%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP303_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 : n014.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 23.86s 7.01s
% Output : Refutation 25.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 405
% Syntax : Number of formulae : 812 ( 178 unt; 0 typ; 0 def)
% Number of atoms : 2698 ( 843 equ; 0 cnn)
% Maximal formula atoms : 34 ( 3 avg)
% Number of connectives : 14268 ( 36 ~; 0 |;1034 &;12346 @)
% ( 51 <=>; 801 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Number of types : 81 ( 80 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 202 ( 199 usr; 36 con; 0-7 aty)
% Number of variables : 2353 ( 0 ^;2327 !; 26 ?;2353 :)
% Comments :
%------------------------------------------------------------------------------
thf('B_ZF_fun_set$_type',type,
'B_ZF_fun_set$': $tType ).
thf('ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$_type',type,
'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$': $tType ).
thf('Unit_set$_type',type,
'Unit_set$': $tType ).
thf('ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$_type',type,
'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_Functor_ext$': $tType ).
thf('B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$_type',type,
'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$': $tType ).
thf('ZF_set$_type',type,
'ZF_set$': $tType ).
thf('ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$_type',type,
'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$': $tType ).
thf('A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$_type',type,
'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_NatTrans_ext$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$': $tType ).
thf('Unit_unit_fun$_type',type,
'Unit_unit_fun$': $tType ).
thf('A_b_b_c_LSCategory_ext_Category_ext$_type',type,
'A_b_b_c_LSCategory_ext_Category_ext$': $tType ).
thf('ZF_ZF_prod_set$_type',type,
'ZF_ZF_prod_set$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$': $tType ).
thf('ZF_set_set$_type',type,
'ZF_set_set$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$': $tType ).
thf('ZF_set_ZF_set_fun$_type',type,
'ZF_set_ZF_set_fun$': $tType ).
thf('A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$_type',type,
'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$': $tType ).
thf('ZF_ZF_set_fun$_type',type,
'ZF_ZF_set_fun$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$': $tType ).
thf('A_b_fun_set$_type',type,
'A_b_fun_set$': $tType ).
thf('ZF_ZF_prod_ZF_fun$_type',type,
'ZF_ZF_prod_ZF_fun$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$': $tType ).
thf('B_c_LSCategory_ext$_type',type,
'B_c_LSCategory_ext$': $tType ).
thf('B_b_fun$_type',type,
'B_b_fun$': $tType ).
thf('ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext$_type',type,
'ZF_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_unit_unit_NatTrans_ext$': $tType ).
thf('ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext$_type',type,
'ZF_unit_ZF_unit_unit_unit_unit_NatTrans_ext$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$': $tType ).
thf('A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$_type',type,
'A_a_b_b_b_c_LSCategory_ext_b_c_LSCategory_ext_unit_Functor_ext$': $tType ).
thf('ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$_type',type,
'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_unit_Category_ext$': $tType ).
thf('A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$_type',type,
'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$': $tType ).
thf('ZF_ZF_prod$_type',type,
'ZF_ZF_prod$': $tType ).
thf('B_b_prod_set$_type',type,
'B_b_prod_set$': $tType ).
thf('B$_type',type,
'B$': $tType ).
thf('A_ZF_fun_set$_type',type,
'A_ZF_fun_set$': $tType ).
thf('ZF_ZF_ZF_fun_fun$_type',type,
'ZF_ZF_ZF_fun_fun$': $tType ).
thf('ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$_type',type,
'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$': $tType ).
thf('Unit_unit_unit_Category_ext$_type',type,
'Unit_unit_unit_Category_ext$': $tType ).
thf('C$_type',type,
'C$': $tType ).
thf('A_ZF_fun_bool_fun$_type',type,
'A_ZF_fun_bool_fun$': $tType ).
thf('B_b_prod_bool_fun$_type',type,
'B_b_prod_bool_fun$': $tType ).
thf('ZF_ZF_prod_ZF_fun_set$_type',type,
'ZF_ZF_prod_ZF_fun_set$': $tType ).
thf('ZF_ZF_fun$_type',type,
'ZF_ZF_fun$': $tType ).
thf('ZF_ZF_prod_bool_fun$_type',type,
'ZF_ZF_prod_bool_fun$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$': $tType ).
thf('ZF_ZF_fun_set$_type',type,
'ZF_ZF_fun_set$': $tType ).
thf('B_b_prod_b_fun_set$_type',type,
'B_b_prod_b_fun_set$': $tType ).
thf('B_a_fun$_type',type,
'B_a_fun$': $tType ).
thf('ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$_type',type,
'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_NatTrans_ext$': $tType ).
thf('B_b_prod$_type',type,
'B_b_prod$': $tType ).
thf('ZF_ZF_fun_ZF_ZF_fun_fun$_type',type,
'ZF_ZF_fun_ZF_ZF_fun_fun$': $tType ).
thf('ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun$_type',type,
'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_fun$': $tType ).
thf('ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun$_type',type,
'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun$': $tType ).
thf('A_bool_fun$_type',type,
'A_bool_fun$': $tType ).
thf('A_set$_type',type,
'A_set$': $tType ).
thf('ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$_type',type,
'ZF_a_ZF_b_unit_b_c_LSCategory_ext_unit_Functor_ext$': $tType ).
thf('A_b_fun$_type',type,
'A_b_fun$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$': $tType ).
thf('B_set$_type',type,
'B_set$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$': $tType ).
thf('A_b_fun_bool_fun$_type',type,
'A_b_fun_bool_fun$': $tType ).
thf('A$_type',type,
'A$': $tType ).
thf('ZF_ZF_unit_Category_ext$_type',type,
'ZF_ZF_unit_Category_ext$': $tType ).
thf('A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$_type',type,
'A_ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext_b_ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_NatTrans_ext$': $tType ).
thf('B_b_prod_b_fun$_type',type,
'B_b_prod_b_fun$': $tType ).
thf('A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$_type',type,
'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$': $tType ).
thf('B_set_b_set_fun$_type',type,
'B_set_b_set_fun$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$': $tType ).
thf('ZF_bool_fun$_type',type,
'ZF_bool_fun$': $tType ).
thf('A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$_type',type,
'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$': $tType ).
thf('B_b_b_fun_fun$_type',type,
'B_b_b_fun_fun$': $tType ).
thf('ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$_type',type,
'ZF_ZF_ZF_fun_fun_ZF_ZF_ZF_fun_fun_fun$': $tType ).
thf('A_ZF_fun$_type',type,
'A_ZF_fun$': $tType ).
thf('Unit$_type',type,
'Unit$': $tType ).
thf('ZF$_type',type,
'ZF$': $tType ).
thf('B_ZF_fun$_type',type,
'B_ZF_fun$': $tType ).
thf('B_a_fun_set$_type',type,
'B_a_fun_set$': $tType ).
thf('B_a_fun_bool_fun$_type',type,
'B_a_fun_bool_fun$': $tType ).
thf('B_bool_fun$_type',type,
'B_bool_fun$': $tType ).
thf('B_ZF_fun_bool_fun$_type',type,
'B_ZF_fun_bool_fun$': $tType ).
thf('functorComp$a_decl',type,
'functorComp$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('id$_decl',type,
'id$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_fun$' ).
thf('makeCat$a_decl',type,
'makeCat$a': 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$' ).
thf('restrict$c_decl',type,
'restrict$c': 'A_ZF_fun$' > 'A_set$' > 'A_ZF_fun$' ).
thf('functorComp$_decl',type,
'functorComp$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('catDom$a_decl',type,
'catDom$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('uun$_decl',type,
'uun$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('c$_decl',type,
'c$': 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('mor_update$a_decl',type,
'mor_update$a': 'B_set_b_set_fun$' > 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$' ).
thf('uum$_decl',type,
'uum$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'A_ZF_fun$' ).
thf('uuq$_decl',type,
'uuq$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A$' > 'ZF_bool_fun$' ).
thf('nt_abbrev$a_decl',type,
'nt_abbrev$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('fun_app$s_decl',type,
'fun_app$s': 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$' > 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('more$b_decl',type,
'more$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'Unit$' ).
thf('natTrans_ext$a_decl',type,
'natTrans_ext$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_fun$' > 'Unit$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('catExp$c_decl',type,
'catExp$c': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' ).
thf('extCategory$_decl',type,
'extCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('the$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$' ).
thf('obj$a_decl',type,
'obj$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_set$' ).
thf('functor_comp_def$c_decl',type,
'functor_comp_def$c': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('lSCategory$_decl',type,
'lSCategory$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('fun_app$a_decl',type,
'fun_app$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > $o ).
thf('natTrans$_decl',type,
'natTrans$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' ).
thf('fun_app$n_decl',type,
'fun_app$n': 'A_ZF_fun$' > 'A$' > 'ZF$' ).
thf('uup$_decl',type,
'uup$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_fun$' ).
thf('member$f_decl',type,
'member$f': 'A_ZF_fun$' > 'A_ZF_fun_set$' > $o ).
thf('catDom_update$a_decl',type,
'catDom_update$a': 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' ).
thf('catCod$_decl',type,
'catCod$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('functor_comp_def$b_decl',type,
'functor_comp_def$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('top$_decl',type,
'top$': 'ZF_set$' ).
thf('more$c_decl',type,
'more$c': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'C$' ).
thf('oppositeCategory$_decl',type,
'oppositeCategory$': 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$' ).
thf('fun_app$r_decl',type,
'fun_app$r': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('mapO$b_decl',type,
'mapO$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_fun$' ).
thf('f$_decl',type,
'f$': 'B$' ).
thf('nTCompDefined$a_decl',type,
'nTCompDefined$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' ).
thf('uus$_decl',type,
'uus$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF$' > 'B_bool_fun$' ).
thf('fun_app$q_decl',type,
'fun_app$q': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > $o ).
thf('fun_app$ab_decl',type,
'fun_app$ab': 'B_a_fun$' > 'B$' > 'A$' ).
thf('category$a_decl',type,
'category$a': 'ZF_ZF_unit_Category_ext$' > $o ).
thf('functor_comp_def$a_decl',type,
'functor_comp_def$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' > $o ).
thf('functorM_axioms$_decl',type,
'functorM_axioms$': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('equivalence_axioms$_decl',type,
'equivalence_axioms$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('category$_decl',type,
'category$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('idNatTrans$d_decl',type,
'idNatTrans$d': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$' ).
thf('uuk$_decl',type,
'uuk$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('uut$_decl',type,
'uut$': 'ZF_bool_fun$' ).
thf('equivalence$_decl',type,
'equivalence$': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('functorM$a_decl',type,
'functorM$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('uu$_decl',type,
'uu$': 'B_set$' > 'B_bool_fun$' ).
thf('set$_decl',type,
'set$': 'ZF_ZF_unit_Category_ext$' ).
thf('unity$_decl',type,
'unity$': 'Unit$' ).
thf('uuo$_decl',type,
'uuo$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' ).
thf('uur$_decl',type,
'uur$': 'ZF$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('fun_app$d_decl',type,
'fun_app$d': 'ZF_bool_fun$' > 'ZF$' > $o ).
thf('fun_app$z_decl',type,
'fun_app$z': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$' ).
thf('oppositeCategory$b_decl',type,
'oppositeCategory$b': 'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun$' ).
thf('fun_app$l_decl',type,
'fun_app$l': 'B_b_fun$' > 'B$' > 'B$' ).
thf('mor2ZF$_decl',type,
'mor2ZF$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_ZF_fun$' ).
thf('idNatTrans$b_decl',type,
'idNatTrans$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('catDom$_decl',type,
'catDom$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('zFfun$_decl',type,
'zFfun$': 'ZF$' > 'ZF$' > 'ZF_ZF_fun$' > 'ZF$' ).
thf('inverse_rel$_decl',type,
'inverse_rel$': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('member$c_decl',type,
'member$c': 'ZF$' > 'ZF_set$' > $o ).
thf('extensional$b_decl',type,
'extensional$b': 'B_set$' > 'B_ZF_fun_set$' ).
thf('fun_app$p_decl',type,
'fun_app$p': 'A_b_fun$' > 'A$' > 'B$' ).
thf('idNatTrans$c_decl',type,
'idNatTrans$c': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' ).
thf('more$a_decl',type,
'more$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'Unit$' ).
thf('functor_comp_def$_decl',type,
'functor_comp_def$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' > $o ).
thf('nTCatCod$_decl',type,
'nTCatCod$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('fun_app$ac_decl',type,
'fun_app$ac': 'ZF_ZF_fun_ZF_ZF_fun_fun$' > 'ZF_ZF_fun$' > 'ZF_ZF_fun$' ).
thf('lSCategory_axioms$_decl',type,
'lSCategory_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('zFfunCod$_decl',type,
'zFfunCod$': 'ZF_ZF_fun$' ).
thf('fun_app$k_decl',type,
'fun_app$k': 'ZF_ZF_ZF_fun_fun$' > 'ZF$' > 'ZF_ZF_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('catDom$b_decl',type,
'catDom$b': 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('nTDom$_decl',type,
'nTDom$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' ).
thf('more$e_decl',type,
'more$e': 'ZF_ZF_unit_Category_ext$' > 'Unit$' ).
thf('set$a_decl',type,
'set$a': 'ZF_ZF_unit_Category_ext$' ).
thf('compDefined$_decl',type,
'compDefined$': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('makeCat$c_decl',type,
'makeCat$c': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' ).
thf('restrict$d_decl',type,
'restrict$d': 'B_a_fun$' > 'B_set$' > 'B_a_fun$' ).
thf('mapM$_decl',type,
'mapM$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'B_ZF_fun$' ).
thf('functor_abbrev$b_decl',type,
'functor_abbrev$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > $o ).
thf('collect$d_decl',type,
'collect$d': 'A_bool_fun$' > 'A_set$' ).
thf('equivalence$a_decl',type,
'equivalence$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('catExp$a_decl',type,
'catExp$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' ).
thf('category_axioms$_decl',type,
'category_axioms$': 'A_b_b_c_LSCategory_ext_Category_ext$' > $o ).
thf('dom$b_decl',type,
'dom$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('functor_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$' > $o ).
thf('fun_app$m_decl',type,
'fun_app$m': 'B_b_b_fun_fun$' > 'B$' > 'B_b_fun$' ).
thf('nTCod_update$a_decl',type,
'nTCod_update$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('natTransMap$_decl',type,
'natTransMap$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_fun$' ).
thf('oppositeCategory$a_decl',type,
'oppositeCategory$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' ).
thf('functor_ext$_decl',type,
'functor_ext$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'B_ZF_fun$' > 'Unit$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('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('collect$b_decl',type,
'collect$b': 'B_bool_fun$' > 'B_set$' ).
thf('functorM$_decl',type,
'functorM$': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('cod$b_decl',type,
'cod$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('zFfunComp$_decl',type,
'zFfunComp$': 'ZF_ZF_ZF_fun_fun$' ).
thf('compDefined$a_decl',type,
'compDefined$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'B_bool_fun$' ).
thf('inverse_rel$a_decl',type,
'inverse_rel$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'B_bool_fun$' ).
thf('the$_decl',type,
'the$': 'ZF_bool_fun$' > 'ZF$' ).
thf('catCod$b_decl',type,
'catCod$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('constFunctor$a_decl',type,
'constFunctor$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('nTDom_update$_decl',type,
'nTDom_update$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('objIso$_decl',type,
'objIso$': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('lSCategory_ext$_decl',type,
'lSCategory_ext$': 'B_ZF_fun$' > 'C$' > 'B_c_LSCategory_ext$' ).
thf('fun_app$j_decl',type,
'fun_app$j': 'A_bool_fun$' > 'A$' > $o ).
thf('functor$b_decl',type,
'functor$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('functor$_decl',type,
'functor$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('natTransMap$a_decl',type,
'natTransMap$a': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > 'ZF_ZF_fun$' ).
thf('cod$a_decl',type,
'cod$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$' ).
thf('makeFtor$_decl',type,
'makeFtor$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' ).
thf('functor_ext$a_decl',type,
'functor_ext$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' > 'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$' > 'Unit$' > 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('natTransExt$a_decl',type,
'natTransExt$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' ).
thf('member$h_decl',type,
'member$h': 'B$' > 'B_set$' > $o ).
thf('fun_app$w_decl',type,
'fun_app$w': 'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun$' > 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' ).
thf('nTCod$_decl',type,
'nTCod$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' ).
thf('member$i_decl',type,
'member$i': 'A$' > 'A_set$' > $o ).
thf('uul$_decl',type,
'uul$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'B_ZF_fun$' ).
