TSTP Solution File: SWW473+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW473+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:14:30 EDT 2023
% Result : Theorem 2.51s 2.63s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW473+1 : TPTP v8.1.2. Released v5.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 19:33:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 2.47/2.58 %-------------------------------------------
% 2.47/2.58 % File :CSE---1.6
% 2.47/2.58 % Problem :theBenchmark
% 2.47/2.58 % Transform :cnf
% 2.47/2.58 % Format :tptp:raw
% 2.47/2.58 % Command :java -jar mcs_scs.jar %d %s
% 2.47/2.58
% 2.47/2.58 % Result :Theorem 1.740000s
% 2.47/2.58 % Output :CNFRefutation 1.740000s
% 2.47/2.58 %-------------------------------------------
% 2.47/2.59 %------------------------------------------------------------------------------
% 2.47/2.59 % File : SWW473+1 : TPTP v8.1.2. Released v5.3.0.
% 2.47/2.59 % Domain : Software Verification
% 2.47/2.59 % Problem : Hoare's Logic with Procedures line 383, 100 axioms selected
% 2.47/2.59 % Version : Especial.
% 2.47/2.59 % English :
% 2.47/2.59
% 2.47/2.59 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 2.47/2.59 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 2.47/2.59 % Source : [Bla11]
% 2.47/2.59 % Names : hoare_100_fofmg_l383 [Bla11]
% 2.47/2.59
% 2.47/2.59 % Status : Theorem
% 2.47/2.59 % Rating : 0.25 v7.5.0, 0.28 v7.4.0, 0.20 v7.3.0, 0.24 v7.2.0, 0.21 v7.1.0, 0.26 v7.0.0, 0.23 v6.4.0, 0.31 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.37 v6.0.0, 0.30 v5.5.0, 0.48 v5.4.0, 0.54 v5.3.0
% 2.47/2.59 % Syntax : Number of formulae : 449 ( 129 unt; 0 def)
% 2.47/2.59 % Number of atoms : 979 ( 168 equ)
% 2.47/2.59 % Maximal formula atoms : 7 ( 2 avg)
% 2.47/2.59 % Number of connectives : 597 ( 67 ~; 40 |; 55 &)
% 2.47/2.59 % ( 42 <=>; 393 =>; 0 <=; 0 <~>)
% 2.47/2.59 % Maximal formula depth : 11 ( 4 avg)
% 2.47/2.59 % Maximal term depth : 7 ( 2 avg)
% 2.47/2.59 % Number of predicates : 9 ( 8 usr; 0 prp; 1-2 aty)
% 2.47/2.59 % Number of functors : 224 ( 224 usr; 56 con; 0-2 aty)
% 2.47/2.59 % Number of variables : 957 ( 951 !; 6 ?)
% 2.47/2.59 % SPC : FOF_THM_RFO_SEQ
% 2.47/2.59
% 2.47/2.59 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 2.47/2.59 % 2011-08-09 15:56:16
% 2.47/2.59 % : Encoded with monomorphized guards.
% 2.47/2.59 %------------------------------------------------------------------------------
% 2.47/2.59 %----Explicit typings (81)
% 2.47/2.59 fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a,axiom,
% 2.47/2.59 ! [B_1_1,B_2] :
% 2.47/2.59 ( is_fun_a_bool(B_2)
% 2.51/2.59 => is_fun_a_bool(cOMBB_bool_bool_a(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_pname_bool(B_2)
% 2.51/2.59 => is_fun_pname_bool(cOMBB_647938656_pname(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun949378684l_bool(B_2)
% 2.51/2.59 => is_fun949378684l_bool(cOMBB_2140588453a_bool(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun1661590463l_bool(B_2)
% 2.51/2.59 => is_fun1661590463l_bool(cOMBB_307249310e_bool(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_a_bool(B_2)
% 2.51/2.59 => is_fun_a_bool(cOMBS_a_bool_bool(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_pname_bool(B_2)
% 2.51/2.59 => is_fun_pname_bool(cOMBS_568398431l_bool(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc__HOL__Obo,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun949378684l_bool(B_2)
% 2.51/2.59 => is_fun949378684l_bool(cOMBS_1035972772l_bool(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun1661590463l_bool(B_2)
% 2.51/2.59 => is_fun1661590463l_bool(cOMBS_350070575l_bool(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Finite__Set_Ofinite_000t__a,axiom,
% 2.51/2.59 is_fun949378684l_bool(finite_finite_a) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Finite__Set_Ofinite_000tc__Com__Opname,hypothesis,
% 2.51/2.59 is_fun1661590463l_bool(finite_finite_pname) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_HOL_Oundefined_000t__a,axiom,
% 2.51/2.59 is_a(undefined_a(x_a)) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_HOL_Oundefined_000tc__Com__Opname,axiom,
% 2.51/2.59 is_pname(undefined_pname(pname)) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_HOL_Oundefined_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.59 is_fun_a_bool(undefined_fun_a_bool(fun(x_a,bool))) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
% 2.51/2.59 is_fun_pname_bool(undefi17486888e_bool(fun(pname,bool))) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,axiom,
% 2.51/2.59 is_fun949378684l_bool(undefi1699038445l_bool(fun(fun(x_a,bool),bool))) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_HOL_Oundefined_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
% 2.51/2.59 is_fun1661590463l_bool(undefi64961550l_bool(fun(fun(pname,bool),bool))) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_OCollect_000t__a,axiom,
% 2.51/2.59 ! [B_1_1] :
% 2.51/2.59 ( is_fun_a_bool(B_1_1)
% 2.51/2.59 => is_fun_a_bool(collect_a(B_1_1)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_OCollect_000tc__Com__Opname,axiom,
% 2.51/2.59 ! [B_1_1] :
% 2.51/2.59 ( is_fun_pname_bool(B_1_1)
% 2.51/2.59 => is_fun_pname_bool(collect_pname(B_1_1)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_OCollect_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.59 ! [B_1_1] :
% 2.51/2.59 ( is_fun949378684l_bool(B_1_1)
% 2.51/2.59 => is_fun949378684l_bool(collect_fun_a_bool(B_1_1)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
% 2.51/2.59 ! [B_1_1] :
% 2.51/2.59 ( is_fun1661590463l_bool(B_1_1)
% 2.51/2.59 => is_fun1661590463l_bool(collec1974731493e_bool(B_1_1)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000t__a_000t__a,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_a_bool(B_2)
% 2.51/2.59 => is_fun_a_bool(image_a_a(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000t__a_000tc__Com__Opname,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_a_bool(B_2)
% 2.51/2.59 => is_fun_pname_bool(image_a_pname(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__Com__Opname_000t__a,hypothesis,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_pname_bool(B_2)
% 2.51/2.59 => is_fun_a_bool(image_pname_a(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_pname_bool(B_2)
% 2.51/2.59 => is_fun_pname_bool(image_pname_pname(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_pname_bool(B_2)
% 2.51/2.59 => is_fun949378684l_bool(image_112932426a_bool(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun_pname_bool(B_2)
% 2.51/2.59 => is_fun1661590463l_bool(image_47868345e_bool(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000t__a,axiom,
% 2.51/2.59 ! [B_1_1,B_2] : is_fun_a_bool(image_nat_a(B_1_1,B_2)) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,axiom,
% 2.51/2.59 ! [B_1_1,B_2] : is_fun_pname_bool(image_nat_pname(B_1_1,B_2)) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.59 ! [B_1_1,B_2] : is_fun949378684l_bool(image_nat_fun_a_bool(B_1_1,B_2)) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
% 2.51/2.59 ! [B_1_1,B_2] : is_fun1661590463l_bool(image_1655916159e_bool(B_1_1,B_2)) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun949378684l_bool(B_2)
% 2.51/2.59 => is_fun_a_bool(image_fun_a_bool_a(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.59 ( is_fun949378684l_bool(B_2)
% 2.51/2.59 => is_fun_pname_bool(image_1854862208_pname(B_1_1,B_2)) ) ).
% 2.51/2.59
% 2.51/2.59 fof(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000t__a,axiom,
% 2.51/2.59 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun1661590463l_bool(B_2)
% 2.51/2.60 => is_fun_a_bool(image_876012084bool_a(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun1661590463l_bool(B_2)
% 2.51/2.60 => is_fun_pname_bool(image_1283814551_pname(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000t__a,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_a_bool(image_fun_nat_bool_a(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opname,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_pname_bool(image_1921560913_pname(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_a_bool(image_573985017bool_a(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_0_001,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_pname_bool(image_990671762_pname(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_a_bool(image_349102846bool_a(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL_002,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_pname_bool(image_1705983821_pname(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_a_bool(image_526090948bool_a(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL___003,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_pname_bool(image_1604018183_pname(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oinsert_000t__a,hypothesis,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( ( is_a(B_1_1)
% 2.51/2.60 & is_fun_a_bool(B_2) )
% 2.51/2.60 => is_fun_a_bool(insert_a(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oinsert_000tc__Com__Opname,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( ( is_pname(B_1_1)
% 2.51/2.60 & is_fun_pname_bool(B_2) )
% 2.51/2.60 => is_fun_pname_bool(insert_pname(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oinsert_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( ( is_fun_a_bool(B_1_1)
% 2.51/2.60 & is_fun949378684l_bool(B_2) )
% 2.51/2.60 => is_fun949378684l_bool(insert_fun_a_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( ( is_fun_pname_bool(B_1_1)
% 2.51/2.60 & is_fun1661590463l_bool(B_2) )
% 2.51/2.60 => is_fun1661590463l_bool(insert1325755072e_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000t__a_000tc__HOL__Obool,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( ( is_fun_a_bool(B_1_1)
% 2.51/2.60 & is_a(B_2) )
% 2.51/2.60 => is_bool(hAPP_a_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_a(B_2)
% 2.51/2.60 => is_fun_a_bool(hAPP_a_fun_a_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_a(B_2)
% 2.51/2.60 => is_fun_pname_bool(hAPP_a93125764e_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000t__a_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J,hypothesis,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_a(B_2)
% 2.51/2.60 => is_fun949378684l_bool(hAPP_a85458249l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__Com__Opname_000t__a,hypothesis,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_pname(B_2)
% 2.51/2.60 => is_a(hAPP_pname_a(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( ( is_fun_pname_bool(B_1_1)
% 2.51/2.60 & is_pname(B_2) )
% 2.51/2.60 => is_bool(hAPP_pname_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_pname(B_2)
% 2.51/2.60 => is_fun_a_bool(hAPP_p1534023578a_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_pname(B_2)
% 2.51/2.60 => is_fun_pname_bool(hAPP_p61793385e_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,hypothesis,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_pname(B_2)
% 2.51/2.60 => is_fun1661590463l_bool(hAPP_p338031245l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_bool(B_2)
% 2.51/2.60 => is_bool(hAPP_bool_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool,hypothesis,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_nat_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_a_bool(hAPP_nat_fun_a_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_fun_pname_bool(hAPP_n1025906991e_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( ( is_fun949378684l_bool(B_1_1)
% 2.51/2.60 & is_fun_a_bool(B_2) )
% 2.51/2.60 => is_bool(hAPP_fun_a_bool_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun_a_bool(B_2)
% 2.51/2.60 => is_fun_a_bool(hAPP_f2050579477a_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL,hypothesis,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun_a_bool(B_2)
% 2.51/2.60 => is_fun949378684l_bool(hAPP_f1631501043l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool,hypothesis,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( ( is_fun1661590463l_bool(B_1_1)
% 2.51/2.60 & is_fun_pname_bool(B_2) )
% 2.51/2.60 => is_bool(hAPP_f1664156314l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun_pname_bool(B_2)
% 2.51/2.60 => is_fun_pname_bool(hAPP_f759274231e_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun_pname_bool(B_2)
% 2.51/2.60 => is_fun1661590463l_bool(hAPP_f434788991l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_f54304608l_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc__,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun949378684l_bool(B_2)
% 2.51/2.60 => is_bool(hAPP_f621171935l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_J_000tc___004,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun949378684l_bool(B_2)
% 2.51/2.60 => is_fun949378684l_bool(hAPP_f2117159681l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun1661590463l_bool(B_2)
% 2.51/2.60 => is_bool(hAPP_f1935102916l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005,axiom,
% 2.51/2.60 ! [B_1_1,B_2] :
% 2.51/2.60 ( is_fun1661590463l_bool(B_2)
% 2.51/2.60 => is_fun1661590463l_bool(hAPP_f559147733l_bool(B_1_1,B_2)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_f1637334154l_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool_,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_f292226953l_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_f389811538l_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HO,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_f937997336l_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HO,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_f1363661463l_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_f595608956l_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
% 2.51/2.60 ! [B_1_1,B_2] : is_bool(hAPP_f1295398978l_bool(B_1_1,B_2)) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_v_G,hypothesis,
% 2.51/2.60 is_fun_a_bool(g) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_v_P,axiom,
% 2.51/2.60 ! [B_1_1] :
% 2.51/2.60 ( is_fun_a_bool(B_1_1)
% 2.51/2.60 => is_fun949378684l_bool(p(B_1_1)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_v_U,hypothesis,
% 2.51/2.60 is_fun_pname_bool(u) ).
% 2.51/2.60
% 2.51/2.60 fof(gsy_v_pn,hypothesis,
% 2.51/2.60 is_pname(pn) ).
% 2.51/2.60
% 2.51/2.60 %----Relevant facts (300)
% 2.51/2.60 fof(fact_0_assms_I1_J,axiom,
% 2.51/2.60 ! [Ts,G] :
% 2.51/2.60 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,Ts),G))
% 2.51/2.60 => hBOOL(hAPP_fun_a_bool_bool(p(G),Ts)) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_1_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.60 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(ord_le1568362934t_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_2_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.60 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(ord_le313189616e_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_3_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
% 2.51/2.60 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(ord_le1311769555a_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_4_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A))
% 2.51/2.60 => hBOOL(hAPP_f1295398978l_bool(finite719726885l_bool,collec1874991203l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(ord_le65145710l_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_5_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
% 2.51/2.60 => hBOOL(hAPP_f595608956l_bool(finite1491191519l_bool,collec792590109l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(ord_le1375671464l_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_6_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A))
% 2.51/2.60 => hBOOL(hAPP_f1363661463l_bool(finite1343359508l_bool,collec1635217238l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(ord_le967226251l_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_7_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
% 2.51/2.60 => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,collec707592106l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(ord_le1375614389l_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_8_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
% 2.51/2.60 => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,collec1613912337l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(ord_le675606854l_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_9_finite__Collect__subsets,axiom,
% 2.51/2.60 ! [A] :
% 2.51/2.60 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
% 2.51/2.60 => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,collec1015864663l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(ord_le1454342156l_bool),A)))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_10_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.60 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_11_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_2089570637ol_nat(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_12_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1079571347ol_nat(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_13_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1802975832ol_nat(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_14_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_fun_a_bool_nat(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_15_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_1551609309ol_nat(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_16_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_496248727ol_nat(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_17_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
% 2.51/2.60 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_a_nat(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_18_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1604018183_pname(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_19_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1705983821_pname(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_20_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_990671762_pname(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_21_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1854862208_pname(H,F_1))) ) ).
