : Number of formulae : 1021 ( 225 unt; 0 typ; 2 def)
% Number of atoms : 3363 ( 850 equ; 0 cnn)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 18439 ( 84 ~; 41 |;1238 &;16035 @)
% ( 56 <=>; 985 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Number of types : 94 ( 93 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 317 ( 314 usr; 31 con; 0-7 aty)
% Number of variables : 2966 ( 4 ^;2910 !; 50 ?;2966 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% 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$': $tType ).
thf('uu$_decl',type,
'uu$': 'A_set$' > 'A_bool_fun$' ).
thf('catDom$_decl',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_decl',type,
'more$b': 'ZF_ZF_unit_Category_ext$' > 'Unit$' ).
thf('functorComp$a_decl',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$e_decl',type,
'collect$e': 'B_ZF_fun_bool_fun$' > 'B_ZF_fun_set$' ).
thf('functor$e_decl',type,
'functor$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_decl',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$' ).
thf('oppositeCategory$_decl',type,
'oppositeCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('functor_comp_def$h_decl',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_decl',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_decl',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$' ).
thf('c$_decl',type,
'c$': 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('fun_app$u_decl',type,
'fun_app$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_decl',type,
'fun_app$s': 'B_ZF_fun_b_ZF_fun_fun$' > 'B_ZF_fun$' > 'B_ZF_fun$' ).
thf('nTCatCod$a_decl',type,
'nTCatCod$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$d_decl',type,
'functorM$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_decl',type,
'fun_app$b': 'ZF_bool_fun$' > 'ZF$' > $o ).
thf('natTransP$b_decl',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_decl',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$' > $o ).
thf('x$_decl',type,
'x$': 'A$' ).
thf('preFunctor$c_decl',type,
'preFunctor$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$' > $o ).
thf('mapsTo$_decl',type,
'mapsTo$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'A$' > 'A_bool_fun$' ).
thf('the$b_decl',type,
'the$b': 'B_bool_fun$' > 'B$' ).
thf('makeFtor$_decl',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_decl',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$' ).
thf('lSCategory$_decl',type,
'lSCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('natTrans$_decl',type,
'natTrans$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' ).
thf('uua$_decl',type,
'uua$': 'ZF_set$' > 'ZF_bool_fun$' ).
thf('idNatTrans$_decl',type,
'idNatTrans$': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' ).
thf('member$_decl',type,
'member$': '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_decl',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$' ).
thf('yMapInv$_decl',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$a_decl',type,
'constFunctor$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$b_decl',type,
'restrict$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$' ).
thf('uud$_decl',type,
'uud$': 'B_ZF_fun_set$' > 'B_ZF_fun_bool_fun$' ).
thf('isomorphism$b_decl',type,
'isomorphism$b': 'ZF_ZF_unit_Category_ext$' > 'ZF_bool_fun$' ).
thf('isomorphism$a_decl',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$' ).
thf('natTransP$_decl',type,
'natTransP$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' ).
thf('fun_app$x_decl',type,
'fun_app$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_decl',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_decl',type,
'functor$a': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
thf('extensional$_decl',type,
'extensional$': 'B_set$' > 'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_set$' ).
thf('functor_abbrev$f_decl',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_decl',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_decl',type,
'category$a': 'ZF_ZF_unit_Category_ext$' > $o ).
thf('fun_app$r_decl',type,
'fun_app$r': 'A_b_fun$' > 'A$' > 'B$' ).
thf('functor_comp_def$c_decl',type,
'functor_comp_def$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_decl',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$' ).
thf('uus$_decl',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_decl',type,
'makeCat$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('functor_abbrev$c_decl',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_decl',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_decl',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_decl',type,
'collect$d': 'B_bool_fun$' > 'B_set$' ).
thf('functorComp$d_decl',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$b_decl',type,
'objIso$b': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A_bool_fun$' ).
thf('equivalence_axioms$_decl',type,
'equivalence_axioms$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('mapM$f_decl',type,
'mapM$f': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > 'B$' > 'B$' ).
thf('constFunctor$_decl',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_decl',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_decl',type,
'nTCatDom$d': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('uur$_decl',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$_decl',type,
'uuk$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('seqSum$_decl',type,
'seqSum$': 'Nat_ZF_fun$' > 'ZF$' ).
thf('idNatTrans$g_decl',type,
'idNatTrans$g': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' ).
thf('collect$h_decl',type,
'collect$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$h_decl',type,
'fun_app$h': 'B_ZF_fun_bool_fun$' > 'B_ZF_fun$' > $o ).
thf('uun$_decl',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$b_decl',type,
'nTCatDom$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('functorM_axioms$c_decl',type,
'functorM_axioms$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_decl',type,
'fun_app$d': 'A_ZF_fun$' > 'A$' > 'ZF$' ).
thf('the$a_decl',type,
'the$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$_decl',type,
'set$': 'ZF_ZF_unit_Category_ext$' ).
thf('functorM$c_decl',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_decl',type,
'natTransMap$d': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > 'ZF_ZF_fun$' ).
thf('uul$_decl',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$f_decl',type,
'mapO$f': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > 'A$' > 'A$' ).
thf('catDom$b_decl',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_decl',type,
'member$d': 'ZF$' > 'ZF_set$' > $o ).
thf('mapsTo$b_decl',type,
'mapsTo$b': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('natTransComp$a_decl',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$_decl',type,
'unity$': 'Unit$' ).
thf('identityFunctor$f_decl',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_decl',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_decl',type,
'natTrans$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > $o ).
thf('catCod$d_decl',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_decl',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$b_decl',type,
'idNatTrans$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$l_decl',type,
'fun_app$l': 'A_bool_fun$' > 'A$' > $o ).
thf('functor_abbrev$a_decl',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_decl',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$h_decl',type,
'functorComp$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_decl',type,
'nTCod$d': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('mor2ZF$_decl',type,
'mor2ZF$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_ZF_fun$' ).
thf('catCod$c_decl',type,
'catCod$c': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('nTCod$a_decl',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$' ).
thf('obj$_decl',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_decl',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_decl',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$s_decl',type,
'constFunctor$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$c_decl',type,
'nt_abbrev$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_decl',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$' ).
thf('zFfun$_decl',type,
'zFfun$': 'ZF$' > 'ZF$' > 'ZF_ZF_fun$' > 'ZF$' ).
thf('makeFtor$e_decl',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$' ).
thf('nTCompDefined$_decl',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$' ).
thf('inverse_rel$_decl',type,
'inverse_rel$': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('idNatTrans$a_decl',type,
'idNatTrans$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$_decl',type,
'objIso$': '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_decl',type,
'obj$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$' ).
thf('constFunctor$c_decl',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$' ).
thf('nTCatCod$_decl',type,
'nTCatCod$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('functor_abbrev$d_decl',type,
'functor_abbrev$d': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('lSCategory_axioms$_decl',type,
'lSCategory_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('yMapInv$a_decl',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$_decl',type,
'zFfunCod$': 'ZF_ZF_fun$' ).
thf('oppositeCategory$b_decl',type,
'oppositeCategory$b': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('more$a_decl',type,
'more$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_c_LSCategory_ext$' ).
thf('catDom$a_decl',type,
'catDom$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('homFtor$_decl',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$_decl',type,
'category_ext$': '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$g_decl',type,
'functorComp$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_decl',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$' ).
thf('mor2ZF_update$_decl',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$c_decl',type,
'category$c': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('cod$_decl',type,
'cod$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$' ).
thf('functor_comp_def$a_decl',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_decl',type,
'restrict$c': 'B_a_fun$' > 'B_set$' > 'B_a_fun$' ).
thf('set$a_decl',type,
'set$a': 'ZF_ZF_unit_Category_ext$' ).
thf('nTDom$d_decl',type,
'nTDom$d': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('compDefined$_decl',type,
'compDefined$': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('uut$_decl',type,
'uut$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_fun$' ).
thf('functorComp$b_decl',type,
'functorComp$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_decl',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$c_decl',type,
'more$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$b_decl',type,
'compDefined$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_decl',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_decl',type,
'natTransMap$c': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$' > 'ZF$' > 'B$' ).
thf('nTCatDom$a_decl',type,
'nTCatDom$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$o_decl',type,
'fun_app$o': 'B_b_b_fun_fun$' > 'B$' > 'B_b_fun$' ).
thf('restrict$e_decl',type,
'restrict$e': 'ZF_ZF_fun$' > 'ZF_set$' > 'ZF_ZF_fun$' ).
thf('functor_ext$a_decl',type,
'functor_ext$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$' ).
thf('category_axioms$_decl',type,
'category_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('dom$b_decl',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$f_decl',type,
'functor_comp_def$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_decl',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$_decl',type,
'functor_abbrev$': '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_decl',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_decl',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$' > $o ).
thf('uuy$_decl',type,
'uuy$': 'ZF_bool_fun$' ).
thf('oppositeCategory$a_decl',type,
'oppositeCategory$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$_decl',type,
'yMap$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'ZF$' ).
thf('homFtorContra$a_decl',type,
'homFtorContra$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('homFtorContra$_decl',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$a_decl',type,
'member$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$' > $o ).
thf('uuu$_decl',type,
'uuu$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A$' > 'ZF_bool_fun$' ).
thf('mapM$d_decl',type,
'mapM$d': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_fun$' ).
thf('mapM$e_decl',type,
'mapM$e': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > 'ZF$' > 'B$' ).
thf('uve$_decl',type,
'uve$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('cod$b_decl',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$_decl',type,
'natTransComp$': '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_decl',type,
'obj$b': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_set$' ).
thf('zFfunComp$_decl',type,
'zFfunComp$': 'ZF_ZF_ZF_fun_fun$' ).
thf('compDefined$a_decl',type,
'compDefined$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'B_bool_fun$' ).
thf('inverse_rel$a_decl',type,
'inverse_rel$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'B_bool_fun$' ).
thf('the$_decl',type,
'the$': 'ZF_bool_fun$' > 'ZF$' ).
thf('functorM_axioms$d_decl',type,
'functorM_axioms$d': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('natTransMap$_decl',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$b_decl',type,
'constFunctor$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$d_decl',type,
'natTransP$d': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$' > $o ).
thf('functorComp$_decl',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$_decl',type,
'mapM$': '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$v_decl',type,
'fun_app$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_decl',type,
'restrict$d': 'A_b_fun$' > 'A_set$' > 'A_b_fun$' ).
thf('implode$_decl',type,
'implode$': 'ZF_set$' > 'ZF$' ).
thf('uuz$_decl',type,
'uuz$': 'ZF_ZF_fun$' ).
thf('mapO$c_decl',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$g_decl',type,
'identityFunctor$g': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('mapO$a_decl',type,
'mapO$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A$' > 'ZF$' ).
thf('nTCod$_decl',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_decl',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$' ).
thf('uuc$_decl',type,
'uuc$': 'B_set$' > 'B_bool_fun$' ).
thf('catCod$e_decl',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$' ).
thf('lSCategory_ext$_decl',type,
'lSCategory_ext$': 'B_ZF_fun$' > 'C$' > 'B_c_LSCategory_ext$' ).
thf('catCod$b_decl',type,
'catCod$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('collect$b_decl',type,
'collect$b': 'A_bool_fun$' > 'A_set$' ).
thf('natTransMap$a_decl',type,
'natTransMap$a': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$' > 'A_b_fun$' ).
thf('equivalence$_decl',type,
'equivalence$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('homSet$_decl',type,
'homSet$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A$' > 'ZF$' ).
thf('fun_app$e_decl',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_decl',type,
'mapM$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'B_ZF_fun$' ).
thf('functor_abbrev$e_decl',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$' > 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('y$_decl',type,
'y$': 'A$' ).
thf('uux$_decl',type,
'uux$': 'ZF_ZF_fun$' ).
thf('catDom$c_decl',type,
'catDom$c': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('functor$b_decl',type,
'functor$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('functor$_decl',type,
'functor$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('extensional$a_decl',type,
'extensional$a': 'B_set$' > 'B_ZF_fun_set$' ).
thf('fun_app$k_decl',type,
'fun_app$k': 'B_bool_fun$' > 'B$' > $o ).
thf('natTrans$b_decl',type,
'natTrans$b': 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > $o ).
thf('eta$_decl',type,
'eta$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('homFtorMapContra$_decl',type,
'homFtorMapContra$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'A$' > 'ZF$' ).
thf('fun_app$n_decl',type,
'fun_app$n': 'B_b_fun$' > 'B$' > 'B$' ).
thf('uuw$_decl',type,
'uuw$': 'ZF$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('functorExt$d_decl',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_decl',type,
'member$h': 'B$' > 'B_set$' > $o ).
thf('functorComp$f_decl',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$e_decl',type,
'functorComp$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_decl',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_decl',type,
'member$i': 'A$' > 'A_set$' > $o ).
thf('category_ext$a_decl',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_decl',type,
'id$b': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_fun$' ).
thf('homFtorMap$_decl',type,
'homFtorMap$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'B_ZF_fun$' ).
thf('uuq$_decl',type,
'uuq$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'ZF_ZF_fun$' ).
thf('inverse$_decl',type,
'inverse$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('mapM$g_decl',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$a_decl',type,
'functorExt$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('natTransP$c_decl',type,
'natTransP$c': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$' > $o ).
thf('zF2mor$_decl',type,
'zF2mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF$' > 'B$' ).
thf('uuo$_decl',type,
'uuo$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'ZF_ZF_fun$' ).
thf('uvc$_decl',type,
'uvc$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('category_ext$b_decl',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_decl',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$a_decl',type,
'nt_abbrev$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$' > $o ).
thf('mapO$_decl',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$_decl',type,
'dom$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$' ).
thf('zFfunDom$_decl',type,
'zFfunDom$': 'ZF_ZF_fun$' ).
thf('fun_app$w_decl',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$d_decl',type,
'mapO$d': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_fun$' ).
thf('zFfunApp$_decl',type,
'zFfunApp$': 'ZF_ZF_ZF_fun_fun$' ).
thf('collect$c_decl',type,
'collect$c': 'ZF_bool_fun$' > 'ZF_set$' ).
thf('fun_app$q_decl',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$a_decl',type,
'equivalence_axioms$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_decl',type,
'category_axioms$a': 'ZF_ZF_unit_Category_ext$' > $o ).
thf('cod$a_decl',type,
'cod$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('functorComp$i_decl',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$i_decl',type,
'functor_comp_def$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$a_decl',type,
'catCod$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('hOMCollection$_decl',type,
'hOMCollection$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A$' > 'ZF_set$' ).
thf('uup$_decl',type,
'uup$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'B_ZF_fun$' ).
thf('mapO$h_decl',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$a_decl',type,
'objIso$a': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('comp$_decl',type,
'comp$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('nTDom$_decl',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$' ).
thf('isomorphism$_decl',type,
'isomorphism$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_bool_fun$' ).
thf('makeNT$_decl',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_decl',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_decl',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$z_decl',type,
'fun_app$z': 'Nat_ZF_fun$' > 'Nat$' > 'ZF$' ).
thf('preFunctor$a_decl',type,
'preFunctor$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('natTransP$a_decl',type,
'natTransP$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > $o ).
thf('catExp$l_decl',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$d_decl',type,
'makeFtor$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$f_decl',type,
'idNatTrans$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$' ).
thf('natTrans_ext$_decl',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$_decl',type,
'functor_ext$': '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$' ).
thf('elem$_decl',type,
'elem$': 'ZF$' > 'ZF_bool_fun$' ).
thf('mapsTo$a_decl',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$' ).
thf('functorM$_decl',type,
'functorM$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('comp$a_decl',type,
'comp$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('fun_app$m_decl',type,
'fun_app$m': 'ZF_ZF_ZF_fun_fun$' > 'ZF$' > 'ZF_ZF_fun$' ).
thf('nTCatCod$d_decl',type,
'nTCatCod$d': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('idNatTrans$e_decl',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_decl',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$b_decl',type,
'functor_abbrev$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$' > $o ).
thf('fun_app$_decl',type,
'fun_app$': 'ZF_ZF_fun$' > 'ZF$' > 'ZF$' ).
thf('makeNT$b_decl',type,
'makeNT$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$_decl',type,
'uuv$': '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_decl',type,
'comp$d': 'ZF_ZF_fun$' > 'ZF_ZF_fun_ZF_ZF_fun_fun$' ).
thf('makeCat$_decl',type,
'makeCat$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('catExp$_decl',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$a_decl',type,
'yFtorNT$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$p_decl',type,
'fun_app$p': 'B_ZF_fun$' > 'B$' > 'ZF$' ).
thf('fun_app$aa_decl',type,
'fun_app$aa': 'ZF_ZF_fun_ZF_ZF_fun_fun$' > 'ZF_ZF_fun$' > 'ZF_ZF_fun$' ).
thf('catDom$d_decl',type,
'catDom$d': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('mor$a_decl',type,
'mor$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$f_decl',type,
'catCod$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$_decl',type,
'uvf$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A$' > 'ZF_bool_fun$' ).
thf('mapO$e_decl',type,
'mapO$e': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > 'ZF$' > 'A$' ).
thf('id$a_decl',type,
'id$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('uuj$_decl',type,
'uuj$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('yFtor$_decl',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_decl',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$_decl',type,
'functor_comp_def$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
thf('preFunctor$_decl',type,
'preFunctor$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('uva$_decl',type,
'uva$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF$' > 'B_bool_fun$' ).
thf('functor$d_decl',type,
'functor$d': 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).
thf('natTransExt$_decl',type,
'natTransExt$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' ).
thf('category$_decl',type,
'category$': '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$' > $o ).
thf('uuh$_decl',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$' ).
thf('more$_decl',type,
'more$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'C$' ).
thf('fun_app$t_decl',type,
'fun_app$t': 'B_a_fun$' > 'B$' > 'A$' ).
thf('yFtorNT$_decl',type,
'yFtorNT$': '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$c_decl',type,
'fun_app$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_decl',type,
'functor$c': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
thf('natTransMap$b_decl',type,
'natTransMap$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A$' > 'ZF$' ).
thf('equivalence$a_decl',type,
'equivalence$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_decl',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$c_decl',type,
'nTCatDom$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$_decl',type,
'nTCatDom$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('isZFfun$_decl',type,
'isZFfun$': 'ZF_bool_fun$' ).
thf('functor_comp_def$g_decl',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$' > $o ).
thf('catCod$_decl',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_decl',type,
'mor$b': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$' ).
thf('uum$_decl',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$b_decl',type,
'nTCatCod$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('dom$a_decl',type,
'dom$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('nt_abbrev$b_decl',type,
'nt_abbrev$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_decl',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$' ).
thf('nt_abbrev$_decl',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$_decl',type,
'id$': '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_decl',type,
'member$e': 'B_ZF_fun$' > 'B_ZF_fun_set$' > $o ).
thf('mor$_decl',type,
'mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_set$' ).
thf(sk1_decl,type,
sk1: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf(sk2_decl,type,
sk2: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
@+[C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
~ ( ( C @ ( B @ 'fun_app$e' ) )
=> ( C @ ( A @ 'fun_app$e' ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [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$'] :
~ ( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) ) ) ) ).
thf(148,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'idNatTrans$d' )
= ( 'unity$' @ ( A @ 'uus$' @ ( A @ ( A @ 'natTrans_ext$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom559) ).
thf(1036,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$'] :
( ( A @ 'idNatTrans$d' )
= ( 'unity$' @ ( A @ 'uus$' @ ( A @ ( A @ 'natTrans_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(241,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom581) ).
thf(1469,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(441,axiom,
! [A: 'B$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$c' ) )
& ( C @ ( B @ 'functorComp$c' ) @ 'catDom$b' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'mapO$' ) @ ( C @ 'mapO$c' ) @ ( A @ ( B @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( B @ 'mapO$' ) @ ( C @ 'mapO$c' ) @ ( A @ ( B @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'mapM$c' ) @ ( C @ 'catCod$d' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom379) ).
thf(2341,plain,
! [A: 'B$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$c' ) )
& ( C @ ( B @ 'functorComp$c' ) @ 'catDom$b' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'mapO$' ) @ ( C @ 'mapO$c' ) @ ( A @ ( B @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( B @ 'mapO$' ) @ ( C @ 'mapO$c' ) @ ( A @ ( B @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'mapM$c' ) @ ( C @ 'catCod$d' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(377,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'makeCat$' @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( C @ ( B @ ( A @ 'makeCat$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom406) ).
thf(2109,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'makeCat$' @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( C @ ( B @ ( A @ 'makeCat$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(269,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$a' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'catDom$a' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'mapO$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom356) ).
thf(1633,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$a' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'catDom$a' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'mapO$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(191,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( C @ ( D @ ( B @ ( A @ 'oppositeCategory$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom87) ).
thf(1237,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( C @ ( D @ ( B @ ( A @ 'oppositeCategory$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(335,axiom,
! [A: 'A$',B: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$i' @ 'fun_app$f' ) )
& ( C @ ( B @ 'functorComp$i' ) @ ( 'preFunctor$' @ 'fun_app$f' ) )
& ( B @ 'catDom$b' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$i' ) @ 'mapO$a' ) )
= ( A @ ( B @ 'mapO$f' ) @ ( C @ 'mapO$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom431) ).
thf(1899,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$'] :
( ( ( C @ ( B @ 'functor_comp_def$i' @ 'fun_app$f' ) )
& ( C @ ( B @ 'functorComp$i' ) @ ( 'preFunctor$' @ 'fun_app$f' ) )
& ( B @ 'catDom$b' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$i' ) @ 'mapO$a' ) )
= ( A @ ( B @ 'mapO$f' ) @ ( C @ 'mapO$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(50,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom497) ).
