%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP302_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 : n005.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 07:37:39 AM UTC 2026
% Result : Theorem 33.02s 9.44s
% Output : Refutation 35.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 626
% Syntax : Number of formulae : 1254 ( 368 unt; 0 typ; 0 def)
% Number of atoms : 3835 ( 935 equ; 0 cnn)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 21037 ( 82 ~; 0 |;1207 &;18374 @)
% ( 138 <=>;1236 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Number of types : 183 ( 182 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 380 ( 377 usr; 40 con; 0-7 aty)
% Number of variables : 4073 ( 0 ^;3972 !; 101 ?;4073 :)
% Comments :
%------------------------------------------------------------------------------
thf('ZF_ZF_ZF_prod_fun$_type',type,
'ZF_ZF_ZF_prod_fun$': $tType ).
thf('B_ZF_fun_set$_type',type,
'B_ZF_fun_set$': $tType ).
thf('Nat_ZF_fun_set$_type',type,
'Nat_ZF_fun_set$': $tType ).
thf('Nat_set_set$_type',type,
'Nat_set_set$': $tType ).
thf('ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_type',type,
'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$': $tType ).
thf('Nat_ZF_ZF_prod_prod_set$_type',type,
'Nat_ZF_ZF_prod_prod_set$': $tType ).
thf('Nat_nat_ZF_set_ZF_set_prod_fun_fun$_type',type,
'Nat_nat_ZF_set_ZF_set_prod_fun_fun$': $tType ).
thf('ZF_ZF_ZF_set_ZF_set_prod_fun_fun$_type',type,
'ZF_ZF_ZF_set_ZF_set_prod_fun_fun$': $tType ).
thf('ZF_set$_type',type,
'ZF_set$': $tType ).
thf('Nat_nat_fun_ZF_set_fun$_type',type,
'Nat_nat_fun_ZF_set_fun$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$': $tType ).
thf('ZF_nat_set_fun$_type',type,
'ZF_nat_set_fun$': $tType ).
thf('Unit_unit_fun$_type',type,
'Unit_unit_fun$': $tType ).
thf('ZF_nat_bool_fun_fun$_type',type,
'ZF_nat_bool_fun_fun$': $tType ).
thf('A_b_b_c_LSCategory_ext_Category_ext$_type',type,
'A_b_b_c_LSCategory_ext_Category_ext$': $tType ).
thf('Nat_set_set_ZF_set_set_fun$_type',type,
'Nat_set_set_ZF_set_set_fun$': $tType ).
thf('ZF_b_set_fun$_type',type,
'ZF_b_set_fun$': $tType ).
thf('Nat_ZF_prod_set$_type',type,
'Nat_ZF_prod_set$': $tType ).
thf('ZF_ZF_prod_set$_type',type,
'ZF_ZF_prod_set$': $tType ).
thf('ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$_type',type,
'ZF_ZF_prod_set_set_ZF_ZF_prod_set_fun$': $tType ).
thf('ZF_ZF_prod_set_set_ZF_set_set_fun$_type',type,
'ZF_ZF_prod_set_set_ZF_set_set_fun$': $tType ).
thf('ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_type',type,
'ZF_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$': $tType ).
thf('ZF_set_bool_fun_set$_type',type,
'ZF_set_bool_fun_set$': $tType ).
thf('ZF_set_set$_type',type,
'ZF_set_set$': $tType ).
thf('A_bool_fun_set$_type',type,
'A_bool_fun_set$': $tType ).
thf('ZF_set_ZF_set_fun$_type',type,
'ZF_set_ZF_set_fun$': $tType ).
thf('ZF_ZF_prod_ZF_ZF_prod_fun$_type',type,
'ZF_ZF_prod_ZF_ZF_prod_fun$': $tType ).
thf('ZF_ZF_set_fun$_type',type,
'ZF_ZF_set_fun$': $tType ).
thf('A_b_fun_set$_type',type,
'A_b_fun_set$': $tType ).
thf('ZF_set_ZF_set_prod_set$_type',type,
'ZF_set_ZF_set_prod_set$': $tType ).
thf('ZF_ZF_fun_ZF_set_fun$_type',type,
'ZF_ZF_fun_ZF_set_fun$': $tType ).
thf('Nat_a_fun$_type',type,
'Nat_a_fun$': $tType ).
thf('A_set_set$_type',type,
'A_set_set$': $tType ).
thf('Nat_nat_fun_set$_type',type,
'Nat_nat_fun_set$': $tType ).
thf('ZF_ZF_prod_ZF_fun$_type',type,
'ZF_ZF_prod_ZF_fun$': $tType ).
thf('ZF_nat_ZF_ZF_prod_set_fun_fun$_type',type,
'ZF_nat_ZF_ZF_prod_set_fun_fun$': $tType ).
thf('B_c_LSCategory_ext$_type',type,
'B_c_LSCategory_ext$': $tType ).
thf('Nat_set_set_nat_set_fun$_type',type,
'Nat_set_set_nat_set_fun$': $tType ).
thf('ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$_type',type,
'ZF_ZF_prod_ZF_ZF_prod_prod_ZF_ZF_prod_fun$': $tType ).
thf('ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_type',type,
'ZF_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$': $tType ).
thf('B_b_fun$_type',type,
'B_b_fun$': $tType ).
thf('ZF_nat_ZF_set_ZF_set_prod_fun_fun$_type',type,
'ZF_nat_ZF_set_ZF_set_prod_fun_fun$': $tType ).
thf('ZF_ZF_set_prod_set$_type',type,
'ZF_ZF_set_prod_set$': $tType ).
thf('Nat_ZF_bool_fun_fun$_type',type,
'Nat_ZF_bool_fun_fun$': $tType ).
thf('ZF_nat_prod_ZF_ZF_prod_set_fun$_type',type,
'ZF_nat_prod_ZF_ZF_prod_set_fun$': $tType ).
thf('ZF_ZF_ZF_set_prod_fun$_type',type,
'ZF_ZF_ZF_set_prod_fun$': $tType ).
thf('ZF_ZF_ZF_ZF_prod_fun_fun$_type',type,
'ZF_ZF_ZF_ZF_prod_fun_fun$': $tType ).
thf('ZF_ZF_ZF_prod_set_fun$_type',type,
'ZF_ZF_ZF_prod_set_fun$': $tType ).
thf('ZF_ZF_prod_ZF_set_fun$_type',type,
'ZF_ZF_prod_ZF_set_fun$': $tType ).
thf('A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_type',type,
'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$': $tType ).
thf('ZF_ZF_prod_nat_set_fun$_type',type,
'ZF_ZF_prod_nat_set_fun$': $tType ).
thf('ZF_nat_ZF_set_fun_fun$_type',type,
'ZF_nat_ZF_set_fun_fun$': $tType ).
thf('ZF_ZF_prod$_type',type,
'ZF_ZF_prod$': $tType ).
thf('B_a_set_fun$_type',type,
'B_a_set_fun$': $tType ).
thf('Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$_type',type,
'Nat_ZF_ZF_prod_ZF_set_ZF_prod_fun_fun$': $tType ).
thf('B_b_prod_set$_type',type,
'B_b_prod_set$': $tType ).
thf('ZF_ZF_set_set_fun$_type',type,
'ZF_ZF_set_set_fun$': $tType ).
thf('Nat_ZF_set_prod_set$_type',type,
'Nat_ZF_set_prod_set$': $tType ).
thf('ZF_ZF_prod_ZF_ZF_prod_prod_set$_type',type,
'ZF_ZF_prod_ZF_ZF_prod_prod_set$': $tType ).
thf('Nat_nat_prod_set$_type',type,
'Nat_nat_prod_set$': $tType ).
thf('B$_type',type,
'B$': $tType ).
thf('ZF_set_set_bool_fun$_type',type,
'ZF_set_set_bool_fun$': $tType ).
thf('ZF_ZF_ZF_fun_fun$_type',type,
'ZF_ZF_ZF_fun_fun$': $tType ).
thf('A_ZF_set_fun$_type',type,
'A_ZF_set_fun$': $tType ).
thf('B_bool_fun_set$_type',type,
'B_bool_fun_set$': $tType ).
thf('ZF_set_a_fun$_type',type,
'ZF_set_a_fun$': $tType ).
thf('ZF_nat_fun_set$_type',type,
'ZF_nat_fun_set$': $tType ).
thf('B_ZF_set_fun$_type',type,
'B_ZF_set_fun$': $tType ).
thf('ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$_type',type,
'ZF_ZF_prod_nat_ZF_ZF_set_prod_fun_fun$': $tType ).
thf('ZF_ZF_ZF_set_fun_fun$_type',type,
'ZF_ZF_ZF_set_fun_fun$': $tType ).
thf('Nat_ZF_ZF_set_ZF_set_prod_fun_fun$_type',type,
'Nat_ZF_ZF_set_ZF_set_prod_fun_fun$': $tType ).
thf('ZF_set_set_ZF_set_bool_fun_fun$_type',type,
'ZF_set_set_ZF_set_bool_fun_fun$': $tType ).
thf('ZF_ZF_set_ZF_set_prod_fun$_type',type,
'ZF_ZF_set_ZF_set_prod_fun$': $tType ).
thf('ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$_type',type,
'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$': $tType ).
thf('Nat_nat_fun$_type',type,
'Nat_nat_fun$': $tType ).
thf('C$_type',type,
'C$': $tType ).
thf('ZF_a_set_fun$_type',type,
'ZF_a_set_fun$': $tType ).
thf('ZF_b_fun$_type',type,
'ZF_b_fun$': $tType ).
thf('ZF_set_set_set_ZF_set_set_fun$_type',type,
'ZF_set_set_set_ZF_set_set_fun$': $tType ).
thf('Nat$_type',type,
'Nat$': $tType ).
thf('Nat_ZF_set_set_fun$_type',type,
'Nat_ZF_set_set_fun$': $tType ).
thf('Nat_set_ZF_set_set_fun$_type',type,
'Nat_set_ZF_set_set_fun$': $tType ).
thf('Nat_nat_prod_ZF_ZF_prod_set_fun$_type',type,
'Nat_nat_prod_ZF_ZF_prod_set_fun$': $tType ).
thf('B_b_prod_bool_fun$_type',type,
'B_b_prod_bool_fun$': $tType ).
thf('Nat_ZF_ZF_prod_fun$_type',type,
'Nat_ZF_ZF_prod_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$': $tType ).
thf('ZF_set_set_ZF_set_set_set_fun$_type',type,
'ZF_set_set_ZF_set_set_set_fun$': $tType ).
thf('Nat_set_ZF_set_fun$_type',type,
'Nat_set_ZF_set_fun$': $tType ).
thf('ZF_ZF_fun_set$_type',type,
'ZF_ZF_fun_set$': $tType ).
thf('ZF_ZF_prod_nat_prod_set$_type',type,
'ZF_ZF_prod_nat_prod_set$': $tType ).
thf('B_b_prod_b_fun_set$_type',type,
'B_b_prod_b_fun_set$': $tType ).
thf('Nat_nat_prod_ZF_set_ZF_set_prod_fun$_type',type,
'Nat_nat_prod_ZF_set_ZF_set_prod_fun$': $tType ).
thf('ZF_ZF_ZF_prod_prod_set$_type',type,
'ZF_ZF_ZF_prod_prod_set$': $tType ).
thf('ZF_set_ZF_prod$_type',type,
'ZF_set_ZF_prod$': $tType ).
thf('Nat_ZF_set_ZF_set_prod_fun$_type',type,
'Nat_ZF_set_ZF_set_prod_fun$': $tType ).
thf('ZF_ZF_prod_set_set$_type',type,
'ZF_ZF_prod_set_set$': $tType ).
thf('B_a_fun$_type',type,
'B_a_fun$': $tType ).
thf('ZF_a_fun$_type',type,
'ZF_a_fun$': $tType ).
thf('ZF_ZF_set_prod$_type',type,
'ZF_ZF_set_prod$': $tType ).
thf('Nat_ZF_set_fun$_type',type,
'Nat_ZF_set_fun$': $tType ).
thf(tlbool_type,type,
tlbool: $tType ).
thf('ZF_nat_prod_set$_type',type,
'ZF_nat_prod_set$': $tType ).
thf('ZF_ZF_prod_ZF_set_ZF_set_prod_fun$_type',type,
'ZF_ZF_prod_ZF_set_ZF_set_prod_fun$': $tType ).
thf('B_b_prod$_type',type,
'B_b_prod$': $tType ).
thf('ZF_set_set_ZF_set_fun$_type',type,
'ZF_set_set_ZF_set_fun$': $tType ).
thf('ZF_ZF_fun_ZF_ZF_fun_fun$_type',type,
'ZF_ZF_fun_ZF_ZF_fun_fun$': $tType ).
thf('A_set_a_bool_fun_fun$_type',type,
'A_set_a_bool_fun_fun$': $tType ).
thf('Nat_ZF_prod_ZF_ZF_prod_set_fun$_type',type,
'Nat_ZF_prod_ZF_ZF_prod_set_fun$': $tType ).
thf('A_bool_fun$_type',type,
'A_bool_fun$': $tType ).
thf('ZF_nat_fun_ZF_set_fun$_type',type,
'ZF_nat_fun_ZF_set_fun$': $tType ).
thf('A_set$_type',type,
'A_set$': $tType ).
thf('ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$_type',type,
'ZF_ZF_prod_ZF_ZF_prod_ZF_ZF_prod_fun_fun$': $tType ).
thf('A_a_set_fun$_type',type,
'A_a_set_fun$': $tType ).
thf('ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_type',type,
'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$': $tType ).
thf('ZF_set_ZF_set_set_fun$_type',type,
'ZF_set_ZF_set_set_fun$': $tType ).
thf('Nat_nat_set_fun$_type',type,
'Nat_nat_set_fun$': $tType ).
thf('A_b_fun$_type',type,
'A_b_fun$': $tType ).
thf('ZF_nat_prod_ZF_set_ZF_set_prod_fun$_type',type,
'ZF_nat_prod_ZF_set_ZF_set_prod_fun$': $tType ).
thf('ZF_ZF_ZF_ZF_prod_set_fun_fun$_type',type,
'ZF_ZF_ZF_ZF_prod_set_fun_fun$': $tType ).
thf('B_set$_type',type,
'B_set$': $tType ).
thf('Nat_nat_ZF_ZF_prod_set_fun_fun$_type',type,
'Nat_nat_ZF_ZF_prod_set_fun_fun$': $tType ).
thf('A_b_fun_bool_fun$_type',type,
'A_b_fun_bool_fun$': $tType ).
thf('Nat_ZF_ZF_prod_set_fun$_type',type,
'Nat_ZF_ZF_prod_set_fun$': $tType ).
thf('A$_type',type,
'A$': $tType ).
thf('B_set_b_bool_fun_fun$_type',type,
'B_set_b_bool_fun_fun$': $tType ).
thf('ZF_ZF_unit_Category_ext$_type',type,
'ZF_ZF_unit_Category_ext$': $tType ).
thf('ZF_set_ZF_bool_fun_fun$_type',type,
'ZF_set_ZF_bool_fun_fun$': $tType ).
thf('ZF_ZF_fun_bool_fun$_type',type,
'ZF_ZF_fun_bool_fun$': $tType ).
thf('ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$_type',type,
'ZF_ZF_prod_ZF_ZF_ZF_set_prod_fun_fun$': $tType ).
thf('Nat_nat_ZF_set_fun_fun$_type',type,
'Nat_nat_ZF_set_fun_fun$': $tType ).
thf('ZF_ZF_prod_set_ZF_set_fun$_type',type,
'ZF_ZF_prod_set_ZF_set_fun$': $tType ).
thf('B_set_bool_fun$_type',type,
'B_set_bool_fun$': $tType ).
thf('A_b_set_fun$_type',type,
'A_b_set_fun$': $tType ).
thf('Nat_b_fun$_type',type,
'Nat_b_fun$': $tType ).
thf('ZF_set_ZF_prod_set$_type',type,
'ZF_set_ZF_prod_set$': $tType ).
thf('B_set_set$_type',type,
'B_set_set$': $tType ).
thf('ZF_set_ZF_set_prod$_type',type,
'ZF_set_ZF_set_prod$': $tType ).
thf('Nat_ZF_ZF_set_prod_fun$_type',type,
'Nat_ZF_ZF_set_prod_fun$': $tType ).
thf('B_b_prod_b_fun$_type',type,
'B_b_prod_b_fun$': $tType ).
thf('ZF_set_ZF_fun$_type',type,
'ZF_set_ZF_fun$': $tType ).
thf('B_set_b_set_fun$_type',type,
'B_set_b_set_fun$': $tType ).
thf('ZF_ZF_prod_set_set_ZF_set_fun$_type',type,
'ZF_ZF_prod_set_set_ZF_set_fun$': $tType ).
thf('B_a_fun_b_a_fun_fun$_type',type,
'B_a_fun_b_a_fun_fun$': $tType ).
thf('A_a_fun$_type',type,
'A_a_fun$': $tType ).
thf('ZF_bool_fun$_type',type,
'ZF_bool_fun$': $tType ).
thf('Nat_ZF_prod_ZF_set_ZF_set_prod_fun$_type',type,
'Nat_ZF_prod_ZF_set_ZF_set_prod_fun$': $tType ).
thf('B_b_b_fun_fun$_type',type,
'B_b_b_fun_fun$': $tType ).
thf('ZF_set_set_ZF_set_set_fun$_type',type,
'ZF_set_set_ZF_set_set_fun$': $tType ).
thf('ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$_type',type,
'ZF_ZF_prod_ZF_prod_ZF_ZF_set_prod_fun$': $tType ).
thf('Nat_set_set_ZF_set_set_set_fun$_type',type,
'Nat_set_set_ZF_set_set_set_fun$': $tType ).
thf('ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$_type',type,
'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$': $tType ).
thf('ZF_nat_fun$_type',type,
'ZF_nat_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$': $tType ).
thf('ZF_set_bool_fun$_type',type,
'ZF_set_bool_fun$': $tType ).
thf('ZF_ZF_prod_ZF_prod_set$_type',type,
'ZF_ZF_prod_ZF_prod_set$': $tType ).
thf('ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$_type',type,
'ZF_ZF_prod_nat_prod_ZF_ZF_set_prod_fun$': $tType ).
thf('Unit$_type',type,
'Unit$': $tType ).
thf('Nat_bool_fun$_type',type,
'Nat_bool_fun$': $tType ).
thf('Bool_set$_type',type,
'Bool_set$': $tType ).
thf('ZF$_type',type,
'ZF$': $tType ).
thf('B_ZF_fun$_type',type,
'B_ZF_fun$': $tType ).
thf('ZF_set_set_set$_type',type,
'ZF_set_set_set$': $tType ).
thf('ZF_set_ZF_ZF_prod_set_fun$_type',type,
'ZF_set_ZF_ZF_prod_set_fun$': $tType ).
thf('B_a_fun_set$_type',type,
'B_a_fun_set$': $tType ).
thf('Nat_ZF_fun_ZF_set_fun$_type',type,
'Nat_ZF_fun_ZF_set_fun$': $tType ).
thf('Nat_set$_type',type,
'Nat_set$': $tType ).
thf('Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$_type',type,
'Nat_ZF_ZF_prod_prod_ZF_set_ZF_prod_fun$': $tType ).
thf('ZF_bool_fun_set$_type',type,
'ZF_bool_fun_set$': $tType ).
thf('Nat_ZF_fun$_type',type,
'Nat_ZF_fun$': $tType ).
thf('ZF_ZF_prod_ZF_ZF_prod_set_fun$_type',type,
'ZF_ZF_prod_ZF_ZF_prod_set_fun$': $tType ).
thf('B_a_fun_bool_fun$_type',type,
'B_a_fun_bool_fun$': $tType ).
thf('B_bool_fun$_type',type,
'B_bool_fun$': $tType ).
thf('Nat_ZF_ZF_ZF_prod_set_fun_fun$_type',type,
'Nat_ZF_ZF_ZF_prod_set_fun_fun$': $tType ).
thf('Nat_ZF_ZF_set_fun_fun$_type',type,
'Nat_ZF_ZF_set_fun_fun$': $tType ).
thf('B_b_set_fun$_type',type,
'B_b_set_fun$': $tType ).
thf('A_set_bool_fun$_type',type,
'A_set_bool_fun$': $tType ).
thf('ZF_ZF_prod_ZF_set_ZF_prod_fun$_type',type,
'ZF_ZF_prod_ZF_set_ZF_prod_fun$': $tType ).
thf('B_ZF_fun_bool_fun$_type',type,
'B_ZF_fun_bool_fun$': $tType ).
thf('ZF_ZF_bool_fun_fun$_type',type,
'ZF_ZF_bool_fun_fun$': $tType ).
thf('sup$_decl',type,
'sup$': 'ZF_set_set_ZF_set_fun$' ).
thf('id$_decl',type,
'id$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_fun$' ).
thf('less_eq$e_decl',type,
'less_eq$e': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set$' > $o ).
thf('catDom$a_decl',type,
'catDom$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('oppositeCategory$_decl',type,
'oppositeCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('c$_decl',type,
'c$': 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('uua$_decl',type,
'uua$': 'B_set_b_bool_fun_fun$' ).
thf('functorM$_decl',type,
'functorM$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).
thf('uwa$_decl',type,
'uwa$': 'B_ZF_fun$' > 'B_set$' > 'ZF_bool_fun$' > 'B_bool_fun$' ).
thf('mapO$a_decl',type,
'mapO$a': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > 'A_a_fun$' ).
thf('uwl$_decl',type,
'uwl$': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_set$' > 'ZF_bool_fun$' ).
thf('unitFunctor$_decl',type,
'unitFunctor$': 'ZF_ZF_unit_Category_ext$' > 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' ).
thf('fun_app$b_decl',type,
'fun_app$b': 'ZF_ZF_ZF_fun_fun$' > 'ZF$' > 'ZF_ZF_fun$' ).
thf('constFunctor$_decl',type,
'constFunctor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' ).
thf('the$a_decl',type,
'the$a': 'B_bool_fun$' > 'B$' ).
thf('mapsTo$_decl',type,
'mapsTo$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'A$' > 'A_bool_fun$' ).
thf('compDefined$_decl',type,
'compDefined$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$' ).
thf('case_prod$_decl',type,
'case_prod$': 'ZF_ZF_ZF_fun_fun$' > 'ZF_ZF_prod_ZF_fun$' ).
thf('uwx$_decl',type,
'uwx$': 'Nat_ZF_fun$' > 'ZF_bool_fun$' ).
thf('constFunctor$d_decl',type,
'constFunctor$d': 'ZF_ZF_unit_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' ).
thf('comp$f_decl',type,
'comp$f': 'ZF_set_ZF_set_set_fun$' > 'ZF_set_set_ZF_set_fun$' > 'ZF_set_set_ZF_set_set_fun$' ).
thf('sup$c_decl',type,
'sup$c': 'B_set_set$' > 'B_set$' ).
thf('fun_app$bk_decl',type,
'fun_app$bk': 'B_a_fun$' > 'B$' > 'A$' ).
thf('extensional$e_decl',type,
'extensional$e': 'B_set$' > 'B_ZF_fun_set$' ).
thf('lSCategory$_decl',type,
'lSCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('uzv$_decl',type,
'uzv$': 'ZF_ZF_bool_fun_fun$' > 'ZF_bool_fun$' ).
thf('member$c_decl',type,
'member$c': 'A$' > 'A_set_bool_fun$' ).
thf('inf$_decl',type,
'inf$': 'ZF_set_set$' > 'ZF_set$' ).
thf('sup$h_decl',type,
'sup$h': 'B_bool_fun_set$' > 'B_bool_fun$' ).
thf('member$a_decl',type,
'member$a': 'ZF_set$' > 'ZF_set_set_bool_fun$' ).
thf('uyh$_decl',type,
'uyh$': 'ZF_ZF_fun$' > 'ZF_set$' > 'ZF_ZF_set_fun$' ).
thf('fun_app$dd_decl',type,
'fun_app$dd': 'ZF_set_set_ZF_set_set_set_fun$' > 'ZF_set_set$' > 'ZF_set_set_set$' ).
thf('restrict$a_decl',type,
'restrict$a': 'B_b_prod_b_fun$' > 'B_b_prod_set$' > 'B_b_prod$' > 'B$' ).
thf('fun_app$cr_decl',type,
'fun_app$cr': 'A_a_set_fun$' > 'A$' > 'A_set$' ).
thf('obj_update$_decl',type,
'obj_update$': 'A_set_a_set_fun$' > 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('uux$_decl',type,
'uux$': 'A_set$' > 'A_bool_fun$' > 'A_bool_fun$' ).
thf('uwd$_decl',type,
'uwd$': 'ZF_set_a_fun$' > 'ZF_set_set$' > 'A_bool_fun$' > 'A_bool_fun$' ).
thf('uuw$_decl',type,
'uuw$': 'ZF_ZF_ZF_fun_fun$' ).
thf('image$e_decl',type,
'image$e': 'A_set_bool_fun$' > 'A_set_set$' > 'Bool_set$' ).
thf('fun_app$o_decl',type,
'fun_app$o': 'A_set_a_bool_fun_fun$' > 'A_set$' > 'A_bool_fun$' ).
thf('inverse_rel$_decl',type,
'inverse_rel$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'B_bool_fun$' ).
thf('mapO$b_decl',type,
'mapO$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_fun$' ).
thf('fun_app$co_decl',type,
'fun_app$co': 'A_ZF_set_fun$' > 'A$' > 'ZF_set$' ).
thf('uwp$_decl',type,
'uwp$': 'ZF_set_ZF_fun$' > 'ZF_set_set$' > 'ZF_bool_fun$' ).
thf('less_eq$k_decl',type,
'less_eq$k': 'B_bool_fun$' > 'B_bool_fun$' > $o ).
thf('f$_decl',type,
'f$': 'B$' ).
thf('sup$j_decl',type,
'sup$j': 'ZF_bool_fun_set$' > 'ZF_bool_fun$' ).
thf('image$f_decl',type,
'image$f': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_set_ZF_set_fun$' ).
thf('uww$_decl',type,
'uww$': 'Nat_ZF_set_fun$' > 'ZF_set_bool_fun$' ).
thf('image$_decl',type,
'image$': 'Nat_ZF_set_fun$' > 'Nat_set_ZF_set_set_fun$' ).
thf('category$a_decl',type,
'category$a': 'ZF_ZF_unit_Category_ext$' > $o ).
thf('uwv$_decl',type,
'uwv$': 'ZF_ZF_fun$' > 'ZF_bool_fun$' ).
thf('uzb$_decl',type,
'uzb$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_set$' > 'Nat_ZF_set_fun$' ).
thf('uxi$_decl',type,
'uxi$': 'ZF_set$' > 'ZF_ZF_set_fun$' ).
thf('fun_app$bf_decl',type,
'fun_app$bf': 'A_ZF_fun$' > 'A$' > 'ZF$' ).
thf('uur$_decl',type,
'uur$': 'ZF_ZF_fun$' ).
thf('comp$e_decl',type,
'comp$e': 'ZF_set_set_set_ZF_set_set_fun$' > 'ZF_set_set_ZF_set_set_set_fun$' > 'ZF_set_set_ZF_set_set_fun$' ).
thf('uuh$_decl',type,
'uuh$': tlbool > 'ZF$' > 'ZF_ZF_bool_fun_fun$' ).
thf('sigma$_decl',type,
'sigma$': 'ZF_set$' > 'ZF_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
thf('sup$i_decl',type,
'sup$i': 'ZF_set_bool_fun_set$' > 'ZF_set_bool_fun$' ).
thf('pair$a_decl',type,
'pair$a': 'B$' > 'B$' > 'B_b_prod$' ).
thf('functorM$b_decl',type,
'functorM$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
thf('category$_decl',type,
'category$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('vao$_decl',type,
'vao$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$' ).
thf('image$m_decl',type,
'image$m': 'B_a_fun$' > 'B_set$' > 'A_set$' ).
thf('uzs$_decl',type,
'uzs$': 'ZF_ZF_set_fun$' > 'ZF_set$' > 'ZF_ZF_set_fun$' ).
thf('extensional$c_decl',type,
'extensional$c': 'B_b_prod_set$' > 'B_b_prod_b_fun_set$' ).
thf('uut$_decl',type,
'uut$': 'ZF_bool_fun$' ).
thf('case_prod$a_decl',type,
'case_prod$a': 'B_b_b_fun_fun$' > 'B_b_prod_b_fun$' ).
thf('uzp$_decl',type,
'uzp$': 'Nat_ZF_set_fun$' > 'Nat_set$' > 'ZF_ZF_set_fun$' ).
thf('collect$i_decl',type,
'collect$i': 'B_bool_fun$' > 'B_set$' ).
thf('uve$_decl',type,
'uve$': 'ZF_set_ZF_set_fun$' > 'Nat_ZF_set_fun$' > 'Nat_ZF_set_fun$' ).
thf('functorM$a_decl',type,
'functorM$a': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
thf('image$a_decl',type,
'image$a': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_set_set_fun$' ).
thf('image$bc_decl',type,
'image$bc': 'Nat_ZF_set_set_fun$' > 'Nat_set$' > 'ZF_set_set_set$' ).
thf('makeCat$_decl',type,
'makeCat$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('image$p_decl',type,
'image$p': 'A_a_fun$' > 'A_set_a_set_fun$' ).
thf('uub$_decl',type,
'uub$': 'ZF_set_set_ZF_set_bool_fun_fun$' ).
thf('image$bh_decl',type,
'image$bh': 'A_set_a_bool_fun_fun$' > 'A_set_set$' > 'A_bool_fun_set$' ).
thf('fun_app$aq_decl',type,
'fun_app$aq': 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' > 'ZF_ZF_ZF_fun_fun$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('mor$a_decl',type,
'mor$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$' ).
thf('fun_app$ck_decl',type,
'fun_app$ck': 'B_a_fun_bool_fun$' > 'B_a_fun$' > $o ).
thf('app$_decl',type,
'app$': 'ZF_ZF_ZF_fun_fun$' ).
thf('catDom$_decl',type,
'catDom$': 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('set$_decl',type,
'set$': 'ZF_ZF_unit_Category_ext$' ).
thf('uui$_decl',type,
'uui$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_prod_bool_fun$' ).
thf('uuz$_decl',type,
'uuz$': 'ZF_set_set$' > 'ZF_set_bool_fun$' > 'ZF_set_bool_fun$' ).
thf('less_eq$m_decl',type,
'less_eq$m': 'ZF_set_bool_fun$' > 'ZF_set_bool_fun$' > $o ).
thf('unity$_decl',type,
'unity$': 'Unit$' ).
thf('fun_app$h_decl',type,
'fun_app$h': 'ZF_set_bool_fun$' > 'ZF_set$' > $o ).
thf('image$h_decl',type,
'image$h': 'ZF_b_fun$' > 'ZF_set$' > 'B_set$' ).
thf('uyv$_decl',type,
'uyv$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_set$' > 'ZF_ZF_set_fun$' ).
thf('inf$b_decl',type,
'inf$b': 'B_set_set$' > 'B_set$' ).
thf('fun_app$x_decl',type,
'fun_app$x': 'ZF_set_ZF_set_set_fun$' > 'ZF_set$' > 'ZF_set_set$' ).
thf('val$_decl',type,
'val$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$' ).
thf('mor2ZF$_decl',type,
'mor2ZF$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_ZF_fun$' ).
thf('uva$_decl',type,
'uva$': 'ZF_set$' > 'ZF_bool_fun$' > 'ZF_bool_fun$' ).
thf('functor$b_decl',type,
'functor$b': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
thf('functor$a_decl',type,
'functor$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).
thf('uvg$_decl',type,
'uvg$': 'ZF_ZF_set_fun$' > 'Nat_ZF_fun$' > 'Nat_ZF_set_fun$' ).
thf('extensional$b_decl',type,
'extensional$b': 'A_set$' > 'A_b_fun_set$' ).
thf('uvb$_decl',type,
'uvb$': 'ZF_bool_fun$' > 'ZF_bool_fun$' > 'ZF_bool_fun$' ).
thf('image$bj_decl',type,
'image$bj': 'ZF_set_set_ZF_set_bool_fun_fun$' > 'ZF_set_set_set$' > 'ZF_set_bool_fun_set$' ).
thf('uuk$_decl',type,
'uuk$': 'ZF_ZF_fun$' > 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' ).
thf('dom_update$_decl',type,
'dom_update$': 'B_a_fun_b_a_fun_fun$' > 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('fun_app$f_decl',type,
'fun_app$f': 'ZF_bool_fun$' > 'ZF$' > $o ).
thf('vaw$_decl',type,
'vaw$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_set_fun$' ).
thf('zFfun$_decl',type,
'zFfun$': 'ZF$' > 'ZF$' > 'ZF_ZF_fun$' > 'ZF$' ).
thf('fun_app$cx_decl',type,
'fun_app$cx': 'B_ZF_set_fun$' > 'B$' > 'ZF_set$' ).
thf('member$j_decl',type,
'member$j': 'B_b_prod$' > 'B_b_prod_set$' > $o ).
thf('uvo$_decl',type,
'uvo$': 'B_a_fun$' > 'B_set$' > 'A_bool_fun$' > 'B_bool_fun$' ).
thf('preFunctor$b_decl',type,
'preFunctor$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).
thf('identityFunctor$b_decl',type,
'identityFunctor$b': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('member$k_decl',type,
'member$k': 'B_b_prod_b_fun$' > 'B_b_prod_b_fun_set$' > $o ).
thf('vac$_decl',type,
'vac$': 'Nat_ZF_set_fun$' > 'Nat_ZF_bool_fun_fun$' ).
thf('fun_app$w_decl',type,
'fun_app$w': 'ZF_nat_fun_ZF_set_fun$' > 'ZF_nat_fun$' > 'ZF_set$' ).
thf('image$an_decl',type,
'image$an': 'B_b_set_fun$' > 'B_set$' > 'B_set_set$' ).
thf('obj$a_decl',type,
'obj$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$' ).
thf('uvr$_decl',type,
'uvr$': 'B_b_fun$' > 'B_set$' > 'B_bool_fun$' > 'B_bool_fun$' ).
thf('uwu$_decl',type,
'uwu$': 'ZF_ZF_set_fun$' > 'ZF_set_bool_fun$' ).
thf('fun_app$aj_decl',type,
'fun_app$aj': 'Nat_ZF_fun$' > 'Nat$' > 'ZF$' ).
thf('lSCategory_axioms$_decl',type,
'lSCategory_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('uzm$_decl',type,
'uzm$': 'ZF_ZF_fun$' > 'Nat_ZF_set_fun$' > 'Nat_ZF_set_fun$' ).
thf('fun_app$ct_decl',type,
'fun_app$ct': 'B_a_set_fun$' > 'B$' > 'A_set$' ).
thf('uvu$_decl',type,
'uvu$': 'ZF_a_fun$' > 'ZF_set$' > 'A_bool_fun$' > 'ZF_bool_fun$' ).
thf('zFfunCod$_decl',type,
'zFfunCod$': 'ZF_ZF_fun$' ).
thf('uyl$_decl',type,
'uyl$': 'ZF$' > 'ZF_ZF_bool_fun_fun$' ).
thf('uun$_decl',type,
'uun$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('fun_app$cn_decl',type,
'fun_app$cn': 'ZF_set_set_ZF_set_set_fun$' > 'ZF_set_set$' > 'ZF_set_set$' ).
thf('image$bb_decl',type,
'image$bb': 'ZF_ZF_set_set_fun$' > 'ZF_set$' > 'ZF_set_set_set$' ).
thf('uug$_decl',type,
'uug$': 'ZF_ZF_bool_fun_fun$' ).
thf('uzd$_decl',type,
'uzd$': 'Nat_ZF_ZF_set_fun_fun$' > 'Nat_set$' > 'ZF_ZF_set_fun$' ).