thf('identityFunctor$_decl',type,
'identityFunctor$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('restrict$e_decl',type,
'restrict$e': 'A_b_fun$' > 'A_set$' > 'A_b_fun$' ).
thf('category_ext$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$' ).
thf('constFunctor$_decl',type,
'constFunctor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('homFtorMap$_decl',type,
'homFtorMap$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'B_ZF_fun$' ).
thf('inverse$_decl',type,
'inverse$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('uuv$_decl',type,
'uuv$': 'ZF_ZF_fun$' ).
thf('fun_app$t_decl',type,
'fun_app$t': 'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$' > 'B$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('extensional$a_decl',type,
'extensional$a': 'A_set$' > 'A_ZF_fun_set$' ).
thf('functorExt$a_decl',type,
'functorExt$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('zF2mor$_decl',type,
'zF2mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'ZF$' > 'B$' ).
thf('fun_app$x_decl',type,
'fun_app$x': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('collect$j_decl',type,
'collect$j': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$' ).
thf('uub$_decl',type,
'uub$': 'A_set$' > 'A_bool_fun$' ).
thf('uux$_decl',type,
'uux$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('uui$_decl',type,
'uui$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('category_ext$b_decl',type,
'category_ext$b': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$' > 'Unit$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' ).
thf('dom$_decl',type,
'dom$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_fun$' ).
thf('more$d_decl',type,
'more$d': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_c_LSCategory_ext$' ).
thf('zFfunDom$_decl',type,
'zFfunDom$': 'ZF_ZF_fun$' ).
thf('natTransP$a_decl',type,
'natTransP$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$' ).
thf('zFfunApp$_decl',type,
'zFfunApp$': 'ZF_ZF_ZF_fun_fun$' ).
thf('collect$c_decl',type,
'collect$c': 'ZF_bool_fun$' > 'ZF_set$' ).
thf('fun_app$ae_decl',type,
'fun_app$ae': 'B_set_b_set_fun$' > 'B_set$' > 'B_set$' ).
thf('category_axioms$a_decl',type,
'category_axioms$a': 'ZF_ZF_unit_Category_ext$' > $o ).
thf('isomorphism$a_decl',type,
'isomorphism$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_bool_fun$' ).
thf('hOMCollection$_decl',type,
'hOMCollection$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A$' > 'ZF_set$' ).
thf('functorM_axioms$a_decl',type,
'functorM_axioms$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('comp$_decl',type,
'comp$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_ZF_fun_fun$' ).
thf('isomorphism$_decl',type,
'isomorphism$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_bool_fun$' ).
thf('makeNT$_decl',type,
'makeNT$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('fun_app$o_decl',type,
'fun_app$o': 'B_ZF_fun$' > 'B$' > 'ZF$' ).
thf('inverse$a_decl',type,
'inverse$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'B$' ).
thf('mapM$b_decl',type,
'mapM$b': 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_fun$' ).
thf('obj$_decl',type,
'obj$': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$' ).
thf('homFtorMapContra$_decl',type,
'homFtorMapContra$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'A_ZF_fun$' ).
thf('fun_app$i_decl',type,
'fun_app$i': 'B_bool_fun$' > 'B$' > $o ).
thf('elem$_decl',type,
'elem$': 'ZF$' > 'ZF_bool_fun$' ).
thf('comp$a_decl',type,
'comp$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('yFtorNT$_decl',type,
'yFtorNT$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('fun_app$v_decl',type,
'fun_app$v': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('member$_decl',type,
'member$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$' > $o ).
thf('fun_app$_decl',type,
'fun_app$': 'ZF_ZF_fun$' > 'ZF$' > 'ZF$' ).
thf('comp$d_decl',type,
'comp$d': 'ZF_ZF_fun$' > 'ZF_ZF_fun_ZF_ZF_fun_fun$' ).
thf('mapO$c_decl',type,
'mapO$c': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' > 'A_ZF_fun$' ).
thf('constFunctor$b_decl',type,
'constFunctor$b': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' ).
thf('collect$i_decl',type,
'collect$i': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$' ).
thf('yFtorNT$a_decl',type,
'yFtorNT$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$' ).
thf('mapsTo$a_decl',type,
'mapsTo$a': 'ZF_ZF_unit_Category_ext$' > 'ZF$' > 'ZF$' > 'ZF_bool_fun$' ).
thf('makeCat$_decl',type,
'makeCat$': 'ZF_ZF_unit_Category_ext_ZF_ZF_unit_Category_ext_fun$' ).
thf('mor$a_decl',type,
'mor$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$' ).
thf('uuu$_decl',type,
'uuu$': 'ZF_ZF_fun$' ).
thf('natTransComp$a_decl',type,
'natTransComp$a': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('id$a_decl',type,
'id$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('image$_decl',type,
'image$': 'ZF_ZF_set_fun$' > 'ZF_set$' > 'ZF_set_set$' ).
thf('restrict$b_decl',type,
'restrict$b': 'B_ZF_fun$' > 'B_set$' > 'B_ZF_fun$' ).
thf('uuj$_decl',type,
'uuj$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_b_b_fun_fun$' ).
thf('nt_abbrev$_decl',type,
'nt_abbrev$': 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$' > $o ).
thf('yFtor$_decl',type,
'yFtor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_b_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('homFtor$a_decl',type,
'homFtor$a': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$' ).
thf('preFunctor$_decl',type,
'preFunctor$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$' ).
thf('member$d_decl',type,
'member$d': 'B_ZF_fun$' > 'B_ZF_fun_set$' > $o ).
thf('cod$_decl',type,
'cod$': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('functor$a_decl',type,
'functor$a': 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$' > $o ).
thf('homSet$_decl',type,
'homSet$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'A$' > 'A_ZF_fun$' ).
thf('member$l_decl',type,
'member$l': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_set$' > $o ).
thf('nTCatDom$_decl',type,
'nTCatDom$': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_b_b_c_LSCategory_ext_Category_ext$' ).
thf('explode$_decl',type,
'explode$': 'ZF_ZF_set_fun$' ).
thf('isZFfun$_decl',type,
'isZFfun$': 'ZF_bool_fun$' ).
thf('fun_app$y_decl',type,
'fun_app$y': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' > 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$' ).
thf('mor$b_decl',type,
'mor$b': 'ZF_ZF_unit_Category_ext$' > 'ZF_set$' ).
thf('dom$a_decl',type,
'dom$a': 'ZF_ZF_unit_Category_ext$' > 'ZF_ZF_fun$' ).
thf('member$o_decl',type,
'member$o': 'ZF_set$' > 'ZF_set_set$' > $o ).
thf('natTransComp$c_decl',type,
'natTransComp$c': 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_fun_fun$' ).
thf('mor$_decl',type,
'mor$': 'A_b_b_c_LSCategory_ext_Category_ext$' > 'B_set$' ).
thf(256,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom372) ).
thf(1586,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(57,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ ( A @ 'uui$' @ 'fun_app$a' ) )
<=> ( A @ ( B @ 'member$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(629,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( B @ 'member$' ) )
=> ( B @ ( A @ 'uui$' @ 'fun_app$a' ) ) )
& ( ( B @ ( A @ 'uui$' @ 'fun_app$a' ) )
=> ( A @ ( B @ 'member$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(382,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) @ ( 'nTCod$' @ 'fun_app$r' ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom208) ).
thf(2131,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) @ ( 'nTCod$' @ 'fun_app$r' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(356,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
=> ( A @ 'catDom$' @ 'mor$' @ 'extensional$b' @ ( A @ 'mapM$' @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom334) ).
thf(1995,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
=> ( A @ 'catDom$' @ 'mor$' @ 'extensional$b' @ ( A @ 'mapM$' @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(250,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom465) ).
thf(1559,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(184,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
<=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom270) ).
thf(1237,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(166,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( D @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( A @ 'functorM_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom327) ).
thf(1179,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( D @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( A @ 'functorM_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(79,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( B @ ( A @ 'functor_comp_def$b' ) )
<=> ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$b' )
& ( A @ 'functor$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom102) ).
thf(777,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$b' )
& ( A @ 'functor$b' ) )
=> ( B @ ( A @ 'functor_comp_def$b' ) ) )
& ( ( B @ ( A @ 'functor_comp_def$b' ) )
=> ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$b' )
& ( A @ 'functor$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(246,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) )
= ( B @ ( A @ 'uuq$' ) @ 'the$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).
thf(1549,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) )
= ( B @ ( A @ 'uuq$' ) @ 'the$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(284,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom444) ).
thf(1686,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(60,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).
thf(645,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(101,axiom,
( 'set$'
= ( 'set$a' @ ( 'makeCat$' @ 'fun_app$w' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom244) ).
thf(892,plain,
( 'set$'
= ( 'set$a' @ ( 'makeCat$' @ 'fun_app$w' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(204,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'mor$' @ ( A @ 'member$h' ) )
=> ( ( A @ ( B @ 'cod$a' @ 'fun_app$ab' ) )
= ( A @ ( B @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'cod$a' @ 'fun_app$ab' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom350) ).
thf(1315,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'mor$' @ ( A @ 'member$h' ) )
=> ( ( A @ ( B @ 'cod$a' @ 'fun_app$ab' ) )
= ( A @ ( B @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'cod$a' @ 'fun_app$ab' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(317,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'catDom$' @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'cod$' @ 'fun_app$' ) @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).
thf(1850,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'catDom$' @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'cod$' @ 'fun_app$' ) @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(65,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom453) ).
thf(666,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(307,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'idNatTrans$d' @ 'fun_app$x' ) )
= ( A @ 'idNatTrans$b' @ 'makeNT$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom169) ).
thf(1818,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'idNatTrans$d' @ 'fun_app$x' ) )
= ( A @ 'idNatTrans$b' @ 'makeNT$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(334,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'catDom$' @ 'isomorphism$' @ 'fun_app$i' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'isomorphism$a' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).
thf(1924,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'catDom$' @ 'isomorphism$' @ 'fun_app$i' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'isomorphism$a' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(260,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_fun$',E: 'Unit$'] :
( ( A
= ( E @ ( D @ ( C @ ( B @ 'natTrans_ext$a' ) ) ) ) )
=> $false )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom202) ).
thf(1596,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
~ ! [B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_fun$',E: 'Unit$'] :
( A
!= ( E @ ( D @ ( C @ ( B @ 'natTrans_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(70,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$c' ) )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).
thf(683,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$c' ) )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(238,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'inverse$' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom494) ).
thf(1522,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'inverse$' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(145,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'yFtor$' )
= ( 'unity$' @ ( A @ 'yFtorNT$a' @ ( 'set$' @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'catExp$a' ) @ ( A @ 'functor_ext$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom529) ).
thf(1073,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'yFtor$' )
= ( 'unity$' @ ( A @ 'yFtorNT$a' @ ( 'set$' @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'catExp$a' ) @ ( A @ 'functor_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(244,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$a' ) )
= ( 'unity$' @ ( B @ ( A @ 'uul$' ) @ ( 'set$' @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'functor_ext$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom524) ).
thf(1544,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$a' ) )
= ( 'unity$' @ ( B @ ( A @ 'uul$' ) @ ( 'set$' @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'functor_ext$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(291,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( B @ ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom370) ).
thf(1728,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( B @ ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(258,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'ZF$'] :
( ( ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( D @ 'elem$' @ 'fun_app$d' ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) @ 'elem$' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383) ).
thf(1591,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'ZF$'] :
( ( ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( D @ 'elem$' @ 'fun_app$d' ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) @ 'elem$' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(192,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'] :
( ! [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( C @ ( A @ 'fun_app$a' ) )
<=> ( C @ ( B @ 'fun_app$a' ) ) )
=> ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom130) ).
thf(1269,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'] :
( ! [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'fun_app$a' ) )
=> ( C @ ( A @ 'fun_app$a' ) ) )
& ( ( C @ ( A @ 'fun_app$a' ) )
=> ( C @ ( B @ 'fun_app$a' ) ) ) )
=> ( ( A @ 'collect$i' )
= ( B @ 'collect$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(54,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom472) ).
thf(614,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(319,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> ( F @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( E @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( D @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( C @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom250) ).
thf(1855,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> ( F @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( E @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( D @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( C @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(173,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'hOMCollection$' ) ) )
= ( B @ ( C @ ( A @ 'hOMCollection$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).
thf(1200,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'hOMCollection$' ) ) )
= ( B @ ( C @ ( A @ 'hOMCollection$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(12,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ ( 'oppositeCategory$b' @ 'fun_app$w' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).
thf(440,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ ( 'oppositeCategory$b' @ 'fun_app$w' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ 'member$c' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$c' ) ) ) )
=> ( A @ 'category_axioms$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom402) ).
thf(511,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ 'member$c' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$c' ) ) ) )
=> ( A @ 'category_axioms$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(147,axiom,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ! [C: 'B$'] :
( ( C @ ( A @ 'fun_app$i' ) )
<=> ( C @ ( B @ 'fun_app$i' ) ) )
=> ( ( A @ 'collect$b' )
= ( B @ 'collect$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom129) ).
thf(1078,plain,
! [A: 'B_bool_fun$',B: 'B_bool_fun$'] :
( ! [C: 'B$'] :
( ( ( C @ ( B @ 'fun_app$i' ) )
=> ( C @ ( A @ 'fun_app$i' ) ) )
& ( ( C @ ( A @ 'fun_app$i' ) )
=> ( C @ ( B @ 'fun_app$i' ) ) ) )
=> ( ( A @ 'collect$b' )
= ( B @ 'collect$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(274,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'mor$' @ 'extensional$b' @ ( A @ 'mor2ZF$' @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom181) ).
thf(1655,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'mor$' @ 'extensional$b' @ ( A @ 'mor2ZF$' @ 'member$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(295,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( B @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ ( 'natTrans$' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).
thf(1756,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( B @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ ( 'natTrans$' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(323,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom390) ).
thf(1867,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(23,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
<=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom269) ).
thf(472,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(107,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'elem$' @ 'fun_app$d' ) )
=> ( C @ ( D @ ( B @ 'fun_app$' ) @ 'elem$' @ 'fun_app$d' ) ) )
=> ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom541) ).
thf(913,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$'] :
( ! [D: 'ZF$'] :
( ( A @ ( D @ 'elem$' @ 'fun_app$d' ) )
=> ( C @ ( D @ ( B @ 'fun_app$' ) @ 'elem$' @ 'fun_app$d' ) ) )
=> ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(269,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom268) ).
thf(1640,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(344,axiom,
'c$' @ 'mor$' @ ( 'f$' @ 'member$h' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom29) ).
thf(1954,plain,
'c$' @ 'mor$' @ ( 'f$' @ 'member$h' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(206,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( B @ ( A @ 'functor_comp_def$c' ) )
=> ( B @ ( A @ 'functorComp$' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom176) ).
thf(1354,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( B @ ( A @ 'functor_comp_def$c' ) )
=> ( B @ ( A @ 'functorComp$' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(161,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'mor$' @ ( A @ 'member$h' ) )
=> ( ( A @ ( B @ 'dom$' @ 'fun_app$ab' ) )
= ( A @ ( B @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'dom$' @ 'fun_app$ab' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).
thf(1164,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( B @ 'mor$' @ ( A @ 'member$h' ) )
=> ( ( A @ ( B @ 'dom$' @ 'fun_app$ab' ) )
= ( A @ ( B @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'dom$' @ 'fun_app$ab' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(84,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'mor$b' )
= ( A @ 'mor$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).
thf(797,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'mor$b' )
= ( A @ 'mor$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(150,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$i' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).
thf(1095,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$i' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ 'member$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(124,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'makeCat$a' @ 'fun_app$s' ) )
= ( A @ 'more$d' @ ( A @ 'uux$' @ ( A @ 'obj$a' @ ( A @ 'id$' @ 'restrict$e' ) @ ( A @ 'mor$' @ ( A @ 'cod$a' @ 'restrict$d' ) @ ( A @ 'mor$' @ ( A @ 'dom$' @ 'restrict$d' ) @ ( A @ 'mor$' @ ( A @ 'obj$a' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).
thf(1001,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'makeCat$a' @ 'fun_app$s' ) )
= ( A @ 'more$d' @ ( A @ 'uux$' @ ( A @ 'obj$a' @ ( A @ 'id$' @ 'restrict$e' ) @ ( A @ 'mor$' @ ( A @ 'cod$a' @ 'restrict$d' ) @ ( A @ 'mor$' @ ( A @ 'dom$' @ 'restrict$d' ) @ ( A @ 'mor$' @ ( A @ 'obj$a' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(185,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ 'member$c' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom400) ).