thf(666,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(420,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ ( A @ ( A @ 'yFtor$' @ 'functor_abbrev$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom138) ).
thf(2280,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ ( A @ ( A @ 'yFtor$' @ 'functor_abbrev$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(1,conjecture,
( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mor2ZF$' @ 'fun_app$p' ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) )
= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture34) ).
thf(2,negated_conjecture,
( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mor2ZF$' @ 'fun_app$p' ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) )
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(481,plain,
( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mor2ZF$' @ 'fun_app$p' ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) )
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( 'functorExt$a' @ 'fun_app$f' ) )
& ( A @ ( 'functorM$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'functor$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom274) ).
thf(628,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( 'functorExt$a' @ 'fun_app$f' ) )
& ( A @ ( 'functorM$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'functor$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(146,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'dom$' @ 'fun_app$t' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom298) ).
thf(1031,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'dom$' @ 'fun_app$t' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(211,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
<=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom301) ).
thf(1315,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(322,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ 'mor$a' @ ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom131) ).
thf(1850,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ 'mor$a' @ ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
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$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$f' ) ) ) )
=> ( ( E @ ( D @ ( B @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'comp$b' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom417) ).
thf(1200,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$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$f' ) ) ) )
=> ( ( E @ ( D @ ( B @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'comp$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(183,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'idNatTrans$c' )
= ( 'unity$' @ ( A @ 'uut$' @ ( A @ ( A @ 'natTrans_ext$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom560) ).
thf(1211,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'idNatTrans$c' )
= ( 'unity$' @ ( A @ 'uut$' @ ( A @ ( A @ 'natTrans_ext$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(83,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'identityFunctor$g' @ 'preFunctor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).
thf(762,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'identityFunctor$g' @ 'preFunctor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(375,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ 'makeFtor$' @ 'mapO$a' ) )
= ( B @ ( A @ 'mapO$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom283) ).
thf(2104,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ 'makeFtor$' @ 'mapO$a' ) )
= ( B @ ( A @ 'mapO$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
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$'] :
( ( A @ 'functor$d' )
=> ( A @ 'functorM$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom203) ).
thf(683,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'functor$d' )
=> ( A @ 'functorM$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(205,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$d' )
= ( A @ 'nTDom$d' @ 'catCod$c' ) )
& ( ( A @ 'nTCatDom$d' )
= ( A @ 'nTCod$d' @ 'catDom$c' ) )
& ( A @ 'nTCod$d' @ 'functor$b' )
& ( A @ 'nTDom$d' @ 'functor$b' ) )
=> ( A @ 'natTransP$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom521) ).
thf(1290,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$d' )
= ( A @ 'nTDom$d' @ 'catCod$c' ) )
& ( ( A @ 'nTCatDom$d' )
= ( A @ 'nTCod$d' @ 'catDom$c' ) )
& ( A @ 'nTCod$d' @ 'functor$b' )
& ( A @ 'nTDom$d' @ 'functor$b' ) )
=> ( A @ 'natTransP$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(455,axiom,
'x$' @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ 'mapO$a' ) @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).
thf(2381,plain,
'x$' @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ 'mapO$a' ) @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(461,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) )
=> ( ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).
thf(2395,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) )
=> ( ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(233,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom331) ).
thf(1443,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
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$',B: 'A$'] :
( ( ( A @ 'nTCatDom$c' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'natTransP$b' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapO$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapO$' ) @ ( B @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom524) ).
thf(2282,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 @ 'nTCatDom$c' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'natTransP$b' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapO$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapO$' ) @ ( B @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
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$'] :
( ( ( ( ( ( A @ 'catCod$a' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom344) ).
thf(1142,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
~ ( ~ ( ( ( A @ 'catCod$a' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(282,axiom,
! [A: 'ZF$'] : ( 'set$' @ 'obj$a' @ ( A @ 'member$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom95) ).
thf(1692,plain,
! [A: 'ZF$'] : ( 'set$' @ 'obj$a' @ ( A @ 'member$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(150,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'preFunctor$' @ 'fun_app$f' ) )
=> ( A @ 'makeFtor$' @ ( 'preFunctor$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom215) ).
thf(1041,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'preFunctor$' @ 'fun_app$f' ) )
=> ( A @ 'makeFtor$' @ ( 'preFunctor$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(171,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ 'mapO$a' ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( C @ ( A @ 'yMapInv$' ) ) ) @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom82) ).
thf(1173,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ 'mapO$a' ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( C @ ( A @ 'yMapInv$' ) ) ) @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(401,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( C @ ( B @ ( A @ 'yMap$' ) ) )
= ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ ( B @ ( C @ 'natTransMap$b' ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom466) ).
thf(2195,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( C @ ( B @ ( A @ 'yMap$' ) ) )
= ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ ( B @ ( C @ 'natTransMap$b' ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(261,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).
thf(1608,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(357,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom299) ).
thf(2035,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(296,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( A
= ( A @ 'more$b' @ ( A @ 'comp$' @ ( A @ 'id$a' @ ( A @ 'cod$a' @ ( A @ 'dom$a' @ ( A @ 'mor$b' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383) ).
thf(1735,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( A
= ( A @ 'more$b' @ ( A @ 'comp$' @ ( A @ 'id$a' @ ( A @ 'cod$a' @ ( A @ 'dom$a' @ ( A @ 'mor$b' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(97,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ! [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$'] :
( ( A
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$a' ) ) ) ) ) ) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom387) ).
thf(797,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
~ ! [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$'] :
( A
!= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(70,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> $false )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom573) ).
thf(715,plain,
! [A: 'ZF$',B: 'ZF$'] :
~ ( ~ ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(62,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$b' @ ( C @ 'member$i' ) )
& ( B @ 'category$c' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$a' ) ) @ 'functor$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom226) ).
thf(698,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$b' @ ( C @ 'member$i' ) )
& ( B @ 'category$c' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$a' ) ) @ 'functor$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(8,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' @ 'obj$a' )
= ( A @ 'obj$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom57) ).
thf(538,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' @ 'obj$a' )
= ( A @ 'obj$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(187,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom297) ).
thf(1222,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(52,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom494) ).
thf(670,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(180,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( B @ 'mor$b' @ ( A @ 'member$d' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom291) ).
thf(1196,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( B @ 'mor$b' @ ( A @ 'member$d' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(307,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'equivalence$' @ 'fun_app$f' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).
thf(1782,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'equivalence$' @ 'fun_app$f' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(232,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom90) ).
thf(1441,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(67,axiom,
! [A: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$',B: 'ZF$'] :
( ( ( A @ 'nTCatDom$b' @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'natTransP$c' ) )
=> ( B @ ( A @ 'nTCod$a' @ 'mapO$e' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapO$e' ) @ ( B @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).
thf(709,plain,
! [A: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$',B: 'ZF$'] :
( ( ( A @ 'nTCatDom$b' @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'natTransP$c' ) )
=> ( B @ ( A @ 'nTCod$a' @ 'mapO$e' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapO$e' ) @ ( B @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(152,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$' )
= ( A @ 'more$b' @ ( A @ 'uve$' @ ( A @ 'obj$a' @ ( A @ 'id$a' @ 'restrict$e' ) @ ( A @ 'mor$b' @ ( A @ 'cod$a' @ 'restrict$e' ) @ ( A @ 'mor$b' @ ( A @ 'dom$a' @ 'restrict$e' ) @ ( A @ 'mor$b' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom583) ).
thf(1046,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$' )
= ( A @ 'more$b' @ ( A @ 'uve$' @ ( A @ 'obj$a' @ ( A @ 'id$a' @ 'restrict$e' ) @ ( A @ 'mor$b' @ ( A @ 'cod$a' @ 'restrict$e' ) @ ( A @ 'mor$b' @ ( A @ 'dom$a' @ 'restrict$e' ) @ ( A @ 'mor$b' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
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$'] :
( ( A @ 'catDom$' @ 'mor$' @ 'extensional$' @ ( A @ 'mapM$' @ 'member$m' ) )
=> ( A @ 'functorExt$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).
thf(1935,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'catDom$' @ 'mor$' @ 'extensional$' @ ( A @ 'mapM$' @ 'member$m' ) )
=> ( A @ 'functorExt$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(223,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
<=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$d' ) )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).
thf(1386,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$d' ) )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) )
=> ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$d' ) )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
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$'] :
( ( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ ( A @ 'nTCompDefined$a' ) ) )
=> ( C @ ( B @ 'natTransMap$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom539) ).
thf(565,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',C: 'ZF$'] :
( ( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ ( A @ 'nTCompDefined$a' ) ) )
=> ( C @ ( B @ 'natTransMap$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(311,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).
thf(1803,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
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$'] :
( ( ( E @ ( D @ ( C @ ( B @ 'catExp$b' ) @ 'compDefined$c' ) ) )
& ( B @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ 'catExp$b' ) @ 'comp$c' ) ) @ 'natTransMap$d' @ 'fun_app$' ) )
= ( A @ ( E @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ ( D @ 'natTransMap$d' @ 'fun_app$' ) @ ( C @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom465) ).
thf(1703,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$'] :
( ( ( E @ ( D @ ( C @ ( B @ 'catExp$b' ) @ 'compDefined$c' ) ) )
& ( B @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ 'catExp$b' ) @ 'comp$c' ) ) @ 'natTransMap$d' @ 'fun_app$' ) )
= ( A @ ( E @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ ( D @ 'natTransMap$d' @ 'fun_app$' ) @ ( C @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(293,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ 'elem$' @ 'fun_app$b' ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom452) ).
thf(1724,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ 'elem$' @ 'fun_app$b' ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(243,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) @ ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom320) ).
thf(1475,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) @ ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(189,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$a' )
= ( A @ 'more$a' @ ( A @ 'uvc$' @ ( A @ 'obj$b' @ ( A @ 'id$b' @ 'restrict$d' ) @ ( A @ 'mor$' @ ( A @ 'cod$' @ 'restrict$c' ) @ ( A @ 'mor$' @ ( A @ 'dom$' @ 'restrict$c' ) @ ( A @ 'mor$' @ ( A @ 'obj$b' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom582) ).
thf(1228,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$a' )
= ( A @ 'more$a' @ ( A @ 'uvc$' @ ( A @ 'obj$b' @ ( A @ 'id$b' @ 'restrict$d' ) @ ( A @ 'mor$' @ ( A @ 'cod$' @ 'restrict$c' ) @ ( A @ 'mor$' @ ( A @ 'dom$' @ 'restrict$c' ) @ ( A @ 'mor$' @ ( A @ 'obj$b' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(265,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom314) ).
thf(1623,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ 'member$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(246,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$e' ) )
=> ( A @ ( 'natTransExt$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom212) ).
thf(1482,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$e' ) )
=> ( A @ ( 'natTransExt$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(267,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ ( A @ 'homFtorContra$' ) @ 'functor_abbrev$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).
thf(1628,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ ( A @ 'homFtorContra$' ) @ 'functor_abbrev$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( D @ 'member$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom209) ).
thf(1055,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$',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$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( D @ 'member$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(20,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).
thf(570,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
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$',N: 'Unit$'] :
( ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) )
= ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ 'category_ext$a' ) ) ) ) ) ) ) )
<=> ( ( G = N )
& ( F = M )
& ( E = L )
& ( D = K )
& ( C = J )
& ( B = I )
& ( A = H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).
thf(504,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$',N: 'Unit$'] :
( ( ( ( G = N )
& ( F = M )
& ( E = L )
& ( D = K )
& ( C = J )
& ( B = I )
& ( A = H ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) )
= ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ 'category_ext$a' ) ) ) ) ) ) ) ) )
& ( ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) )
= ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ 'category_ext$a' ) ) ) ) ) ) ) )
=> ( ( G = N )
& ( F = M )
& ( E = L )
& ( D = K )
& ( C = J )
& ( B = I )
& ( A = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(210,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( B @ 'elem$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( B @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ 'elem$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom570) ).
thf(1313,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( B @ 'elem$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( B @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ 'elem$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(178,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$' @ 'fun_app$e' ) )
=> ( A @ 'makeNT$' @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom124) ).
thf(1191,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$' @ 'fun_app$e' ) )
=> ( A @ 'makeNT$' @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(382,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ ( A @ 'uuh$' @ 'fun_app$f' ) )
<=> ( A @ ( B @ 'member$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
thf(2126,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( B @ 'member$a' ) )
=> ( B @ ( A @ 'uuh$' @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ 'uuh$' @ 'fun_app$f' ) )
=> ( A @ ( B @ 'member$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(447,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_ZF_fun$',D: 'B_ZF_fun_b_ZF_fun_fun$',E: 'B_ZF_fun_b_ZF_fun_fun$'] :
( ( ! [F: 'B_ZF_fun$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$s' ) )
= ( F @ ( E @ 'fun_app$s' ) ) ) )
& ( ( B @ 'mor2ZF$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'mor2ZF_update$' ) )
= ( B @ ( E @ 'mor2ZF_update$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).
thf(2356,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$'] :
( ( ! [F: 'B_ZF_fun$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$s' ) )
= ( F @ ( E @ 'fun_app$s' ) ) ) )
& ( ( B @ 'mor2ZF$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'mor2ZF_update$' ) )
= ( B @ ( E @ 'mor2ZF_update$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(310,axiom,
! [A: 'A_bool_fun$',B: 'A_bool_fun$'] :
( ! [C: 'A$'] :
( ( C @ ( A @ 'fun_app$l' ) )
<=> ( C @ ( B @ 'fun_app$l' ) ) )
=> ( ( A @ 'collect$b' )
= ( B @ 'collect$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).
thf(1792,plain,
! [A: 'A_bool_fun$',B: 'A_bool_fun$'] :
( ! [C: 'A$'] :
( ( ( C @ ( B @ 'fun_app$l' ) )
=> ( C @ ( A @ 'fun_app$l' ) ) )
& ( ( C @ ( A @ 'fun_app$l' ) )
=> ( C @ ( B @ 'fun_app$l' ) ) ) )
=> ( ( A @ 'collect$b' )
= ( B @ 'collect$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(229,axiom,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( B @ 'lSCategory$' )
& ( B @ 'yFtor$a' @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( B @ 'yFtor$a' @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( B @ 'yFtor$a' @ 'mapM$' @ 'fun_app$q' ) )
= ( A @ ( B @ 'homFtorContra$' ) @ ( B @ 'yFtor$a' @ 'catCod$' @ 'id$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom342) ).
thf(1430,plain,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( B @ 'lSCategory$' )
& ( B @ 'yFtor$a' @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( B @ 'yFtor$a' @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( B @ 'yFtor$a' @ 'mapM$' @ 'fun_app$q' ) )
= ( A @ ( B @ 'homFtorContra$' ) @ ( B @ 'yFtor$a' @ 'catCod$' @ 'id$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(417,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',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$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$f' ) ) ) )
=> ( F @ ( A @ 'mapO$' ) @ ( E @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom78) ).
thf(2274,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$',F: 'A$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$f' ) ) ) )
=> ( F @ ( A @ 'mapO$' ) @ ( E @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(120,axiom,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'obj$b' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ 'id$b' @ 'fun_app$r' ) )
= ( A @ ( B @ 'makeCat$a' @ 'id$b' @ 'fun_app$r' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).
thf(917,plain,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'obj$b' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ 'id$b' @ 'fun_app$r' ) )
= ( A @ ( B @ 'makeCat$a' @ 'id$b' @ 'fun_app$r' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(64,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$' @ 'fun_app$f' ) )
=> ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).
thf(702,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$' @ 'fun_app$f' ) )
=> ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(239,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ~ ( A @ ( B @ 'elem$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom598) ).
thf(1462,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ~ ( A @ ( B @ 'elem$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(157,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',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$'] :
( ( ( ( A @ 'more$c' )
= ( B @ 'more$c' ) )
& ( ( A @ 'mapM$' )
= ( B @ 'mapM$' ) )
& ( ( A @ 'catCod$' )
= ( B @ 'catCod$' ) )
& ( ( A @ 'catDom$' )
= ( B @ 'catDom$' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom472) ).
thf(1059,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',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$'] :
( ( ( ( A @ 'more$c' )
= ( B @ 'more$c' ) )
& ( ( A @ 'mapM$' )
= ( B @ 'mapM$' ) )
& ( ( A @ 'catCod$' )
= ( B @ 'catCod$' ) )
& ( ( A @ 'catDom$' )
= ( B @ 'catDom$' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(104,axiom,
! [A: 'A_set$'] :
( ( A @ 'uu$' @ 'collect$b' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom107) ).
thf(815,plain,
! [A: 'A_set$'] :
( ( A @ 'uu$' @ 'collect$b' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(816,plain,
! [A: 'A_set$'] :
( ( A @ 'uu$' @ 'collect$b' )
= A ),
inference(cnf,[status(esa)],[815]) ).
thf(817,plain,
! [A: 'A_set$'] :
( ( A @ 'uu$' @ 'collect$b' )
= A ),
inference(lifteq,[status(thm)],[816]) ).
thf(16,axiom,
! [A: 'ZF_set$'] :
( ( A @ 'uua$' @ 'collect$c' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).
thf(559,plain,
! [A: 'ZF_set$'] :
( ( A @ 'uua$' @ 'collect$c' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(394,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).
thf(2169,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(433,axiom,
'c$' @ 'lSCategory$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom35) ).
thf(2313,plain,
'c$' @ 'lSCategory$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(37,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
<=> ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom471) ).
thf(618,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$c' ) )
=> ( A @ 'lSCategory$' ) )
& ( ( A @ 'lSCategory$' )
=> ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(619,plain,
( ! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$c' ) )
=> ( A @ 'lSCategory$' ) )
& ! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$c' ) ) ) ),
inference(miniscope,[status(thm)],[618]) ).
thf(620,plain,
! [B: 'A_b_b_c_LSCategory_ext_Category_ext$',A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( B @ 'lSCategory$' )
| ~ ( B @ 'lSCategory_axioms$' )
| ~ ( B @ 'category$c' ) )
& ( ( A @ 'lSCategory_axioms$' )
| ~ ( A @ 'lSCategory$' ) )
& ( ( A @ 'category$c' )
| ~ ( A @ 'lSCategory$' ) ) ),
inference(cnf,[status(esa)],[619]) ).
thf(621,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$c' )
| ~ ( A @ 'lSCategory$' ) ),
inference(cnfConj,[status(thm)],[620]) ).
thf(2550,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( 'c$' @ 'lSCategory$' )
!= ( A @ 'lSCategory$' ) )
| ( A @ 'category$c' )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2313,621]) ).
thf(2551,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( 'c$' @ 'lSCategory$' )
!= ( A @ 'lSCategory$' ) )
| ( A @ 'category$c' ) ),
inference(simp,[status(thm)],[2550]) ).
thf(2552,plain,
'c$' @ 'category$c',
inference(pattern_uni,[status(thm)],[2551:[bind(A,$thf( 'c$' ))]]) ).
thf(86,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtor$' ) )
= ( B @ ( A @ 'homFtor$a' ) @ 'makeFtor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom160) ).
thf(770,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtor$' ) )
= ( B @ ( A @ 'homFtor$a' ) @ 'makeFtor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(356,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
<=> ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom453) ).
thf(2024,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
=> ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom85) ).
thf(1963,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$',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$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(305,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$e' ) )
=> ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom132) ).
thf(1778,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$e' ) )
=> ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(34,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= C )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= B )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom572) ).
thf(606,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= C )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= B )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(218,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).
thf(1347,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(253,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom413) ).
thf(1572,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
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$'] :
( ( A @ 'preFunctor$c' )
<=> ( ( A @ 'catCod$' @ 'category$' )
& ( A @ 'catDom$' @ 'category$c' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ? [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'comp$b' ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom436) ).
thf(1741,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$'] :
( ( ( ( A @ 'catCod$' @ 'category$' )
& ( A @ 'catDom$' @ 'category$c' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ? [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'comp$b' ) ) ) ) ) )
=> ( A @ 'preFunctor$c' ) )
& ( ( A @ 'preFunctor$c' )
=> ( ( A @ 'catCod$' @ 'category$' )
& ( A @ 'catDom$' @ 'category$c' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ? [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'comp$b' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(225,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).
thf(1398,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(397,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$a' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( B @ ( A @ 'catDom$a' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'catDom$a' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom327) ).
thf(2178,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$a' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( B @ ( A @ 'catDom$a' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'catDom$a' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(123,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ ( 'functorM$' @ 'fun_app$f' ) ) )
=> ( D @ ( A @ 'mapO$a' ) @ ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom349) ).
thf(924,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ ( 'functorM$' @ 'fun_app$f' ) ) )
=> ( D @ ( A @ 'mapO$a' ) @ ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(81,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' @ 'oppositeCategory$b' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom93) ).
thf(756,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' @ 'oppositeCategory$b' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(29,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom496) ).
thf(591,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(473,axiom,
! [A: 'A_set$',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$'] :
( ( H @ ( G @ 'lSCategory_ext$' ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) @ 'mor2ZF$' )
= G ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).
thf(2469,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$',H: 'C$'] :
( ( H @ ( G @ 'lSCategory_ext$' ) @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) @ 'mor2ZF$' )
= G ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(412,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$' @ ( A @ 'mor2ZF$' @ 'lSCategory_ext$' ) @ ( A @ 'comp$a' @ ( A @ 'id$b' @ ( A @ 'cod$' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$b' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).
thf(2259,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$' @ ( A @ 'mor2ZF$' @ 'lSCategory_ext$' ) @ ( A @ 'comp$a' @ ( A @ 'id$b' @ ( A @ 'cod$' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$b' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(318,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom323) ).
thf(1828,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(425,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) )
=> ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).
thf(2291,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) )
=> ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(276,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom568) ).