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$' ).
thf('uxk$_decl',type,
'uxk$': 'ZF_bool_fun$' > 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_bool_fun_fun$' ).
thf('vau$_decl',type,
'vau$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$' ).
thf('fun_app$bm_decl',type,
'fun_app$bm': 'A_a_fun$' > 'A$' > 'A$' ).
thf('extCategory$a_decl',type,
'extCategory$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('vaf$_decl',type,
'vaf$': 'ZF_set_set_set$' > 'ZF_set_bool_fun$' ).
thf('collect$b_decl',type,
'collect$b': 'B_b_prod_bool_fun$' > 'B_b_prod_set$' ).
thf('uvz$_decl',type,
'uvz$': 'B_ZF_fun$' > 'B_set$' > 'ZF_bool_fun$' > 'ZF_bool_fun$' ).
thf('cod$_decl',type,
'cod$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$' ).
thf('collect$d_decl',type,
'collect$d': 'B_ZF_fun_bool_fun$' > 'B_ZF_fun_set$' ).
thf('uxg$_decl',type,
'uxg$': 'ZF_bool_fun$' > 'ZF_bool_fun$' > 'ZF_ZF_bool_fun_fun$' ).
thf('set$a_decl',type,
'set$a': 'ZF_ZF_unit_Category_ext$' ).
thf('member$g_decl',type,
'member$g': 'B_ZF_fun$' > 'B_ZF_fun_set$' > $o ).
thf(tltrue_decl,type,
tltrue: tlbool ).
thf('mapM$_decl',type,
'mapM$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'B_ZF_fun$' ).
thf('obj$_decl',type,
'obj$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_set$' ).
thf('inverse$_decl',type,
'inverse$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_fun$' ).
thf('uvv$_decl',type,
'uvv$': 'ZF_b_fun$' > 'ZF_set$' > 'B_bool_fun$' > 'B_bool_fun$' ).
thf('collect$j_decl',type,
'collect$j': 'ZF_set_bool_fun$' > 'ZF_set_set$' ).
thf('uud$_decl',type,
'uud$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('less_eq$i_decl',type,
'less_eq$i': 'Nat_set$' > 'Nat_set$' > $o ).
thf('uvc$_decl',type,
'uvc$': 'ZF_set_ZF_set_fun$' > 'ZF_ZF_set_fun$' > 'ZF_ZF_set_fun$' ).
thf('category_axioms$_decl',type,
'category_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('fun_app$ad_decl',type,
'fun_app$ad': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF$' > 'ZF_ZF_set_fun$' ).
thf('constFunctor$e_decl',type,
'constFunctor$e': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('fun_app$be_decl',type,
'fun_app$be': 'ZF_set_ZF_fun$' > 'ZF_set$' > 'ZF$' ).
thf('uza$_decl',type,
'uza$': 'ZF_nat_ZF_set_fun_fun$' > 'ZF_set$' > 'Nat_ZF_set_fun$' ).
thf('mapsTo$a_decl',type,
'mapsTo$a': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_ZF_bool_fun_fun$' ).
thf('image$aq_decl',type,
'image$aq': 'A_ZF_set_fun$' > 'A_set$' > 'ZF_set_set$' ).
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$' > $o ).
thf('uvp$_decl',type,
'uvp$': 'A_b_fun$' > 'A_set$' > 'B_bool_fun$' > 'B_bool_fun$' ).
thf('fun_app$bi_decl',type,
'fun_app$bi': 'ZF_a_fun$' > 'ZF$' > 'A$' ).
thf('image$al_decl',type,
'image$al': 'A_b_set_fun$' > 'A_set$' > 'B_set_set$' ).
thf('sup$g_decl',type,
'sup$g': 'A_bool_fun_set$' > 'A_bool_fun$' ).
thf('homFtorContra$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$' ).
thf('uyz$_decl',type,
'uyz$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_ZF_ZF_set_fun_fun$' ).
thf('image$w_decl',type,
'image$w': 'ZF_set_ZF_fun$' > 'ZF_set_set$' > 'ZF_set$' ).
thf('fun_app$u_decl',type,
'fun_app$u': 'ZF_set_set_ZF_set_fun$' > 'ZF_set_set$' > 'ZF_set$' ).
thf('inf$a_decl',type,
'inf$a': 'A_set_set$' > 'A_set$' ).
thf('uzw$_decl',type,
'uzw$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_bool_fun_fun$' ).
thf('image$n_decl',type,
'image$n': 'A_ZF_fun$' > 'A_set$' > 'ZF_set$' ).
thf('image$r_decl',type,
'image$r': 'Nat_ZF_fun$' > 'Nat_set$' > 'ZF_set$' ).
thf('image$ak_decl',type,
'image$ak': 'A_a_set_fun$' > 'A_set$' > 'A_set_set$' ).
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('oppositeCategory$a_decl',type,
'oppositeCategory$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('the$_decl',type,
'the$': 'ZF_bool_fun$' > 'ZF$' ).
thf('constFunctor$a_decl',type,
'constFunctor$a': '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('uwb$_decl',type,
'uwb$': 'ZF_ZF_fun$' > 'ZF_set$' > 'ZF_bool_fun$' > 'ZF_bool_fun$' ).
thf('fun_app$a_decl',type,
'fun_app$a': 'ZF_ZF_fun_ZF_ZF_fun_fun$' > 'ZF_ZF_fun$' > 'ZF_ZF_fun$' ).
thf('uvw$_decl',type,
'uvw$': 'ZF_b_fun$' > 'ZF_set$' > 'B_bool_fun$' > 'ZF_bool_fun$' ).
thf('vap$_decl',type,
'vap$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_fun$' > 'ZF_ZF_set_fun$' ).
thf('fun_app$as_decl',type,
'fun_app$as': 'ZF_b_fun$' > 'ZF$' > 'B$' ).
thf('image$g_decl',type,
'image$g': 'ZF_ZF_fun$' > 'ZF_set_ZF_set_fun$' ).
thf('fun_app$bh_decl',type,
'fun_app$bh': 'A_set_a_set_fun$' > 'A_set$' > 'A_set$' ).
thf('vag$_decl',type,
'vag$': 'ZF_set_set$' > 'ZF_bool_fun$' ).
thf('gr$c_decl',type,
'gr$c': 'ZF_set$' > 'ZF_ZF_fun$' > 'ZF_ZF_prod_set$' ).
thf('uvm$_decl',type,
'uvm$': 'A_a_fun$' > 'A_set$' > 'A_bool_fun$' > 'A_bool_fun$' ).
thf('uvf$_decl',type,
'uvf$': 'ZF_ZF_set_fun$' > 'ZF_ZF_fun$' > 'ZF_ZF_set_fun$' ).
thf('vaq$_decl',type,
'vaq$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_fun_ZF_set_fun$' ).
thf('uwn$_decl',type,
'uwn$': 'B_ZF_fun$' > 'B_set$' > 'ZF_bool_fun$' ).
thf('identityFunctor$_decl',type,
'identityFunctor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$' ).
thf('image$i_decl',type,
'image$i': 'ZF_a_fun$' > 'ZF_set$' > 'A_set$' ).
thf('lSCategory_ext$_decl',type,
'lSCategory_ext$': 'B_ZF_fun$' > 'C$' > 'B_c_LSCategory_ext$' ).
thf('identityFunctor$a_decl',type,
'identityFunctor$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('top$a_decl',type,
'top$a': 'ZF_set$' ).
thf('fun_app$ar_decl',type,
'fun_app$ar': 'B_ZF_fun$' > 'B$' > 'ZF$' ).
thf('restrict$b_decl',type,
'restrict$b': 'B_a_fun$' > 'B_set$' > 'B_a_fun$' ).
thf('fun_app$cp_decl',type,
'fun_app$cp': 'Nat_a_fun$' > 'Nat$' > 'A$' ).
thf('uyw$_decl',type,
'uyw$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_ZF_set_fun_fun$' ).
thf('image$c_decl',type,
'image$c': 'ZF_set_set_bool_fun$' > 'ZF_set_set_set$' > 'Bool_set$' ).
thf('inverse_rel$a_decl',type,
'inverse_rel$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$' ).
thf('image$x_decl',type,
'image$x': 'Nat_a_fun$' > 'Nat_set$' > 'A_set$' ).
thf('less_eq$_decl',type,
'less_eq$': 'A_set$' > 'A_set$' > $o ).
thf('less_eq$j_decl',type,
'less_eq$j': 'A_bool_fun$' > 'A_bool_fun$' > $o ).
thf('less_eq$a_decl',type,
'less_eq$a': 'B_set$' > 'B_set$' > $o ).
thf('uvy$_decl',type,
'uvy$': 'A_ZF_fun$' > 'A_set$' > 'ZF_bool_fun$' > 'A_bool_fun$' ).
thf('fun_app$ab_decl',type,
'fun_app$ab': 'ZF_nat_ZF_set_fun_fun$' > 'ZF$' > 'Nat_ZF_set_fun$' ).
thf('vai$_decl',type,
'vai$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$' ).
thf('fun_app$cl_decl',type,
'fun_app$cl': 'A_b_fun_bool_fun$' > 'A_b_fun$' > $o ).
thf('uvq$_decl',type,
'uvq$': 'A_b_fun$' > 'A_set$' > 'B_bool_fun$' > 'A_bool_fun$' ).
thf('sup$a_decl',type,
'sup$a': 'Bool_set$' > $o ).
thf('member$_decl',type,
'member$': 'ZF$' > 'ZF_set_bool_fun$' ).
thf('uyn$_decl',type,
'uyn$': 'ZF_set_ZF_set_fun$' ).
thf('fun_app$cu_decl',type,
'fun_app$cu': 'B_b_set_fun$' > 'B$' > 'B_set$' ).
thf('uwe$_decl',type,
'uwe$': 'ZF_set_a_fun$' > 'ZF_set_set$' > 'A_bool_fun$' > 'ZF_set_bool_fun$' ).
thf('uum$_decl',type,
'uum$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('uyx$_decl',type,
'uyx$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_set$' > 'ZF_ZF_set_fun$' ).
thf('image$b_decl',type,
'image$b': 'ZF_set_bool_fun$' > 'ZF_set_set$' > 'Bool_set$' ).
thf('uwo$_decl',type,
'uwo$': 'ZF_ZF_fun$' > 'ZF_set$' > 'ZF_bool_fun$' ).
thf('less_eq$l_decl',type,
'less_eq$l': 'ZF_bool_fun$' > 'ZF_bool_fun$' > $o ).
thf('collect$f_decl',type,
'collect$f': 'A_b_fun_bool_fun$' > 'A_b_fun_set$' ).
thf('fun_app$k_decl',type,
'fun_app$k': 'B_bool_fun$' > 'B$' > $o ).
thf('hOMCollection$_decl',type,
'hOMCollection$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A_ZF_set_fun$' ).
thf('image$y_decl',type,
'image$y': 'Nat_b_fun$' > 'Nat_set$' > 'B_set$' ).
thf('fun_app$s_decl',type,
'fun_app$s': 'ZF_ZF_set_fun$' > 'ZF$' > 'ZF_set$' ).
thf('fun_app$cq_decl',type,
'fun_app$cq': 'Nat_b_fun$' > 'Nat$' > 'B$' ).
thf('member$i_decl',type,
'member$i': 'A_b_fun$' > 'A_b_fun_set$' > $o ).
thf('fun_app$ae_decl',type,
'fun_app$ae': 'ZF_set_ZF_set_fun$' > 'ZF_set$' > 'ZF_set$' ).
thf('inverse$a_decl',type,
'inverse$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('mapO$_decl',type,
'mapO$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_fun$' ).
thf('image$ap_decl',type,
'image$ap': 'ZF_b_set_fun$' > 'ZF_set$' > 'B_set_set$' ).
thf('fun_app$al_decl',type,
'fun_app$al': 'B_b_prod_bool_fun$' > 'B_b_prod$' > $o ).
thf('fun_app$bg_decl',type,
'fun_app$bg': 'B_set_b_set_fun$' > 'B_set$' > 'B_set$' ).
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('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('extensional$_decl',type,
'extensional$': 'B_set$' > 'B_a_fun_set$' ).
thf('image$d_decl',type,
'image$d': 'B_set_bool_fun$' > 'B_set_set$' > 'Bool_set$' ).
thf('fun_app$cw_decl',type,
'fun_app$cw': 'ZF_b_set_fun$' > 'ZF$' > 'B_set$' ).
thf('uuo$_decl',type,
'uuo$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF$' > 'B_bool_fun$' ).
thf('opair$_decl',type,
'opair$': 'ZF_ZF_ZF_fun_fun$' ).
thf('uuy$_decl',type,
'uuy$': 'B_set$' > 'B_bool_fun$' > 'B_bool_fun$' ).
thf('uyy$_decl',type,
'uyy$': 'ZF_nat_ZF_set_fun_fun$' > 'Nat_set$' > 'ZF_ZF_set_fun$' ).
thf('collect$_decl',type,
'collect$': 'ZF_bool_fun$' > 'ZF_set$' ).
thf('fun_app$ao_decl',type,
'fun_app$ao': 'ZF_nat_fun$' > 'ZF$' > 'Nat$' ).
thf('g$_decl',type,
'g$': 'B$' ).
thf('vae$_decl',type,
'vae$': 'B_set_set$' > 'B_bool_fun$' ).
thf('member$b_decl',type,
'member$b': 'B$' > 'B_set_bool_fun$' ).
thf('fun_app$ac_decl',type,
'fun_app$ac': 'Nat_ZF_ZF_set_fun_fun$' > 'Nat$' > 'ZF_ZF_set_fun$' ).
thf('uxw$_decl',type,
'uxw$': 'Nat_ZF_set_fun$' > 'Nat_set$' > 'ZF_ZF_set_set_fun$' ).
thf('comp$b_decl',type,
'comp$b': 'ZF_ZF_fun$' > 'ZF_ZF_fun_ZF_ZF_fun_fun$' ).
thf('top$f_decl',type,
'top$f': 'ZF_ZF_fun_set$' ).
thf('more$_decl',type,
'more$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_c_LSCategory_ext$' ).
thf('uyr$_decl',type,
'uyr$': 'ZF_ZF_set_fun$' > 'ZF_ZF_set_fun$' > 'ZF_ZF_set_fun$' ).
thf('image$bi_decl',type,
'image$bi': 'B_set_b_bool_fun_fun$' > 'B_set_set$' > 'B_bool_fun_set$' ).
thf('more$a_decl',type,
'more$a': 'ZF_ZF_unit_Category_ext$' > 'Unit$' ).
thf('uvs$_decl',type,
'uvs$': 'B_b_fun$' > 'B_set$' > 'B_bool_fun$' > 'B_bool_fun$' ).
thf('image$bn_decl',type,
'image$bn': 'ZF_ZF_fun_ZF_set_fun$' > 'ZF_ZF_fun_set$' > 'ZF_set_set$' ).
thf('vaj$_decl',type,
'vaj$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_fun$' > 'ZF_ZF_set_fun$' ).
thf('restrict$c_decl',type,
'restrict$c': 'A_b_fun$' > 'A_set$' > 'A_b_fun$' ).
thf('dom$_decl',type,
'dom$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$' ).
thf('elem$_decl',type,
'elem$': 'ZF_ZF_bool_fun_fun$' ).
thf('zFfunDom$_decl',type,
'zFfunDom$': 'ZF_ZF_fun$' ).
thf('uzk$_decl',type,
'uzk$': 'ZF_ZF_set_fun$' > 'Nat_ZF_set_fun$' > 'Nat_ZF_set_set_fun$' ).
thf('vak$_decl',type,
'vak$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_fun_ZF_set_fun$' ).
thf('image$o_decl',type,
'image$o': 'A_b_fun$' > 'A_set$' > 'B_set$' ).
thf('uyk$_decl',type,
'uyk$': 'ZF_ZF_ZF_set_fun_fun$' ).
thf('zFfunApp$_decl',type,
'zFfunApp$': 'ZF_ZF_ZF_fun_fun$' ).
thf('uwg$_decl',type,
'uwg$': 'ZF_ZF_set_fun$' > 'ZF_bool_fun$' > 'ZF_set_bool_fun$' ).
thf('category_axioms$a_decl',type,
'category_axioms$a': 'ZF_ZF_unit_Category_ext$' > $o ).
thf('lambda$_decl',type,
'lambda$': 'ZF$' > 'ZF_ZF_fun$' > 'ZF$' ).
thf('uu$_decl',type,
'uu$': 'A_set_a_bool_fun_fun$' ).
thf('cod$a_decl',type,
'cod$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('uvn$_decl',type,
'uvn$': 'B_a_fun$' > 'B_set$' > 'A_bool_fun$' > 'A_bool_fun$' ).
thf('uwy$_decl',type,
'uwy$': 'ZF_ZF_bool_fun_fun$' ).
thf('more$b_decl',type,
'more$b': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'C$' ).
thf('fun_app$v_decl',type,
'fun_app$v': 'Nat_set_ZF_set_set_fun$' > 'Nat_set$' > 'ZF_set_set$' ).
thf('vad$_decl',type,
'vad$': 'A_set_set$' > 'A_bool_fun$' ).
thf('comp$_decl',type,
'comp$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('uuv$_decl',type,
'uuv$': 'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$' ).
thf('image$ar_decl',type,
'image$ar': 'B_ZF_set_fun$' > 'B_set$' > 'ZF_set_set$' ).
thf('zF2mor$_decl',type,
'zF2mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_b_fun$' ).
thf('uus$_decl',type,
'uus$': 'ZF$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('uwm$_decl',type,
'uwm$': 'A_ZF_fun$' > 'A_set$' > 'ZF_bool_fun$' ).
thf('fun_app$at_decl',type,
'fun_app$at': 'Nat_ZF_bool_fun_fun$' > 'Nat$' > 'ZF_bool_fun$' ).
thf('homFtorMapContra$_decl',type,
'homFtorMapContra$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'A_ZF_fun$' ).
thf('uue$_decl',type,
'uue$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('uzj$_decl',type,
'uzj$': 'ZF_ZF_set_fun$' > 'ZF_ZF_set_fun$' > 'ZF_ZF_set_set_fun$' ).
thf('functor$_decl',type,
'functor$': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('fun_app$am_decl',type,
'fun_app$am': 'B_b_fun$' > 'B$' > 'B$' ).
thf('collect$h_decl',type,
'collect$h': 'A_bool_fun$' > 'A_set$' ).
thf('comp$a_decl',type,
'comp$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('less_eq$b_decl',type,
'less_eq$b': 'ZF_set_set$' > 'ZF_set_set$' > $o ).
thf('fun_app$n_decl',type,
'fun_app$n': 'A_bool_fun$' > 'A$' > $o ).
thf('fun_app$au_decl',type,
'fun_app$au': 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' > 'ZF_set$' ).
thf('uyu$_decl',type,
'uyu$': 'ZF_ZF_set_fun$' > 'ZF_set_ZF_set_fun$' ).
thf('image$j_decl',type,
'image$j': 'ZF_set_a_fun$' > 'ZF_set_set$' > 'A_set$' ).
thf('fun_app$_decl',type,
'fun_app$': 'ZF_ZF_fun$' > 'ZF$' > 'ZF$' ).
thf('fun_app$l_decl',type,
'fun_app$l': 'B_set_b_bool_fun_fun$' > 'B_set$' > 'B_bool_fun$' ).
thf('functor$c_decl',type,
'functor$c': 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' > $o ).
thf('objIso$_decl',type,
'objIso$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_bool_fun_fun$' ).
thf('fun_app$ax_decl',type,
'fun_app$ax': 'ZF_ZF_set_set_fun$' > 'ZF$' > 'ZF_set_set$' ).
thf('uuc$_decl',type,
'uuc$': 'ZF_set_ZF_bool_fun_fun$' ).
thf('fun_app$cs_decl',type,
'fun_app$cs': 'A_b_set_fun$' > 'A$' > 'B_set$' ).
thf('collect$e_decl',type,
'collect$e': 'B_a_fun_bool_fun$' > 'B_a_fun_set$' ).
thf('fun_app$g_decl',type,
'fun_app$g': 'ZF_set_ZF_bool_fun_fun$' > 'ZF_set$' > 'ZF_bool_fun$' ).
thf('restrict$d_decl',type,
'restrict$d': 'ZF_ZF_fun$' > 'ZF_set$' > 'ZF_ZF_fun$' ).
thf('uvl$_decl',type,
'uvl$': 'A_a_fun$' > 'A_set$' > 'A_bool_fun$' > 'A_bool_fun$' ).
thf('isomorphism$a_decl',type,
'isomorphism$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_bool_fun$' ).
thf('image$q_decl',type,
'image$q': 'ZF_set_ZF_set_fun$' > 'ZF_set_set_ZF_set_set_fun$' ).
thf('fun_app$an_decl',type,
'fun_app$an': 'B_b_b_fun_fun$' > 'B$' > 'B_b_fun$' ).
thf('uwz$_decl',type,
'uwz$': 'ZF_ZF_set_fun$' > 'ZF_set$' > 'ZF_set_ZF_set_set_fun$' ).
thf('uuu$_decl',type,
'uuu$': 'ZF_ZF_fun$' ).
thf('image$bp_decl',type,
'image$bp': 'ZF_nat_fun_ZF_set_fun$' > 'ZF_nat_fun_set$' > 'ZF_set_set$' ).
thf('member$e_decl',type,
'member$e': 'Nat$' > 'Nat_set$' > $o ).
thf('image$am_decl',type,
'image$am': 'B_a_set_fun$' > 'B_set$' > 'A_set_set$' ).
thf('vab$_decl',type,
'vab$': 'ZF_ZF_set_fun$' > 'ZF_ZF_bool_fun_fun$' ).
thf('sup$b_decl',type,
'sup$b': 'A_set_set$' > 'A_set$' ).
thf('fun_app$z_decl',type,
'fun_app$z': 'ZF_ZF_fun_ZF_set_fun$' > 'ZF_ZF_fun$' > 'ZF_set$' ).
thf('isomorphism$_decl',type,
'isomorphism$': 'ZF_ZF_unit_Category_ext$' > 'ZF_bool_fun$' ).
thf('fun_app$j_decl',type,
'fun_app$j': 'ZF_set_set_bool_fun$' > 'ZF_set_set$' > $o ).
thf('id$a_decl',type,
'id$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('uzc$_decl',type,
'uzc$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_ZF_set_fun_fun$' ).
thf('uvd$_decl',type,
'uvd$': 'ZF_ZF_fun$' > 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_ZF_fun$' ).
thf('uvt$_decl',type,
'uvt$': 'ZF_a_fun$' > 'ZF_set$' > 'A_bool_fun$' > 'A_bool_fun$' ).
thf('top$h_decl',type,
'top$h': 'ZF_nat_fun_set$' ).
thf('constFunctor$b_decl',type,
'constFunctor$b': 'ZF_ZF_unit_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' ).
thf('uwi$_decl',type,
'uwi$': 'ZF_ZF_fun$' > 'ZF_bool_fun$' > 'ZF_bool_fun$' ).
thf('image$k_decl',type,
'image$k': 'B_ZF_fun$' > 'B_set$' > 'ZF_set$' ).
thf('homFtor$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('fun_app$bj_decl',type,
'fun_app$bj': 'ZF_set_a_fun$' > 'ZF_set$' > 'A$' ).
thf('uzx$_decl',type,
'uzx$': 'ZF_ZF_bool_fun_fun$' > 'ZF_ZF_set_fun$' ).
thf('fun_app$m_decl',type,
'fun_app$m': 'B_set_bool_fun$' > 'B_set$' > $o ).
thf('preFunctor$_decl',type,
'preFunctor$': 'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$' > $o ).
thf('vav$_decl',type,
'vav$': 'ZF_ZF_ZF_set_fun_fun$' > 'ZF_ZF_fun_ZF_set_fun$' ).
thf('fun_app$ch_decl',type,
'fun_app$ch': 'B_a_fun_b_a_fun_fun$' > 'B_a_fun$' > 'B_a_fun$' ).
thf('image$bl_decl',type,
'image$bl': 'ZF_ZF_bool_fun_fun$' > 'ZF_set$' > 'ZF_bool_fun_set$' ).
thf('fun_app$da_decl',type,
'fun_app$da': 'ZF_set_set_set_ZF_set_set_fun$' > 'ZF_set_set_set$' > 'ZF_set_set$' ).
thf('member$h_decl',type,
'member$h': 'B_a_fun$' > 'B_a_fun_set$' > $o ).
thf('uvx$_decl',type,
'uvx$': 'A_ZF_fun$' > 'A_set$' > 'ZF_bool_fun$' > 'ZF_bool_fun$' ).
thf('homSet$_decl',type,
'homSet$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A_ZF_fun$' ).
thf('fun_app$cj_decl',type,
'fun_app$cj': 'B_ZF_fun_bool_fun$' > 'B_ZF_fun$' > $o ).
thf('image$bm_decl',type,
'image$bm': 'Nat_ZF_bool_fun_fun$' > 'Nat_set$' > 'ZF_bool_fun_set$' ).
thf('fun_app$cv_decl',type,
'fun_app$cv': 'ZF_a_set_fun$' > 'ZF$' > 'A_set$' ).
thf('uzl$_decl',type,
'uzl$': 'ZF_ZF_fun$' > 'ZF_ZF_set_fun$' > 'ZF_ZF_set_fun$' ).
thf('fun_app$p_decl',type,
'fun_app$p': 'A_set_bool_fun$' > 'A_set$' > $o ).
thf('top$_decl',type,
'top$': 'Nat_set$' ).
thf('image$l_decl',type,
'image$l': 'B_b_fun$' > 'B_set_b_set_fun$' ).
thf('uxt$_decl',type,
'uxt$': 'ZF_ZF_set_fun$' > 'ZF_set$' > 'ZF_ZF_set_set_fun$' ).
thf('vaz$_decl',type,
'vaz$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_nat_fun_ZF_set_fun$' ).
thf('fun_app$q_decl',type,
'fun_app$q': 'ZF_ZF_bool_fun_fun$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('uwc$_decl',type,
'uwc$': 'ZF_ZF_fun$' > 'ZF_set$' > 'ZF_bool_fun$' > 'ZF_bool_fun$' ).
thf('fun_app$bl_decl',type,
'fun_app$bl': 'A_b_fun$' > 'A$' > 'B$' ).
thf('uys$_decl',type,
'uys$': 'ZF_ZF_set_fun$' > 'Nat_ZF_set_fun$' > 'Nat_ZF_set_fun$' ).
thf('less_eq$c_decl',type,
'less_eq$c': 'ZF_set$' > 'ZF_set_bool_fun$' ).
thf('explode$_decl',type,
'explode$': 'ZF_ZF_set_fun$' ).
thf('isZFfun$_decl',type,
'isZFfun$': 'ZF_bool_fun$' ).
thf('vay$_decl',type,
'vay$': 'Nat_ZF_ZF_set_fun_fun$' > 'ZF_ZF_set_fun$' ).
thf('cartProd$_decl',type,
'cartProd$': 'ZF_ZF_ZF_fun_fun$' ).
thf('image$au_decl',type,
'image$au': 'ZF_set_ZF_set_set_fun$' > 'ZF_set_set_ZF_set_set_set_fun$' ).
thf('sup$e_decl',type,
'sup$e': 'ZF_set_set_set_ZF_set_set_fun$' ).
thf('makeCat$a_decl',type,
'makeCat$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('uym$_decl',type,
'uym$': 'ZF_ZF_fun_ZF_ZF_fun_fun$' ).
thf('uuf$_decl',type,
'uuf$': 'ZF_ZF_bool_fun_fun$' ).
thf('dom$a_decl',type,
'dom$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('fun_app$r_decl',type,
'fun_app$r': 'Nat_ZF_set_fun$' > 'Nat$' > 'ZF_set$' ).
thf('fun_app$i_decl',type,
'fun_app$i': 'ZF_set_set_ZF_set_bool_fun_fun$' > 'ZF_set_set$' > 'ZF_set_bool_fun$' ).
thf('uup$_decl',type,
'uup$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'ZF_ZF_fun$' ).
thf('uwj$_decl',type,
'uwj$': 'Nat_ZF_set_fun$' > 'Nat_set$' > 'ZF_set_bool_fun$' ).
thf('image$bk_decl',type,
'image$bk': 'ZF_set_ZF_bool_fun_fun$' > 'ZF_set_set$' > 'ZF_bool_fun_set$' ).
thf('image$ao_decl',type,
'image$ao': 'ZF_a_set_fun$' > 'ZF_set$' > 'A_set_set$' ).
thf('mor$_decl',type,
'mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_set$' ).
thf(8,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uve$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) @ ( A @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).
thf(645,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uve$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) @ ( A @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(174,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uum$' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( C @ ( B @ 'pair$a' ) @ ( A @ 'uui$' @ 'collect$b' @ ( A @ 'comp$a' @ 'case_prod$a' @ 'restrict$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).
thf(1322,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uum$' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( C @ ( B @ 'pair$a' ) @ ( A @ 'uui$' @ 'collect$b' @ ( A @ 'comp$a' @ 'case_prod$a' @ 'restrict$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(103,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' @ 'oppositeCategory$a' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom233) ).
thf(1036,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' @ 'oppositeCategory$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(250,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ ( C @ ( B @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom443) ).
thf(1718,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ ( C @ ( B @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(3,axiom,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyy$' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'fun_app$ab' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom107) ).
thf(629,plain,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyy$' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'fun_app$ab' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(479,axiom,
! [A: 'A_a_fun$',B: 'A_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'fun_app$n' ) )
<=> ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$p' @ 'fun_app$bh' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom137) ).
thf(2744,plain,
! [A: 'A_a_fun$',B: 'A_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$p' @ 'fun_app$bh' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'fun_app$n' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'fun_app$n' ) )
=> ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$p' @ 'fun_app$bh' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(340,axiom,
! [A: 'B_ZF_fun$',B: 'B_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uwn$' ) @ 'fun_app$f' ) )
<=> ? [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( C
= ( D @ ( A @ 'fun_app$ar' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).
thf(2109,plain,
! [A: 'B_ZF_fun$',B: 'B_set$',C: 'ZF$'] :
( ( ? [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( C
= ( D @ ( A @ 'fun_app$ar' ) ) ) )
=> ( C @ ( B @ ( A @ 'uwn$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uwn$' ) @ 'fun_app$f' ) )
=> ? [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( C
= ( D @ ( A @ 'fun_app$ar' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(487,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom435) ).
thf(2778,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(253,axiom,
! [A: 'ZF$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( ( D @ ( B @ 'fun_app$s' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> $false )
& ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom739) ).
thf(1729,plain,
! [A: 'ZF$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
~ ( ! [D: 'ZF$'] :
~ ( ( D @ ( B @ 'fun_app$s' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
& ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(603,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom316) ).
thf(3397,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(275,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( A @ 'more$a' )
= ( B @ 'more$a' ) )
& ( ( A @ 'comp$' )
= ( B @ 'comp$' ) )
& ( ( A @ 'id$a' )
= ( B @ 'id$a' ) )
& ( ( A @ 'cod$a' )
= ( B @ 'cod$a' ) )
& ( ( A @ 'dom$a' )
= ( B @ 'dom$a' ) )
& ( ( A @ 'mor$a' )
= ( B @ 'mor$a' ) )
& ( ( A @ 'obj$a' )
= ( B @ 'obj$a' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom342) ).
thf(1840,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( A @ 'more$a' )
= ( B @ 'more$a' ) )
& ( ( A @ 'comp$' )
= ( B @ 'comp$' ) )
& ( ( A @ 'id$a' )
= ( B @ 'id$a' ) )
& ( ( A @ 'cod$a' )
= ( B @ 'cod$a' ) )
& ( ( A @ 'dom$a' )
= ( B @ 'dom$a' ) )
& ( ( A @ 'mor$a' )
= ( B @ 'mor$a' ) )
& ( ( A @ 'obj$a' )
= ( B @ 'obj$a' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(44,axiom,
! [A: 'B_ZF_fun$',B: 'B_set$',C: 'ZF_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvz$' ) ) @ 'collect$' )
= ( C @ ( B @ ( A @ 'uwa$' ) ) @ 'collect$i' @ ( A @ 'image$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).