thf(1243,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ 'member$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(403,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( C @ ( B @ ( A @ 'uuo$' ) @ 'fun_app$q' ) )
<=> ( ( ( C @ 'nTCatCod$' )
= B )
& ( ( C @ 'nTCatDom$' )
= A )
& ( C @ ( 'natTrans$' @ 'fun_app$q' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).
thf(2227,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( ( C @ 'nTCatCod$' )
= B )
& ( ( C @ 'nTCatDom$' )
= A )
& ( C @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( C @ ( B @ ( A @ 'uuo$' ) @ 'fun_app$q' ) ) )
& ( ( C @ ( B @ ( A @ 'uuo$' ) @ 'fun_app$q' ) )
=> ( ( ( C @ 'nTCatCod$' )
= B )
& ( ( C @ 'nTCatDom$' )
= A )
& ( C @ ( 'natTrans$' @ 'fun_app$q' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(264,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ 'elem$' @ 'fun_app$d' ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).
thf(1613,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ 'elem$' @ 'fun_app$d' ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(338,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( A @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom164) ).
thf(1935,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( A @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(208,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).
thf(1359,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(215,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorContra$' ) @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( B @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom237) ).
thf(1386,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorContra$' ) @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( B @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(190,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$a' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom192) ).
thf(1265,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$a' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(62,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'compDefined$a' ) @ 'fun_app$i' ) )
<=> ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom276) ).
thf(651,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(271,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( B @ ( A @ 'homFtor$a' ) @ ( 'preFunctor$' @ 'fun_app$a' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$a' ) @ 'mapO$c' @ 'fun_app$n' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom384) ).
thf(1645,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( B @ ( A @ 'homFtor$a' ) @ ( 'preFunctor$' @ 'fun_app$a' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$a' ) @ 'mapO$c' @ 'fun_app$n' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(333,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).
thf(1921,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(376,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) )
=> ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom343) ).
thf(2067,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) )
=> ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(350,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( B @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( B @ 'natTransMap$' @ 'member$f' ) )
& ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) )
& ! [C: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
=> ( ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) )
= ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) ) ) )
& ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTCod$' @ 'fun_app$r' ) ) )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom167) ).
thf(1967,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( B @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( B @ 'natTransMap$' @ 'member$f' ) )
& ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) )
& ! [C: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
=> ( ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) )
= ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) ) ) )
& ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTCod$' @ 'fun_app$r' ) ) )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(139,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom303) ).
thf(1055,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(367,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'] :
( ( ! [F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$v' ) )
= ( F @ ( E @ 'fun_app$v' ) ) ) )
& ( ( B @ ( 'nTDom$' @ 'fun_app$r' ) )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'nTDom_update$' ) )
= ( B @ ( E @ 'nTDom_update$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).
thf(2039,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'] :
( ( ! [F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$v' ) )
= ( F @ ( E @ 'fun_app$v' ) ) ) )
& ( ( B @ ( 'nTDom$' @ 'fun_app$r' ) )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'nTDom_update$' ) )
= ( B @ ( E @ 'nTDom_update$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(29,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' ) )
& ( B @ 'category$a' )
& ( A @ 'category$' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$' ) ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).
thf(504,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' ) )
& ( B @ 'category$a' )
& ( A @ 'category$' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$' ) ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(108,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
<=> ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).
thf(917,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) )
& ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
=> ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(310,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom266) ).
thf(1826,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(203,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'B$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( C @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom288) ).
thf(1313,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'B$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( C @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(170,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'mor$' )
= ( A @ 'mor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom274) ).
thf(1191,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'mor$' )
= ( A @ 'mor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(355,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( C @ ( B @ 'catExp$a' ) @ 'mor$a' @ ( A @ 'member$l' ) )
=> ( ( A @ ( C @ ( B @ 'catExp$a' ) @ 'cod$b' ) )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom514) ).
thf(1992,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( C @ ( B @ 'catExp$a' ) @ 'mor$a' @ ( A @ 'member$l' ) )
=> ( ( A @ ( C @ ( B @ 'catExp$a' ) @ 'cod$b' ) )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(297,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$a' ) )
<=> ( B @ ( A @ ( C @ 'functor_abbrev$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
thf(1760,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( B @ ( A @ ( C @ 'functor_abbrev$' ) ) )
=> ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ 'uun$' ) @ 'fun_app$a' ) )
=> ( B @ ( A @ ( C @ 'functor_abbrev$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(276,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom80) ).
thf(1660,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(105,axiom,
! [A: 'ZF_set$',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$a' ) ) ) ) ) ) @ 'comp$' )
= F ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom421) ).
thf(902,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$' )
= F ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(328,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ! [B: 'ZF$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$c' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ) )
=> ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).
thf(1890,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ! [B: 'ZF$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$c' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ) )
=> ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(253,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'ZF$'] :
( ( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom399) ).
thf(1572,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'ZF$'] :
( ( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(127,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom496) ).
thf(1013,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(306,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mor$' )
= ( A @ 'mor$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).
thf(1815,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mor$' )
= ( A @ 'mor$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(152,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory_axioms$' )
<=> ( ( A @ 'mor$' @ 'extensional$b' @ ( A @ 'mor2ZF$' @ 'member$d' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ( 'top$' @ ( 'explode$' @ 'image$' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'member$o' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom587) ).
thf(1100,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'mor$' @ 'extensional$b' @ ( A @ 'mor2ZF$' @ 'member$d' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ( 'top$' @ ( 'explode$' @ 'image$' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'member$o' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> ( B = C ) ) )
=> ( A @ 'lSCategory_axioms$' ) )
& ( ( A @ 'lSCategory_axioms$' )
=> ( ( A @ 'mor$' @ 'extensional$b' @ ( A @ 'mor2ZF$' @ 'member$d' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ( 'top$' @ ( 'explode$' @ 'image$' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'member$o' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(59,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF_ZF_fun$',D: 'ZF$'] :
( ! [E: 'ZF$'] :
( ( A @ ( E @ 'elem$' @ 'fun_app$d' ) )
=> ( ( E @ ( B @ 'fun_app$' ) )
= ( E @ ( C @ 'fun_app$' ) ) ) )
=> ( ( B @ ( D @ ( A @ 'zFfun$' ) ) )
= ( C @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).
thf(638,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF_ZF_fun$',D: 'ZF$'] :
( ! [E: 'ZF$'] :
( ( A @ ( E @ 'elem$' @ 'fun_app$d' ) )
=> ( ( E @ ( B @ 'fun_app$' ) )
= ( E @ ( C @ 'fun_app$' ) ) ) )
=> ( ( B @ ( D @ ( A @ 'zFfun$' ) ) )
= ( C @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(98,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uuj$' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
thf(853,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uuj$' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( B @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(209,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'lSCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).
thf(1362,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'lSCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(348,axiom,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ 'makeNT$' @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( B @ 'natTransMap$' @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom153) ).
thf(1963,plain,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ 'makeNT$' @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( B @ 'natTransMap$' @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(341,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'preFunctor$' @ 'fun_app$a' ) )
=> ( A @ 'catDom$' @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).
thf(1946,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'preFunctor$' @ 'fun_app$a' ) )
=> ( A @ 'catDom$' @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(13,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( C @ ( D @ ( B @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom267) ).
thf(443,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( C @ ( D @ ( B @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(135,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= C )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= B )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).
thf(1040,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= C )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= B )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(95,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] :
( ( B @ ( A @ 'functor_comp_def$a' ) )
<=> ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$a' )
& ( A @ 'functor$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom101) ).
thf(834,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] :
( ( ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$a' )
& ( A @ 'functor$b' ) )
=> ( B @ ( A @ 'functor_comp_def$a' ) ) )
& ( ( B @ ( A @ 'functor_comp_def$a' ) )
=> ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$a' )
& ( A @ 'functor$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(311,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ! [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( C @ ( A @ 'fun_app$q' ) )
<=> ( C @ ( B @ 'fun_app$q' ) ) )
=> ( ( A @ 'collect$j' )
= ( B @ 'collect$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom131) ).
thf(1828,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_bool_fun$'] :
( ! [C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'fun_app$q' ) )
=> ( C @ ( A @ 'fun_app$q' ) ) )
& ( ( C @ ( A @ 'fun_app$q' ) )
=> ( C @ ( B @ 'fun_app$q' ) ) ) )
=> ( ( A @ 'collect$j' )
= ( B @ 'collect$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(43,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$c' @ ( A @ 'mor2ZF$' @ 'lSCategory_ext$' ) @ ( A @ 'comp$a' @ ( A @ 'id$' @ ( A @ 'cod$a' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$a' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
thf(574,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$c' @ ( A @ 'mor2ZF$' @ 'lSCategory_ext$' ) @ ( A @ 'comp$a' @ ( A @ 'id$' @ ( A @ 'cod$a' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$a' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(167,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom443) ).
thf(1183,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(106,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'catCod$' @ 'category$a' )
& ( A @ 'catDom$' @ 'category$' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ? [C: 'ZF$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).
thf(905,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'catCod$' @ 'category$a' )
& ( A @ 'catDom$' @ 'category$' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ? [C: 'ZF$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(372,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
=> ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).
thf(2058,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
=> ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(213,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$' ) @ 'mapO$c' @ 'fun_app$n' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).
thf(1377,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtor$' ) @ 'mapO$c' @ 'fun_app$n' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(397,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'] :
( ( ! [F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$v' ) )
= ( F @ ( E @ 'fun_app$v' ) ) ) )
& ( ( B @ ( 'nTDom$' @ 'fun_app$r' ) )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'nTDom_update$' ) )
= ( B @ ( E @ 'nTDom_update$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom565) ).
thf(2190,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'] :
( ( ! [F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$v' ) )
= ( F @ ( E @ 'fun_app$v' ) ) ) )
& ( ( B @ ( 'nTDom$' @ 'fun_app$r' ) )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'nTDom_update$' ) )
= ( B @ ( E @ 'nTDom_update$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(303,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom339) ).
thf(1796,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(78,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom257) ).
thf(774,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(384,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) )
& ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) )
& ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).
thf(2137,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) )
& ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) )
& ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(123,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom467) ).
thf(998,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(406,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ ( A @ 'catExp$c' ) )
= ( 'unity$' @ ( 'natTransComp$c' @ ( 'idNatTrans$d' @ ( 'nTCod$' @ ( 'nTDom$' @ ( B @ ( A @ 'uuo$' ) @ 'collect$j' @ ( B @ ( A @ 'uun$' ) @ 'collect$i' @ 'category_ext$b' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).
thf(2242,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ ( A @ 'catExp$c' ) )
= ( 'unity$' @ ( 'natTransComp$c' @ ( 'idNatTrans$d' @ ( 'nTCod$' @ ( 'nTDom$' @ ( B @ ( A @ 'uuo$' ) @ 'collect$j' @ ( B @ ( A @ 'uun$' ) @ 'collect$i' @ 'category_ext$b' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(220,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom256) ).
thf(1405,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(340,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) @ 'catDom$' )
= ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom39) ).
thf(1943,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) @ 'catDom$' )
= ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(261,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_fun$',E: 'Unit$'] :
( ( E @ ( D @ ( C @ ( B @ 'natTrans_ext$a' ) ) ) @ ( A @ 'nTCod_update$a' ) )
= ( E @ ( D @ ( C @ ( A @ 'fun_app$v' ) @ ( B @ 'natTrans_ext$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom216) ).
thf(1600,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_fun$',E: 'Unit$'] :
( ( E @ ( D @ ( C @ ( B @ 'natTrans_ext$a' ) ) ) @ ( A @ 'nTCod_update$a' ) )
= ( E @ ( D @ ( C @ ( A @ 'fun_app$v' ) @ ( B @ 'natTrans_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(388,axiom,
! [A: 'B$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$c' ) )
& ( C @ ( B @ 'functorComp$a' ) @ 'catDom$' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$' @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ 'mapO$b' @ 'fun_app$' ) @ ( A @ ( B @ 'catDom$' @ 'dom$' @ 'fun_app$ab' ) @ ( B @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ 'mapO$b' @ 'fun_app$' ) @ ( A @ ( B @ 'mapM$' @ 'fun_app$o' ) @ ( C @ 'mapM$b' @ 'fun_app$' ) @ ( C @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom355) ).
thf(2154,plain,
! [A: 'B$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( C @ ( B @ 'functor_comp_def$c' ) )
& ( C @ ( B @ 'functorComp$a' ) @ 'catDom$' @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( A @ ( B @ 'catDom$' @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ 'mapO$b' @ 'fun_app$' ) @ ( A @ ( B @ 'catDom$' @ 'dom$' @ 'fun_app$ab' ) @ ( B @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ 'mapO$b' @ 'fun_app$' ) @ ( A @ ( B @ 'mapM$' @ 'fun_app$o' ) @ ( C @ 'mapM$b' @ 'fun_app$' ) @ ( C @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(352,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
<=> ( A @ 'catDom$' @ 'mor$' @ 'extensional$b' @ ( A @ 'mapM$' @ 'member$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom332) ).
thf(1975,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ 'extensional$b' @ ( A @ 'mapM$' @ 'member$d' ) )
=> ( A @ ( 'functorExt$a' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
=> ( A @ 'catDom$' @ 'mor$' @ 'extensional$b' @ ( A @ 'mapM$' @ 'member$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(252,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( A @ 'functorM_axioms$' )
<=> ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( D @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom325) ).
thf(1564,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( D @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( A @ 'functorM_axioms$' ) )
& ( ( A @ 'functorM_axioms$' )
=> ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( D @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(360,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).
thf(2011,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(175,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom240) ).
thf(1206,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(75,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom470) ).
thf(761,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(89,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'obj$' @ ( A @ 'member$c' ) )
=> ( ( A @ ( B @ 'id$a' @ 'fun_app$' ) )
= ( A @ ( B @ ( 'makeCat$' @ 'fun_app$w' ) @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom389) ).
thf(810,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'obj$' @ ( A @ 'member$c' ) )
=> ( ( A @ ( B @ 'id$a' @ 'fun_app$' ) )
= ( A @ ( B @ ( 'makeCat$' @ 'fun_app$w' ) @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(368,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom86) ).
thf(2047,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(202,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'compDefined$a' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom179) ).
thf(1311,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( B @ ( C @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'compDefined$a' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(144,axiom,
! [A: 'B$',B: 'B_bool_fun$'] :
( ( B @ 'collect$b' @ ( A @ 'member$h' ) )
<=> ( A @ ( B @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom109) ).
thf(1067,plain,
! [A: 'B$',B: 'B_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$i' ) )
=> ( B @ 'collect$b' @ ( A @ 'member$h' ) ) )
& ( ( B @ 'collect$b' @ ( A @ 'member$h' ) )
=> ( A @ ( B @ 'fun_app$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(299,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( B @ ( A @ 'natTransComp$a' ) @ ( 'natTransP$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom158) ).
thf(1768,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( B @ ( A @ 'natTransComp$a' ) @ ( 'natTransP$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(374,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) @ ( 'nTDom$' @ 'fun_app$r' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).
thf(2061,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) @ ( 'nTDom$' @ 'fun_app$r' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(358,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_b_b_c_LSCategory_ext_Category_ext$',D: 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$',E: 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$'] :
( ( ! [F: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$s' ) )
= ( F @ ( E @ 'fun_app$s' ) ) ) )
& ( ( B @ 'catDom$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'catDom_update$a' @ 'fun_app$v' ) )
= ( B @ ( E @ 'catDom_update$a' @ 'fun_app$v' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).
thf(2000,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_b_b_c_LSCategory_ext_Category_ext$',D: 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$',E: 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$'] :
( ( ! [F: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$s' ) )
= ( F @ ( E @ 'fun_app$s' ) ) ) )
& ( ( B @ 'catDom$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'catDom_update$a' @ 'fun_app$v' ) )
= ( B @ ( E @ 'catDom_update$a' @ 'fun_app$v' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(136,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom466) ).
thf(1047,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(292,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'cod$' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom369) ).
thf(1730,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'cod$' @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(102,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'top$' @ ( 'explode$' @ 'image$' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'member$o' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom588) ).
thf(894,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'top$' @ ( 'explode$' @ 'image$' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'member$o' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(130,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF_ZF_fun$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$d' ) )
=> ( ( A @ ( D @ ( C @ ( B @ 'zFfun$' ) ) @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( A @ ( D @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).
thf(1021,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF_ZF_fun$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$d' ) )
=> ( ( A @ ( D @ ( C @ ( B @ 'zFfun$' ) ) @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( A @ ( D @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(111,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).
thf(952,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(385,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).
thf(2147,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(8,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).