thf(1677,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(100,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( ( B @ 'category$a' )
& ( A @ 'category$c' ) )
=> ( B @ ( A @ 'catExp$' ) @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom176) ).
thf(806,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( ( B @ 'category$a' )
& ( A @ 'category$c' ) )
=> ( B @ ( A @ 'catExp$' ) @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(215,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'equivalence$a' ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).
thf(1334,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'equivalence$a' ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(44,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'more$b' )
= G ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom400) ).
thf(646,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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'more$b' )
= G ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(278,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'preFunctor$c' ) )
=> ( ( B @ ( A @ 'mapO$' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).
thf(1682,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'preFunctor$c' ) )
=> ( ( B @ ( A @ 'mapO$' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(163,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'ZF$',E: 'A$'] :
( ( E @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( A @ 'uul$' ) @ 'fun_app$m' ) @ ( E @ ( C @ 'mapO$a' ) @ ( B @ ( E @ ( A @ 'homSet$' ) ) @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).
thf(1136,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'ZF$',E: 'A$'] :
( ( E @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ 'fun_app$d' ) )
= ( D @ ( C @ ( A @ 'uul$' ) @ 'fun_app$m' ) @ ( E @ ( C @ 'mapO$a' ) @ ( B @ ( E @ ( A @ 'homSet$' ) ) @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(108,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$a' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$i' ) ) @ 'functor$e' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom234) ).
thf(834,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$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$a' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$i' ) ) @ 'functor$e' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(169,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'inverse_rel$a' ) @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).
thf(1169,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'inverse_rel$a' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(221,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom330) ).
thf(1377,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(332,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ ( C @ ( B @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).
thf(1886,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ ( C @ ( B @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(230,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'preFunctor$c' ) )
=> ? [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom348) ).
thf(1433,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 @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'preFunctor$c' ) )
=> ? [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(193,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( A @ ( 'natTransExt$' @ 'fun_app$e' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) )
=> ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).
thf(1242,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( A @ ( 'natTransExt$' @ 'fun_app$e' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) )
=> ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(404,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'equivalence_axioms$a' )
<=> ( ! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$a' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).
thf(2205,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$a' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) )
=> ( A @ 'equivalence_axioms$a' ) )
& ( ( A @ 'equivalence_axioms$a' )
=> ( ! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$a' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(284,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$b' @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom137) ).
thf(1696,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$b' @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
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$'] :
( ( A @ 'functorExt$d' )
<=> ( A @ 'catDom$' @ 'mor$' @ 'extensional$' @ ( A @ 'mapM$' @ 'member$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom477) ).
thf(1564,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ 'extensional$' @ ( A @ 'mapM$' @ 'member$m' ) )
=> ( A @ 'functorExt$d' ) )
& ( ( A @ 'functorExt$d' )
=> ( A @ 'catDom$' @ 'mor$' @ 'extensional$' @ ( A @ 'mapM$' @ 'member$m' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(277,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uuy$' @ 'fun_app$b' ) )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom33) ).
thf(1680,plain,
! [A: 'ZF$'] : ( A @ ( 'uuy$' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(1681,plain,
! [A: 'ZF$'] : ( A @ ( 'uuy$' @ 'fun_app$b' ) ),
inference(cnf,[status(esa)],[1680]) ).
thf(386,axiom,
! [A: 'ZF$'] :
~ ( A @ ( A @ 'elem$' @ 'fun_app$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom595) ).
thf(2140,plain,
! [A: 'ZF$'] :
~ ( A @ ( A @ 'elem$' @ 'fun_app$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(2141,plain,
~ ? [A: 'ZF$'] : ( A @ ( A @ 'elem$' @ 'fun_app$b' ) ),
inference(miniscope,[status(thm)],[2140]) ).
thf(2142,plain,
! [A: 'ZF$'] :
~ ( A @ ( A @ 'elem$' @ 'fun_app$b' ) ),
inference(cnf,[status(esa)],[2141]) ).
thf(2514,plain,
! [B: 'ZF$',A: 'ZF$'] :
( ( ( A @ ( 'uuy$' @ 'fun_app$b' ) )
!= ( B @ ( B @ 'elem$' @ 'fun_app$b' ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1681,2142]) ).
thf(2515,plain,
! [B: 'ZF$',A: 'ZF$'] :
( ( A @ ( 'uuy$' @ 'fun_app$b' ) )
!= ( B @ ( B @ 'elem$' @ 'fun_app$b' ) ) ),
inference(simp,[status(thm)],[2514]) ).
thf(2520,plain,
! [B: 'ZF$',A: 'ZF$'] :
( ( A != B )
| ( ( B @ 'elem$' )
!= 'uuy$' ) ),
inference(simp,[status(thm)],[2515]) ).
thf(2523,plain,
! [A: 'ZF$'] :
( ( A @ 'elem$' )
!= 'uuy$' ),
inference(simp,[status(thm)],[2520]) ).
thf(423,axiom,
'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom39) ).
thf(2287,plain,
'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(1463,plain,
! [B: 'ZF$',A: 'ZF$'] :
( ~ ( A @ ( B @ 'elem$' @ 'fun_app$b' ) )
| ~ ( B @ ( A @ 'elem$' @ 'fun_app$b' ) ) ),
inference(cnf,[status(esa)],[1462]) ).
thf(2528,plain,
! [B: 'ZF$',A: 'ZF$'] :
( ( ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ) )
!= ( B @ ( A @ 'elem$' @ 'fun_app$b' ) ) )
| ~ ( A @ ( B @ 'elem$' @ 'fun_app$b' ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2287,1463]) ).
thf(2529,plain,
! [B: 'ZF$',A: 'ZF$'] :
( ( ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ) )
!= ( B @ ( A @ 'elem$' @ 'fun_app$b' ) ) )
| ~ ( A @ ( B @ 'elem$' @ 'fun_app$b' ) ) ),
inference(simp,[status(thm)],[2528]) ).
thf(2530,plain,
~ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ 'elem$' @ 'fun_app$b' ) ),
inference(pattern_uni,[status(thm)],[2529:[bind(A,$thf( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) )),bind(B,$thf( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) ))]]) ).
thf(328,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'functor$d' )
=> ( A @ 'idNatTrans$d' @ 'natTransP$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom264) ).
thf(1863,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'functor$d' )
=> ( A @ 'idNatTrans$d' @ 'natTransP$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(121,axiom,
! [A: 'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$',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$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$a' ) ) ) )
=> ( F @ ( A @ 'mapO$b' ) @ ( E @ ( A @ 'mapO$b' ) @ ( D @ ( A @ 'mapM$b' ) @ ( C @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).
thf(920,plain,
! [A: 'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$',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$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$a' ) ) ) )
=> ( F @ ( A @ 'mapO$b' ) @ ( E @ ( A @ 'mapO$b' ) @ ( D @ ( A @ 'mapM$b' ) @ ( C @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(231,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$a' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'catDom$a' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'mapO$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom359) ).
thf(1438,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$a' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'catDom$a' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'mapO$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(95,axiom,
( 'set$a'
= ( 'unity$' @ ( 'zFfunComp$' @ ( 'uuz$' @ ( 'zFfunCod$' @ ( 'zFfunDom$' @ ( 'isZFfun$' @ 'collect$c' @ ( 'uuy$' @ 'collect$c' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom578) ).
thf(792,plain,
( 'set$a'
= ( 'unity$' @ ( 'zFfunComp$' @ ( 'uuz$' @ ( 'zFfunCod$' @ ( 'zFfunDom$' @ ( 'isZFfun$' @ 'collect$c' @ ( 'uuy$' @ 'collect$c' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(793,plain,
( ( 'unity$' @ ( 'zFfunComp$' @ ( 'uuz$' @ ( 'zFfunCod$' @ ( 'zFfunDom$' @ ( 'isZFfun$' @ 'collect$c' @ ( 'uuy$' @ 'collect$c' @ 'category_ext$a' ) ) ) ) ) ) )
= 'set$a' ),
inference(lifteq,[status(thm)],[792]) ).
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$',D: 'A$'] :
( ( ( B @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( ( D @ ( B @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( D @ ( A @ 'mapO$a' ) @ ( C @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).
thf(2118,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$',D: 'A$'] :
( ( ( B @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( ( D @ ( B @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( D @ ( A @ 'mapO$a' ) @ ( C @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
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$'] :
( ( ( E @ ( D @ ( C @ ( B @ 'catExp$' ) @ 'compDefined$b' ) @ 'fun_app$e' ) )
& ( B @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ 'catExp$' ) @ 'comp$b' ) ) @ 'natTransMap$b' ) )
= ( A @ ( E @ 'natTransMap$b' ) @ ( A @ ( D @ 'natTransMap$b' ) @ ( C @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom464) ).
thf(2083,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$'] :
( ( ( E @ ( D @ ( C @ ( B @ 'catExp$' ) @ 'compDefined$b' ) @ 'fun_app$e' ) )
& ( B @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ 'catExp$' ) @ 'comp$b' ) ) @ 'natTransMap$b' ) )
= ( A @ ( E @ 'natTransMap$b' ) @ ( A @ ( D @ 'natTransMap$b' ) @ ( C @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
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$',D: 'ZF$'] :
( ( ( B @ 'catDom$d' @ 'obj$a' @ ( D @ 'member$d' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$c' ) ) ) )
=> ( D @ ( C @ 'mapO$e' ) @ ( D @ ( B @ 'mapO$e' ) @ ( D @ ( A @ 'natTransMap$c' ) @ ( C @ 'catCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom457) ).
thf(1057,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$',D: 'ZF$'] :
( ( ( B @ 'catDom$d' @ 'obj$a' @ ( D @ 'member$d' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$c' ) ) ) )
=> ( D @ ( C @ 'mapO$e' ) @ ( D @ ( B @ 'mapO$e' ) @ ( D @ ( A @ 'natTransMap$c' ) @ ( C @ 'catCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
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$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$a' ) )
& ( A @ 'equivalence$a' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom374) ).
thf(2364,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$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$a' ) )
& ( A @ 'equivalence$a' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
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$',F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> ( F @ ( A @ 'mapO$c' ) @ ( E @ ( A @ 'mapO$c' ) @ ( D @ ( A @ 'mapM$c' ) @ ( C @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).
thf(2164,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$',F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> ( F @ ( A @ 'mapO$c' ) @ ( E @ ( A @ 'mapO$c' ) @ ( D @ ( A @ 'mapM$c' ) @ ( C @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(338,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom325) ).
thf(1915,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( ( B @ ( A @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'cod$b' ) @ ( A @ 'catCod$' @ 'id$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom355) ).
thf(1708,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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( ( B @ ( A @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'cod$b' ) @ ( A @ 'catCod$' @ 'id$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(209,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$a' ) @ ( 'functorM$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom140) ).
thf(1311,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$a' ) @ ( 'functorM$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(427,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).
thf(2296,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(431,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).
thf(2307,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
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$'] :
( ( A @ 'makeFtor$d' )
= ( A @ 'more$c' @ ( A @ 'catDom$' @ 'mor$' @ ( A @ 'mapM$' @ 'restrict$b' ) @ ( A @ 'catCod$' @ ( A @ 'catDom$' @ 'functor_ext$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).
thf(1768,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$'] :
( ( A @ 'makeFtor$d' )
= ( A @ 'more$c' @ ( A @ 'catDom$' @ 'mor$' @ ( A @ 'mapM$' @ 'restrict$b' ) @ ( A @ 'catCod$' @ ( A @ 'catDom$' @ 'functor_ext$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(330,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ! [B: 'ZF$'] :
( ( A @ 'catCod$a' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'objIso$a' ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) )
=> ( A @ ( 'equivalence_axioms$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).
thf(1868,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ! [B: 'ZF$'] :
( ( A @ 'catCod$a' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'objIso$a' ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) )
=> ( A @ ( 'equivalence_axioms$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
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$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'yMapInv$' ) ) ) )
= ( D @ ( C @ ( B @ ( A @ 'yMapInv$a' ) ) ) @ 'makeNT$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom47) ).
thf(2382,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'yMapInv$' ) ) ) )
= ( D @ ( C @ ( B @ ( A @ 'yMapInv$a' ) ) ) @ 'makeNT$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
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$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'natTrans$b' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom537) ).
thf(2061,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'natTrans$b' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(270,axiom,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'] :
( ( A @ 'natTransP$d' )
<=> ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( B @ ( A @ 'nTDom$' @ 'mapM$f' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$' @ 'mapM$f' ) @ ( C @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$' @ 'mapO$f' ) @ ( B @ ( A @ 'nTDom$' @ 'mapO$f' ) @ ( B @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$a' )
= ( A @ 'nTDom$' @ 'catCod$f' ) )
& ( ( A @ 'nTCatDom$a' )
= ( A @ 'nTCod$' @ 'catDom$b' ) )
& ( A @ 'nTCod$' @ 'functor$a' )
& ( A @ 'nTDom$' @ 'functor$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom512) ).
thf(1636,plain,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'] :
( ( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( B @ ( A @ 'nTDom$' @ 'mapM$f' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$' @ 'mapM$f' ) @ ( C @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$' @ 'mapO$f' ) @ ( B @ ( A @ 'nTDom$' @ 'mapO$f' ) @ ( B @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$a' )
= ( A @ 'nTDom$' @ 'catCod$f' ) )
& ( ( A @ 'nTCatDom$a' )
= ( A @ 'nTCod$' @ 'catDom$b' ) )
& ( A @ 'nTCod$' @ 'functor$a' )
& ( A @ 'nTDom$' @ 'functor$a' ) )
=> ( A @ 'natTransP$d' ) )
& ( ( A @ 'natTransP$d' )
=> ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( B @ ( A @ 'nTDom$' @ 'mapM$f' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$' @ 'mapM$f' ) @ ( C @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$' @ 'mapO$f' ) @ ( B @ ( A @ 'nTDom$' @ 'mapO$f' ) @ ( B @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$a' )
= ( A @ 'nTDom$' @ 'catCod$f' ) )
& ( ( A @ 'nTCatDom$a' )
= ( A @ 'nTCod$' @ 'catDom$b' ) )
& ( A @ 'nTCod$' @ 'functor$a' )
& ( A @ 'nTDom$' @ 'functor$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
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$'] :
( ( C @ ( B @ ( A @ 'nt_abbrev$' ) @ 'fun_app$f' ) )
<=> ( ( ( A @ ( 'nTCod$c' @ 'fun_app$v' ) )
= C )
& ( ( A @ ( 'nTDom$c' @ 'fun_app$v' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).
thf(1255,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( ( A @ ( 'nTCod$c' @ 'fun_app$v' ) )
= C )
& ( ( A @ ( 'nTDom$c' @ 'fun_app$v' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) )
=> ( C @ ( B @ ( A @ 'nt_abbrev$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'nt_abbrev$' ) @ 'fun_app$f' ) )
=> ( ( ( A @ ( 'nTCod$c' @ 'fun_app$v' ) )
= C )
& ( ( A @ ( 'nTDom$c' @ 'fun_app$v' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(252,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( C @ ( B @ ( A @ 'makeCat$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom307) ).
thf(1570,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( C @ ( B @ ( A @ 'makeCat$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
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$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$a' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$s' ) ) @ 'preFunctor$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).
thf(788,plain,
! [A: 'ZF_ZF_unit_Category_ext$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$a' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$s' ) ) @ 'preFunctor$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(383,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).
thf(2132,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
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$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'yMapInv$a' ) ) ) )
= ( 'unity$' @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ ( C @ ( B @ ( A @ 'yFtor$' @ 'mapO$' ) @ 'natTrans_ext$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom558) ).
thf(2249,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$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'yMapInv$a' ) ) ) )
= ( 'unity$' @ ( D @ ( C @ ( B @ ( A @ 'uur$' ) ) ) @ ( C @ ( B @ ( A @ 'yFtor$' @ 'mapO$' ) @ 'natTrans_ext$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(89,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$' @ 'obj$a' )
= ( A @ 'obj$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom305) ).
thf(778,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$' @ 'obj$a' )
= ( A @ 'obj$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(185,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom401) ).
thf(1217,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(32,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom567) ).
thf(598,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(250,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category_axioms$' )
<=> ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ 'member$i' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom443) ).
thf(1502,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ 'member$i' ) ) ) )
=> ( A @ 'category_axioms$' ) )
& ( ( A @ 'category_axioms$' )
=> ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ 'member$i' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(106,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( ( 'uux$' @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom569) ).
thf(820,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( ( 'uux$' @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(560,plain,
! [A: 'ZF_set$'] :
( ( A @ 'uua$' @ 'collect$c' )
= A ),
inference(cnf,[status(esa)],[559]) ).
thf(561,plain,
! [A: 'ZF_set$'] :
( ( A @ 'uua$' @ 'collect$c' )
= A ),
inference(lifteq,[status(thm)],[560]) ).
thf(273,axiom,
! [A: 'A_set$',B: 'B_set$',C: 'B_a_fun$',D: 'B_a_fun$',E: 'A_b_fun$',F: 'B_b_b_fun_fun$',G: 'B_c_LSCategory_ext$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) @ 'obj$b' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom392) ).
thf(1666,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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) @ 'obj$b' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(60,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'category_axioms$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom447) ).
thf(693,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'category_axioms$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(40,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ ( A @ 'catExp$l' ) )
= ( 'unity$' @ ( 'natTransComp$' @ ( 'idNatTrans$f' @ ( 'nTCod$c' @ ( 'nTDom$c' @ ( B @ ( A @ 'uun$' ) @ 'collect$i' @ ( B @ ( A @ 'uum$' ) @ 'collect$h' @ 'category_ext$b' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).
thf(630,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ ( A @ 'catExp$l' ) )
= ( 'unity$' @ ( 'natTransComp$' @ ( 'idNatTrans$f' @ ( 'nTCod$c' @ ( 'nTDom$c' @ ( B @ ( A @ 'uun$' ) @ 'collect$i' @ ( B @ ( A @ 'uum$' ) @ 'collect$h' @ 'category_ext$b' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(466,axiom,
! [A: 'B$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$' ) )
& ( C @ ( B @ 'functorComp$' ) @ 'catDom$b' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$a' @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$e' ) @ ( A @ ( B @ 'catDom$a' @ 'dom$' @ 'fun_app$t' ) @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$e' ) @ ( A @ ( B @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'mapM$e' ) @ ( C @ 'catCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom376) ).
thf(2445,plain,
! [A: 'B$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$' ) )
& ( C @ ( B @ 'functorComp$' ) @ 'catDom$b' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$a' @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$e' ) @ ( A @ ( B @ 'catDom$a' @ 'dom$' @ 'fun_app$t' ) @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$e' ) @ ( A @ ( B @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'mapM$e' ) @ ( C @ 'catCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(320,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( C @ ( D @ 'elem$' @ 'fun_app$b' ) )
=> ( D @ ( A @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'fun_app$b' ) ) )
& ? [C: 'ZF$'] :
! [D: 'ZF$'] :
( ~ ( C @ ( D @ 'elem$' @ 'fun_app$b' ) )
=> ( D @ ( A @ 'fun_app$b' ) ) ) )
=> ( B @ ( A @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom596) ).
thf(1837,plain,
! [A: 'ZF_bool_fun$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( C @ ( D @ 'elem$' @ 'fun_app$b' ) )
=> ( D @ ( A @ 'fun_app$b' ) ) )
=> ( C @ ( A @ 'fun_app$b' ) ) )
& ? [C: 'ZF$'] :
! [D: 'ZF$'] :
( ~ ( C @ ( D @ 'elem$' @ 'fun_app$b' ) )
=> ( D @ ( A @ 'fun_app$b' ) ) ) )
=> ( B @ ( A @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(340,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).
thf(1920,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(38,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$a' ) )
= ( B @ ( A @ 'oppositeCategory$' @ 'homFtor$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom130) ).
thf(625,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$a' ) )
= ( B @ ( A @ 'oppositeCategory$' @ 'homFtor$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(173,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom463) ).
thf(1178,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(25,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom498) ).
thf(583,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(308,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'oppositeCategory$' @ 'lSCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).
thf(1787,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'oppositeCategory$' @ 'lSCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(436,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ ( D @ ( A @ 'homFtorContra$' ) @ ( C @ ( A @ 'yMapInv$' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom83) ).
thf(2327,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ ( D @ ( A @ 'homFtorContra$' ) @ ( C @ ( A @ 'yMapInv$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(378,axiom,
! [A: 'B_set$',B: 'B$'] :
( ( B @ ( A @ 'uuc$' @ 'fun_app$k' ) )
<=> ( A @ ( B @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
thf(2112,plain,
! [A: 'B_set$',B: 'B$'] :
( ( ( A @ ( B @ 'member$h' ) )
=> ( B @ ( A @ 'uuc$' @ 'fun_app$k' ) ) )
& ( ( B @ ( A @ 'uuc$' @ 'fun_app$k' ) )
=> ( A @ ( B @ 'member$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(280,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).
thf(1687,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(237,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$q' ) @ 'makeNT$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom129) ).
thf(1457,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$q' ) @ 'makeNT$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
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$'] :
( ( A @ 'oppositeCategory$a' @ 'obj$' )
= ( A @ 'obj$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).
thf(551,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$'] :
( ( A @ 'oppositeCategory$a' @ 'obj$' )
= ( A @ 'obj$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
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$'] :
( ( A @ 'functor$e' )
=> ( A @ 'preFunctor$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom198) ).
thf(1350,plain,
! [A: 'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'] :
( ( A @ 'functor$e' )
=> ( A @ 'preFunctor$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(200,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'inverse$' @ 'fun_app$' ) )
= ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom499) ).