% 2.51/2.60
% 2.51/2.60 fof(fact_22_finite__imageI,axiom,
% 2.51/2.60 ! [H,F_1] :
% 2.51/2.60 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
% 2.51/2.60 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1283814551_pname(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_23_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
% 2.51/2.61 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_1921560913_pname(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_24_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
% 2.51/2.61 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_a_pname(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_25_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
% 2.51/2.61 => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1607900221l_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_26_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
% 2.51/2.61 => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1874789623l_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_27_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
% 2.51/2.61 => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1208015684l_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_28_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
% 2.51/2.61 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_nat_fun_a_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_29_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
% 2.51/2.61 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_1655916159e_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_30_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
% 2.51/2.61 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_26036933t_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_31_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
% 2.51/2.61 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_nat_a(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_32_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.61 => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,image_1154884483l_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_33_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.61 => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,image_1642285373l_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_34_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.61 => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,image_1420695166l_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_35_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.61 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,image_112932426a_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_36_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.61 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,image_47868345e_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_37_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.61 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,image_2129980159t_bool(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_38_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.61 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_pname_pname(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_39_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,F_1))
% 2.51/2.61 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_a_a(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_40_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,F_1))
% 2.51/2.61 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_nat_bool_a(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_41_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,F_1))
% 2.51/2.61 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_876012084bool_a(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_42_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,F_1))
% 2.51/2.61 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_fun_a_bool_a(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_43_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,F_1))
% 2.51/2.61 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,image_pname_nat(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_44_finite__imageI,axiom,
% 2.51/2.61 ! [H,F_1] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,F_1))
% 2.51/2.61 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,image_nat_pname(H,F_1))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_45_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
% 2.51/2.61 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_46_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_47_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_48_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A))
% 2.51/2.61 => hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,insert2003652156l_bool(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_49_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
% 2.51/2.61 => hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,insert1117693814l_bool(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_50_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A))
% 2.51/2.61 => hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,insert1457093509l_bool(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_51_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
% 2.51/2.61 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_52_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
% 2.51/2.61 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_53_finite_OinsertI,axiom,
% 2.51/2.61 ! [A_1,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
% 2.51/2.61 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_54_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_pname_nat(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_55_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_a_nat(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_56_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_496248727ol_nat(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_57_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_1551609309ol_nat(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_58_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,image_fun_a_bool_nat(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_59_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_a_pname(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_60_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_nat_pname(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_61_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_62_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f937997336l_bool(finite1701474069l_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_526090948bool_a(F,A))),hAPP_f1690079119ol_nat(finite1352710292l_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_63_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f389811538l_bool(finite786885583l_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_349102846bool_a(F,A))),hAPP_f98387925ol_nat(finite269641166l_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_64_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f292226953l_bool(finite1381704300l_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_573985017bool_a(F,A))),hAPP_f1253658590ol_nat(finite1659325229l_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_65_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_a_bool_a(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_66_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_876012084bool_a(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_67_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_fun_nat_bool_a(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_68_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_a_a(F,A))),hAPP_fun_a_bool_nat(finite_card_a,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_69_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_pname_pname(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_70_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_2129980159t_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_71_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_47868345e_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_72_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_112932426a_bool(F,A))),hAPP_f921600141ol_nat(finite_card_pname,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_73_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,image_nat_a(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_74_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,image_26036933t_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_75_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,image_1655916159e_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_76_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,image_nat_fun_a_bool(F,A))),hAPP_f22106695ol_nat(finite_card_nat,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_77_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1921560913_pname(F,A))),hAPP_f696928925ol_nat(finite346522414t_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_78_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1283814551_pname(F,A))),hAPP_f55526627ol_nat(finite1340463720e_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_79_card__image__le,axiom,
% 2.51/2.61 ! [F,A] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,image_1854862208_pname(F,A))),hAPP_f2009550088ol_nat(finite1306199131a_bool,A))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_80_card__mono,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
% 2.51/2.61 => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,B))) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_81_card__mono,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
% 2.51/2.61 => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,B))) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_82_card__mono,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
% 2.51/2.61 => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,B))) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_83_card__mono,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
% 2.51/2.61 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,B))) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_84_card__mono,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
% 2.51/2.61 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,B))) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_85_card__mono,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
% 2.51/2.61 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,B))) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_86_card__seteq,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
% 2.51/2.61 => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
% 2.51/2.61 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,B)),hAPP_f696928925ol_nat(finite346522414t_bool,A)))
% 2.51/2.61 => A = B ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_87_card__seteq,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( ( is_fun1661590463l_bool(A)
% 2.51/2.61 & is_fun1661590463l_bool(B) )
% 2.51/2.61 => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
% 2.51/2.61 => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
% 2.51/2.61 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,B)),hAPP_f55526627ol_nat(finite1340463720e_bool,A)))
% 2.51/2.61 => A = B ) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_88_card__seteq,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( ( is_fun949378684l_bool(A)
% 2.51/2.61 & is_fun949378684l_bool(B) )
% 2.51/2.61 => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
% 2.51/2.61 => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
% 2.51/2.61 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,B)),hAPP_f2009550088ol_nat(finite1306199131a_bool,A)))
% 2.51/2.61 => A = B ) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_89_card__seteq,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( ( is_fun_pname_bool(A)
% 2.51/2.61 & is_fun_pname_bool(B) )
% 2.51/2.61 => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
% 2.51/2.61 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.61 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,B)),hAPP_f921600141ol_nat(finite_card_pname,A)))
% 2.51/2.61 => A = B ) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_90_card__seteq,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( ( is_fun_a_bool(A)
% 2.51/2.61 & is_fun_a_bool(B) )
% 2.51/2.61 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
% 2.51/2.61 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.61 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,B)),hAPP_fun_a_bool_nat(finite_card_a,A)))
% 2.51/2.61 => A = B ) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_91_card__seteq,axiom,
% 2.51/2.61 ! [A,B] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
% 2.51/2.61 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.61 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,B)),hAPP_f22106695ol_nat(finite_card_nat,A)))
% 2.51/2.61 => A = B ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_92_card__insert__le,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f696928925ol_nat(finite346522414t_bool,A)),hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_93_card__insert__le,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f55526627ol_nat(finite1340463720e_bool,A)),hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_94_card__insert__le,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)),hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_95_card__insert__le,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f921600141ol_nat(finite_card_pname,A)),hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_96_card__insert__le,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_f22106695ol_nat(finite_card_nat,A)),hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_97_card__insert__le,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
% 2.51/2.61 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_fun_a_bool_nat(finite_card_a,A)),hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_98_card__insert__if,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
% 2.51/2.61 => ( ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A))
% 2.51/2.61 => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_f696928925ol_nat(finite346522414t_bool,A) )
% 2.51/2.61 & ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A))
% 2.51/2.61 => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A)) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_99_card__insert__if,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
% 2.51/2.61 => ( ( hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
% 2.51/2.61 => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_f55526627ol_nat(finite1340463720e_bool,A) )
% 2.51/2.61 & ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
% 2.51/2.61 => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A)) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_100_card__insert__if,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
% 2.51/2.61 => ( ( hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A))
% 2.51/2.61 => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_f2009550088ol_nat(finite1306199131a_bool,A) )
% 2.51/2.61 & ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A))
% 2.51/2.61 => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_101_card__insert__if,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => ( ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.61 => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_f22106695ol_nat(finite_card_nat,A) )
% 2.51/2.61 & ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.61 => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A)) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_102_card__insert__if,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => ( ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.61 => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_f921600141ol_nat(finite_card_pname,A) )
% 2.51/2.61 & ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.61 => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A)) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_103_card__insert__if,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
% 2.51/2.61 => ( ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.61 => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_fun_a_bool_nat(finite_card_a,A) )
% 2.51/2.61 & ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.61 => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A)) ) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_104_card__insert__disjoint,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A))
% 2.51/2.61 => ( ~ hBOOL(hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(member_fun_nat_bool,X_2),A))
% 2.51/2.61 => hAPP_f696928925ol_nat(finite346522414t_bool,insert_fun_nat_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f696928925ol_nat(finite346522414t_bool,A)) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_105_card__insert__disjoint,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A))
% 2.51/2.61 => ( ~ hBOOL(hAPP_f1935102916l_bool(hAPP_f556039215l_bool(member799430823e_bool,X_2),A))
% 2.51/2.61 => hAPP_f55526627ol_nat(finite1340463720e_bool,insert1325755072e_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f55526627ol_nat(finite1340463720e_bool,A)) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_106_card__insert__disjoint,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A))
% 2.51/2.61 => ( ~ hBOOL(hAPP_f621171935l_bool(hAPP_f285962445l_bool(member_fun_a_bool,X_2),A))
% 2.51/2.61 => hAPP_f2009550088ol_nat(finite1306199131a_bool,insert_fun_a_bool(X_2,A)) = hAPP_nat_nat(suc,hAPP_f2009550088ol_nat(finite1306199131a_bool,A)) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_107_card__insert__disjoint,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A))
% 2.51/2.61 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.61 => hAPP_f22106695ol_nat(finite_card_nat,insert_nat(X_2,A)) = hAPP_nat_nat(suc,hAPP_f22106695ol_nat(finite_card_nat,A)) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_108_card__insert__disjoint,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.61 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.61 => hAPP_f921600141ol_nat(finite_card_pname,insert_pname(X_2,A)) = hAPP_nat_nat(suc,hAPP_f921600141ol_nat(finite_card_pname,A)) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_109_card__insert__disjoint,axiom,
% 2.51/2.61 ! [X_2,A] :
% 2.51/2.61 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A))
% 2.51/2.61 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.61 => hAPP_fun_a_bool_nat(finite_card_a,insert_a(X_2,A)) = hAPP_nat_nat(suc,hAPP_fun_a_bool_nat(finite_card_a,A)) ) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_110_finite__Collect__conjI,axiom,
% 2.51/2.61 ! [Q_1,Pa] :
% 2.51/2.61 ( ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa)))
% 2.51/2.61 | hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1))) )
% 2.51/2.61 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fconj,Pa),Q_1)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_111_finite__Collect__conjI,axiom,
% 2.51/2.61 ! [Q_1,Pa] :
% 2.51/2.61 ( ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa)))
% 2.51/2.61 | hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))) )
% 2.51/2.61 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fconj,Pa),Q_1)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_112_finite__Collect__conjI,axiom,
% 2.51/2.61 ! [Q_1,Pa] :
% 2.51/2.61 ( ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa)))
% 2.51/2.61 | hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1))) )
% 2.51/2.61 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fconj,Pa),Q_1)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_113_finite__Collect__conjI,axiom,
% 2.51/2.61 ! [Q_1,Pa] :
% 2.51/2.61 ( ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa)))
% 2.51/2.61 | hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1))) )
% 2.51/2.61 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fconj,Pa),Q_1)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_114_finite__Collect__conjI,axiom,
% 2.51/2.61 ! [Q_1,Pa] :
% 2.51/2.61 ( ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa)))
% 2.51/2.61 | hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))) )
% 2.51/2.61 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,Pa),Q_1)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_115_finite__Collect__conjI,axiom,
% 2.51/2.61 ! [Q_1,Pa] :
% 2.51/2.61 ( ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa)))
% 2.51/2.61 | hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1))) )
% 2.51/2.61 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fconj,Pa),Q_1)))) ) ).
% 2.51/2.61
% 2.51/2.61 fof(fact_116_Suc__diff__le,axiom,
% 2.51/2.61 ! [N_1,M_2] :
% 2.51/2.61 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
% 2.51/2.61 => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),N_1) = hAPP_nat_nat(suc,hAPP_nat_nat(minus_minus_nat(M_2),N_1)) ) ).
% 2.51/2.61
% 2.51/2.62 fof(fact_117_finite__Collect__le__nat,axiom,
% 2.51/2.62 ! [K] : hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),K)))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_118_card__Collect__le__nat,axiom,
% 2.51/2.62 ! [Na] : hAPP_f22106695ol_nat(finite_card_nat,collect_nat(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(ord_less_eq_nat),Na))) = hAPP_nat_nat(suc,Na) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_119_Suc__inject,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( hAPP_nat_nat(suc,X) = hAPP_nat_nat(suc,Y)
% 2.51/2.62 => X = Y ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_120_nat_Oinject,axiom,
% 2.51/2.62 ! [Nat_1,Nat] :
% 2.51/2.62 ( hAPP_nat_nat(suc,Nat_1) = hAPP_nat_nat(suc,Nat)
% 2.51/2.62 <=> Nat_1 = Nat ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_121_Suc__n__not__n,axiom,
% 2.51/2.62 ! [N_1] : hAPP_nat_nat(suc,N_1) != N_1 ).
% 2.51/2.62
% 2.51/2.62 fof(fact_122_n__not__Suc__n,axiom,
% 2.51/2.62 ! [N_1] : N_1 != hAPP_nat_nat(suc,N_1) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_123_le__antisym,axiom,
% 2.51/2.62 ! [M_2,N_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2))
% 2.51/2.62 => M_2 = N_1 ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_124_le__trans,axiom,
% 2.51/2.62 ! [K_1,I_1,J] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),J))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,J),K_1))
% 2.51/2.62 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),K_1)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_125_eq__imp__le,axiom,
% 2.51/2.62 ! [M_2,N_1] :
% 2.51/2.62 ( M_2 = N_1
% 2.51/2.62 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_126_nat__le__linear,axiom,
% 2.51/2.62 ! [M_2,N_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
% 2.51/2.62 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),M_2)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_127_le__refl,axiom,
% 2.51/2.62 ! [N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),N_1)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_128_diff__commute,axiom,
% 2.51/2.62 ! [I_1,J,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),J)),K_1) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(I_1),K_1)),J) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_129_finite__Collect__disjI,axiom,
% 2.51/2.62 ! [Pa,Q_1] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,Pa),Q_1))))
% 2.51/2.62 <=> ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Pa)))
% 2.51/2.62 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(Q_1))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_130_finite__Collect__disjI,axiom,
% 2.51/2.62 ! [Pa,Q_1] :
% 2.51/2.62 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,Pa),Q_1))))
% 2.51/2.62 <=> ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Pa)))
% 2.51/2.62 & hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,collect_fun_nat_bool(Q_1))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_131_finite__Collect__disjI,axiom,
% 2.51/2.62 ! [Pa,Q_1] :
% 2.51/2.62 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,Pa),Q_1))))
% 2.51/2.62 <=> ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Pa)))
% 2.51/2.62 & hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,collec1974731493e_bool(Q_1))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_132_finite__Collect__disjI,axiom,
% 2.51/2.62 ! [Pa,Q_1] :
% 2.51/2.62 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,Pa),Q_1))))
% 2.51/2.62 <=> ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Pa)))
% 2.51/2.62 & hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,collect_fun_a_bool(Q_1))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_133_finite__Collect__disjI,axiom,
% 2.51/2.62 ! [Pa,Q_1] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,Pa),Q_1))))