thf(429,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(309,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'A$',F: 'A$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( F @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( E @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( C @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom251) ).
thf(1824,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'A$',F: 'A$'] :
( ( ( F @ ( E @ ( D @ ( B @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( F @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( E @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( C @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(1,conjecture,
( ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ 'nTCatDom$' )
= ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture27) ).
thf(2,negated_conjecture,
( ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ 'nTCatDom$' )
!= ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(407,plain,
( ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ 'nTCatDom$' )
!= ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(72,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$' @ ( C @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).
thf(693,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$' @ ( C @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(21,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'identityFunctor$' @ 'functorM$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).
thf(467,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'identityFunctor$' @ 'functorM$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(343,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom315) ).
thf(1951,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(327,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).
thf(1888,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(46,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunDom$' @ 'fun_app$' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).
thf(583,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)],[46]) ).
thf(394,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'] :
( ( ! [F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$v' ) )
= ( F @ ( E @ 'fun_app$v' ) ) ) )
& ( ( B @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'nTCod_update$a' ) )
= ( B @ ( E @ 'nTCod_update$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).
thf(2179,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'] :
( ( ! [F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$v' ) )
= ( F @ ( E @ 'fun_app$v' ) ) ) )
& ( ( B @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'nTCod_update$a' ) )
= ( B @ ( E @ 'nTCod_update$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(177,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ! [D: 'ZF$'] :
( ( B @ ( D @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( B @ ( D @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= D ) )
& ( C @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( A @ 'id$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom471) ).
thf(1210,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ! [D: 'ZF$'] :
( ( B @ ( D @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( B @ ( D @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= D ) )
& ( C @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( A @ 'id$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(132,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).
thf(1027,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(38,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$d' )
= ( B @ 'more$d' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$' )
= ( B @ 'id$' ) )
& ( ( A @ 'cod$a' )
= ( B @ 'cod$a' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$a' )
= ( B @ 'obj$a' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom406) ).
thf(551,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$d' )
= ( B @ 'more$d' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$' )
= ( B @ 'id$' ) )
& ( ( A @ 'cod$a' )
= ( B @ 'cod$a' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$a' )
= ( B @ 'obj$a' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(267,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'B$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( ( E @ ( D @ ( B @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( C @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).
thf(1634,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'B$',E: 'B$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( ( E @ ( D @ ( B @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( C @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(198,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uus$' ) @ 'fun_app$i' ) )
<=> ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).
thf(1291,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$',C: 'B$'] :
( ( ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$h' ) ) )
=> ( C @ ( B @ ( A @ 'uus$' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( A @ 'uus$' ) @ 'fun_app$i' ) )
=> ( ( ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= B )
& ( A @ 'mor$' @ ( C @ 'member$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(17,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'category$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom433) ).
thf(456,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(126,axiom,
'set$' @ 'category$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom432) ).
thf(1012,plain,
'set$' @ 'category$a',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(248,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) )
=> ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).
thf(1555,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) )
=> ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(10,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( B @ ( C @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom178) ).
thf(435,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( B @ ( C @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(159,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) @ 'elem$' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom392) ).
thf(1159,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ 'lSCategory$' ) )
=> ( D @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) @ 'elem$' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(19,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'obj$' )
= ( A @ 'obj$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom83) ).
thf(461,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'obj$' )
= ( A @ 'obj$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(148,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( A @ ( 'functorM_axioms$a' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom328) ).
thf(1089,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( A @ ( 'functorM_axioms$a' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(301,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',G: 'A_ZF_fun$',H: 'Unit$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) )
= ( H @ ( G @ ( F @ ( E @ 'natTrans_ext$a' ) ) ) ) )
<=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom201) ).
thf(1772,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',G: 'A_ZF_fun$',H: 'Unit$'] :
( ( ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) )
= ( H @ ( G @ ( F @ ( E @ 'natTrans_ext$a' ) ) ) ) ) )
& ( ( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) )
= ( H @ ( G @ ( F @ ( E @ 'natTrans_ext$a' ) ) ) ) )
=> ( ( D = H )
& ( C = G )
& ( B = F )
& ( A = E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(302,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
& ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) )
=> ( A @ ( 'functor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom337) ).
thf(1794,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
& ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) )
=> ( A @ ( 'functor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(143,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) @ ( A @ 'zF2mor$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom141) ).
thf(1064,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) @ ( A @ 'zF2mor$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(182,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' ) @ 'fun_app$i' ) )
& ( A @ 'category$' ) )
=> ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).
thf(1227,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$a' ) @ 'fun_app$i' ) )
& ( A @ 'category$' ) )
=> ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(279,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'obj$a' )
= ( A @ 'obj$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).
thf(1672,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'obj$a' )
= ( A @ 'obj$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(27,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$' @ ( D @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).
thf(499,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$' @ ( D @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(117,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'obj$' @ ( C @ 'member$c' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).
thf(980,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'obj$' @ ( C @ 'member$c' ) )
& ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(230,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).
thf(1498,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(153,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ ( 'natTrans$' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom184) ).
thf(1138,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ ( 'natTrans$' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(288,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'ZF$',E: 'ZF$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> ( ( E @ ( D @ ( B @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapM$b' @ 'fun_app$' ) )
= ( E @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( C @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).
thf(1719,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'ZF$',E: 'ZF$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> ( ( E @ ( D @ ( B @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapM$b' @ 'fun_app$' ) )
= ( E @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( C @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(39,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom452) ).
thf(554,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(33,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',D: 'ZF$'] :
( ( ( B @ 'catDom$a' @ 'obj$' @ ( D @ 'member$c' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$' ) ) ) )
=> ( D @ ( C @ 'mapO$b' @ 'fun_app$' ) @ ( D @ ( B @ 'mapO$b' @ 'fun_app$' ) @ ( D @ ( A @ 'natTransMap$a' @ 'fun_app$' ) @ ( C @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom308) ).
thf(537,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_NatTrans_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',C: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',D: 'ZF$'] :
( ( ( B @ 'catDom$a' @ 'obj$' @ ( D @ 'member$c' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$' ) ) ) )
=> ( D @ ( C @ 'mapO$b' @ 'fun_app$' ) @ ( D @ ( B @ 'mapO$b' @ 'fun_app$' ) @ ( D @ ( A @ 'natTransMap$a' @ 'fun_app$' ) @ ( C @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( ( 'uuu$' @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom547) ).
thf(669,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( ( 'uuu$' @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(128,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uur$' @ 'fun_app$k' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom539) ).
thf(1016,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uur$' @ 'fun_app$k' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(228,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uul$' ) @ 'fun_app$o' ) )
= ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).
thf(1493,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'uul$' ) @ 'fun_app$o' ) )
= ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(283,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuk$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
thf(1683,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuk$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(370,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'catDom$' @ 'mor$' @ 'extensional$b' @ ( A @ 'mapM$' @ 'member$d' ) )
=> ( A @ ( 'functorExt$a' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom335) ).
thf(2053,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ 'catDom$' @ 'mor$' @ 'extensional$b' @ ( A @ 'mapM$' @ 'member$d' ) )
=> ( A @ ( 'functorExt$a' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(313,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( A @ 'catCod$' @ 'mor$b' @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom243) ).
thf(1842,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( A @ 'catCod$' @ 'mor$b' @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(26,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
<=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$c' ) )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom378) ).
thf(489,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$c' ) )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) )
=> ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
& ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$a' @ 'fun_app$' ) ) )
& ( A @ 'mor$b' @ ( C @ 'member$c' ) )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(339,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [C: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
=> ( ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) )
= ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) ) ) )
& ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTCod$' @ 'fun_app$r' ) ) )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) ) )
=> ( ( A @ 'makeNT$' )
= ( B @ 'makeNT$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).
thf(1937,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [C: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
=> ( ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) )
= ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) ) ) )
& ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTCod$' @ 'fun_app$r' ) ) )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) ) )
=> ( ( A @ 'makeNT$' )
= ( B @ 'makeNT$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(189,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$b' @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).
thf(1263,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$b' @ ( B @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(241,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( D @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$a' @ 'obj$' @ ( C @ 'member$c' ) )
& ( A @ 'catDom$a' @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'equivalence$' ) )
=> ? [E: 'ZF$'] :
( ( ( E @ ( A @ 'mapM$b' @ 'fun_app$' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom323) ).
thf(1530,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( D @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$a' @ 'obj$' @ ( C @ 'member$c' ) )
& ( A @ 'catDom$a' @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'equivalence$' ) )
=> ? [E: 'ZF$'] :
( ( ( E @ ( A @ 'mapM$b' @ 'fun_app$' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(183,axiom,
! [A: 'B_set$',B: 'B$'] :
( ( B @ ( A @ 'uu$' @ 'fun_app$i' ) )
<=> ( A @ ( B @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
thf(1231,plain,
! [A: 'B_set$',B: 'B$'] :
( ( ( A @ ( B @ 'member$h' ) )
=> ( B @ ( A @ 'uu$' @ 'fun_app$i' ) ) )
& ( ( B @ ( A @ 'uu$' @ 'fun_app$i' ) )
=> ( A @ ( B @ 'member$h' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(247,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorContra$' ) @ 'mapO$c' @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom381) ).
thf(1552,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorContra$' ) @ 'mapO$c' @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(337,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatDom$' )
= ( A @ 'makeNT$' @ 'nTCatDom$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).
thf(1932,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatDom$' )
= ( A @ 'makeNT$' @ 'nTCatDom$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(141,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category_axioms$' )
=> ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'category_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom408) ).
thf(1060,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category_axioms$' )
=> ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'category_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(354,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'nt_abbrev$a' ) @ 'fun_app$a' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom99) ).
thf(1984,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
~ ( ~ ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$a' ) @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(239,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom264) ).
thf(1525,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(51,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom504) ).
thf(605,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(217,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'equivalence$a' @ 'fun_app$a' ) )
<=> ( ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom353) ).
thf(1393,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'equivalence$a' @ 'fun_app$a' ) )
=> ( ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(320,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$' )
=> ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom434) ).
thf(1857,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'category$' )
=> ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(205,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) )
<=> ( ! [B: 'ZF$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$c' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom346) ).
thf(1318,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ! [B: 'ZF$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$c' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ) )
=> ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) )
=> ( ! [B: 'ZF$'] :
( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$c' ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) ) ) )
& ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$'] :
( ( ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) ) )
& ( D @ ( C @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( B = E ) )
& ! [B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(82,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( ( A @ ( 'uuu$' @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom546) ).
thf(792,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( ( A @ ( 'uuu$' @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(87,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom457) ).
thf(805,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(35,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( A @ 'mor$b' @ ( C @ 'member$c' ) )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom447) ).
thf(541,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( A @ 'mor$b' @ ( C @ 'member$c' ) )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(63,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom458) ).
thf(657,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(315,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> ( C @ ( B @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom214) ).
thf(1846,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> ( C @ ( B @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(196,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( ( A @ 'nTCatCod$' )
= ( B @ 'nTCatCod$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom147) ).
thf(1286,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( ( A @ 'nTCatCod$' )
= ( B @ 'nTCatCod$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(68,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'compDefined$' ) @ 'fun_app$d' ) )
<=> ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).
thf(674,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'compDefined$' ) @ 'fun_app$d' ) ) )
& ( ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(277,axiom,
! [A: 'A$',B: 'A_bool_fun$'] :
( ( B @ 'collect$d' @ ( A @ 'member$i' ) )
<=> ( A @ ( B @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom111) ).
thf(1663,plain,
! [A: 'A$',B: 'A_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$j' ) )
=> ( B @ 'collect$d' @ ( A @ 'member$i' ) ) )
& ( ( B @ 'collect$d' @ ( A @ 'member$i' ) )
=> ( A @ ( B @ 'fun_app$j' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(162,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( D @ ( A @ 'functor_comp_def$b' ) )
& ( C @ ( B @ ( A @ 'catDom$a' @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( C @ ( B @ ( A @ 'catDom$a' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) )
= ( C @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'catCod$b' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).
thf(1167,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( D @ ( A @ 'functor_comp_def$b' ) )
& ( C @ ( B @ ( A @ 'catDom$a' @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( C @ ( B @ ( A @ 'catDom$a' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) )
= ( C @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'catCod$b' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(168,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'cod$' @ 'fun_app$' ) )
= ( B @ ( A @ 'catDom$' @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'mapO$c' @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom349) ).
thf(1185,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'cod$' @ 'fun_app$' ) )
= ( B @ ( A @ 'catDom$' @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'mapO$c' @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(47,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( D @ ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom253) ).
thf(586,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( D @ ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(378,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) )
<=> ( ( ( A @ 'catCod$' )
= C )
& ( ( A @ 'catDom$' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom75) ).
thf(2076,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( ( A @ 'catCod$' )
= C )
& ( ( A @ 'catDom$' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
& ( ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) )
=> ( ( ( A @ 'catCod$' )
= C )
& ( ( A @ 'catDom$' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(163,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( D @ ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).
thf(1170,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( D @ ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(396,axiom,
'set$' @ ( 'c$' @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTCod$' @ 'fun_app$r' ) @ 'functor_abbrev$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom32) ).
thf(2189,plain,
'set$' @ ( 'c$' @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTCod$' @ 'fun_app$r' ) @ 'functor_abbrev$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(265,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( B @ ( A @ 'functor_comp_def$c' ) )
<=> ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$b' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom103) ).
thf(1616,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$b' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'functor_comp_def$c' ) ) )
& ( ( B @ ( A @ 'functor_comp_def$c' ) )
=> ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$b' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(329,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
<=> ( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom200) ).
thf(1906,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) )
=> ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
& ( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(235,axiom,
! [A: 'A_set$',B: 'A$'] :
( ( B @ ( A @ 'uub$' @ 'fun_app$j' ) )
<=> ( A @ ( B @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
thf(1510,plain,
! [A: 'A_set$',B: 'A$'] :
( ( ( A @ ( B @ 'member$i' ) )
=> ( B @ ( A @ 'uub$' @ 'fun_app$j' ) ) )
& ( ( B @ ( A @ 'uub$' @ 'fun_app$j' ) )
=> ( A @ ( B @ 'member$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(187,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
<=> ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).
thf(1251,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) )
=> ( A @ 'lSCategory$' ) )
& ( ( A @ 'lSCategory$' )
=> ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(224,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'category$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom431) ).
thf(1483,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'category$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(99,axiom,
! [A: 'ZF_set$',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$a' ) ) ) ) ) ) ) )
<=> ( ( G = N )
& ( F = M )
& ( E = L )
& ( D = K )
& ( C = J )
& ( B = I )
& ( A = H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).
thf(856,plain,
! [A: 'ZF_set$',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$a' ) ) ) ) ) ) ) )
=> ( ( G = N )
& ( F = M )
& ( E = L )
& ( D = K )
& ( C = J )
& ( B = I )
& ( A = H ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(212,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'uum$' ) @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).
thf(1374,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'uum$' ) @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(272,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( D @ 'elem$' @ 'fun_app$d' ) )
& ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).
thf(1648,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( D @ 'elem$' @ 'fun_app$d' ) )
& ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( D @ ( A @ 'zF2mor$' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(4,axiom,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$'] :
( ! [C: 'ZF$'] :
( ( C @ ( A @ 'fun_app$d' ) )
<=> ( C @ ( B @ 'fun_app$d' ) ) )
=> ( ( A @ 'collect$c' )
= ( B @ 'collect$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).
thf(412,plain,
! [A: 'ZF_bool_fun$',B: 'ZF_bool_fun$'] :
( ! [C: 'ZF$'] :
( ( ( C @ ( B @ 'fun_app$d' ) )
=> ( C @ ( A @ 'fun_app$d' ) ) )
& ( ( C @ ( A @ 'fun_app$d' ) )
=> ( C @ ( B @ 'fun_app$d' ) ) ) )
=> ( ( A @ 'collect$c' )
= ( B @ 'collect$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( C @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom435) ).
thf(425,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( C @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(393,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'B_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'functor_ext$' ) ) ) @ 'catDom$' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).
thf(2176,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'B_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'functor_ext$' ) ) ) @ 'catDom$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(365,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$t' ) @ 'nTCatDom$' )
= ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).
thf(2033,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$t' ) @ 'nTCatDom$' )
= ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(386,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'makeFtor$' @ 'fun_app$v' ) )
= ( A @ 'more$b' @ ( A @ 'catDom$' @ 'mor$' @ ( A @ 'mapM$' @ 'restrict$b' ) @ ( A @ 'catCod$' @ ( A @ 'catDom$' @ 'functor_ext$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom490) ).