thf(1270,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'inverse$' @ 'fun_app$' ) )
= ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(453,axiom,
'c$' @ 'obj$b' @ ( 'y$' @ 'member$i' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).
thf(2377,plain,
'c$' @ 'obj$b' @ ( 'y$' @ 'member$i' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(141,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$a' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).
thf(1017,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$a' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
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$'] :
( ( A @ 'oppositeCategory$a' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).
thf(615,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$'] :
( ( A @ 'oppositeCategory$a' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(213,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom434) ).
thf(1328,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(159,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom409) ).
thf(1064,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(72,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$'] :
( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$b' ) )
<=> ( C @ ( B @ 'fun_app$b' ) ) )
=> ( ( A @ 'collect$c' )
= ( B @ 'collect$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).
thf(725,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$'] :
( ! [C: 'ZF$'] :
( ( ( C @ ( B @ 'fun_app$b' ) )
=> ( C @ ( A @ 'fun_app$b' ) ) )
& ( ( C @ ( A @ 'fun_app$b' ) )
=> ( C @ ( B @ 'fun_app$b' ) ) ) )
=> ( ( A @ 'collect$c' )
= ( B @ 'collect$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(134,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom346) ).
thf(980,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(227,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom402) ).
thf(1425,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
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$',F: 'ZF$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$d' ) ) ) )
=> ( F @ ( A @ 'mapO$e' ) @ ( E @ ( A @ 'mapO$e' ) @ ( D @ ( A @ 'mapM$e' ) @ ( C @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom76) ).
thf(1006,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$',F: 'ZF$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$d' ) ) ) )
=> ( F @ ( A @ 'mapO$e' ) @ ( E @ ( A @ 'mapO$e' ) @ ( D @ ( A @ 'mapM$e' ) @ ( C @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(291,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$q' ) @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom123) ).
thf(1719,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$q' ) @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(30,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF$'] :
( ( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'natTransP$a' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).
thf(593,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF$'] :
( ( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'natTransP$a' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(91,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'inverse$' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).
thf(783,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'inverse$' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'dom$b' ) )
= ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'mapO$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).
thf(2268,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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'dom$b' ) )
= ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'mapO$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(75,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uux$' @ 'fun_app$' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom32) ).
thf(740,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uux$' @ 'fun_app$' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(741,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uux$' @ 'fun_app$' ) )
= A ),
inference(cnf,[status(esa)],[740]) ).
thf(742,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uux$' @ 'fun_app$' ) )
= A ),
inference(lifteq,[status(thm)],[741]) ).
thf(23,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$c' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$b' ) ) @ ( 'functor$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom227) ).
thf(578,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$c' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$b' ) ) @ ( 'functor$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(145,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( B @ ( A @ 'uut$' @ 'fun_app$d' ) )
= ( B @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
thf(1028,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( B @ ( A @ 'uut$' @ 'fun_app$d' ) )
= ( B @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(3,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ( B @ 'collect$i' @ ( A @ 'member$' ) )
<=> ( A @ ( B @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).
thf(483,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$e' ) )
=> ( B @ 'collect$i' @ ( A @ 'member$' ) ) )
& ( ( B @ 'collect$i' @ ( A @ 'member$' ) )
=> ( A @ ( B @ 'fun_app$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(484,plain,
( ! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ( A @ ( B @ 'fun_app$e' ) )
=> ( B @ 'collect$i' @ ( A @ 'member$' ) ) )
& ! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ( B @ 'collect$i' @ ( A @ 'member$' ) )
=> ( A @ ( B @ 'fun_app$e' ) ) ) ),
inference(miniscope,[status(thm)],[483]) ).
thf(485,plain,
! [D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( D @ 'collect$i' @ ( C @ 'member$' ) )
| ~ ( C @ ( D @ 'fun_app$e' ) ) )
& ( ( A @ ( B @ 'fun_app$e' ) )
| ~ ( B @ 'collect$i' @ ( A @ 'member$' ) ) ) ),
inference(cnf,[status(esa)],[484]) ).
thf(487,plain,
! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ 'collect$i' @ ( A @ 'member$' ) )
| ~ ( A @ ( B @ 'fun_app$e' ) ) ),
inference(cnfConj,[status(thm)],[485]) ).
thf(488,plain,
! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ 'collect$i' @ ( A @ 'member$' ) )
| ~ ( A @ ( B @ 'fun_app$e' ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(175,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'equivalence$a' ) )
=> ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom373) ).
thf(1182,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'equivalence$a' ) )
=> ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(117,axiom,
! [A: 'ZF$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$c' @ 'obj$a' @ ( A @ 'member$d' ) )
=> ( ( A @ ( B @ 'idNatTrans$g' @ 'natTransMap$d' @ 'fun_app$' ) )
= ( A @ ( B @ 'mapO$d' @ 'fun_app$' ) @ ( B @ 'catCod$c' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom469) ).
thf(901,plain,
! [A: 'ZF$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$c' @ 'obj$a' @ ( A @ 'member$d' ) )
=> ( ( A @ ( B @ 'idNatTrans$g' @ 'natTransMap$d' @ 'fun_app$' ) )
= ( A @ ( B @ 'mapO$d' @ 'fun_app$' ) @ ( B @ 'catCod$c' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(470,axiom,
! [A: 'A$',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$'] :
( ( B @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ 'idNatTrans$e' @ 'natTransMap$' ) )
= ( A @ ( B @ 'mapO$' ) @ ( B @ 'catCod$' @ 'id$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom467) ).
thf(2455,plain,
! [A: 'A$',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$'] :
( ( B @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ 'idNatTrans$e' @ 'natTransMap$' ) )
= ( A @ ( B @ 'mapO$' ) @ ( B @ 'catCod$' @ 'id$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(184,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) @ ( 'set$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom313) ).
thf(1214,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) @ ( 'set$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(333,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'functorM_axioms$c' )
<=> ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$' ) @ ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom354) ).
thf(1889,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$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$' ) @ ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
=> ( A @ 'functorM_axioms$c' ) )
& ( ( A @ 'functorM_axioms$c' )
=> ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$' ) @ ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(435,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) )
= ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$c' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapO$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapO$' ) @ ( B @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
& ( ( A @ 'nTCatCod$c' )
= ( A @ 'nTDom$b' @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$c' )
= ( A @ 'nTCod$b' @ 'catDom$' ) )
& ( A @ 'nTCod$b' @ 'functor$d' )
& ( A @ 'nTDom$b' @ 'functor$d' ) )
=> ( A @ 'natTransP$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom519) ).
thf(2317,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) )
= ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$c' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapO$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapO$' ) @ ( B @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
& ( ( A @ 'nTCatCod$c' )
= ( A @ 'nTDom$b' @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$c' )
= ( A @ 'nTCod$b' @ 'catDom$' ) )
& ( A @ 'nTCod$b' @ 'functor$d' )
& ( A @ 'nTDom$b' @ 'functor$d' ) )
=> ( A @ 'natTransP$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(14,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'id$a' )
= E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).
thf(554,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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'id$a' )
= E ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(80,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).
thf(753,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(369,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uuz$' @ 'fun_app$' ) )
= ( 'uux$' @ ( A @ ( A @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).
thf(2080,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uuz$' @ 'fun_app$' ) )
= ( 'uux$' @ ( A @ ( A @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(42,axiom,
! [A: 'B_ZF_fun_set$'] :
( ( A @ 'uud$' @ 'collect$e' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom111) ).
thf(640,plain,
! [A: 'B_ZF_fun_set$'] :
( ( A @ 'uud$' @ 'collect$e' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(641,plain,
! [A: 'B_ZF_fun_set$'] :
( ( A @ 'uud$' @ 'collect$e' )
= A ),
inference(cnf,[status(esa)],[640]) ).
thf(642,plain,
! [A: 'B_ZF_fun_set$'] :
( ( A @ 'uud$' @ 'collect$e' )
= A ),
inference(lifteq,[status(thm)],[641]) ).
thf(4,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( A @ 'natTrans$a' )
=> ( A @ 'natTransP$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom133) ).
thf(489,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( A @ 'natTrans$a' )
=> ( A @ 'natTransP$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(345,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$d' ) ) ) )
=> ( A @ 'category_axioms$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom442) ).
thf(1937,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$d' ) ) ) )
=> ( A @ 'category_axioms$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(358,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homFtorContra$' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homFtorContra$' ) @ ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom288) ).
thf(2038,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homFtorContra$' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homFtorContra$' ) @ ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(234,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'id$b' @ 'fun_app$r' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom340) ).
thf(1446,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'id$b' @ 'fun_app$r' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(474,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'mor$' @ 'extensional$a' @ ( A @ 'mor2ZF$' @ 'member$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).
thf(2472,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'mor$' @ 'extensional$a' @ ( A @ 'mor2ZF$' @ 'member$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(149,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'functor$d' ) )
=> ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom421) ).
thf(1039,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'functor$d' ) )
=> ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(622,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory_axioms$' )
| ~ ( A @ 'lSCategory$' ) ),
inference(cnfConj,[status(thm)],[620]) ).
thf(304,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( B @ ( C @ ( A @ 'oppositeCategory$' @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).
thf(1776,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( B @ ( C @ ( A @ 'oppositeCategory$' @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
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$'] :
( ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) )
<=> ( ( ( A @ 'catCod$a' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom343) ).
thf(1150,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$'] :
( ( ( ( ( A @ 'catCod$a' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
& ( ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) )
=> ( ( ( A @ 'catCod$a' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(323,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom172) ).
thf(1852,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(33,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'natTrans$b' )
=> ( A @ 'natTransP$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).
thf(604,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$'] :
( ( A @ 'natTrans$b' )
=> ( A @ 'natTransP$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(605,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'natTransP$b' )
| ~ ( A @ 'natTrans$b' ) ),
inference(cnf,[status(esa)],[604]) ).
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$'] :
( ( ( C @ ( B @ 'functor_comp_def$a' ) )
& ( C @ ( B @ 'functorComp$a' ) @ 'catDom$a' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$a' @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$d' @ 'fun_app$' ) @ ( A @ ( B @ 'catDom$a' @ 'dom$' @ 'fun_app$t' ) @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$d' @ 'fun_app$' ) @ ( A @ ( B @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'mapM$d' @ 'fun_app$' ) @ ( C @ 'catCod$c' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom377) ).
thf(2370,plain,
! [A: 'B$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$a' ) )
& ( C @ ( B @ 'functorComp$a' ) @ 'catDom$a' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$a' @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$d' @ 'fun_app$' ) @ ( A @ ( B @ 'catDom$a' @ 'dom$' @ 'fun_app$t' ) @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$d' @ 'fun_app$' ) @ ( A @ ( B @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'mapM$d' @ 'fun_app$' ) @ ( C @ 'catCod$c' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(236,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'makeCat$' @ 'compDefined$' ) @ 'fun_app$b' ) )
<=> ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).
thf(1451,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( C @ ( B @ ( A @ 'makeCat$' @ 'compDefined$' ) @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ 'makeCat$' @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(74,axiom,
( 'set$'
= ( 'set$a' @ 'makeCat$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom289) ).
thf(738,plain,
( 'set$'
= ( 'set$a' @ 'makeCat$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(430,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( B @ ( A @ 'uus$' @ 'fun_app$c' ) )
= ( B @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'id$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
thf(2304,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 @ ( A @ 'uus$' @ 'fun_app$c' ) )
= ( B @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'id$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(198,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( C @ ( D @ ( B @ ( A @ 'oppositeCategory$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom86) ).
thf(1266,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( C @ ( D @ ( B @ ( A @ 'oppositeCategory$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(388,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$' ) @ 'mapO$a' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom81) ).
thf(2153,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$' ) @ 'mapO$a' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(458,axiom,
! [A: 'ZF$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$',D: 'A$'] :
( ( D @ ( C @ ( B @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'homSet$' ) ) @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ( ( A @ ( D @ ( C @ ( B @ 'homFtorMapContra$' ) ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( A @ ( B @ 'zF2mor$' ) @ ( C @ ( B @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ 'mor2ZF$' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom370) ).
thf(2387,plain,
! [A: 'ZF$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$',D: 'A$'] :
( ( D @ ( C @ ( B @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'homSet$' ) ) @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ( ( A @ ( D @ ( C @ ( B @ 'homFtorMapContra$' ) ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( A @ ( B @ 'zF2mor$' ) @ ( C @ ( B @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ 'mor2ZF$' @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(190,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
<=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).
thf(1231,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( C @ ( D @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
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$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'preFunctor$c' ) )
=> ( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( B @ ( A @ 'mapO$' ) @ 'member$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom364) ).
thf(1131,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 @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'preFunctor$c' ) )
=> ( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( B @ ( A @ 'mapO$' ) @ 'member$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(47,axiom,
! [A: 'B_set$'] :
( ( A @ 'uuc$' @ 'collect$d' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).
thf(654,plain,
! [A: 'B_set$'] :
( ( A @ 'uuc$' @ 'collect$d' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(352,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ 'elem$' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom571) ).
thf(2006,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ 'elem$' @ 'fun_app$b' ) )
=> ( ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(479,axiom,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( B @ 'lSCategory$' )
& ( B @ 'yFtor$a' @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( B @ 'yFtor$a' @ 'mapO$' ) )
= ( A @ ( B @ 'homFtorContra$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom333) ).
thf(2497,plain,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( B @ 'lSCategory$' )
& ( B @ 'yFtor$a' @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( B @ 'yFtor$a' @ 'mapO$' ) )
= ( A @ ( B @ 'homFtorContra$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(362,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$e' ) )
<=> ( ( A @ ( 'natTransExt$' @ 'fun_app$e' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom166) ).
thf(2052,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( A @ ( 'natTransExt$' @ 'fun_app$e' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) )
=> ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) )
& ( ( A @ ( 'natTrans$' @ 'fun_app$e' ) )
=> ( ( A @ ( 'natTransExt$' @ 'fun_app$e' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(476,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'yFtor$' @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ ( D @ ( A @ 'yFtor$' @ 'mapO$' ) @ ( C @ ( A @ 'yMapInv$' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).
thf(2482,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'yFtor$' @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ ( D @ ( A @ 'yFtor$' @ 'mapO$' ) @ ( C @ ( A @ 'yMapInv$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
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$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'functorM$c' ) )
=> ( D @ ( A @ 'mapO$' ) @ ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom350) ).
thf(1857,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'functorM$c' ) )
=> ( D @ ( A @ 'mapO$' ) @ ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(348,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( C @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).
thf(1991,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( C @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(314,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'mor$' )
= ( A @ 'mor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom55) ).
thf(1814,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'mor$' )
= ( A @ 'mor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
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$'] :
( ( A @ 'functorM$c' )
<=> ( ( A @ 'functorM_axioms$c' )
& ( A @ 'preFunctor$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom158) ).
thf(633,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$'] :
( ( ( ( A @ 'functorM_axioms$c' )
& ( A @ 'preFunctor$c' ) )
=> ( A @ 'functorM$c' ) )
& ( ( A @ 'functorM$c' )
=> ( ( A @ 'functorM_axioms$c' )
& ( A @ 'preFunctor$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(9,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$' ) ) @ 'functor$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom225) ).
thf(541,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$' ) ) @ 'functor$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'objIso$a' ) @ 'fun_app$b' ) )
<=> ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom482) ).
thf(657,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( C @ ( B @ ( A @ 'objIso$a' ) @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ 'objIso$a' ) @ 'fun_app$b' ) )
=> ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
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$',D: 'A$'] :
( ( ( B @ 'catDom$b' @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$b' ) ) ) )
=> ( D @ ( C @ 'mapO$f' ) @ ( D @ ( B @ 'mapO$f' ) @ ( D @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( C @ 'catCod$f' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).
thf(2076,plain,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$',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$'] :
( ( ( B @ 'catDom$b' @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$b' ) ) ) )
=> ( D @ ( C @ 'mapO$f' ) @ ( D @ ( B @ 'mapO$f' ) @ ( D @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( C @ 'catCod$f' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(449,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'ZF$'] :
( ( ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ 'elem$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom326) ).
thf(2368,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'ZF$'] :
( ( ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ 'elem$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
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$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$a' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$s' ) ) @ 'functorM$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom245) ).
thf(674,plain,
! [A: 'ZF_ZF_unit_Category_ext$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$a' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$s' ) ) @ 'functorM$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(272,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( B @ 'dom$a' @ 'fun_app$' ) ) )
& ( B @ 'mor$b' @ ( C @ 'member$d' ) )
& ( B @ 'mor$b' @ ( A @ 'member$d' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom386) ).
thf(1663,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( B @ 'dom$a' @ 'fun_app$' ) ) )
& ( B @ 'mor$b' @ ( C @ 'member$d' ) )
& ( B @ 'mor$b' @ ( A @ 'member$d' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(399,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) )
= ( B @ ( A @ 'oppositeCategory$' @ 'homFtor$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom91) ).
thf(2189,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) )
= ( B @ ( A @ 'oppositeCategory$' @ 'homFtor$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
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$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( ( E @ ( D @ ( B @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( D @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).
thf(1185,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$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( ( E @ ( D @ ( B @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( D @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(124,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uuj$' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
thf(926,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uuj$' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(87,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'hOMCollection$' ) ) )
= ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'collect$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom589) ).
thf(773,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'hOMCollection$' ) ) )
= ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'collect$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(96,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$' @ 'mor$b' )
= ( A @ 'mor$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).
thf(794,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$' @ 'mor$b' )
= ( A @ 'mor$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
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$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'functor_ext$' ) ) ) @ 'mapM$' )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom478) ).
thf(586,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$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'functor_ext$' ) ) ) @ 'mapM$' )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
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$',B: 'A$'] :
( ( B @ ( A @ 'mapO$' ) )
= ( B @ ( A @ 'uuv$' ) @ 'the$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom562) ).
thf(2338,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( B @ ( A @ 'mapO$' ) )
= ( B @ ( A @ 'uuv$' ) @ 'the$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(380,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( ( B @ ( A @ 'id$b' @ 'fun_app$r' ) )
= ( C @ ( A @ 'id$b' @ 'fun_app$r' ) ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom309) ).
thf(2121,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( ( B @ ( A @ 'id$b' @ 'fun_app$r' ) )
= ( C @ ( A @ 'id$b' @ 'fun_app$r' ) ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
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$'] :
( ( ( C @ ( B @ 'functor_comp_def$b' @ 'fun_app$f' ) )
& ( C @ ( B @ 'functorComp$b' ) @ 'preFunctor$a' )
& ( B @ 'catDom$d' @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$b' ) @ 'mapO$d' @ 'fun_app$' ) )
= ( A @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom433) ).
thf(1698,plain,
! [A: 'ZF$',B: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$b' @ 'fun_app$f' ) )
& ( C @ ( B @ 'functorComp$b' ) @ 'preFunctor$a' )
& ( B @ 'catDom$d' @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$b' ) @ 'mapO$d' @ 'fun_app$' ) )
= ( A @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(186,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homFtorMapContra$' ) ) )
= ( B @ ( A @ 'uuo$' ) @ ( C @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) @ ( C @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).
thf(1219,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homFtorMapContra$' ) ) )
= ( B @ ( A @ 'uuo$' ) @ ( C @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) @ ( C @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(201,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'elem$' @ 'fun_app$b' ) )
=> ( C @ ( D @ ( B @ 'fun_app$' ) @ 'elem$' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom575) ).
thf(1273,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'elem$' @ 'fun_app$b' ) )
=> ( C @ ( D @ ( B @ 'fun_app$' ) @ 'elem$' @ 'fun_app$b' ) ) )
=> ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(77,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' @ 'mor$b' )
= ( A @ 'mor$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).
thf(745,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' @ 'mor$b' )
= ( A @ 'mor$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(257,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$a' @ 'mor$b' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).
thf(1595,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$a' @ 'mor$b' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(21,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$c' ) )
=> ( A @ 'lSCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom470) ).
thf(573,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$c' ) )
=> ( A @ 'lSCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(130,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'oppositeCategory$' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).
thf(965,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'oppositeCategory$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(79,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) )
= ( B @ ( A @ 'homFtorContra$a' ) @ 'makeFtor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom171) ).
thf(750,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) )
= ( B @ ( A @ 'homFtorContra$a' ) @ 'makeFtor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
<=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom59) ).
thf(1727,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$',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$'] :
( ( ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
=> ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(360,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( A @ 'catCod$' @ 'mor$a' @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).
thf(2048,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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( A @ 'catCod$' @ 'mor$a' @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ 'member$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(331,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$',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$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).
thf(1884,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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(264,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' )
= ( A @ 'more$a' @ ( A @ 'uuj$' @ ( A @ 'id$b' @ ( A @ 'dom$' @ ( A @ 'cod$' @ ( A @ 'mor$' @ ( A @ 'obj$b' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom544) ).
thf(1620,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' )
= ( A @ 'more$a' @ ( A @ 'uuj$' @ ( A @ 'id$b' @ ( A @ 'dom$' @ ( A @ 'cod$' @ ( A @ 'mor$' @ ( A @ 'obj$b' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(460,axiom,
! [A: 'B$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$d' ) )
& ( C @ ( B @ 'functorComp$d' ) @ 'catDom$a' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'mapO$' ) @ ( C @ 'mapO$g' ) @ ( A @ ( B @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( B @ 'mapO$' ) @ ( C @ 'mapO$g' ) @ ( A @ ( B @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'mapM$g' ) @ ( C @ 'catCod$e' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).