% 2.51/2.62 <=> ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Pa)))
% 2.51/2.62 & hBOOL(hAPP_f54304608l_bool(finite_finite_nat,collect_nat(Q_1))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_134_finite__Collect__disjI,axiom,
% 2.51/2.62 ! [Pa,Q_1] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,Pa),Q_1))))
% 2.51/2.62 <=> ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Pa)))
% 2.51/2.62 & hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,collect_a(Q_1))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_135_finite__insert,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,insert_nat(A_1,A)))
% 2.51/2.62 <=> hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_136_finite__insert,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,insert_pname(A_1,A)))
% 2.51/2.62 <=> hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_137_finite__insert,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,insert_a(A_1,A)))
% 2.51/2.62 <=> hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_138_finite__insert,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,insert_fun_nat_bool(A_1,A)))
% 2.51/2.62 <=> hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_139_finite__insert,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,insert1325755072e_bool(A_1,A)))
% 2.51/2.62 <=> hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_140_finite__insert,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,insert_fun_a_bool(A_1,A)))
% 2.51/2.62 <=> hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_141_finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
% 2.51/2.62 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_142_finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
% 2.51/2.62 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_143_finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_144_finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
% 2.51/2.62 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_145_finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_146_finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_147_rev__finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,B))
% 2.51/2.62 => ( hBOOL(hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(ord_le1454342156l_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f1637334154l_bool(finite2012431853t_bool,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_148_rev__finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,B))
% 2.51/2.62 => ( hBOOL(hAPP_f1935102916l_bool(hAPP_f510955609l_bool(ord_le675606854l_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f1935102916l_bool(finite595471783e_bool,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_149_rev__finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_150_rev__finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,B))
% 2.51/2.62 => ( hBOOL(hAPP_f621171935l_bool(hAPP_f1434722111l_bool(ord_le1375614389l_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f621171935l_bool(finite347923420a_bool,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_151_rev__finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,B))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(finite_finite_nat,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_152_rev__finite__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,B))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_153_Suc__leD,axiom,
% 2.51/2.62 ! [M_2,N_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,M_2)),N_1))
% 2.51/2.62 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_154_le__SucE,axiom,
% 2.51/2.62 ! [M_2,N_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1)))
% 2.51/2.62 => ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
% 2.51/2.62 => M_2 = hAPP_nat_nat(suc,N_1) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_155_le__SucI,axiom,
% 2.51/2.62 ! [M_2,N_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
% 2.51/2.62 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),hAPP_nat_nat(suc,N_1))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_156_Suc__le__mono,axiom,
% 2.51/2.62 ! [Na,M_3] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),hAPP_nat_nat(suc,M_3)))
% 2.51/2.62 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),M_3)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_157_le__Suc__eq,axiom,
% 2.51/2.62 ! [M_3,Na] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),hAPP_nat_nat(suc,Na)))
% 2.51/2.62 <=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na))
% 2.51/2.62 | M_3 = hAPP_nat_nat(suc,Na) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_158_not__less__eq__eq,axiom,
% 2.51/2.62 ! [M_3,Na] :
% 2.51/2.62 ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na))
% 2.51/2.62 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,Na)),M_3)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_159_Suc__n__not__le__n,axiom,
% 2.51/2.62 ! [N_1] : ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),N_1)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_160_Suc__diff__diff,axiom,
% 2.51/2.62 ! [M_2,N_1,K_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),N_1)),hAPP_nat_nat(suc,K_1)) = hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M_2),N_1)),K_1) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_161_diff__Suc__Suc,axiom,
% 2.51/2.62 ! [M_2,N_1] : hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(suc,M_2)),hAPP_nat_nat(suc,N_1)) = hAPP_nat_nat(minus_minus_nat(M_2),N_1) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_162_le__diff__iff,axiom,
% 2.51/2.62 ! [Na,K,M_3] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_3))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_3),K)),hAPP_nat_nat(minus_minus_nat(Na),K)))
% 2.51/2.62 <=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_3),Na)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_163_Nat_Odiff__diff__eq,axiom,
% 2.51/2.62 ! [N_1,K_1,M_2] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),M_2))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K_1),N_1))
% 2.51/2.62 => hAPP_nat_nat(minus_minus_nat(hAPP_nat_nat(minus_minus_nat(M_2),K_1)),hAPP_nat_nat(minus_minus_nat(N_1),K_1)) = hAPP_nat_nat(minus_minus_nat(M_2),N_1) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_164_eq__diff__iff,axiom,
% 2.51/2.62 ! [Na,K,M_3] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),M_3))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,K),Na))
% 2.51/2.62 => ( hAPP_nat_nat(minus_minus_nat(M_3),K) = hAPP_nat_nat(minus_minus_nat(Na),K)
% 2.51/2.62 <=> M_3 = Na ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_165_diff__diff__cancel,axiom,
% 2.51/2.62 ! [I_1,N_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,I_1),N_1))
% 2.51/2.62 => hAPP_nat_nat(minus_minus_nat(N_1),hAPP_nat_nat(minus_minus_nat(N_1),I_1)) = I_1 ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_166_diff__le__mono,axiom,
% 2.51/2.62 ! [L,M_2,N_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
% 2.51/2.62 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),L)),hAPP_nat_nat(minus_minus_nat(N_1),L))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_167_diff__le__mono2,axiom,
% 2.51/2.62 ! [L,M_2,N_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,M_2),N_1))
% 2.51/2.62 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(L),N_1)),hAPP_nat_nat(minus_minus_nat(L),M_2))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_168_diff__le__self,axiom,
% 2.51/2.62 ! [M_2,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(minus_minus_nat(M_2),N_1)),M_2)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_169_finite__surj,axiom,
% 2.51/2.62 ! [B,F,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_170_finite__subset__image,axiom,
% 2.51/2.62 ! [F,A,B] :
% 2.51/2.62 ( is_fun_a_bool(B)
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,B))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
% 2.51/2.62 => ? [C_2] :
% 2.51/2.62 ( is_fun_pname_bool(C_2)
% 2.51/2.62 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C_2),A))
% 2.51/2.62 & hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,C_2))
% 2.51/2.62 & B = image_pname_a(F,C_2) ) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_171_lift__Suc__mono__le,axiom,
% 2.51/2.62 ! [Na,N_3,F] :
% 2.51/2.62 ( ! [N_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,N_2)),hAPP_n1699378549t_bool(F,hAPP_nat_nat(suc,N_2))))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,hAPP_n1699378549t_bool(F,Na)),hAPP_n1699378549t_bool(F,N_3))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_172_lift__Suc__mono__le,axiom,
% 2.51/2.62 ! [Na,N_3,F] :
% 2.51/2.62 ( ! [N_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,N_2)),hAPP_n1025906991e_bool(F,hAPP_nat_nat(suc,N_2))))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,hAPP_n1025906991e_bool(F,Na)),hAPP_n1025906991e_bool(F,N_3))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_173_lift__Suc__mono__le,axiom,
% 2.51/2.62 ! [Na,N_3,F] :
% 2.51/2.62 ( ! [N_2] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,N_2)),hAPP_nat_nat(F,hAPP_nat_nat(suc,N_2))))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
% 2.51/2.62 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(F,Na)),hAPP_nat_nat(F,N_3))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_174_lift__Suc__mono__le,axiom,
% 2.51/2.62 ! [Na,N_3,F] :
% 2.51/2.62 ( ! [N_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,N_2)),hAPP_nat_fun_a_bool(F,hAPP_nat_nat(suc,N_2))))
% 2.51/2.62 => ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,Na),N_3))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,hAPP_nat_fun_a_bool(F,Na)),hAPP_nat_fun_a_bool(F,N_3))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_175_pigeonhole__infinite,axiom,
% 2.51/2.62 ! [F,A] :
% 2.51/2.62 ( ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,A))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(finite_finite_a,image_pname_a(F,A)))
% 2.51/2.62 => ? [X_1] :
% 2.51/2.62 ( is_pname(X_1)
% 2.51/2.62 & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
% 2.51/2.62 & ~ hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fconj,hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),A)),hAPP_a93125764e_bool(cOMBC_pname_a_bool(cOMBB_1897541054_pname(fequal_a,F)),hAPP_pname_a(F,X_1)))))) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_176_image__eqI,axiom,
% 2.51/2.62 ! [A,B_1,F,X_2] :
% 2.51/2.62 ( B_1 = hAPP_pname_a(F,X_2)
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_177_equalityI,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A))
% 2.51/2.62 => A = B ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_178_equalityI,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( ( is_fun_pname_bool(A)
% 2.51/2.62 & is_fun_pname_bool(B) )
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A))
% 2.51/2.62 => A = B ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_179_equalityI,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( ( is_fun_a_bool(A)
% 2.51/2.62 & is_fun_a_bool(B) )
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A))
% 2.51/2.62 => A = B ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_180_subsetD,axiom,
% 2.51/2.62 ! [C_1,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),A))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,C_1),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_181_subsetD,axiom,
% 2.51/2.62 ! [C_1,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),A))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,C_1),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_182_subsetD,axiom,
% 2.51/2.62 ! [C_1,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),A))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,C_1),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_183_insertCI,axiom,
% 2.51/2.62 ! [B_1,A_1,B] :
% 2.51/2.62 ( ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B))
% 2.51/2.62 => A_1 = B_1 )
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_184_insertCI,axiom,
% 2.51/2.62 ! [B_1,A_1,B] :
% 2.51/2.62 ( ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B))
% 2.51/2.62 => A_1 = B_1 )
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_185_insertCI,axiom,
% 2.51/2.62 ! [B_1,A_1,B] :
% 2.51/2.62 ( ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),B))
% 2.51/2.62 => A_1 = B_1 )
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_186_insertE,axiom,
% 2.51/2.62 ! [A_1,B_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A)))
% 2.51/2.62 => ( A_1 != B_1
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_187_insertE,axiom,
% 2.51/2.62 ! [A_1,B_1,A] :
% 2.51/2.62 ( ( is_pname(A_1)
% 2.51/2.62 & is_pname(B_1) )
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A)))
% 2.51/2.62 => ( A_1 != B_1
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_188_insertE,axiom,
% 2.51/2.62 ! [A_1,B_1,A] :
% 2.51/2.62 ( ( is_a(A_1)
% 2.51/2.62 & is_a(B_1) )
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A)))
% 2.51/2.62 => ( A_1 != B_1
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_189_insertI1,axiom,
% 2.51/2.62 ! [A_1,B] : hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(A_1,B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_190_insertI1,axiom,
% 2.51/2.62 ! [A_1,B] : hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(A_1,B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_191_insertI1,axiom,
% 2.51/2.62 ! [A_1,B] : hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(A_1,B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_192_insert__compr,axiom,
% 2.51/2.62 ! [A_1,B] : insert_nat(A_1,B) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_193_insert__compr,axiom,
% 2.51/2.62 ! [A_1,B] : insert_pname(A_1,B) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_194_insert__compr,axiom,
% 2.51/2.62 ! [A_1,B] : insert_a(A_1,B) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_195_insert__compr,axiom,
% 2.51/2.62 ! [A_1,B] : insert_fun_nat_bool(A_1,B) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_196_insert__compr,axiom,
% 2.51/2.62 ! [A_1,B] : insert1325755072e_bool(A_1,B) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_197_insert__compr,axiom,
% 2.51/2.62 ! [A_1,B] : insert_fun_a_bool(A_1,B) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_198_insert__Collect,axiom,
% 2.51/2.62 ! [A_1,Pa] : insert_nat(A_1,collect_nat(Pa)) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fimplies,cOMBB_bool_bool_nat(fNot,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),A_1))),Pa)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_199_insert__Collect,axiom,
% 2.51/2.62 ! [A_1,Pa] : insert_pname(A_1,collect_pname(Pa)) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fimplies,cOMBB_647938656_pname(fNot,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),A_1))),Pa)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_200_insert__Collect,axiom,
% 2.51/2.62 ! [A_1,Pa] : insert_a(A_1,collect_a(Pa)) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fimplies,cOMBB_bool_bool_a(fNot,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),A_1))),Pa)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_201_insert__Collect,axiom,
% 2.51/2.62 ! [A_1,Pa] : insert_fun_nat_bool(A_1,collect_fun_nat_bool(Pa)) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fimplies,cOMBB_238756964t_bool(fNot,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),A_1))),Pa)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_202_insert__Collect,axiom,
% 2.51/2.62 ! [A_1,Pa] : insert1325755072e_bool(A_1,collec1974731493e_bool(Pa)) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fimplies,cOMBB_307249310e_bool(fNot,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),A_1))),Pa)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_203_insert__Collect,axiom,
% 2.51/2.62 ! [A_1,Pa] : insert_fun_a_bool(A_1,collect_fun_a_bool(Pa)) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fimplies,cOMBB_2140588453a_bool(fNot,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),A_1))),Pa)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_204_insert__absorb2,axiom,
% 2.51/2.62 ! [X_2,A] : insert_nat(X_2,insert_nat(X_2,A)) = insert_nat(X_2,A) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_205_insert__absorb2,axiom,
% 2.51/2.62 ! [X_2,A] : insert_pname(X_2,insert_pname(X_2,A)) = insert_pname(X_2,A) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_206_insert__absorb2,axiom,
% 2.51/2.62 ! [X_2,A] : insert_a(X_2,insert_a(X_2,A)) = insert_a(X_2,A) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_207_insert__commute,axiom,
% 2.51/2.62 ! [X_2,Y_1,A] : insert_nat(X_2,insert_nat(Y_1,A)) = insert_nat(Y_1,insert_nat(X_2,A)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_208_insert__commute,axiom,
% 2.51/2.62 ! [X_2,Y_1,A] : insert_pname(X_2,insert_pname(Y_1,A)) = insert_pname(Y_1,insert_pname(X_2,A)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_209_insert__commute,axiom,
% 2.51/2.62 ! [X_2,Y_1,A] : insert_a(X_2,insert_a(Y_1,A)) = insert_a(Y_1,insert_a(X_2,A)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_210_insert__iff,axiom,
% 2.51/2.62 ! [A_1,B_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,A)))
% 2.51/2.62 <=> ( A_1 = B_1
% 2.51/2.62 | hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_211_insert__iff,axiom,
% 2.51/2.62 ! [A_1,B_1,A] :
% 2.51/2.62 ( ( is_pname(A_1)
% 2.51/2.62 & is_pname(B_1) )
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,A)))
% 2.51/2.62 <=> ( A_1 = B_1
% 2.51/2.62 | hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_212_insert__iff,axiom,
% 2.51/2.62 ! [A_1,B_1,A] :
% 2.51/2.62 ( ( is_a(A_1)
% 2.51/2.62 & is_a(B_1) )
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,A)))
% 2.51/2.62 <=> ( A_1 = B_1
% 2.51/2.62 | hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_213_insert__code,axiom,
% 2.51/2.62 ! [Y_1,A,X_2] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(insert_nat(Y_1,A),X_2))
% 2.51/2.62 <=> ( Y_1 = X_2
% 2.51/2.62 | hBOOL(hAPP_nat_bool(A,X_2)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_214_insert__code,axiom,
% 2.51/2.62 ! [Y_1,A,X_2] :
% 2.51/2.62 ( ( is_pname(Y_1)
% 2.51/2.62 & is_pname(X_2) )
% 2.51/2.62 => ( hBOOL(hAPP_pname_bool(insert_pname(Y_1,A),X_2))
% 2.51/2.62 <=> ( Y_1 = X_2
% 2.51/2.62 | hBOOL(hAPP_pname_bool(A,X_2)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_215_insert__code,axiom,
% 2.51/2.62 ! [Y_1,A,X_2] :
% 2.51/2.62 ( ( is_a(Y_1)
% 2.51/2.62 & is_a(X_2) )
% 2.51/2.62 => ( hBOOL(hAPP_a_bool(insert_a(Y_1,A),X_2))
% 2.51/2.62 <=> ( Y_1 = X_2
% 2.51/2.62 | hBOOL(hAPP_a_bool(A,X_2)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_216_insert__ident,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.62 => ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
% 2.51/2.62 => ( insert_nat(X_2,A) = insert_nat(X_2,B)
% 2.51/2.62 <=> A = B ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_217_insert__ident,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( ( is_fun_pname_bool(B)
% 2.51/2.62 & is_fun_pname_bool(A) )
% 2.51/2.62 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
% 2.51/2.62 => ( insert_pname(X_2,A) = insert_pname(X_2,B)
% 2.51/2.62 <=> A = B ) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_218_insert__ident,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( ( is_fun_a_bool(B)
% 2.51/2.62 & is_fun_a_bool(A) )
% 2.51/2.62 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.62 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
% 2.51/2.62 => ( insert_a(X_2,A) = insert_a(X_2,B)
% 2.51/2.62 <=> A = B ) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_219_insertI2,axiom,
% 2.51/2.62 ! [B_1,A_1,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),B))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),insert_nat(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_220_insertI2,axiom,
% 2.51/2.62 ! [B_1,A_1,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),B))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),insert_pname(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_221_insertI2,axiom,
% 2.51/2.62 ! [B_1,A_1,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),B))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),insert_a(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_222_insert__absorb,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,A_1),A))
% 2.51/2.62 => insert_nat(A_1,A) = A ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_223_insert__absorb,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( is_fun_pname_bool(A)
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,A_1),A))
% 2.51/2.62 => insert_pname(A_1,A) = A ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_224_insert__absorb,axiom,
% 2.51/2.62 ! [A_1,A] :
% 2.51/2.62 ( is_fun_a_bool(A)
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,A_1),A))
% 2.51/2.62 => insert_a(A_1,A) = A ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_225_subset__refl,axiom,
% 2.51/2.62 ! [A] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),A)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_226_subset__refl,axiom,
% 2.51/2.62 ! [A] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),A)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_227_subset__refl,axiom,
% 2.51/2.62 ! [A] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),A)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_228_set__eq__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_229_set__eq__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( ( is_fun_pname_bool(A)
% 2.51/2.62 & is_fun_pname_bool(B) )
% 2.51/2.62 => ( A = B
% 2.51/2.62 <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_230_set__eq__subset,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( ( is_fun_a_bool(A)
% 2.51/2.62 & is_fun_a_bool(B) )
% 2.51/2.62 => ( A = B
% 2.51/2.62 <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_231_equalityD1,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_232_equalityD1,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_233_equalityD1,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_234_equalityD2,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_235_equalityD2,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_236_equalityD2,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_237_in__mono,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_238_in__mono,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_239_in__mono,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_240_set__rev__mp,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_241_set__rev__mp,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_242_set__rev__mp,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_243_set__mp,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_244_set__mp,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_245_set__mp,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_246_subset__trans,axiom,
% 2.51/2.62 ! [C,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),C))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),C)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_247_subset__trans,axiom,
% 2.51/2.62 ! [C,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),C))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),C)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_248_subset__trans,axiom,
% 2.51/2.62 ! [C,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),C))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),C)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_249_equalityE,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => ~ ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_250_equalityE,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => ~ ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_251_equalityE,axiom,
% 2.51/2.62 ! [A,B] :
% 2.51/2.62 ( A = B
% 2.51/2.62 => ~ ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),A)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_252_mem__def,axiom,
% 2.51/2.62 ! [X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.62 <=> hBOOL(hAPP_nat_bool(A,X_2)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_253_mem__def,axiom,
% 2.51/2.62 ! [X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.62 <=> hBOOL(hAPP_a_bool(A,X_2)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_254_mem__def,axiom,
% 2.51/2.62 ! [X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 <=> hBOOL(hAPP_pname_bool(A,X_2)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_255_Collect__def,axiom,
% 2.51/2.62 ! [Pa] :
% 2.51/2.62 ( is_fun_pname_bool(Pa)
% 2.51/2.62 => collect_pname(Pa) = Pa ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_256_Collect__def,axiom,
% 2.51/2.62 ! [Pa] : collect_fun_nat_bool(Pa) = Pa ).
% 2.51/2.62
% 2.51/2.62 fof(fact_257_Collect__def,axiom,
% 2.51/2.62 ! [Pa] :
% 2.51/2.62 ( is_fun1661590463l_bool(Pa)
% 2.51/2.62 => collec1974731493e_bool(Pa) = Pa ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_258_Collect__def,axiom,
% 2.51/2.62 ! [Pa] :
% 2.51/2.62 ( is_fun949378684l_bool(Pa)
% 2.51/2.62 => collect_fun_a_bool(Pa) = Pa ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_259_Collect__def,axiom,
% 2.51/2.62 ! [Pa] : collect_nat(Pa) = Pa ).