thf(2149,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'makeFtor$' @ 'fun_app$v' ) )
= ( A @ 'more$b' @ ( A @ 'catDom$' @ 'mor$' @ ( A @ 'mapM$' @ 'restrict$b' ) @ ( A @ 'catCod$' @ ( A @ 'catDom$' @ 'functor_ext$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(157,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).
thf(1154,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(92,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) )
= ( A @ 'more$e' @ ( A @ 'uuk$' @ ( A @ 'id$a' @ ( A @ 'dom$a' @ ( A @ 'cod$' @ ( A @ 'mor$b' @ ( A @ 'obj$' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).
thf(819,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) )
= ( A @ 'more$e' @ ( A @ 'uuk$' @ ( A @ 'id$a' @ ( A @ 'dom$a' @ ( A @ 'cod$' @ ( A @ 'mor$b' @ ( A @ 'obj$' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(115,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$d' @ ( A @ 'comp$a' @ ( A @ 'id$' @ ( A @ 'cod$a' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$a' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom411) ).
thf(975,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( A
= ( A @ 'more$d' @ ( A @ 'comp$a' @ ( A @ 'id$' @ ( A @ 'cod$a' @ ( A @ 'dom$' @ ( A @ 'mor$' @ ( A @ 'obj$a' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(5,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category_axioms$a' )
=> ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'category$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).
thf(423,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category_axioms$a' )
=> ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(331,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ 'idNatTrans$b' @ ( 'natTransP$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).
thf(1916,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ 'idNatTrans$b' @ ( 'natTransP$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(336,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( A @ 'more$b' )
= ( B @ 'more$b' ) )
& ( ( A @ 'mapM$' )
= ( B @ 'mapM$' ) )
& ( ( A @ 'catCod$' )
= ( B @ 'catCod$' ) )
& ( ( A @ 'catDom$' )
= ( B @ 'catDom$' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom387) ).
thf(1929,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( A @ 'more$b' )
= ( B @ 'more$b' ) )
& ( ( A @ 'mapM$' )
= ( B @ 'mapM$' ) )
& ( ( A @ 'catCod$' )
= ( B @ 'catCod$' ) )
& ( ( A @ 'catDom$' )
= ( B @ 'catDom$' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(44,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).
thf(577,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(242,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$b' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> $false )
& ( B @ ( A @ 'functor_comp_def$c' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom107) ).
thf(1535,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
~ ( ~ ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$b' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
& ( B @ ( A @ 'functor_comp_def$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(237,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).
thf(1520,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(383,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( A
= ( A @ 'more$a' @ ( A @ 'natTransMap$' @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'natTrans_ext$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).
thf(2134,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( A
= ( A @ 'more$a' @ ( A @ 'natTransMap$' @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'natTrans_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(112,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'cod$' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).
thf(958,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'cod$' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(219,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> ( C @ ( B @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom212) ).
thf(1403,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> ( C @ ( B @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(36,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( A @ 'more$e' )
= ( B @ 'more$e' ) )
& ( ( A @ 'comp$' )
= ( B @ 'comp$' ) )
& ( ( A @ 'id$a' )
= ( B @ 'id$a' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$a' )
= ( B @ 'dom$a' ) )
& ( ( A @ 'mor$b' )
= ( B @ 'mor$b' ) )
& ( ( A @ 'obj$' )
= ( B @ 'obj$' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom407) ).
thf(545,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( A @ 'more$e' )
= ( B @ 'more$e' ) )
& ( ( A @ 'comp$' )
= ( B @ 'comp$' ) )
& ( ( A @ 'id$a' )
= ( B @ 'id$a' ) )
& ( ( A @ 'cod$' )
= ( B @ 'cod$' ) )
& ( ( A @ 'dom$a' )
= ( B @ 'dom$a' ) )
& ( ( A @ 'mor$b' )
= ( B @ 'mor$b' ) )
& ( ( A @ 'obj$' )
= ( B @ 'obj$' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(226,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) )
=> ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom330) ).
thf(1488,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) )
=> ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(232,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'A$'] :
( ( ( B @ 'obj$a' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( ( D @ ( B @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom393) ).
thf(1503,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'A$'] :
( ( ( B @ 'obj$a' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> ( ( D @ ( B @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(278,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).
thf(1669,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( B @ ( A @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(14,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'category_axioms$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).
thf(445,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ 'category$a' )
=> ( A @ 'category_axioms$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(211,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'] :
( ( A @ 'makeCat$c' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).
thf(1371,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'] :
( ( A @ 'makeCat$c' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(293,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'mor$' @ 'extensional$b' @ ( A @ 'mor2ZF$' @ 'member$d' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ( 'top$' @ ( 'explode$' @ 'image$' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'member$o' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> ( B = C ) ) )
=> ( A @ 'lSCategory_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom586) ).
thf(1733,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'mor$' @ 'extensional$b' @ ( A @ 'mor2ZF$' @ 'member$d' ) )
& ! [B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) ) )
=> ( 'top$' @ ( 'explode$' @ 'image$' ) @ ( C @ ( B @ ( A @ 'hOMCollection$' ) ) @ 'member$o' ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( ( ( B @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mor2ZF$' @ 'fun_app$o' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> ( B = C ) ) )
=> ( A @ 'lSCategory_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(140,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom340) ).
thf(1058,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(357,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'natTransComp$a' ) )
= ( 'unity$' @ ( B @ ( A @ 'uup$' ) @ ( B @ ( 'nTCod$' @ 'fun_app$r' ) @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'natTrans_ext$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).
thf(1997,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'natTransComp$a' ) )
= ( 'unity$' @ ( B @ ( A @ 'uup$' ) @ ( B @ ( 'nTCod$' @ 'fun_app$r' ) @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'natTrans_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(371,axiom,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$'] :
( ( C @ ( B @ 'yFtorNT$a' @ 'fun_app$t' ) @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) )
=> ( ( A @ ( C @ ( B @ 'yFtorNT$a' @ 'fun_app$t' ) @ 'natTransMap$' @ 'fun_app$n' ) )
= ( C @ ( A @ ( B @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).
thf(2055,plain,
! [A: 'A$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$'] :
( ( C @ ( B @ 'yFtorNT$a' @ 'fun_app$t' ) @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) )
=> ( ( A @ ( C @ ( B @ 'yFtorNT$a' @ 'fun_app$t' ) @ 'natTransMap$' @ 'fun_app$n' ) )
= ( C @ ( A @ ( B @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(188,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).
thf(1258,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'A$',D: 'ZF$'] :
( ( ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) )
=> ? [E: 'B$'] :
( ( ( E @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= D )
& ( C @ ( B @ ( E @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(181,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).
thf(1224,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( E @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(207,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom180) ).
thf(1356,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(280,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) @ 'more$a' )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom209) ).
thf(1675,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) @ 'more$a' )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(67,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom461) ).
thf(672,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ 'member$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(53,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom463) ).
thf(611,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'dom$a' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(80,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ 'zF2mor$' ) )
= ( B @ ( A @ 'uus$' ) @ 'the$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom537) ).
thf(787,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ 'zF2mor$' ) )
= ( B @ ( A @ 'uus$' ) @ 'the$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(76,axiom,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$',D: 'ZF$',E: 'ZF_ZF_fun$'] :
( ! [F: 'ZF$'] :
( ( A @ ( F @ 'elem$' @ 'fun_app$d' ) )
=> ( C @ ( F @ ( B @ 'fun_app$' ) @ 'elem$' @ 'fun_app$d' ) ) )
=> ( ( E @ ( D @ ( C @ 'zFfun$' ) ) @ ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( E @ 'comp$d' @ 'fun_app$ac' ) @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom563) ).
thf(764,plain,
! [A: 'ZF$',B: 'ZF_ZF_fun$',C: 'ZF$',D: 'ZF$',E: 'ZF_ZF_fun$'] :
( ! [F: 'ZF$'] :
( ( A @ ( F @ 'elem$' @ 'fun_app$d' ) )
=> ( C @ ( F @ ( B @ 'fun_app$' ) @ 'elem$' @ 'fun_app$d' ) ) )
=> ( ( E @ ( D @ ( C @ 'zFfun$' ) ) @ ( B @ ( C @ ( A @ 'zFfun$' ) ) @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( E @ 'comp$d' @ 'fun_app$ac' ) @ ( D @ ( A @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(171,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom336) ).
thf(1194,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$'] :
( ( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(194,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'equivalence$a' @ 'fun_app$a' ) )
=> ( A @ ( 'functor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).
thf(1282,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'equivalence$a' @ 'fun_app$a' ) )
=> ( A @ ( 'functor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(262,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'objIso$' ) @ 'fun_app$d' ) )
<=> ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).
thf(1603,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( C @ ( B @ ( A @ 'objIso$' ) @ 'fun_app$d' ) ) )
& ( ( C @ ( B @ ( A @ 'objIso$' ) @ 'fun_app$d' ) )
=> ? [D: 'ZF$'] :
( ( D @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( D @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(243,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom91) ).
thf(1542,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(31,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$a' ) ) @ 'functor$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom475) ).
thf(509,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$a' ) ) @ 'functor$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(286,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$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ 'member$i' ) ) ) )
=> ( A @ 'category_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom401) ).
thf(1690,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$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ 'member$i' ) ) ) )
=> ( A @ 'category_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(50,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
<=> ( 'set$' @ 'mor$b' @ ( A @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom542) ).
thf(599,plain,
! [A: 'ZF$'] :
( ( ( 'set$' @ 'mor$b' @ ( A @ 'member$c' ) )
=> ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
& ( ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( 'set$' @ 'mor$b' @ ( A @ 'member$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(200,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$i' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'inverse$a' ) @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom497) ).
thf(1307,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( B @ ( A @ 'isomorphism$' @ 'fun_app$i' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'inverse$a' ) @ 'member$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(165,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$',D: 'A$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$ab' ) )
= D )
& ( ( A @ ( B @ 'dom$' @ 'fun_app$ab' ) )
= C )
& ( B @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).
thf(1175,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'A$',D: 'A$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$ab' ) )
= D )
& ( ( A @ ( B @ 'dom$' @ 'fun_app$ab' ) )
= C )
& ( B @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(318,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$' ) @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom473) ).
thf(1853,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( C @ ( A @ 'cod$' @ 'fun_app$' ) @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(221,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$b' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom156) ).
thf(1408,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ 'mor$b' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(257,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'ZF$',E: 'ZF$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> ( E @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( C @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom287) ).
thf(1589,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$',D: 'ZF$',E: 'ZF$'] :
( ( ( E @ ( D @ ( B @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> ( E @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( D @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( C @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(120,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom459) ).
thf(990,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(289,axiom,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( C @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ ( B @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom229) ).
thf(1722,plain,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( C @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ ( B @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(155,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM_axioms$a' @ 'fun_app$a' ) )
<=> ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom326) ).
thf(1144,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( A @ ( 'functorM_axioms$a' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'functorM_axioms$a' @ 'fun_app$a' ) )
=> ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'catDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( D @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(100,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$b' ) ) @ 'functorM$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).
thf(890,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( B @ 'obj$' @ ( C @ 'member$c' ) )
& ( B @ 'category$a' )
& ( A @ 'category$a' ) )
=> ( C @ ( B @ ( A @ 'constFunctor$b' ) ) @ 'functorM$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(364,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_b_b_c_LSCategory_ext_Category_ext$',D: 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$',E: 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$'] :
( ( ! [F: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$s' ) )
= ( F @ ( E @ 'fun_app$s' ) ) ) )
& ( ( B @ 'catDom$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'catDom_update$a' @ 'fun_app$v' ) )
= ( B @ ( E @ 'catDom_update$a' @ 'fun_app$v' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).
thf(2025,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_b_b_c_LSCategory_ext_Category_ext$',D: 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$',E: 'A_b_b_c_LSCategory_ext_Category_ext_a_b_b_c_LSCategory_ext_Category_ext_fun$'] :
( ( ! [F: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$s' ) )
= ( F @ ( E @ 'fun_app$s' ) ) ) )
& ( ( B @ 'catDom$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'catDom_update$a' @ 'fun_app$v' ) )
= ( B @ ( E @ 'catDom_update$a' @ 'fun_app$v' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(249,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ ( B @ ( A @ 'homFtorContra$' ) @ 'functor_abbrev$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).
thf(1557,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$' @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ ( B @ ( A @ 'homFtorContra$' ) @ 'functor_abbrev$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(91,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$' )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).
thf(816,plain,
! [A: 'ZF_set$',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$a' ) ) ) ) ) ) @ 'cod$' )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(308,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$n' ) )
= ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
thf(1821,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A$'] :
( ( C @ ( B @ ( A @ 'uup$' ) @ 'fun_app$n' ) )
= ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(322,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ? [C: 'ZF$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom395) ).
thf(1862,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ? [C: 'ZF$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(114,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) )
<=> ( ( ( A @ 'catCod$b' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ 'functor$b' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).
thf(964,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( ( A @ 'catCod$b' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ 'functor$b' ) )
=> ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
& ( ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) )
=> ( ( ( A @ 'catCod$b' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ 'functor$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(56,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$b' @ ( A @ 'member$c' ) )
=> ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= ( A @ ( B @ ( 'makeCat$' @ 'fun_app$w' ) @ 'dom$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).
thf(626,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$b' @ ( A @ 'member$c' ) )
=> ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= ( A @ ( B @ ( 'makeCat$' @ 'fun_app$w' ) @ 'dom$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(285,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$' )
=> ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'extCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom516) ).
thf(1688,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'extCategory$' )
=> ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'extCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(118,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom254) ).
thf(983,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(335,axiom,
! [A: 'B$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$' @ 'mor$' @ ( A @ 'member$h' ) )
=> ( ( A @ ( B @ ( 'makeFtor$' @ 'fun_app$v' ) @ 'mapM$' @ 'fun_app$o' ) )
= ( A @ ( B @ 'mapM$' @ 'fun_app$o' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom348) ).
thf(1926,plain,
! [A: 'B$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$' @ 'mor$' @ ( A @ 'member$h' ) )
=> ( ( A @ ( B @ ( 'makeFtor$' @ 'fun_app$v' ) @ 'mapM$' @ 'fun_app$o' ) )
= ( A @ ( B @ 'mapM$' @ 'fun_app$o' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(399,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$t' ) )
= ( B @ ( A @ 'yFtorNT$' ) @ 'makeNT$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom40) ).
thf(2212,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$t' ) )
= ( B @ ( A @ 'yFtorNT$' ) @ 'makeNT$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(240,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( A @ 'makeNT$' @ ( 'natTrans$' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom76) ).
thf(1528,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( A @ 'makeNT$' @ ( 'natTrans$' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(375,axiom,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ 'makeNT$' @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( B @ 'makeNT$' @ 'natTransMap$' @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom151) ).
thf(2064,plain,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ 'makeNT$' @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( B @ 'makeNT$' @ 'natTransMap$' @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(52,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( 'set$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).
thf(608,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( ( A @ 'obj$a' @ ( C @ 'member$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) )
= ( C @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( 'set$a' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(119,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 )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom417) ).
thf(986,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
~ ! [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)],[119]) ).
thf(363,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$' ) )
= ( 'unity$' @ ( B @ ( A @ 'uum$' ) @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'homFtorContra$' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'homFtorContra$' ) @ 'natTrans_ext$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom525) ).
thf(2022,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$' ) )
= ( 'unity$' @ ( B @ ( A @ 'uum$' ) @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'homFtorContra$' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'homFtorContra$' ) @ 'natTrans_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(210,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> $false )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom553) ).
thf(1364,plain,
! [A: 'ZF$',B: 'ZF$'] :
~ ( ~ ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
& ( B @ ( A @ ( 'set$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(229,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom456) ).
thf(1496,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ 'member$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(389,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( ( A @ 'nTCatDom$' )
= ( B @ 'nTCatDom$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom146) ).
thf(2156,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( ( A @ 'nTCatDom$' )
= ( B @ 'nTCatDom$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(251,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ ( 'functorExt$a' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom342) ).
thf(1562,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( A @ ( 'functorExt$a' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(351,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom248) ).
thf(1973,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(305,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
<=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom377) ).
thf(1805,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
& ( ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(146,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom354) ).
thf(1076,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( A @ ( 'equivalence_axioms$' @ 'fun_app$a' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(266,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_set$',D: 'B_set_b_set_fun$',E: 'B_set_b_set_fun$'] :
( ( ! [F: 'B_set$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$ae' ) )
= ( F @ ( E @ 'fun_app$ae' ) ) ) )
& ( ( B @ 'mor$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'mor_update$a' @ 'fun_app$s' ) )
= ( B @ ( E @ 'mor_update$a' @ 'fun_app$s' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom572) ).