thf(777,plain,
! [A: 'B_ZF_fun$',B: 'B_set$',C: 'ZF_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvz$' ) ) @ 'collect$' )
= ( C @ ( B @ ( A @ 'uwa$' ) ) @ 'collect$i' @ ( A @ 'image$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(270,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_ZF_set_fun$'] :
( ( B @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( B @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom700) ).
thf(1818,plain,
! [A: 'B$',B: 'B_set$',C: 'B_ZF_set_fun$'] :
( ( B @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( B @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(299,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom319) ).
thf(1950,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(379,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom329) ).
thf(2280,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(424,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).
thf(2452,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(54,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_bool_fun$'] :
( ( B @ ( A @ 'less_eq$a' ) )
=> ( ( C @ ( B @ 'uuy$' ) @ 'collect$i' @ ( A @ 'less_eq$a' ) )
<=> ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$k' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).
thf(809,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_bool_fun$'] :
( ( B @ ( A @ 'less_eq$a' ) )
=> ( ( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$k' ) ) )
=> ( C @ ( B @ 'uuy$' ) @ 'collect$i' @ ( A @ 'less_eq$a' ) ) )
& ( ( C @ ( B @ 'uuy$' ) @ 'collect$i' @ ( A @ 'less_eq$a' ) )
=> ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$k' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(387,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_ZF_ZF_fun_fun$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuk$' @ 'fun_app$aq' ) @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( B @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom164) ).
thf(2306,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_ZF_ZF_fun_fun$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuk$' @ 'fun_app$aq' ) @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( B @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(541,axiom,
! [A: 'A_set$',B: 'A_set$',C: 'A_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ( E @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$' ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom763) ).
thf(3053,plain,
! [A: 'A_set$',B: 'A_set$',C: 'A_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ( E @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$' ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(412,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'app$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uyl$' @ 'fun_app$q' ) @ 'the$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom626) ).
thf(2412,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'app$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uyl$' @ 'fun_app$q' ) @ 'the$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(503,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom330) ).
thf(2876,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(1,conjecture,
'c$' @ 'obj$' @ ( 'f$' @ ( 'c$' @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture185) ).
thf(2,negated_conjecture,
~ ( 'c$' @ 'obj$' @ ( 'f$' @ ( 'c$' @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(628,plain,
~ ( 'c$' @ 'obj$' @ ( 'f$' @ ( 'c$' @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(101,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom460) ).
thf(1031,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(417,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom697) ).
thf(2427,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(116,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF$'] :
( ( ( B @ ( A @ 'fun_app$f' ) )
& ? [C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) )
=> ( ( A @ 'the$' )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom394) ).
thf(1083,plain,
! [A: 'ZF_bool_fun$',B: 'ZF$'] :
( ( ( B @ ( A @ 'fun_app$f' ) )
& ? [C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) )
=> ( ( A @ 'the$' )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(363,axiom,
! [A: 'B_set$',B: 'B_bool_fun$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uuy$' ) @ 'fun_app$k' ) )
<=> ( ( C @ ( B @ 'fun_app$k' ) )
& ( A @ ( C @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).
thf(2210,plain,
! [A: 'B_set$',B: 'B_bool_fun$',C: 'B$'] :
( ( ( ( C @ ( B @ 'fun_app$k' ) )
& ( A @ ( C @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ ( A @ 'uuy$' ) @ 'fun_app$k' ) ) )
& ( ( C @ ( B @ ( A @ 'uuy$' ) @ 'fun_app$k' ) )
=> ( ( C @ ( B @ 'fun_app$k' ) )
& ( A @ ( C @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(585,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$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$a' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
thf(3317,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$a' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(17,axiom,
! [A: 'ZF$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( ! [D: 'Nat$'] :
( ( ( D @ ( B @ 'fun_app$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$e' ) ) )
=> $false )
& ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom736) ).
thf(683,plain,
! [A: 'ZF$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
~ ( ! [D: 'Nat$'] :
~ ( ( D @ ( B @ 'fun_app$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$e' ) ) )
& ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(456,axiom,
! [A: 'ZF_set$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'fun_app$f' ) )
<=> ( A @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
thf(2644,plain,
! [A: 'ZF_set$',B: 'ZF$'] :
( ( ( A @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'fun_app$f' ) )
=> ( A @ ( B @ 'member$' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(32,axiom,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'ZF_set$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uza$' ) @ 'fun_app$r' ) )
= ( B @ ( C @ ( A @ 'uyz$' @ 'fun_app$ac' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom104) ).
thf(741,plain,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'ZF_set$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uza$' ) @ 'fun_app$r' ) )
= ( B @ ( C @ ( A @ 'uyz$' @ 'fun_app$ac' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(553,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).
thf(3108,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(71,axiom,
! [A: 'ZF_ZF_set_fun$'] :
( ( A @ 'image$a' @ 'image$au' @ ( 'sup$e' @ 'comp$e' ) )
= ( 'sup$' @ ( A @ 'image$a' @ 'comp$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom710) ).
thf(873,plain,
! [A: 'ZF_ZF_set_fun$'] :
( ( A @ 'image$a' @ 'image$au' @ ( 'sup$e' @ 'comp$e' ) )
= ( 'sup$' @ ( A @ 'image$a' @ 'comp$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(265,axiom,
! [A: 'B_set$',B: 'B$',C: 'B_b_set_fun$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$cu' ) @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( A @ ( C @ 'image$an' ) @ 'inf$b' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom817) ).
thf(1793,plain,
! [A: 'B_set$',B: 'B$',C: 'B_b_set_fun$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$cu' ) @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( A @ ( C @ 'image$an' ) @ 'inf$b' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(169,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom254) ).
thf(1305,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(138,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_set$',D: 'ZF_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( ( B @ 'uxi$' @ ( C @ 'sigma$' ) )
= ( B @ 'uxi$' @ ( D @ 'sigma$' ) ) )
<=> ( C = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom602) ).
thf(1173,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_set$',D: 'ZF_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( ( C = D )
=> ( ( B @ 'uxi$' @ ( C @ 'sigma$' ) )
= ( B @ 'uxi$' @ ( D @ 'sigma$' ) ) ) )
& ( ( ( B @ 'uxi$' @ ( C @ 'sigma$' ) )
= ( B @ 'uxi$' @ ( D @ 'sigma$' ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(388,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzs$' ) @ 'fun_app$s' ) )
= ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom114) ).
thf(2309,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzs$' ) @ 'fun_app$s' ) )
= ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(39,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ ( A @ 'uve$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom717) ).
thf(762,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ ( A @ 'uve$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(198,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$' @ 'mor$' )
= ( A @ 'mor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom231) ).
thf(1443,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$' @ 'mor$' )
= ( A @ 'mor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(486,axiom,
! [A: 'A$',B: 'A_set$',C: 'ZF_set$',D: 'A_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$co' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom684) ).
thf(2776,plain,
! [A: 'A$',B: 'A_set$',C: 'ZF_set$',D: 'A_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$co' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(460,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom268) ).
thf(2659,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(599,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 @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom267) ).
thf(3377,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(538,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom249) ).
thf(3040,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(217,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'ZF$'] :
( ( B @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( ( E @ ( C @ 'fun_app$s' ) )
= D ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( ( B @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom773) ).
thf(1544,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'ZF$'] :
( ( B @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( ( E @ ( C @ 'fun_app$s' ) )
= D ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( ( B @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(317,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( C @ ( B @ ( A @ 'uzj$' ) @ 'image$bb' ) @ ( 'sup$e' @ 'fun_app$da' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom742) ).
thf(2014,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( C @ ( B @ ( A @ 'uzj$' ) @ 'image$bb' ) @ ( 'sup$e' @ 'fun_app$da' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(245,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'mor$' )
= ( A @ 'mor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom227) ).
thf(1692,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'mor$' )
= ( A @ 'mor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(15,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uus$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).
thf(677,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uus$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(534,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$a' @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).
thf(3017,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$a' @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(236,axiom,
! [A: 'ZF$',B: 'ZF_bool_fun$'] :
( ( B @ 'collect$' @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ( A @ ( B @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).
thf(1655,plain,
! [A: 'ZF$',B: 'ZF_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$f' ) )
=> ( B @ 'collect$' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( B @ 'collect$' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( A @ ( B @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(556,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).
thf(3120,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(171,axiom,
! [A: 'B_a_fun$',B: 'B_a_fun_bool_fun$'] :
( ( B @ 'collect$e' @ ( A @ 'member$h' ) )
<=> ( A @ ( B @ 'fun_app$ck' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom271) ).
thf(1310,plain,
! [A: 'B_a_fun$',B: 'B_a_fun_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$ck' ) )
=> ( B @ 'collect$e' @ ( A @ 'member$h' ) ) )
& ( ( B @ 'collect$e' @ ( A @ 'member$h' ) )
=> ( A @ ( B @ 'fun_app$ck' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(559,axiom,
! [A: 'A_ZF_set_fun$',B: 'A_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( A @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom704) ).
thf(3135,plain,
! [A: 'A_ZF_set_fun$',B: 'A_set$',C: 'ZF_set$'] :
( ( ! [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( A @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( A @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(510,axiom,
! [A: 'A$',B: 'A_a_set_fun$',C: 'A_set$'] :
( ( C @ ( B @ 'image$ak' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) )
<=> ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom802) ).
thf(2918,plain,
! [A: 'A$',B: 'A_a_set_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( B @ 'image$ak' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
& ( ( C @ ( B @ 'image$ak' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(51,axiom,
! [A: 'Nat_set$',B: 'Nat_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'Nat$'] :
( ( A @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( B @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom666) ).
thf(797,plain,
! [A: 'Nat_set$',B: 'Nat_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'Nat$'] :
( ( A @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( B @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(26,axiom,
! [A: 'ZF_set$'] :
( ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'collect$' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).
thf(715,plain,
! [A: 'ZF_set$'] :
( ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'collect$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(283,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) )
= ( B @ ( A @ 'oppositeCategory$' @ 'homFtor$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244) ).
thf(1872,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) )
= ( B @ ( A @ 'oppositeCategory$' @ 'homFtor$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(86,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',axiom211) ).
thf(945,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)],[86]) ).
thf(301,axiom,
'set$' @ 'category$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom407) ).
thf(1954,plain,
'set$' @ 'category$a',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(202,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom676) ).
thf(1458,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(578,axiom,
! [A: 'A_set$',B: 'A$'] :
( ( B @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'fun_app$n' ) )
<=> ( A @ ( B @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
thf(3276,plain,
! [A: 'A_set$',B: 'A$'] :
( ( ( A @ ( B @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'fun_app$n' ) ) )
& ( ( B @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'fun_app$n' ) )
=> ( A @ ( B @ 'member$c' @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(354,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'vac$' @ 'fun_app$at' ) @ 'fun_app$f' ) )
<=> ( B @ ( A @ 'fun_app$r' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).
thf(2168,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat$',C: 'ZF$'] :
( ( ( B @ ( A @ 'fun_app$r' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( B @ ( A @ 'vac$' @ 'fun_app$at' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'vac$' @ 'fun_app$at' ) @ 'fun_app$f' ) )
=> ( B @ ( A @ 'fun_app$r' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(21,axiom,
( 'set$a'
= ( 'unity$' @ ( 'zFfunComp$' @ ( 'uuu$' @ ( 'zFfunCod$' @ ( 'zFfunDom$' @ ( 'isZFfun$' @ 'collect$' @ ( 'uut$' @ 'collect$' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom469) ).
thf(698,plain,
( 'set$a'
= ( 'unity$' @ ( 'zFfunComp$' @ ( 'uuu$' @ ( 'zFfunCod$' @ ( 'zFfunDom$' @ ( 'isZFfun$' @ 'collect$' @ ( 'uut$' @ 'collect$' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(607,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom203) ).
thf(3414,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(34,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uus$' @ 'fun_app$b' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom457) ).
thf(747,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uus$' @ 'fun_app$b' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(151,axiom,
! [A: 'ZF_set_set_set$'] :
( ( A @ ( 'sup$e' @ 'fun_app$da' ) )
= ( A @ 'vaf$' @ 'collect$j' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom783) ).
thf(1222,plain,
! [A: 'ZF_set_set_set$'] :
( ( A @ ( 'sup$e' @ 'fun_app$da' ) )
= ( A @ 'vaf$' @ 'collect$j' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(83,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_set$'] :
( ( B @ ( A @ 'less_eq$b' ) )
<=> ( B @ ( 'uub$' @ 'fun_app$i' ) @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'less_eq$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom788) ).
thf(930,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_set$'] :
( ( ( B @ ( 'uub$' @ 'fun_app$i' ) @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'less_eq$m' ) )
=> ( B @ ( A @ 'less_eq$b' ) ) )
& ( ( B @ ( A @ 'less_eq$b' ) )
=> ( B @ ( 'uub$' @ 'fun_app$i' ) @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'less_eq$m' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(76,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$a' @ 'obj$a' )
= ( A @ 'obj$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom200) ).
thf(898,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$a' @ 'obj$a' )
= ( A @ 'obj$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(474,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ ( A @ 'uyr$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom748) ).
thf(2723,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ ( A @ 'uyr$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(524,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$a' )
<=> ( ( A @ 'uui$' @ 'collect$b' @ 'extensional$c' @ ( A @ 'comp$a' @ 'case_prod$a' @ 'member$k' ) )
& ( A @ 'obj$' @ 'extensional$b' @ ( A @ 'id$' @ 'member$i' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'cod$' @ 'member$h' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'dom$' @ 'member$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom400) ).
thf(2972,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'uui$' @ 'collect$b' @ 'extensional$c' @ ( A @ 'comp$a' @ 'case_prod$a' @ 'member$k' ) )
& ( A @ 'obj$' @ 'extensional$b' @ ( A @ 'id$' @ 'member$i' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'cod$' @ 'member$h' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'dom$' @ 'member$h' ) ) )
=> ( A @ 'extCategory$a' ) )
& ( ( A @ 'extCategory$a' )
=> ( ( A @ 'uui$' @ 'collect$b' @ 'extensional$c' @ ( A @ 'comp$a' @ 'case_prod$a' @ 'member$k' ) )
& ( A @ 'obj$' @ 'extensional$b' @ ( A @ 'id$' @ 'member$i' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'cod$' @ 'member$h' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'dom$' @ 'member$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(293,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).
thf(1914,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(127,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$'] :
( ( B @ ( A @ 'uwo$' ) @ 'collect$' )
= ( B @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom560) ).
thf(1127,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$'] :
( ( B @ ( A @ 'uwo$' ) @ 'collect$' )
= ( B @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(527,axiom,
! [A: 'A_set_set$',B: 'A$'] :
( ( B @ ( A @ 'vad$' @ 'fun_app$n' ) )
<=> ( A @ ( B @ 'member$c' @ 'image$e' ) @ 'sup$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom33) ).
thf(2985,plain,
! [A: 'A_set_set$',B: 'A$'] :
( ( ( A @ ( B @ 'member$c' @ 'image$e' ) @ 'sup$a' )
=> ( B @ ( A @ 'vad$' @ 'fun_app$n' ) ) )
& ( ( B @ ( A @ 'vad$' @ 'fun_app$n' ) )
=> ( A @ ( B @ 'member$c' @ 'image$e' ) @ 'sup$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(572,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( B @ 'dom$' @ 'fun_app$bk' ) ) )
& ( B @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( B @ 'mor$' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom265) ).
thf(3249,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( B @ 'dom$' @ 'fun_app$bk' ) ) )
& ( B @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( B @ 'mor$' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(547,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A_set$',D: 'A_set_a_set_fun$',E: 'A_set_a_set_fun$'] :
( ( ! [F: 'A_set$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$bh' ) )
= ( F @ ( E @ 'fun_app$bh' ) ) ) )
& ( ( B @ 'obj$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'obj_update$' ) )
= ( B @ ( E @ 'obj_update$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom197) ).
thf(3088,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A_set$',D: 'A_set_a_set_fun$',E: 'A_set_a_set_fun$'] :
( ( ! [F: 'A_set$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$bh' ) )
= ( F @ ( E @ 'fun_app$bh' ) ) ) )
& ( ( B @ 'obj$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'obj_update$' ) )
= ( B @ ( E @ 'obj_update$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(225,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ( ! [E: 'ZF$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( E @ ( D @ 'fun_app$s' ) @ ( E @ ( C @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom765) ).
thf(1613,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ( ! [E: 'ZF$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( E @ ( D @ 'fun_app$s' ) @ ( E @ ( C @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(179,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'oppositeCategory$' @ 'lSCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).
thf(1359,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'oppositeCategory$' @ 'lSCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(430,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'set$' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom442) ).
thf(2531,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'set$' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(59,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$'] :
( ( B @ ( A @ 'uwj$' ) @ 'collect$j' )
= ( B @ ( A @ 'image$' @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).
thf(829,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$'] :
( ( B @ ( A @ 'uwj$' ) @ 'collect$j' )
= ( B @ ( A @ 'image$' @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(597,axiom,
! [A: 'A_set$',B: 'A_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( B @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom694) ).
thf(3370,plain,
! [A: 'A_set$',B: 'A_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( B @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(119,axiom,
! [A: 'ZF_set_set$'] :
( ( A @ ( 'uyn$' @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( A @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom630) ).
thf(1095,plain,
! [A: 'ZF_set_set$'] :
( ( A @ ( 'uyn$' @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( A @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(153,axiom,
! [A: 'ZF_ZF_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uzm$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom78) ).
thf(1228,plain,
! [A: 'ZF_ZF_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uzm$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(228,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'objIso$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom361) ).
thf(1623,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( C @ ( B @ ( A @ 'objIso$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'objIso$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(576,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( D @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( ( D @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= D )
& ( C @ ( B @ ( D @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).
thf(3263,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( D @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( ( D @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= D )
& ( C @ ( B @ ( D @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(248,axiom,
! [A: 'B_set_set$',B: 'B$'] :
( ( B @ ( A @ ( 'uua$' @ 'image$bi' ) @ 'sup$h' @ 'fun_app$k' ) )
<=> ( A @ 'sup$c' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom776) ).
thf(1709,plain,
! [A: 'B_set_set$',B: 'B$'] :
( ( ( A @ 'sup$c' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( B @ ( A @ ( 'uua$' @ 'image$bi' ) @ 'sup$h' @ 'fun_app$k' ) ) )
& ( ( B @ ( A @ ( 'uua$' @ 'image$bi' ) @ 'sup$h' @ 'fun_app$k' ) )
=> ( A @ 'sup$c' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(397,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uys$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom111) ).
thf(2339,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uys$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$r' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(591,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom253) ).
thf(3342,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(481,axiom,
! [A: 'ZF$',B: 'A_ZF_set_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( ( D @ ( B @ 'fun_app$co' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> $false )
& ( C @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom737) ).
thf(2755,plain,
! [A: 'ZF$',B: 'A_ZF_set_fun$',C: 'A_set$'] :
~ ( ! [D: 'A$'] :
~ ( ( D @ ( B @ 'fun_app$co' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
& ( C @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(364,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( B @ ( C @ ( A @ 'oppositeCategory$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom323) ).
thf(2217,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( B @ ( C @ ( A @ 'oppositeCategory$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(562,axiom,
! [A: 'A$',B: 'A_a_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( A
= ( D @ ( B @ 'fun_app$bm' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$p' @ 'fun_app$bh' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).
thf(3148,plain,
! [A: 'A$',B: 'A_a_fun$',C: 'A_set$'] :
~ ( ! [D: 'A$'] :
~ ( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( A
= ( D @ ( B @ 'fun_app$bm' ) ) ) )
& ( C @ ( B @ 'image$p' @ 'fun_app$bh' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(23,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( ( 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',axiom466) ).
thf(702,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( ( 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)],[23]) ).
thf(163,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).
thf(1279,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(312,axiom,
! [A: 'B$',B: 'ZF_b_fun$'] :
( ( ! [C: 'ZF$'] :
( ( A
= ( C @ ( B @ 'fun_app$as' ) ) )
=> $false )
& ( 'top$a' @ ( B @ 'image$h' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom567) ).
thf(1992,plain,
! [A: 'B$',B: 'ZF_b_fun$'] :
~ ( ! [C: 'ZF$'] :
( A
!= ( C @ ( B @ 'fun_app$as' ) ) )
& ( 'top$a' @ ( B @ 'image$h' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(539,axiom,
! [A: 'A_a_fun$',B: 'A_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvm$' ) ) @ 'fun_app$n' ) )
<=> ( ( D @ ( A @ 'fun_app$bm' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom147) ).
thf(3043,plain,
! [A: 'A_a_fun$',B: 'A_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( ( ( D @ ( A @ 'fun_app$bm' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvm$' ) ) @ 'fun_app$n' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvm$' ) ) @ 'fun_app$n' ) )
=> ( ( D @ ( A @ 'fun_app$bm' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(108,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( C @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( C @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( ( C @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( C @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom464) ).
thf(1055,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( C @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( C @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( ( C @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( ( B @ ( C @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(29,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyw$' @ 'fun_app$ad' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'fun_app$ad' ) @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).
thf(724,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyw$' @ 'fun_app$ad' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'fun_app$ad' ) @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(549,axiom,
! [A: 'A$',B: 'A_set$',C: 'A$',D: 'A_a_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cr' ) @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( B @ ( D @ 'image$ak' ) @ 'sup$b' @ ( C @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom631) ).
thf(3099,plain,
! [A: 'A$',B: 'A_set$',C: 'A$',D: 'A_a_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cr' ) @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( B @ ( D @ 'image$ak' ) @ 'sup$b' @ ( C @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(598,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$am' ) @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).
thf(3374,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$am' ) @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(133,axiom,
! [A: 'Nat$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$'] :
( ( B @ ( A @ 'member$e' ) )
=> ( B @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom698) ).
thf(1147,plain,
! [A: 'Nat$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$'] :
( ( B @ ( A @ 'member$e' ) )
=> ( B @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(483,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) @ 'fun_app$co' ) @ 'member$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).
thf(2767,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) @ 'fun_app$co' ) @ 'member$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(96,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'cartProd$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'explode$' @ 'fun_app$s' ) )
= ( B @ ( 'uyk$' @ 'fun_app$ad' ) @ ( A @ ( 'explode$' @ 'fun_app$s' ) @ 'sigma$' ) @ ( 'opair$' @ 'case_prod$' @ 'image$f' @ 'fun_app$au' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom625) ).
thf(1013,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'cartProd$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'explode$' @ 'fun_app$s' ) )
= ( B @ ( 'uyk$' @ 'fun_app$ad' ) @ ( A @ ( 'explode$' @ 'fun_app$s' ) @ 'sigma$' ) @ ( 'opair$' @ 'case_prod$' @ 'image$f' @ 'fun_app$au' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(255,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).
thf(1741,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( B = A )
=> ( B @ ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(232,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom375) ).
thf(1641,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(259,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ( ! [E: 'ZF$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( E @ ( D @ 'fun_app$s' ) @ ( E @ ( C @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom691) ).
thf(1773,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ( ! [E: 'ZF$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( E @ ( D @ 'fun_app$s' ) @ ( E @ ( C @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(385,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'inverse$' @ 'fun_app$am' ) @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom372) ).
thf(2301,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'inverse$' @ 'fun_app$am' ) @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(284,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom291) ).
thf(1875,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(567,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$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom420) ).
thf(3231,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(577,axiom,
! [A: 'B$',B: 'A_b_set_fun$',C: 'A_set$'] :
( ( C @ ( B @ 'image$al' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) )
<=> ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$cs' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom805) ).
thf(3268,plain,
! [A: 'B$',B: 'A_b_set_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$cs' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ 'image$al' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
& ( ( C @ ( B @ 'image$al' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$cs' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(295,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set_set$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$s' ) @ 'member$a' @ 'fun_app$j' ) ) )
=> ( C @ ( A @ 'collect$' @ ( B @ 'image$a' @ 'fun_app$x' ) @ 'less_eq$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom521) ).
thf(1922,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set_set$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$s' ) @ 'member$a' @ 'fun_app$j' ) ) )
=> ( C @ ( A @ 'collect$' @ ( B @ 'image$a' @ 'fun_app$x' ) @ 'less_eq$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(55,axiom,
! [A: 'B_ZF_fun$',B: 'B_set$'] :
( ( B @ ( A @ 'uwn$' ) @ 'collect$' )
= ( B @ ( A @ 'image$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom559) ).
thf(817,plain,
! [A: 'B_ZF_fun$',B: 'B_set$'] :
( ( B @ ( A @ 'uwn$' ) @ 'collect$' )
= ( B @ ( A @ 'image$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(467,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).
thf(2691,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(6,axiom,
! [A: 'ZF_set$'] :
( ( A @ ( 'uyn$' @ 'fun_app$ae' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom178) ).
thf(638,plain,
! [A: 'ZF_set$'] :
( ( A @ ( 'uyn$' @ 'fun_app$ae' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(66,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ ( A @ 'uys$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom757) ).
thf(853,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ ( A @ 'uys$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(324,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uyr$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom722) ).
thf(2049,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uyr$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(434,axiom,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( B @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom696) ).
thf(2552,plain,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( B @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(173,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom327) ).
thf(1319,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(70,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uvf$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom715) ).
thf(870,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uvf$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(512,axiom,
! [A: 'A$',B: 'ZF_a_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$ao' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) )
<=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$cv' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom643) ).
thf(2929,plain,
! [A: 'A$',B: 'ZF_a_set_fun$',C: 'ZF_set$'] :
( ( ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$cv' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'image$ao' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
& ( ( C @ ( B @ 'image$ao' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$cv' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(616,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ 'category$' )
& ( A @ 'category$' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$' ) ) @ 'functorM$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom240) ).
thf(3470,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ 'category$' )
& ( A @ 'category$' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$' ) ) @ 'functorM$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(366,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'ZF_set$'] :
( ( A @ ( E @ 'member$a' @ 'fun_app$j' ) )
=> ( D @ ( E @ ( B @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom655) ).
thf(2222,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'ZF_set$'] :
( ( A @ ( E @ 'member$a' @ 'fun_app$j' ) )
=> ( D @ ( E @ ( B @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(81,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$a' )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom322) ).
thf(924,plain,
! [A: 'ZF_set$',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)],[81]) ).
thf(48,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uut$' @ 'fun_app$f' ) )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom183) ).
thf(789,plain,
! [A: 'ZF$'] : ( A @ ( 'uut$' @ 'fun_app$f' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(200,axiom,
! [A: 'ZF$',B: 'B_ZF_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( A
= ( D @ ( B @ 'fun_app$ar' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$k' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom529) ).
thf(1450,plain,
! [A: 'ZF$',B: 'B_ZF_fun$',C: 'B_set$'] :
~ ( ! [D: 'B$'] :
~ ( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( A
= ( D @ ( B @ 'fun_app$ar' ) ) ) )
& ( C @ ( B @ 'image$k' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(183,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom305) ).
thf(1373,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(292,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom326) ).
thf(1911,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(457,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).
thf(2650,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(242,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyr$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).
thf(1682,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyr$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(280,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( A @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom681) ).
thf(1858,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( A @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( A @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(185,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'mor$' @ 'extensional$e' @ ( A @ 'mor2ZF$' @ 'member$g' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).
thf(1383,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'mor$' @ 'extensional$e' @ ( A @ 'mor2ZF$' @ 'member$g' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(396,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ! [B: 'A_set$',C: 'B_set$',D: 'B_a_fun$',E: 'B_a_fun$',F: 'A_b_fun$',G: 'B_b_b_fun_fun$',H: 'B_c_LSCategory_ext$'] :
( ( A
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$' ) ) ) ) ) ) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom225) ).
thf(2335,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
~ ! [B: 'A_set$',C: 'B_set$',D: 'B_a_fun$',E: 'B_a_fun$',F: 'A_b_fun$',G: 'B_b_b_fun_fun$',H: 'B_c_LSCategory_ext$'] :
( A
!= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(318,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyl$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( A @ ( C @ ( B @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).
thf(2017,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( A @ ( C @ ( B @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( B @ ( A @ 'uyl$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uyl$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( A @ ( C @ ( B @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(168,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uxt$' ) @ 'fun_app$ax' ) )
= ( B @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).
thf(1302,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uxt$' ) @ 'fun_app$ax' ) )
= ( B @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(37,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uyk$' @ 'fun_app$ad' ) @ 'fun_app$s' ) )
= ( A @ ( 'explode$' @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).
thf(756,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uyk$' @ 'fun_app$ad' ) @ 'fun_app$s' ) )
= ( A @ ( 'explode$' @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(238,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom309) ).
thf(1664,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(392,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'obj$a' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( A @ ( B @ 'id$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom237) ).
thf(2324,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'obj$a' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( A @ ( B @ 'id$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(320,axiom,
! [A: 'B_set$',B: 'B_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( E @ ( B @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( B @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom653) ).
thf(2027,plain,
! [A: 'B_set$',B: 'B_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( E @ ( B @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( B @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(507,axiom,
! [A: 'A_set$',B: 'A_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( E @ ( B @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( B @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom652) ).
thf(2893,plain,
! [A: 'A_set$',B: 'A_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( E @ ( B @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( B @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(230,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom355) ).
thf(1632,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(429,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category_axioms$a' )
<=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom301) ).
thf(2469,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ) )
=> ( A @ 'category_axioms$a' ) )
& ( ( A @ 'category_axioms$a' )
=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(304,axiom,
! [A: 'ZF_set$',B: 'ZF_set_bool_fun$'] :
( ( B @ 'collect$j' @ ( A @ 'member$a' @ 'fun_app$j' ) )
<=> ( A @ ( B @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom277) ).
thf(1960,plain,
! [A: 'ZF_set$',B: 'ZF_set_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$h' ) )
=> ( B @ 'collect$j' @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
& ( ( B @ 'collect$j' @ ( A @ 'member$a' @ 'fun_app$j' ) )
=> ( A @ ( B @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(582,axiom,
! [A: 'A$',B: 'B_a_set_fun$',C: 'B_set$'] :
( ( C @ ( B @ 'image$am' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) )
<=> ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$ct' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom642) ).
thf(3300,plain,
! [A: 'A$',B: 'B_a_set_fun$',C: 'B_set$'] :
( ( ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$ct' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ 'image$am' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
& ( ( C @ ( B @ 'image$am' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$ct' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(140,axiom,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set_set$',D: 'ZF_set_bool_fun$'] :
( ( ( D @ ( C @ 'uuz$' ) @ 'collect$j' @ ( B @ 'less_eq$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> ( A @ ( D @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).
thf(1183,plain,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set_set$',D: 'ZF_set_bool_fun$'] :
( ( ( D @ ( C @ 'uuz$' ) @ 'collect$j' @ ( B @ 'less_eq$b' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> ( A @ ( D @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(332,axiom,
! [A: 'A_set$',B: 'A_set$'] :
( ( B @ ( 'uu$' @ 'fun_app$o' ) @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'less_eq$j' ) )
<=> ( B @ ( A @ 'less_eq$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom789) ).
thf(2073,plain,
! [A: 'A_set$',B: 'A_set$'] :
( ( ( B @ ( A @ 'less_eq$' ) )
=> ( B @ ( 'uu$' @ 'fun_app$o' ) @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'less_eq$j' ) ) )
& ( ( B @ ( 'uu$' @ 'fun_app$o' ) @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'less_eq$j' ) )
=> ( B @ ( A @ 'less_eq$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(420,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'lSCategory$' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).
thf(2437,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'lSCategory$' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(403,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).
thf(2371,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(178,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'uwv$' @ 'fun_app$f' ) )
<=> ? [C: 'ZF$'] :
( B
= ( C @ ( A @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom40) ).
thf(1351,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF$'] :
( ( ? [C: 'ZF$'] :
( B
= ( C @ ( A @ 'fun_app$' ) ) )
=> ( B @ ( A @ 'uwv$' @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ 'uwv$' @ 'fun_app$f' ) )
=> ? [C: 'ZF$'] :
( B
= ( C @ ( A @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(11,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'ZF_set$'] :
( ( B @ ( A @ 'uww$' @ 'fun_app$h' ) )
<=> ? [C: 'Nat$'] :
( B
= ( C @ ( A @ 'fun_app$r' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).
thf(660,plain,
! [A: 'Nat_ZF_set_fun$',B: 'ZF_set$'] :
( ( ? [C: 'Nat$'] :
( B
= ( C @ ( A @ 'fun_app$r' ) ) )
=> ( B @ ( A @ 'uww$' @ 'fun_app$h' ) ) )
& ( ( B @ ( A @ 'uww$' @ 'fun_app$h' ) )
=> ? [C: 'Nat$'] :
( B
= ( C @ ( A @ 'fun_app$r' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(370,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B_b_prod$'] :
( ( B @ ( A @ 'uui$' @ 'fun_app$al' ) )
<=> ? [C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( B
= ( D @ ( C @ 'pair$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).
thf(2242,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B_b_prod$'] :
( ( ? [C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( B
= ( D @ ( C @ 'pair$a' ) ) ) )
=> ( B @ ( A @ 'uui$' @ 'fun_app$al' ) ) )
& ( ( B @ ( A @ 'uui$' @ 'fun_app$al' ) )
=> ? [C: 'B$',D: 'B$'] :
( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( B
= ( D @ ( C @ 'pair$a' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(521,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$a' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).
thf(2965,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$a' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(441,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_set_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( A @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom707) ).
thf(2586,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_set_set$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( A @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( A @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(276,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).
thf(1843,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(326,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$a' )
=> ( A @ 'mor$' @ 'extensional$' @ ( A @ 'cod$' @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).
thf(2058,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$a' )
=> ( A @ 'mor$' @ 'extensional$' @ ( A @ 'cod$' @ 'member$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(449,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uwz$' ) @ 'fun_app$x' ) )
= ( B @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom85) ).