% 2.51/2.62
% 2.51/2.62 fof(fact_260_image__iff,axiom,
% 2.51/2.62 ! [Z,F,A] :
% 2.51/2.62 ( is_a(Z)
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,Z),image_pname_a(F,A)))
% 2.51/2.62 <=> ? [X_1] :
% 2.51/2.62 ( is_pname(X_1)
% 2.51/2.62 & hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
% 2.51/2.62 & Z = hAPP_pname_a(F,X_1) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_261_imageI,axiom,
% 2.51/2.62 ! [F,X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_2)),image_pname_a(F,A))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_262_rev__image__eqI,axiom,
% 2.51/2.62 ! [B_1,F,X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => ( B_1 = hAPP_pname_a(F,X_2)
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_263_insert__compr__raw,axiom,
% 2.51/2.62 ! [X_1,Xa] : insert_nat(X_1,Xa) = collect_nat(cOMBS_nat_bool_bool(cOMBB_1015721476ol_nat(fdisj,hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(fequal_nat),X_1)),hAPP_f800510211t_bool(cOMBC_226598744l_bool(member_nat),Xa))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_264_insert__compr__raw,axiom,
% 2.51/2.62 ! [X_1,Xa] : insert_pname(X_1,Xa) = collect_pname(cOMBS_568398431l_bool(cOMBB_675860798_pname(fdisj,hAPP_p61793385e_bool(cOMBC_1149511130e_bool(fequal_pname),X_1)),hAPP_f759274231e_bool(cOMBC_1058051404l_bool(member_pname),Xa))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_265_insert__compr__raw,axiom,
% 2.51/2.62 ! [X_1,Xa] : insert_a(X_1,Xa) = collect_a(cOMBS_a_bool_bool(cOMBB_1972296269bool_a(fdisj,hAPP_a_fun_a_bool(cOMBC_a_a_bool(fequal_a),X_1)),hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(member_a),Xa))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_266_insert__compr__raw,axiom,
% 2.51/2.62 ! [X_1,Xa] : insert_fun_nat_bool(X_1,Xa) = collect_fun_nat_bool(cOMBS_1187019125l_bool(cOMBB_444170502t_bool(fdisj,hAPP_f103356543l_bool(cOMBC_1693257480l_bool(fequal_fun_nat_bool),X_1)),hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(member_fun_nat_bool),Xa))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_267_insert__compr__raw,axiom,
% 2.51/2.62 ! [X_1,Xa] : insert1325755072e_bool(X_1,Xa) = collec1974731493e_bool(cOMBS_350070575l_bool(cOMBB_2095475776e_bool(fdisj,hAPP_f434788991l_bool(cOMBC_1284144636l_bool(fequal533582459e_bool),X_1)),hAPP_f559147733l_bool(cOMBC_1988546018l_bool(member799430823e_bool),Xa))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_268_insert__compr__raw,axiom,
% 2.51/2.62 ! [X_1,Xa] : insert_fun_a_bool(X_1,Xa) = collect_fun_a_bool(cOMBS_1035972772l_bool(cOMBB_338059395a_bool(fdisj,hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(fequal_fun_a_bool),X_1)),hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(member_fun_a_bool),Xa))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_269_subset__insertI,axiom,
% 2.51/2.62 ! [B,A_1] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,B),insert_nat(A_1,B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_270_subset__insertI,axiom,
% 2.51/2.62 ! [B,A_1] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,B),insert_pname(A_1,B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_271_subset__insertI,axiom,
% 2.51/2.62 ! [B,A_1] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),insert_a(A_1,B))) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_272_insert__subset,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(X_2,A)),B))
% 2.51/2.62 <=> ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),B))
% 2.51/2.62 & hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_273_insert__subset,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(X_2,A)),B))
% 2.51/2.62 <=> ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),B))
% 2.51/2.62 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_274_insert__subset,axiom,
% 2.51/2.62 ! [X_2,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(X_2,A)),B))
% 2.51/2.62 <=> ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),B))
% 2.51/2.62 & hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_275_subset__insert,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_2),A))
% 2.51/2.62 => ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(X_2,B)))
% 2.51/2.62 <=> hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_276_subset__insert,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(X_2,B)))
% 2.51/2.62 <=> hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_277_subset__insert,axiom,
% 2.51/2.62 ! [B,X_2,A] :
% 2.51/2.62 ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_2),A))
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(X_2,B)))
% 2.51/2.62 <=> hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_278_subset__insertI2,axiom,
% 2.51/2.62 ! [B_1,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),insert_nat(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_279_subset__insertI2,axiom,
% 2.51/2.62 ! [B_1,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),insert_pname(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_280_subset__insertI2,axiom,
% 2.51/2.62 ! [B_1,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),insert_a(B_1,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_281_insert__mono,axiom,
% 2.51/2.62 ! [A_1,C,D] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,C),D))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,insert_nat(A_1,C)),insert_nat(A_1,D))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_282_insert__mono,axiom,
% 2.51/2.62 ! [A_1,C,D] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,C),D))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,insert_pname(A_1,C)),insert_pname(A_1,D))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_283_insert__mono,axiom,
% 2.51/2.62 ! [A_1,C,D] :
% 2.51/2.62 ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,C),D))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(A_1,C)),insert_a(A_1,D))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_284_image__insert,axiom,
% 2.51/2.62 ! [F,A_1,B] : image_pname_a(F,insert_pname(A_1,B)) = insert_a(hAPP_pname_a(F,A_1),image_pname_a(F,B)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_285_insert__image,axiom,
% 2.51/2.62 ! [F,X_2,A] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_2),A))
% 2.51/2.62 => insert_a(hAPP_pname_a(F,X_2),image_pname_a(F,A)) = image_pname_a(F,A) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_286_subset__image__iff,axiom,
% 2.51/2.62 ! [B,F,A] :
% 2.51/2.62 ( is_fun_a_bool(B)
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,B),image_pname_a(F,A)))
% 2.51/2.62 <=> ? [AA] :
% 2.51/2.62 ( is_fun_pname_bool(AA)
% 2.51/2.62 & hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,AA),A))
% 2.51/2.62 & B = image_pname_a(F,AA) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_287_image__mono,axiom,
% 2.51/2.62 ! [F,A,B] :
% 2.51/2.62 ( hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),image_pname_a(F,B))) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_288_imageE,axiom,
% 2.51/2.62 ! [B_1,F,A] :
% 2.51/2.62 ( is_a(B_1)
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,B_1),image_pname_a(F,A)))
% 2.51/2.62 => ~ ! [X_1] :
% 2.51/2.62 ( is_pname(X_1)
% 2.51/2.62 => ( B_1 = hAPP_pname_a(F,X_1)
% 2.51/2.62 => ~ hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A)) ) ) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_289_subsetI,axiom,
% 2.51/2.62 ! [B,A] :
% 2.51/2.62 ( ! [X_1] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),A))
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),B)) )
% 2.51/2.62 => hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,A),B)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_290_subsetI,axiom,
% 2.51/2.62 ! [B,A] :
% 2.51/2.62 ( ! [X_1] :
% 2.51/2.62 ( is_a(X_1)
% 2.51/2.62 => ( hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),A))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,X_1),B)) ) )
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,A),B)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_291_subsetI,axiom,
% 2.51/2.62 ! [B,A] :
% 2.51/2.62 ( ! [X_1] :
% 2.51/2.62 ( is_pname(X_1)
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),B)) ) )
% 2.51/2.62 => hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,A),B)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_292_zero__induct__lemma,axiom,
% 2.51/2.62 ! [I,Pa,K] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(Pa,K))
% 2.51/2.62 => ( ! [N_2] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(suc,N_2)))
% 2.51/2.62 => hBOOL(hAPP_nat_bool(Pa,N_2)) )
% 2.51/2.62 => hBOOL(hAPP_nat_bool(Pa,hAPP_nat_nat(minus_minus_nat(K),I))) ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_293_Suc__le__D,axiom,
% 2.51/2.62 ! [N_1,M_1] :
% 2.51/2.62 ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,N_1)),M_1))
% 2.51/2.62 => ? [M] : M_1 = hAPP_nat_nat(suc,M) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_294_image__subsetI,axiom,
% 2.51/2.62 ! [F,B,A] :
% 2.51/2.62 ( ! [X_1] :
% 2.51/2.62 ( is_pname(X_1)
% 2.51/2.62 => ( hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,X_1),A))
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(F,X_1)),B)) ) )
% 2.51/2.62 => hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,image_pname_a(F,A)),B)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_295_order__refl,axiom,
% 2.51/2.62 ! [X_2] : hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(ord_le1568362934t_bool,X_2),X_2)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_296_order__refl,axiom,
% 2.51/2.62 ! [X_2] : hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(ord_le313189616e_bool,X_2),X_2)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_297_order__refl,axiom,
% 2.51/2.62 ! [X_3] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_3),X_3)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_298_order__refl,axiom,
% 2.51/2.62 ! [X_2] : hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,X_2),X_2)) ).
% 2.51/2.62
% 2.51/2.62 fof(fact_299_finite__nat__set__iff__bounded__le,axiom,
% 2.51/2.62 ! [N] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(finite_finite_nat,N))
% 2.51/2.62 <=> ? [M] :
% 2.51/2.62 ! [X_1] :
% 2.51/2.62 ( hBOOL(hAPP_f54304608l_bool(hAPP_n215258509l_bool(member_nat,X_1),N))
% 2.51/2.62 => hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,X_1),M)) ) ) ).
% 2.51/2.62
% 2.51/2.62 %----Helper facts (61)
% 2.51/2.62 fof(help_fNot_1_1_U,axiom,
% 2.51/2.62 ! [P] :
% 2.51/2.62 ( ~ hBOOL(hAPP_bool_bool(fNot,P))
% 2.51/2.62 | ~ hBOOL(P) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fNot_2_1_U,axiom,
% 2.51/2.62 ! [P] :
% 2.51/2.62 ( hBOOL(P)
% 2.51/2.62 | hBOOL(hAPP_bool_bool(fNot,P)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fconj_1_1_U,axiom,
% 2.51/2.62 ! [Q,P] :
% 2.51/2.62 ( ~ hBOOL(P)
% 2.51/2.62 | ~ hBOOL(Q)
% 2.51/2.62 | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fconj_2_1_U,axiom,
% 2.51/2.62 ! [P,Q] :
% 2.51/2.62 ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
% 2.51/2.62 | hBOOL(P) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fconj_3_1_U,axiom,
% 2.51/2.62 ! [P,Q] :
% 2.51/2.62 ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fconj,P),Q))
% 2.51/2.62 | hBOOL(Q) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fdisj_1_1_U,axiom,
% 2.51/2.62 ! [Q,P] :
% 2.51/2.62 ( ~ hBOOL(P)
% 2.51/2.62 | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fdisj_2_1_U,axiom,
% 2.51/2.62 ! [P,Q] :
% 2.51/2.62 ( ~ hBOOL(Q)
% 2.51/2.62 | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fdisj_3_1_U,axiom,
% 2.51/2.62 ! [P,Q] :
% 2.51/2.62 ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fdisj,P),Q))
% 2.51/2.62 | hBOOL(P)
% 2.51/2.62 | hBOOL(Q) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fimplies_1_1_U,axiom,
% 2.51/2.62 ! [Q,P] :
% 2.51/2.62 ( hBOOL(P)
% 2.51/2.62 | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fimplies_2_1_U,axiom,
% 2.51/2.62 ! [P,Q] :
% 2.51/2.62 ( ~ hBOOL(Q)
% 2.51/2.62 | hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fimplies_3_1_U,axiom,
% 2.51/2.62 ! [P,Q] :
% 2.51/2.62 ( ~ hBOOL(hAPP_bool_bool(hAPP_b589554111l_bool(fimplies,P),Q))
% 2.51/2.62 | ~ hBOOL(P)
% 2.51/2.62 | hBOOL(Q) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_1_1_fequal_000t__a_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( ( is_a(X)
% 2.51/2.62 & is_a(Y) )
% 2.51/2.62 => ( ~ hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y))
% 2.51/2.62 | X = Y ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_2_1_fequal_000t__a_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( X != Y
% 2.51/2.62 | hBOOL(hAPP_a_bool(hAPP_a_fun_a_bool(fequal_a,X),Y)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y))
% 2.51/2.62 | X = Y ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( X != Y
% 2.51/2.62 | hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(fequal_nat,X),Y)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( ( is_pname(X)
% 2.51/2.62 & is_pname(Y) )
% 2.51/2.62 => ( ~ hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y))
% 2.51/2.62 | X = Y ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( X != Y
% 2.51/2.62 | hBOOL(hAPP_pname_bool(hAPP_p61793385e_bool(fequal_pname,X),Y)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_a_bool(hAPP_a_fun_a_bool(cOMBC_a_a_bool(P),Q),R) = hAPP_a_bool(hAPP_a_fun_a_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( ( is_fun_a_bool(X)
% 2.51/2.62 & is_fun_a_bool(Y) )
% 2.51/2.62 => ( ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y))
% 2.51/2.62 | X = Y ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( X != Y
% 2.51/2.62 | hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(fequal_fun_a_bool,X),Y)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_a_bool(cOMBB_bool_bool_a(P,Q),R) = hAPP_bool_bool(P,hAPP_a_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_a_bool(cOMBS_a_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_a_fun_bool_bool(P,R),hAPP_a_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_pname_bool(hAPP_a93125764e_bool(cOMBC_pname_a_bool(P),Q),R) = hAPP_a_bool(hAPP_p1534023578a_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( ~ hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y))
% 2.51/2.62 | X = Y ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( X != Y
% 2.51/2.62 | hBOOL(hAPP_f54304608l_bool(hAPP_f103356543l_bool(fequal_fun_nat_bool,X),Y)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( ( is_fun_pname_bool(X)
% 2.51/2.62 & is_fun_pname_bool(Y) )
% 2.51/2.62 => ( ~ hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y))
% 2.51/2.62 | X = Y ) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T,axiom,
% 2.51/2.62 ! [X,Y] :
% 2.51/2.62 ( X != Y
% 2.51/2.62 | hBOOL(hAPP_f1664156314l_bool(hAPP_f434788991l_bool(fequal533582459e_bool,X),Y)) ) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_nat_bool(hAPP_n1699378549t_bool(cOMBC_nat_nat_bool(P),Q),R) = hAPP_nat_bool(hAPP_n1699378549t_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_nat_bool(cOMBB_bool_bool_nat(P,Q),R) = hAPP_bool_bool(P,hAPP_nat_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_nat_bool(cOMBS_nat_bool_bool(P,Q),R) = hAPP_bool_bool(hAPP_n1006566506l_bool(P,R),hAPP_nat_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_pname_bool(cOMBB_647938656_pname(P,Q),R) = hAPP_bool_bool(P,hAPP_pname_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_pname_bool(cOMBS_568398431l_bool(P,Q),R) = hAPP_bool_bool(hAPP_p393069232l_bool(P,R),hAPP_pname_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_pname_bool(hAPP_p61793385e_bool(cOMBC_1149511130e_bool(P),Q),R) = hAPP_pname_bool(hAPP_p61793385e_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_a_bool(hAPP_f2050579477a_bool(cOMBC_1355376034l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_p1534023578a_bool(cOMBB_1897541054_pname(P,Q),R) = hAPP_a_fun_a_bool(P,hAPP_pname_a(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_fun_a_bool_bool(cOMBB_2140588453a_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_fun_a_bool_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_a_fun_bool_bool(cOMBB_1972296269bool_a(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_a_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_fun_a_bool_bool(cOMBS_1035972772l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f198738859l_bool(P,R),hAPP_fun_a_bool_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_nat_bool(hAPP_f800510211t_bool(cOMBC_226598744l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_n215258509l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f54304608l_bool(cOMBB_238756964t_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f54304608l_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_n1006566506l_bool(cOMBB_1015721476ol_nat(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_nat_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f54304608l_bool(cOMBS_1187019125l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1748468828l_bool(P,R),hAPP_f54304608l_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBB_307249310e_bool(P,Q),R) = hAPP_bool_bool(P,hAPP_f1664156314l_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_007,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_p393069232l_bool(cOMBB_675860798_pname(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_pname_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f1664156314l_bool(cOMBS_350070575l_bool(P,Q),R) = hAPP_bool_bool(hAPP_f1476298914l_bool(P,R),hAPP_f1664156314l_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_pname_bool(hAPP_f759274231e_bool(cOMBC_1058051404l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_p338031245l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(cOMBC_1732670874l_bool(P),Q),R) = hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f198738859l_bool(cOMBB_338059395a_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_fun_a_bool_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f103356543l_bool(cOMBC_1693257480l_bool(P),Q),R) = hAPP_f54304608l_bool(hAPP_f103356543l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f1748468828l_bool(cOMBB_444170502t_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f54304608l_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f1476298914l_bool(cOMBB_2095475776e_bool(P,Q),R) = hAPP_b589554111l_bool(P,hAPP_f1664156314l_bool(Q,R)) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f434788991l_bool(cOMBC_1284144636l_bool(P),Q),R) = hAPP_f1664156314l_bool(hAPP_f434788991l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_fun_a_bool_bool(hAPP_f2117159681l_bool(cOMBC_1880041174l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f285962445l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__011,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f54304608l_bool(hAPP_f1246832597l_bool(cOMBC_1245412066l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1951378235l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_012,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f1664156314l_bool(hAPP_f559147733l_bool(cOMBC_1988546018l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f556039215l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f621171935l_bool(hAPP_f1434722111l_bool(cOMBC_331553030l_bool(P),Q),R) = hAPP_f621171935l_bool(hAPP_f1434722111l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(cOMBC_595898202l_bool(P),Q),R) = hAPP_f1637334154l_bool(hAPP_f1772781669l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_,axiom,
% 2.51/2.62 ! [P,Q,R] : hAPP_f1935102916l_bool(hAPP_f510955609l_bool(cOMBC_7971162l_bool(P),Q),R) = hAPP_f1935102916l_bool(hAPP_f510955609l_bool(P,R),Q) ).
% 2.51/2.62
% 2.51/2.62 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H,axiom,
% 2.51/2.63 ! [P,Q,R] : hAPP_f292226953l_bool(hAPP_f1050622307l_bool(cOMBC_636888218l_bool(P),Q),R) = hAPP_f292226953l_bool(hAPP_f1050622307l_bool(P,R),Q) ).
% 2.51/2.63
% 2.51/2.63 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool,axiom,
% 2.51/2.63 ! [P,Q,R] : hAPP_f937997336l_bool(hAPP_f760187903l_bool(cOMBC_1269652216l_bool(P),Q),R) = hAPP_f937997336l_bool(hAPP_f760187903l_bool(P,R),Q) ).
% 2.51/2.63
% 2.51/2.63 fof(help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo,axiom,
% 2.51/2.63 ! [P,Q,R] : hAPP_f389811538l_bool(hAPP_f1759205631l_bool(cOMBC_336095980l_bool(P),Q),R) = hAPP_f389811538l_bool(hAPP_f1759205631l_bool(P,R),Q) ).
% 2.51/2.63
% 2.51/2.63 %----Conjectures (7)
% 2.51/2.63 fof(conj_0,hypothesis,
% 2.51/2.63 hBOOL(hAPP_f1664156314l_bool(finite_finite_pname,u)) ).
% 2.51/2.63
% 2.51/2.63 fof(conj_1,hypothesis,
% 2.51/2.63 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,g),image_pname_a(mgt_call,u))) ).
% 2.51/2.63
% 2.51/2.63 fof(conj_2,hypothesis,
% 2.51/2.63 hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,hAPP_nat_nat(suc,na)),hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u)))) ).
% 2.51/2.63
% 2.51/2.63 fof(conj_3,hypothesis,
% 2.51/2.63 hAPP_fun_a_bool_nat(finite_card_a,g) = hAPP_nat_nat(minus_minus_nat(hAPP_fun_a_bool_nat(finite_card_a,image_pname_a(mgt_call,u))),hAPP_nat_nat(suc,na)) ).