thf(2393,plain,
! [A: 'B$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$d' ) )
& ( C @ ( B @ 'functorComp$d' ) @ 'catDom$a' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( B @ 'mapO$' ) @ ( C @ 'mapO$g' ) @ ( A @ ( B @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( B @ 'mapO$' ) @ ( C @ 'mapO$g' ) @ ( A @ ( B @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'mapM$g' ) @ ( C @ 'catCod$e' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(76,axiom,
! [A: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'] :
( ( A @ 'functor$c' )
=> ( A @ 'idNatTrans$a' @ 'natTransP$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).
thf(743,plain,
! [A: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$'] :
( ( A @ 'functor$c' )
=> ( A @ 'idNatTrans$a' @ 'natTransP$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(68,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( C @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom459) ).
thf(711,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( C @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(347,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ 'member$i' ) ) ) )
=> ( A @ 'category_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).
thf(1965,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ 'member$i' ) ) ) )
=> ( A @ 'category_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(17,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$'] :
( ( A @ 'uuh$' @ 'collect$h' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom115) ).
thf(562,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$'] :
( ( A @ 'uuh$' @ 'collect$h' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(118,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'catCod$a' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'catDom$a' ) )
& ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) )
& ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom520) ).
thf(904,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'catCod$a' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'catDom$a' ) )
& ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) )
& ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(132,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'homSet$' ) ) )
= ( B @ ( C @ ( A @ 'homSet$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).
thf(975,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'homSet$' ) ) )
= ( B @ ( C @ ( A @ 'homSet$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(286,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom315) ).
thf(1701,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(462,axiom,
! [A: 'A$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$d' ) )
& ( C @ ( B @ 'functorComp$d' ) @ ( 'preFunctor$' @ 'fun_app$f' ) )
& ( B @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$d' ) @ 'mapO$a' ) )
= ( A @ ( B @ 'mapO$' ) @ ( C @ 'mapO$g' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).
thf(2398,plain,
! [A: 'A$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$d' ) )
& ( C @ ( B @ 'functorComp$d' ) @ ( 'preFunctor$' @ 'fun_app$f' ) )
& ( B @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$d' ) @ 'mapO$a' ) )
= ( A @ ( B @ 'mapO$' ) @ ( C @ 'mapO$g' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(11,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom490) ).
thf(545,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(248,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
<=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$t' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom300) ).
thf(1488,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$t' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$t' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(391,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$a' @ ( A @ 'comp$a' @ ( A @ 'id$b' @ ( A @ 'cod$' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$b' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).
thf(2161,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$a' @ ( A @ 'comp$a' @ ( A @ 'id$b' @ ( A @ 'cod$' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$b' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(164,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( A @ 'more$b' )
= ( B @ 'more$b' ) )
& ( ( A @ 'comp$' )
= ( B @ 'comp$' ) )
& ( ( A @ 'id$a' )
= ( B @ 'id$a' ) )
& ( ( A @ 'cod$a' )
= ( B @ 'cod$a' ) )
& ( ( A @ 'dom$a' )
= ( B @ 'dom$a' ) )
& ( ( A @ 'mor$b' )
= ( B @ 'mor$b' ) )
& ( ( A @ 'obj$a' )
= ( B @ 'obj$a' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom369) ).
thf(1139,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( A @ 'more$b' )
= ( B @ 'more$b' ) )
& ( ( A @ 'comp$' )
= ( B @ 'comp$' ) )
& ( ( A @ 'id$a' )
= ( B @ 'id$a' ) )
& ( ( A @ 'cod$a' )
= ( B @ 'cod$a' ) )
& ( ( A @ 'dom$a' )
= ( B @ 'dom$a' ) )
& ( ( A @ 'mor$b' )
= ( B @ 'mor$b' ) )
& ( ( A @ 'obj$a' )
= ( B @ 'obj$a' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(274,axiom,
! [A: 'ZF$',B: 'ZF_bool_fun$'] :
( ( B @ 'collect$c' @ ( A @ 'member$d' ) )
<=> ( A @ ( B @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom98) ).
thf(1669,plain,
! [A: 'ZF$',B: 'ZF_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$b' ) )
=> ( B @ 'collect$c' @ ( A @ 'member$d' ) ) )
& ( ( B @ 'collect$c' @ ( A @ 'member$d' ) )
=> ( A @ ( B @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(426,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$' )
= ( B @ 'more$' ) )
& ( ( A @ 'mor2ZF$' )
= ( B @ 'mor2ZF$' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$b' )
= ( B @ 'id$b' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$b' )
= ( B @ 'obj$b' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom365) ).
thf(2293,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$' )
= ( B @ 'more$' ) )
& ( ( A @ 'mor2ZF$' )
= ( B @ 'mor2ZF$' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$b' )
= ( B @ 'id$b' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$b' )
= ( B @ 'obj$b' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
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$',D: 'A$'] :
( ( ( B @ 'catDom$a' @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$' ) @ 'fun_app$f' ) ) )
=> ( D @ ( C @ 'mapO$a' ) @ ( D @ ( B @ 'mapO$a' ) @ ( D @ ( A @ 'natTransMap$b' ) @ ( C @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom456) ).
thf(1733,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',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$'] :
( ( ( B @ 'catDom$a' @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$' ) @ 'fun_app$f' ) ) )
=> ( D @ ( C @ 'mapO$a' ) @ ( D @ ( B @ 'mapO$a' ) @ ( D @ ( A @ 'natTransMap$b' ) @ ( C @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
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$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'preFunctor$c' ) )
=> ( ( B @ ( A @ 'makeFtor$d' @ 'mapO$' ) )
= ( B @ ( A @ 'mapO$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).
thf(2442,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'preFunctor$c' ) )
=> ( ( B @ ( A @ 'makeFtor$d' @ 'mapO$' ) )
= ( B @ ( A @ 'mapO$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'dom$a' )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom399) ).
thf(704,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'dom$a' )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(275,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( B @ ( C @ ( A @ 'oppositeCategory$b' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom390) ).
thf(1675,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( B @ ( C @ ( A @ 'oppositeCategory$b' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(53,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).
thf(672,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(69,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category_axioms$a' )
=> ( A @ 'makeCat$' @ 'category$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).
thf(713,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category_axioms$a' )
=> ( A @ 'makeCat$' @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
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$'] :
( ( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'preFunctor$c' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'comp$b' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).
thf(1865,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'preFunctor$c' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'comp$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
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$'] :
( ( C @ ( A @ 'fun_app$e' ) )
<=> ( C @ ( B @ 'fun_app$e' ) ) )
=> ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).
thf(491,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ! [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'fun_app$e' ) )
=> ( C @ ( A @ 'fun_app$e' ) ) )
& ( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) ) )
=> ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(492,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$'] :
( ( C @ ( B @ 'fun_app$e' ) )
=> ( C @ ( A @ 'fun_app$e' ) ) )
& ! [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( C @ ( A @ 'fun_app$e' ) )
=> ( C @ ( B @ 'fun_app$e' ) ) ) )
=> ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) ) ),
inference(miniscope,[status(thm)],[491]) ).
thf(493,plain,
! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ( ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) )
| ~ ( A @ ( B @ sk2 ) @ ( A @ 'fun_app$e' ) )
| ~ ( A @ ( B @ sk1 ) @ ( B @ 'fun_app$e' ) ) )
& ( ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) )
| ( A @ ( B @ sk2 ) @ ( B @ 'fun_app$e' ) )
| ~ ( A @ ( B @ sk1 ) @ ( B @ 'fun_app$e' ) ) )
& ( ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) )
| ~ ( A @ ( B @ sk2 ) @ ( A @ 'fun_app$e' ) )
| ( A @ ( B @ sk1 ) @ ( A @ 'fun_app$e' ) ) )
& ( ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) )
| ( A @ ( B @ sk2 ) @ ( B @ 'fun_app$e' ) )
| ( A @ ( B @ sk1 ) @ ( A @ 'fun_app$e' ) ) ) ),
inference(cnf,[status(esa)],[492]) ).
thf(494,plain,
! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) )
| ( A @ ( B @ sk2 ) @ ( B @ 'fun_app$e' ) )
| ( A @ ( B @ sk1 ) @ ( A @ 'fun_app$e' ) ) ),
inference(cnfConj,[status(thm)],[493]) ).
thf(498,plain,
! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ( A @ ( B @ sk2 ) @ ( B @ 'fun_app$e' ) )
| ( A @ ( B @ sk1 ) @ ( A @ 'fun_app$e' ) )
| ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) ) ),
inference(lifteq,[status(thm)],[494]) ).
thf(192,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom473) ).
thf(1239,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(350,axiom,
! [A: 'A_set$',B: 'A$'] :
( ( B @ ( A @ 'uu$' @ 'fun_app$l' ) )
<=> ( A @ ( B @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
thf(1997,plain,
! [A: 'A_set$',B: 'A$'] :
( ( ( A @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'uu$' @ 'fun_app$l' ) ) )
& ( ( B @ ( A @ 'uu$' @ 'fun_app$l' ) )
=> ( A @ ( B @ 'member$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(393,axiom,
! [A: 'ZF$',B: 'ZF$'] :
~ ( ( A @ ( B @ 'elem$' @ 'fun_app$b' ) )
& ( B @ ( A @ 'elem$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom594) ).
thf(2166,plain,
! [A: 'ZF$',B: 'ZF$'] :
~ ( ( A @ ( B @ 'elem$' @ 'fun_app$b' ) )
& ( B @ ( A @ 'elem$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(300,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorContra$' ) @ 'mapO$a' ) )
= ( B @ ( C @ ( A @ 'homSet$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom62) ).
thf(1765,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorContra$' ) @ 'mapO$a' ) )
= ( B @ ( C @ ( A @ 'homSet$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(334,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).
thf(1897,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(99,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'natTransP$b' )
=> ( A @ 'makeNT$b' @ 'natTrans$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom126) ).
thf(804,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'natTransP$b' )
=> ( A @ 'makeNT$b' @ 'natTrans$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(240,axiom,
! [A: 'ZF$',B: 'ZF_bool_fun$',C: 'ZF$'] :
( ( ( A @ ( C @ 'elem$' @ 'fun_app$b' ) )
& ! [D: 'ZF$'] :
( ( ( A @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ! [E: 'ZF$'] :
( ( ( A @ ( E @ 'elem$' @ 'fun_app$b' ) )
& ( D @ ( E @ 'elem$' @ 'fun_app$b' ) ) )
=> ( E @ ( B @ 'fun_app$b' ) ) ) )
=> ( D @ ( B @ 'fun_app$b' ) ) ) )
=> ( C @ ( B @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom597) ).
thf(1464,plain,
! [A: 'ZF$',B: 'ZF_bool_fun$',C: 'ZF$'] :
( ( ( A @ ( C @ 'elem$' @ 'fun_app$b' ) )
& ! [D: 'ZF$'] :
( ( ( A @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ! [E: 'ZF$'] :
( ( ( A @ ( E @ 'elem$' @ 'fun_app$b' ) )
& ( D @ ( E @ 'elem$' @ 'fun_app$b' ) ) )
=> ( E @ ( B @ 'fun_app$b' ) ) ) )
=> ( D @ ( B @ 'fun_app$b' ) ) ) )
=> ( C @ ( B @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(475,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_ZF_fun$',D: 'B_ZF_fun_b_ZF_fun_fun$',E: 'B_ZF_fun_b_ZF_fun_fun$'] :
( ( ! [F: 'B_ZF_fun$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$s' ) )
= ( F @ ( E @ 'fun_app$s' ) ) ) )
& ( ( B @ 'mor2ZF$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'mor2ZF_update$' ) )
= ( B @ ( E @ 'mor2ZF_update$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).
thf(2474,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$'] :
( ( ! [F: 'B_ZF_fun$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$s' ) )
= ( F @ ( E @ 'fun_app$s' ) ) ) )
& ( ( B @ 'mor2ZF$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'mor2ZF_update$' ) )
= ( B @ ( E @ 'mor2ZF_update$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(443,axiom,
'set$' @ ( 'c$' @ 'oppositeCategory$' @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ 'functor_abbrev$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).
thf(2346,plain,
'set$' @ ( 'c$' @ 'oppositeCategory$' @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ 'functor_abbrev$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(204,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( ( ( A @ ( 'nTCod$c' @ 'fun_app$v' ) )
= C )
& ( ( A @ ( 'nTDom$c' @ 'fun_app$v' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'nt_abbrev$' ) @ 'fun_app$f' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).
thf(1282,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
~ ( ~ ( ( ( A @ ( 'nTCod$c' @ 'fun_app$v' ) )
= C )
& ( ( A @ ( 'nTDom$c' @ 'fun_app$v' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(73,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$f' ) )
=> ( A @ ( 'functorM$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom200) ).
thf(736,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$f' ) )
=> ( A @ ( 'functorM$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
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$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' ) )
& ( B @ 'nTCatDom$d' @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( C @ ( B @ 'natTransComp$a' ) @ 'natTransMap$d' @ 'fun_app$' ) )
= ( A @ ( C @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ ( B @ 'natTransMap$d' @ 'fun_app$' ) @ ( C @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).
thf(567,plain,
! [A: 'ZF$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' ) )
& ( B @ 'nTCatDom$d' @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( C @ ( B @ 'natTransComp$a' ) @ 'natTransMap$d' @ 'fun_app$' ) )
= ( A @ ( C @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ ( B @ 'natTransMap$d' @ 'fun_app$' ) @ ( C @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
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$'] :
( ( ( C @ ( B @ 'nTCompDefined$' @ 'fun_app$e' ) )
& ( B @ 'nTCatDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ ( 'natTransComp$' @ 'fun_app$x' ) @ 'fun_app$w' ) @ 'natTransMap$b' ) )
= ( A @ ( C @ 'natTransMap$b' ) @ ( A @ ( B @ 'natTransMap$b' ) @ ( C @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom542) ).
thf(1771,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$'] :
( ( ( C @ ( B @ 'nTCompDefined$' @ 'fun_app$e' ) )
& ( B @ 'nTCatDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ ( 'natTransComp$' @ 'fun_app$x' ) @ 'fun_app$w' ) @ 'natTransMap$b' ) )
= ( A @ ( C @ 'natTransMap$b' ) @ ( A @ ( B @ 'natTransMap$b' ) @ ( C @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(172,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom422) ).
thf(1175,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(84,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uuw$' @ 'fun_app$m' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom576) ).
thf(764,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uuw$' @ 'fun_app$m' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(312,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
<=> ( 'set$' @ 'mor$b' @ ( A @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom577) ).
thf(1806,plain,
! [A: 'ZF$'] :
( ( ( 'set$' @ 'mor$b' @ ( A @ 'member$d' ) )
=> ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
& ( ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( 'set$' @ 'mor$b' @ ( A @ 'member$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(139,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'set$' @ 'id$a' @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom372) ).
thf(1011,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ( ( A @ ( B @ ( 'set$' @ 'id$a' @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(256,axiom,
! [A: 'ZF_set$',B: 'ZF$'] :
( ( B @ ( A @ 'uua$' @ 'fun_app$b' ) )
<=> ( A @ ( B @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
thf(1589,plain,
! [A: 'ZF_set$',B: 'ZF$'] :
( ( ( A @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'uua$' @ 'fun_app$b' ) ) )
& ( ( B @ ( A @ 'uua$' @ 'fun_app$b' ) )
=> ( A @ ( B @ 'member$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(422,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$p' ) )
= ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
thf(2284,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$p' ) )
= ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(343,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom89) ).
thf(1933,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
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$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uul$' ) @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( D @ ( A @ 'zF2mor$' ) @ ( B @ 'mapM$a' @ 'fun_app$p' ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom29) ).
thf(2246,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uul$' ) @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( D @ ( A @ 'zF2mor$' ) @ ( B @ 'mapM$a' @ 'fun_app$p' ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(259,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( C @ ( B @ ( A @ 'makeCat$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).
thf(1603,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( C @ ( B @ ( A @ 'makeCat$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'cod$b' ) )
= ( B @ ( A @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'mapO$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom357) ).
thf(2299,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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'cod$b' ) )
= ( B @ ( A @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'mapO$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(45,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( C @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( C @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( ( C @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( ( B @ ( C @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom565) ).
thf(649,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( C @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( C @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( ( C @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( ( B @ ( C @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(151,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homSet$' ) ) )
= ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'implode$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom591) ).
thf(1043,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homSet$' ) ) )
= ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'implode$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(454,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuo$' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'zF2mor$' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).
thf(2378,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuo$' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'zF2mor$' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(281,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$' ) @ ( 'functor$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom173) ).
thf(1690,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$' ) @ ( 'functor$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
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$'] :
( ( C @ ( B @ ( A @ 'uuv$' ) @ 'fun_app$f' ) )
<=> ( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).
thf(2180,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) )
=> ( C @ ( B @ ( A @ 'uuv$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uuv$' ) @ 'fun_app$f' ) )
=> ( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(102,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom491) ).
thf(811,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(268,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).
thf(1630,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
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$'] :
( ( A @ 'functorM$d' )
=> ( A @ 'preFunctor$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).
thf(1460,plain,
! [A: 'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'] :
( ( A @ 'functorM$d' )
=> ( A @ 'preFunctor$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(409,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'yFtor$' )
= ( A @ 'yFtor$a' @ 'makeFtor$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom339) ).
thf(2252,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'yFtor$' )
= ( A @ 'yFtor$a' @ 'makeFtor$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(126,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'obj$b' )
= ( A @ 'obj$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).
thf(932,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'obj$b' )
= ( A @ 'obj$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
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$',F: 'ZF$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$c' ) ) ) )
=> ( F @ ( A @ 'mapO$d' @ 'fun_app$' ) @ ( E @ ( A @ 'mapO$d' @ 'fun_app$' ) @ ( D @ ( A @ 'mapM$d' @ 'fun_app$' ) @ ( C @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom75) ).
thf(1820,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$c' ) ) ) )
=> ( F @ ( A @ 'mapO$d' @ 'fun_app$' ) @ ( E @ ( A @ 'mapO$d' @ 'fun_app$' ) @ ( D @ ( A @ 'mapM$d' @ 'fun_app$' ) @ ( C @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(757,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' @ 'oppositeCategory$b' )
= A ),
inference(cnf,[status(esa)],[756]) ).
thf(758,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' @ 'oppositeCategory$b' )
= A ),
inference(lifteq,[status(thm)],[757]) ).
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$'] :
( ( A @ 'functorExt$d' )
=> ( A @ 'catDom$' @ 'mor$' @ 'extensional$' @ ( A @ 'mapM$' @ 'member$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).
thf(1339,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'functorExt$d' )
=> ( A @ 'catDom$' @ 'mor$' @ 'extensional$' @ ( A @ 'mapM$' @ 'member$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(434,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuq$' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'zF2mor$' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).
thf(2314,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuq$' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'zF2mor$' ) @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
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$'] :
( ( ( C @ ( B @ 'functor_comp_def$f' ) )
& ( C @ ( B @ 'functorComp$f' ) @ 'preFunctor$c' )
& ( B @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$f' ) @ 'mapO$' ) )
= ( A @ ( B @ 'mapO$' ) @ ( C @ 'mapO$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
thf(2343,plain,
! [A: 'A$',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$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$f' ) )
& ( C @ ( B @ 'functorComp$f' ) @ 'preFunctor$c' )
& ( B @ 'catDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$f' ) @ 'mapO$' ) )
= ( A @ ( B @ 'mapO$' ) @ ( C @ 'mapO$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
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$'] :
( ( C @ ( B @ 'catExp$' ) @ 'mor$a' @ ( A @ 'member$' ) )
=> ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).
thf(848,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$'] :
( ( C @ ( B @ 'catExp$' ) @ 'mor$a' @ ( A @ 'member$' ) )
=> ( A @ ( 'natTrans$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(63,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$' @ 'fun_app$f' ) )
=> ( A @ 'makeFtor$' @ ( 'functor$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).
thf(700,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$' @ 'fun_app$f' ) )
=> ( A @ 'makeFtor$' @ ( 'functor$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(419,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( C @ ( A @ 'homSet$' ) ) @ ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ 'elem$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).
thf(2278,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( C @ ( A @ 'homSet$' ) ) @ ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ 'elem$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(51,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$j' ) ) @ 'preFunctor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom250) ).
thf(668,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$j' ) ) @ 'preFunctor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(135,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( A = B )
<=> ! [C: 'ZF$'] :
( ( A @ ( C @ 'elem$' @ 'fun_app$b' ) )
<=> ( B @ ( C @ 'elem$' @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom593) ).
thf(983,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( ( B @ ( C @ 'elem$' @ 'fun_app$b' ) )
=> ( A @ ( C @ 'elem$' @ 'fun_app$b' ) ) )
& ( ( A @ ( C @ 'elem$' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'elem$' @ 'fun_app$b' ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: 'ZF$'] :
( ( ( B @ ( C @ 'elem$' @ 'fun_app$b' ) )
=> ( A @ ( C @ 'elem$' @ 'fun_app$b' ) ) )
& ( ( A @ ( C @ 'elem$' @ 'fun_app$b' ) )
=> ( B @ ( C @ 'elem$' @ 'fun_app$b' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(224,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category_axioms$' )
=> ( A @ 'oppositeCategory$' @ 'category_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).
thf(1396,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category_axioms$' )
=> ( A @ 'oppositeCategory$' @ 'category_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(445,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ 'oppositeCategory$' @ 'zF2mor$' ) )
= ( B @ ( A @ 'zF2mor$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).
thf(2350,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ 'oppositeCategory$' @ 'zF2mor$' ) )
= ( B @ ( A @ 'zF2mor$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(463,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$a' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) )
=> ( A @ 'equivalence_axioms$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).
thf(2401,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$a' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapO$' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) )
=> ( A @ 'equivalence_axioms$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(395,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$b' @ ( A @ 'member$d' ) )
=> ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$' @ 'cod$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).