thf(2618,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uwz$' ) @ 'fun_app$x' ) )
= ( B @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(493,axiom,
! [A: 'A_set_set$',B: 'A$'] :
( ( B @ ( A @ ( 'uu$' @ 'image$bh' ) @ 'sup$g' @ 'fun_app$n' ) )
<=> ( A @ 'sup$b' @ ( B @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom775) ).
thf(2833,plain,
! [A: 'A_set_set$',B: 'A$'] :
( ( ( A @ 'sup$b' @ ( B @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( A @ ( 'uu$' @ 'image$bh' ) @ 'sup$g' @ 'fun_app$n' ) ) )
& ( ( B @ ( A @ ( 'uu$' @ 'image$bh' ) @ 'sup$g' @ 'fun_app$n' ) )
=> ( A @ 'sup$b' @ ( B @ 'member$c' @ 'fun_app$p' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(359,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$',D: 'ZF$',E: 'ZF_ZF_fun$'] :
( ! [F: 'ZF$'] :
( ( A @ ( F @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( F @ ( B @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( E @ ( D @ ( C @ 'zFfun$' ) ) @ ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( E @ 'comp$b' @ 'fun_app$a' ) @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).
thf(2190,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$',D: 'ZF$',E: 'ZF_ZF_fun$'] :
( ! [F: 'ZF$'] :
( ( A @ ( F @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( F @ ( B @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( E @ ( D @ ( C @ 'zFfun$' ) ) @ ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( E @ 'comp$b' @ 'fun_app$a' ) @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(610,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$a' ) @ 'functor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom386) ).
thf(3421,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$a' ) @ 'functor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(122,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uug$' @ 'fun_app$q' ) @ 'the$' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).
thf(1104,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uug$' @ 'fun_app$q' ) @ 'the$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(157,axiom,
! [A: 'ZF$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ! [D: 'Nat$'] :
( ( C @ ( D @ 'member$e' ) )
=> ( D @ ( B @ 'fun_app$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom808) ).
thf(1242,plain,
! [A: 'ZF$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( ! [D: 'Nat$'] :
( ( C @ ( D @ 'member$e' ) )
=> ( D @ ( B @ 'fun_app$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ! [D: 'Nat$'] :
( ( C @ ( D @ 'member$e' ) )
=> ( D @ ( B @ 'fun_app$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(473,axiom,
! [A: 'ZF$',B: 'B_ZF_set_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( ( D @ ( B @ 'fun_app$cx' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> $false )
& ( C @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom738) ).
thf(2718,plain,
! [A: 'ZF$',B: 'B_ZF_set_fun$',C: 'B_set$'] :
~ ( ! [D: 'B$'] :
~ ( ( D @ ( B @ 'fun_app$cx' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
& ( C @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(361,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set_set$'] :
( ( B @ ( A @ 'uyu$' @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( B @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom725) ).
thf(2205,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set_set$'] :
( ( B @ ( A @ 'uyu$' @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( B @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(85,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyx$' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'uyw$' @ 'fun_app$ad' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom105) ).
thf(942,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyx$' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'uyw$' @ 'fun_app$ad' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(566,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category_axioms$' )
<=> ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [B: 'B$',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$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom300) ).
thf(3169,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$' ) ) @ 'fun_app$n' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [B: 'B$',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$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( A @ 'category_axioms$' ) )
& ( ( A @ 'category_axioms$' )
=> ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [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$an' ) @ 'fun_app$am' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(341,axiom,
! [A: 'ZF_set_set$'] :
( ( A @ ( 'sup$' @ 'fun_app$u' ) )
= ( A @ 'vag$' @ 'collect$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom784) ).
thf(2118,plain,
! [A: 'ZF_set_set$'] :
( ( A @ ( 'sup$' @ 'fun_app$u' ) )
= ( A @ 'vag$' @ 'collect$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(337,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF_bool_fun$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwc$' ) ) @ 'fun_app$f' ) )
<=> ( ( D @ ( A @ 'fun_app$' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom138) ).
thf(2093,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF_bool_fun$',D: 'ZF$'] :
( ( ( ( D @ ( A @ 'fun_app$' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uwc$' ) ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uwc$' ) ) @ 'fun_app$f' ) )
=> ( ( D @ ( A @ 'fun_app$' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(367,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom297) ).
thf(2232,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(609,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( B @ ( A @ 'homFtor$' ) @ 'preFunctor$b' )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$' ) @ 'mapO$' @ 'fun_app$bf' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).
thf(3418,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( B @ ( A @ 'homFtor$' ) @ 'preFunctor$b' )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$' ) @ 'mapO$' @ 'fun_app$bf' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(626,axiom,
! [A: 'A_set$',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$' ) ) ) ) ) ) @ 'obj$' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).
thf(3503,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$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(614,axiom,
! [A: 'A$',B: 'ZF_a_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$ao' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) )
<=> ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$cv' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom804) ).
thf(3459,plain,
! [A: 'A$',B: 'ZF_a_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$cv' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( B @ 'image$ao' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
& ( ( C @ ( B @ 'image$ao' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$cv' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(402,axiom,
! [A: 'ZF$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$s' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom650) ).
thf(2364,plain,
! [A: 'ZF$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$s' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$s' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(353,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom452) ).
thf(2164,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(334,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_prod_ZF_fun$'] :
( ( ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( B @ 'member$a' @ 'fun_app$j' ) )
& ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( B @ 'uxi$' @ ( A @ 'sigma$' ) @ ( C @ 'image$f' @ 'fun_app$au' ) @ 'member$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom617) ).
thf(2083,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_prod_ZF_fun$'] :
( ( ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( B @ 'member$a' @ 'fun_app$j' ) )
& ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( B @ 'uxi$' @ ( A @ 'sigma$' ) @ ( C @ 'image$f' @ 'fun_app$au' ) @ 'member$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(112,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category_axioms$a' )
=> ( A @ 'makeCat$a' @ 'category$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom248) ).
thf(1067,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category_axioms$a' )
=> ( A @ 'makeCat$a' @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(450,axiom,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat$'] :
( ( B @ ( A @ 'vaw$' @ 'fun_app$r' ) )
= ( 'top$a' @ ( B @ ( A @ 'uyz$' @ 'fun_app$ac' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).
thf(2621,plain,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat$'] :
( ( B @ ( A @ 'vaw$' @ 'fun_app$r' ) )
= ( 'top$a' @ ( B @ ( A @ 'uyz$' @ 'fun_app$ac' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(485,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$am' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).
thf(2773,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$am' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(314,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ 'zF2mor$' @ 'fun_app$as' ) )
= ( B @ ( A @ 'uuo$' ) @ 'the$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).
thf(2000,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ 'zF2mor$' @ 'fun_app$as' ) )
= ( B @ ( A @ 'uuo$' ) @ 'the$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(463,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_bool_fun$',D: 'ZF_bool_fun$'] :
( ( ! [E: 'ZF$'] :
( ( ( E @ ( C @ 'fun_app$f' ) )
& ( A @ ( E @ 'member$' @ 'fun_app$h' ) ) )
=> ( E @ ( D @ 'fun_app$f' ) ) )
& ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( B @ 'uva$' ) @ 'collect$' @ ( C @ ( A @ 'uva$' ) @ 'collect$' @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).
thf(2673,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_bool_fun$',D: 'ZF_bool_fun$'] :
( ( ! [E: 'ZF$'] :
( ( ( E @ ( C @ 'fun_app$f' ) )
& ( A @ ( E @ 'member$' @ 'fun_app$h' ) ) )
=> ( E @ ( D @ 'fun_app$f' ) ) )
& ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( B @ 'uva$' ) @ 'collect$' @ ( C @ ( A @ 'uva$' ) @ 'collect$' @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(575,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$b' ) ) @ 'functorM$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom242) ).
thf(3261,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$b' ) ) @ 'functorM$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(476,axiom,
! [A: 'A$',B: 'ZF_set_a_fun$',C: 'ZF_set_set$'] :
( ( ! [D: 'ZF_set$'] :
( ( ( C @ ( D @ 'member$a' @ 'fun_app$j' ) )
& ( A
= ( D @ ( B @ 'fun_app$bj' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$j' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).
thf(2733,plain,
! [A: 'A$',B: 'ZF_set_a_fun$',C: 'ZF_set_set$'] :
~ ( ! [D: 'ZF_set$'] :
~ ( ( C @ ( D @ 'member$a' @ 'fun_app$j' ) )
& ( A
= ( D @ ( B @ 'fun_app$bj' ) ) ) )
& ( C @ ( B @ 'image$j' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(56,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) )
= ( C @ ( B @ ( A @ 'uve$' ) @ 'image$' @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).
thf(820,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) )
= ( C @ ( B @ ( A @ 'uve$' ) @ 'image$' @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(204,axiom,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( B @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom669) ).
thf(1487,plain,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( B @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(523,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom432) ).
thf(2969,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$' @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(569,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).
thf(3239,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(20,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_set$',C: 'ZF_set_bool_fun$',D: 'ZF_set_bool_fun$'] :
( ( ! [E: 'ZF_set$'] :
( ( ( E @ ( C @ 'fun_app$h' ) )
& ( A @ ( E @ 'member$a' @ 'fun_app$j' ) ) )
=> ( E @ ( D @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$b' ) ) )
=> ( D @ ( B @ 'uuz$' ) @ 'collect$j' @ ( C @ ( A @ 'uuz$' ) @ 'collect$j' @ 'less_eq$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom491) ).
thf(693,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_set$',C: 'ZF_set_bool_fun$',D: 'ZF_set_bool_fun$'] :
( ( ! [E: 'ZF_set$'] :
( ( ( E @ ( C @ 'fun_app$h' ) )
& ( A @ ( E @ 'member$a' @ 'fun_app$j' ) ) )
=> ( E @ ( D @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$b' ) ) )
=> ( D @ ( B @ 'uuz$' ) @ 'collect$j' @ ( C @ ( A @ 'uuz$' ) @ 'collect$j' @ 'less_eq$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(446,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'inverse$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom370) ).
thf(2606,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'inverse$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(563,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'ZF$'] :
( ( ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( D @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( D @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).
thf(3154,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'ZF$'] :
( ( ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( D @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( D @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(272,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_bool_fun$'] :
( ( B @ ( A @ 'uwg$' ) @ 'collect$j' )
= ( B @ 'collect$' @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).
thf(1824,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_bool_fun$'] :
( ( B @ ( A @ 'uwg$' ) @ 'collect$j' )
= ( B @ 'collect$' @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(506,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( ( B @ ( A @ 'id$' @ 'fun_app$bl' ) )
= ( C @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom221) ).
thf(2890,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( ( B @ ( A @ 'id$' @ 'fun_app$bl' ) )
= ( C @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(590,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'identityFunctor$' @ 'catDom$' @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'identityFunctor$' @ 'mapO$a' @ 'fun_app$bm' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom472) ).
thf(3339,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'identityFunctor$' @ 'catDom$' @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'identityFunctor$' @ 'mapO$a' @ 'fun_app$bm' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(287,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ 'category$a' )
& ( A @ 'category$' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$a' ) ) @ 'functorM$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom241) ).
thf(1883,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ 'category$a' )
& ( A @ 'category$' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$a' ) ) @ 'functorM$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(290,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ! [D: 'ZF$'] :
( ( B @ ( D @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( B @ ( D @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= D ) )
& ( C @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( A @ 'id$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).
thf(1900,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ! [D: 'ZF$'] :
( ( B @ ( D @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( B @ ( D @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= D ) )
& ( C @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( A @ 'id$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(252,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uwy$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( A @ ( B @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
thf(1723,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( A @ ( B @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( B @ ( A @ ( 'uwy$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ ( 'uwy$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( A @ ( B @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(241,axiom,
! [A: 'B_set_set$',B: 'B$'] :
( ( B @ ( A @ 'vae$' @ 'fun_app$k' ) )
<=> ( A @ ( B @ 'member$b' @ 'image$d' ) @ 'sup$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom32) ).
thf(1676,plain,
! [A: 'B_set_set$',B: 'B$'] :
( ( ( A @ ( B @ 'member$b' @ 'image$d' ) @ 'sup$a' )
=> ( B @ ( A @ 'vae$' @ 'fun_app$k' ) ) )
& ( ( B @ ( A @ 'vae$' @ 'fun_app$k' ) )
=> ( A @ ( B @ 'member$b' @ 'image$d' ) @ 'sup$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(345,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_bool_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uuz$' ) @ 'fun_app$h' ) )
<=> ( ( C @ ( B @ 'fun_app$h' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$j' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).
thf(2133,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_bool_fun$',C: 'ZF_set$'] :
( ( ( ( C @ ( B @ 'fun_app$h' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$j' ) ) )
=> ( C @ ( B @ ( A @ 'uuz$' ) @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'uuz$' ) @ 'fun_app$h' ) )
=> ( ( C @ ( B @ 'fun_app$h' ) )
& ( A @ ( C @ 'member$a' @ 'fun_app$j' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(65,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_set$',D: 'ZF_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ 'uxi$' @ ( D @ 'sigma$' ) @ ( B @ 'uxi$' @ ( C @ 'sigma$' ) @ 'less_eq$e' ) )
<=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom605) ).
thf(847,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_set$',D: 'ZF_set$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( B @ 'uxi$' @ ( D @ 'sigma$' ) @ ( B @ 'uxi$' @ ( C @ 'sigma$' ) @ 'less_eq$e' ) ) )
& ( ( B @ 'uxi$' @ ( D @ 'sigma$' ) @ ( B @ 'uxi$' @ ( C @ 'sigma$' ) @ 'less_eq$e' ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(294,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$a' @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom307) ).
thf(1920,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$a' @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(73,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( ( A @ ( 'uur$' @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).
thf(879,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( ( A @ ( 'uur$' @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(581,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom296) ).
thf(3297,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(502,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$',D: 'A$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$bk' ) )
= D )
& ( ( A @ ( B @ 'dom$' @ 'fun_app$bk' ) )
= C )
& ( B @ 'mor$' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom263) ).
thf(2872,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$',D: 'A$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$bk' ) )
= D )
& ( ( A @ ( B @ 'dom$' @ 'fun_app$bk' ) )
= C )
& ( B @ 'mor$' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(166,axiom,
! [A: 'A_set_a_set_fun$',B: 'A_set$',C: 'B_set$',D: 'B_a_fun$',E: 'B_a_fun$',F: 'A_b_fun$',G: 'B_b_b_fun_fun$',H: 'B_c_LSCategory_ext$'] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$' ) ) ) ) ) ) @ ( A @ 'obj_update$' ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'fun_app$bh' ) @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).
thf(1296,plain,
! [A: 'A_set_a_set_fun$',B: 'A_set$',C: 'B_set$',D: 'B_a_fun$',E: 'B_a_fun$',F: 'A_b_fun$',G: 'B_b_b_fun_fun$',H: 'B_c_LSCategory_ext$'] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$' ) ) ) ) ) ) @ ( A @ 'obj_update$' ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'fun_app$bh' ) @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(330,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom320) ).
thf(2068,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ ( A @ 'oppositeCategory$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(447,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF$',D: 'ZF_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$s' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom640) ).
thf(2609,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF$',D: 'ZF_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$s' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(147,axiom,
! [A: 'Nat_ZF_set_fun$'] :
( ( A @ 'uww$' @ 'collect$j' )
= ( 'top$' @ ( A @ 'image$' @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom589) ).
thf(1210,plain,
! [A: 'Nat_ZF_set_fun$'] :
( ( A @ 'uww$' @ 'collect$j' )
= ( 'top$' @ ( A @ 'image$' @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(393,axiom,
! [A: 'ZF_a_fun$',B: 'ZF_set$',C: 'A_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvt$' ) ) @ 'collect$h' )
= ( C @ ( B @ ( A @ 'uvu$' ) ) @ 'collect$' @ ( A @ 'image$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).
thf(2327,plain,
! [A: 'ZF_a_fun$',B: 'ZF_set$',C: 'A_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvt$' ) ) @ 'collect$h' )
= ( C @ ( B @ ( A @ 'uvu$' ) ) @ 'collect$' @ ( A @ 'image$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(191,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom359) ).
thf(1407,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(231,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uvb$' ) @ 'fun_app$f' ) )
<=> ( ( C @ ( B @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
thf(1634,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$',C: 'ZF$'] :
( ( ( ( C @ ( B @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) )
=> ( C @ ( B @ ( A @ 'uvb$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uvb$' ) @ 'fun_app$f' ) )
=> ( ( C @ ( B @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(63,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_ZF_set_fun$'] :
( ( 'top$a' @ ( B @ ( A @ 'uvc$' ) @ 'image$a' @ 'fun_app$x' ) )
= ( 'top$a' @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom580) ).
thf(842,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_ZF_set_fun$'] :
( ( 'top$a' @ ( B @ ( A @ 'uvc$' ) @ 'image$a' @ 'fun_app$x' ) )
= ( 'top$a' @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(484,axiom,
! [A: 'A_set$',B: 'ZF$',C: 'A_ZF_set_fun$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$co' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( C @ 'image$aq' ) @ 'inf$' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom815) ).
thf(2769,plain,
! [A: 'A_set$',B: 'ZF$',C: 'A_ZF_set_fun$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$co' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( C @ 'image$aq' ) @ 'inf$' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(458,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom250) ).
thf(2653,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(579,axiom,
! [A: 'A_ZF_fun$',B: 'A_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uwm$' ) @ 'fun_app$f' ) )
<=> ? [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( C
= ( D @ ( A @ 'fun_app$bf' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom122) ).
thf(3282,plain,
! [A: 'A_ZF_fun$',B: 'A_set$',C: 'ZF$'] :
( ( ? [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( C
= ( D @ ( A @ 'fun_app$bf' ) ) ) )
=> ( C @ ( B @ ( A @ 'uwm$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uwm$' ) @ 'fun_app$f' ) )
=> ? [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( C
= ( D @ ( A @ 'fun_app$bf' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(194,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'makeCat$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom325) ).
thf(1423,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( B @ ( A @ 'makeCat$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'makeCat$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(583,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_a_fun$',D: 'B_a_fun_b_a_fun_fun$',E: 'B_a_fun_b_a_fun_fun$'] :
( ( ! [F: 'B_a_fun$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$ch' ) )
= ( F @ ( E @ 'fun_app$ch' ) ) ) )
& ( ( B @ 'dom$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'dom_update$' ) )
= ( B @ ( E @ 'dom_update$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom193) ).
thf(3307,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_a_fun$',D: 'B_a_fun_b_a_fun_fun$',E: 'B_a_fun_b_a_fun_fun$'] :
( ( ! [F: 'B_a_fun$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$ch' ) )
= ( F @ ( E @ 'fun_app$ch' ) ) ) )
& ( ( B @ 'dom$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'dom_update$' ) )
= ( B @ ( E @ 'dom_update$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(181,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$a' @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).
thf(1365,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$a' @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(462,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_ZF_fun$'] :
( ( B @ ( A @ 'vak$' @ 'fun_app$z' ) )
= ( 'top$a' @ ( B @ ( A @ 'vaj$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
thf(2670,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_ZF_fun$'] :
( ( B @ ( A @ 'vak$' @ 'fun_app$z' ) )
= ( 'top$a' @ ( B @ ( A @ 'vaj$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(540,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'mor$' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( ( A @ ( B @ 'cod$' @ 'fun_app$bk' ) )
= ( A @ ( B @ 'makeCat$' @ 'cod$' @ 'fun_app$bk' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom335) ).
thf(3050,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'mor$' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( ( A @ ( B @ 'cod$' @ 'fun_app$bk' ) )
= ( A @ ( B @ 'makeCat$' @ 'cod$' @ 'fun_app$bk' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(399,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'lSCategory_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom356) ).
thf(2345,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'lSCategory_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(214,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uuw$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).
thf(1534,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uuw$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(267,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom368) ).
thf(1804,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(176,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom371) ).
thf(1328,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(111,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzp$' ) @ 'fun_app$s' ) )
= ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom115) ).
thf(1064,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzp$' ) @ 'fun_app$s' ) )
= ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(124,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$a' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom232) ).
thf(1111,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$a' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(468,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'identityFunctor$b' @ 'functor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).
thf(2694,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'identityFunctor$b' @ 'functor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(551,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$' @ ( A @ 'comp$a' @ ( A @ 'id$' @ ( A @ 'cod$' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom339) ).
thf(3102,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$' @ ( A @ 'comp$a' @ ( A @ 'id$' @ ( A @ 'cod$' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(94,axiom,
! [A: 'Nat_set$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ? [F: 'Nat$'] :
( ( F @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$e' ) ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom656) ).
thf(1006,plain,
! [A: 'Nat_set$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ? [F: 'Nat$'] :
( ( F @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$e' ) ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(475,axiom,
! [A: 'B$',B: 'A_b_set_fun$',C: 'A_set$'] :
( ( C @ ( B @ 'image$al' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) )
<=> ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$cs' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom644) ).
thf(2726,plain,
! [A: 'B$',B: 'A_b_set_fun$',C: 'A_set$'] :
( ( ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$cs' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( B @ 'image$al' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
& ( ( C @ ( B @ 'image$al' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$cs' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(499,axiom,
! [A: 'A$',B: 'A_a_set_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> $false )
& ( C @ ( B @ 'image$ak' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom730) ).
thf(2858,plain,
! [A: 'A$',B: 'A_a_set_fun$',C: 'A_set$'] :
~ ( ! [D: 'A$'] :
~ ( ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
& ( C @ ( B @ 'image$ak' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(46,axiom,
! [A: 'Nat_set$',B: 'ZF$',C: 'Nat_ZF_set_fun$'] :
( ! [D: 'Nat$'] :
( ( A @ ( D @ 'member$e' ) )
=> ( D @ ( C @ 'fun_app$r' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ 'inf$' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom812) ).
thf(783,plain,
! [A: 'Nat_set$',B: 'ZF$',C: 'Nat_ZF_set_fun$'] :
( ! [D: 'Nat$'] :
( ( A @ ( D @ 'member$e' ) )
=> ( D @ ( C @ 'fun_app$r' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ 'inf$' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(376,axiom,
! [A: 'A_b_fun$',B: 'A_set$',C: 'B_bool_fun$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'fun_app$k' ) )
<=> ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$o' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom136) ).
thf(2268,plain,
! [A: 'A_b_fun$',B: 'A_set$',C: 'B_bool_fun$',D: 'B$'] :
( ( ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$o' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'fun_app$k' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'fun_app$k' ) )
=> ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$o' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(552,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).
thf(3105,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(615,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$am' ) @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom364) ).
thf(3467,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$am' ) @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(117,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( ( 'uur$' @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom465) ).
thf(1089,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( ( 'uur$' @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(216,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).
thf(1541,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(619,axiom,
! [A: 'B$',B: 'B_set$',C: 'A$',D: 'B_a_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$ct' ) @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B @ ( D @ 'image$am' ) @ 'sup$b' @ ( C @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom633) ).
thf(3482,plain,
! [A: 'B$',B: 'B_set$',C: 'A$',D: 'B_a_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$ct' ) @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B @ ( D @ 'image$am' ) @ 'sup$b' @ ( C @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(338,axiom,
! [A: 'Nat_ZF_set_fun$'] :
( ! [B: 'Nat$'] : ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( B @ ( A @ 'fun_app$r' ) @ 'member$a' @ 'fun_app$j' ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( 'top$' @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'member$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom769) ).
thf(2100,plain,
! [A: 'Nat_ZF_set_fun$'] :
( ! [B: 'Nat$'] : ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( B @ ( A @ 'fun_app$r' ) @ 'member$a' @ 'fun_app$j' ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( 'top$' @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'member$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(279,axiom,
! [A: 'ZF_set$',B: 'ZF_bool_fun$',C: 'ZF_bool_fun$'] :
( ( C @ ( B @ 'uvb$' ) @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ( ( C @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom505) ).
thf(1851,plain,
! [A: 'ZF_set$',B: 'ZF_bool_fun$',C: 'ZF_bool_fun$'] :
( ( ( ( C @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'uvb$' ) @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'uvb$' ) @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( ( C @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(557,axiom,
! [A: 'A$',B: 'ZF_a_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( A
= ( D @ ( B @ 'fun_app$bi' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$i' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom524) ).
thf(3122,plain,
! [A: 'A$',B: 'ZF_a_fun$',C: 'ZF_set$'] :
~ ( ! [D: 'ZF$'] :
~ ( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( A
= ( D @ ( B @ 'fun_app$bi' ) ) ) )
& ( C @ ( B @ 'image$i' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(516,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom257) ).
thf(2946,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(207,axiom,
! [A: 'B$',B: 'B_set$',C: 'ZF_set$',D: 'B_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cx' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom685) ).
thf(1498,plain,
! [A: 'B$',B: 'B_set$',C: 'ZF_set$',D: 'B_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cx' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(220,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom258) ).
thf(1587,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(543,axiom,
! [A: 'A$',B: 'A_set$',C: 'ZF$',D: 'A_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$co' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom638) ).
thf(3060,plain,
! [A: 'A$',B: 'A_set$',C: 'ZF$',D: 'A_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$co' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(189,axiom,
! [A: 'B$',B: 'ZF_b_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( A
= ( D @ ( B @ 'fun_app$as' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$h' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).
thf(1397,plain,
! [A: 'B$',B: 'ZF_b_fun$',C: 'ZF_set$'] :
~ ( ! [D: 'ZF$'] :
~ ( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( A
= ( D @ ( B @ 'fun_app$as' ) ) ) )
& ( C @ ( B @ 'image$h' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(427,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'B$',D: 'ZF_b_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cw' ) @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$ap' ) @ 'sup$c' @ ( C @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom636) ).
thf(2460,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'B$',D: 'ZF_b_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cw' ) @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$ap' ) @ 'sup$c' @ ( C @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(560,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$a' )
=> ( A @ 'mor$' @ 'extensional$' @ ( A @ 'dom$' @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom378) ).
thf(3143,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$a' )
=> ( A @ 'mor$' @ 'extensional$' @ ( A @ 'dom$' @ 'member$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(180,axiom,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$'] :
( ( ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'member$a' @ 'fun_app$j' ) )
& ! [C: 'ZF$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$h' ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ 'fun_app$s' ) @ 'member$a' @ 'fun_app$j' ) ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( A @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'member$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom629) ).
thf(1361,plain,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$'] :
( ( ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'member$a' @ 'fun_app$j' ) )
& ! [C: 'ZF$'] :
( ( A @ ( C @ 'member$' @ 'fun_app$h' ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ 'fun_app$s' ) @ 'member$a' @ 'fun_app$j' ) ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( A @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'member$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(531,axiom,
! [A: 'ZF$',B: 'A_ZF_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( A
= ( D @ ( B @ 'fun_app$bf' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$n' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).
thf(3000,plain,
! [A: 'ZF$',B: 'A_ZF_fun$',C: 'A_set$'] :
~ ( ! [D: 'A$'] :
~ ( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( A
= ( D @ ( B @ 'fun_app$bf' ) ) ) )
& ( C @ ( B @ 'image$n' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(492,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$' )
= ( B @ 'more$' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$' )
= ( B @ 'id$' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$' )
= ( B @ 'obj$' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).
thf(2830,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$' )
= ( B @ 'more$' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$' )
= ( B @ 'id$' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$' )
= ( B @ 'obj$' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(203,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ) )
=> ( A @ 'category_axioms$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom303) ).
thf(1461,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ) )
=> ( A @ 'category_axioms$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(193,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uwo$' ) @ 'fun_app$f' ) )
<=> ? [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( C
= ( D @ ( A @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).
thf(1414,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( ? [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( C
= ( D @ ( A @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'uwo$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uwo$' ) @ 'fun_app$f' ) )
=> ? [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( C
= ( D @ ( A @ 'fun_app$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(264,axiom,
( 'top$a'
= ( 'uut$' @ 'collect$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom584) ).
thf(1791,plain,
( 'top$a'
= ( 'uut$' @ 'collect$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(199,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_ZF_set_fun$',D: 'B_ZF_set_fun$'] :
( ( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ( E @ ( D @ 'fun_app$cx' ) @ ( E @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$a' ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom690) ).
thf(1446,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_ZF_set_fun$',D: 'B_ZF_set_fun$'] :
( ( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ( E @ ( D @ 'fun_app$cx' ) @ ( E @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$a' ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(104,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$f' ) ) )
=> ( ( A @ 'the$' )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom389) ).
thf(1039,plain,
! [A: 'ZF_bool_fun$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$f' ) ) )
=> ( ( A @ 'the$' )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(488,axiom,
! [A: 'A_set$',B: 'A_set$',C: 'A_bool_fun$'] :
( ( B @ ( A @ 'less_eq$' ) )
=> ( ( C @ ( B @ 'uux$' ) @ 'collect$h' @ ( A @ 'less_eq$' ) )
<=> ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$n' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).
thf(2781,plain,
! [A: 'A_set$',B: 'A_set$',C: 'A_bool_fun$'] :
( ( B @ ( A @ 'less_eq$' ) )
=> ( ( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$n' ) ) )
=> ( C @ ( B @ 'uux$' ) @ 'collect$h' @ ( A @ 'less_eq$' ) ) )
& ( ( C @ ( B @ 'uux$' ) @ 'collect$h' @ ( A @ 'less_eq$' ) )
=> ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$n' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(100,axiom,
! [A: 'B_b_fun$',B: 'B_set$',C: 'B_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvr$' ) ) @ 'collect$i' )
= ( C @ ( B @ ( A @ 'uvs$' ) ) @ 'collect$i' @ ( A @ 'image$l' @ 'fun_app$bg' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom544) ).
thf(1028,plain,
! [A: 'B_b_fun$',B: 'B_set$',C: 'B_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvr$' ) ) @ 'collect$i' )
= ( C @ ( B @ ( A @ 'uvs$' ) ) @ 'collect$i' @ ( A @ 'image$l' @ 'fun_app$bg' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(319,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorContra$a' ) @ 'mapM$' @ 'fun_app$ar' ) )
= ( C @ ( B @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom470) ).
thf(2023,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorContra$a' ) @ 'mapM$' @ 'fun_app$ar' ) )
= ( C @ ( B @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(587,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'uui$' @ 'collect$b' @ 'extensional$c' @ ( A @ 'comp$a' @ 'case_prod$a' @ 'member$k' ) )
& ( A @ 'obj$' @ 'extensional$b' @ ( A @ 'id$' @ 'member$i' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'cod$' @ 'member$h' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'dom$' @ 'member$h' ) ) )
=> ( A @ 'extCategory$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom402) ).
thf(3326,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'uui$' @ 'collect$b' @ 'extensional$c' @ ( A @ 'comp$a' @ 'case_prod$a' @ 'member$k' ) )
& ( A @ 'obj$' @ 'extensional$b' @ ( A @ 'id$' @ 'member$i' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'cod$' @ 'member$h' ) )
& ( A @ 'mor$' @ 'extensional$' @ ( A @ 'dom$' @ 'member$h' ) ) )
=> ( A @ 'extCategory$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(605,axiom,
! [A: 'A_set$',B: 'A_set$',C: 'A_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ( E @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$' ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom689) ).
thf(3407,plain,
! [A: 'A_set$',B: 'A_set$',C: 'A_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ( E @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$' ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(36,axiom,
! [A: 'ZF_ZF_bool_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'uzx$' @ 'fun_app$s' ) )
= ( B @ ( A @ 'uzw$' @ 'fun_app$q' ) @ 'collect$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
thf(753,plain,
! [A: 'ZF_ZF_bool_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'uzx$' @ 'fun_app$s' ) )
= ( B @ ( A @ 'uzw$' @ 'fun_app$q' ) @ 'collect$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(77,axiom,
! [A: 'ZF_set_set_set$',B: 'ZF_set$'] :
( ( B @ ( A @ ( 'uub$' @ 'image$bj' ) @ 'sup$i' @ 'fun_app$h' ) )
<=> ( A @ ( 'sup$e' @ 'fun_app$da' ) @ ( B @ 'member$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom777) ).
thf(901,plain,
! [A: 'ZF_set_set_set$',B: 'ZF_set$'] :
( ( ( A @ ( 'sup$e' @ 'fun_app$da' ) @ ( B @ 'member$a' @ 'fun_app$j' ) )
=> ( B @ ( A @ ( 'uub$' @ 'image$bj' ) @ 'sup$i' @ 'fun_app$h' ) ) )
& ( ( B @ ( A @ ( 'uub$' @ 'image$bj' ) @ 'sup$i' @ 'fun_app$h' ) )
=> ( A @ ( 'sup$e' @ 'fun_app$da' ) @ ( B @ 'member$a' @ 'fun_app$j' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(414,axiom,
! [A: 'B_set$',B: 'Nat_set$',C: 'B_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ? [F: 'Nat$'] :
( ( F @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$e' ) ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom664) ).
thf(2419,plain,
! [A: 'B_set$',B: 'Nat_set$',C: 'B_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ? [F: 'Nat$'] :
( ( F @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$e' ) ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(389,axiom,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$j' ) )
=> ( B @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom677) ).
thf(2312,plain,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$j' ) )
=> ( B @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(533,axiom,
! [A: 'B_a_fun$',B: 'B_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'fun_app$n' ) )
<=> ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$m' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).
thf(3010,plain,
! [A: 'B_a_fun$',B: 'B_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$m' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'fun_app$n' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'fun_app$n' ) )
=> ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$m' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(537,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( ( ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom298) ).
thf(3032,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
~ ( ~ ( ( ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(297,axiom,
! [A: 'ZF_a_fun$',B: 'ZF_set$',C: 'A_bool_fun$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) @ 'fun_app$f' ) )
<=> ( ( D @ ( A @ 'fun_app$bi' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom140) ).