% 2.51/2.63
% 2.51/2.63 fof(conj_4,hypothesis,
% 2.51/2.63 hBOOL(hAPP_f1664156314l_bool(hAPP_p338031245l_bool(member_pname,pn),u)) ).
% 2.51/2.63
% 2.51/2.63 fof(conj_5,hypothesis,
% 2.51/2.63 ~ hBOOL(hAPP_fun_a_bool_bool(hAPP_a85458249l_bool(member_a,hAPP_pname_a(mgt_call,pn)),g)) ).
% 2.51/2.63
% 2.51/2.63 fof(conj_6,conjecture,
% 2.51/2.63 hBOOL(hAPP_fun_a_bool_bool(hAPP_f1631501043l_bool(ord_le1311769555a_bool,insert_a(hAPP_pname_a(mgt_call,pn),g)),image_pname_a(mgt_call,u))) ).
% 2.51/2.63
% 2.51/2.63 %------------------------------------------------------------------------------
% 2.51/2.63 %-------------------------------------------
% 2.51/2.63 % Proof found
% 2.51/2.63 % SZS status Theorem for theBenchmark
% 2.51/2.63 % SZS output start Proof
% 2.51/2.63 %ClaNum:866(EqnAxiom:337)
% 2.51/2.63 %VarNum:2019(SingletonVarNum:982)
% 2.51/2.63 %MaxLitNum:6
% 2.51/2.63 %MaxfuncDepth:7
% 2.51/2.63 %SharedTerms:128
% 2.51/2.63 %goalClause: 452
% 2.51/2.63 %singleGoalClaCount:1
% 2.51/2.63 [338]P1(a1)
% 2.51/2.63 [339]P7(a100)
% 2.51/2.63 [340]P2(a2)
% 2.51/2.63 [341]P3(a97)
% 2.51/2.63 [342]P8(a101)
% 2.51/2.63 [343]P4(f228(a227))
% 2.51/2.63 [344]P8(f232(a225))
% 2.51/2.63 [345]P5(f102(a97,a100))
% 2.51/2.63 [369]P1(f233(f99(a227,a3)))
% 2.51/2.63 [370]P7(f229(f99(a225,a3)))
% 2.51/2.63 [372]P5(f102(f165(a200,a101),a100))
% 2.51/2.63 [421]P5(f154(f117(a212,a1),f201(a214,a100)))
% 2.51/2.63 [424]E(f164(f213(f157(a43,f201(a214,a100))),f164(a226,a215)),f157(a43,a1))
% 2.51/2.63 [452]~P5(f154(f117(a212,f46(f37(f11(a44,f111(f19(a75),f168(a214,a101))),f136(f20(a203),a1)))),f201(a214,a100)))
% 2.51/2.63 [422]P2(f230(f99(f99(a227,a3),a3)))
% 2.51/2.63 [423]P3(f231(f99(f99(a225,a3),a3)))
% 2.51/2.63 [427]P5(f158(f159(a199,f164(a226,a215)),f157(a43,f201(a214,a100))))
% 2.51/2.63 [450]~P5(f154(f108(a203,f168(a214,a101)),a1))
% 2.51/2.63 [449]~E(f164(a226,x4491),x4491)
% 2.51/2.63 [374]P5(f158(f159(a199,x3741),x3741))
% 2.51/2.63 [376]P5(f154(f117(a212,x3761),x3761))
% 2.51/2.63 [378]P5(f102(f141(a216,x3781),x3781))
% 2.51/2.63 [380]P5(f126(f106(a217,x3801),x3801))
% 2.51/2.63 [371]E(f128(a4,f159(f5(a199),x3711)),f164(a226,x3711))
% 2.51/2.63 [394]P5(f126(a98,f159(f5(a199),x3941)))
% 2.51/2.63 [451]~P5(f158(f159(a199,f164(a226,x4511)),x4511))
% 2.51/2.63 [346]P1(f120(x3461,x3462))
% 2.51/2.63 [347]P1(f121(x3471,x3472))
% 2.51/2.63 [348]P1(f122(x3481,x3482))
% 2.51/2.63 [349]P1(f123(x3491,x3492))
% 2.51/2.63 [350]P1(f187(x3501,x3502))
% 2.51/2.63 [351]P1(f124(x3511,x3512))
% 2.51/2.63 [352]P7(f197(x3521,x3522))
% 2.51/2.63 [353]P7(f161(x3531,x3532))
% 2.51/2.63 [354]P7(f190(x3541,x3542))
% 2.51/2.63 [355]P7(f162(x3551,x3552))
% 2.51/2.63 [356]P7(f163(x3561,x3562))
% 2.51/2.63 [357]P7(f125(x3571,x3572))
% 2.51/2.63 [358]P2(f198(x3581,x3582))
% 2.51/2.63 [359]P3(f178(x3591,x3592))
% 2.51/2.63 [360]P6(f158(x3601,x3602))
% 2.51/2.63 [361]P6(f126(x3611,x3612))
% 2.51/2.63 [362]P6(f103(x3621,x3622))
% 2.51/2.63 [363]P6(f127(x3631,x3632))
% 2.51/2.63 [364]P6(f140(x3641,x3642))
% 2.51/2.63 [365]P6(f143(x3651,x3652))
% 2.51/2.63 [366]P6(f104(x3661,x3662))
% 2.51/2.63 [367]P6(f144(x3671,x3672))
% 2.51/2.63 [368]P6(f105(x3681,x3682))
% 2.51/2.63 [420]E(f164(f213(f164(a226,x4201)),f164(a226,x4202)),f164(f213(x4201),x4202))
% 2.51/2.63 [426]P5(f158(f159(a199,f164(f213(x4261),x4262)),x4261))
% 2.51/2.63 [431]P5(f126(f106(a217,x4311),f42(f9(a44,f159(f5(a79),x4312)),f151(f26(a211),x4311))))
% 2.51/2.63 [432]P5(f126(f160(a211,x4321),f42(f9(a44,f159(f5(a79),x4321)),f151(f26(a211),x4322))))
% 2.51/2.63 [428]E(f41(f16(a44,f106(f28(a74),x4281)),f114(f24(a202),x4282)),f41(f16(a78,f14(a45,f106(f28(a74),x4281))),x4282))
% 2.51/2.63 [429]E(f42(f9(a44,f159(f5(a79),x4291)),f151(f26(a211),x4292)),f42(f9(a78,f18(a45,f159(f5(a79),x4291))),x4292))
% 2.51/2.63 [437]E(f42(f9(a44,f159(f5(a79),x4371)),f151(f26(a211),f42(f9(a44,f159(f5(a79),x4371)),f151(f26(a211),x4372)))),f42(f9(a44,f159(f5(a79),x4371)),f151(f26(a211),x4372)))
% 2.51/2.63 [439]P5(f154(f108(a203,x4391),f46(f37(f11(a44,f111(f19(a75),x4391)),f136(f20(a203),x4392)))))
% 2.51/2.63 [440]P5(f154(f117(a212,x4401),f46(f37(f11(a44,f111(f19(a75),x4402)),f136(f20(a203),x4401)))))
% 2.51/2.63 [441]P5(f102(f165(a200,x4411),f54(f38(f17(a44,f170(f21(a80),x4411)),f148(f22(a200),x4412)))))
% 2.51/2.63 [442]P5(f102(f141(a216,x4421),f54(f38(f17(a44,f170(f21(a80),x4422)),f148(f22(a200),x4421)))))
% 2.51/2.63 [433]E(f46(f37(f11(a44,f111(f19(a75),x4331)),f136(f20(a203),f46(x4332)))),f46(f37(f11(a78,f6(a45,f111(f19(a75),x4331))),x4332)))
% 2.51/2.63 [434]E(f54(f38(f17(a44,f170(f21(a80),x4341)),f148(f22(a200),f54(x4342)))),f54(f38(f17(a78,f7(a45,f170(f21(a80),x4341))),x4342)))
% 2.51/2.63 [435]E(f55(f39(f15(a44,f117(f27(a77),x4351)),f138(f29(a210),f55(x4352)))),f55(f39(f15(a78,f10(a45,f117(f27(a77),x4351))),x4352)))
% 2.51/2.63 [436]E(f47(f40(f12(a44,f141(f23(a76),x4361)),f145(f30(a204),f47(x4362)))),f47(f40(f12(a78,f13(a45,f141(f23(a76),x4361))),x4362)))
% 2.51/2.63 [444]E(f46(f37(f11(a44,f111(f19(a75),x4441)),f136(f20(a203),f46(f37(f11(a44,f111(f19(a75),x4441)),f136(f20(a203),x4442)))))),f46(f37(f11(a44,f111(f19(a75),x4441)),f136(f20(a203),x4442))))
% 2.51/2.63 [445]E(f54(f38(f17(a44,f170(f21(a80),x4451)),f148(f22(a200),f54(f38(f17(a44,f170(f21(a80),x4451)),f148(f22(a200),x4452)))))),f54(f38(f17(a44,f170(f21(a80),x4451)),f148(f22(a200),x4452))))
% 2.51/2.63 [381]E(f110(x3811,f107(x3812,x3813)),f107(f6(x3811,x3812),x3813))
% 2.51/2.63 [382]E(f167(f7(x3821,x3822),x3823),f110(x3821,f167(x3822,x3823)))
% 2.51/2.63 [383]E(f111(x3831,f168(x3832,x3833)),f166(f8(x3831,x3832),x3833))
% 2.51/2.63 [384]E(f110(x3841,f158(x3842,x3843)),f158(f18(x3841,x3842),x3843))
% 2.51/2.63 [385]E(f110(x3851,f154(x3852,x3853)),f154(f10(x3851,x3852),x3853))
% 2.51/2.63 [386]E(f110(x3861,f102(x3862,x3863)),f102(f13(x3861,x3862),x3863))
% 2.51/2.63 [387]E(f110(x3871,f126(x3872,x3873)),f126(f14(x3871,x3872),x3873))
% 2.51/2.63 [388]E(f112(x3881,f107(x3882,x3883)),f113(f11(x3881,x3882),x3883))
% 2.51/2.63 [389]E(f156(f9(x3891,x3892),x3893),f112(x3891,f158(x3892,x3893)))
% 2.51/2.63 [390]E(f169(f17(x3901,x3902),x3903),f112(x3901,f167(x3902,x3903)))
% 2.51/2.63 [391]E(f129(f15(x3911,x3912),x3913),f112(x3911,f154(x3912,x3913)))
% 2.51/2.63 [392]E(f130(f16(x3921,x3922),x3923),f112(x3921,f126(x3922,x3923)))
% 2.51/2.63 [393]E(f118(f12(x3931,x3932),x3933),f112(x3931,f102(x3932,x3933)))
% 2.51/2.63 [414]E(f110(f113(x4141,x4142),f107(x4143,x4142)),f107(f37(x4141,x4143),x4142))
% 2.51/2.63 [415]E(f110(f169(x4151,x4152),f167(x4153,x4152)),f167(f38(x4151,x4153),x4152))
% 2.51/2.63 [416]E(f110(f156(x4161,x4162),f158(x4163,x4162)),f158(f42(x4161,x4163),x4162))
% 2.51/2.63 [417]E(f110(f129(x4171,x4172),f154(x4173,x4172)),f154(f39(x4171,x4173),x4172))
% 2.51/2.63 [418]E(f110(f118(x4181,x4182),f102(x4183,x4182)),f102(f40(x4181,x4183),x4182))
% 2.51/2.63 [419]E(f110(f130(x4191,x4192),f126(x4193,x4192)),f126(f41(x4191,x4193),x4192))
% 2.51/2.63 [395]E(f107(f111(f19(x3951),x3952),x3953),f107(f111(x3951,x3953),x3952))
% 2.51/2.63 [396]E(f107(f136(f20(x3961),x3962),x3963),f154(f108(x3961,x3963),x3962))
% 2.51/2.63 [397]E(f167(f109(f36(x3971),x3972),x3973),f107(f166(x3971,x3973),x3972))
% 2.51/2.63 [398]E(f167(f170(f21(x3981),x3982),x3983),f167(f170(x3981,x3983),x3982))
% 2.51/2.63 [399]E(f167(f148(f22(x3991),x3992),x3993),f102(f165(x3991,x3993),x3992))
% 2.51/2.63 [400]E(f158(f159(f5(x4001),x4002),x4003),f158(f159(x4001,x4003),x4002))
% 2.51/2.63 [401]E(f158(f151(f26(x4011),x4012),x4013),f126(f160(x4011,x4013),x4012))
% 2.51/2.63 [402]E(f154(f117(f27(x4021),x4022),x4023),f154(f117(x4021,x4023),x4022))
% 2.51/2.63 [403]E(f154(f138(f29(x4031),x4032),x4033),f149(f139(x4031,x4033),x4032))
% 2.51/2.63 [404]E(f102(f141(f23(x4041),x4042),x4043),f102(f141(x4041,x4043),x4042))
% 2.51/2.63 [405]E(f102(f145(f30(x4051),x4052),x4053),f132(f146(x4051,x4053),x4052))
% 2.51/2.63 [406]E(f126(f106(f28(x4061),x4062),x4063),f126(f106(x4061,x4063),x4062))
% 2.51/2.63 [407]E(f126(f114(f24(x4071),x4072),x4073),f103(f135(x4071,x4073),x4072))
% 2.51/2.63 [408]E(f149(f119(f31(x4081),x4082),x4083),f149(f119(x4081,x4083),x4082))
% 2.51/2.63 [409]E(f132(f142(f32(x4091),x4092),x4093),f132(f142(x4091,x4093),x4092))
% 2.51/2.63 [410]E(f103(f133(f33(x4101),x4102),x4103),f103(f133(x4101,x4103),x4102))
% 2.51/2.63 [411]E(f127(f115(f35(x4111),x4112),x4113),f127(f115(x4111,x4113),x4112))
% 2.51/2.63 [412]E(f140(f134(f34(x4121),x4122),x4123),f140(f134(x4121,x4123),x4122))
% 2.51/2.63 [413]E(f143(f152(f25(x4131),x4132),x4133),f143(f152(x4131,x4133),x4132))
% 2.51/2.63 [425]E(f164(f213(f164(f213(x4251),x4252)),x4253),f164(f213(f164(f213(x4251),x4253)),x4252))
% 2.51/2.63 [430]E(f164(f213(f164(f213(f164(a226,x4301)),x4302)),f164(a226,x4303)),f164(f213(f164(f213(x4301),x4302)),x4303))
% 2.51/2.63 [438]E(f46(f37(f11(a44,f111(f19(a75),f168(x4381,x4382))),f136(f20(a203),f201(x4381,x4383)))),f201(x4381,f54(f38(f17(a44,f170(f21(a80),x4382)),f148(f22(a200),x4383)))))
% 2.51/2.63 [443]E(f42(f9(a44,f159(f5(a79),x4431)),f151(f26(a211),f42(f9(a44,f159(f5(a79),x4432)),f151(f26(a211),x4433)))),f42(f9(a44,f159(f5(a79),x4432)),f151(f26(a211),f42(f9(a44,f159(f5(a79),x4431)),f151(f26(a211),x4433)))))
% 2.51/2.63 [446]E(f46(f37(f11(a44,f111(f19(a75),x4461)),f136(f20(a203),f46(f37(f11(a44,f111(f19(a75),x4462)),f136(f20(a203),x4463)))))),f46(f37(f11(a44,f111(f19(a75),x4462)),f136(f20(a203),f46(f37(f11(a44,f111(f19(a75),x4461)),f136(f20(a203),x4463)))))))
% 2.51/2.63 [447]E(f54(f38(f17(a44,f170(f21(a80),x4471)),f148(f22(a200),f54(f38(f17(a44,f170(f21(a80),x4472)),f148(f22(a200),x4473)))))),f54(f38(f17(a44,f170(f21(a80),x4472)),f148(f22(a200),f54(f38(f17(a44,f170(f21(a80),x4471)),f148(f22(a200),x4473)))))))
% 2.51/2.63 [453]~P7(x4531)+E(f54(x4531),x4531)
% 2.51/2.63 [454]~P2(x4541)+E(f55(x4541),x4541)
% 2.51/2.63 [455]~P3(x4551)+E(f47(x4551),x4551)
% 2.51/2.63 [456]~P1(x4561)+P1(f46(x4561))
% 2.51/2.63 [457]~P7(x4571)+P7(f54(x4571))
% 2.51/2.63 [458]~P2(x4581)+P2(f55(x4581))
% 2.51/2.63 [459]~P1(x4591)+P2(f224(x4591))
% 2.51/2.63 [460]~P3(x4601)+P3(f47(x4601))
% 2.51/2.63 [461]P5(x4611)+P5(f110(a45,x4611))
% 2.51/2.63 [502]~P5(x5021)+~P5(f110(a45,x5021))
% 2.51/2.63 [582]~P5(f126(a98,x5821))+P5(f103(a82,f106(f28(a217),x5821)))
% 2.51/2.63 [608]~P5(f154(a2,x6081))+P5(f149(a81,f55(f117(f27(a212),x6081))))
% 2.51/2.63 [609]~P5(f102(a97,x6091))+P5(f132(a93,f47(f141(f23(a216),x6091))))
% 2.51/2.63 [610]~P5(f149(a81,x6101))+P5(f127(a83,f52(f119(f31(a218),x6101))))