thf(1626,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_set$',D: 'B_set_b_set_fun$',E: 'B_set_b_set_fun$'] :
( ( ! [F: 'B_set$'] :
( ( F = C )
=> ( ( F @ ( D @ 'fun_app$ae' ) )
= ( F @ ( E @ 'fun_app$ae' ) ) ) )
& ( ( B @ 'mor$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'mor_update$a' @ 'fun_app$s' ) )
= ( B @ ( E @ 'mor_update$a' @ 'fun_app$s' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(342,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'makeNT$' )
= ( 'unity$' @ ( A @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'natTransMap$' @ 'restrict$c' ) @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'natTrans_ext$a' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom505) ).
thf(1948,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'makeNT$' )
= ( 'unity$' @ ( A @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'natTransMap$' @ 'restrict$c' ) @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'natTrans_ext$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(405,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).
thf(2239,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(325,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> $false )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom375) ).
thf(1873,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(296,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uut$' @ 'fun_app$d' ) )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).
thf(1758,plain,
! [A: 'ZF$'] : ( A @ ( 'uut$' @ 'fun_app$d' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(37,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom468) ).
thf(548,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(61,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'identityFunctor$' @ 'catDom$a' @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'identityFunctor$' @ 'mapO$b' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom477) ).
thf(648,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'identityFunctor$' @ 'catDom$a' @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'identityFunctor$' @ 'mapO$b' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(55,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uuq$' ) @ 'fun_app$d' ) )
<=> ( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
thf(617,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$',C: 'ZF$'] :
( ( ( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) )
=> ( C @ ( B @ ( A @ 'uuq$' ) @ 'fun_app$d' ) ) )
& ( ( C @ ( B @ ( A @ 'uuq$' ) @ 'fun_app$d' ) )
=> ( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(223,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
<=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom373) ).
thf(1472,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= D )
& ( ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) )
= C )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(346,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ ( 'makeFtor$' @ 'fun_app$v' ) @ 'mapO$c' @ 'fun_app$n' ) )
= ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).
thf(1958,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A$'] :
( ( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ ( 'makeFtor$' @ 'fun_app$v' ) @ 'mapO$c' @ 'fun_app$n' ) )
= ( B @ ( A @ 'mapO$c' @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(18,axiom,
! [A: 'ZF_set$',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$a' ) ) ) ) ) ) @ 'more$e' )
= G ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom425) ).
thf(458,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$e' )
= G ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(137,axiom,
! [A: 'B_set$'] :
( ( A @ 'uu$' @ 'collect$b' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).
thf(1049,plain,
! [A: 'B_set$'] :
( ( A @ 'uu$' @ 'collect$b' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(174,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).
thf(1203,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'compDefined$' ) @ 'fun_app$d' ) )
=> ( ( C @ ( B @ ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(176,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom368) ).
thf(1208,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(83,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom498) ).
thf(795,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(69,axiom,
! [A: 'ZF_set$',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',axiom424) ).
thf(680,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$a' )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(245,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'functorM$' ) )
=> ( D @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom329) ).
thf(1547,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'catDom$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'functorM$' ) )
=> ( D @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( C @ ( A @ 'mapO$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(304,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom379) ).
thf(1798,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) ) )
& ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(300,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ 'member$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom454) ).
thf(1770,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ 'member$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(45,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$' )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).
thf(580,plain,
! [A: 'A_set$',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)],[45]) ).
thf(347,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).
thf(1961,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(131,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).
thf(1025,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(158,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom398) ).
thf(1156,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(3,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uuv$' @ 'fun_app$' ) )
= ( 'uuu$' @ ( A @ ( A @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).
thf(409,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uuv$' @ 'fun_app$' ) )
= ( 'uuu$' @ ( A @ ( A @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(71,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'cod$' @ 'fun_app$' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom460) ).
thf(690,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( A @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'cod$' @ 'fun_app$' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(236,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF$'] :
( ( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom344) ).
thf(1516,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF$'] :
( ( ( A @ 'catCod$' @ 'obj$' @ ( B @ 'member$c' ) )
& ( A @ ( 'equivalence$a' @ 'fun_app$a' ) ) )
=> ? [C: 'A$'] :
( ( B @ ( C @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( A @ 'catCod$' @ 'objIso$' ) @ 'fun_app$d' ) )
& ( A @ 'catDom$' @ 'obj$a' @ ( C @ 'member$i' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(373,axiom,
'set$' @ ( 'c$' @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTDom$' @ 'fun_app$r' ) @ 'functor_abbrev$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).
thf(2060,plain,
'set$' @ ( 'c$' @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ ( 'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTDom$' @ 'fun_app$r' ) @ 'functor_abbrev$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(218,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$'] :
( ( A @ 'uui$' @ 'collect$i' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).
thf(1400,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_set$'] :
( ( A @ 'uui$' @ 'collect$i' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(294,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) )
= ( B @ ( A @ 'natTransComp$a' ) @ 'makeNT$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom222) ).
thf(1753,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) )
= ( B @ ( A @ 'natTransComp$a' ) @ 'makeNT$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(191,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( B @ ( D @ 'elem$' @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( C @ ( D @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ 'elem$' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom410) ).
thf(1267,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( B @ ( D @ 'elem$' @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( C @ ( D @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ 'elem$' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(392,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( C @ ( B @ ( A @ 'nt_abbrev$a' ) @ 'fun_app$a' ) )
<=> ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).
thf(2165,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( C @ ( B @ ( A @ 'nt_abbrev$a' ) @ 'fun_app$a' ) ) )
& ( ( C @ ( B @ ( A @ 'nt_abbrev$a' ) @ 'fun_app$a' ) )
=> ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= B )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(169,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom464) ).
thf(1188,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( A @ 'cod$' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(179,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'homSet$' ) @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom364) ).
thf(1218,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'A$'] :
( ( C @ ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'homSet$' ) @ 'fun_app$n' ) )
= ( B @ ( C @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(287,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) @ 'catCod$' )
= 'set$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom95) ).
thf(1716,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) @ 'catCod$' )
= 'set$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(402,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) )
=> ( ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).
thf(2224,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'B$',C: 'A$',D: 'A$'] :
( ( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) )
=> ( ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(199,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functor$' @ 'fun_app$a' ) )
<=> ( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
& ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).
thf(1300,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
& ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) )
=> ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'functor$' @ 'fun_app$a' ) )
=> ( ( A @ ( 'functorExt$a' @ 'fun_app$a' ) )
& ( A @ ( 'functorM$a' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(268,axiom,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( C @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ ( B @ 'natTransMap$' @ 'fun_app$n' ) @ ( C @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).
thf(1637,plain,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ 'nTCatDom$' @ 'obj$a' @ ( A @ 'member$i' ) ) )
=> ( ( A @ ( C @ ( B @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( C @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ ( B @ 'natTransMap$' @ 'fun_app$n' ) @ ( C @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(298,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom499) ).
thf(1766,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(353,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom196) ).
thf(1981,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(345,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( A @ 'more$a' )
= ( B @ 'more$a' ) )
& ( ( A @ 'natTransMap$' )
= ( B @ 'natTransMap$' ) )
& ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTCod$' @ 'fun_app$r' ) ) )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom160) ).
thf(1955,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( A @ 'more$a' )
= ( B @ 'more$a' ) )
& ( ( A @ 'natTransMap$' )
= ( B @ 'natTransMap$' ) )
& ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTCod$' @ 'fun_app$r' ) ) )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(42,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).
thf(571,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(326,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] :
( ( ( ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$a' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> $false )
& ( B @ ( A @ 'functor_comp_def$' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom104) ).
thf(1881,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] :
~ ( ~ ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$a' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
& ( B @ ( A @ 'functor_comp_def$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(180,axiom,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$ab' ) )
= ( C @ ( B @ 'dom$' @ 'fun_app$ab' ) ) )
& ( B @ 'mor$' @ ( C @ 'member$h' ) )
& ( B @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$a' ) @ 'fun_app$i' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).
thf(1221,plain,
! [A: 'B$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B$'] :
( ( ( ( A @ ( B @ 'cod$a' @ 'fun_app$ab' ) )
= ( C @ ( B @ 'dom$' @ 'fun_app$ab' ) ) )
& ( B @ 'mor$' @ ( C @ 'member$h' ) )
& ( B @ 'mor$' @ ( A @ 'member$h' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$a' ) @ 'fun_app$i' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(195,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).
thf(1284,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(225,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$a' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).
thf(1485,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( D @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$a' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(138,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ ( 'oppositeCategory$' @ 'fun_app$s' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
thf(1052,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ ( 'oppositeCategory$' @ 'fun_app$s' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(233,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom174) ).
thf(1506,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(116,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).
thf(978,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( A @ 'mor$b' @ ( B @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(154,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ! [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 )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom506) ).
thf(1140,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
~ ! [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)],[154]) ).
thf(361,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( ( ( A @ 'catCod$' )
= C )
& ( ( A @ 'catDom$' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).
thf(2013,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
~ ( ~ ( ( ( A @ 'catCod$' )
= C )
& ( ( A @ 'catDom$' )
= B )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(312,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'zF2mor$' ) )
= ( B @ ( A @ 'zF2mor$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom149) ).
thf(1839,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'ZF$'] :
( ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'zF2mor$' ) )
= ( B @ ( A @ 'zF2mor$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(34,axiom,
! [A: 'ZF$'] : ( 'set$' @ 'obj$' @ ( A @ 'member$c' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom144) ).
thf(539,plain,
! [A: 'ZF$'] : ( 'set$' @ 'obj$' @ ( A @ 'member$c' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(330,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) )
= ( C @ ( B @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom210) ).
thf(1913,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( C @ ( B @ 'nTCompDefined$a' @ 'fun_app$q' ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> ( ( C @ ( B @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) )
= ( C @ ( B @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) @ ( A @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(314,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).
thf(1844,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(400,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom34) ).
thf(2215,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(178,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom495) ).
thf(1216,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(395,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).
thf(2187,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(77,axiom,
! [A: 'ZF_set$',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',axiom422) ).
thf(771,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$a' )
= E ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(332,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( ( B @ 'nTCatCod$' )
= ( A @ 'nTCatCod$' ) )
& ( ( B @ 'nTCatDom$' )
= ( A @ 'nTCatDom$' ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom138) ).
thf(1918,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( ( B @ 'nTCatCod$' )
= ( A @ 'nTCatCod$' ) )
& ( ( B @ 'nTCatDom$' )
= ( A @ 'nTCatDom$' ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(16,axiom,
! [A: 'ZF$',B: 'ZF_bool_fun$'] :
( ( B @ 'collect$c' @ ( A @ 'member$c' ) )
<=> ( A @ ( B @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).
thf(450,plain,
! [A: 'ZF$',B: 'ZF_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$d' ) )
=> ( B @ 'collect$c' @ ( A @ 'member$c' ) ) )
& ( ( B @ 'collect$c' @ ( A @ 'member$c' ) )
=> ( A @ ( B @ 'fun_app$d' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(349,axiom,
'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).
thf(1966,plain,
'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(40,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$' ) )
= D )
& ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( B @ 'mor$b' @ ( A @ 'member$c' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom361) ).
thf(556,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$' ) )
= D )
& ( ( A @ ( B @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( B @ 'mor$b' @ ( A @ 'member$c' ) ) )
=> ( D @ ( C @ ( A @ ( B @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(216,axiom,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$' @ 'obj$a' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( B @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom386) ).
thf(1390,plain,
! [A: 'A$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$' @ 'obj$a' @ ( A @ 'member$i' ) )
=> ( ( A @ ( B @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ 'natTransMap$' @ 'fun_app$n' ) )
= ( A @ ( B @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(254,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatCod$' )
= ( A @ 'makeNT$' @ 'nTCatCod$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom89) ).
thf(1575,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatCod$' )
= ( A @ 'makeNT$' @ 'nTCatCod$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(197,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'catDom$a' @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'functor$b' ) )
=> ( C @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom239) ).
thf(1289,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( B @ ( A @ 'catDom$a' @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'functor$b' ) )
=> ( C @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ ( A @ 'catCod$b' @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(96,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ 'elem$' @ 'fun_app$d' ) )
=> ( ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).
thf(844,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ! [C: 'ZF$'] :
( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( C @ 'elem$' @ 'fun_app$d' ) )
=> ( ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( B @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( ( 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)],[96]) ).
thf(48,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ( ( ( A @ 'catCod$b' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ 'functor$b' ) )
=> $false )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).
thf(588,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
~ ( ~ ( ( ( A @ 'catCod$b' )
= C )
& ( ( A @ 'catDom$a' )
= B )
& ( A @ 'functor$b' ) )
& ( C @ ( B @ ( A @ 'functor_abbrev$b' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(74,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$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ 'member$c' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$c' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).
thf(699,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ 'member$c' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$c' ) ) ) )
=> ( A @ 'category_axioms$a' ) )
& ( ( A @ 'category_axioms$a' )
=> ( ! [B: 'ZF$',C: 'ZF$',D: 'ZF$',E: 'ZF$',F: 'ZF$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( ( B @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= B ) )
& ! [B: 'ZF$'] :
( ( A @ 'obj$' @ ( B @ 'member$c' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$a' @ 'fun_app$' ) @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ 'member$c' ) ) )
& ! [B: 'ZF$'] :
( ( A @ 'mor$b' @ ( B @ 'member$c' ) )
=> ( A @ 'obj$' @ ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ 'member$c' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(113,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom469) ).
thf(961,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'category$' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(90,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom536) ).
thf(813,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF_ZF_fun$'] :
( ( C @ ( B @ ( A @ 'zFfun$' ) ) @ ( 'zFfunCod$' @ 'fun_app$' ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(103,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom540) ).
thf(896,plain,
! [A: 'ZF$'] :
( ( A @ ( 'isZFfun$' @ 'fun_app$d' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(380,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'] :
( ( ! [F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$v' ) )
= ( F @ ( E @ 'fun_app$v' ) ) ) )
& ( ( B @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'nTCod_update$a' ) )
= ( B @ ( E @ 'nTCod_update$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).
thf(2098,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$',E: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_fun$'] :
( ( ! [F: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$v' ) )
= ( F @ ( E @ 'fun_app$v' ) ) ) )
& ( ( B @ ( 'nTCod$' @ 'fun_app$r' ) )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'nTCod_update$a' ) )
= ( B @ ( E @ 'nTCod_update$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(142,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'catDom$' @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom356) ).
thf(1062,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'catDom$' @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(234,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) )
=> ( A @ 'lSCategory$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).
thf(1508,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( A @ 'lSCategory_axioms$' )
& ( A @ 'category$' ) )
=> ( A @ 'lSCategory$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(122,axiom,
! [A: 'ZF_set$',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 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).
thf(995,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$' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(387,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) )
=> ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).
thf(2152,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) )
=> ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(133,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( B @ 'dom$a' @ 'fun_app$' ) ) )
& ( B @ 'mor$b' @ ( C @ 'member$c' ) )
& ( B @ 'mor$b' @ ( A @ 'member$c' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom363) ).
thf(1030,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$',C: 'ZF$'] :
( ( ( ( A @ ( B @ 'cod$' @ 'fun_app$' ) )
= ( C @ ( B @ 'dom$a' @ 'fun_app$' ) ) )
& ( B @ 'mor$b' @ ( C @ 'member$c' ) )
& ( B @ 'mor$b' @ ( A @ 'member$c' ) ) )
=> ( C @ ( A @ ( B @ 'compDefined$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(398,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
<=> ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( ( B @ 'nTCatCod$' )
= ( A @ 'nTCatCod$' ) )
& ( ( B @ 'nTCatDom$' )
= ( A @ 'nTCatDom$' ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom140) ).
thf(2198,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( ( B @ 'nTCatCod$' )
= ( A @ 'nTCatCod$' ) )
& ( ( B @ 'nTCatDom$' )
= ( A @ 'nTCatDom$' ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
& ( ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) )
=> ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( ( B @ 'nTCatCod$' )
= ( A @ 'nTCatCod$' ) )
& ( ( B @ 'nTCatDom$' )
= ( A @ 'nTCatDom$' ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(104,axiom,
! [A: 'A_set$'] :
( ( A @ 'uub$' @ 'collect$d' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).
thf(899,plain,
! [A: 'A_set$'] :
( ( A @ 'uub$' @ 'collect$d' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(94,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).
thf(832,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(24,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
=> $false )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).
thf(478,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
~ ( ~ ( ( ( B @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) ) )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(391,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( C @ ( B @ 'catExp$a' ) @ 'mor$a' @ ( A @ 'member$l' ) )
=> ( ( A @ ( C @ ( B @ 'catExp$a' ) @ 'dom$b' ) )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).