thf(1937,plain,
! [A: 'ZF_a_fun$',B: 'ZF_set$',C: 'A_bool_fun$',D: 'ZF$'] :
( ( ( ( D @ ( A @ 'fun_app$bi' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvu$' ) ) @ 'fun_app$f' ) )
=> ( ( D @ ( A @ 'fun_app$bi' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(97,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_bool_fun$'] :
( ( B @ ( A @ 'uwi$' ) @ 'collect$' )
= ( B @ 'collect$' @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).
thf(1016,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_bool_fun$'] :
( ( B @ ( A @ 'uwi$' ) @ 'collect$' )
= ( B @ 'collect$' @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(146,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uvc$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom714) ).
thf(1207,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uvc$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(92,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_fun$'] :
( ( 'top$a' @ ( B @ ( A @ 'uvf$' ) @ 'image$a' @ 'fun_app$x' ) )
= ( 'top$a' @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom574) ).
thf(997,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_fun$'] :
( ( 'top$a' @ ( B @ ( A @ 'uvf$' ) @ 'image$a' @ 'fun_app$x' ) )
= ( 'top$a' @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(134,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( A @ 'less_eq$a' ) )
<=> ( B @ ( 'uua$' @ 'fun_app$l' ) @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'less_eq$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom786) ).
thf(1150,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( 'uua$' @ 'fun_app$l' ) @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'less_eq$k' ) )
=> ( B @ ( A @ 'less_eq$a' ) ) )
& ( ( B @ ( A @ 'less_eq$a' ) )
=> ( B @ ( 'uua$' @ 'fun_app$l' ) @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'less_eq$k' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(154,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B$'] :
( ( ( E @ ( C @ 'fun_app$k' ) )
& ( A @ ( E @ 'member$b' @ 'fun_app$m' ) ) )
=> ( E @ ( D @ 'fun_app$k' ) ) )
& ( B @ ( A @ 'less_eq$a' ) ) )
=> ( D @ ( B @ 'uuy$' ) @ 'collect$i' @ ( C @ ( A @ 'uuy$' ) @ 'collect$i' @ 'less_eq$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom490) ).
thf(1231,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_bool_fun$',D: 'B_bool_fun$'] :
( ( ! [E: 'B$'] :
( ( ( E @ ( C @ 'fun_app$k' ) )
& ( A @ ( E @ 'member$b' @ 'fun_app$m' ) ) )
=> ( E @ ( D @ 'fun_app$k' ) ) )
& ( B @ ( A @ 'less_eq$a' ) ) )
=> ( D @ ( B @ 'uuy$' ) @ 'collect$i' @ ( C @ ( A @ 'uuy$' ) @ 'collect$i' @ 'less_eq$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(309,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'inverse$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).
thf(1984,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'inverse$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(195,axiom,
! [A: 'ZF$',B: 'B_ZF_set_fun$',C: 'B_set$'] :
( ( C @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$cx' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom649) ).
thf(1429,plain,
! [A: 'ZF$',B: 'B_ZF_set_fun$',C: 'B_set$'] :
( ( ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$cx' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$cx' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(325,axiom,
! [A: 'B_b_prod$',B: 'B_b_prod_bool_fun$'] :
( ( B @ 'collect$b' @ ( A @ 'member$j' ) )
<=> ( A @ ( B @ 'fun_app$al' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).
thf(2052,plain,
! [A: 'B_b_prod$',B: 'B_b_prod_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$al' ) )
=> ( B @ 'collect$b' @ ( A @ 'member$j' ) ) )
& ( ( B @ 'collect$b' @ ( A @ 'member$j' ) )
=> ( A @ ( B @ 'fun_app$al' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(249,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom701) ).
thf(1715,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$'] :
( ( B @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( C @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(307,axiom,
! [A: 'A_set$',B: 'A_bool_fun$'] : ( A @ ( B @ ( A @ 'uux$' ) @ 'collect$h' @ 'less_eq$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom497) ).
thf(1979,plain,
! [A: 'A_set$',B: 'A_bool_fun$'] : ( A @ ( B @ ( A @ 'uux$' ) @ 'collect$h' @ 'less_eq$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(346,axiom,
! [A: 'A_b_fun$',B: 'A_set$',C: 'B_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'collect$i' )
= ( C @ ( B @ ( A @ 'uvq$' ) ) @ 'collect$h' @ ( A @ 'image$o' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).
thf(2140,plain,
! [A: 'A_b_fun$',B: 'A_set$',C: 'B_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvp$' ) ) @ 'collect$i' )
= ( C @ ( B @ ( A @ 'uvq$' ) ) @ 'collect$h' @ ( A @ 'image$o' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(565,axiom,
! [A: 'ZF_set_a_fun$',B: 'ZF_set_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwd$' ) ) @ 'fun_app$n' ) )
<=> ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$j' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom131) ).
thf(3162,plain,
! [A: 'ZF_set_a_fun$',B: 'ZF_set_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$j' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uwd$' ) ) @ 'fun_app$n' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uwd$' ) ) @ 'fun_app$n' ) )
=> ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$j' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(381,axiom,
! [A: 'A_a_fun$',B: 'A_set$',C: 'A_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'collect$h' )
= ( C @ ( B @ ( A @ 'uvm$' ) ) @ 'collect$h' @ ( A @ 'image$p' @ 'fun_app$bh' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom541) ).
thf(2285,plain,
! [A: 'A_a_fun$',B: 'A_set$',C: 'A_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvl$' ) ) @ 'collect$h' )
= ( C @ ( B @ ( A @ 'uvm$' ) ) @ 'collect$h' @ ( A @ 'image$p' @ 'fun_app$bh' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(125,axiom,
! [A: 'ZF_ZF_fun$'] :
( ( A @ 'uwv$' @ 'collect$' )
= ( 'top$a' @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom588) ).
thf(1114,plain,
! [A: 'ZF_ZF_fun$'] :
( ( A @ 'uwv$' @ 'collect$' )
= ( 'top$a' @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(423,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( D @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom333) ).
thf(2450,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( D @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(89,axiom,
! [A: 'ZF$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ? [D: 'Nat$'] :
( ( D @ ( B @ 'fun_app$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$e' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom647) ).
thf(985,plain,
! [A: 'ZF$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( ? [D: 'Nat$'] :
( ( D @ ( B @ 'fun_app$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$e' ) ) )
=> ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ? [D: 'Nat$'] :
( ( D @ ( B @ 'fun_app$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$e' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(213,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ 'collect$' @ ( B @ 'image$g' @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom520) ).
thf(1530,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ 'collect$' @ ( B @ 'image$g' @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(201,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom212) ).
thf(1456,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(316,axiom,
! [A: 'B_ZF_set_fun$',B: 'B_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( A @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom680) ).
thf(2006,plain,
! [A: 'B_ZF_set_fun$',B: 'B_set$',C: 'ZF_set$'] :
( ( ! [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( A @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( A @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(28,axiom,
! [A: 'ZF_set$',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',axiom208) ).
thf(721,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$a' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(511,axiom,
! [A: 'A_set$',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$' ) ) ) ) ) ) @ 'dom$' )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom201) ).
thf(2926,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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) @ 'dom$' )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(261,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> $false )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom459) ).
thf(1779,plain,
! [A: 'ZF$',B: 'ZF$'] :
~ ( ~ ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(362,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom374) ).
thf(2208,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(322,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( C @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom328) ).
thf(2043,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( C @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(246,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom290) ).
thf(1695,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(80,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uus$' @ 'fun_app$b' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom458) ).
thf(921,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uus$' @ 'fun_app$b' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(10,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uvc$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) @ ( A @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).
thf(657,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uvc$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) @ ( A @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(40,axiom,
! [A: 'ZF_ZF_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) )
= ( C @ ( B @ ( A @ 'uzm$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom745) ).
thf(765,plain,
! [A: 'ZF_ZF_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) )
= ( C @ ( B @ ( A @ 'uzm$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(137,axiom,
! [A: 'B_set$'] :
( ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'collect$i' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom280) ).
thf(1170,plain,
! [A: 'B_set$'] :
( ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'collect$i' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(336,axiom,
! [A: 'ZF_set$',B: 'B$',C: 'ZF_b_set_fun$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$cw' ) @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( A @ ( C @ 'image$ap' ) @ 'inf$b' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom820) ).
thf(2089,plain,
! [A: 'ZF_set$',B: 'B$',C: 'ZF_b_set_fun$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$cw' ) @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( A @ ( C @ 'image$ap' ) @ 'inf$b' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(14,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uzc$' @ 'fun_app$ab' ) @ 'fun_app$r' ) )
= ( B @ ( C @ ( A @ 'fun_app$ac' ) @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom61) ).
thf(674,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uzc$' @ 'fun_app$ab' ) @ 'fun_app$r' ) )
= ( B @ ( C @ ( A @ 'fun_app$ac' ) @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(421,axiom,
! [A: 'ZF_set_a_fun$',B: 'ZF_set_set$',C: 'A_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uwd$' ) ) @ 'collect$h' )
= ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'collect$j' @ ( A @ 'image$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).
thf(2440,plain,
! [A: 'ZF_set_a_fun$',B: 'ZF_set_set$',C: 'A_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uwd$' ) ) @ 'collect$h' )
= ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'collect$j' @ ( A @ 'image$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(461,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( A @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom706) ).
thf(2662,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( A @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'ZF$'] :
( ( B @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( A @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(141,axiom,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyz$' @ 'fun_app$ac' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'fun_app$ab' ) @ 'fun_app$r' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).
thf(1185,plain,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyz$' @ 'fun_app$ac' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'fun_app$ab' ) @ 'fun_app$r' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(43,axiom,
! [A: 'Nat_set$',B: 'ZF_set$',C: 'Nat_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ? [F: 'ZF$'] :
( ( F @ ( D @ 'fun_app$s' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$' @ 'fun_app$h' ) ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom659) ).
thf(773,plain,
! [A: 'Nat_set$',B: 'ZF_set$',C: 'Nat_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ? [F: 'ZF$'] :
( ( F @ ( D @ 'fun_app$s' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$' @ 'fun_app$h' ) ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(50,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'vaj$' ) @ 'fun_app$s' ) )
= ( C @ ( C @ ( B @ 'fun_app$' ) @ ( A @ 'fun_app$ad' ) @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).
thf(794,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'vaj$' ) @ 'fun_app$s' ) )
= ( C @ ( C @ ( B @ 'fun_app$' ) @ ( A @ 'fun_app$ad' ) @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(313,axiom,
! [A: 'ZF$',B: 'Nat_ZF_fun$'] :
( ( ! [C: 'Nat$'] :
( ( A
= ( C @ ( B @ 'fun_app$aj' ) ) )
=> $false )
& ( 'top$' @ ( B @ 'image$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom572) ).
thf(1996,plain,
! [A: 'ZF$',B: 'Nat_ZF_fun$'] :
~ ( ! [C: 'Nat$'] :
( A
!= ( C @ ( B @ 'fun_app$aj' ) ) )
& ( 'top$' @ ( B @ 'image$r' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(415,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( D @ ( C @ ( B @ ( A @ 'makeCat$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).
thf(2423,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( D @ ( C @ ( B @ ( A @ 'makeCat$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(27,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uwb$' ) ) @ 'collect$' )
= ( C @ ( B @ ( A @ 'uwc$' ) ) @ 'collect$' @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).
thf(718,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uwb$' ) ) @ 'collect$' )
= ( C @ ( B @ ( A @ 'uwc$' ) ) @ 'collect$' @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(291,axiom,
! [A: 'B$',B: 'B_b_set_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> $false )
& ( C @ ( B @ 'image$an' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom734) ).
thf(1906,plain,
! [A: 'B$',B: 'B_b_set_fun$',C: 'B_set$'] :
~ ( ! [D: 'B$'] :
~ ( ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
& ( C @ ( B @ 'image$an' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(150,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' )
= ( A @ 'more$a' @ ( A @ 'uue$' @ ( A @ 'id$a' @ ( A @ 'dom$a' @ ( A @ 'cod$a' @ ( A @ 'mor$a' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom377) ).
thf(1219,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' )
= ( A @ 'more$a' @ ( A @ 'uue$' @ ( A @ 'id$a' @ ( A @ 'dom$a' @ ( A @ 'cod$a' @ ( A @ 'mor$a' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(67,axiom,
! [A: 'Nat_ZF_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'uwx$' @ 'fun_app$f' ) )
<=> ? [C: 'Nat$'] :
( B
= ( C @ ( A @ 'fun_app$aj' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).
thf(856,plain,
! [A: 'Nat_ZF_fun$',B: 'ZF$'] :
( ( ? [C: 'Nat$'] :
( B
= ( C @ ( A @ 'fun_app$aj' ) ) )
=> ( B @ ( A @ 'uwx$' @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ 'uwx$' @ 'fun_app$f' ) )
=> ? [C: 'Nat$'] :
( B
= ( C @ ( A @ 'fun_app$aj' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(222,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$' @ 'fun_app$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom222) ).
thf(1595,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$' @ 'fun_app$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(405,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uug$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
thf(2376,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( A = B )
=> ( B @ ( A @ ( 'uug$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ ( 'uug$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(31,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ( ! [E: 'ZF$'] :
( ( B @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( ( E @ ( C @ 'fun_app$s' ) )
= ( E @ ( D @ 'fun_app$s' ) ) ) )
& ( A = B ) )
=> ( ( C @ ( A @ 'sigma$' ) )
= ( D @ ( B @ 'sigma$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom603) ).
thf(733,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ( ! [E: 'ZF$'] :
( ( B @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( ( E @ ( C @ 'fun_app$s' ) )
= ( E @ ( D @ 'fun_app$s' ) ) ) )
& ( A = B ) )
=> ( ( C @ ( A @ 'sigma$' ) )
= ( D @ ( B @ 'sigma$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(373,axiom,
! [A: 'ZF_set$',B: 'ZF_bool_fun$'] : ( A @ ( B @ ( A @ 'uva$' ) @ 'collect$' @ 'less_eq$c' @ 'fun_app$h' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).
thf(2260,plain,
! [A: 'ZF_set$',B: 'ZF_bool_fun$'] : ( A @ ( B @ ( A @ 'uva$' ) @ 'collect$' @ 'less_eq$c' @ 'fun_app$h' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(342,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$' )
=> ( A @ 'identityFunctor$' @ 'functorM$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).
thf(2121,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$' )
=> ( A @ 'identityFunctor$' @ 'functorM$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(368,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom357) ).
thf(2235,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(513,axiom,
! [A: 'A$',B: 'ZF_a_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( ( D @ ( B @ 'fun_app$cv' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> $false )
& ( C @ ( B @ 'image$ao' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom732) ).
thf(2936,plain,
! [A: 'A$',B: 'ZF_a_set_fun$',C: 'ZF_set$'] :
~ ( ! [D: 'ZF$'] :
~ ( ( D @ ( B @ 'fun_app$cv' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
& ( C @ ( B @ 'image$ao' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(130,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$f' ) ) )
=> ( A @ 'the$' @ ( A @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom393) ).
thf(1135,plain,
! [A: 'ZF_bool_fun$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$f' ) ) )
=> ( A @ 'the$' @ ( A @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(35,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ ( A @ 'uvg$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$r' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom718) ).
thf(750,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ ( A @ 'uvg$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$r' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(209,axiom,
! [A: 'A_b_fun$',B: 'A_b_fun_bool_fun$'] :
( ( B @ 'collect$f' @ ( A @ 'member$i' ) )
<=> ( A @ ( B @ 'fun_app$cl' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).
thf(1510,plain,
! [A: 'A_b_fun$',B: 'A_b_fun_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$cl' ) )
=> ( B @ 'collect$f' @ ( A @ 'member$i' ) ) )
& ( ( B @ 'collect$f' @ ( A @ 'member$i' ) )
=> ( A @ ( B @ 'fun_app$cl' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(247,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom311) ).
thf(1698,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(435,axiom,
! [A: 'ZF$',B: 'B_ZF_set_fun$',C: 'B_set$'] :
( ( C @ ( B @ 'image$ar' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$cx' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom810) ).
thf(2556,plain,
! [A: 'ZF$',B: 'B_ZF_set_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$cx' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'image$ar' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'image$ar' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$cx' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(595,axiom,
'c$' @ 'mor$' @ ( 'f$' @ 'member$b' @ 'fun_app$m' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).
thf(3358,plain,
'c$' @ 'mor$' @ ( 'f$' @ 'member$b' @ 'fun_app$m' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(377,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) )
= ( C @ ( A @ 'lambda$' ) @ ( B @ ( A @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom627) ).
thf(2275,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) )
= ( C @ ( A @ 'lambda$' ) @ ( B @ ( A @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(349,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$'] :
( ( B @ ( A @ 'uyu$' @ 'fun_app$ae' ) )
= ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom34) ).
thf(2149,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$'] :
( ( B @ ( A @ 'uyu$' @ 'fun_app$ae' ) )
= ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(437,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyv$' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'fun_app$ad' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).
thf(2570,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyv$' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'fun_app$ad' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(514,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom308) ).
thf(2941,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 @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(568,axiom,
! [A: 'A_set$',B: 'A_set$',C: 'A_bool_fun$',D: 'A_bool_fun$'] :
( ( ! [E: 'A$'] :
( ( ( E @ ( C @ 'fun_app$n' ) )
& ( A @ ( E @ 'member$c' @ 'fun_app$p' ) ) )
=> ( E @ ( D @ 'fun_app$n' ) ) )
& ( B @ ( A @ 'less_eq$' ) ) )
=> ( D @ ( B @ 'uux$' ) @ 'collect$h' @ ( C @ ( A @ 'uux$' ) @ 'collect$h' @ 'less_eq$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).
thf(3234,plain,
! [A: 'A_set$',B: 'A_set$',C: 'A_bool_fun$',D: 'A_bool_fun$'] :
( ( ! [E: 'A$'] :
( ( ( E @ ( C @ 'fun_app$n' ) )
& ( A @ ( E @ 'member$c' @ 'fun_app$p' ) ) )
=> ( E @ ( D @ 'fun_app$n' ) ) )
& ( B @ ( A @ 'less_eq$' ) ) )
=> ( D @ ( B @ 'uux$' ) @ 'collect$h' @ ( C @ ( A @ 'uux$' ) @ 'collect$h' @ 'less_eq$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(489,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory_axioms$' )
<=> ( ( A @ 'mor$' @ 'extensional$e' @ ( A @ 'mor2ZF$' @ 'member$g' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) @ 'fun_app$co' ) @ 'member$a' @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom562) ).
thf(2789,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'mor$' @ 'extensional$e' @ ( A @ 'mor2ZF$' @ 'member$g' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) @ 'fun_app$co' ) @ 'member$a' @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B = C ) ) )
=> ( A @ 'lSCategory_axioms$' ) )
& ( ( A @ 'lSCategory_axioms$' )
=> ( ( A @ 'mor$' @ 'extensional$e' @ ( A @ 'mor2ZF$' @ 'member$g' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) @ 'fun_app$co' ) @ 'member$a' @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(235,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom447) ).
thf(1652,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(187,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$' )
=> ( A @ 'oppositeCategory$' @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom229) ).
thf(1388,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$' )
=> ( A @ 'oppositeCategory$' @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(528,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$b' @ ( A @ 'mor2ZF$' @ 'lSCategory_ext$' ) @ ( A @ 'comp$a' @ ( A @ 'id$' @ ( A @ 'cod$' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom422) ).
thf(2991,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$b' @ ( A @ 'mor2ZF$' @ 'lSCategory_ext$' ) @ ( A @ 'comp$a' @ ( A @ 'id$' @ ( A @ 'cod$' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(190,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$',D: 'ZF_set_ZF_set_fun$'] :
( ( ! [E: 'ZF_set$'] :
( ( A @ ( E @ 'member$a' @ 'fun_app$j' ) )
=> ( E @ ( D @ 'fun_app$ae' ) @ ( E @ ( C @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$b' ) ) )
=> ( B @ ( D @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom766) ).
thf(1403,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$',D: 'ZF_set_ZF_set_fun$'] :
( ( ! [E: 'ZF_set$'] :
( ( A @ ( E @ 'member$a' @ 'fun_app$j' ) )
=> ( E @ ( D @ 'fun_app$ae' ) @ ( E @ ( C @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$b' ) ) )
=> ( B @ ( D @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(160,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'vac$' @ 'image$bm' ) @ 'sup$j' @ 'fun_app$f' ) )
<=> ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom780) ).
thf(1256,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( B @ ( A @ 'vac$' @ 'image$bm' ) @ 'sup$j' @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'vac$' @ 'image$bm' ) @ 'sup$j' @ 'fun_app$f' ) )
=> ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(490,axiom,
'c$' @ 'lSCategory$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).
thf(2827,plain,
'c$' @ 'lSCategory$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(358,axiom,
! [A: 'ZF_set$',B: 'ZF_bool_fun$'] : ( A @ ( B @ ( A @ 'uva$' ) @ 'collect$' @ 'less_eq$c' @ 'fun_app$h' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom496) ).
thf(2188,plain,
! [A: 'ZF_set$',B: 'ZF_bool_fun$'] : ( A @ ( B @ ( A @ 'uva$' ) @ 'collect$' @ 'less_eq$c' @ 'fun_app$h' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(525,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( D @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom332) ).
thf(2981,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$' @ ( D @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(227,axiom,
! [A: 'Nat_ZF_fun$'] :
( ( A @ 'uwx$' @ 'collect$' )
= ( 'top$' @ ( A @ 'image$r' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom590) ).
thf(1620,plain,
! [A: 'Nat_ZF_fun$'] :
( ( A @ 'uwx$' @ 'collect$' )
= ( 'top$' @ ( A @ 'image$r' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(617,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorContra$a' ) @ 'mapO$' @ 'fun_app$bf' ) )
= ( B @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom454) ).
thf(3472,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorContra$a' ) @ 'mapO$' @ 'fun_app$bf' ) )
= ( B @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(58,axiom,
! [A: 'ZF_ZF_prod_ZF_fun$',B: 'ZF_ZF_prod_set$'] :
( ( B @ ( A @ 'uwl$' ) @ 'collect$' )
= ( B @ ( A @ 'image$f' @ 'fun_app$au' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom557) ).
thf(826,plain,
! [A: 'ZF_ZF_prod_ZF_fun$',B: 'ZF_ZF_prod_set$'] :
( ( B @ ( A @ 'uwl$' ) @ 'collect$' )
= ( B @ ( A @ 'image$f' @ 'fun_app$au' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(25,axiom,
! [A: 'Nat_set$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ( E @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$i' ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom688) ).
thf(711,plain,
! [A: 'Nat_set$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ( E @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$i' ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(211,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uud$' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).
thf(1520,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uud$' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(604,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$' )
= ( A @ 'more$' @ ( A @ 'uum$' @ ( A @ 'obj$' @ ( A @ 'id$' @ 'restrict$c' ) @ ( A @ 'mor$' @ ( A @ 'cod$' @ 'restrict$b' ) @ ( A @ 'mor$' @ ( A @ 'dom$' @ 'restrict$b' ) @ ( A @ 'mor$' @ ( A @ 'obj$' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).
thf(3404,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$' )
= ( A @ 'more$' @ ( A @ 'uum$' @ ( A @ 'obj$' @ ( A @ 'id$' @ 'restrict$c' ) @ ( A @ 'mor$' @ ( A @ 'cod$' @ 'restrict$b' ) @ ( A @ 'mor$' @ ( A @ 'dom$' @ 'restrict$b' ) @ ( A @ 'mor$' @ ( A @ 'obj$' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(262,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uzb$' ) @ 'fun_app$r' ) )
= ( B @ ( C @ ( A @ 'fun_app$ac' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).
thf(1786,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uzb$' ) @ 'fun_app$r' ) )
= ( B @ ( C @ ( A @ 'fun_app$ac' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(84,axiom,
! [A: 'ZF_set$',B: 'ZF_set$'] :
( ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ( B @ ( 'uuc$' @ 'fun_app$g' ) @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'less_eq$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom787) ).
thf(936,plain,
! [A: 'ZF_set$',B: 'ZF_set$'] :
( ( ( B @ ( 'uuc$' @ 'fun_app$g' ) @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'less_eq$l' ) )
=> ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( B @ ( 'uuc$' @ 'fun_app$g' ) @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'less_eq$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(162,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( A @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom703) ).
thf(1271,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF_set$'] :
( ( ! [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( A @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( A @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(47,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_bool_fun$'] : ( A @ ( B @ ( A @ 'uuz$' ) @ 'collect$j' @ 'less_eq$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom495) ).
thf(787,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_bool_fun$'] : ( A @ ( B @ ( A @ 'uuz$' ) @ 'collect$j' @ 'less_eq$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(156,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uur$' @ 'fun_app$' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom177) ).
thf(1239,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uur$' @ 'fun_app$' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(258,axiom,
! [A: 'ZF$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$s' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom811) ).
thf(1765,plain,
! [A: 'ZF$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$s' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$s' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(426,axiom,
! [A: 'ZF_set_ZF_fun$',B: 'ZF_set_set$'] :
( ( B @ ( A @ 'uwp$' ) @ 'collect$' )
= ( B @ ( A @ 'image$w' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).
thf(2457,plain,
! [A: 'ZF_set_ZF_fun$',B: 'ZF_set_set$'] :
( ( B @ ( A @ 'uwp$' ) @ 'collect$' )
= ( B @ ( A @ 'image$w' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(594,axiom,
! [A: 'A$',B: 'A_set$',C: 'A_ZF_set_fun$'] :
( ( B @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom699) ).
thf(3355,plain,
! [A: 'A$',B: 'A_set$',C: 'A_ZF_set_fun$'] :
( ( B @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(7,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ! [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 )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom471) ).
thf(641,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
~ ! [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)],[7]) ).
thf(352,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'oppositeCategory$' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom234) ).
thf(2161,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'oppositeCategory$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(109,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$a' )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom202) ).
thf(1058,plain,
! [A: 'ZF_set$',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)],[109]) ).
thf(123,axiom,
! [A: 'Nat_set$',B: 'Nat_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'Nat$'] :
( ( A @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( B @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom693) ).
thf(1107,plain,
! [A: 'Nat_set$',B: 'Nat_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'Nat$'] :
( ( A @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( B @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(621,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$b' )
= ( B @ 'more$b' ) )
& ( ( A @ 'mor2ZF$' )
= ( B @ 'mor2ZF$' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$' )
= ( B @ 'id$' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$' )
= ( B @ 'obj$' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).
thf(3487,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$b' )
= ( B @ 'more$b' ) )
& ( ( A @ 'mor2ZF$' )
= ( B @ 'mor2ZF$' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$' )
= ( B @ 'id$' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$' )
= ( B @ 'obj$' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(118,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'the$' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom390) ).
thf(1092,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uuf$' @ 'fun_app$q' ) @ 'the$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(416,axiom,
( 'set$'
= ( 'set$a' @ 'makeCat$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).
thf(2425,plain,
( 'set$'
= ( 'set$a' @ 'makeCat$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(608,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$d' ) ) @ 'functor$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom387) ).
thf(3416,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$d' ) ) @ 'functor$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(438,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) )
= ( C @ ( B @ ( A @ 'uzl$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom744) ).
thf(2573,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) )
= ( C @ ( B @ ( A @ 'uzl$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(401,axiom,
! [A: 'ZF_set_set$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uuc$' @ 'image$bk' ) @ 'sup$j' @ 'fun_app$f' ) )
<=> ( A @ ( 'sup$' @ 'fun_app$u' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom778) ).
thf(2358,plain,
! [A: 'ZF_set_set$',B: 'ZF$'] :
( ( ( A @ ( 'sup$' @ 'fun_app$u' ) @ ( B @ 'member$' @ 'fun_app$h' ) )
=> ( B @ ( A @ ( 'uuc$' @ 'image$bk' ) @ 'sup$j' @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ ( 'uuc$' @ 'image$bk' ) @ 'sup$j' @ 'fun_app$f' ) )
=> ( A @ ( 'sup$' @ 'fun_app$u' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(87,axiom,
! [A: 'B_set_set$'] :
( ( A @ 'sup$c' )
= ( A @ 'vae$' @ 'collect$i' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom782) ).
thf(979,plain,
! [A: 'B_set_set$'] :
( ( A @ 'sup$c' )
= ( A @ 'vae$' @ 'collect$i' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(143,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'vai$' @ 'fun_app$s' ) )
= ( 'top$a' @ ( B @ ( A @ 'uyw$' @ 'fun_app$ad' ) @ 'image$a' @ 'fun_app$x' ) @ 'inf$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom29) ).
thf(1194,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'vai$' @ 'fun_app$s' ) )
= ( 'top$a' @ ( B @ ( A @ 'uyw$' @ 'fun_app$ad' ) @ 'image$a' @ 'fun_app$x' ) @ 'inf$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(333,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$'] :
( ( ! [C: 'ZF$'] :
( ( A
= ( C @ ( B @ 'fun_app$' ) ) )
=> $false )
& ( 'top$a' @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom568) ).
thf(2079,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$'] :
~ ( ! [C: 'ZF$'] :
( A
!= ( C @ ( B @ 'fun_app$' ) ) )
& ( 'top$a' @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(550,axiom,
'c$' @ 'mor$' @ ( 'g$' @ 'member$b' @ 'fun_app$m' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom188) ).
thf(3101,plain,
'c$' @ 'mor$' @ ( 'g$' @ 'member$b' @ 'fun_app$m' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(451,axiom,
! [A: 'B$',B: 'B_set$',C: 'B$',D: 'B_b_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cu' ) @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B @ ( D @ 'image$an' ) @ 'sup$c' @ ( C @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom634) ).
thf(2624,plain,
! [A: 'B$',B: 'B_set$',C: 'B$',D: 'B_b_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cu' ) @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B @ ( D @ 'image$an' ) @ 'sup$c' @ ( C @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(413,axiom,
! [A: 'A_set$',B: 'ZF_set$',C: 'A_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ? [F: 'ZF$'] :
( ( F @ ( D @ 'fun_app$s' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$' @ 'fun_app$h' ) ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom663) ).
thf(2415,plain,
! [A: 'A_set$',B: 'ZF_set$',C: 'A_ZF_set_fun$',D: 'ZF_ZF_set_fun$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ? [F: 'ZF$'] :
( ( F @ ( D @ 'fun_app$s' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$' @ 'fun_app$h' ) ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(268,axiom,
! [A: 'B$',B: 'B_bool_fun$'] :
( ( B @ 'collect$i' @ ( A @ 'member$b' @ 'fun_app$m' ) )
<=> ( A @ ( B @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom276) ).
thf(1806,plain,
! [A: 'B$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$k' ) )
=> ( B @ 'collect$i' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
& ( ( B @ 'collect$i' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ ( B @ 'fun_app$k' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(106,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 )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom226) ).
thf(1048,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
~ ! [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)],[106]) ).
thf(132,axiom,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat$'] :
( ( B @ ( A @ 'val$' @ 'fun_app$r' ) )
= ( 'top$a' @ ( B @ ( A @ 'uyz$' @ 'fun_app$ac' ) @ 'image$a' @ 'fun_app$x' ) @ 'inf$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).
thf(1144,plain,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat$'] :
( ( B @ ( A @ 'val$' @ 'fun_app$r' ) )
= ( 'top$a' @ ( B @ ( A @ 'uyz$' @ 'fun_app$ac' ) @ 'image$a' @ 'fun_app$x' ) @ 'inf$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(494,axiom,
! [A: 'B_set$',B: 'A$',C: 'B_a_set_fun$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$ct' ) @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( A @ ( C @ 'image$am' ) @ 'inf$a' @ ( B @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom816) ).
thf(2839,plain,
! [A: 'B_set$',B: 'A$',C: 'B_a_set_fun$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$ct' ) @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( A @ ( C @ 'image$am' ) @ 'inf$a' @ ( B @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(625,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'id$' @ 'fun_app$bl' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom337) ).
thf(3500,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'id$' @ 'fun_app$bl' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(601,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
<=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom314) ).
thf(3384,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
& ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(184,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
<=> ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom343) ).
thf(1376,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) )
=> ( A @ 'lSCategory$' ) )
& ( ( A @ 'lSCategory$' )
=> ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(454,axiom,
! [A: 'A_set$'] :
( ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'collect$h' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom279) ).
thf(2637,plain,
! [A: 'A_set$'] :
( ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'collect$h' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(126,axiom,
! [A: 'Nat_set$',B: 'Nat_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ( D @ ( E @ ( B @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'Nat$'] :
( ( A @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( B @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom651) ).
thf(1117,plain,
! [A: 'Nat_set$',B: 'Nat_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ( D @ ( E @ ( B @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'Nat$'] :
( ( A @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( B @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(372,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom456) ).
thf(2257,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(221,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set$'] :
( ( B @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'fun_app$h' ) )
<=> ( A @ ( B @ 'member$a' @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).
thf(1589,plain,
! [A: 'ZF_set_set$',B: 'ZF_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'fun_app$j' ) )
=> ( B @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'fun_app$h' ) ) )
& ( ( B @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'fun_app$h' ) )
=> ( A @ ( B @ 'member$a' @ 'fun_app$j' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(360,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$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> $false )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom313) ).
thf(2197,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(306,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom315) ).
thf(1969,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(170,axiom,
! [A: 'A_ZF_fun$',B: 'A_set$',C: 'ZF_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvx$' ) ) @ 'collect$' )
= ( C @ ( B @ ( A @ 'uvy$' ) ) @ 'collect$h' @ ( A @ 'image$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom547) ).
thf(1307,plain,
! [A: 'A_ZF_fun$',B: 'A_set$',C: 'ZF_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvx$' ) ) @ 'collect$' )
= ( C @ ( B @ ( A @ 'uvy$' ) ) @ 'collect$h' @ ( A @ 'image$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(285,axiom,
! [A: 'Nat_set$',B: 'B_set$',C: 'Nat_ZF_set_fun$',D: 'B_ZF_set_fun$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ? [F: 'B$'] :
( ( F @ ( D @ 'fun_app$cx' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$b' @ 'fun_app$m' ) ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom658) ).