% 2.51/2.63 [611]~P5(f132(a93,x6111))+P5(f140(a94,f48(f142(f32(a221),x6111))))
% 2.51/2.63 [612]~P5(f103(a82,x6121))+P5(f143(a88,f49(f133(f33(a219),x6121))))
% 2.51/2.63 [613]~P5(f127(a83,x6131))+P5(f104(a84,f50(f115(f35(a223),x6131))))
% 2.51/2.63 [614]~P5(f140(a94,x6141))+P5(f144(a89,f53(f134(f34(a220),x6141))))
% 2.51/2.63 [615]~P5(f143(a88,x6151))+P5(f105(a95,f51(f152(f25(a222),x6151))))
% 2.51/2.63 [462]~P1(x4622)+P1(f6(x4621,x4622))
% 2.51/2.63 [463]~P1(x4632)+P1(f37(x4631,x4632))
% 2.51/2.63 [464]~P1(x4642)+P1(f192(x4641,x4642))
% 2.51/2.63 [465]~P7(x4652)+P1(f201(x4651,x4652))
% 2.51/2.63 [466]~P2(x4662)+P1(f193(x4661,x4662))
% 2.51/2.63 [467]~P3(x4672)+P1(f191(x4671,x4672))
% 2.51/2.63 [468]~P4(x4682)+P1(f111(x4681,x4682))
% 2.51/2.63 [469]~P8(x4692)+P1(f166(x4691,x4692))
% 2.51/2.63 [470]~P1(x4702)+P1(f136(x4701,x4702))
% 2.51/2.63 [471]~P7(x4712)+P7(f7(x4711,x4712))
% 2.51/2.63 [472]~P7(x4722)+P7(f38(x4721,x4722))
% 2.51/2.63 [473]~P1(x4732)+P7(f194(x4731,x4732))
% 2.51/2.63 [474]~P7(x4742)+P7(f205(x4741,x4742))
% 2.51/2.63 [475]~P2(x4752)+P7(f181(x4751,x4752))
% 2.51/2.63 [476]~P3(x4762)+P7(f171(x4761,x4762))
% 2.51/2.63 [477]~P4(x4772)+P7(f109(x4771,x4772))
% 2.51/2.63 [478]~P8(x4782)+P7(f170(x4781,x4782))
% 2.51/2.63 [479]~P7(x4792)+P7(f148(x4791,x4792))
% 2.51/2.63 [480]~P2(x4802)+P2(f10(x4801,x4802))
% 2.51/2.63 [481]~P2(x4812)+P2(f39(x4811,x4812))
% 2.51/2.63 [482]~P7(x4822)+P2(f172(x4821,x4822))
% 2.51/2.63 [483]~P4(x4832)+P2(f108(x4831,x4832))
% 2.51/2.63 [484]~P1(x4842)+P2(f117(x4841,x4842))
% 2.51/2.63 [485]~P2(x4852)+P2(f138(x4851,x4852))
% 2.51/2.63 [486]~P3(x4862)+P3(f13(x4861,x4862))
% 2.51/2.63 [487]~P3(x4872)+P3(f40(x4871,x4872))
% 2.51/2.63 [488]~P7(x4882)+P3(f188(x4881,x4882))
% 2.51/2.63 [489]~P8(x4892)+P3(f165(x4891,x4892))
% 2.51/2.63 [490]~P7(x4902)+P3(f141(x4901,x4902))
% 2.51/2.63 [491]~P3(x4912)+P3(f145(x4911,x4912))
% 2.51/2.63 [492]~P8(x4922)+P4(f168(x4921,x4922))
% 2.51/2.63 [493]~P6(x4932)+P6(f110(x4931,x4932))
% 2.51/2.63 [494]~P2(x4942)+P6(f149(x4941,x4942))
% 2.51/2.63 [495]~P3(x4952)+P6(f132(x4951,x4952))
% 2.51/2.63 [497]E(x4971,x4972)+~E(f164(a226,x4971),f164(a226,x4972))
% 2.51/2.63 [503]~E(x5031,x5032)+P5(f107(f111(a75,x5031),x5032))
% 2.51/2.63 [504]~E(x5041,x5042)+P5(f167(f170(a80,x5041),x5042))
% 2.51/2.63 [505]~E(x5051,x5052)+P5(f158(f159(a199,x5051),x5052))
% 2.51/2.63 [506]~E(x5061,x5062)+P5(f158(f159(a79,x5061),x5062))
% 2.51/2.63 [507]~E(x5072,x5071)+P5(f154(f117(a212,x5071),x5072))
% 2.51/2.63 [510]~E(x5101,x5102)+P5(f154(f117(a212,x5101),x5102))
% 2.51/2.63 [511]~E(x5111,x5112)+P5(f154(f117(a77,x5111),x5112))
% 2.51/2.63 [512]~E(x5122,x5121)+P5(f102(f141(a216,x5121),x5122))
% 2.51/2.63 [515]~E(x5151,x5152)+P5(f102(f141(a216,x5151),x5152))
% 2.51/2.63 [516]~E(x5161,x5162)+P5(f102(f141(a76,x5161),x5162))
% 2.51/2.63 [517]~E(x5172,x5171)+P5(f126(f106(a217,x5171),x5172))
% 2.51/2.63 [522]~E(x5221,x5222)+P5(f126(f106(a217,x5221),x5222))
% 2.51/2.63 [523]~E(x5231,x5232)+P5(f126(f106(a74,x5231),x5232))
% 2.51/2.63 [524]P5(x5241)+P5(f110(f112(a78,x5241),x5242))
% 2.51/2.63 [525]~P5(x5252)+P5(f110(f112(a44,x5251),x5252))
% 2.51/2.63 [526]~P5(x5261)+P5(f110(f112(a44,x5261),x5262))
% 2.51/2.63 [527]~P5(x5272)+P5(f110(f112(a78,x5271),x5272))
% 2.51/2.63 [533]P4(f56(x5331,x5332))+P5(f154(f117(a212,x5332),x5331))
% 2.51/2.63 [534]P8(f58(x5341,x5342))+P5(f102(f141(a216,x5342),x5341))
% 2.51/2.63 [535]E(x5351,x5352)+~P5(f158(f159(a79,x5351),x5352))
% 2.51/2.63 [536]E(x5361,x5362)+~P5(f126(f106(a74,x5361),x5362))
% 2.51/2.63 [537]~P5(f154(a2,x5372))+P5(f154(a2,f192(x5371,x5372)))
% 2.51/2.63 [538]~P5(f102(a97,x5382))+P5(f154(a2,f201(x5381,x5382)))
% 2.51/2.63 [539]~P5(f126(a98,x5392))+P5(f154(a2,f120(x5391,x5392)))
% 2.51/2.63 [540]~P5(f149(a81,x5402))+P5(f154(a2,f193(x5401,x5402)))
% 2.51/2.63 [541]~P5(f132(a93,x5412))+P5(f154(a2,f191(x5411,x5412)))
% 2.51/2.63 [542]~P5(f103(a82,x5422))+P5(f154(a2,f121(x5421,x5422)))
% 2.51/2.63 [543]~P5(f154(a2,x5432))+P5(f102(a97,f194(x5431,x5432)))
% 2.51/2.63 [544]~P5(f102(a97,x5442))+P5(f102(a97,f205(x5441,x5442)))
% 2.51/2.63 [545]~P5(f126(a98,x5452))+P5(f102(a97,f197(x5451,x5452)))
% 2.51/2.63 [546]~P5(f149(a81,x5462))+P5(f102(a97,f181(x5461,x5462)))
% 2.51/2.63 [547]~P5(f132(a93,x5472))+P5(f102(a97,f171(x5471,x5472)))
% 2.51/2.63 [548]~P5(f103(a82,x5482))+P5(f102(a97,f161(x5481,x5482)))
% 2.51/2.63 [549]~P5(f127(a83,x5492))+P5(f102(a97,f190(x5491,x5492)))
% 2.51/2.63 [550]~P5(f140(a94,x5502))+P5(f102(a97,f162(x5501,x5502)))
% 2.51/2.63 [551]~P5(f143(a88,x5512))+P5(f102(a97,f163(x5511,x5512)))
% 2.51/2.63 [552]~P5(f143(a88,x5522))+P5(f126(a98,f184(x5521,x5522)))
% 2.51/2.63 [553]~P5(f140(a94,x5532))+P5(f126(a98,f173(x5531,x5532)))
% 2.51/2.63 [554]~P5(f127(a83,x5542))+P5(f126(a98,f182(x5541,x5542)))
% 2.51/2.63 [555]~P5(f149(a81,x5552))+P5(f126(a98,f196(x5551,x5552)))
% 2.51/2.63 [556]~P5(f132(a93,x5562))+P5(f126(a98,f176(x5561,x5562)))
% 2.51/2.63 [557]~P5(f103(a82,x5572))+P5(f126(a98,f189(x5571,x5572)))
% 2.51/2.63 [558]~P5(f154(a2,x5582))+P5(f126(a98,f195(x5581,x5582)))
% 2.51/2.63 [559]~P5(f102(a97,x5592))+P5(f126(a98,f206(x5591,x5592)))
% 2.51/2.63 [560]~P5(f102(a97,x5602))+P5(f149(a81,f172(x5601,x5602)))
% 2.51/2.63 [561]~P5(f126(a98,x5612))+P5(f149(a81,f198(x5611,x5612)))
% 2.51/2.63 [562]~P5(f102(a97,x5622))+P5(f132(a93,f188(x5621,x5622)))
% 2.51/2.63 [563]~P5(f126(a98,x5632))+P5(f132(a93,f178(x5631,x5632)))
% 2.51/2.63 [564]~P5(f126(a98,x5642))+P5(f103(a82,f185(x5641,x5642)))
% 2.51/2.63 [565]~P5(f102(a97,x5652))+P5(f103(a82,f186(x5651,x5652)))
% 2.51/2.63 [566]~P5(f126(a98,x5662))+P5(f127(a83,f174(x5661,x5662)))
% 2.51/2.63 [567]~P5(f102(a97,x5672))+P5(f127(a83,f177(x5671,x5672)))
% 2.51/2.63 [568]~P5(f127(a83,x5682))+P5(f127(a83,f207(x5681,x5682)))
% 2.51/2.63 [569]~P5(f126(a98,x5692))+P5(f140(a94,f183(x5691,x5692)))
% 2.51/2.63 [570]~P5(f102(a97,x5702))+P5(f140(a94,f179(x5701,x5702)))
% 2.51/2.63 [571]~P5(f140(a94,x5712))+P5(f140(a94,f208(x5711,x5712)))
% 2.51/2.63 [572]~P5(f126(a98,x5722))+P5(f143(a88,f180(x5721,x5722)))
% 2.51/2.63 [573]~P5(f102(a97,x5732))+P5(f143(a88,f175(x5731,x5732)))
% 2.51/2.63 [574]~P5(f143(a88,x5742))+P5(f143(a88,f209(x5741,x5742)))
% 2.51/2.63 [575]~P5(f107(x5752,x5751))+P5(f154(f108(a203,x5751),x5752))
% 2.51/2.63 [576]~P5(f167(x5762,x5761))+P5(f102(f165(a200,x5761),x5762))
% 2.51/2.63 [577]~P5(f158(x5772,x5771))+P5(f126(f160(a211,x5771),x5772))
% 2.51/2.63 [578]P5(x5781)+~P5(f110(f112(a73,x5782),x5781))
% 2.51/2.63 [579]P5(x5791)+~P5(f110(f112(a73,x5791),x5792))
% 2.51/2.63 [588]P5(f107(x5881,x5882))+~P5(f154(f108(a203,x5882),x5881))
% 2.51/2.63 [589]P5(f167(x5891,x5892))+~P5(f102(f165(a200,x5892),x5891))
% 2.51/2.63 [590]P5(f158(x5901,x5902))+~P5(f126(f160(a211,x5902),x5901))
% 2.51/2.63 [591]P5(f158(f159(a199,x5912),x5911))+P5(f158(f159(a199,x5911),x5912))
% 2.51/2.63 [592]P5(f154(f224(x5921),x5922))+~P5(f154(f117(a212,x5922),x5921))
% 2.51/2.63 [622]~P5(f158(f159(a199,x6221),x6222))+P5(f158(f159(a199,x6221),f164(a226,x6222)))
% 2.51/2.63 [676]~P5(f158(f159(a199,x6761),x6762))+P5(f158(f159(a199,f164(a226,x6761)),f164(a226,x6762)))
% 2.51/2.63 [703]P5(f158(f159(a199,x7031),x7032))+~P5(f158(f159(a199,f164(a226,x7031)),f164(a226,x7032)))
% 2.51/2.63 [716]~P5(f149(a81,x7162))+P5(f158(f159(a199,f128(a4,f196(x7161,x7162))),f137(a86,x7162)))
% 2.51/2.63 [717]~P5(f132(a93,x7172))+P5(f158(f159(a199,f128(a4,f176(x7171,x7172))),f147(a85,x7172)))
% 2.51/2.63 [718]~P5(f103(a82,x7182))+P5(f158(f159(a199,f128(a4,f189(x7181,x7182))),f150(a91,x7182)))
% 2.51/2.63 [719]~P5(f154(a2,x7192))+P5(f158(f159(a199,f128(a4,f195(x7191,x7192))),f157(a43,x7192)))
% 2.51/2.63 [720]~P5(f102(a97,x7202))+P5(f158(f159(a199,f128(a4,f206(x7201,x7202))),f153(a96,x7202)))
% 2.51/2.63 [721]~P5(f154(a2,x7212))+P5(f158(f159(a199,f153(a96,f194(x7211,x7212))),f157(a43,x7212)))
% 2.51/2.63 [722]~P5(f102(a97,x7222))+P5(f158(f159(a199,f153(a96,f205(x7221,x7222))),f153(a96,x7222)))
% 2.51/2.63 [723]~P5(f126(a98,x7232))+P5(f158(f159(a199,f153(a96,f197(x7231,x7232))),f128(a4,x7232)))
% 2.51/2.63 [724]~P5(f149(a81,x7242))+P5(f158(f159(a199,f153(a96,f181(x7241,x7242))),f137(a86,x7242)))
% 2.51/2.63 [725]~P5(f132(a93,x7252))+P5(f158(f159(a199,f153(a96,f171(x7251,x7252))),f147(a85,x7252)))
% 2.51/2.63 [726]~P5(f103(a82,x7262))+P5(f158(f159(a199,f153(a96,f161(x7261,x7262))),f150(a91,x7262)))
% 2.51/2.63 [727]~P5(f154(a2,x7272))+P5(f158(f159(a199,f157(a43,f192(x7271,x7272))),f157(a43,x7272)))
% 2.51/2.63 [728]~P5(f102(a97,x7282))+P5(f158(f159(a199,f157(a43,f201(x7281,x7282))),f153(a96,x7282)))
% 2.51/2.63 [729]~P5(f126(a98,x7292))+P5(f158(f159(a199,f157(a43,f120(x7291,x7292))),f128(a4,x7292)))
% 2.51/2.63 [730]~P5(f149(a81,x7302))+P5(f158(f159(a199,f157(a43,f193(x7301,x7302))),f137(a86,x7302)))
% 2.51/2.63 [731]~P5(f132(a93,x7312))+P5(f158(f159(a199,f157(a43,f191(x7311,x7312))),f147(a85,x7312)))
% 2.51/2.63 [732]~P5(f103(a82,x7322))+P5(f158(f159(a199,f157(a43,f121(x7321,x7322))),f150(a91,x7322)))
% 2.51/2.63 [733]~P5(f127(a83,x7332))+P5(f158(f159(a199,f157(a43,f122(x7331,x7332))),f116(a90,x7332)))
% 2.51/2.63 [734]~P5(f140(a94,x7342))+P5(f158(f159(a199,f157(a43,f123(x7341,x7342))),f155(a92,x7342)))
% 2.51/2.63 [735]~P5(f143(a88,x7352))+P5(f158(f159(a199,f157(a43,f187(x7351,x7352))),f131(a87,x7352)))
% 2.51/2.63 [736]~P5(f126(a98,x7362))+P5(f158(f159(a199,f150(a91,f185(x7361,x7362))),f128(a4,x7362)))
% 2.51/2.63 [737]~P5(f102(a97,x7372))+P5(f158(f159(a199,f150(a91,f186(x7371,x7372))),f153(a96,x7372)))
% 2.51/2.63 [738]~P5(f102(a97,x7382))+P5(f158(f159(a199,f147(a85,f188(x7381,x7382))),f153(a96,x7382)))
% 2.51/2.63 [739]~P5(f126(a98,x7392))+P5(f158(f159(a199,f147(a85,f178(x7391,x7392))),f128(a4,x7392)))
% 2.51/2.63 [740]~P5(f102(a97,x7402))+P5(f158(f159(a199,f137(a86,f172(x7401,x7402))),f153(a96,x7402)))
% 2.51/2.63 [741]~P5(f126(a98,x7412))+P5(f158(f159(a199,f137(a86,f198(x7411,x7412))),f128(a4,x7412)))
% 2.51/2.63 [593]E(f164(f213(x5931),f164(f213(x5931),x5932)),x5932)+~P5(f158(f159(a199,x5932),x5931))
% 2.51/2.63 [607]P5(f126(a98,x6071))+P5(f126(f160(a211,f60(x6071,x6072)),x6071))
% 2.51/2.63 [616]~P5(f126(a98,x6162))+P5(f126(a98,f42(f9(a73,x6161),x6162)))
% 2.51/2.63 [617]~P5(f126(a98,x6171))+P5(f126(a98,f42(f9(a73,x6171),x6172)))
% 2.51/2.63 [618]~P5(f103(a82,x6182))+P5(f103(a82,f41(f16(a73,x6181),x6182)))
% 2.51/2.63 [619]~P5(f103(a82,x6191))+P5(f103(a82,f41(f16(a73,x6191),x6192)))
% 2.51/2.63 [620]E(f164(f213(f164(a226,x6201)),x6202),f164(a226,f164(f213(x6201),x6202)))+~P5(f158(f159(a199,x6202),x6201))