thf(2171,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$b' @ ( A @ 'member$d' ) )
=> ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$' @ 'cod$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(61,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$a' @ 'obj$b' )
= ( A @ 'obj$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).
thf(695,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$a' @ 'obj$b' )
= ( A @ 'obj$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(160,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).
thf(1066,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(371,axiom,
! [A: 'B_ZF_fun_set$',B: 'B_ZF_fun$'] :
( ( B @ ( A @ 'uud$' @ 'fun_app$h' ) )
<=> ( A @ ( B @ 'member$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
thf(2086,plain,
! [A: 'B_ZF_fun_set$',B: 'B_ZF_fun$'] :
( ( ( A @ ( B @ 'member$e' ) )
=> ( B @ ( A @ 'uud$' @ 'fun_app$h' ) ) )
& ( ( B @ ( A @ 'uud$' @ 'fun_app$h' ) )
=> ( A @ ( B @ 'member$e' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(365,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF_ZF_fun$',D: 'ZF$'] :
( ! [E: 'ZF$'] :
( ( A @ ( E @ 'elem$' @ 'fun_app$b' ) )
=> ( ( E @ ( B @ 'fun_app$' ) )
= ( E @ ( C @ 'fun_app$' ) ) ) )
=> ( ( B @ ( D @ ( A @ 'zFfun$' ) ) )
= ( C @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom551) ).
thf(2064,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF_ZF_fun$',D: 'ZF$'] :
( ! [E: 'ZF$'] :
( ( A @ ( E @ 'elem$' @ 'fun_app$b' ) )
=> ( ( E @ ( B @ 'fun_app$' ) )
= ( E @ ( C @ 'fun_app$' ) ) ) )
=> ( ( B @ ( D @ ( A @ 'zFfun$' ) ) )
= ( C @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(424,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) )
= ( C @ ( A @ 'uuq$' ) @ ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom557) ).
thf(2288,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) )
= ( C @ ( A @ 'uuq$' ) @ ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( B @ ( C @ ( A @ 'yFtor$' @ 'mapO$' ) @ ( D @ 'nt_abbrev$' ) @ 'fun_app$f' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( B @ 'mapO$a' ) @ ( D @ ( C @ ( A @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
thf(2244,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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( B @ ( C @ ( A @ 'yFtor$' @ 'mapO$' ) @ ( D @ 'nt_abbrev$' ) @ 'fun_app$f' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( B @ 'mapO$a' ) @ ( D @ ( C @ ( A @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(244,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom329) ).
thf(1477,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homSet$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(112,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'cod$' @ 'fun_app$t' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom296) ).
thf(851,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'cod$' @ 'fun_app$t' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(389,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$a' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom435) ).
thf(2156,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$a' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(57,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom460) ).
thf(685,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(170,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom317) ).
thf(1171,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(2526,plain,
! [A: 'ZF$'] :
( ( ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ) )
!= ( A @ ( A @ 'elem$' @ 'fun_app$b' ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2287,2142]) ).
thf(2527,plain,
! [A: 'ZF$'] :
( ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' @ 'fun_app$b' ) )
!= ( A @ ( A @ 'elem$' @ 'fun_app$b' ) ) ),
inference(simp,[status(thm)],[2526]) ).
thf(2534,plain,
! [A: 'ZF$'] :
( ( ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) )
!= A )
| ( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' )
!= ( A @ 'elem$' ) ) ),
inference(simp,[status(thm)],[2527]) ).
thf(2535,plain,
( ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ 'elem$' )
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ 'elem$' ) ),
inference(simp,[status(thm)],[2534]) ).
thf(374,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).
thf(2101,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(459,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'yFtor$' @ 'mapO$' ) @ 'mapO$a' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).
thf(2390,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'yFtor$' @ 'mapO$' ) @ 'mapO$a' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(195,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'identityFunctor$g' @ 'catDom$c' @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'identityFunctor$g' @ 'mapO$d' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom287) ).
thf(1250,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'identityFunctor$g' @ 'catDom$c' @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'identityFunctor$g' @ 'mapO$d' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(283,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'lSCategory_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).
thf(1694,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'lSCategory_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(122,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$' @ 'fun_app$f' ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom144) ).
thf(922,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$' @ 'fun_app$f' ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(71,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uuw$' @ 'fun_app$m' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom563) ).
thf(722,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uuw$' @ 'fun_app$m' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(147,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom319) ).
thf(1034,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(490,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( A @ 'natTransP$a' )
| ~ ( A @ 'natTrans$a' ) ),
inference(cnf,[status(esa)],[489]) ).
thf(376,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$f' ) )
=> ( A @ 'idNatTrans$c' @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom263) ).
thf(2107,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$f' ) )
=> ( A @ 'idNatTrans$c' @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(416,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'yFtor$' @ 'mapO$' ) )
= ( B @ ( A @ 'homFtorContra$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).
thf(2271,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'yFtor$' @ 'mapO$' ) )
= ( B @ ( A @ 'homFtorContra$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(12,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'isZFfun$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom566) ).
thf(548,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$b' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$b' ) ) )
=> ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( 'isZFfun$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(468,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'homSet$' ) ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).
thf(2449,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'homSet$' ) ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
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$'] :
( ( ( C @ ( B @ 'functor_comp_def$e' ) )
& ( C @ ( B @ 'functorComp$e' ) @ 'preFunctor$d' )
& ( B @ 'catDom$d' @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$e' ) @ 'mapO$b' ) )
= ( A @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom432) ).
thf(2202,plain,
! [A: 'ZF$',B: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$',C: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$e' ) )
& ( C @ ( B @ 'functorComp$e' ) @ 'preFunctor$d' )
& ( B @ 'catDom$d' @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$e' ) @ 'mapO$b' ) )
= ( A @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
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$'] :
( ( ( C @ ( B @ 'functor_comp_def$a' ) )
& ( C @ ( B @ 'functorComp$a' ) @ ( 'preFunctor$' @ 'fun_app$f' ) )
& ( B @ 'catDom$a' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$a' ) @ 'mapO$a' ) )
= ( A @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$d' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).
thf(1472,plain,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$a' ) )
& ( C @ ( B @ 'functorComp$a' ) @ ( 'preFunctor$' @ 'fun_app$f' ) )
& ( B @ 'catDom$a' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$a' ) @ 'mapO$a' ) )
= ( A @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$d' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
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$'] :
( ( A
= ( 'unity$' @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$a' ) ) ) ) ) ) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).
thf(836,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
~ ! [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
!= ( 'unity$' @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(153,axiom,
! [A: 'B$',B: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$' @ 'mor$' @ ( A @ 'member$h' ) )
=> ( ( A @ ( B @ 'makeFtor$d' @ 'mapM$' @ 'fun_app$q' ) )
= ( A @ ( B @ 'mapM$' @ 'fun_app$q' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom318) ).
thf(1049,plain,
! [A: 'B$',B: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$' @ 'mor$' @ ( A @ 'member$h' ) )
=> ( ( A @ ( B @ 'makeFtor$d' @ 'mapM$' @ 'fun_app$q' ) )
= ( A @ ( B @ 'mapM$' @ 'fun_app$q' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(182,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) )
<=> ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$a' ) @ ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom353) ).
thf(1203,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$a' ) @ ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) ) )
& ( ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) )
=> ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$a' ) @ ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(28,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'functorExt$d' )
& ( A @ 'functorM$c' ) )
=> ( A @ 'functor$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom277) ).
thf(589,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'functorExt$d' )
& ( A @ 'functorM$c' ) )
=> ( A @ 'functor$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(202,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$b' @ ( A @ 'member$d' ) )
=> ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$' @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).
thf(1277,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$b' @ ( A @ 'member$d' ) )
=> ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$' @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(381,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'yFtor$a' @ 'functorM$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom337) ).
thf(2124,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'yFtor$a' @ 'functorM$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(438,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorContra$' ) @ 'mapM$a' @ 'fun_app$p' ) )
= ( C @ ( B @ ( A @ 'homFtorMapContra$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom139) ).
thf(2333,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorContra$' ) @ 'mapM$a' @ 'fun_app$p' ) )
= ( C @ ( B @ ( A @ 'homFtorMapContra$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(411,axiom,
! [A: 'A$',B: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$',C: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$h' ) )
& ( C @ ( B @ 'functorComp$h' ) @ 'preFunctor$c' )
& ( B @ 'catDom$b' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$h' ) @ 'mapO$' ) )
= ( A @ ( B @ 'mapO$f' ) @ ( C @ 'mapO$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).
thf(2256,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$'] :
( ( ( C @ ( B @ 'functor_comp_def$h' ) )
& ( C @ ( B @ 'functorComp$h' ) @ 'preFunctor$c' )
& ( B @ 'catDom$b' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$h' ) @ 'mapO$' ) )
= ( A @ ( B @ 'mapO$f' ) @ ( C @ 'mapO$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(131,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$d' ) )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).
thf(968,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$d' ) )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
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$'] :
( ( C @ ( A @ 'fun_app$f' ) )
<=> ( C @ ( B @ 'fun_app$f' ) ) )
=> ( ( A @ 'collect$h' )
= ( B @ 'collect$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom118) ).
thf(823,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'] :
( ! [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'fun_app$f' ) )
=> ( C @ ( A @ 'fun_app$f' ) ) )
& ( ( C @ ( A @ 'fun_app$f' ) )
=> ( C @ ( B @ 'fun_app$f' ) ) ) )
=> ( ( A @ 'collect$h' )
= ( B @ 'collect$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(482,plain,
( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mor2ZF$' @ 'fun_app$p' ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) )
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) ) ),
inference(lifteq,[status(thm)],[481]) ).
thf(2512,plain,
( ( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mor2ZF$' @ 'fun_app$p' ) )
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) ) )
| ( ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) )
!= ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) ) )
| ( 'x$' != 'x$' )
| ( 'c$' != 'c$' ) ),
inference(simp,[status(thm)],[482]) ).
thf(2513,plain,
( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mor2ZF$' @ 'fun_app$p' ) )
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) ) ),
inference(simp,[status(thm)],[2512]) ).
thf(88,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( A @ 'functor$b' )
=> ( A @ 'idNatTrans$' @ 'natTransP$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).
thf(776,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( A @ 'functor$b' )
=> ( A @ 'idNatTrans$' @ 'natTransP$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(15,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom495) ).
thf(557,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'obj$a' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom393) ).
thf(580,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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'obj$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(144,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' )
= ( A @ 'more$b' @ ( A @ 'uuk$' @ ( A @ 'id$a' @ ( A @ 'dom$a' @ ( A @ 'cod$a' @ ( A @ 'mor$b' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).
thf(1025,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$b' )
= ( A @ 'more$b' @ ( A @ 'uuk$' @ ( A @ 'id$a' @ ( A @ 'dom$a' @ ( A @ 'cod$a' @ ( A @ 'mor$b' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(452,axiom,
! [A: 'ZF$',B: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$',C: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$e' ) )
& ( C @ ( B @ 'functorComp$e' ) @ 'catDom$e' @ 'mor$b' @ ( A @ 'member$d' ) ) )
=> ( A @ ( B @ 'catDom$d' @ 'cod$a' @ 'fun_app$' ) @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$' ) @ ( A @ ( B @ 'catDom$d' @ 'dom$a' @ 'fun_app$' ) @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$' ) @ ( A @ ( B @ 'mapM$e' ) @ ( C @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom381) ).
thf(2375,plain,
! [A: 'ZF$',B: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$',C: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$e' ) )
& ( C @ ( B @ 'functorComp$e' ) @ 'catDom$e' @ 'mor$b' @ ( A @ 'member$d' ) ) )
=> ( A @ ( B @ 'catDom$d' @ 'cod$a' @ 'fun_app$' ) @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$' ) @ ( A @ ( B @ 'catDom$d' @ 'dom$a' @ 'fun_app$' ) @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$' ) @ ( A @ ( B @ 'mapM$e' ) @ ( C @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(400,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'yFtor$' @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).
thf(2192,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'yFtor$' @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(739,plain,
( ( 'set$a' @ 'makeCat$' )
= 'set$' ),
inference(lifteq,[status(thm)],[738]) ).
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$'] :
( ( A @ 'functor$d' )
=> ( A @ 'preFunctor$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom197) ).
thf(1780,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'functor$d' )
=> ( A @ 'preFunctor$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(247,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$a' ) @ ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom351) ).
thf(1484,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$a' ) @ ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(188,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'hOMCollection$' ) ) )
= ( B @ ( C @ ( A @ 'hOMCollection$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom590) ).
thf(1225,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'hOMCollection$' ) ) )
= ( B @ ( C @ ( A @ 'hOMCollection$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(226,axiom,
! [A: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'] :
( ( A @ 'natTransP$c' )
<=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$c' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapM$e' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$a' @ 'mapM$e' ) @ ( C @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$b' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$a' @ 'mapO$e' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapO$e' ) @ ( B @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$b' )
= ( A @ 'nTDom$a' @ 'catCod$b' ) )
& ( ( A @ 'nTCatDom$b' )
= ( A @ 'nTCod$a' @ 'catDom$d' ) )
& ( A @ 'nTCod$a' @ 'functor$c' )
& ( A @ 'nTDom$a' @ 'functor$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom513) ).
thf(1400,plain,
! [A: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'] :
( ( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$c' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapM$e' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$a' @ 'mapM$e' ) @ ( C @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$b' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$a' @ 'mapO$e' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapO$e' ) @ ( B @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$b' )
= ( A @ 'nTDom$a' @ 'catCod$b' ) )
& ( ( A @ 'nTCatDom$b' )
= ( A @ 'nTCod$a' @ 'catDom$d' ) )
& ( A @ 'nTCod$a' @ 'functor$c' )
& ( A @ 'nTDom$a' @ 'functor$c' ) )
=> ( A @ 'natTransP$c' ) )
& ( ( A @ 'natTransP$c' )
=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$c' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapM$e' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$a' @ 'mapM$e' ) @ ( C @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$b' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$a' @ 'mapO$e' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapO$e' ) @ ( B @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$b' )
= ( A @ 'nTDom$a' @ 'catCod$b' ) )
& ( ( A @ 'nTCatDom$b' )
= ( A @ 'nTCod$a' @ 'catDom$d' ) )
& ( A @ 'nTCod$a' @ 'functor$c' )
& ( A @ 'nTDom$a' @ 'functor$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(66,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'functorM_axioms$c' )
& ( A @ 'preFunctor$c' ) )
=> ( A @ 'functorM$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom153) ).
thf(707,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'functorM_axioms$c' )
& ( A @ 'preFunctor$c' ) )
=> ( A @ 'functorM$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(387,axiom,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( B @ ( A @ 'nTDom$' @ 'mapM$f' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$' @ 'mapM$f' ) @ ( C @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$' @ 'mapO$f' ) @ ( B @ ( A @ 'nTDom$' @ 'mapO$f' ) @ ( B @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$a' )
= ( A @ 'nTDom$' @ 'catCod$f' ) )
& ( ( A @ 'nTCatDom$a' )
= ( A @ 'nTCod$' @ 'catDom$b' ) )
& ( A @ 'nTCod$' @ 'functor$a' )
& ( A @ 'nTDom$' @ 'functor$a' ) )
=> ( A @ 'natTransP$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).
thf(2143,plain,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( B @ ( A @ 'nTDom$' @ 'mapM$f' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$' @ 'mapM$f' ) @ ( C @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$' @ 'mapO$f' ) @ ( B @ ( A @ 'nTDom$' @ 'mapO$f' ) @ ( B @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$a' )
= ( A @ 'nTDom$' @ 'catCod$f' ) )
& ( ( A @ 'nTCatDom$a' )
= ( A @ 'nTCod$' @ 'catDom$b' ) )
& ( A @ 'nTCod$' @ 'functor$a' )
& ( A @ 'nTDom$' @ 'functor$a' ) )
=> ( A @ 'natTransP$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(353,axiom,
! [A: 'B_ZF_fun$',B: 'B_ZF_fun_bool_fun$'] :
( ( B @ 'collect$e' @ ( A @ 'member$e' ) )
<=> ( A @ ( B @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom101) ).
thf(2012,plain,
! [A: 'B_ZF_fun$',B: 'B_ZF_fun_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$h' ) )
=> ( B @ 'collect$e' @ ( A @ 'member$e' ) ) )
& ( ( B @ 'collect$e' @ ( A @ 'member$e' ) )
=> ( A @ ( B @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(372,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'obj$b' @ ( C @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).
thf(2092,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'obj$b' @ ( C @ 'member$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(469,axiom,
'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'eta$' @ 'nt_abbrev$' ) @ 'fun_app$f' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).
thf(2454,plain,
'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'eta$' @ 'nt_abbrev$' ) @ 'fun_app$f' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(206,axiom,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$a' @ 'obj$b' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ ( 'idNatTrans$f' @ 'fun_app$u' ) @ 'natTransMap$b' ) )
= ( A @ ( B @ 'mapO$a' ) @ ( B @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom468) ).
thf(1300,plain,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$a' @ 'obj$b' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ ( 'idNatTrans$f' @ 'fun_app$u' ) @ 'natTransMap$b' ) )
= ( A @ ( B @ 'mapO$a' ) @ ( B @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(177,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom403) ).
thf(1188,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(26,axiom,
'set$' @ 'category$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom279) ).
thf(585,plain,
'set$' @ 'category$a',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'functorM$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom154) ).
thf(502,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'functorM$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(110,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).
thf(840,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
~ ( ~ ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(439,axiom,
'c$' @ 'obj$b' @ ( 'x$' @ 'member$i' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).
thf(2337,plain,
'c$' @ 'obj$b' @ ( 'x$' @ 'member$i' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(418,axiom,
! [A: 'ZF$',B: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$b' @ 'fun_app$f' ) )
& ( C @ ( B @ 'functorComp$b' ) @ 'catDom$c' @ 'mor$b' @ ( A @ 'member$d' ) ) )
=> ( A @ ( B @ 'catDom$d' @ 'cod$a' @ 'fun_app$' ) @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$a' ) @ ( A @ ( B @ 'catDom$d' @ 'dom$a' @ 'fun_app$' ) @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$a' ) @ ( A @ ( B @ 'mapM$e' ) @ ( C @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom378) ).
thf(2276,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$'] :
( ( ( C @ ( B @ 'functor_comp_def$b' @ 'fun_app$f' ) )
& ( C @ ( B @ 'functorComp$b' ) @ 'catDom$c' @ 'mor$b' @ ( A @ 'member$d' ) ) )
=> ( A @ ( B @ 'catDom$d' @ 'cod$a' @ 'fun_app$' ) @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$a' ) @ ( A @ ( B @ 'catDom$d' @ 'dom$a' @ 'fun_app$' ) @ ( B @ 'mapO$e' ) @ ( C @ 'mapO$a' ) @ ( A @ ( B @ 'mapM$e' ) @ ( C @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(297,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'yFtor$a' )
= ( 'unity$' @ ( A @ 'yFtorNT$' @ ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ ( A @ 'functor_ext$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom556) ).
thf(1738,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'yFtor$a' )
= ( 'unity$' @ ( A @ 'yFtorNT$' @ ( 'set$' @ ( A @ 'oppositeCategory$' @ 'catExp$' ) @ ( A @ 'functor_ext$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(43,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( ( A @ ( 'uux$' @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom580) ).
thf(643,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( ( A @ ( 'uux$' @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(290,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$t' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> $false )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).
thf(1711,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$' @ 'fun_app$t' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$t' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(249,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'obj$a' @ ( A @ 'member$d' ) )
=> ( ( A @ ( B @ 'id$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom293) ).
thf(1499,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'obj$a' @ ( A @ 'member$d' ) )
=> ( ( A @ ( B @ 'id$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(319,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$',D: 'ZF$',E: 'ZF_ZF_fun$'] :
( ! [F: 'ZF$'] :
( ( A @ ( F @ 'elem$' @ 'fun_app$b' ) )
=> ( C @ ( F @ ( B @ 'fun_app$' ) @ 'elem$' @ 'fun_app$b' ) ) )
=> ( ( E @ ( D @ ( C @ 'zFfun$' ) ) @ ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( E @ 'comp$d' @ 'fun_app$aa' ) @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom601) ).
thf(1830,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$',D: 'ZF$',E: 'ZF_ZF_fun$'] :
( ! [F: 'ZF$'] :
( ( A @ ( F @ 'elem$' @ 'fun_app$b' ) )
=> ( C @ ( F @ ( B @ 'fun_app$' ) @ 'elem$' @ 'fun_app$b' ) ) )
=> ( ( E @ ( D @ ( C @ 'zFfun$' ) ) @ ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( E @ 'comp$d' @ 'fun_app$aa' ) @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(299,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom411) ).
thf(1763,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(2541,plain,
! [A: 'ZF$'] :
( ( ( A @ ( 'uuy$' @ 'fun_app$b' ) )
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ 'elem$' @ 'fun_app$b' ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1681,2530]) ).
thf(2542,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uuy$' @ 'fun_app$b' ) )
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ 'elem$' @ 'fun_app$b' ) ) ),
inference(simp,[status(thm)],[2541]) ).
thf(2544,plain,
! [A: 'ZF$'] :
( ( A
!= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) ) )
| ( ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ 'elem$' )
!= 'uuy$' ) ),
inference(simp,[status(thm)],[2542]) ).
thf(2545,plain,
( ( 'y$' @ ( 'x$' @ ( 'c$' @ 'homSet$' ) ) @ 'elem$' )
!= 'uuy$' ),
inference(simp,[status(thm)],[2544]) ).
thf(101,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'comp$' )
= F ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom395) ).
thf(808,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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'comp$' )
= F ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(480,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'fun_app$b' ) )
<=> ? [E: 'B$'] :
( ( C @ ( B @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D
= ( E @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).