thf(2162,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'ZF_ZF_unit_Category_ext$'] :
( ( C @ ( B @ 'catExp$a' ) @ 'mor$a' @ ( A @ 'member$l' ) )
=> ( ( A @ ( C @ ( B @ 'catExp$a' ) @ 'dom$b' ) )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(366,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom198) ).
thf(2036,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( ( A @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'idNatTrans$d' @ 'fun_app$x' ) @ ( 'natTransComp$c' @ 'fun_app$z' ) @ 'fun_app$y' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(201,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$a' @ 'mor$b' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom185) ).
thf(1309,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( 'set$a' @ 'mor$b' @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(160,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$t' ) @ 'nTCatCod$' )
= 'set$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom78) ).
thf(1161,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$'] :
( ( B @ ( A @ 'yFtorNT$a' @ 'fun_app$t' ) @ 'nTCatCod$' )
= 'set$' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(85,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'obj$' )
= ( A @ 'obj$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).
thf(800,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'makeCat$' @ 'fun_app$w' ) @ 'obj$' )
= ( A @ 'obj$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(401,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
<=> ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).
thf(2218,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) )
=> ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) ) )
& ( ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) )
=> ( A @ 'nTCatDom$' @ 'obj$a' @ 'extensional$a' @ ( A @ 'natTransMap$' @ 'member$f' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(270,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$',D: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( D @ ( A @ 'functor_comp_def$c' ) )
& ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'catCod$b' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).
thf(1642,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$',C: 'B$',D: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( D @ ( A @ 'functor_comp_def$c' ) )
& ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( D @ 'mapM$b' @ 'fun_app$' ) @ ( D @ 'catCod$b' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(15,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mor$b' )
= ( A @ 'mor$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).
thf(447,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mor$b' )
= ( A @ 'mor$b' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(255,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_set$',D: 'B_set_b_set_fun$',E: 'B_set_b_set_fun$'] :
( ( ! [F: 'B_set$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$ae' ) )
= ( F @ ( E @ 'fun_app$ae' ) ) ) )
& ( ( B @ 'mor$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'mor_update$a' @ 'fun_app$s' ) )
= ( B @ ( E @ 'mor_update$a' @ 'fun_app$s' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom570) ).
thf(1578,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$',C: 'B_set$',D: 'B_set_b_set_fun$',E: 'B_set_b_set_fun$'] :
( ( ! [F: 'B_set$'] :
( ( C = F )
=> ( ( F @ ( D @ 'fun_app$ae' ) )
= ( F @ ( E @ 'fun_app$ae' ) ) ) )
& ( ( B @ 'mor$' )
= C )
& ( A = B ) )
=> ( ( A @ ( D @ 'mor_update$a' @ 'fun_app$s' ) )
= ( B @ ( E @ 'mor_update$a' @ 'fun_app$s' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(281,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) )
= ( A @ 'more$d' @ ( A @ 'uuj$' @ ( A @ 'id$' @ ( A @ 'dom$' @ ( A @ 'cod$a' @ ( A @ 'mor$' @ ( A @ 'obj$a' @ 'category_ext$' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).
thf(1678,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) )
= ( A @ 'more$d' @ ( A @ 'uuj$' @ ( A @ 'id$' @ ( A @ 'dom$' @ ( A @ 'cod$a' @ ( A @ 'mor$' @ ( A @ 'obj$a' @ 'category_ext$' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(9,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom436) ).
thf(432,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'inverse_rel$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(359,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catCod$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom82) ).
thf(2008,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catCod$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(290,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) @ 'natTransMap$' )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).
thf(1725,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_fun$',D: 'Unit$'] :
( ( D @ ( C @ ( B @ ( A @ 'natTrans_ext$a' ) ) ) @ 'natTransMap$' )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(193,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$a' @ 'fun_app$a' ) )
=> ( A @ ( 'makeFtor$' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom352) ).
thf(1280,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'functorM$a' @ 'fun_app$a' ) )
=> ( A @ ( 'makeFtor$' @ 'fun_app$v' ) @ ( 'functor$' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(110,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$'] :
( ( ( A @ 'catDom$a' @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'functor$b' ) )
=> ( A @ 'catCod$b' @ 'mor$b' @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ 'member$c' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom242) ).
thf(950,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF$'] :
( ( ( A @ 'catDom$a' @ 'mor$b' @ ( B @ 'member$c' ) )
& ( A @ 'functor$b' ) )
=> ( A @ 'catCod$b' @ 'mor$b' @ ( B @ ( A @ 'mapM$b' @ 'fun_app$' ) @ 'member$c' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(151,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mor2ZF$' )
= ( A @ 'mor2ZF$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom93) ).
thf(1097,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'mor2ZF$' )
= ( A @ 'mor2ZF$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(259,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom365) ).
thf(1593,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'dom$a' @ 'fun_app$' ) )
= ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(214,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'] :
( ( B @ 'collect$i' @ ( A @ 'member$' ) )
<=> ( A @ ( B @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom118) ).
thf(1380,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_bool_fun$'] :
( ( ( A @ ( B @ 'fun_app$a' ) )
=> ( B @ 'collect$i' @ ( A @ 'member$' ) ) )
& ( ( B @ 'collect$i' @ ( A @ 'member$' ) )
=> ( A @ ( B @ 'fun_app$a' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(186,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'mapO$c' @ 'fun_app$n' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom359) ).
thf(1248,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'B$'] :
( ( ( A @ 'catDom$' @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'dom$a' @ 'fun_app$' ) )
= ( B @ ( A @ 'catDom$' @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'mapO$c' @ 'fun_app$n' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(81,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( B @ 'elem$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( B @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ 'elem$' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom551) ).
thf(790,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ ( B @ 'elem$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( A @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( B @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ 'elem$' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(369,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catDom$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).
thf(2050,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catDom$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(321,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$a' ) )
= ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'homFtor$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom413) ).
thf(1859,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$a' ) )
= ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'homFtor$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(275,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).
thf(1657,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext_a_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext_unit_Category_ext$'] :
( ( A @ 'oppositeCategory$a' @ 'mor$a' )
= ( A @ 'mor$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(30,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uur$' @ 'fun_app$k' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).
thf(506,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'uur$' @ 'fun_app$k' ) @ ( B @ ( 'zFfunCod$' @ 'fun_app$' ) @ ( A @ ( 'zFfunDom$' @ 'fun_app$' ) @ 'zFfun$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(88,axiom,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'mor$b' )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom420) ).
thf(807,plain,
! [A: 'ZF_set$',B: 'ZF_set$',C: 'ZF_ZF_fun$',D: 'ZF_ZF_fun$',E: 'ZF_ZF_fun$',F: 'ZF_ZF_ZF_fun_fun$',G: 'Unit$'] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ 'category_ext$a' ) ) ) ) ) ) @ 'mor$b' )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(58,axiom,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$b' @ ( A @ 'member$c' ) )
=> ( ( A @ ( B @ 'cod$' @ 'fun_app$' ) )
= ( A @ ( B @ ( 'makeCat$' @ 'fun_app$w' ) @ 'cod$' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom351) ).
thf(635,plain,
! [A: 'ZF$',B: 'ZF_ZF_unit_Category_ext$'] :
( ( B @ 'mor$b' @ ( A @ 'member$c' ) )
=> ( ( A @ ( B @ 'cod$' @ 'fun_app$' ) )
= ( A @ ( B @ ( 'makeCat$' @ 'fun_app$w' ) @ 'cod$' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(73,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( C @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( C @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( ( C @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( ( B @ ( C @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).
thf(696,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( ( ( A @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( C @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( C @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( ( C @ ( 'zFfunCod$' @ 'fun_app$' ) )
= ( B @ ( 'zFfunDom$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( ( B @ ( C @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( C @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(109,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( A @ ( 'preFunctor$' @ 'fun_app$a' ) )
<=> ( ( A @ 'catCod$' @ 'category$a' )
& ( A @ 'catDom$' @ 'category$' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ? [C: 'ZF$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).
thf(928,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( ( ( ( A @ 'catCod$' @ 'category$a' )
& ( A @ 'catDom$' @ 'category$' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ? [C: 'ZF$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) )
=> ( A @ ( 'preFunctor$' @ 'fun_app$a' ) ) )
& ( ( A @ ( 'preFunctor$' @ 'fun_app$a' ) )
=> ( ( A @ 'catCod$' @ 'category$a' )
& ( A @ 'catDom$' @ 'category$' )
& ! [B: 'A$'] :
( ( A @ 'catDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ? [C: 'ZF$'] :
( ( ( B @ ( A @ 'catDom$' @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'catCod$' @ 'id$a' @ 'fun_app$' ) ) )
& ( A @ 'catCod$' @ 'obj$' @ ( C @ 'member$c' ) ) ) )
& ! [B: 'B$',C: 'B$'] :
( ( C @ ( B @ ( A @ 'catDom$' @ 'compDefined$a' ) @ 'fun_app$i' ) )
=> ( ( C @ ( B @ ( A @ 'catDom$' @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapM$' @ 'fun_app$o' ) )
= ( C @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( B @ ( A @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'catCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(11,axiom,
! [A: 'ZF$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$a' @ 'obj$' @ ( A @ 'member$c' ) )
=> ( ( A @ ( B @ 'idNatTrans$c' @ 'natTransMap$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'mapO$b' @ 'fun_app$' ) @ ( B @ 'catCod$b' @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).
thf(437,plain,
! [A: 'ZF$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( B @ 'catDom$a' @ 'obj$' @ ( A @ 'member$c' ) )
=> ( ( A @ ( B @ 'idNatTrans$c' @ 'natTransMap$a' @ 'fun_app$' ) )
= ( A @ ( B @ 'mapO$b' @ 'fun_app$' ) @ ( B @ 'catCod$b' @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(377,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [C: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
=> ( ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) )
= ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) ) ) )
& ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTCod$' @ 'fun_app$r' ) ) )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom155) ).
thf(2070,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ! [C: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( C @ 'member$i' ) )
=> ( ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) )
= ( C @ ( B @ 'natTransMap$' @ 'fun_app$n' ) ) ) )
& ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTCod$' @ 'fun_app$r' ) ) )
& ( ( A @ ( 'nTDom$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(164,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( B @ ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom357) ).
thf(1172,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'B$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'mor$' @ ( B @ 'member$h' ) )
& ( A @ 'lSCategory$' ) )
=> ( ( B @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( C @ ( A @ 'homFtorMapContra$' ) @ 'fun_app$n' ) @ ( B @ ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(222,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$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ 'member$i' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom403) ).
thf(1410,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$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ 'member$i' ) ) ) )
=> ( A @ 'category_axioms$' ) )
& ( ( A @ 'category_axioms$' )
=> ( ! [B: 'B$',C: 'A$',D: 'A$',E: 'B$',F: 'A$'] :
( ( ( F @ ( D @ ( E @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
=> ( F @ ( C @ ( E @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$',C: 'B$',D: 'B$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) )
& ( C @ ( B @ ( A @ 'compDefined$a' ) @ 'fun_app$i' ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= ( D @ ( C @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( B @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( ( B @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'comp$a' @ 'fun_app$m' ) @ 'fun_app$l' ) )
= B ) )
& ! [B: 'A$'] :
( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( B @ ( B @ ( A @ 'id$' @ 'fun_app$p' ) @ ( A @ 'mapsTo$' ) ) @ 'fun_app$j' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ 'member$i' ) ) )
& ! [B: 'B$'] :
( ( A @ 'mor$' @ ( B @ 'member$h' ) )
=> ( A @ 'obj$a' @ ( B @ ( A @ 'dom$' @ 'fun_app$ab' ) @ 'member$i' ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(134,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] :
( ( ( ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$a' )
& ( A @ 'functor$b' ) )
=> $false )
& ( B @ ( A @ 'functor_comp_def$a' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom105) ).
thf(1033,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] :
~ ( ~ ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$a' )
& ( A @ 'functor$b' ) )
& ( B @ ( A @ 'functor_comp_def$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(172,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ ( C @ ( B @ 'zFfun$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).
thf(1197,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ ( 'set$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( A
= ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ ( C @ ( B @ 'zFfun$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(362,axiom,
'c$' @ 'lSCategory$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).
thf(2021,plain,
'c$' @ 'lSCategory$',
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(263,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'inverse$' @ 'fun_app$' ) )
= ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).
thf(1610,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$'] :
( ( ( C @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'inverse$' @ 'fun_app$' ) )
= ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( C @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(149,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom218) ).
thf(1093,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTrans$' @ 'fun_app$q' ) )
=> ( A @ ( 'natTransExt$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(49,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'isZFfun$' @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom544) ).
thf(596,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( ( ( B @ ( 'zFfunDom$' @ 'fun_app$' ) )
= ( A @ ( 'zFfunCod$' @ 'fun_app$' ) ) )
& ( B @ ( 'isZFfun$' @ 'fun_app$d' ) )
& ( A @ ( 'isZFfun$' @ 'fun_app$d' ) ) )
=> ( B @ ( A @ ( 'zFfunComp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( 'isZFfun$' @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(129,axiom,
( 'set$a'
= ( 'unity$' @ ( 'zFfunComp$' @ ( 'uuv$' @ ( 'zFfunCod$' @ ( 'zFfunDom$' @ ( 'isZFfun$' @ 'collect$c' @ ( 'uut$' @ 'collect$c' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom538) ).
thf(1019,plain,
( 'set$a'
= ( 'unity$' @ ( 'zFfunComp$' @ ( 'uuv$' @ ( 'zFfunCod$' @ ( 'zFfunDom$' @ ( 'isZFfun$' @ 'collect$c' @ ( 'uut$' @ 'collect$c' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(121,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom491) ).
thf(992,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$'] :
( ( ( B @ ( A @ 'isomorphism$a' @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( B @ ( A @ 'inverse$' @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ 'dom$a' @ 'fun_app$' ) @ ( A @ 'id$a' @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(231,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) )
= ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'homFtor$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).
thf(1500,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( B @ ( A @ 'homFtorContra$' ) )
= ( B @ ( A @ ( 'oppositeCategory$' @ 'fun_app$s' ) @ 'homFtor$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(93,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] :
( ( B @ ( A @ 'functor_comp_def$' ) )
<=> ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$a' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom100) ).
thf(822,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',B: 'ZF_unit_ZF_unit_unit_unit_unit_Functor_ext$'] :
( ( ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$a' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( B @ ( A @ 'functor_comp_def$' ) ) )
& ( ( B @ ( A @ 'functor_comp_def$' ) )
=> ( ( ( B @ 'catDom$b' )
= ( A @ 'catCod$' ) )
& ( B @ 'functor$a' )
& ( A @ ( 'functor$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(97,axiom,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$d' ) )
=> ( ( A @ ( B @ ( 'set$' @ 'id$a' @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom409) ).
thf(850,plain,
! [A: 'ZF$',B: 'ZF$'] :
( ( B @ ( A @ 'elem$' @ 'fun_app$d' ) )
=> ( ( A @ ( B @ ( 'set$' @ 'id$a' @ 'fun_app$' ) @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(125,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) )
=> $false )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom376) ).
thf(1004,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
~ ( ~ ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) )
& ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(28,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$c' )
= ( B @ 'more$c' ) )
& ( ( A @ 'mor2ZF$' )
= ( B @ 'mor2ZF$' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$' )
= ( B @ 'id$' ) )
& ( ( A @ 'cod$a' )
= ( B @ 'cod$a' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$a' )
= ( B @ 'obj$a' ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).
thf(501,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( ( ( A @ 'more$c' )
= ( B @ 'more$c' ) )
& ( ( A @ 'mor2ZF$' )
= ( B @ 'mor2ZF$' ) )
& ( ( A @ 'comp$a' )
= ( B @ 'comp$a' ) )
& ( ( A @ 'id$' )
= ( B @ 'id$' ) )
& ( ( A @ 'cod$a' )
= ( B @ 'cod$a' ) )
& ( ( A @ 'dom$' )
= ( B @ 'dom$' ) )
& ( ( A @ 'mor$' )
= ( B @ 'mor$' ) )
& ( ( A @ 'obj$a' )
= ( B @ 'obj$a' ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(390,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( A
= ( A @ 'more$b' @ ( A @ 'mapM$' @ ( A @ 'catCod$' @ ( A @ 'catDom$' @ 'functor_ext$' ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom482) ).