thf(1877,plain,
! [A: 'Nat_set$',B: 'B_set$',C: 'Nat_ZF_set_fun$',D: 'B_ZF_set_fun$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ? [F: 'B$'] :
( ( F @ ( D @ 'fun_app$cx' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$b' @ 'fun_app$m' ) ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(115,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ ( A @ 'uys$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom723) ).
thf(1080,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ ( A @ 'uys$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(478,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$a' @ 'mor$a' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).
thf(2742,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$a' @ 'mor$a' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(536,axiom,
! [A: 'B$',B: 'A_b_set_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( ( D @ ( B @ 'fun_app$cs' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> $false )
& ( C @ ( B @ 'image$al' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom733) ).
thf(3027,plain,
! [A: 'B$',B: 'A_b_set_fun$',C: 'A_set$'] :
~ ( ! [D: 'A$'] :
~ ( ( D @ ( B @ 'fun_app$cs' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
& ( C @ ( B @ 'image$al' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(229,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).
thf(1630,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(271,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ ( A @ 'uyr$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom756) ).
thf(1821,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ ( A @ 'uyr$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(136,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( A @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom678) ).
thf(1162,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF_set$'] :
( ( ! [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( A @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
=> ( C @ ( D @ ( A @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(22,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_set$',D: 'B_bool_fun$'] :
( ( ( D @ ( C @ 'uuy$' ) @ 'collect$i' @ ( B @ 'less_eq$a' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( A @ ( D @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).
thf(700,plain,
! [A: 'B$',B: 'B_set$',C: 'B_set$',D: 'B_bool_fun$'] :
( ( ( D @ ( C @ 'uuy$' ) @ 'collect$i' @ ( B @ 'less_eq$a' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( A @ ( D @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(175,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$'] :
( ( 'top$a' @ ( A @ 'vai$' @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( 'top$f' @ ( A @ 'vak$' @ 'image$bn' ) @ 'inf$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom794) ).
thf(1325,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$'] :
( ( 'top$a' @ ( A @ 'vai$' @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( 'top$f' @ ( A @ 'vak$' @ 'image$bn' ) @ 'inf$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(532,axiom,
! [A: 'A$',B: 'ZF_a_fun$'] :
( ( ! [C: 'ZF$'] :
( ( A
= ( C @ ( B @ 'fun_app$bi' ) ) )
=> $false )
& ( 'top$a' @ ( B @ 'image$i' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom566) ).
thf(3006,plain,
! [A: 'A$',B: 'ZF_a_fun$'] :
~ ( ! [C: 'ZF$'] :
( A
!= ( C @ ( B @ 'fun_app$bi' ) ) )
& ( 'top$a' @ ( B @ 'image$i' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(472,axiom,
! [A: 'B_ZF_set_fun$',B: 'B_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( A @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom705) ).
thf(2710,plain,
! [A: 'B_ZF_set_fun$',B: 'B_set$',C: 'ZF_set$'] :
( ( ! [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( A @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'B$'] :
( ( B @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( A @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(244,axiom,
! [A: 'B_set$',B: 'B_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( B @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom668) ).
thf(1688,plain,
! [A: 'B_set$',B: 'B_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( B @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(75,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_set$',C: 'ZF_set_bool_fun$'] :
( ( B @ ( A @ 'less_eq$b' ) )
=> ( ( C @ ( B @ 'uuz$' ) @ 'collect$j' @ ( A @ 'less_eq$b' ) )
<=> ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( D @ ( C @ 'fun_app$h' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).
thf(890,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_set$',C: 'ZF_set_bool_fun$'] :
( ( B @ ( A @ 'less_eq$b' ) )
=> ( ( ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( D @ ( C @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'uuz$' ) @ 'collect$j' @ ( A @ 'less_eq$b' ) ) )
& ( ( C @ ( B @ 'uuz$' ) @ 'collect$j' @ ( A @ 'less_eq$b' ) )
=> ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( D @ ( C @ 'fun_app$h' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(239,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'vab$' @ 'image$bl' ) @ 'sup$j' @ 'fun_app$f' ) )
<=> ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom779) ).
thf(1667,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( B @ ( A @ 'vab$' @ 'image$bl' ) @ 'sup$j' @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'vab$' @ 'image$bl' ) @ 'sup$j' @ 'fun_app$f' ) )
=> ( B @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(165,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$r' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( C @ ( B @ ( A @ 'uvg$' ) @ 'image$' @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom536) ).
thf(1293,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$r' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( C @ ( B @ ( A @ 'uvg$' ) @ 'image$' @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(378,axiom,
! [A: 'ZF$'] : ( 'set$' @ 'obj$a' @ ( A @ 'member$' @ 'fun_app$h' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom406) ).
thf(2278,plain,
! [A: 'ZF$'] : ( 'set$' @ 'obj$a' @ ( A @ 'member$' @ 'fun_app$h' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(12,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'vao$' @ 'fun_app$s' ) )
= ( 'top$' @ ( B @ ( A @ 'uzc$' @ 'fun_app$ab' ) @ 'image$' @ 'fun_app$v' ) @ 'inf$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).
thf(668,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'vao$' @ 'fun_app$s' ) )
= ( 'top$' @ ( B @ ( A @ 'uzc$' @ 'fun_app$ab' ) @ 'image$' @ 'fun_app$v' ) @ 'inf$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(110,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'vay$' @ 'fun_app$s' ) )
= ( 'top$' @ ( B @ ( A @ 'uzc$' @ 'fun_app$ab' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
thf(1061,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'vay$' @ 'fun_app$s' ) )
= ( 'top$' @ ( B @ ( A @ 'uzc$' @ 'fun_app$ab' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(300,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom246) ).
thf(1952,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(79,axiom,
! [A: tlbool,B: 'ZF$',C: 'ZF$'] :
( ( ( A != tltrue )
=> ( C
= ( C @ ( B @ ( A @ 'uuh$' ) @ 'fun_app$q' ) @ 'the$' ) ) )
& ( ( A = tltrue )
=> ( B
= ( C @ ( B @ ( A @ 'uuh$' ) @ 'fun_app$q' ) @ 'the$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).
thf(912,plain,
! [A: tlbool,B: 'ZF$',C: 'ZF$'] :
( ( ( A != tltrue )
=> ( C
= ( C @ ( B @ ( A @ 'uuh$' ) @ 'fun_app$q' ) @ 'the$' ) ) )
& ( ( A = tltrue )
=> ( B
= ( C @ ( B @ ( A @ 'uuh$' ) @ 'fun_app$q' ) @ 'the$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(409,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'explode$' @ 'fun_app$s' ) )
= ( A @ ( 'uwy$' @ 'fun_app$q' ) @ 'collect$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom591) ).
thf(2401,plain,
! [A: 'ZF$'] :
( ( A @ ( 'explode$' @ 'fun_app$s' ) )
= ( A @ ( 'uwy$' @ 'fun_app$q' ) @ 'collect$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(611,axiom,
! [A: 'A_set$',B: 'A_bool_fun$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'uux$' ) @ 'fun_app$n' ) )
<=> ( ( C @ ( B @ 'fun_app$n' ) )
& ( A @ ( C @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).
thf(3423,plain,
! [A: 'A_set$',B: 'A_bool_fun$',C: 'A$'] :
( ( ( ( C @ ( B @ 'fun_app$n' ) )
& ( A @ ( C @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( B @ ( A @ 'uux$' ) @ 'fun_app$n' ) ) )
& ( ( C @ ( B @ ( A @ 'uux$' ) @ 'fun_app$n' ) )
=> ( ( C @ ( B @ 'fun_app$n' ) )
& ( A @ ( C @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(328,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'unitFunctor$' @ 'functor$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom392) ).
thf(2064,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'unitFunctor$' @ 'functor$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(382,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) )
=> ( A @ 'lSCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom344) ).
thf(2288,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) )
=> ( A @ 'lSCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(570,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'obj$' )
= ( A @ 'obj$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).
thf(3241,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' @ 'obj$' )
= ( A @ 'obj$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(93,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_set$'] :
( ( B @ ( 'uub$' @ 'fun_app$i' ) @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'less_eq$m' ) )
<=> ( B @ ( A @ 'less_eq$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom792) ).
thf(1000,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_set$'] :
( ( ( B @ ( A @ 'less_eq$b' ) )
=> ( B @ ( 'uub$' @ 'fun_app$i' ) @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'less_eq$m' ) ) )
& ( ( B @ ( 'uub$' @ 'fun_app$i' ) @ ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'less_eq$m' ) )
=> ( B @ ( A @ 'less_eq$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(453,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$',D: 'ZF_set_ZF_set_fun$'] :
( ( ! [E: 'ZF_set$'] :
( ( A @ ( E @ 'member$a' @ 'fun_app$j' ) )
=> ( E @ ( D @ 'fun_app$ae' ) @ ( E @ ( C @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$b' ) ) )
=> ( B @ ( D @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom692) ).
thf(2633,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$',D: 'ZF_set_ZF_set_fun$'] :
( ( ! [E: 'ZF_set$'] :
( ( A @ ( E @ 'member$a' @ 'fun_app$j' ) )
=> ( E @ ( D @ 'fun_app$ae' ) @ ( E @ ( C @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$b' ) ) )
=> ( B @ ( D @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(386,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_nat_fun$'] :
( ( B @ ( A @ 'vaq$' @ 'fun_app$w' ) )
= ( 'top$a' @ ( B @ ( A @ 'vap$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
thf(2303,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_nat_fun$'] :
( ( B @ ( A @ 'vaq$' @ 'fun_app$w' ) )
= ( 'top$a' @ ( B @ ( A @ 'vap$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(296,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$'] :
( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
<=> ( C @ ( B @ 'fun_app$f' ) ) )
=> ( ( A @ 'collect$' )
= ( B @ 'collect$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom283) ).
thf(1926,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$'] :
( ! [C: 'ZF$'] :
( ( ( C @ ( B @ 'fun_app$f' ) )
=> ( C @ ( A @ 'fun_app$f' ) ) )
& ( ( C @ ( A @ 'fun_app$f' ) )
=> ( C @ ( B @ 'fun_app$f' ) ) ) )
=> ( ( A @ 'collect$' )
= ( B @ 'collect$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(520,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$a' ) @ 'mapO$' @ 'fun_app$bf' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).
thf(2962,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$a' ) @ 'mapO$' @ 'fun_app$bf' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(148,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_fun$'] :
( ( 'top$' @ ( B @ ( A @ 'uvg$' ) @ 'image$' @ 'fun_app$v' ) )
= ( 'top$' @ ( B @ 'image$r' ) @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom576) ).
thf(1213,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_fun$'] :
( ( 'top$' @ ( B @ ( A @ 'uvg$' ) @ 'image$' @ 'fun_app$v' ) )
= ( 'top$' @ ( B @ 'image$r' ) @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(41,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$a' )
= ( A @ 'more$a' @ ( A @ 'uun$' @ ( A @ 'obj$a' @ ( A @ 'id$a' @ 'restrict$d' ) @ ( A @ 'mor$a' @ ( A @ 'cod$a' @ 'restrict$d' ) @ ( A @ 'mor$a' @ ( A @ 'dom$a' @ 'restrict$d' ) @ ( A @ 'mor$a' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom417) ).
thf(768,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'makeCat$a' )
= ( A @ 'more$a' @ ( A @ 'uun$' @ ( A @ 'obj$a' @ ( A @ 'id$a' @ 'restrict$d' ) @ ( A @ 'mor$a' @ ( A @ 'cod$a' @ 'restrict$d' ) @ ( A @ 'mor$a' @ ( A @ 'dom$a' @ 'restrict$d' ) @ ( A @ 'mor$a' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(554,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'A$',D: 'ZF_a_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cv' ) @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$ao' ) @ 'sup$b' @ ( C @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom635) ).
thf(3110,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'A$',D: 'ZF_a_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cv' ) @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$ao' ) @ 'sup$b' @ ( C @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(335,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$'] :
( ( 'top$a' @ ( A @ 'vay$' @ 'image$a' @ 'fun_app$x' ) @ 'inf$' )
= ( 'top$h' @ ( A @ 'vaz$' @ 'image$bp' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom800) ).
thf(2086,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$'] :
( ( 'top$a' @ ( A @ 'vay$' @ 'image$a' @ 'fun_app$x' ) @ 'inf$' )
= ( 'top$h' @ ( A @ 'vaz$' @ 'image$bp' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(45,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( C @ ( B @ ( A @ 'uvf$' ) @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).
thf(780,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( C @ ( B @ ( A @ 'uvf$' ) @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(233,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'vab$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( B @ ( A @ 'fun_app$s' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).
thf(1643,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF$',C: 'ZF$'] :
( ( ( B @ ( A @ 'fun_app$s' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( B @ ( A @ 'vab$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'vab$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( B @ ( A @ 'fun_app$s' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(522,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$b' ) ) @ 'preFunctor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).
thf(2967,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( B @ 'category$' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$b' ) ) @ 'preFunctor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(158,axiom,
! [A: 'Nat$',B: 'Nat_set$',C: 'ZF_set$',D: 'Nat_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$r' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$e' ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom683) ).
thf(1250,plain,
! [A: 'Nat$',B: 'Nat_set$',C: 'ZF_set$',D: 'Nat_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$r' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$e' ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(622,axiom,
! [A: 'A$',B: 'Nat_a_fun$'] :
( ( ! [C: 'Nat$'] :
( ( A
= ( C @ ( B @ 'fun_app$cp' ) ) )
=> $false )
& ( 'top$' @ ( B @ 'image$x' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom570) ).
thf(3490,plain,
! [A: 'A$',B: 'Nat_a_fun$'] :
~ ( ! [C: 'Nat$'] :
( A
!= ( C @ ( B @ 'fun_app$cp' ) ) )
& ( 'top$' @ ( B @ 'image$x' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(600,axiom,
! [A: 'ZF_set$',B: 'A$',C: 'ZF_a_set_fun$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$cv' ) @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( A @ ( C @ 'image$ao' ) @ 'inf$a' @ ( B @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom819) ).
thf(3380,plain,
! [A: 'ZF_set$',B: 'A$',C: 'ZF_a_set_fun$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$cv' ) @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( A @ ( C @ 'image$ao' ) @ 'inf$a' @ ( B @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(102,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'category_axioms$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom334) ).
thf(1034,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'category_axioms$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(257,axiom,
! [A: 'A_ZF_fun$',B: 'A_set$',C: 'ZF_bool_fun$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) @ 'fun_app$f' ) )
<=> ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$n' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom135) ).
thf(1758,plain,
! [A: 'A_ZF_fun$',B: 'A_set$',C: 'ZF_bool_fun$',D: 'ZF$'] :
( ( ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$n' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvx$' ) ) @ 'fun_app$f' ) )
=> ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$n' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(529,axiom,
! [A: 'A_set$',B: 'B_set$',C: 'A_ZF_set_fun$',D: 'B_ZF_set_fun$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ? [F: 'B$'] :
( ( F @ ( D @ 'fun_app$cx' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$b' @ 'fun_app$m' ) ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom662) ).
thf(2994,plain,
! [A: 'A_set$',B: 'B_set$',C: 'A_ZF_set_fun$',D: 'B_ZF_set_fun$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ? [F: 'B$'] :
( ( F @ ( D @ 'fun_app$cx' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$b' @ 'fun_app$m' ) ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(9,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uwj$' ) @ 'fun_app$h' ) )
<=> ? [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
& ( C
= ( D @ ( A @ 'fun_app$r' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom120) ).
thf(648,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF_set$'] :
( ( ? [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
& ( C
= ( D @ ( A @ 'fun_app$r' ) ) ) )
=> ( C @ ( B @ ( A @ 'uwj$' ) @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'uwj$' ) @ 'fun_app$h' ) )
=> ? [D: 'Nat$'] :
( ( B @ ( D @ 'member$e' ) )
& ( C
= ( D @ ( A @ 'fun_app$r' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(311,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$e' ) ) @ 'functor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).
thf(1990,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$e' ) ) @ 'functor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(391,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( A
= ( D @ ( B @ 'fun_app$' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).
thf(2318,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
~ ( ! [D: 'ZF$'] :
~ ( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
& ( A
= ( D @ ( B @ 'fun_app$' ) ) ) )
& ( C @ ( B @ 'image$g' @ 'fun_app$ae' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(16,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_fun$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uvg$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$aj' ) @ ( A @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom95) ).
thf(680,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_fun$',C: 'Nat$'] :
( ( C @ ( B @ ( A @ 'uvg$' ) @ 'fun_app$r' ) )
= ( C @ ( B @ 'fun_app$aj' ) @ ( A @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(82,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' @ 'obj$a' )
= ( A @ 'obj$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom190) ).
thf(927,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' @ 'obj$a' )
= ( A @ 'obj$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(321,axiom,
! [A: 'A_set$',B: 'A_set$'] :
( ( B @ ( A @ 'less_eq$' ) )
<=> ( B @ ( 'uu$' @ 'fun_app$o' ) @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'less_eq$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom785) ).
thf(2037,plain,
! [A: 'A_set$',B: 'A_set$'] :
( ( ( B @ ( 'uu$' @ 'fun_app$o' ) @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'less_eq$j' ) )
=> ( B @ ( A @ 'less_eq$' ) ) )
& ( ( B @ ( A @ 'less_eq$' ) )
=> ( B @ ( 'uu$' @ 'fun_app$o' ) @ ( A @ ( 'uu$' @ 'fun_app$o' ) @ 'less_eq$j' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(395,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'isomorphism$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom369) ).
thf(2333,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'isomorphism$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(436,axiom,
! [A: 'ZF_set_set_set$',B: 'ZF_set$'] :
( ( B @ ( A @ 'vaf$' @ 'fun_app$h' ) )
<=> ( A @ ( B @ 'member$a' @ 'image$c' ) @ 'sup$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).
thf(2564,plain,
! [A: 'ZF_set_set_set$',B: 'ZF_set$'] :
( ( ( A @ ( B @ 'member$a' @ 'image$c' ) @ 'sup$a' )
=> ( B @ ( A @ 'vaf$' @ 'fun_app$h' ) ) )
& ( ( B @ ( A @ 'vaf$' @ 'fun_app$h' ) )
=> ( A @ ( B @ 'member$a' @ 'image$c' ) @ 'sup$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(443,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'makeCat$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( C @ ( B @ ( A @ 'makeCat$a' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom293) ).
thf(2597,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'makeCat$a' @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( C @ ( B @ ( A @ 'makeCat$a' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(303,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_set$',D: 'ZF_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$s' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom686) ).
thf(1958,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_set$',D: 'ZF_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$s' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( B @ ( D @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(139,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_bool_fun$'] : ( A @ ( B @ ( A @ 'uuz$' ) @ 'collect$j' @ 'less_eq$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom499) ).
thf(1181,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_bool_fun$'] : ( A @ ( B @ ( A @ 'uuz$' ) @ 'collect$j' @ 'less_eq$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(57,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ! [D: 'Nat$'] : ( D @ ( B @ 'fun_app$r' ) @ ( D @ ( A @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom672) ).
thf(823,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ! [D: 'Nat$'] : ( D @ ( B @ 'fun_app$r' ) @ ( D @ ( A @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ ( A @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(277,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uue$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).
thf(1845,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uue$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(99,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( C @ ( B @ ( A @ 'uzk$' ) @ 'image$bc' ) @ ( 'sup$e' @ 'fun_app$da' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom743) ).
thf(1025,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( C @ ( B @ ( A @ 'uzk$' ) @ 'image$bc' ) @ ( 'sup$e' @ 'fun_app$da' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(555,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A_set$',D: 'A_set_a_set_fun$',E: 'A_set_a_set_fun$'] :
( ( ! [F: 'A_set$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$bh' ) )
= ( F @ ( E @ 'fun_app$bh' ) ) ) )
& ( ( B @ 'obj$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'obj_update$' ) )
= ( B @ ( E @ 'obj_update$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).
thf(3112,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A_set$',D: 'A_set_a_set_fun$',E: 'A_set_a_set_fun$'] :
( ( ! [F: 'A_set$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$bh' ) )
= ( F @ ( E @ 'fun_app$bh' ) ) ) )
& ( ( B @ 'obj$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'obj_update$' ) )
= ( B @ ( E @ 'obj_update$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(135,axiom,
! [A: 'B_set$',B: 'B_set$'] :
( ( B @ ( 'uua$' @ 'fun_app$l' ) @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'less_eq$k' ) )
<=> ( B @ ( A @ 'less_eq$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom790) ).
thf(1156,plain,
! [A: 'B_set$',B: 'B_set$'] :
( ( ( B @ ( A @ 'less_eq$a' ) )
=> ( B @ ( 'uua$' @ 'fun_app$l' ) @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'less_eq$k' ) ) )
& ( ( B @ ( 'uua$' @ 'fun_app$l' ) @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'less_eq$k' ) )
=> ( B @ ( A @ 'less_eq$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(545,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom433) ).
thf(3082,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(347,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom289) ).
thf(2143,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(159,axiom,
! [A: 'Nat_set$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ( E @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$i' ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom762) ).
thf(1252,plain,
! [A: 'Nat_set$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ( E @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$i' ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(464,axiom,
! [A: 'A_set$',B: 'A_bool_fun$'] : ( A @ ( B @ ( A @ 'uux$' ) @ 'collect$h' @ 'less_eq$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).
thf(2678,plain,
! [A: 'A_set$',B: 'A_bool_fun$'] : ( A @ ( B @ ( A @ 'uux$' ) @ 'collect$h' @ 'less_eq$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(120,axiom,
! [A: 'Nat$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$'] :
( ( B @ ( A @ 'member$e' ) )
=> ( B @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom673) ).
thf(1098,plain,
! [A: 'Nat$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$'] :
( ( B @ ( A @ 'member$e' ) )
=> ( B @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(505,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> $false )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom312) ).
thf(2882,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(210,axiom,
! [A: 'B_set$',B: 'ZF$',C: 'B_ZF_set_fun$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$cx' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( C @ 'image$ar' ) @ 'inf$' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom818) ).
thf(1516,plain,
! [A: 'B_set$',B: 'ZF$',C: 'B_ZF_set_fun$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( C @ 'fun_app$cx' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( C @ 'image$ar' ) @ 'inf$' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(500,axiom,
! [A: 'A$',B: 'A_a_set_fun$',C: 'A_set$'] :
( ( C @ ( B @ 'image$ak' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) )
<=> ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom641) ).
thf(2863,plain,
! [A: 'A$',B: 'A_a_set_fun$',C: 'A_set$'] :
( ( ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( B @ 'image$ak' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
& ( ( C @ ( B @ 'image$ak' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$cr' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(584,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$a' )
=> ( A @ 'obj$' @ 'extensional$b' @ ( A @ 'id$' @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).
thf(3315,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$a' )
=> ( A @ 'obj$' @ 'extensional$b' @ ( A @ 'id$' @ 'member$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(223,axiom,
! [A: 'B$',B: 'ZF_b_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$ap' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) )
<=> ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$cw' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom807) ).
thf(1598,plain,
! [A: 'B$',B: 'ZF_b_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$cw' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ 'image$ap' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
& ( ( C @ ( B @ 'image$ap' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ! [D: 'ZF$'] :
( ( C @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( B @ 'fun_app$cw' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(152,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'Nat_set$'] :
( ( C @ ( B @ ( A @ 'uzb$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( B @ ( C @ ( A @ 'uzd$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom728) ).
thf(1225,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'Nat_set$'] :
( ( C @ ( B @ ( A @ 'uzb$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( B @ ( C @ ( A @ 'uzd$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(327,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( A @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom256) ).
thf(2060,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( A @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(411,axiom,
! [A: 'B$',B: 'ZF_b_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF$'] :
( ( ( D @ ( B @ 'fun_app$cw' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> $false )
& ( C @ ( B @ 'image$ap' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom735) ).
thf(2407,plain,
! [A: 'B$',B: 'ZF_b_set_fun$',C: 'ZF_set$'] :
~ ( ! [D: 'ZF$'] :
~ ( ( D @ ( B @ 'fun_app$cw' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
& ( C @ ( B @ 'image$ap' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(407,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom299) ).
thf(2386,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
~ ( ~ ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(49,axiom,
! [A: 'ZF_b_fun$',B: 'ZF_set$',C: 'B_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvv$' ) ) @ 'collect$i' )
= ( C @ ( B @ ( A @ 'uvw$' ) ) @ 'collect$' @ ( A @ 'image$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom546) ).
thf(791,plain,
! [A: 'ZF_b_fun$',B: 'ZF_set$',C: 'B_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvv$' ) ) @ 'collect$i' )
= ( C @ ( B @ ( A @ 'uvw$' ) ) @ 'collect$' @ ( A @ 'image$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(142,axiom,
! [A: 'ZF_set$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ( C @ 'uxi$' @ ( A @ 'sigma$' ) @ ( B @ ( A @ 'gr$c' ) @ 'less_eq$e' ) )
<=> ( C @ ( A @ ( B @ 'image$g' @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom621) ).
thf(1188,plain,
! [A: 'ZF_set$',B: 'ZF_ZF_fun$',C: 'ZF_set$'] :
( ( ( C @ ( A @ ( B @ 'image$g' @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( C @ 'uxi$' @ ( A @ 'sigma$' ) @ ( B @ ( A @ 'gr$c' ) @ 'less_eq$e' ) ) )
& ( ( C @ 'uxi$' @ ( A @ 'sigma$' ) @ ( B @ ( A @ 'gr$c' ) @ 'less_eq$e' ) )
=> ( C @ ( A @ ( B @ 'image$g' @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(592,axiom,
! [A: 'ZF_a_fun$',B: 'ZF_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvt$' ) ) @ 'fun_app$n' ) )
<=> ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$i' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom130) ).
thf(3344,plain,
! [A: 'ZF_a_fun$',B: 'ZF_set$',C: 'A_bool_fun$',D: 'A$'] :
( ( ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$i' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvt$' ) ) @ 'fun_app$n' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvt$' ) ) @ 'fun_app$n' ) )
=> ( ( D @ ( C @ 'fun_app$n' ) )
& ( B @ ( A @ 'image$i' ) @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(282,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom331) ).
thf(1869,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(618,axiom,
! [A: 'A_b_fun$',B: 'A_set$',C: 'B_bool_fun$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvq$' ) ) @ 'fun_app$n' ) )
<=> ( ( D @ ( A @ 'fun_app$bl' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom146) ).
thf(3475,plain,
! [A: 'A_b_fun$',B: 'A_set$',C: 'B_bool_fun$',D: 'A$'] :
( ( ( ( D @ ( A @ 'fun_app$bl' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvq$' ) ) @ 'fun_app$n' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvq$' ) ) @ 'fun_app$n' ) )
=> ( ( D @ ( A @ 'fun_app$bl' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(161,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_bool_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uwg$' ) @ 'fun_app$h' ) )
<=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$f' ) )
& ( C
= ( D @ ( A @ 'fun_app$s' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom125) ).
thf(1262,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_bool_fun$',C: 'ZF_set$'] :
( ( ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$f' ) )
& ( C
= ( D @ ( A @ 'fun_app$s' ) ) ) )
=> ( C @ ( B @ ( A @ 'uwg$' ) @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'uwg$' ) @ 'fun_app$h' ) )
=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$f' ) )
& ( C
= ( D @ ( A @ 'fun_app$s' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(365,axiom,
! [A: 'A_set_set$'] :
( ( A @ 'sup$b' )
= ( A @ 'vad$' @ 'collect$h' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom781) ).
thf(2219,plain,
! [A: 'A_set_set$'] :
( ( A @ 'sup$b' )
= ( A @ 'vad$' @ 'collect$h' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(508,axiom,
! [A: 'A_set$',B: 'B$',C: 'A_b_set_fun$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$cs' ) @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( A @ ( C @ 'image$al' ) @ 'inf$b' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom814) ).
thf(2903,plain,
! [A: 'A_set$',B: 'B$',C: 'A_b_set_fun$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$cs' ) @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( A @ ( C @ 'image$al' ) @ 'inf$b' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(596,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) )
<=> ( ( ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom287) ).
thf(3359,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) ) )
& ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) )
=> ( ( ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(128,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$a' )
= E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom214) ).
thf(1130,plain,
! [A: 'ZF_set$',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)],[128]) ).
thf(164,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$'] :
( ( B @ ( A @ 'uwu$' @ 'fun_app$h' ) )
<=> ? [C: 'ZF$'] :
( B
= ( C @ ( A @ 'fun_app$s' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).
thf(1285,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set$'] :
( ( ? [C: 'ZF$'] :
( B
= ( C @ ( A @ 'fun_app$s' ) ) )
=> ( B @ ( A @ 'uwu$' @ 'fun_app$h' ) ) )
& ( ( B @ ( A @ 'uwu$' @ 'fun_app$h' ) )
=> ? [C: 'ZF$'] :
( B
= ( C @ ( A @ 'fun_app$s' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(78,axiom,
! [A: 'ZF_bool_fun$'] :
( ? [B: 'ZF$'] :
( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$f' ) ) )
=> ( A @ 'the$' @ ( A @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom398) ).
thf(907,plain,
! [A: 'ZF_bool_fun$'] :
( ? [B: 'ZF$'] :
( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
=> ( C = B ) )
& ( B @ ( A @ 'fun_app$f' ) ) )
=> ( A @ 'the$' @ ( A @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(459,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( A @ ( B @ ( 'set$' @ 'id$a' @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom444) ).
thf(2656,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( A @ ( B @ ( 'set$' @ 'id$a' @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(535,axiom,
! [A: 'ZF$',B: 'A_ZF_set_fun$',C: 'A_set$'] :
( ( C @ ( B @ 'image$aq' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$co' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom809) ).
thf(3019,plain,
! [A: 'ZF$',B: 'A_ZF_set_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$co' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'image$aq' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'image$aq' ) @ 'inf$' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ! [D: 'A$'] :
( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( B @ 'fun_app$co' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(310,axiom,
! [A: 'ZF_ZF_set_fun$'] :
( ( A @ 'uwu$' @ 'collect$j' )
= ( 'top$a' @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom587) ).
thf(1987,plain,
! [A: 'ZF_ZF_set_fun$'] :
( ( A @ 'uwu$' @ 'collect$j' )
= ( 'top$a' @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(425,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).
thf(2454,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(517,axiom,
! [A: 'A$',B: 'B_a_set_fun$',C: 'B_set$'] :
( ( C @ ( B @ 'image$am' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) )
<=> ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$ct' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom803) ).
thf(2948,plain,
! [A: 'A$',B: 'B_a_set_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$ct' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( B @ 'image$am' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
& ( ( C @ ( B @ 'image$am' ) @ 'inf$a' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$ct' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(33,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$' )
= F ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom318) ).
thf(744,plain,
! [A: 'ZF_set$',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)],[33]) ).
thf(432,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'B$'] :
( ( B @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ( ( E @ ( C @ 'fun_app$cx' ) )
= D ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( ( B @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom772) ).
thf(2543,plain,
! [A: 'B$',B: 'B_set$',C: 'B_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'B$'] :
( ( B @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ( ( E @ ( C @ 'fun_app$cx' ) )
= D ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( ( B @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(107,axiom,
! [A: 'ZF_set$',B: 'ZF$'] :
( ( B @ ( A @ 'uxi$' @ 'fun_app$s' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom170) ).
thf(1052,plain,
! [A: 'ZF_set$',B: 'ZF$'] :
( ( B @ ( A @ 'uxi$' @ 'fun_app$s' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(68,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_nat_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'vap$' ) @ 'fun_app$s' ) )
= ( C @ ( C @ ( B @ 'fun_app$ao' ) @ ( A @ 'fun_app$ac' ) @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).
thf(864,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_nat_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'vap$' ) @ 'fun_app$s' ) )
= ( C @ ( C @ ( B @ 'fun_app$ao' ) @ ( A @ 'fun_app$ac' ) @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(256,axiom,
! [A: 'ZF_set_ZF_fun$',B: 'ZF_set_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uwp$' ) @ 'fun_app$f' ) )
<=> ? [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
& ( C
= ( D @ ( A @ 'fun_app$be' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).
thf(1749,plain,
! [A: 'ZF_set_ZF_fun$',B: 'ZF_set_set$',C: 'ZF$'] :
( ( ? [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
& ( C
= ( D @ ( A @ 'fun_app$be' ) ) ) )
=> ( C @ ( B @ ( A @ 'uwp$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uwp$' ) @ 'fun_app$f' ) )
=> ? [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
& ( C
= ( D @ ( A @ 'fun_app$be' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(30,axiom,
! [A: 'ZF_set$',B: 'ZF_set$'] :
( ( B @ ( 'uuc$' @ 'fun_app$g' ) @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'less_eq$l' ) )
<=> ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom791) ).
thf(727,plain,
! [A: 'ZF_set$',B: 'ZF_set$'] :
( ( ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( B @ ( 'uuc$' @ 'fun_app$g' ) @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'less_eq$l' ) ) )
& ( ( B @ ( 'uuc$' @ 'fun_app$g' ) @ ( A @ ( 'uuc$' @ 'fun_app$g' ) @ 'less_eq$l' ) )
=> ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(266,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom317) ).
thf(1797,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(72,axiom,
! [A: 'ZF_ZF_fun$'] :
( ( A @ ( 'uur$' @ 'comp$b' @ 'fun_app$a' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom478) ).
thf(876,plain,
! [A: 'ZF_ZF_fun$'] :
( ( A @ ( 'uur$' @ 'comp$b' @ 'fun_app$a' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(226,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$'] :
( ( 'top$a' @ ( A @ 'vao$' @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( 'top$h' @ ( A @ 'vaq$' @ 'image$bp' ) @ 'inf$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom796) ).
thf(1617,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$'] :
( ( 'top$a' @ ( A @ 'vao$' @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( 'top$h' @ ( A @ 'vaq$' @ 'image$bp' ) @ 'inf$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(131,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'uuw$' @ 'fun_app$b' ) @ 'comp$b' @ 'fun_app$a' ) @ 'fun_app$' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).