thf(2500,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ? [E: 'B$'] :
( ( C @ ( B @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D
= ( E @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'fun_app$b' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvf$' ) ) @ 'fun_app$b' ) )
=> ? [E: 'B$'] :
( ( C @ ( B @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D
= ( E @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(35,axiom,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'] :
( ( A @ 'functor$a' )
=> ( A @ 'idNatTrans$b' @ 'natTransP$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).
thf(613,plain,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$'] :
( ( A @ 'functor$a' )
=> ( A @ 'idNatTrans$b' @ 'natTransP$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
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$'] :
( ( ( C @ ( B @ 'nTCompDefined$' @ 'fun_app$e' ) )
& ( B @ 'nTCatDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ ( 'natTransComp$' @ 'fun_app$x' ) @ 'fun_app$w' ) @ 'natTransMap$b' ) )
= ( A @ ( C @ 'natTransMap$b' ) @ ( A @ ( B @ 'natTransMap$b' ) @ ( B @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom540) ).
thf(1052,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$'] :
( ( ( C @ ( B @ 'nTCompDefined$' @ 'fun_app$e' ) )
& ( B @ 'nTCatDom$' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ ( 'natTransComp$' @ 'fun_app$x' ) @ 'fun_app$w' ) @ 'natTransMap$b' ) )
= ( A @ ( C @ 'natTransMap$b' ) @ ( A @ ( B @ 'natTransMap$b' ) @ ( B @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(228,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuw$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).
thf(1427,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuw$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(138,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'ZF$'] :
( ( ( ( B @ ( A @ 'catDom$a' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( C @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$a' @ 'obj$a' @ ( C @ 'member$d' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ 'mapO$a' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom361) ).
thf(1008,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'ZF$'] :
( ( ( ( B @ ( A @ 'catDom$a' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( C @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$a' @ 'obj$a' @ ( C @ 'member$d' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ 'mapO$a' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(31,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'natTransP$a' ) )
=> ( ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).
thf(595,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'natTransP$a' ) )
=> ( ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
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$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'natTransP$b' ) )
=> ( ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) )
= ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom529) ).
thf(1617,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$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'natTransP$b' ) )
=> ( ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) )
= ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(655,plain,
! [A: 'B_set$'] :
( ( A @ 'uuc$' @ 'collect$d' )
= A ),
inference(cnf,[status(esa)],[654]) ).
thf(656,plain,
! [A: 'B_set$'] :
( ( A @ 'uuc$' @ 'collect$d' )
= A ),
inference(lifteq,[status(thm)],[655]) ).
thf(143,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$b' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom149) ).
thf(1023,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$b' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(255,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( A @ 'mor$b' @ ( C @ 'member$d' ) )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom461) ).
thf(1585,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( A @ 'mor$b' @ ( C @ 'member$d' ) )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
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$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( B @ ( A @ 'nTCompDefined$' @ 'fun_app$e' ) ) )
=> ( C @ ( B @ 'natTransMap$b' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom538) ).
thf(978,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( B @ ( A @ 'nTCompDefined$' @ 'fun_app$e' ) ) )
=> ( C @ ( B @ 'natTransMap$b' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(471,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuu$' ) @ 'fun_app$b' ) )
<=> ( ( ( B @ ( A @ 'catDom$a' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( C @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$a' @ 'obj$a' @ ( C @ 'member$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).
thf(2458,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'ZF$'] :
( ( ( ( ( B @ ( A @ 'catDom$a' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( C @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$a' @ 'obj$a' @ ( C @ 'member$d' ) ) )
=> ( C @ ( B @ ( A @ 'uuu$' ) @ 'fun_app$b' ) ) )
& ( ( C @ ( B @ ( A @ 'uuu$' ) @ 'fun_app$b' ) )
=> ( ( ( B @ ( A @ 'catDom$a' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( C @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$a' @ 'obj$a' @ ( C @ 'member$d' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(174,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'preFunctor$c' )
=> ( A @ 'makeFtor$d' @ 'preFunctor$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom218) ).
thf(1180,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'preFunctor$c' )
=> ( A @ 'makeFtor$d' @ 'preFunctor$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(279,axiom,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A_b_b_c_LSCategory_ext_Category_ext$',D: 'B$',E: 'A$',F: 'A$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$e' ) ) ) )
=> ( F @ ( A @ 'mapO$f' ) @ ( E @ ( A @ 'mapO$f' ) @ ( D @ ( A @ 'mapM$f' ) @ ( C @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom77) ).
thf(1685,plain,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A_b_b_c_LSCategory_ext_Category_ext$',D: 'B$',E: 'A$',F: 'A$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$e' ) ) ) )
=> ( F @ ( A @ 'mapO$f' ) @ ( E @ ( A @ 'mapO$f' ) @ ( D @ ( A @ 'mapM$f' ) @ ( C @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(315,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$a' )
= ( B @ 'more$a' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$b' )
= ( B @ 'id$b' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$b' )
= ( B @ 'obj$b' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom368) ).
thf(1817,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$a' )
= ( B @ 'more$a' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$b' )
= ( B @ 'id$b' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$b' )
= ( B @ 'obj$b' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(444,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ 'zF2mor$' ) )
= ( B @ ( A @ 'uva$' ) @ 'the$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom579) ).
thf(2347,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ 'zF2mor$' ) )
= ( B @ ( A @ 'uva$' ) @ 'the$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(82,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).
thf(759,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$b' @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(254,axiom,
! [A: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$c' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapM$e' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$a' @ 'mapM$e' ) @ ( C @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$b' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$a' @ 'mapO$e' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapO$e' ) @ ( B @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$b' )
= ( A @ 'nTDom$a' @ 'catCod$b' ) )
& ( ( A @ 'nTCatDom$b' )
= ( A @ 'nTCod$a' @ 'catDom$d' ) )
& ( A @ 'nTCod$a' @ 'functor$c' )
& ( A @ 'nTDom$a' @ 'functor$c' ) )
=> ( A @ 'natTransP$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).
thf(1575,plain,
! [A: 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$b' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$c' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapM$e' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= ( B @ ( A @ 'nTCod$a' @ 'mapM$e' ) @ ( C @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$b' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$a' @ 'mapO$e' ) @ ( B @ ( A @ 'nTDom$a' @ 'mapO$e' ) @ ( B @ ( A @ 'natTransMap$c' ) @ ( A @ 'nTCatCod$b' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( A @ 'nTCatCod$b' )
= ( A @ 'nTDom$a' @ 'catCod$b' ) )
& ( ( A @ 'nTCatDom$b' )
= ( A @ 'nTCod$a' @ 'catDom$d' ) )
& ( A @ 'nTCod$a' @ 'functor$c' )
& ( A @ 'nTDom$a' @ 'functor$c' ) )
=> ( A @ 'natTransP$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(366,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( ( ( B @ ( A @ 'catDom$a' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( B @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$a' @ 'obj$a' @ ( B @ ( A @ 'mapO$a' ) @ 'member$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom363) ).
thf(2071,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( ( ( B @ ( A @ 'catDom$a' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( B @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$a' @ 'obj$a' @ ( B @ ( A @ 'mapO$a' ) @ 'member$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(368,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'yFtor$a' @ 'preFunctor$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).
thf(2078,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'yFtor$a' @ 'preFunctor$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(337,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom412) ).
thf(1913,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(432,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homFtorMapContra$' ) ) )
= ( B @ ( C @ ( A @ 'oppositeCategory$' @ 'homFtorMap$' ) @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom220) ).
thf(2310,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homFtorMapContra$' ) ) )
= ( B @ ( C @ ( A @ 'oppositeCategory$' @ 'homFtorMap$' ) @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(58,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'mor$b' )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom394) ).
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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'mor$b' )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(212,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom336) ).
thf(1326,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(196,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( D @ ( C @ ( B @ ( A @ 'makeCat$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom308) ).
thf(1253,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( D @ ( C @ ( B @ ( A @ 'makeCat$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(129,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom316) ).
thf(963,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(396,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF$'] :
( ( ( A @ 'catCod$a' @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ ( 'equivalence$' @ 'fun_app$f' ) ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'objIso$a' ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom375) ).
thf(2174,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF$'] :
( ( ( A @ 'catCod$a' @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ ( 'equivalence$' @ 'fun_app$f' ) ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'objIso$a' ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(384,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( B @ ( A @ 'homFtor$a' ) @ ( 'preFunctor$' @ 'fun_app$f' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$a' ) @ 'mapO$a' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom92) ).
thf(2135,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( B @ ( A @ 'homFtor$a' ) @ ( 'preFunctor$' @ 'fun_app$f' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$a' ) @ 'mapO$a' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(158,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom410) ).
thf(1062,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(46,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'oppositeCategory$b' @ 'category$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).
thf(652,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'oppositeCategory$b' @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(324,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) @ 'catDom$a' )
= ( A @ 'oppositeCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom311) ).
thf(1854,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) @ 'catDom$a' )
= ( A @ 'oppositeCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(92,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$c' )
=> ( A @ 'oppositeCategory$' @ 'category$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom192) ).
thf(786,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$c' )
=> ( A @ 'oppositeCategory$' @ 'category$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(90,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'category$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).
thf(781,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'category$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(413,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ 'mapO$a' ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( C @ ( A @ 'yMapInv$' ) ) ) @ ( C @ ( A @ 'yMap$' ) ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).
thf(2262,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$',D: 'ZF$'] :
( ( ( C @ ( B @ 'mapO$a' ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( C @ ( A @ 'yMapInv$' ) ) ) @ ( C @ ( A @ 'yMap$' ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(103,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'] :
( ( A @ 'category$' )
=> ( A @ 'oppositeCategory$a' @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).
thf(813,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'] :
( ( A @ 'category$' )
=> ( A @ 'oppositeCategory$a' @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(292,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$a' ) )
= ( 'unity$' @ ( B @ ( A @ 'uup$' ) @ ( 'set$' @ ( A @ 'oppositeCategory$' @ 'functor_ext$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).
thf(1721,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$a' ) )
= ( 'unity$' @ ( B @ ( A @ 'uup$' ) @ ( 'set$' @ ( A @ 'oppositeCategory$' @ 'functor_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(217,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( C @ ( B @ ( A @ 'uum$' ) @ 'fun_app$f' ) )
<=> ( B @ ( A @ ( C @ 'functor_abbrev$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
thf(1341,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ ( C @ 'functor_abbrev$' ) ) )
=> ( C @ ( B @ ( A @ 'uum$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uum$' ) @ 'fun_app$f' ) )
=> ( B @ ( A @ ( C @ 'functor_abbrev$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(115,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom334) ).
thf(896,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( C @ ( A @ 'homFtorMapContra$' ) ) @ ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
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$'] :
( ( A @ 'functorM$c' )
=> ( A @ 'functorM_axioms$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom223) ).
thf(748,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'functorM$c' )
=> ( A @ 'functorM_axioms$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(194,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'] :
( ( B @ 'collect$h' @ ( A @ 'member$a' ) )
<=> ( A @ ( B @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom105) ).
thf(1244,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$f' ) )
=> ( B @ 'collect$h' @ ( A @ 'member$a' ) ) )
& ( ( B @ 'collect$h' @ ( A @ 'member$a' ) )
=> ( A @ ( B @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(317,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ! [D: 'ZF$'] :
( ( B @ ( D @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( B @ ( D @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= D ) )
& ( C @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( A @ 'id$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom420) ).
thf(1822,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ! [D: 'ZF$'] :
( ( B @ ( D @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
=> ( ( B @ ( D @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= D ) )
& ( C @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( A @ 'id$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(467,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'B$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( D @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom408) ).
thf(2447,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'B$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( D @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(327,axiom,
! [A: 'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'] :
( ( A @ 'preFunctor$d' )
=> ( A @ 'makeFtor$e' @ 'preFunctor$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).
thf(1861,plain,
! [A: 'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'] :
( ( A @ 'preFunctor$d' )
=> ( A @ 'makeFtor$e' @ 'preFunctor$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(119,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ 'nTCatDom$' )
= ( A @ 'oppositeCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom506) ).
thf(914,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$' @ 'fun_app$q' ) @ 'nTCatDom$' )
= ( A @ 'oppositeCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(402,axiom,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',E: 'ZF$'] :
( ( ( B @ 'lSCategory$' )
& ( B @ 'obj$b' @ ( C @ 'member$i' ) )
& ( B @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( C @ ( E @ ( D @ ( A @ ( B @ 'yMapInv$' ) ) ) @ 'natTransMap$b' ) )
= ( E @ ( D @ ( B @ 'uul$' ) @ 'fun_app$m' ) @ ( C @ ( D @ 'mapO$a' ) @ ( A @ ( C @ ( B @ 'homSet$' ) ) @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom547) ).
thf(2198,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$'] :
( ( ( B @ 'lSCategory$' )
& ( B @ 'obj$b' @ ( C @ 'member$i' ) )
& ( B @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( C @ ( E @ ( D @ ( A @ ( B @ 'yMapInv$' ) ) ) @ 'natTransMap$b' ) )
= ( E @ ( D @ ( B @ 'uul$' ) @ 'fun_app$m' ) @ ( C @ ( D @ 'mapO$a' ) @ ( A @ ( C @ ( B @ 'homSet$' ) ) @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(373,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
<=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom61) ).
thf(2095,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
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$'] :
( ( A @ 'functorM$c' )
=> ( A @ 'makeFtor$d' @ 'functor$d' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom188) ).
thf(1309,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$'] :
( ( A @ 'functorM$c' )
=> ( A @ 'makeFtor$d' @ 'functor$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(478,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ ( A @ 'zF2mor$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).
thf(2494,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) @ ( A @ 'zF2mor$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( C @ 'member$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).
thf(1994,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$',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$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$f' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( C @ 'member$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(167,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF_ZF_fun$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ( ( A @ ( D @ ( C @ ( B @ 'zFfun$' ) ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( A @ ( D @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom553) ).
thf(1161,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF_ZF_fun$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ( ( A @ ( D @ ( C @ ( B @ 'zFfun$' ) ) @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( A @ ( D @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(125,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom574) ).
thf(929,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$b' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( B @ ( C @ ( A @ 'yFtor$' @ 'mapO$' ) @ ( D @ 'nt_abbrev$' ) @ 'fun_app$f' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( C @ ( A @ 'yMap$' ) ) @ ( B @ ( C @ ( A @ 'yMapInv$' ) ) ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).
thf(2330,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$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( B @ ( C @ ( A @ 'yFtor$' @ 'mapO$' ) @ ( D @ 'nt_abbrev$' ) @ 'fun_app$f' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( C @ ( A @ 'yMap$' ) ) @ ( B @ ( C @ ( A @ 'yMapInv$' ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(288,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).
thf(1706,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'cod$' @ 'fun_app$t' ) @ 'member$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(179,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom389) ).
thf(1193,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
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$',D: 'ZF$'] :
( ( ( B @ 'catDom$c' @ 'obj$a' @ ( D @ 'member$d' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$d' ) ) ) )
=> ( D @ ( C @ 'mapO$d' @ 'fun_app$' ) @ ( D @ ( B @ 'mapO$d' @ 'fun_app$' ) @ ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( C @ 'catCod$c' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom458) ).
thf(899,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',D: 'ZF$'] :
( ( ( B @ 'catDom$c' @ 'obj$a' @ ( D @ 'member$d' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$d' ) ) ) )
=> ( D @ ( C @ 'mapO$d' @ 'fun_app$' ) @ ( D @ ( B @ 'mapO$d' @ 'fun_app$' ) @ ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( C @ 'catCod$c' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(271,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'obj$b' @ ( D @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom210) ).
thf(1661,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'obj$b' @ ( D @ 'member$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(303,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom322) ).
thf(1774,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$c' ) )
=> ( A @ 'obj$b' @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ 'member$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
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$',D: 'ZF$'] :
( ( ( C @ ( B @ 'mapO$a' ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( C @ ( A @ 'yFtor$' @ 'mapO$' ) @ ( D @ ( B @ ( C @ ( A @ 'yMapInv$' ) ) ) @ 'nt_abbrev$' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).
thf(2302,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$',D: 'ZF$'] :
( ( ( C @ ( B @ 'mapO$a' ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( C @ ( A @ 'yFtor$' @ 'mapO$' ) @ ( D @ ( B @ ( C @ ( A @ 'yMapInv$' ) ) ) @ 'nt_abbrev$' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(203,axiom,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$',B: 'A$'] :
( ( ( A @ 'nTCatDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'natTransP$d' ) )
=> ( B @ ( A @ 'nTCod$' @ 'mapO$f' ) @ ( B @ ( A @ 'nTDom$' @ 'mapO$f' ) @ ( B @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom525) ).
thf(1280,plain,
! [A: 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$',B: 'A$'] :
( ( ( A @ 'nTCatDom$a' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'natTransP$d' ) )
=> ( B @ ( A @ 'nTCod$' @ 'mapO$f' ) @ ( B @ ( A @ 'nTDom$' @ 'mapO$f' ) @ ( B @ ( A @ 'natTransMap$a' @ 'fun_app$r' ) @ ( A @ 'nTCatCod$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(457,axiom,
( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'yFtor$' @ 'mapM$' @ 'fun_app$q' ) )
= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mor2ZF$' @ 'fun_app$p' ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom40) ).
thf(2385,plain,
( ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'yFtor$' @ 'mapM$' @ 'fun_app$q' ) )
= ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mor2ZF$' @ 'fun_app$p' ) @ ( 'y$' @ ( 'c$' @ 'yFtor$' @ 'mapO$' ) @ ( 'x$' @ ( 'c$' @ 'yMapInv$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(410,axiom,
'y$' @ ( 'x$' @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mapsTo$' ) ) @ 'fun_app$l' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).
thf(2255,plain,
'y$' @ ( 'x$' @ ( 'eta$' @ ( 'x$' @ ( 'c$' @ 'yMap$' ) ) @ ( 'c$' @ 'zF2mor$' ) @ ( 'c$' @ 'mapsTo$' ) ) @ 'fun_app$l' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(966,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'oppositeCategory$' )
= A ),
inference(cnf,[status(esa)],[965]) ).
thf(967,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'oppositeCategory$' )
= A ),
inference(lifteq,[status(thm)],[966]) ).
thf(266,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'identityFunctor$f' @ 'catDom$b' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( ( B @ ( A @ 'identityFunctor$f' @ 'mapO$f' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).
thf(1625,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'identityFunctor$f' @ 'catDom$b' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'category$c' ) )
=> ( ( B @ ( A @ 'identityFunctor$f' @ 'mapO$f' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(105,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( A @ 'functor$b' )
=> ( A @ 'preFunctor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).
thf(818,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( A @ 'functor$b' )
=> ( A @ 'preFunctor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(222,axiom,
! [A: 'B$',B: 'B_bool_fun$'] :
( ( B @ 'collect$d' @ ( A @ 'member$h' ) )
<=> ( A @ ( B @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom100) ).
thf(1380,plain,
! [A: 'B$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$k' ) )
=> ( B @ 'collect$d' @ ( A @ 'member$h' ) ) )
& ( ( B @ 'collect$d' @ ( A @ 'member$h' ) )
=> ( A @ ( B @ 'fun_app$k' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(245,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( B @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( C @ ( D @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ 'elem$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom371) ).
thf(1480,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( B @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( C @ ( D @ ( A @ ( 'zFfunApp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ 'elem$' @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(351,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom332) ).
thf(2003,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'homSet$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(113,axiom,
! [A: 'ZF$',B: 'Nat_ZF_fun$'] :
( ( B @ 'seqSum$' @ ( A @ 'elem$' @ 'fun_app$b' ) )
<=> ? [C: 'Nat$'] : ( C @ ( B @ 'fun_app$z' ) @ ( A @ 'elem$' @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom599) ).
thf(854,plain,
! [A: 'ZF$',B: 'Nat_ZF_fun$'] :
( ( ? [C: 'Nat$'] : ( C @ ( B @ 'fun_app$z' ) @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ( B @ 'seqSum$' @ ( A @ 'elem$' @ 'fun_app$b' ) ) )
& ( ( B @ 'seqSum$' @ ( A @ 'elem$' @ 'fun_app$b' ) )
=> ? [C: 'Nat$'] : ( C @ ( B @ 'fun_app$z' ) @ ( A @ 'elem$' @ 'fun_app$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(207,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( ! [D: 'B$'] :
( ( B @ ( D @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( ( B @ ( D @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= D ) )
& ( C @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'category$c' ) )
=> ( ( C @ ( A @ 'id$b' @ 'fun_app$r' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).
thf(1303,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( ! [D: 'B$'] :
( ( B @ ( D @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( ( B @ ( D @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) )
= D ) )
& ( C @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'category$c' ) )
=> ( ( C @ ( A @ 'id$b' @ 'fun_app$r' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(94,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'natTrans$a' ) )
=> ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).
thf(790,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'natTrans$a' ) )
=> ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
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$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'natTrans$b' ) )
=> ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).
thf(2050,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'natTrans$b' ) )
=> ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(563,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$'] :
( ( A @ 'uuh$' @ 'collect$h' )
= A ),
inference(cnf,[status(esa)],[562]) ).
thf(564,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$'] :
( ( A @ 'uuh$' @ 'collect$h' )
= A ),
inference(lifteq,[status(thm)],[563]) ).