thf(2159,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$'] :
( A
= ( A @ 'more$b' @ ( A @ 'mapM$' @ ( A @ 'catCod$' @ ( A @ 'catDom$' @ 'functor_ext$' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(20,axiom,
! [A: 'ZF$'] :
( ( A @ ( 'uuu$' @ 'fun_app$' ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).
thf(464,plain,
! [A: 'ZF$'] :
( ( A @ ( 'uuu$' @ 'fun_app$' ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(156,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A$'] :
( ( ( B @ 'catDom$' @ 'obj$a' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$a' ) @ 'fun_app$a' ) ) )
=> ( D @ ( C @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( B @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( C @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom309) ).
thf(1152,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',C: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_Functor_ext$',D: 'A$'] :
( ( ( B @ 'catDom$' @ 'obj$a' @ ( D @ 'member$i' ) )
& ( C @ ( B @ ( A @ 'nt_abbrev$a' ) @ 'fun_app$a' ) ) )
=> ( D @ ( C @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( B @ 'mapO$c' @ 'fun_app$n' ) @ ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( C @ 'catCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(7,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom265) ).
thf(427,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ ( 'oppositeCategory$b' @ 'fun_app$w' ) @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( C @ ( D @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,axiom,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( A
= ( A @ 'more$e' @ ( A @ 'comp$' @ ( A @ 'id$a' @ ( A @ 'cod$' @ ( A @ 'dom$a' @ ( A @ 'mor$b' @ ( A @ 'obj$' @ 'category_ext$a' ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom412) ).
thf(486,plain,
! [A: 'ZF_ZF_unit_Category_ext$'] :
( A
= ( A @ 'more$e' @ ( A @ 'comp$' @ ( A @ 'id$a' @ ( A @ 'cod$' @ ( A @ 'dom$a' @ ( A @ 'mor$b' @ ( A @ 'obj$' @ 'category_ext$a' ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(86,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'lSCategory_axioms$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).
thf(803,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ 'lSCategory$' )
=> ( A @ 'lSCategory_axioms$' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(282,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$a' ) @ ( 'functorM$a' @ 'fun_app$a' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom394) ).
thf(1681,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( B @ ( A @ 'homFtor$a' ) @ ( 'functorM$a' @ 'fun_app$a' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(64,axiom,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
( ( ( ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$b' )
& ( A @ 'functor$b' ) )
=> $false )
& ( B @ ( A @ 'functor_comp_def$b' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).
thf(659,plain,
! [A: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$',B: 'ZF_ZF_ZF_ZF_unit_unit_unit_Functor_ext$'] :
~ ( ~ ( ( ( B @ 'catDom$a' )
= ( A @ 'catCod$b' ) )
& ( B @ 'functor$b' )
& ( A @ 'functor$b' ) )
& ( B @ ( A @ 'functor_comp_def$b' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(316,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'id$' @ 'fun_app$p' ) @ 'member$h' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).
thf(1848,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$'] :
( ( ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'category$' ) )
=> ( A @ 'mor$' @ ( B @ ( A @ 'id$' @ 'fun_app$p' ) @ 'member$h' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(324,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'obj$a' )
= ( A @ 'obj$a' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom271) ).
thf(1870,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$'] :
( ( A @ ( 'makeCat$a' @ 'fun_app$s' ) @ 'obj$a' )
= ( A @ 'obj$a' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(273,axiom,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom371) ).
thf(1653,plain,
! [A: 'A_b_b_c_LSCategory_ext_Category_ext$',B: 'A$',C: 'B$'] :
( ( ( A @ 'mor$' @ ( C @ 'member$h' ) )
& ( A @ 'obj$a' @ ( B @ 'member$i' ) )
& ( A @ 'lSCategory$' ) )
=> ( C @ ( A @ 'cod$a' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( A @ 'dom$' @ 'fun_app$ab' ) @ ( B @ ( A @ 'homSet$' ) @ 'fun_app$n' ) @ ( C @ ( B @ ( A @ 'homFtorMap$' ) @ 'fun_app$o' ) @ ( 'set$a' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(22,axiom,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uur$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom24) ).
thf(469,plain,
! [A: 'ZF$',B: 'ZF$',C: 'ZF$'] :
( ( C @ ( B @ ( A @ 'uur$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( C @ ( A @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( 'zFfunApp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(404,axiom,
'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).
thf(2238,plain,
'f$' @ ( 'c$' @ 'yFtorNT$' ) @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(227,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom442) ).
thf(1490,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( D @ ( C @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( C @ ( B @ ( A @ 'compDefined$' ) @ 'fun_app$d' ) )
& ( A @ 'category$a' ) )
=> ( ( D @ ( C @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( D @ ( C @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) @ ( B @ ( A @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(41,axiom,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
<=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom374) ).
thf(560,plain,
! [A: 'ZF_ZF_unit_Category_ext$',B: 'ZF$',C: 'ZF$',D: 'ZF$'] :
( ( ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) )
=> ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ( ( D @ ( C @ ( B @ ( A @ 'mapsTo$a' ) ) @ 'fun_app$d' ) )
=> ( ( ( B @ ( A @ 'cod$' @ 'fun_app$' ) )
= D )
& ( ( B @ ( A @ 'dom$a' @ 'fun_app$' ) )
= C )
& ( A @ 'mor$b' @ ( B @ 'member$c' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(381,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
<=> ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) )
& ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) )
& ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).
thf(2106,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) )
& ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) )
& ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) )
=> ( A @ ( 'natTransP$a' @ 'fun_app$q' ) ) )
& ( ( A @ ( 'natTransP$a' @ 'fun_app$q' ) )
=> ( ! [B: 'B$',C: 'A$',D: 'A$'] :
( ( D @ ( C @ ( B @ ( A @ 'nTCatDom$' @ 'mapsTo$' ) ) @ 'fun_app$j' ) )
=> ( ( D @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) )
= ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapM$' @ 'fun_app$o' ) @ ( C @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'comp$' @ 'fun_app$k' ) @ 'fun_app$' ) ) ) )
& ! [B: 'A$'] :
( ( A @ 'nTCatDom$' @ 'obj$a' @ ( B @ 'member$i' ) )
=> ( B @ ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'mapO$c' @ 'fun_app$n' ) @ ( B @ ( A @ 'natTransMap$' @ 'fun_app$n' ) @ ( A @ 'nTCatCod$' @ 'mapsTo$a' ) ) @ 'fun_app$d' ) ) )
& ( ( A @ 'nTCatCod$' )
= ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ 'catCod$' ) )
& ( ( A @ 'nTCatDom$' )
= ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ 'catDom$' ) )
& ( A @ ( 'nTCod$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) )
& ( A @ ( 'nTDom$' @ 'fun_app$r' ) @ ( 'functor$' @ 'fun_app$a' ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(379,axiom,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
( ( ( ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( ( B @ 'nTCatCod$' )
= ( A @ 'nTCatCod$' ) )
& ( ( B @ 'nTCatDom$' )
= ( A @ 'nTCatDom$' ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
=> $false )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom136) ).
thf(2087,plain,
! [A: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$',B: 'A_ZF_b_ZF_b_c_LSCategory_ext_unit_unit_NatTrans_ext$'] :
~ ( ~ ( ( ( A @ ( 'nTCod$' @ 'fun_app$r' ) )
= ( B @ ( 'nTDom$' @ 'fun_app$r' ) ) )
& ( ( B @ 'nTCatCod$' )
= ( A @ 'nTCatCod$' ) )
& ( ( B @ 'nTCatDom$' )
= ( A @ 'nTCatDom$' ) )
& ( B @ ( 'natTrans$' @ 'fun_app$q' ) )
& ( A @ ( 'natTrans$' @ 'fun_app$q' ) ) )
& ( B @ ( A @ 'nTCompDefined$a' @ 'fun_app$q' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(2767,plain,
$false,
inference(e,[status(thm)],[1586,629,2131,1995,1559,1237,1179,777,1549,1686,645,892,1315,1850,666,1818,1924,1596,683,1522,1073,1544,1728,1591,1269,614,1855,1200,440,511,1078,1655,1756,1867,472,913,1640,1954,1354,1164,797,1095,1001,1243,2227,1613,1935,1359,1386,1265,651,1645,1921,2067,1967,1055,2039,504,917,1826,1313,1191,1992,1760,1660,902,1890,1572,1013,1815,1100,638,853,1362,1963,1946,443,1040,834,1828,574,1183,905,2058,1377,2190,1796,774,2137,998,2242,1405,1943,1600,2154,1975,1564,2011,1206,761,810,2047,1311,1067,1768,2061,2000,1047,1730,894,1021,952,2147,429,1824,407,693,467,1951,1888,583,2179,1210,1027,551,1634,1291,456,1012,1555,435,1159,461,1089,1772,1794,1064,1227,1672,499,980,1498,1138,1719,554,537,669,1016,1493,1683,2053,1842,489,1937,1263,1530,1231,1552,1932,1060,1984,1525,605,1393,1857,1318,792,805,541,657,1846,1286,674,1663,1167,1185,586,2076,1170,2189,1616,1906,1510,1251,1483,856,1374,1648,412,425,2176,2033,2149,1154,819,975,423,1916,1929,577,1535,1520,2134,958,1403,545,1488,1503,1669,445,1371,1733,1058,1997,2055,1258,1224,1356,1675,672,611,787,764,1194,1282,1603,1542,509,1690,599,1307,1175,1853,1408,1589,990,1722,1144,890,2025,1557,816,1821,1862,964,626,1688,983,1926,2212,1528,2064,608,986,2022,1364,1496,2156,1562,1973,1805,1076,1626,1948,2239,1873,1758,548,648,617,1472,1958,458,1049,1203,1208,795,680,1547,1798,1770,580,1961,1025,1156,409,690,1516,2060,1400,1753,1267,2165,1188,1218,1716,2224,1300,1637,1766,1981,1955,571,1881,1221,1284,1485,1052,1506,978,1140,2013,1839,539,1913,1844,2215,1216,2187,771,1918,450,1966,556,1390,1575,1289,844,588,699,961,813,896,2098,1062,1508,995,2152,1030,2198,899,832,478,2162,2036,1309,1161,800,2218,1642,447,1578,1678,432,2008,1725,1280,950,1097,1593,1380,1248,790,2050,1859,1657,506,807,635,696,928,437,2070,1172,1410,1033,1197,2021,1610,1093,596,1019,992,1500,822,850,1004,501,2159,464,1152,427,486,803,1681,659,1848,1870,1653,469,2238,1490,560,2106,2087]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP303_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.42 % Computer : n014.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Fri Sep 25 19:05:47 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.70/1.73 % [INFO] Parsing done (715ms).
% 3.70/1.74 % [INFO] Running in sequential loop mode.
% 4.85/2.13 % [INFO] eprover registered as external prover.
% 4.85/2.14 % [INFO] Scanning for conjecture ...
% 5.65/2.44 % [INFO] Found a conjecture (or negated_conjecture) and 588 axioms. Running axiom selection ...
% 7.01/2.75 % [INFO] Axiom selection finished. Selected 404 axioms (removed 184 axioms).
% 8.67/3.14 % [INFO] Problem is typed first-order (TPTP TFF).
% 8.67/3.17 % [INFO] Type checking passed.
% 8.67/3.17 % [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 ...
% 23.86/7.00 % External prover 'e' found a proof!
% 23.86/7.00 % [INFO] Killing All external provers ...
% 23.86/7.00 % Time passed: 6439ms (effective reasoning time: 5257ms)
% 23.86/7.01 % 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)>
% 23.86/7.01 % Axioms used in derivation (404): axiom326, axiom32, axiom260, axiom315, axiom546, axiom273, axiom527, axiom452, axiom491, axiom100, axiom28, axiom76, axiom564, axiom503, axiom553, axiom549, axiom480, axiom396, axiom25, axiom369, axiom404, axiom474, axiom295, axiom485, axiom214, axiom516, axiom36, axiom496, axiom284, axiom423, axiom169, axiom65, axiom531, axiom441, axiom430, axiom50, axiom158, axiom131, axiom10, axiom386, axiom392, axiom337, axiom344, axiom138, axiom119, axiom210, axiom407, axiom191, axiom17, axiom401, axiom22, axiom397, axiom412, axiom460, axiom354, axiom587, axiom477, axiom467, axiom257, axiom535, axiom147, axiom524, axiom434, axiom341, axiom504, axiom109, axiom350, axiom348, axiom184, axiom376, axiom266, axiom445, axiom42, axiom239, axiom561, axiom329, axiom372, axiom162, axiom358, axiom542, axiom383, axiom134, axiom104, axiom456, axiom572, axiom130, axiom235, axiom484, axiom473, axiom365, axiom39, axiom499, axiom330, axiom418, axiom304, axiom488, axiom251, axiom64, axiom343, axiom530, axiom352, axiom411, axiom539, axiom427, axiom179, axiom363, axiom437, axiom151, axiom405, axiom94, axiom83, axiom101, axiom336, axiom308, axiom321, axiom78, axiom24, axiom278, axiom272, axiom455, axiom475, axiom121, axiom490, axiom56, axiom466, axiom563, axiom240, axiom206, axiom53, axiom60, axiom0, axiom433, axiom143, axiom359, axiom416, axiom489, axiom545, axiom108, axiom395, axiom387, axiom528, axiom16, axiom459, axiom400, axiom75, axiom325, axiom448, axiom552, axiom385, axiom332, axiom9, axiom303, axiom366, axiom494, axiom538, axiom80, axiom371, axiom586, axiom422, axiom185, axiom472, axiom202, axiom252, axiom146, axiom97, axiom192, axiom355, axiom391, axiom415, axiom254, axiom444, axiom82, axiom174, axiom541, axiom360, axiom398, axiom382, axiom483, axiom229, axiom347, axiom180, axiom67, axiom534, axiom450, axiom196, axiom523, axiom463, axiom243, axiom426, axiom72, axiom461, axiom449, axiom224, axiom438, axiom267, axiom408, axiom89, axiom111, axiom38, axiom419, axiom377, axiom500, axiom91, axiom1, axiom105, axiom218, axiom86, axiom447, axiom52, axiom432, axiom156, axiom390, axiom37, axiom212, axiom501, axiom342, axiom364, axiom381, axiom34, axiom79, axiom544, axiom425, axiom167, axiom454, axiom443, axiom149, axiom189, axiom375, axiom394, axiom23, axiom93, axiom476, axiom216, axiom410, axiom409, axiom286, axiom428, axiom118, axiom275, axiom63, axiom19, axiom458, axiom102, axiom30, axiom370, axiom201, axiom178, axiom259, axiom74, axiom276, axiom451, axiom570, axiom302, axiom367, axiom378, axiom471, axiom506, axiom497, axiom164, axiom374, axiom440, axiom244, axiom271, axiom287, axiom153, axiom324, axiom71, axiom462, axiom15, axiom129, axiom136, axiom414, axiom106, axiom533, axiom268, axiom181, axiom403, axiom522, axiom436, axiom482, axiom237, axiom486, axiom346, axiom262, axiom68, axiom335, axiom26, axiom219, axiom493, axiom356, axiom46, axiom439, axiom469, axiom110, axiom49, axiom248, axiom421, axiom547, axiom389, axiom18, axiom457, axiom338, axiom242, axiom379, axiom88, axiom442, axiom327, axiom399, axiom345, axiom464, axiom204, axiom141, axiom357, axiom274, axiom393, axiom44, axiom222, axiom515, axiom323, axiom446, axiom84, axiom554, axiom269, axiom453, axiom502, axiom103, axiom155, axiom495, axiom253, axiom349, axiom368, axiom29, axiom550, axiom565, axiom99, axiom128, axiom285, axiom540, axiom537, axiom361, axiom429, axiom380, axiom532, axiom31, axiom264, axiom431, axiom208, axiom20, axiom588, axiom487, axiom402, axiom384, axiom551, axiom107, axiom417, axiom339, axiom40, axiom265, axiom165, axiom270, axiom176, axiom424, axiom187, axiom288, axiom69, axiom198, axiom529, axiom144, axiom435, axiom95, axiom465, axiom536, axiom373, axiom543, axiom351, axiom505, axiom261, axiom413, axiom256, axiom334, axiom160, axiom514, axiom406, axiom388, axiom420, axiom498, axiom209, axiom21, axiom200, axiom250, axiom58, axiom525, axiom362, axiom51, axiom548, axiom309, axiom470, axiom468, axiom492, axiom328, axiom140, axiom340, axiom194, axiom353
% 23.86/7.01 % No. of inferences in proof: 812
% 23.86/7.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6439 ms resp. 5257 ms w/o parsing
% 25.90/7.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.90/7.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------