% 2.51/2.63 [626]P5(f158(f159(a199,x6261),x6262))+P5(f158(f159(a199,f164(a226,x6262)),x6261))
% 2.51/2.63 [628]E(f42(f9(a44,f159(f5(a79),x6281)),f151(f26(a211),x6282)),x6282)+~P5(f126(f160(a211,x6281),x6282))
% 2.51/2.63 [629]P5(f154(f117(a212,x6291),x6292))+P5(f154(f108(a203,f56(x6292,x6291)),x6291))
% 2.51/2.63 [630]P5(f102(f141(a216,x6301),x6302))+P5(f102(f165(a200,f58(x6302,x6301)),x6301))
% 2.51/2.63 [631]P5(f126(f106(a217,x6311),x6312))+P5(f126(f160(a211,f57(x6312,x6311)),x6311))
% 2.51/2.63 [646]P5(f126(a98,x6461))+~P5(f126(a98,f42(f9(a44,x6462),x6461)))
% 2.51/2.63 [647]P5(f126(a98,x6471))+~P5(f126(a98,f42(f9(a44,x6471),x6472)))
% 2.51/2.63 [648]P5(f103(a82,x6481))+~P5(f103(a82,f41(f16(a44,x6482),x6481)))
% 2.51/2.63 [649]P5(f103(a82,x6491))+~P5(f103(a82,f41(f16(a44,x6491),x6492)))
% 2.51/2.63 [650]E(f164(a226,f63(x6501,x6502)),x6502)+~P5(f158(f159(a199,f164(a226,x6501)),x6502))
% 2.51/2.63 [652]P5(f126(a98,x6521))+~P5(f158(f159(a199,f60(x6521,x6522)),x6522))
% 2.51/2.63 [677]P5(f158(f159(a199,x6771),x6772))+~P5(f158(f159(a199,f164(a226,x6771)),x6772))
% 2.51/2.63 [680]P5(f154(f117(a212,x6801),x6802))+~P5(f154(f108(a203,f56(x6802,x6801)),x6802))
% 2.51/2.63 [681]P5(f102(f141(a216,x6811),x6812))+~P5(f102(f165(a200,f58(x6812,x6811)),x6812))
% 2.51/2.63 [682]P5(f126(f106(a217,x6821),x6822))+~P5(f126(f160(a211,f57(x6822,x6821)),x6822))
% 2.51/2.63 [691]~P5(f158(f159(a199,x6911),x6912))+~P5(f158(f159(a199,f164(a226,x6912)),x6911))
% 2.51/2.63 [692]~P5(f154(a2,f46(x6922)))+P5(f154(a2,f46(f37(f11(a73,x6921),x6922))))
% 2.51/2.63 [693]~P5(f154(a2,f46(x6931)))+P5(f154(a2,f46(f37(f11(a73,x6931),x6932))))
% 2.51/2.63 [694]~P5(f102(a97,f54(x6942)))+P5(f102(a97,f54(f38(f17(a73,x6941),x6942))))
% 2.51/2.63 [695]~P5(f102(a97,f54(x6951)))+P5(f102(a97,f54(f38(f17(a73,x6951),x6952))))
% 2.51/2.63 [696]~P5(f149(a81,f55(x6962)))+P5(f149(a81,f55(f39(f15(a73,x6961),x6962))))
% 2.51/2.63 [697]~P5(f149(a81,f55(x6971)))+P5(f149(a81,f55(f39(f15(a73,x6971),x6972))))
% 2.51/2.63 [698]~P5(f132(a93,f47(x6982)))+P5(f132(a93,f47(f40(f12(a73,x6981),x6982))))
% 2.51/2.63 [699]~P5(f132(a93,f47(x6991)))+P5(f132(a93,f47(f40(f12(a73,x6991),x6992))))
% 2.51/2.63 [750]P5(f154(a2,f46(x7501)))+~P5(f154(a2,f46(f37(f11(a44,x7502),x7501))))
% 2.51/2.63 [751]P5(f154(a2,f46(x7511)))+~P5(f154(a2,f46(f37(f11(a44,x7511),x7512))))
% 2.51/2.63 [752]P5(f102(a97,f54(x7521)))+~P5(f102(a97,f54(f38(f17(a44,x7522),x7521))))
% 2.51/2.63 [753]P5(f102(a97,f54(x7531)))+~P5(f102(a97,f54(f38(f17(a44,x7531),x7532))))
% 2.51/2.63 [754]P5(f149(a81,f55(x7541)))+~P5(f149(a81,f55(f39(f15(a44,x7542),x7541))))
% 2.51/2.63 [755]P5(f149(a81,f55(x7551)))+~P5(f149(a81,f55(f39(f15(a44,x7551),x7552))))
% 2.51/2.63 [756]P5(f132(a93,f47(x7561)))+~P5(f132(a93,f47(f40(f12(a44,x7562),x7561))))
% 2.51/2.63 [757]P5(f132(a93,f47(x7571)))+~P5(f132(a93,f47(f40(f12(a44,x7571),x7572))))
% 2.51/2.63 [765]~P5(f126(a98,x7652))+P5(f126(a98,f42(f9(a44,f159(f5(a79),x7651)),f151(f26(a211),x7652))))
% 2.51/2.63 [767]~P5(f103(a82,x7672))+P5(f103(a82,f41(f16(a44,f106(f28(a74),x7671)),f114(f24(a202),x7672))))
% 2.51/2.63 [797]P5(f126(a98,x7971))+~P5(f126(a98,f42(f9(a44,f159(f5(a79),x7972)),f151(f26(a211),x7971))))
% 2.51/2.63 [798]P5(f103(a82,x7981))+~P5(f103(a82,f41(f16(a44,f106(f28(a74),x7982)),f114(f24(a202),x7981))))
% 2.51/2.63 [808]~P5(f154(a2,x8082))+P5(f154(a2,f46(f37(f11(a44,f111(f19(a75),x8081)),f136(f20(a203),x8082)))))
% 2.51/2.63 [810]~P5(f102(a97,x8102))+P5(f102(a97,f54(f38(f17(a44,f170(f21(a80),x8101)),f148(f22(a200),x8102)))))
% 2.51/2.63 [812]~P5(f149(a81,x8122))+P5(f149(a81,f55(f39(f15(a44,f117(f27(a77),x8121)),f138(f29(a210),x8122)))))
% 2.51/2.63 [814]~P5(f132(a93,x8142))+P5(f132(a93,f47(f40(f12(a44,f141(f23(a76),x8141)),f145(f30(a204),x8142)))))
% 2.51/2.63 [829]~P5(f126(a98,x8291))+P5(f158(f159(a199,f128(a4,x8291)),f128(a4,f42(f9(a44,f159(f5(a79),x8292)),f151(f26(a211),x8291)))))
% 2.51/2.63 [830]~P5(f103(a82,x8301))+P5(f158(f159(a199,f150(a91,x8301)),f150(a91,f41(f16(a44,f106(f28(a74),x8302)),f114(f24(a202),x8301)))))
% 2.51/2.63 [834]P5(f154(a2,x8341))+~P5(f154(a2,f46(f37(f11(a44,f111(f19(a75),x8342)),f136(f20(a203),x8341)))))
% 2.51/2.63 [835]P5(f102(a97,x8351))+~P5(f102(a97,f54(f38(f17(a44,f170(f21(a80),x8352)),f148(f22(a200),x8351)))))
% 2.51/2.63 [836]P5(f149(a81,x8361))+~P5(f149(a81,f55(f39(f15(a44,f117(f27(a77),x8362)),f138(f29(a210),x8361)))))
% 2.51/2.63 [837]P5(f132(a93,x8371))+~P5(f132(a93,f47(f40(f12(a44,f141(f23(a76),x8372)),f145(f30(a204),x8371)))))
% 2.51/2.63 [850]~P5(f102(a97,x8501))+P5(f158(f159(a199,f153(a96,x8501)),f153(a96,f54(f38(f17(a44,f170(f21(a80),x8502)),f148(f22(a200),x8501))))))
% 2.51/2.63 [851]~P5(f154(a2,x8511))+P5(f158(f159(a199,f157(a43,x8511)),f157(a43,f46(f37(f11(a44,f111(f19(a75),x8512)),f136(f20(a203),x8511))))))
% 2.51/2.63 [852]~P5(f132(a93,x8521))+P5(f158(f159(a199,f147(a85,x8521)),f147(a85,f47(f40(f12(a44,f141(f23(a76),x8522)),f145(f30(a204),x8521))))))
% 2.51/2.63 [853]~P5(f149(a81,x8531))+P5(f158(f159(a199,f137(a86,x8531)),f137(a86,f55(f39(f15(a44,f117(f27(a77),x8532)),f138(f29(a210),x8531))))))
% 2.51/2.63 [678]~P5(f102(f165(a200,x6782),x6783))+P5(f154(f108(a203,f168(x6781,x6782)),f201(x6781,x6783)))
% 2.51/2.63 [679]~P5(f102(f141(a216,x6792),x6793))+P5(f154(f117(a212,f201(x6791,x6792)),f201(x6791,x6793)))
% 2.51/2.63 [645]P8(f62(x6451,x6452,x6453))+P5(f154(f117(a212,f201(x6451,x6453)),x6452))
% 2.51/2.63 [704]~P5(f158(f159(a199,x7043),x7042))+P5(f158(f159(a199,f164(f213(x7041),x7042)),f164(f213(x7041),x7043)))
% 2.51/2.63 [705]~P5(f158(f159(a199,x7051),x7053))+P5(f158(f159(a199,f164(f213(x7051),x7052)),f164(f213(x7053),x7052)))
% 2.51/2.63 [773]P5(f102(f165(a200,f62(x7731,x7733,x7732)),x7732))+P5(f154(f117(a212,f201(x7731,x7732)),x7733))
% 2.51/2.63 [762]~E(x7621,x7623)+P5(f158(f42(f9(a44,f159(f5(a79),x7621)),f151(f26(a211),x7622)),x7623))
% 2.51/2.63 [768]~P5(f158(x7682,x7683))+P5(f158(f42(f9(a44,f159(f5(a79),x7681)),f151(f26(a211),x7682)),x7683))
% 2.51/2.63 [770]~E(x7701,x7702)+P5(f126(f160(a211,x7701),f42(f9(a44,f159(f5(a79),x7702)),f151(f26(a211),x7703))))
% 2.51/2.63 [785]E(f46(f37(f11(a44,f111(f19(a75),f168(x7851,x7852))),f136(f20(a203),f201(x7851,x7853)))),f201(x7851,x7853))+~P5(f102(f165(a200,x7852),x7853))
% 2.51/2.63 [790]~P5(f126(f106(a217,x7901),x7903))+P5(f126(f106(a217,x7901),f42(f9(a44,f159(f5(a79),x7902)),f151(f26(a211),x7903))))
% 2.51/2.63 [793]~P5(f126(f160(a211,x7931),x7933))+P5(f126(f160(a211,x7931),f42(f9(a44,f159(f5(a79),x7932)),f151(f26(a211),x7933))))
% 2.51/2.63 [840]~P5(f126(f106(a217,x8402),x8403))+P5(f126(f106(a217,f42(f9(a44,f159(f5(a79),x8401)),f151(f26(a211),x8402))),f42(f9(a44,f159(f5(a79),x8401)),f151(f26(a211),x8403))))
% 2.51/2.63 [841]P5(f154(f117(a212,f201(x8411,x8412)),x8413))+~P5(f154(f108(a203,f168(x8411,f62(x8411,x8413,x8412))),x8413))
% 2.51/2.63 [815]~E(x8151,x8152)+P5(f154(f108(a203,x8151),f46(f37(f11(a44,f111(f19(a75),x8152)),f136(f20(a203),x8153)))))
% 2.51/2.63 [816]~E(x8161,x8162)+P5(f102(f165(a200,x8161),f54(f38(f17(a44,f170(f21(a80),x8162)),f148(f22(a200),x8163)))))
% 2.51/2.63 [822]~P5(f154(f108(a203,x8221),x8223))+P5(f154(f108(a203,x8221),f46(f37(f11(a44,f111(f19(a75),x8222)),f136(f20(a203),x8223)))))
% 2.51/2.63 [823]~P5(f154(f117(a212,x8231),x8233))+P5(f154(f117(a212,x8231),f46(f37(f11(a44,f111(f19(a75),x8232)),f136(f20(a203),x8233)))))
% 2.51/2.63 [825]~P5(f102(f165(a200,x8251),x8253))+P5(f102(f165(a200,x8251),f54(f38(f17(a44,f170(f21(a80),x8252)),f148(f22(a200),x8253)))))
% 2.51/2.63 [826]~P5(f102(f141(a216,x8261),x8263))+P5(f102(f141(a216,x8261),f54(f38(f17(a44,f170(f21(a80),x8262)),f148(f22(a200),x8263)))))
% 2.51/2.63 [842]P5(f126(f106(a217,x8421),x8422))+~P5(f126(f106(a217,f42(f9(a44,f159(f5(a79),x8423)),f151(f26(a211),x8421))),x8422))
% 2.51/2.63 [843]P5(f126(f160(a211,x8431),x8432))+~P5(f126(f106(a217,f42(f9(a44,f159(f5(a79),x8431)),f151(f26(a211),x8433))),x8432))
% 2.51/2.63 [856]~P5(f154(f117(a212,x8562),x8563))+P5(f154(f117(a212,f46(f37(f11(a44,f111(f19(a75),x8561)),f136(f20(a203),x8562)))),f46(f37(f11(a44,f111(f19(a75),x8561)),f136(f20(a203),x8563)))))
% 2.51/2.63 [857]~P5(f102(f141(a216,x8572),x8573))+P5(f102(f141(a216,f54(f38(f17(a44,f170(f21(a80),x8571)),f148(f22(a200),x8572)))),f54(f38(f17(a44,f170(f21(a80),x8571)),f148(f22(a200),x8573)))))
% 2.51/2.63 [862]P5(f154(f108(a203,x8621),x8622))+~P5(f154(f117(a212,f46(f37(f11(a44,f111(f19(a75),x8621)),f136(f20(a203),x8623)))),x8622))
% 2.51/2.63 [863]P5(f154(f117(a212,x8631),x8632))+~P5(f154(f117(a212,f46(f37(f11(a44,f111(f19(a75),x8633)),f136(f20(a203),x8631)))),x8632))
% 2.51/2.63 [864]P5(f102(f165(a200,x8641),x8642))+~P5(f102(f141(a216,f54(f38(f17(a44,f170(f21(a80),x8641)),f148(f22(a200),x8643)))),x8642))
% 2.51/2.63 [865]P5(f102(f141(a216,x8651),x8652))+~P5(f102(f141(a216,f54(f38(f17(a44,f170(f21(a80),x8653)),f148(f22(a200),x8651)))),x8652))
% 2.51/2.63 [498]~P1(x4981)+~P4(x4982)+P6(f107(x4981,x4982))
% 2.51/2.63 [499]~P7(x4991)+~P8(x4992)+P6(f167(x4991,x4992))
% 2.51/2.63 [500]~P1(x5002)+~P2(x5001)+P6(f154(x5001,x5002))
% 2.51/2.63 [501]~P7(x5012)+~P3(x5011)+P6(f102(x5011,x5012))
% 2.51/2.63 [528]~P5(x5282)+~P5(x5281)+P5(f110(f112(a73,x5281),x5282))
% 2.51/2.63 [580]P5(x5801)+P5(x5802)+~P5(f110(f112(a44,x5802),x5801))
% 2.51/2.63 [581]P5(x5811)+~P5(x5812)+~P5(f110(f112(a78,x5812),x5811))
% 2.51/2.63 [594]P8(f59(x5941,x5942))+P5(f102(a97,x5942))+~P5(f154(a2,f201(x5941,x5942)))
% 2.51/2.63 [596]P5(f154(a2,x5961))+~P5(f154(a2,x5962))+~P5(f154(f117(a212,x5961),x5962))
% 2.51/2.63 [598]P5(f102(a97,x5981))+~P5(f102(a97,x5982))+~P5(f102(f141(a216,x5981),x5982))
% 2.51/2.63 [600]P5(f126(a98,x6001))+~P5(f126(a98,x6002))+~P5(f126(f106(a217,x6001),x6002))
% 2.51/2.63 [602]P5(f149(a81,x6021))+~P5(f149(a81,x6022))+~P5(f149(f119(a218,x6021),x6022))
% 2.51/2.63 [604]P5(f132(a93,x6041))+~P5(f132(a93,x6042))+~P5(f132(f142(a221,x6041),x6042))
% 2.51/2.63 [606]P5(f103(a82,x6061))+~P5(f103(a82,x6062))+~P5(f103(f133(a219,x6061),x6062))
% 2.51/2.63 [623]E(x6231,x6232)+~P5(f158(f159(a199,x6232),x6231))+~P5(f158(f159(a199,x6231),x6232))
% 2.51/2.63 [625]E(x6251,x6252)+~P5(f126(f106(a217,x6252),x6251))+~P5(f126(f106(a217,x6251),x6252))
% 2.51/2.63 [627]~P5(f126(a98,x6272))+~P5(f126(f160(a211,x6271),x6272))+P5(f158(f159(a199,x6271),f61(x6272)))
% 2.51/2.63 [642]E(x6421,f164(a226,x6422))+P5(f158(f159(a199,x6421),x6422))+~P5(f158(f159(a199,x6421),f164(a226,x6422)))
% 2.51/2.63 [685]~P5(f126(a98,x6852))+~P5(f126(f106(a217,x6851),x6852))+P5(f158(f159(a199,f128(a4,x6851)),f128(a4,x6852)))