thf(1141,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'uuw$' @ 'fun_app$b' ) @ 'comp$b' @ 'fun_app$a' ) @ 'fun_app$' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(308,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).
thf(1981,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(302,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uuu$' @ 'fun_app$' ) )
= ( 'uur$' @ ( A @ ( A @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).
thf(1955,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uuu$' @ 'fun_app$' ) )
= ( 'uur$' @ ( A @ ( A @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(495,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_a_fun$',C: 'A_set$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$bi' ) @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( A @ 'collect$' @ ( B @ 'image$i' ) @ 'less_eq$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).
thf(2843,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_a_fun$',C: 'A_set$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$bi' ) @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( A @ 'collect$' @ ( B @ 'image$i' ) @ 'less_eq$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(348,axiom,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$'] :
( ( ! [C: 'ZF$'] :
( ( A
= ( C @ ( B @ 'fun_app$s' ) ) )
=> $false )
& ( 'top$a' @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom569) ).
thf(2145,plain,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$'] :
~ ( ! [C: 'ZF$'] :
( A
!= ( C @ ( B @ 'fun_app$s' ) ) )
& ( 'top$a' @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'member$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(286,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).
thf(1881,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(564,axiom,
! [A: 'B$',B: 'A_b_fun$',C: 'A_set$'] :
( ( ! [D: 'A$'] :
( ( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( A
= ( D @ ( B @ 'fun_app$bl' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$o' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom525) ).
thf(3156,plain,
! [A: 'B$',B: 'A_b_fun$',C: 'A_set$'] :
~ ( ! [D: 'A$'] :
~ ( ( C @ ( D @ 'member$c' @ 'fun_app$p' ) )
& ( A
= ( D @ ( B @ 'fun_app$bl' ) ) ) )
& ( C @ ( B @ 'image$o' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(613,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [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$an' ) @ 'fun_app$am' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( A @ 'category_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).
thf(3433,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$' ) ) @ 'fun_app$n' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [B: 'B$',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$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( A @ 'category_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(323,axiom,
! [A: 'A_set$',B: 'Nat_set$',C: 'A_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ? [F: 'Nat$'] :
( ( F @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$e' ) ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom660) ).
thf(2045,plain,
! [A: 'A_set$',B: 'Nat_set$',C: 'A_ZF_set_fun$',D: 'Nat_ZF_set_fun$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ? [F: 'Nat$'] :
( ( F @ ( D @ 'fun_app$r' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$e' ) ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(305,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uyv$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( B @ ( C @ ( A @ 'uyx$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom726) ).
thf(1966,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uyv$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( B @ ( C @ ( A @ 'uyx$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(243,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).
thf(1685,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(274,axiom,
! [A: 'ZF_ZF_bool_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'uzv$' @ 'fun_app$f' ) )
<=> ? [C: 'ZF$'] : ( C @ ( B @ ( A @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).
thf(1834,plain,
! [A: 'ZF_ZF_bool_fun_fun$',B: 'ZF$'] :
( ( ? [C: 'ZF$'] : ( C @ ( B @ ( A @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( B @ ( A @ 'uzv$' @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ 'uzv$' @ 'fun_app$f' ) )
=> ? [C: 'ZF$'] : ( C @ ( B @ ( A @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(18,axiom,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uxw$' ) @ 'fun_app$ax' ) )
= ( B @ ( A @ 'image$' @ 'fun_app$v' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom86) ).
thf(688,plain,
! [A: 'Nat_ZF_set_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uxw$' ) @ 'fun_app$ax' ) )
= ( B @ ( A @ 'image$' @ 'fun_app$v' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(400,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom288) ).
thf(2347,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(149,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzl$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom77) ).
thf(1216,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzl$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$s' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(281,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'vau$' @ 'fun_app$s' ) )
= ( 'top$a' @ ( B @ ( A @ 'uyw$' @ 'fun_app$ad' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
thf(1866,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF$'] :
( ( B @ ( A @ 'vau$' @ 'fun_app$s' ) )
= ( 'top$a' @ ( B @ ( A @ 'uyw$' @ 'fun_app$ad' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(419,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom354) ).
thf(2435,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(64,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( B @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( B @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom467) ).
thf(845,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( B @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( B @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(482,axiom,
! [A: 'B_a_fun$',B: 'B_set$',C: 'A_bool_fun$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvo$' ) ) @ 'fun_app$k' ) )
<=> ( ( D @ ( A @ 'fun_app$bk' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom144) ).
thf(2760,plain,
! [A: 'B_a_fun$',B: 'B_set$',C: 'A_bool_fun$',D: 'B$'] :
( ( ( ( D @ ( A @ 'fun_app$bk' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvo$' ) ) @ 'fun_app$k' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvo$' ) ) @ 'fun_app$k' ) )
=> ( ( D @ ( A @ 'fun_app$bk' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(452,axiom,
! [A: 'B$',B: 'B_b_set_fun$',C: 'B_set$'] :
( ( C @ ( B @ 'image$an' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) )
<=> ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom645) ).
thf(2626,plain,
! [A: 'B$',B: 'B_b_set_fun$',C: 'B_set$'] :
( ( ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ 'image$an' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
& ( ( C @ ( B @ 'image$an' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ? [D: 'B$'] :
( ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(172,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_nat_fun$'] :
( ( B @ ( A @ 'vaz$' @ 'fun_app$w' ) )
= ( 'top$a' @ ( B @ ( A @ 'vap$' ) @ 'image$a' @ 'fun_app$x' ) @ 'inf$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).
thf(1316,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'ZF_nat_fun$'] :
( ( B @ ( A @ 'vaz$' @ 'fun_app$w' ) )
= ( 'top$a' @ ( B @ ( A @ 'vap$' ) @ 'image$a' @ 'fun_app$x' ) @ 'inf$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(234,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_ZF_fun$'] :
( ( B @ ( A @ 'vav$' @ 'fun_app$z' ) )
= ( 'top$a' @ ( B @ ( A @ 'vaj$' ) @ 'image$a' @ 'fun_app$x' ) @ 'inf$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).
thf(1649,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$',B: 'ZF_ZF_fun$'] :
( ( B @ ( A @ 'vav$' @ 'fun_app$z' ) )
= ( 'top$a' @ ( B @ ( A @ 'vaj$' ) @ 'image$a' @ 'fun_app$x' ) @ 'inf$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(469,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).
thf(2696,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(219,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$',H: 'A_set$',I: 'B_set$',J: 'B_a_fun$',K: 'B_a_fun$',L: 'A_b_fun$',M: 'B_b_b_fun_fun$',N: 'B_c_LSCategory_ext$'] :
( ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) )
= ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ 'category_ext$' ) ) ) ) ) ) ) )
<=> ( ( G = N )
& ( F = M )
& ( E = L )
& ( D = K )
& ( C = J )
& ( B = I )
& ( A = H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom210) ).
thf(1553,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$',H: 'A_set$',I: 'B_set$',J: 'B_a_fun$',K: 'B_a_fun$',L: 'A_b_fun$',M: 'B_b_b_fun_fun$',N: 'B_c_LSCategory_ext$'] :
( ( ( ( G = N )
& ( F = M )
& ( E = L )
& ( D = K )
& ( C = J )
& ( B = I )
& ( A = H ) )
=> ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) )
= ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ 'category_ext$' ) ) ) ) ) ) ) ) )
& ( ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) )
= ( N @ ( M @ ( L @ ( K @ ( J @ ( I @ ( H @ 'category_ext$' ) ) ) ) ) ) ) )
=> ( ( G = N )
& ( F = M )
& ( E = L )
& ( D = K )
& ( C = J )
& ( B = I )
& ( A = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(501,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom223) ).
thf(2870,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(491,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).
thf(2828,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(13,axiom,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzd$' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'uzc$' @ 'fun_app$ab' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom103) ).
thf(671,plain,
! [A: 'Nat_ZF_ZF_set_fun_fun$',B: 'Nat_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzd$' ) @ 'fun_app$s' ) )
= ( B @ ( C @ ( A @ 'uzc$' @ 'fun_app$ab' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(519,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom245) ).
thf(2960,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(448,axiom,
! [A: 'ZF_b_fun$',B: 'ZF_set$',C: 'B_bool_fun$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) @ 'fun_app$k' ) )
<=> ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$h' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom129) ).
thf(2611,plain,
! [A: 'ZF_b_fun$',B: 'ZF_set$',C: 'B_bool_fun$',D: 'B$'] :
( ( ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$h' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) @ 'fun_app$k' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvv$' ) ) @ 'fun_app$k' ) )
=> ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$h' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(38,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'Nat_ZF_set_fun$'] :
( ( 'top$' @ ( B @ ( A @ 'uve$' ) @ 'image$' @ 'fun_app$v' ) )
= ( 'top$' @ ( B @ 'image$' @ 'fun_app$v' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom582) ).
thf(759,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'Nat_ZF_set_fun$'] :
( ( 'top$' @ ( B @ ( A @ 'uve$' ) @ 'image$' @ 'fun_app$v' ) )
= ( 'top$' @ ( B @ 'image$' @ 'fun_app$v' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(586,axiom,
! [A: 'A$',B: 'A_bool_fun$'] :
( ( B @ 'collect$h' @ ( A @ 'member$c' @ 'fun_app$p' ) )
<=> ( A @ ( B @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).
thf(3320,plain,
! [A: 'A$',B: 'A_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$n' ) )
=> ( B @ 'collect$h' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
& ( ( B @ 'collect$h' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ( A @ ( B @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(95,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_set_set$'] :
( ( B @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) )
= ( B @ ( A @ 'image$g' @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom753) ).
thf(1010,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_set_set$'] :
( ( B @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) )
= ( B @ ( A @ 'image$g' @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(188,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= C )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= B )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom468) ).
thf(1390,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= C )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= B )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(398,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF$'] : ( D @ ( B @ 'fun_app$s' ) @ ( D @ ( A @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom671) ).
thf(2342,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF$'] : ( D @ ( B @ 'fun_app$s' ) @ ( D @ ( A @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(254,axiom,
! [A: 'ZF_set_a_fun$',B: 'ZF_set_set$',C: 'A_bool_fun$',D: 'ZF_set$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$h' ) )
<=> ( ( D @ ( A @ 'fun_app$bj' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$j' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom141) ).
thf(1734,plain,
! [A: 'ZF_set_a_fun$',B: 'ZF_set_set$',C: 'A_bool_fun$',D: 'ZF_set$'] :
( ( ( ( D @ ( A @ 'fun_app$bj' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$j' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$h' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uwe$' ) ) @ 'fun_app$h' ) )
=> ( ( D @ ( A @ 'fun_app$bj' ) @ ( C @ 'fun_app$n' ) )
& ( B @ ( D @ 'member$a' @ 'fun_app$j' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(42,axiom,
! [A: 'B_set$',B: 'B_bool_fun$'] : ( A @ ( B @ ( A @ 'uuy$' ) @ 'collect$i' @ 'less_eq$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom498) ).
thf(771,plain,
! [A: 'B_set$',B: 'B_bool_fun$'] : ( A @ ( B @ ( A @ 'uuy$' ) @ 'collect$i' @ 'less_eq$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(509,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
<=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom310) ).
thf(2907,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) )
=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(422,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxg$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( ( D @ ( B @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom163) ).
thf(2443,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( D @ ( B @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uxg$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uxg$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( D @ ( B @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(471,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( C @ ( B @ ( A @ 'makeCat$a' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).
thf(2707,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( C @ ( B @ ( A @ 'makeCat$a' @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(620,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( 'set$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).
thf(3484,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( 'set$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(498,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom251) ).
thf(2855,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( A @ 'cod$' @ 'fun_app$bk' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(121,axiom,
! [A: 'ZF_set_set$'] :
( ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'collect$j' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom281) ).
thf(1101,plain,
! [A: 'ZF_set_set$'] :
( ( A @ ( 'uub$' @ 'fun_app$i' ) @ 'collect$j' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(589,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'mor$' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( ( A @ ( B @ 'dom$' @ 'fun_app$bk' ) )
= ( A @ ( B @ 'makeCat$' @ 'dom$' @ 'fun_app$bk' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom238) ).
thf(3336,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'mor$' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( ( A @ ( B @ 'dom$' @ 'fun_app$bk' ) )
= ( A @ ( B @ 'makeCat$' @ 'dom$' @ 'fun_app$bk' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(4,axiom,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uyy$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( B @ ( C @ ( A @ 'uza$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom727) ).
thf(632,plain,
! [A: 'ZF_nat_ZF_set_fun_fun$',B: 'Nat_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'uyy$' ) @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( B @ ( C @ ( A @ 'uza$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(418,axiom,
! [A: 'B_set$',B: 'B_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( B @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom695) ).
thf(2431,plain,
! [A: 'B_set$',B: 'B_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'B$'] :
( ( A @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( C @ ( D @ ( B @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(212,axiom,
! [A: 'B_ZF_fun$',B: 'B_set$',C: 'ZF_bool_fun$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) @ 'fun_app$k' ) )
<=> ( ( D @ ( A @ 'fun_app$ar' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom142) ).
thf(1523,plain,
! [A: 'B_ZF_fun$',B: 'B_set$',C: 'ZF_bool_fun$',D: 'B$'] :
( ( ( ( D @ ( A @ 'fun_app$ar' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) @ 'fun_app$k' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uwa$' ) ) @ 'fun_app$k' ) )
=> ( ( D @ ( A @ 'fun_app$ar' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(573,axiom,
! [A: 'ZF$',B: 'A_ZF_set_fun$',C: 'A_set$'] :
( ( C @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
<=> ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$co' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom648) ).
thf(3252,plain,
! [A: 'ZF$',B: 'A_ZF_set_fun$',C: 'A_set$'] :
( ( ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$co' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( C @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ? [D: 'A$'] :
( ( D @ ( B @ 'fun_app$co' ) @ ( A @ 'member$' @ 'fun_app$h' ) )
& ( C @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(186,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom461) ).
thf(1385,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(442,axiom,
! [A: 'A_ZF_fun$',B: 'A_set$'] :
( ( B @ ( A @ 'uwm$' ) @ 'collect$' )
= ( B @ ( A @ 'image$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom558) ).
thf(2594,plain,
! [A: 'A_ZF_fun$',B: 'A_set$'] :
( ( B @ ( A @ 'uwm$' ) @ 'collect$' )
= ( B @ ( A @ 'image$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(251,axiom,
! [A: 'B$',B: 'B_set$',C: 'ZF$',D: 'B_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cx' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom639) ).
thf(1721,plain,
! [A: 'B$',B: 'B_set$',C: 'ZF$',D: 'B_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cx' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(355,axiom,
! [A: 'A_set$',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$' ) ) ) ) ) ) @ 'mor$' )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom215) ).
thf(2174,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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) @ 'mor$' )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(380,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).
thf(2283,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(497,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$' ) @ 'functorM$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom209) ).
thf(2853,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$' ) @ 'functorM$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(383,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_b_fun$',C: 'B_set$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$as' ) @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( A @ 'collect$' @ ( B @ 'image$h' ) @ 'less_eq$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom519) ).
thf(2290,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_b_fun$',C: 'B_set$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( C @ ( D @ ( B @ 'fun_app$as' ) @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( A @ 'collect$' @ ( B @ 'image$h' ) @ 'less_eq$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(371,axiom,
! [A: 'B_set$',B: 'B$'] :
( ( B @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'fun_app$k' ) )
<=> ( A @ ( B @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
thf(2251,plain,
! [A: 'B_set$',B: 'B$'] :
( ( ( A @ ( B @ 'member$b' @ 'fun_app$m' ) )
=> ( B @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'fun_app$k' ) ) )
& ( ( B @ ( A @ ( 'uua$' @ 'fun_app$l' ) @ 'fun_app$k' ) )
=> ( A @ ( B @ 'member$b' @ 'fun_app$m' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(91,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).
thf(995,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( B @ ( A @ 'inverse_rel$a' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(350,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom365) ).
thf(2152,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(374,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set_set$'] :
( ( B @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( B @ ( A @ 'image$a' @ 'image$au' @ 'fun_app$dd' ) @ ( 'sup$e' @ 'fun_app$da' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom752) ).
thf(2262,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_set_set$'] :
( ( B @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) )
= ( B @ ( A @ 'image$a' @ 'image$au' @ 'fun_app$dd' ) @ ( 'sup$e' @ 'fun_app$da' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(408,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_ZF_bool_fun_fun$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uxk$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( ( D @ ( C @ ( B @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).
thf(2394,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_ZF_bool_fun_fun$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( D @ ( C @ ( B @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uxk$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uxk$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( D @ ( C @ ( B @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(546,axiom,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'obj$' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ( ( A @ ( B @ 'id$' @ 'fun_app$bl' ) )
= ( A @ ( B @ 'makeCat$' @ 'id$' @ 'fun_app$bl' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom236) ).
thf(3085,plain,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'obj$' @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ( ( A @ ( B @ 'id$' @ 'fun_app$bl' ) )
= ( A @ ( B @ 'makeCat$' @ 'id$' @ 'fun_app$bl' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(515,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 @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).
thf(2944,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(406,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'isomorphism$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).
thf(2384,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( A @ 'isomorphism$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(428,axiom,
! [A: 'B_ZF_fun$',B: 'B_set$',C: 'ZF_bool_fun$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) @ 'fun_app$f' ) )
<=> ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$k' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom132) ).
thf(2462,plain,
! [A: 'B_ZF_fun$',B: 'B_set$',C: 'ZF_bool_fun$',D: 'ZF$'] :
( ( ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$k' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvz$' ) ) @ 'fun_app$f' ) )
=> ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$k' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(114,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyh$' ) @ 'fun_app$s' ) )
= ( B @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom83) ).
thf(1077,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uyh$' ) @ 'fun_app$s' ) )
= ( B @ ( A @ 'image$g' @ 'fun_app$ae' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(465,axiom,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$j' ) )
=> ( B @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom702) ).
thf(2680,plain,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$'] :
( ( B @ ( A @ 'member$a' @ 'fun_app$j' ) )
=> ( B @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(593,axiom,
! [A: 'A_set$',B: 'A_set$',C: 'A_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ? [F: 'A$'] :
( ( F @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom661) ).
thf(3351,plain,
! [A: 'A_set$',B: 'A_set$',C: 'A_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ! [E: 'A$'] :
( ( A @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ? [F: 'A$'] :
( ( F @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(237,axiom,
! [A: 'B$',B: 'B_set$',C: 'B_ZF_set_fun$'] :
( ( B @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( B @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom675) ).
thf(1661,plain,
! [A: 'B$',B: 'B_set$',C: 'B_ZF_set_fun$'] :
( ( B @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ( B @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(60,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'isZFfun$' @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom463) ).
thf(832,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$f' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
=> ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'isZFfun$' @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(390,axiom,
! [A: 'B_a_fun$',B: 'B_set$',C: 'A_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'collect$h' )
= ( C @ ( B @ ( A @ 'uvo$' ) ) @ 'collect$i' @ ( A @ 'image$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom542) ).
thf(2315,plain,
! [A: 'B_a_fun$',B: 'B_set$',C: 'A_bool_fun$'] :
( ( C @ ( B @ ( A @ 'uvn$' ) ) @ 'collect$h' )
= ( C @ ( B @ ( A @ 'uvo$' ) ) @ 'collect$i' @ ( A @ 'image$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(477,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) )
= ( B @ ( A @ 'uup$' ) @ ( C @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom436) ).
thf(2739,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) )
= ( B @ ( A @ 'uup$' ) @ ( C @ ( B @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( B @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(105,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$a' )
= G ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom353) ).
thf(1045,plain,
! [A: 'ZF_set$',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$a' ) ) ) ) ) ) @ 'more$a' )
= G ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(518,axiom,
! [A: 'B_set$',B: 'A_set$',C: 'B_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ? [F: 'A$'] :
( ( F @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom665) ).
thf(2956,plain,
! [A: 'B_set$',B: 'A_set$',C: 'B_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ? [F: 'A$'] :
( ( F @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(205,axiom,
! [A: 'Nat_set$',B: 'A_set$',C: 'Nat_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ? [F: 'A$'] :
( ( F @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom657) ).
thf(1491,plain,
! [A: 'Nat_set$',B: 'A_set$',C: 'Nat_ZF_set_fun$',D: 'A_ZF_set_fun$'] :
( ! [E: 'Nat$'] :
( ( A @ ( E @ 'member$e' ) )
=> ? [F: 'A$'] :
( ( F @ ( D @ 'fun_app$co' ) @ ( E @ ( C @ 'fun_app$r' ) @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( F @ 'member$c' @ 'fun_app$p' ) ) ) )
=> ( B @ ( D @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(612,axiom,
! [A: 'A$',B: 'A_set$',C: 'A_ZF_set_fun$'] :
( ( B @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom674) ).
thf(3430,plain,
! [A: 'A$',B: 'A_set$',C: 'A_ZF_set_fun$'] :
( ( B @ ( A @ 'member$c' @ 'fun_app$p' ) )
=> ( B @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(260,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category_axioms$' )
=> ( A @ 'makeCat$' @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom247) ).
thf(1777,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category_axioms$' )
=> ( A @ 'makeCat$' @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(197,axiom,
! [A: 'B_a_fun_b_a_fun_fun$',B: 'A_set$',C: 'B_set$',D: 'B_a_fun$',E: 'B_a_fun$',F: 'A_b_fun$',G: 'B_b_b_fun_fun$',H: 'B_c_LSCategory_ext$'] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$' ) ) ) ) ) ) @ ( A @ 'dom_update$' ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ 'fun_app$ch' ) @ ( C @ ( B @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom217) ).
thf(1440,plain,
! [A: 'B_a_fun_b_a_fun_fun$',B: 'A_set$',C: 'B_set$',D: 'B_a_fun$',E: 'B_a_fun$',F: 'A_b_fun$',G: 'B_b_b_fun_fun$',H: 'B_c_LSCategory_ext$'] :
( ( H @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ 'category_ext$' ) ) ) ) ) ) @ ( A @ 'dom_update$' ) )
= ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ 'fun_app$ch' ) @ ( C @ ( B @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(394,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuq$' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).
thf(2330,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuq$' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'zF2mor$' @ 'fun_app$as' ) @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(439,axiom,
! [A: 'B_b_fun$',B: 'B_set$',C: 'B_bool_fun$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvs$' ) ) @ 'fun_app$k' ) )
<=> ( ( D @ ( A @ 'fun_app$am' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).
thf(2576,plain,
! [A: 'B_b_fun$',B: 'B_set$',C: 'B_bool_fun$',D: 'B$'] :
( ( ( ( D @ ( A @ 'fun_app$am' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvs$' ) ) @ 'fun_app$k' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvs$' ) ) @ 'fun_app$k' ) )
=> ( ( D @ ( A @ 'fun_app$am' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(329,axiom,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set$',D: 'ZF_set_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$ae' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> ( B @ ( D @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom687) ).
thf(2066,plain,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set$',D: 'ZF_set_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$ae' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> ( B @ ( D @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(289,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF_ZF_fun$',D: 'ZF$'] :
( ! [E: 'ZF$'] :
( ( A @ ( E @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( E @ ( B @ 'fun_app$' ) )
= ( E @ ( C @ 'fun_app$' ) ) ) )
=> ( ( B @ ( D @ ( A @ 'zFfun$' ) ) )
= ( C @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).
thf(1893,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF_ZF_fun$',D: 'ZF$'] :
( ! [E: 'ZF$'] :
( ( A @ ( E @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( E @ ( B @ 'fun_app$' ) )
= ( E @ ( C @ 'fun_app$' ) ) ) )
=> ( ( B @ ( D @ ( A @ 'zFfun$' ) ) )
= ( C @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(384,axiom,
! [A: 'ZF_b_fun$',B: 'ZF_set$',C: 'B_bool_fun$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) @ 'fun_app$f' ) )
<=> ( ( D @ ( A @ 'fun_app$as' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom139) ).
thf(2294,plain,
! [A: 'ZF_b_fun$',B: 'ZF_set$',C: 'B_bool_fun$',D: 'ZF$'] :
( ( ( ( D @ ( A @ 'fun_app$as' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvw$' ) ) @ 'fun_app$f' ) )
=> ( ( D @ ( A @ 'fun_app$as' ) @ ( C @ 'fun_app$k' ) )
& ( B @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(315,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom363) ).
thf(2003,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ ( A @ 'cod$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(404,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).
thf(2374,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(339,axiom,
! [A: 'B$',B: 'ZF_b_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$ap' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) )
<=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$cw' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom646) ).
thf(2102,plain,
! [A: 'B$',B: 'ZF_b_set_fun$',C: 'ZF_set$'] :
( ( ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$cw' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ 'image$ap' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
& ( ( C @ ( B @ 'image$ap' ) @ 'sup$c' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$cw' ) @ ( A @ 'member$b' @ 'fun_app$m' ) )
& ( C @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(466,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_set_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( A @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom682) ).
thf(2683,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_set_set$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( A @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'ZF_set$'] :
( ( B @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( A @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(580,axiom,
! [A: 'A$',B: 'B_a_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( A
= ( D @ ( B @ 'fun_app$bk' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$m' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).
thf(3291,plain,
! [A: 'A$',B: 'B_a_fun$',C: 'B_set$'] :
~ ( ! [D: 'B$'] :
~ ( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( A
= ( D @ ( B @ 'fun_app$bk' ) ) ) )
& ( C @ ( B @ 'image$m' ) @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(526,axiom,
! [A: 'A$',B: 'A_set$',C: 'B$',D: 'A_b_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cs' ) @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( B @ ( D @ 'image$al' ) @ 'sup$c' @ ( C @ 'member$b' @ 'fun_app$m' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom632) ).
thf(2983,plain,
! [A: 'A$',B: 'A_set$',C: 'B$',D: 'A_b_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$cs' ) @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( B @ ( D @ 'image$al' ) @ 'sup$c' @ ( C @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(61,axiom,
! [A: 'ZF_set$',B: 'Nat_ZF_set_fun$'] :
( ( ! [C: 'Nat$'] :
( ( A
= ( C @ ( B @ 'fun_app$r' ) ) )
=> $false )
& ( 'top$' @ ( B @ 'image$' @ 'fun_app$v' ) @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom573) ).
thf(835,plain,
! [A: 'ZF_set$',B: 'Nat_ZF_set_fun$'] :
~ ( ! [C: 'Nat$'] :
( A
!= ( C @ ( B @ 'fun_app$r' ) ) )
& ( 'top$' @ ( B @ 'image$' @ 'fun_app$v' ) @ ( A @ 'member$a' @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(445,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( B @ ( D @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( C @ ( D @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).
thf(2604,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( B @ ( D @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
& ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
=> ( C @ ( D @ ( A @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(240,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( A
= ( A @ 'more$a' @ ( A @ 'comp$' @ ( A @ 'id$a' @ ( A @ 'cod$a' @ ( A @ 'dom$a' @ ( A @ 'mor$a' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom340) ).
thf(1673,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( A
= ( A @ 'more$a' @ ( A @ 'comp$' @ ( A @ 'id$a' @ ( A @ 'cod$a' @ ( A @ 'dom$a' @ ( A @ 'mor$a' @ ( A @ 'obj$a' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(544,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'mor$' @ 'extensional$e' @ ( A @ 'mor2ZF$' @ 'member$g' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) @ 'fun_app$co' ) @ 'member$a' @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B = C ) ) )
=> ( A @ 'lSCategory_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom563) ).
thf(3062,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'mor$' @ 'extensional$e' @ ( A @ 'mor2ZF$' @ 'member$g' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( 'top$a' @ ( 'explode$' @ 'image$a' @ 'fun_app$x' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) @ 'fun_app$co' ) @ 'member$a' @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) )
=> ( B = C ) ) )
=> ( A @ 'lSCategory_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(343,axiom,
! [A: 'ZF_set$',B: 'ZF$',C: 'ZF_ZF_set_fun$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$s' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( C @ 'image$a' @ 'fun_app$x' ) @ 'inf$' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom821) ).
thf(2123,plain,
! [A: 'ZF_set$',B: 'ZF$',C: 'ZF_ZF_set_fun$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$s' ) @ ( B @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( C @ 'image$a' @ 'fun_app$x' ) @ 'inf$' @ ( B @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(129,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'oppositeCategory$a' @ 'category$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom230) ).
thf(1133,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'oppositeCategory$a' @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(351,axiom,
! [A: 'ZF_set_set$',B: 'ZF$'] :
( ( B @ ( A @ 'vag$' @ 'fun_app$f' ) )
<=> ( A @ ( B @ 'member$' @ 'image$b' ) @ 'sup$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).
thf(2155,plain,
! [A: 'ZF_set_set$',B: 'ZF$'] :
( ( ( A @ ( B @ 'member$' @ 'image$b' ) @ 'sup$a' )
=> ( B @ ( A @ 'vag$' @ 'fun_app$f' ) ) )
& ( ( B @ ( A @ 'vag$' @ 'fun_app$f' ) )
=> ( A @ ( B @ 'member$' @ 'image$b' ) @ 'sup$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(431,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_bool_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uwi$' ) @ 'fun_app$f' ) )
<=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$f' ) )
& ( C
= ( D @ ( A @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom124) ).
thf(2534,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_bool_fun$',C: 'ZF$'] :
( ( ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$f' ) )
& ( C
= ( D @ ( A @ 'fun_app$' ) ) ) )
=> ( C @ ( B @ ( A @ 'uwi$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uwi$' ) @ 'fun_app$f' ) )
=> ? [D: 'ZF$'] :
( ( D @ ( B @ 'fun_app$f' ) )
& ( C
= ( D @ ( A @ 'fun_app$' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(69,axiom,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) )
= ( C @ ( B @ ( A @ 'uvc$' ) @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).
thf(867,plain,
! [A: 'ZF_set_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( C @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( A @ 'image$q' @ 'fun_app$cn' ) )
= ( C @ ( B @ ( A @ 'uvc$' ) @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(624,axiom,
! [A: 'A_set$',B: 'A$',C: 'A_a_set_fun$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$cr' ) @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( A @ ( C @ 'image$ak' ) @ 'inf$a' @ ( B @ 'member$c' @ 'fun_app$p' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom813) ).
thf(3496,plain,
! [A: 'A_set$',B: 'A$',C: 'A_a_set_fun$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( D @ ( C @ 'fun_app$cr' ) @ ( B @ 'member$c' @ 'fun_app$p' ) ) )
=> ( A @ ( C @ 'image$ak' ) @ 'inf$a' @ ( B @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(561,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$' @ 'obj$' )
= ( A @ 'obj$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom199) ).
thf(3145,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'makeCat$' @ 'obj$' )
= ( A @ 'obj$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(196,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF_ZF_fun$'] :
( ( B @ ( A @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( A @ ( D @ ( C @ ( B @ 'zFfun$' ) ) @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( A @ ( D @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).
thf(1436,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF_ZF_fun$'] :
( ( B @ ( A @ ( 'elem$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( A @ ( D @ ( C @ ( B @ 'zFfun$' ) ) @ ( 'zFfunApp$' @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( A @ ( D @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(480,axiom,
! [A: 'A_set$',B: 'A_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( B @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom667) ).
thf(2751,plain,
! [A: 'A_set$',B: 'A_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'A$'] :
( ( A @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( B @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(588,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_a_fun$',D: 'B_a_fun_b_a_fun_fun$',E: 'B_a_fun_b_a_fun_fun$'] :
( ( ! [F: 'B_a_fun$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$ch' ) )
= ( F @ ( E @ 'fun_app$ch' ) ) ) )
& ( ( B @ 'dom$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'dom_update$' ) )
= ( B @ ( E @ 'dom_update$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).
thf(3328,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_a_fun$',D: 'B_a_fun_b_a_fun_fun$',E: 'B_a_fun_b_a_fun_fun$'] :
( ( ! [F: 'B_a_fun$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$ch' ) )
= ( F @ ( E @ 'fun_app$ch' ) ) ) )
& ( ( B @ 'dom$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'dom_update$' ) )
= ( B @ ( E @ 'dom_update$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(52,axiom,
! [A: 'Nat$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'Nat$'] :
( ( B @ ( E @ 'member$e' ) )
=> ( ( E @ ( C @ 'fun_app$r' ) )
= D ) )
& ( B @ ( A @ 'member$e' ) ) )
=> ( ( B @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom770) ).
thf(801,plain,
! [A: 'Nat$',B: 'Nat_set$',C: 'Nat_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'Nat$'] :
( ( B @ ( E @ 'member$e' ) )
=> ( ( E @ ( C @ 'fun_app$r' ) )
= D ) )
& ( B @ ( A @ 'member$e' ) ) )
=> ( ( B @ ( C @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(206,axiom,
! [A: 'ZF_ZF_bool_fun_fun$'] :
( ( A @ 'uzv$' @ 'collect$' )
= ( 'top$a' @ ( A @ 'uzx$' @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom767) ).
thf(1495,plain,
! [A: 'ZF_ZF_bool_fun_fun$'] :
( ( A @ 'uzv$' @ 'collect$' )
= ( 'top$a' @ ( A @ 'uzx$' @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(357,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$a' @ ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom373) ).
thf(2186,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$f' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$a' @ ( B @ ( A @ 'inverse$a' @ 'fun_app$' ) @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(53,axiom,
! [A: 'B_set$',B: 'B_bool_fun$'] : ( A @ ( B @ ( A @ 'uuy$' ) @ 'collect$i' @ 'less_eq$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom494) ).
thf(807,plain,
! [A: 'B_set$',B: 'B_bool_fun$'] : ( A @ ( B @ ( A @ 'uuy$' ) @ 'collect$i' @ 'less_eq$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(331,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) @ ( A @ 'zF2mor$' @ 'fun_app$as' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom421) ).
thf(2070,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) @ ( A @ 'zF2mor$' @ 'fun_app$as' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(192,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$a' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom264) ).