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$',F: 'A$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( F @ ( A @ 'mapO$a' ) @ ( E @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).
thf(1859,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'A$',F: 'A$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( F @ ( A @ 'mapO$a' ) @ ( E @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
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$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' ) )
& ( B @ 'nTCatDom$d' @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( C @ ( B @ 'natTransComp$a' ) @ 'natTransMap$d' @ 'fun_app$' ) )
= ( A @ ( C @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ ( B @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom541) ).
thf(801,plain,
! [A: 'ZF$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' ) )
& ( B @ 'nTCatDom$d' @ 'obj$a' @ ( A @ 'member$d' ) ) )
=> ( ( A @ ( C @ ( B @ 'natTransComp$a' ) @ 'natTransMap$d' @ 'fun_app$' ) )
= ( A @ ( C @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ ( B @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(1693,plain,
! [A: 'ZF$'] : ( 'set$' @ 'obj$a' @ ( A @ 'member$d' ) ),
inference(cnf,[status(esa)],[1692]) ).
thf(128,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) @ ( 'set$' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom312) ).
thf(960,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$b' @ 'fun_app$r' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$p' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) ) @ ( 'set$' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
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$'] :
( ( ( A @ 'catCod$' @ 'category$' )
& ( A @ 'catDom$' @ 'category$c' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ? [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'comp$b' ) ) ) ) ) )
=> ( A @ 'preFunctor$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom384) ).
thf(2040,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$'] :
( ( ( A @ 'catCod$' @ 'category$' )
& ( A @ 'catDom$' @ 'category$c' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ? [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'catCod$' @ 'id$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$a' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'comp$b' ) ) ) ) ) )
=> ( A @ 'preFunctor$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
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$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$' ) @ ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
=> ( A @ 'functorM_axioms$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom352) ).
thf(1165,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( D @ ( A @ 'mapO$' ) @ ( C @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
=> ( A @ 'functorM_axioms$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'cod$a' )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom398) ).
thf(767,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'cod$a' )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
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$'] :
( ( A @ 'natTransP$b' )
<=> ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) )
= ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$c' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapO$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapO$' ) @ ( B @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
& ( ( A @ 'nTCatCod$c' )
= ( A @ 'nTDom$b' @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$c' )
= ( A @ 'nTCod$b' @ 'catDom$' ) )
& ( A @ 'nTCod$b' @ 'functor$d' )
& ( A @ 'nTDom$b' @ 'functor$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom514) ).
thf(2417,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$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) )
= ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$c' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapO$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapO$' ) @ ( B @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
& ( ( A @ 'nTCatCod$c' )
= ( A @ 'nTDom$b' @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$c' )
= ( A @ 'nTCod$b' @ 'catDom$' ) )
& ( A @ 'nTCod$b' @ 'functor$d' )
& ( A @ 'nTDom$b' @ 'functor$d' ) )
=> ( A @ 'natTransP$b' ) )
& ( ( A @ 'natTransP$b' )
=> ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$c' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) )
= ( B @ ( A @ 'nTCod$b' @ 'mapM$' @ 'fun_app$q' ) @ ( C @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'comp$b' ) ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$c' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'nTCod$b' @ 'mapO$' ) @ ( B @ ( A @ 'nTDom$b' @ 'mapO$' ) @ ( B @ ( A @ 'natTransMap$' ) @ ( A @ 'nTCatCod$c' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) )
& ( ( A @ 'nTCatCod$c' )
= ( A @ 'nTDom$b' @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$c' )
= ( A @ 'nTCod$b' @ 'catDom$' ) )
& ( A @ 'nTCod$b' @ 'functor$d' )
& ( A @ 'nTDom$b' @ 'functor$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(309,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( B @ ( A @ 'mapO$a' ) )
= ( B @ ( A @ 'uuu$' ) @ 'the$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).
thf(1789,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( B @ ( A @ 'mapO$a' ) )
= ( B @ ( A @ 'uuu$' ) @ 'the$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(49,axiom,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'functorM$c' )
=> ( A @ 'preFunctor$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom147) ).
thf(664,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$'] :
( ( A @ 'functorM$c' )
=> ( A @ 'preFunctor$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(355,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).
thf(2021,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(262,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'objIso$b' ) @ 'fun_app$l' ) )
<=> ? [D: 'B$'] :
( ( D @ ( A @ 'isomorphism$' @ 'fun_app$k' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom481) ).
thf(1610,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ? [D: 'B$'] :
( ( D @ ( A @ 'isomorphism$' @ 'fun_app$k' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( C @ ( B @ ( A @ 'objIso$b' ) @ 'fun_app$l' ) ) )
& ( ( C @ ( B @ ( A @ 'objIso$b' ) @ 'fun_app$l' ) )
=> ? [D: 'B$'] :
( ( D @ ( A @ 'isomorphism$' @ 'fun_app$k' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
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$',D: 'A$'] :
( ( ( B @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$f' ) ) ) )
=> ( ( D @ ( B @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( D @ ( A @ 'mapO$' ) @ ( C @ 'id$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).
thf(2353,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',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$'] :
( ( ( B @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$f' ) ) ) )
=> ( ( D @ ( B @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( D @ ( A @ 'mapO$' ) @ ( C @ 'id$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
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$'] :
( ( ( C @ ( B @ 'functor_comp_def$g' ) )
& ( C @ ( B @ 'functorComp$g' ) @ 'preFunctor$c' )
& ( B @ 'catDom$a' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$g' ) @ 'mapO$' ) )
= ( A @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$b' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).
thf(2241,plain,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_ZF_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$g' ) )
& ( C @ ( B @ 'functorComp$g' ) @ 'preFunctor$c' )
& ( B @ 'catDom$a' @ 'obj$b' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ 'functorComp$g' ) @ 'mapO$' ) )
= ( A @ ( B @ 'mapO$a' ) @ ( C @ 'mapO$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(114,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'equivalence_axioms$' @ 'fun_app$f' ) )
<=> ( ! [B: 'ZF$'] :
( ( A @ 'catCod$a' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'objIso$a' ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).
thf(860,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ! [B: 'ZF$'] :
( ( A @ 'catCod$a' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'objIso$a' ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) )
=> ( A @ ( 'equivalence_axioms$' @ 'fun_app$f' ) ) )
& ( ( A @ ( 'equivalence_axioms$' @ 'fun_app$f' ) )
=> ( ! [B: 'ZF$'] :
( ( A @ 'catCod$a' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$a' ) @ ( A @ 'catCod$a' @ 'objIso$a' ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$a' ) @ ( B @ ( A @ 'mapO$a' ) @ ( D @ ( A @ 'catCod$a' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$a' @ 'obj$b' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$a' @ 'fun_app$p' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(477,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uva$' ) @ 'fun_app$k' ) )
<=> ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom24) ).
thf(2485,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$',C: 'B$'] :
( ( ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$h' ) ) )
=> ( C @ ( B @ ( A @ 'uva$' ) @ 'fun_app$k' ) ) )
& ( ( C @ ( B @ ( A @ 'uva$' ) @ 'fun_app$k' ) )
=> ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$p' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
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$',D: 'A$'] :
( ( ( B @ 'catDom$' @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$a' ) ) ) )
=> ( D @ ( C @ 'mapO$' ) @ ( D @ ( B @ 'mapO$' ) @ ( D @ ( A @ 'natTransMap$' ) @ ( C @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom454) ).
thf(2467,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$',D: 'A$'] :
( ( ( B @ 'catDom$' @ 'obj$b' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$a' ) ) ) )
=> ( D @ ( C @ 'mapO$' ) @ ( D @ ( B @ 'mapO$' ) @ ( D @ ( A @ 'natTransMap$' ) @ ( C @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( B @ ( A @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom328) ).
thf(1923,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( B @ ( A @ 'catDom$' @ 'cod$' @ 'fun_app$t' ) @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'mapO$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(342,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) )
=> $false )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom303) ).
thf(1925,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$d' ) ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(451,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'mor2ZF$' )
= ( A @ 'mor2ZF$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).
thf(2372,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'mor2ZF$' )
= ( A @ 'mor2ZF$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(385,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$c' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).
thf(2138,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$c' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$t' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$t' ) @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(390,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( D @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom211) ).
thf(2159,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( D @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(220,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$' @ 'fun_app$e' ) )
<=> ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'catCod$a' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'catDom$a' ) )
& ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) )
& ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).
thf(1352,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'catCod$a' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'catDom$a' ) )
& ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) )
& ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) )
& ( ( A @ ( 'natTransP$' @ 'fun_app$e' ) )
=> ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
=> ( ( D @ ( A @ 'natTransMap$b' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapM$a' @ 'fun_app$p' ) @ ( C @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'catCod$a' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'catDom$a' ) )
& ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) )
& ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(199,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$f' ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).
thf(1268,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$f' ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(22,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'natTrans$a' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom536) ).
thf(575,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( A @ 'natTrans$a' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'compDefined$' ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(414,axiom,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$'] :
( ( C @ ( B @ 'yFtorNT$' @ 'fun_app$q' ) @ 'nTCatDom$' @ 'obj$b' @ ( A @ 'member$i' ) )
=> ( ( A @ ( C @ ( B @ 'yFtorNT$' @ 'fun_app$q' ) @ 'natTransMap$b' ) )
= ( C @ ( A @ ( B @ 'homFtorMap$' ) @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom507) ).
thf(2265,plain,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$'] :
( ( C @ ( B @ 'yFtorNT$' @ 'fun_app$q' ) @ 'nTCatDom$' @ 'obj$b' @ ( A @ 'member$i' ) )
=> ( ( A @ ( C @ ( B @ 'yFtorNT$' @ 'fun_app$q' ) @ 'natTransMap$b' ) )
= ( C @ ( A @ ( B @ 'homFtorMap$' ) @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(142,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$',D: 'A$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$t' ) )
= D )
& ( ( A @ ( B @ 'dom$' @ 'fun_app$t' ) )
= C )
& ( B @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom290) ).
thf(1019,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$',D: 'A$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$t' ) )
= D )
& ( ( A @ ( B @ 'dom$' @ 'fun_app$t' ) )
= C )
& ( B @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(258,axiom,
! [A: 'A$',B: 'A_bool_fun$'] :
( ( B @ 'collect$b' @ ( A @ 'member$i' ) )
<=> ( A @ ( B @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).
thf(1597,plain,
! [A: 'A$',B: 'A_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$l' ) )
=> ( B @ 'collect$b' @ ( A @ 'member$i' ) ) )
& ( ( B @ 'collect$b' @ ( A @ 'member$i' ) )
=> ( A @ ( B @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(136,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$c' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$l' ) ) @ ( 'preFunctor$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).
thf(1004,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$c' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$l' ) ) @ ( 'preFunctor$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
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$'] :
( ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$e' ) )
<=> ( ( ( C @ 'nTCatCod$' )
= B )
& ( ( C @ 'nTCatDom$' )
= A )
& ( C @ ( 'natTrans$' @ 'fun_app$e' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).
thf(1902,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( ( C @ 'nTCatCod$' )
= B )
& ( ( C @ 'nTCatDom$' )
= A )
& ( C @ ( 'natTrans$' @ 'fun_app$e' ) ) )
=> ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$e' ) ) )
& ( ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$e' ) )
=> ( ( ( C @ 'nTCatCod$' )
= B )
& ( ( C @ 'nTCatDom$' )
= A )
& ( C @ ( 'natTrans$' @ 'fun_app$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(59,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$b' @ ( C @ 'member$i' ) )
& ( B @ 'category$c' )
& ( A @ 'category$c' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$c' ) ) @ 'functor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).
thf(691,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$b' @ ( C @ 'member$i' ) )
& ( B @ 'category$c' )
& ( A @ 'category$c' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$c' ) ) @ 'functor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(486,plain,
! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( B @ 'fun_app$e' ) )
| ~ ( B @ 'collect$i' @ ( A @ 'member$' ) ) ),
inference(cnfConj,[status(thm)],[485]) ).
thf(127,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( A @ 'natTransP$a' )
<=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$d' )
= ( A @ 'nTDom$d' @ 'catCod$c' ) )
& ( ( A @ 'nTCatDom$d' )
= ( A @ 'nTCod$d' @ 'catDom$c' ) )
& ( A @ 'nTCod$d' @ 'functor$b' )
& ( A @ 'nTDom$d' @ 'functor$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom516) ).
thf(935,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$'] :
( ( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$d' )
= ( A @ 'nTDom$d' @ 'catCod$c' ) )
& ( ( A @ 'nTCatDom$d' )
= ( A @ 'nTCod$d' @ 'catDom$c' ) )
& ( A @ 'nTCod$d' @ 'functor$b' )
& ( A @ 'nTDom$d' @ 'functor$b' ) )
=> ( A @ 'natTransP$a' ) )
& ( ( A @ 'natTransP$a' )
=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
=> ( ( D @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapM$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'nTCod$d' @ 'mapM$d' @ 'fun_app$' ) @ ( C @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'nTCatDom$d' @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( A @ 'nTCod$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'nTDom$d' @ 'mapO$d' @ 'fun_app$' ) @ ( B @ ( A @ 'natTransMap$d' @ 'fun_app$' ) @ ( A @ 'nTCatCod$d' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ( ( A @ 'nTCatCod$d' )
= ( A @ 'nTDom$d' @ 'catCod$c' ) )
& ( ( A @ 'nTCatDom$d' )
= ( A @ 'nTCod$d' @ 'catDom$c' ) )
& ( A @ 'nTCod$d' @ 'functor$b' )
& ( A @ 'nTDom$d' @ 'functor$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(161,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category_axioms$a' )
<=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$d' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom444) ).
thf(1069,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$d' ) ) ) )
=> ( A @ 'category_axioms$a' ) )
& ( ( A @ 'category_axioms$a' )
=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$b' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$d' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$d' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$d' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'dom$b' ) @ ( A @ 'catCod$' @ 'id$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).
thf(1014,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$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'functor$d' ) )
=> ( ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$t' ) @ ( A @ 'catDom$' @ 'id$b' @ 'fun_app$r' ) @ ( A @ 'mapM$' @ 'fun_app$q' ) )
= ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'dom$b' ) @ ( A @ 'catCod$' @ 'id$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(214,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'obj$a' @ ( C @ 'member$d' ) )
& ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom310) ).
thf(1331,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'obj$a' @ ( C @ 'member$d' ) )
& ( A @ 'obj$a' @ ( B @ 'member$d' ) )
& ( A @ 'category$a' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
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$',B: 'B$'] :
( ( ( B @ ( A @ 'catDom$' @ 'isomorphism$' @ 'fun_app$k' ) )
& ( A @ 'functor$d' ) )
=> ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'isomorphism$a' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).
thf(1606,plain,
! [A: 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'catDom$' @ 'isomorphism$' @ 'fun_app$k' ) )
& ( A @ 'functor$d' ) )
=> ( B @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( A @ 'catCod$' @ 'isomorphism$a' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(10,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$c' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$l' ) ) @ ( 'functorM$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom238) ).
thf(543,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$d' ) )
& ( B @ 'category$a' )
& ( A @ 'category$c' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$l' ) ) @ ( 'functorM$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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$'] :
( A
= ( A @ 'more$c' @ ( A @ 'mapM$' @ ( A @ 'catCod$' @ ( A @ 'catDom$' @ 'functor_ext$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom475) ).
thf(2018,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$'] :
( A
= ( A @ 'more$c' @ ( A @ 'mapM$' @ ( A @ 'catCod$' @ ( A @ 'catDom$' @ 'functor_ext$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
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$',D: 'ZF$'] :
( ( ( C @ ( B @ 'mapO$a' ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( C @ ( A @ 'yMapInv$a' ) ) ) @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom80) ).
thf(1848,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$',D: 'ZF$'] :
( ( ( C @ ( B @ 'mapO$a' ) @ ( D @ 'elem$' @ 'fun_app$b' ) )
& ( A @ 'obj$b' @ ( C @ 'member$i' ) )
& ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ 'functor_abbrev$' ) ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( C @ ( A @ 'yMapInv$a' ) ) ) @ ( 'natTransP$' @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(363,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom526) ).
thf(2059,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$b' @ ( B @ 'member$i' ) )
& ( A @ ( 'natTransP$' @ 'fun_app$e' ) ) )
=> ( B @ ( A @ ( 'nTCod$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ ( 'nTDom$c' @ 'fun_app$v' ) @ 'mapO$a' ) @ ( B @ ( A @ 'natTransMap$b' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$b' ) ) @ 'fun_app$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(339,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuk$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).
thf(1917,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuk$' @ 'fun_app$m' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$m' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(55,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$' @ 'fun_app$f' ) )
<=> ( ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).
thf(676,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'functorM$' @ 'fun_app$f' ) ) )
& ( ( A @ ( 'functorM$' @ 'fun_app$f' ) )
=> ( ( A @ ( 'functorM_axioms$d' @ 'fun_app$f' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
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$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$f' ) ) ) )
=> ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom407) ).
thf(1449,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$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$f' ) ) ) )
=> ( E @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$q' ) @ ( C @ 'compDefined$b' ) @ 'fun_app$e' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(313,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'category$c' ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom335) ).
thf(1812,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) )
& ( A @ 'category$c' ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$o' ) @ 'fun_app$n' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(4414,plain,
$false,
inference(e,[status(thm)],[1036,1469,2341,2109,1633,1237,1899,666,2280,481,628,1031,1315,1850,1200,1211,762,2104,683,1290,2381,2395,1443,2282,1142,1692,1041,1173,2195,1608,2035,1735,797,715,698,538,1222,670,1196,1782,1441,709,1046,1935,1386,565,1803,1703,1724,1475,1228,1623,1482,1628,1055,570,504,1313,1191,2126,2356,1792,1430,2274,917,702,1462,1059,817,559,2169,2552,770,2024,1963,1778,606,1347,1572,1741,1398,2178,924,756,591,2469,2259,1828,2291,1677,806,1334,646,1682,1136,834,1169,1377,1886,1433,1242,2205,1696,1564,2523,2530,1863,920,1438,793,2118,2083,1057,2364,2164,1915,1708,1311,2296,2307,1768,1868,2382,2061,1636,1255,1570,788,815,2132,2249,778,1217,598,1502,820,561,1666,693,630,2445,1837,1920,625,1178,583,1787,2327,2112,1687,1457,2313,551,1350,1270,2377,1017,615,1328,1064,725,980,1425,1006,1719,593,783,2268,742,578,1028,488,1182,901,2455,1214,1889,2317,554,753,2080,642,489,1937,2038,1446,2472,1039,622,1776,1150,1852,2140,605,2370,1451,738,2304,1266,2153,2387,1231,1131,654,2006,2497,2052,2482,1857,1991,792,1814,633,541,657,2076,2368,674,1663,2189,1185,926,773,794,586,2338,2121,618,1680,1698,1219,1273,745,1595,573,965,750,1727,2048,1884,1620,2393,743,711,1965,562,904,975,1701,2398,545,1488,2161,1139,1669,2293,1733,2442,704,1675,672,713,1865,498,1239,1997,2166,1765,1897,804,1464,2474,2346,1282,736,567,1771,1175,764,604,1806,1011,1589,2284,1933,2246,1603,2299,649,1043,2378,1690,2180,811,1630,621,483,1460,2252,932,1820,758,1339,2314,2343,848,700,2278,668,983,1396,2350,2401,2171,695,1066,2086,2064,2288,2244,1477,851,2156,685,1171,2535,2101,2390,1250,1694,922,722,1034,490,2107,2271,548,2449,2202,1472,836,1049,1203,589,1277,2124,2333,2256,968,823,2513,776,557,580,640,1025,2375,2192,739,1780,1484,1225,1400,707,2143,2012,2092,2454,1300,1188,585,502,840,2337,2276,1738,643,1711,1499,1830,1763,2545,808,2500,613,1052,1427,1008,595,1617,656,1023,1585,978,2458,1180,1685,482,1817,2347,759,1575,2071,2078,1913,2310,688,1326,1253,963,2174,2135,1062,652,1854,786,781,2262,813,1721,1341,896,748,1244,1822,2447,1861,914,2198,2095,1309,2494,1994,1161,929,2330,1706,1193,899,1661,2287,1774,2302,1280,2385,2255,967,1625,818,1380,1480,2003,2142,854,1303,790,2050,564,1859,801,1693,960,2040,1165,767,2417,1789,664,2021,1610,2353,740,2241,860,2485,2467,1923,1925,2372,2138,2159,1352,1268,575,2265,1019,1597,1004,1902,691,486,935,1681,1463,491,1069,1014,1331,1606,543,2018,1848,2059,1917,676,1449,1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP305_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.42 % Computer : n026.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.43 % CPULimit : 300
% 0.14/0.43 % WCLimit : 300
% 0.14/0.43 % DateTime : Fri Sep 25 19:08:54 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.85/1.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.70/1.73 % [INFO] Parsing done (708ms).
% 3.70/1.75 % [INFO] Running in sequential loop mode.
% 4.73/2.14 % [INFO] eprover registered as external prover.
% 4.73/2.14 % [INFO] Scanning for conjecture ...
% 5.37/2.43 % [INFO] Found a conjecture (or negated_conjecture) and 623 axioms. Running axiom selection ...
% 6.71/2.78 % [INFO] Axiom selection finished. Selected 478 axioms (removed 145 axioms).
% 8.45/3.25 % [INFO] Problem is typed first-order (TPTP TFF).
% 8.45/3.28 % [INFO] Type checking passed.
% 8.45/3.28 % [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 ...
% 35.76/9.46 % External prover 'e' found a proof!
% 35.76/9.46 % [INFO] Killing All external provers ...
% 35.76/9.46 % Time passed: 8892ms (effective reasoning time: 7706ms)
% 35.76/9.46 % 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)>
% 35.76/9.46 % 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
% 35.76/9.46 % No. of inferences in proof: 1019
% 35.76/9.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8892 ms resp. 7706 ms w/o parsing
% 35.92/9.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.92/9.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------