thf(1410,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$a' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(263,axiom,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_set$',D: 'ZF_bool_fun$'] :
( ( ( D @ ( C @ 'uva$' ) @ 'collect$' @ ( B @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( D @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom504) ).
thf(1789,plain,
! [A: 'ZF$',B: 'ZF_set$',C: 'ZF_set$',D: 'ZF_bool_fun$'] :
( ( ( D @ ( C @ 'uva$' ) @ 'collect$' @ ( B @ 'less_eq$c' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( A @ ( D @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(144,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF_bool_fun$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) @ 'fun_app$f' ) )
<=> ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$g' @ 'fun_app$ae' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).
thf(1197,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_set$',C: 'ZF_bool_fun$',D: 'ZF$'] :
( ( ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$g' @ 'fun_app$ae' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uwb$' ) ) @ 'fun_app$f' ) )
=> ( ( D @ ( C @ 'fun_app$f' ) )
& ( B @ ( A @ 'image$g' @ 'fun_app$ae' ) @ ( D @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(410,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$a' @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom239) ).
thf(2404,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$a' @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(5,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uvf$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$' ) @ ( A @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).
thf(635,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uvf$' ) @ 'fun_app$s' ) )
= ( C @ ( B @ 'fun_app$' ) @ ( A @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(627,axiom,
! [A: 'A_ZF_set_fun$',B: 'A_set$',C: 'ZF_set$'] :
( ( C @ ( B @ ( A @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( A @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom679) ).
thf(3506,plain,
! [A: 'A_ZF_set_fun$',B: 'A_set$',C: 'ZF_set$'] :
( ( ! [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( A @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ ( A @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'A$'] :
( ( B @ ( D @ 'member$c' @ 'fun_app$p' ) )
=> ( C @ ( D @ ( A @ 'fun_app$co' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(433,axiom,
! [A: 'ZF_ZF_ZF_set_fun_fun$'] :
( ( 'top$a' @ ( A @ 'vau$' @ 'image$a' @ 'fun_app$x' ) @ 'inf$' )
= ( 'top$f' @ ( A @ 'vav$' @ 'image$bn' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom798) ).
thf(2549,plain,
! [A: 'ZF_ZF_ZF_set_fun_fun$'] :
( ( 'top$a' @ ( A @ 'vau$' @ 'image$a' @ 'fun_app$x' ) @ 'inf$' )
= ( 'top$f' @ ( A @ 'vav$' @ 'image$bn' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(62,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).
thf(839,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(571,axiom,
! [A: 'A$',B: 'B_a_set_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( ( D @ ( B @ 'fun_app$ct' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> $false )
& ( C @ ( B @ 'image$am' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom731) ).
thf(3244,plain,
! [A: 'A$',B: 'B_a_set_fun$',C: 'B_set$'] :
~ ( ! [D: 'B$'] :
~ ( ( D @ ( B @ 'fun_app$ct' ) @ ( A @ 'member$c' @ 'fun_app$p' ) )
& ( C @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
& ( C @ ( B @ 'image$am' ) @ 'sup$b' @ ( A @ 'member$c' @ 'fun_app$p' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(558,axiom,
! [A: 'A_ZF_fun$',B: 'A_set$',C: 'ZF_bool_fun$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) @ 'fun_app$n' ) )
<=> ( ( D @ ( A @ 'fun_app$bf' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom145) ).
thf(3128,plain,
! [A: 'A_ZF_fun$',B: 'A_set$',C: 'ZF_bool_fun$',D: 'A$'] :
( ( ( ( D @ ( A @ 'fun_app$bf' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) @ 'fun_app$n' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvy$' ) ) @ 'fun_app$n' ) )
=> ( ( D @ ( A @ 'fun_app$bf' ) @ ( C @ 'fun_app$f' ) )
& ( B @ ( D @ 'member$c' @ 'fun_app$p' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(273,axiom,
! [A: 'ZF_set$',B: 'ZF_bool_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uva$' ) @ 'fun_app$f' ) )
<=> ( ( C @ ( B @ 'fun_app$f' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).
thf(1827,plain,
! [A: 'ZF_set$',B: 'ZF_bool_fun$',C: 'ZF$'] :
( ( ( ( C @ ( B @ 'fun_app$f' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( B @ ( A @ 'uva$' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uva$' ) @ 'fun_app$f' ) )
=> ( ( C @ ( B @ 'fun_app$f' ) )
& ( A @ ( C @ 'member$' @ 'fun_app$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(218,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'identityFunctor$a' @ 'catDom$a' @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'identityFunctor$a' @ 'mapO$b' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom473) ).
thf(1550,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'identityFunctor$a' @ 'catDom$a' @ 'obj$a' @ ( B @ 'member$' @ 'fun_app$h' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'identityFunctor$a' @ 'mapO$b' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(90,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uym$' @ 'fun_app$a' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'fun_app$' ) @ ( B @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(992,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF$'] :
( ( B @ ( A @ ( 'uym$' @ 'fun_app$a' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'fun_app$' ) @ ( B @ ( 'opair$' @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(208,axiom,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'ZF$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( E @ ( B @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( B @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom654) ).
thf(1500,plain,
! [A: 'ZF_set$',B: 'ZF_ZF_set_fun$',C: 'ZF_set$'] :
( ( ! [D: 'ZF_set$'] :
( ! [E: 'ZF$'] :
( ( A @ ( E @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( E @ ( B @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( D @ ( C @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( C @ ( D @ ( B @ 'fun_app$s' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ) )
=> ( ( A @ ( B @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(88,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzj$' ) @ 'fun_app$ax' ) )
= ( C @ ( B @ 'fun_app$s' ) @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).
thf(982,plain,
! [A: 'ZF_ZF_set_fun$',B: 'ZF_ZF_set_fun$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzj$' ) @ 'fun_app$ax' ) )
= ( C @ ( B @ 'fun_app$s' ) @ ( A @ 'image$a' @ 'fun_app$x' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(167,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$a' @ 'cod$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom336) ).
thf(1299,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'makeCat$a' @ 'cod$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(155,axiom,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ ( A @ 'uys$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom749) ).
thf(1236,plain,
! [A: 'ZF_ZF_set_fun$',B: 'Nat_ZF_set_fun$',C: 'Nat_set$'] :
( ( C @ ( B @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ 'image$a' @ 'fun_app$x' ) @ ( 'sup$' @ 'fun_app$u' ) )
= ( C @ ( B @ ( A @ 'uys$' ) @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(344,axiom,
! [A: 'B_ZF_fun$',B: 'B_ZF_fun_bool_fun$'] :
( ( B @ 'collect$d' @ ( A @ 'member$g' ) )
<=> ( A @ ( B @ 'fun_app$cj' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom270) ).
thf(2127,plain,
! [A: 'B_ZF_fun$',B: 'B_ZF_fun_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$cj' ) )
=> ( B @ 'collect$d' @ ( A @ 'member$g' ) ) )
& ( ( B @ 'collect$d' @ ( A @ 'member$g' ) )
=> ( A @ ( B @ 'fun_app$cj' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(542,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( 'set$' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom431) ).
thf(3057,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$' @ ( C @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$' @ 'fun_app$bl' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( 'set$' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(496,axiom,
! [A: 'A$',B: 'A_set$',C: 'A_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'A$'] :
( ( B @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ( ( E @ ( C @ 'fun_app$co' ) )
= D ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( ( B @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom771) ).
thf(2847,plain,
! [A: 'A$',B: 'A_set$',C: 'A_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'A$'] :
( ( B @ ( E @ 'member$c' @ 'fun_app$p' ) )
=> ( ( E @ ( C @ 'fun_app$co' ) )
= D ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( ( B @ ( C @ 'image$aq' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(444,axiom,
! [A: 'B$',B: 'Nat_b_fun$'] :
( ( ! [C: 'Nat$'] :
( ( A
= ( C @ ( B @ 'fun_app$cq' ) ) )
=> $false )
& ( 'top$' @ ( B @ 'image$y' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom571) ).
thf(2600,plain,
! [A: 'B$',B: 'Nat_b_fun$'] :
~ ( ! [C: 'Nat$'] :
( A
!= ( C @ ( B @ 'fun_app$cq' ) ) )
& ( 'top$' @ ( B @ 'image$y' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(606,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom434) ).
thf(3411,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$bf' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(215,axiom,
! [A: 'B_set$',B: 'B_set$',C: 'B_ZF_set_fun$',D: 'B_ZF_set_fun$'] :
( ( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ( E @ ( D @ 'fun_app$cx' ) @ ( E @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$a' ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom764) ).
thf(1537,plain,
! [A: 'B_set$',B: 'B_set$',C: 'B_ZF_set_fun$',D: 'B_ZF_set_fun$'] :
( ( ! [E: 'B$'] :
( ( A @ ( E @ 'member$b' @ 'fun_app$m' ) )
=> ( E @ ( D @ 'fun_app$cx' ) @ ( E @ ( C @ 'fun_app$cx' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( B @ ( A @ 'less_eq$a' ) ) )
=> ( B @ ( D @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( A @ ( C @ 'image$ar' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(375,axiom,
! [A: 'ZF_ZF_ZF_fun_fun$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'uuv$' @ 'fun_app$aq' ) @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).
thf(2265,plain,
! [A: 'ZF_ZF_ZF_fun_fun$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'uuv$' @ 'fun_app$aq' ) @ 'fun_app$b' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'fun_app$b' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(98,axiom,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'ZF_set$'] :
( ( B @ ( E @ 'member$a' @ 'fun_app$j' ) )
=> ( ( E @ ( C @ 'fun_app$ae' ) )
= D ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> ( ( B @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom774) ).
thf(1019,plain,
! [A: 'ZF_set$',B: 'ZF_set_set$',C: 'ZF_set_ZF_set_fun$',D: 'ZF_set$'] :
( ( ! [E: 'ZF_set$'] :
( ( B @ ( E @ 'member$a' @ 'fun_app$j' ) )
=> ( ( E @ ( C @ 'fun_app$ae' ) )
= D ) )
& ( B @ ( A @ 'member$a' @ 'fun_app$j' ) ) )
=> ( ( B @ ( C @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(440,axiom,
! [A: 'A_set$',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$' ) ) ) ) ) ) @ 'id$' )
= E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom213) ).
thf(2583,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$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$' ) ) ) ) ) ) @ 'id$' )
= E ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(574,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ ( A @ 'homFtorContra$a' ) @ 'functor_abbrev$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom399) ).
thf(3259,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ ( A @ 'oppositeCategory$' @ ( B @ ( A @ 'homFtorContra$a' ) @ 'functor_abbrev$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(602,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) )
= ( C @ ( A @ 'uuq$' ) @ ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).
thf(3394,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) )
= ( C @ ( A @ 'uuq$' ) @ ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(19,axiom,
! [A: 'Nat$',B: 'Nat_set$',C: 'ZF$',D: 'Nat_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$r' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$e' ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom637) ).
thf(691,plain,
! [A: 'Nat$',B: 'Nat_set$',C: 'ZF$',D: 'Nat_ZF_set_fun$'] :
( ( ( A @ ( D @ 'fun_app$r' ) @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ ( A @ 'member$e' ) ) )
=> ( B @ ( D @ 'image$' @ 'fun_app$v' ) @ ( 'sup$' @ 'fun_app$u' ) @ ( C @ 'member$' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(288,axiom,
! [A: 'B$',B: 'B_b_set_fun$',C: 'B_set$'] :
( ( C @ ( B @ 'image$an' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) )
<=> ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom806) ).
thf(1885,plain,
! [A: 'B$',B: 'B_b_set_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ 'image$an' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
& ( ( C @ ( B @ 'image$an' ) @ 'inf$b' @ ( A @ 'member$b' @ 'fun_app$m' ) )
=> ! [D: 'B$'] :
( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
=> ( D @ ( B @ 'fun_app$cu' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(470,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_bool_fun$'] :
( ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( ( C @ ( B @ 'uva$' ) @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
<=> ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$f' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).
thf(2699,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_bool_fun$'] :
( ( B @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
=> ( ( ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$f' ) ) )
=> ( C @ ( B @ 'uva$' ) @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) ) )
& ( ( C @ ( B @ 'uva$' ) @ 'collect$' @ ( A @ 'less_eq$c' @ 'fun_app$h' ) )
=> ! [D: 'ZF$'] :
( ( A @ ( D @ 'member$' @ 'fun_app$h' ) )
=> ( D @ ( C @ 'fun_app$f' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(623,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).
thf(3494,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' @ 'fun_app$p' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$bf' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$ar' ) @ ( 'set$a' @ 'mapsTo$a' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(548,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' )
= ( A @ 'more$' @ ( A @ 'uud$' @ ( A @ 'id$' @ ( A @ 'dom$' @ ( A @ 'cod$' @ ( A @ 'mor$' @ ( A @ 'obj$' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom376) ).
thf(3096,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'oppositeCategory$' )
= ( A @ 'more$' @ ( A @ 'uud$' @ ( A @ 'id$' @ ( A @ 'dom$' @ ( A @ 'cod$' @ ( A @ 'mor$' @ ( A @ 'obj$' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(530,axiom,
! [A: 'A$',B: 'A_set$',C: 'A_set$',D: 'A_bool_fun$'] :
( ( ( D @ ( C @ 'uux$' ) @ 'collect$h' @ ( B @ 'less_eq$' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( A @ ( D @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).
thf(2998,plain,
! [A: 'A$',B: 'A_set$',C: 'A_set$',D: 'A_bool_fun$'] :
( ( ( D @ ( C @ 'uux$' ) @ 'collect$h' @ ( B @ 'less_eq$' ) )
& ( B @ ( A @ 'member$c' @ 'fun_app$p' ) ) )
=> ( A @ ( D @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(278,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( B @ 'dom$a' @ 'fun_app$' ) ) )
& ( B @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom266) ).
thf(1848,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$' ) )
= ( C @ ( B @ 'dom$a' @ 'fun_app$' ) ) )
& ( B @ 'mor$a' @ ( C @ 'member$' @ 'fun_app$h' ) )
& ( B @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(369,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom255) ).
thf(2238,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) )
& ( A @ 'mor$' @ ( B @ 'member$b' @ 'fun_app$m' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(113,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$'] :
( ( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
=> ( C @ ( B @ 'fun_app$f' ) ) )
& ? [C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) )
=> ( A @ 'the$' @ ( B @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom395) ).
thf(1069,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$'] :
( ( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$f' ) )
=> ( C @ ( B @ 'fun_app$f' ) ) )
& ? [C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( D = C ) )
& ( C @ ( A @ 'fun_app$f' ) ) ) )
=> ( A @ 'the$' @ ( B @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(24,axiom,
! [A: 'ZF_set$',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$a' ) ) ) ) ) ) @ 'mor$a' )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom216) ).
thf(708,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$a' )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(177,axiom,
! [A: tlbool,B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'uuh$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( ( ( ( A = tltrue )
<=> $false )
=> ( D = C ) )
& ( ( ( A = tltrue )
<=> $true )
=> ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom127) ).
thf(1331,plain,
! [A: tlbool,B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( ( A != tltrue )
=> ( D = C ) )
& ( ( A = tltrue )
=> ( D = B ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uuh$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uuh$' ) @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( ( ( A != tltrue )
=> ( D = C ) )
& ( ( A = tltrue )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(224,axiom,
! [A: 'B_b_fun$',B: 'B_set$',C: 'B_bool_fun$',D: 'B$'] :
( ( D @ ( C @ ( B @ ( A @ 'uvr$' ) ) @ 'fun_app$k' ) )
<=> ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$l' @ 'fun_app$bg' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom133) ).
thf(1606,plain,
! [A: 'B_b_fun$',B: 'B_set$',C: 'B_bool_fun$',D: 'B$'] :
( ( ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$l' @ 'fun_app$bg' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'uvr$' ) ) @ 'fun_app$k' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'uvr$' ) ) @ 'fun_app$k' ) )
=> ( ( D @ ( C @ 'fun_app$k' ) )
& ( B @ ( A @ 'image$l' @ 'fun_app$bg' ) @ ( D @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(504,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$',D: 'B$'] :
( ( ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).
thf(2879,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$',D: 'B$'] :
( ( ( ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$an' ) @ 'fun_app$am' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$bk' ) @ ( A @ 'id$' @ 'fun_app$bl' ) ) )
& ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$k' ) )
& ( A @ 'category$' ) )
=> ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(455,axiom,
! [A: 'ZF_set_set$',B: 'ZF_set_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom670) ).
thf(2640,plain,
! [A: 'ZF_set_set$',B: 'ZF_set_ZF_set_fun$',C: 'ZF_set$'] :
( ! [D: 'ZF_set$'] :
( ( A @ ( D @ 'member$a' @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ 'fun_app$ae' ) @ 'less_eq$c' @ 'fun_app$h' ) ) )
=> ( C @ ( A @ ( B @ 'image$q' @ 'fun_app$cn' ) @ ( 'sup$' @ 'fun_app$u' ) @ 'less_eq$c' @ 'fun_app$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(298,axiom,
! [A: 'ZF_ZF_bool_fun_fun$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uzw$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
<=> ( B @ ( C @ ( A @ 'fun_app$q' ) @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom57) ).
thf(1944,plain,
! [A: 'ZF_ZF_bool_fun_fun$',B: 'ZF$',C: 'ZF$'] :
( ( ( B @ ( C @ ( A @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( C @ ( B @ ( A @ 'uzw$' @ 'fun_app$q' ) @ 'fun_app$f' ) ) )
& ( ( C @ ( B @ ( A @ 'uzw$' @ 'fun_app$q' ) @ 'fun_app$f' ) )
=> ( B @ ( C @ ( A @ 'fun_app$q' ) @ 'fun_app$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(182,axiom,
! [A: 'B$',B: 'B_b_fun$',C: 'B_set$'] :
( ( ! [D: 'B$'] :
( ( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( A
= ( D @ ( B @ 'fun_app$am' ) ) ) )
=> $false )
& ( C @ ( B @ 'image$l' @ 'fun_app$bg' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom526) ).
thf(1367,plain,
! [A: 'B$',B: 'B_b_fun$',C: 'B_set$'] :
~ ( ! [D: 'B$'] :
~ ( ( C @ ( D @ 'member$b' @ 'fun_app$m' ) )
& ( A
= ( D @ ( B @ 'fun_app$am' ) ) ) )
& ( C @ ( B @ 'image$l' @ 'fun_app$bg' ) @ ( A @ 'member$b' @ 'fun_app$m' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(145,axiom,
! [A: 'ZF_ZF_fun$',B: 'ZF_ZF_prod_ZF_fun$',C: 'ZF_ZF_prod_set$'] :
( ( C @ ( B @ 'image$f' @ 'fun_app$au' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) )
= ( C @ ( B @ ( A @ 'uvd$' ) @ 'image$f' @ 'fun_app$au' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).
thf(1204,plain,
! [A: 'ZF_ZF_fun$',B: 'ZF_ZF_prod_ZF_fun$',C: 'ZF_ZF_prod_set$'] :
( ( C @ ( B @ 'image$f' @ 'fun_app$au' ) @ ( A @ 'image$g' @ 'fun_app$ae' ) )
= ( C @ ( B @ ( A @ 'uvd$' ) @ 'image$f' @ 'fun_app$au' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(269,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
<=> ( 'set$' @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom453) ).
thf(1812,plain,
! [A: 'ZF$'] :
( ( ( 'set$' @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) )
=> ( A @ ( 'isZFfun$' @ 'fun_app$f' ) ) )
& ( ( A @ ( 'isZFfun$' @ 'fun_app$f' ) )
=> ( 'set$' @ 'mor$a' @ ( A @ 'member$' @ 'fun_app$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(74,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF$',C: 'ZF_bool_fun$'] :
( ( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( D @ ( C @ 'fun_app$f' ) ) )
& ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( D = B ) )
& ( B @ ( A @ 'fun_app$f' ) ) )
=> ( A @ 'the$' @ ( C @ 'fun_app$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).
thf(882,plain,
! [A: 'ZF_bool_fun$',B: 'ZF$',C: 'ZF_bool_fun$'] :
( ( ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( D @ ( C @ 'fun_app$f' ) ) )
& ! [D: 'ZF$'] :
( ( D @ ( A @ 'fun_app$f' ) )
=> ( D = B ) )
& ( B @ ( A @ 'fun_app$f' ) ) )
=> ( A @ 'the$' @ ( C @ 'fun_app$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(356,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uuo$' ) @ 'fun_app$k' ) )
<=> ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).
thf(2177,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$',C: 'B$'] :
( ( ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) ) )
=> ( C @ ( B @ ( A @ 'uuo$' ) @ 'fun_app$k' ) ) )
& ( ( C @ ( B @ ( A @ 'uuo$' ) @ 'fun_app$k' ) )
=> ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$ar' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$b' @ 'fun_app$m' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(5293,plain,
$false,
inference(e,[status(thm)],[645,1322,1036,1718,629,2744,2109,2778,1729,3397,1840,777,1818,1950,2280,2452,809,2306,3053,2412,2876,628,1031,2427,1083,2210,3317,683,2644,741,3108,873,1793,1305,1173,2309,762,1443,2776,2659,3377,3040,1544,2014,1692,677,3017,1655,3120,1310,3135,2918,797,715,1872,945,1954,1458,3276,2168,698,3414,747,1222,930,898,2723,2972,1914,1127,2985,3249,3088,1613,1359,2531,829,3370,1095,1228,1623,3263,1709,2339,3342,2755,2217,3148,702,1279,1992,3043,1055,724,3099,3374,1147,2767,1013,1741,1641,1773,2301,1875,3231,3268,1922,817,2691,638,853,2049,2552,1319,870,2929,3470,2222,924,789,1450,1373,1911,2650,1682,1858,1383,2335,2017,1302,756,1664,2324,2027,2893,1632,2469,1960,3300,1183,2073,2437,2371,1351,660,2242,2965,2586,1843,2058,2618,2833,2190,3421,1104,1242,2718,2205,942,3169,2118,2093,2232,3418,3503,3459,2364,2164,2083,1067,2621,2773,2000,2673,3261,2733,820,1487,2969,3239,693,2606,3154,1824,2890,3339,1883,1900,1723,1676,2133,847,1920,879,3297,2872,1296,2068,2609,1210,2327,1407,1634,842,2769,2653,3282,1423,3307,1365,2670,3050,2345,1534,1804,1328,1064,1111,2694,3102,1006,2726,2858,783,2268,3105,3467,1089,1541,3482,2100,1851,3122,2946,1498,1587,3060,1397,2460,3143,1361,3000,2830,1461,1414,1791,1446,1039,2781,1028,2023,3326,3407,753,901,2419,2312,3010,3032,1937,1016,1207,997,1150,1231,1984,1429,2052,1715,1979,2140,3162,2285,1114,2450,985,1530,1456,2006,721,2926,1779,2208,2043,1695,921,657,765,1170,2089,674,2440,2662,1185,773,794,1996,2423,718,1906,1219,856,1595,2376,733,2260,2121,2235,2936,1135,750,1510,1698,2556,3358,2275,2149,2570,2941,3234,2789,1652,1388,2991,1403,1256,2827,2188,2981,1620,3472,826,711,1520,3404,1786,936,1271,787,1239,1765,2457,3355,641,2161,1058,1107,3487,1092,2425,3416,2573,2358,979,1194,2079,3101,2624,2415,1806,1048,1144,2839,3500,3384,1376,2637,1117,2257,1589,2197,1969,1307,1877,1080,2742,3027,1630,1821,1162,700,1325,3006,2710,1688,890,1667,1293,2278,668,1061,1952,912,2401,3423,2064,2288,3241,1000,2633,2303,1926,2962,1213,768,3110,2086,780,1643,2967,1250,3490,3380,1034,1758,2994,648,1990,2318,680,927,2037,2333,2564,2597,1958,1181,823,1845,1025,3112,1156,3082,2143,1252,2678,1098,2882,1516,2863,3315,1598,1225,2060,2407,2386,791,1188,3344,1869,3475,1262,2219,2903,3359,1130,1285,907,2656,3019,1987,2454,2948,744,2543,1052,864,1749,727,1797,876,1617,1141,1981,1955,2843,2145,1881,3156,3433,2045,1966,1685,1834,688,2347,1216,1866,2435,845,2760,2626,1316,1649,2696,1553,2870,2828,671,2960,2611,759,3320,1010,1390,2342,1734,771,2907,2443,2707,3484,2855,1101,3336,632,2431,1523,3252,1385,2594,1721,2174,2283,2853,2290,2251,995,2152,2262,2394,3085,2944,2384,2462,1077,2680,3351,1661,832,2315,2739,1045,2956,1491,3430,1777,1440,2330,2576,2066,1893,2294,2003,2374,2102,2683,3291,2983,835,2604,1673,3062,2123,1133,2155,2534,867,3496,3145,1436,2751,3328,801,1495,2186,807,2070,1410,1789,1197,2404,635,3506,2549,839,3244,3128,1827,1550,992,1500,982,1299,1236,2127,3057,2847,2600,3411,1537,2265,1019,2583,3259,3394,691,1885,2699,3494,3096,2998,1848,2238,1069,708,1331,1606,2879,2640,1944,1367,1204,1812,882,2177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP302_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % 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
% 0.12/0.38 % Computer : n005.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 19:05:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.83/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.24/1.67 % [INFO] Parsing done (709ms).
% 3.24/1.68 % [INFO] Running in sequential loop mode.
% 4.21/2.06 % [INFO] eprover registered as external prover.
% 4.21/2.07 % [INFO] Scanning for conjecture ...
% 4.79/2.35 % [INFO] Found a conjecture (or negated_conjecture) and 823 axioms. Running axiom selection ...
% 6.48/2.78 % [INFO] Axiom selection finished. Selected 625 axioms (removed 198 axioms).
% 8.20/3.29 % [INFO] Problem is typed first-order (TPTP TFF).
% 8.60/3.32 % [INFO] Type checking passed.
% 8.60/3.33 % [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 ...
% 33.02/9.43 % External prover 'e' found a proof!
% 33.02/9.43 % [INFO] Killing All external provers ...
% 33.02/9.43 % Time passed: 8911ms (effective reasoning time: 7745ms)
% 33.02/9.43 % 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)>
% 33.02/9.44 % Axioms used in derivation (625): axiom326, axiom32, axiom635, axiom280, axiom127, axiom626, axiom315, axiom546, axiom745, axiom452, axiom491, axiom770, axiom681, axiom241, axiom28, axiom702, axiom260, axiom273, axiom61, axiom527, axiom730, axiom717, axiom230, axiom6, axiom781, axiom564, axiom503, axiom54, axiom549, axiom723, axiom785, axiom396, axiom25, axiom810, axiom404, axiom769, axiom333, axiom804, axiom221, axiom295, axiom485, axiom809, axiom369, axiom214, axiom670, axiom322, axiom307, axiom203, axiom496, axiom284, axiom749, axiom662, axiom423, axiom734, axiom65, axiom142, axiom311, axiom739, axiom531, axiom291, axiom430, axiom50, axiom131, axiom10, axiom386, axiom392, axiom337, axiom344, axiom820, axiom138, axiom441, axiom699, axiom580, axiom728, axiom119, axiom210, axiom407, axiom191, axiom692, axiom587, axiom17, axiom673, axiom766, axiom773, axiom397, axiom460, axiom354, axiom467, axiom257, axiom147, axiom434, axiom341, axiom504, axiom638, axiom300, axiom376, axiom684, axiom654, axiom815, axiom535, axiom735, axiom266, axiom445, axiom524, axiom695, axiom42, axiom239, axiom561, axiom329, axiom372, axiom777, axiom195, axiom358, axiom706, axiom632, axiom33, axiom542, axiom762, axiom246, axiom701, axiom605, axiom134, axiom104, axiom456, axiom572, axiom568, axiom130, axiom557, axiom235, axiom808, axiom499, axiom330, axiom650, axiom418, axiom11, axiom819, axiom304, axiom488, axiom643, axiom225, axiom473, axiom796, axiom520, axiom365, axiom251, axiom687, axiom64, axiom247, axiom676, axiom530, axiom636, axiom27, axiom294, axiom283, axiom427, axiom625, axiom591, axiom642, axiom742, axiom682, axiom803, axiom821, axiom217, axiom343, axiom363, axiom705, axiom314, axiom289, axiom437, axiom236, axiom115, axiom94, axiom83, axiom5, axiom336, axiom308, axiom321, axiom647, axiom78, axiom661, axiom668, axiom278, axiom272, axiom228, axiom405, axiom455, axiom121, axiom132, axiom56, axiom137, axiom563, axiom206, axiom13, axiom318, axiom60, axiom631, axiom0, axiom574, axiom490, axiom671, axiom466, axiom240, axiom290, axiom433, axiom143, axiom359, axiom416, axiom489, axiom545, axiom108, axiom395, axiom387, axiom528, axiom459, axiom400, axiom258, axiom653, axiom698, axiom448, axiom552, axiom385, axiom784, axiom658, axiom332, axiom9, axiom814, axiom325, axiom800, axiom811, axiom478, axiom693, axiom303, axiom366, axiom207, axiom494, axiom133, axiom371, axiom567, axiom355, axiom738, axiom422, axiom472, axiom202, axiom252, axiom146, axiom97, axiom391, axiom263, axiom415, axiom589, axiom254, axiom776, axiom444, axiom790, axiom694, axiom45, axiom679, axiom669, axiom229, axiom788, axiom541, axiom360, axiom398, axiom382, axiom818, axiom657, axiom426, axiom639, axiom319, axiom347, axiom765, axiom672, axiom646, axiom67, axiom213, axiom534, axiom450, axiom523, axiom232, axiom629, axiom683, axiom807, axiom798, axiom72, axiom461, axiom463, axiom310, axiom449, axiom438, axiom727, axiom500, axiom86, axiom772, axiom267, axiom163, axiom665, axiom664, axiom731, axiom224, axiom122, axiom419, axiom377, axiom1, axiom105, axiom111, axiom120, axiom660, axiom297, axiom447, axiom52, axiom783, axiom279, axiom641, axiom390, axiom37, axiom331, axiom212, axiom602, axiom432, axiom223, axiom571, axiom501, axiom342, axiom193, axiom34, axiom630, axiom79, axiom544, axiom425, axiom764, axiom454, axiom205, axiom364, axiom190, axiom707, axiom573, axiom710, axiom443, axiom96, axiom189, axiom375, axiom23, axiom227, axiom560, axiom562, axiom41, axiom394, axiom667, axiom476, axiom216, axiom320, axiom704, axiom286, axiom313, axiom275, axiom63, axiom19, axiom743, axiom458, axiom8, axiom30, axiom370, axiom201, axiom178, axiom479, axiom659, axiom428, axiom259, axiom74, axiom276, axiom451, axiom570, axiom697, axiom233, axiom302, axiom367, axiom794, axiom57, axiom802, axiom85, axiom652, axiom566, axiom817, axiom145, axiom471, axiom186, axiom497, axiom164, axiom726, axiom378, axiom374, axiom748, axiom440, axiom678, axiom282, axiom271, axiom287, axiom255, axiom775, axiom324, axiom71, axiom462, axiom15, axiom129, axiom114, axiom244, axiom136, axiom414, axiom106, axiom533, axiom813, axiom522, axiom436, axiom753, axiom237, axiom486, axiom645, axiom806, axiom68, axiom686, axiom335, axiom737, axiom170, axiom656, axiom718, axiom791, axiom268, axiom293, axiom787, axiom555, axiom493, axiom356, axiom46, axiom439, axiom634, axiom469, axiom110, axiom125, axiom675, axiom603, axiom49, axiom771, axiom715, axiom219, axiom197, axiom690, axiom298, axiom732, axiom248, axiom421, axiom590, axiom338, axiom242, axiom792, axiom666, axiom558, axiom691, axiom663, axiom199, axiom547, axiom389, axiom226, axiom526, axiom559, axiom457, axiom521, axiom651, axiom757, axiom442, axiom327, axiom779, axiom782, axiom399, axiom66, axiom763, axiom345, axiom464, axiom204, axiom296, axiom569, axiom752, axiom700, axiom215, axiom576, axiom141, axiom357, axiom117, axiom393, axiom621, axiom453, axiom222, axiom7, axiom323, axiom774, axiom446, axiom84, axiom554, axiom495, axiom502, axiom103, axiom231, axiom306, axiom253, axiom640, axiom249, axiom368, axiom680, axiom550, axiom780, axiom703, axiom148, axiom128, axiom316, axiom285, axiom744, axiom183, axiom301, axiom649, axiom211, axiom29, axiom789, axiom689, axiom361, axiom429, axiom532, axiom177, axiom31, axiom380, axiom188, axiom264, axiom431, axiom208, axiom20, axiom588, axiom627, axiom270, axiom733, axiom487, axiom519, axiom402, axiom73, axiom107, axiom339, axiom265, axiom816, axiom165, axiom518, axiom714, axiom417, axiom40, axiom778, axiom305, axiom187, axiom245, axiom288, axiom317, axiom277, axiom529, axiom144, axiom281, axiom424, axiom633, axiom644, axiom69, axiom685, axiom135, axiom536, axiom373, axiom435, axiom312, axiom95, axiom70, axiom238, axiom617, axiom465, axiom584, axiom736, axiom543, axiom299, axiom77, axiom256, axiom334, axiom812, axiom696, axiom43, axiom722, axiom124, axiom505, axiom261, axiom725, axiom655, axiom786, axiom406, axiom388, axiom677, axiom582, axiom637, axiom420, axiom756, axiom674, axiom21, axiom139, axiom200, axiom58, axiom292, axiom525, axiom234, axiom362, axiom51, axiom548, axiom309, axiom470, axiom767, axiom498, axiom805, axiom648, axiom209, axiom468, axiom492, axiom328, axiom140, axiom250, axiom688, axiom340, axiom353
% 33.02/9.44 % No. of inferences in proof: 1254
% 33.02/9.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8911 ms resp. 7745 ms w/o parsing
% 35.28/10.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.79/10.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------