% 2.51/2.63 [686]~P5(f102(a97,x6862))+~P5(f102(f141(a216,x6861),x6862))+P5(f158(f159(a199,f153(a96,x6861)),f153(a96,x6862)))
% 2.51/2.63 [687]~P5(f154(a2,x6872))+~P5(f154(f117(a212,x6871),x6872))+P5(f158(f159(a199,f157(a43,x6871)),f157(a43,x6872)))
% 2.51/2.63 [688]~P5(f103(a82,x6882))+~P5(f103(f133(a219,x6881),x6882))+P5(f158(f159(a199,f150(a91,x6881)),f150(a91,x6882)))
% 2.51/2.63 [689]~P5(f132(a93,x6892))+~P5(f132(f142(a221,x6891),x6892))+P5(f158(f159(a199,f147(a85,x6891)),f147(a85,x6892)))
% 2.51/2.63 [690]~P5(f149(a81,x6902))+~P5(f149(f119(a218,x6901),x6902))+P5(f158(f159(a199,f137(a86,x6901)),f137(a86,x6902)))
% 2.51/2.63 [636]~P5(f126(a98,x6362))+~P5(f126(a98,x6361))+P5(f126(a98,f42(f9(a44,x6361),x6362)))
% 2.51/2.63 [637]~P5(f103(a82,x6372))+~P5(f103(a82,x6371))+P5(f103(a82,f41(f16(a44,x6371),x6372)))
% 2.51/2.63 [675]P5(f102(a97,x6751))+~P5(f154(a2,f201(x6752,x6751)))+P5(f102(f165(a200,f59(x6752,x6751)),x6751))
% 2.51/2.63 [701]~P1(x7012)+E(f46(f37(f11(a44,f111(f19(a75),x7011)),f136(f20(a203),x7012))),x7012)+~P5(f154(f108(a203,x7011),x7012))
% 2.51/2.63 [702]~P7(x7022)+E(f54(f38(f17(a44,f170(f21(a80),x7021)),f148(f22(a200),x7022))),x7022)+~P5(f102(f165(a200,x7021),x7022))
% 2.51/2.63 [707]~P5(f126(a98,x7072))+P5(f126(f160(a211,x7071),x7072))+E(f128(a4,f42(f9(a44,f159(f5(a79),x7071)),f151(f26(a211),x7072))),f164(a226,f128(a4,x7072)))
% 2.51/2.63 [709]~P5(f103(a82,x7092))+P5(f103(f135(a202,x7091),x7092))+E(f150(a91,f41(f16(a44,f106(f28(a74),x7091)),f114(f24(a202),x7092))),f164(a226,f150(a91,x7092)))
% 2.51/2.63 [710]~P5(f154(a2,f46(x7102)))+~P5(f154(a2,f46(x7101)))+P5(f154(a2,f46(f37(f11(a44,x7101),x7102))))
% 2.51/2.63 [711]~P5(f102(a97,f54(x7112)))+~P5(f102(a97,f54(x7111)))+P5(f102(a97,f54(f38(f17(a44,x7111),x7112))))
% 2.51/2.63 [712]~P5(f149(a81,f55(x7122)))+~P5(f149(a81,f55(x7121)))+P5(f149(a81,f55(f39(f15(a44,x7121),x7122))))
% 2.51/2.63 [713]~P5(f132(a93,f47(x7132)))+~P5(f132(a93,f47(x7131)))+P5(f132(a93,f47(f40(f12(a44,x7131),x7132))))
% 2.51/2.63 [714]~P5(f126(a98,x7142))+~P5(f126(f160(a211,x7141),x7142))+E(f128(a4,f42(f9(a44,f159(f5(a79),x7141)),f151(f26(a211),x7142))),f128(a4,x7142))
% 2.51/2.63 [715]~P5(f103(a82,x7152))+~P5(f103(f135(a202,x7151),x7152))+E(f150(a91,f41(f16(a44,f106(f28(a74),x7151)),f114(f24(a202),x7152))),f150(a91,x7152))
% 2.51/2.63 [758]~P1(x7582)+~P4(x7581)+P1(f46(f37(f11(a44,f111(f19(a75),x7581)),f136(f20(a203),x7582))))
% 2.51/2.63 [759]~P7(x7592)+~P8(x7591)+P7(f54(f38(f17(a44,f170(f21(a80),x7591)),f148(f22(a200),x7592))))
% 2.51/2.63 [760]~P1(x7601)+~P2(x7602)+P2(f55(f39(f15(a44,f117(f27(a77),x7601)),f138(f29(a210),x7602))))
% 2.51/2.63 [761]~P7(x7611)+~P3(x7612)+P3(f47(f40(f12(a44,f141(f23(a76),x7611)),f145(f30(a204),x7612))))
% 2.51/2.63 [775]~P5(f102(a97,x7752))+P5(f102(f165(a200,x7751),x7752))+E(f153(a96,f54(f38(f17(a44,f170(f21(a80),x7751)),f148(f22(a200),x7752)))),f164(a226,f153(a96,x7752)))
% 2.51/2.63 [777]~P5(f154(a2,x7772))+P5(f154(f108(a203,x7771),x7772))+E(f157(a43,f46(f37(f11(a44,f111(f19(a75),x7771)),f136(f20(a203),x7772)))),f164(a226,f157(a43,x7772)))
% 2.51/2.63 [779]~P5(f132(a93,x7792))+P5(f132(f146(a204,x7791),x7792))+E(f147(a85,f47(f40(f12(a44,f141(f23(a76),x7791)),f145(f30(a204),x7792)))),f164(a226,f147(a85,x7792)))
% 2.51/2.63 [781]~P5(f149(a81,x7812))+P5(f149(f139(a210,x7811),x7812))+E(f137(a86,f55(f39(f15(a44,f117(f27(a77),x7811)),f138(f29(a210),x7812)))),f164(a226,f137(a86,x7812)))
% 2.51/2.63 [786]~P5(f102(a97,x7862))+~P5(f102(f165(a200,x7861),x7862))+E(f153(a96,f54(f38(f17(a44,f170(f21(a80),x7861)),f148(f22(a200),x7862)))),f153(a96,x7862))
% 2.51/2.63 [787]~P5(f154(a2,x7872))+~P5(f154(f108(a203,x7871),x7872))+E(f157(a43,f46(f37(f11(a44,f111(f19(a75),x7871)),f136(f20(a203),x7872)))),f157(a43,x7872))
% 2.51/2.63 [788]~P5(f132(a93,x7882))+~P5(f132(f146(a204,x7881),x7882))+E(f147(a85,f47(f40(f12(a44,f141(f23(a76),x7881)),f145(f30(a204),x7882)))),f147(a85,x7882))
% 2.51/2.63 [789]~P5(f149(a81,x7892))+~P5(f149(f139(a210,x7891),x7892))+E(f137(a86,f55(f39(f15(a44,f117(f27(a77),x7891)),f138(f29(a210),x7892)))),f137(a86,x7892))
% 2.51/2.63 [866]P5(f102(a97,x8661))+~P5(f154(a2,f201(x8662,x8661)))+~P5(f102(a97,f54(f38(f17(a73,f148(f22(a200),x8661)),f109(f36(f8(a75,x8662)),f168(x8662,f59(x8662,x8661)))))))
% 2.51/2.63 [640]P5(f154(a2,x6401))+~P5(f102(a97,x6402))+~P5(f154(f117(a212,x6401),f201(x6403,x6402)))
% 2.51/2.63 [653]~P5(f158(f159(a199,x6531),x6533))+P5(f158(f159(a199,x6531),x6532))+~P5(f158(f159(a199,x6533),x6532))
% 2.51/2.63 [657]~P5(f154(f108(a203,x6571),x6573))+~P5(f154(f117(a212,x6573),x6572))+P5(f154(f108(a203,x6571),x6572))
% 2.51/2.63 [658]~P5(f154(f117(a212,x6581),x6583))+P5(f154(f117(a212,x6581),x6582))+~P5(f154(f117(a212,x6583),x6582))
% 2.51/2.63 [662]~P5(f102(f165(a200,x6621),x6623))+~P5(f102(f141(a216,x6623),x6622))+P5(f102(f165(a200,x6621),x6622))
% 2.51/2.63 [663]~P5(f102(f141(a216,x6631),x6633))+P5(f102(f141(a216,x6631),x6632))+~P5(f102(f141(a216,x6633),x6632))
% 2.51/2.63 [664]~P5(f126(f106(a217,x6641),x6643))+P5(f126(f106(a217,x6641),x6642))+~P5(f126(f106(a217,x6643),x6642))
% 2.51/2.63 [668]~P5(f126(f160(a211,x6681),x6683))+P5(f126(f160(a211,x6681),x6682))+~P5(f126(f106(a217,x6683),x6682))
% 2.51/2.63 [669]~P1(x6691)+P7(f70(x6691,x6692,x6693))+~P5(f154(f117(a212,x6691),f201(x6692,x6693)))
% 2.51/2.63 [670]~P4(x6701)+P8(f71(x6701,x6702,x6703))+~P5(f154(f108(a203,x6701),f201(x6702,x6703)))
% 2.51/2.63 [671]~P4(x6711)+P8(f72(x6711,x6712,x6713))+~P5(f154(f108(a203,x6711),f201(x6712,x6713)))
% 2.51/2.63 [672]~P1(x6722)+E(f201(x6721,f70(x6722,x6721,x6723)),x6722)+~P5(f154(f117(a212,x6722),f201(x6721,x6723)))
% 2.51/2.63 [673]~P4(x6732)+E(f168(x6731,f71(x6732,x6731,x6733)),x6732)+~P5(f154(f108(a203,x6732),f201(x6731,x6733)))
% 2.51/2.63 [674]~P4(x6742)+E(f168(x6741,f72(x6742,x6741,x6743)),x6742)+~P5(f154(f108(a203,x6742),f201(x6741,x6743)))
% 2.51/2.63 [700]E(f164(f213(f164(f213(x7001),x7002)),f164(f213(x7003),x7002)),f164(f213(x7001),x7003))+~P5(f158(f159(a199,x7002),x7001))+~P5(f158(f159(a199,x7002),x7003))
% 2.51/2.63 [749]~P5(f158(x7491,x7492))+~P5(f158(x7491,f64(x7493,x7491,x7492)))+P5(f158(x7491,f164(f213(x7492),x7493)))
% 2.51/2.63 [771]~P5(f158(x7711,x7712))+P5(f158(x7711,f164(f213(x7712),x7713)))+P5(f158(x7711,f164(a226,f64(x7713,x7711,x7712))))
% 2.51/2.63 [782]~P4(x7821)+~P5(f154(f108(a203,x7821),f201(x7822,x7823)))+P5(f102(f165(a200,f71(x7821,x7822,x7823)),x7823))
% 2.51/2.63 [783]~P4(x7831)+~P5(f154(f108(a203,x7831),f201(x7832,x7833)))+P5(f102(f165(a200,f72(x7831,x7832,x7833)),x7833))
% 2.51/2.63 [784]~P1(x7841)+~P5(f154(f117(a212,x7841),f201(x7842,x7843)))+P5(f102(f141(a216,f70(x7841,x7842,x7843)),x7843))
% 2.51/2.63 [799]E(x7991,x7992)+P5(f158(x7993,x7992))+~P5(f158(f42(f9(a44,f159(f5(a79),x7991)),f151(f26(a211),x7993)),x7992))
% 2.51/2.63 [803]E(x8031,x8032)+P5(f126(f160(a211,x8031),x8033))+~P5(f126(f160(a211,x8031),f42(f9(a44,f159(f5(a79),x8032)),f151(f26(a211),x8033))))
% 2.51/2.63 [804]P5(f126(f106(a217,x8041),x8042))+P5(f126(f160(a211,x8043),x8041))+~P5(f126(f106(a217,x8041),f42(f9(a44,f159(f5(a79),x8043)),f151(f26(a211),x8042))))
% 2.51/2.63 [858]~P5(f158(f159(a199,x8582),x8583))+P5(f158(f159(a199,f164(x8581,x8582)),f164(x8581,x8583)))+~P5(f158(f159(a199,f164(x8581,f66(x8582,x8583,x8581))),f164(x8581,f164(a226,f66(x8582,x8583,x8581)))))
% 2.51/2.63 [859]~P5(f158(f159(a199,x8592),x8593))+P5(f154(f117(a212,f124(x8591,x8592)),f124(x8591,x8593)))+~P5(f154(f117(a212,f124(x8591,f69(x8592,x8593,x8591))),f124(x8591,f164(a226,f69(x8592,x8593,x8591)))))
% 2.51/2.63 [860]~P5(f158(f159(a199,x8602),x8603))+P5(f102(f141(a216,f125(x8601,x8602)),f125(x8601,x8603)))+~P5(f102(f141(a216,f125(x8601,f67(x8602,x8603,x8601))),f125(x8601,f164(a226,f67(x8602,x8603,x8601)))))
% 2.51/2.63 [861]~P5(f158(f159(a199,x8612),x8613))+P5(f126(f106(a217,f159(x8611,x8612)),f159(x8611,x8613)))+~P5(f126(f106(a217,f159(x8611,f68(x8612,x8613,x8611))),f159(x8611,f164(a226,f68(x8612,x8613,x8611)))))
% 2.51/2.63 [833]~P5(f126(f106(a217,x8332),x8333))+~P5(f126(f160(a211,x8331),x8333))+P5(f126(f106(a217,f42(f9(a44,f159(f5(a79),x8331)),f151(f26(a211),x8332))),x8333))
% 2.51/2.63 [848]P5(f154(f108(a203,x8481),x8482))+P5(f154(f117(a212,x8482),x8483))+~P5(f154(f117(a212,x8482),f46(f37(f11(a44,f111(f19(a75),x8481)),f136(f20(a203),x8483)))))
% 2.51/2.63 [849]P5(f102(f165(a200,x8491),x8492))+P5(f102(f141(a216,x8492),x8493))+~P5(f102(f141(a216,x8492),f54(f38(f17(a44,f170(f21(a80),x8491)),f148(f22(a200),x8493)))))
% 2.51/2.63 [854]~P5(f154(f108(a203,x8541),x8543))+~P5(f154(f117(a212,x8542),x8543))+P5(f154(f117(a212,f46(f37(f11(a44,f111(f19(a75),x8541)),f136(f20(a203),x8542)))),x8543))
% 2.51/2.63 [855]~P5(f102(f165(a200,x8551),x8553))+~P5(f102(f141(a216,x8552),x8553))+P5(f102(f141(a216,f54(f38(f17(a44,f170(f21(a80),x8551)),f148(f22(a200),x8552)))),x8553))
% 2.51/2.63 [639]~E(x6391,f168(x6392,x6394))+~P5(f102(f165(a200,x6394),x6393))+P5(f154(f108(a203,x6391),f201(x6392,x6393)))
% 2.51/2.63 [583]~P1(x5832)+~P1(x5831)+E(x5831,x5832)+~P5(f154(f117(a77,x5831),x5832))
% 2.51/2.63 [584]~P7(x5842)+~P7(x5841)+E(x5841,x5842)+~P5(f102(f141(a76,x5841),x5842))
% 2.51/2.63 [585]~P4(x5852)+~P4(x5851)+E(x5851,x5852)+~P5(f107(f111(a75,x5851),x5852))
% 2.51/2.63 [586]~P8(x5862)+~P8(x5861)+E(x5861,x5862)+~P5(f167(f170(a80,x5861),x5862))
% 2.51/2.63 [743]E(x7431,x7432)+~P5(f126(a98,x7431))+~P5(f126(f106(a217,x7432),x7431))+~P5(f158(f159(a199,f128(a4,x7431)),f128(a4,x7432)))
% 2.51/2.63 [744]E(x7441,x7442)+~P5(f103(a82,x7441))+~P5(f103(f133(a219,x7442),x7441))+~P5(f158(f159(a199,f150(a91,x7441)),f150(a91,x7442)))
% 2.51/2.63 [651]E(x6511,x6512)+~E(f164(f213(x6511),x6513),f164(f213(x6512),x6513))+~P5(f158(f159(a199,x6513),x6511))+~P5(f158(f159(a199,x6513),x6512))
% 2.51/2.63 [683]~P1(x6833)+P7(f65(x6831,x6832,x6833))+~P5(f154(a2,x6833))+~P5(f154(f117(a212,x6833),f201(x6831,x6832)))
% 2.51/2.63 [684]~P1(x6843)+E(f201(x6841,f65(x6841,x6842,x6843)),x6843)+~P5(f154(a2,x6843))+~P5(f154(f117(a212,x6843),f201(x6841,x6842)))
% 2.51/2.63 [742]~P1(x7423)+~P5(f154(a2,x7423))+~P5(f154(f117(a212,x7423),f201(x7421,x7422)))+P5(f102(a97,f65(x7421,x7422,x7423)))
% 2.51/2.63 [763]E(x7631,x7632)+~E(f42(f9(a44,f159(f5(a79),x7633)),f151(f26(a211),x7631)),f42(f9(a44,f159(f5(a79),x7633)),f151(f26(a211),x7632)))+P5(f126(f160(a211,x7633),x7631))+P5(f126(f160(a211,x7633),x7632))
% 2.51/2.63 [794]~P1(x7943)+~P5(f154(a2,x7943))+~P5(f154(f117(a212,x7943),f201(x7941,x7942)))+P5(f102(f141(a216,f65(x7941,x7942,x7943)),x7942))
% 2.51/2.63 [795]~P5(f158(f159(a199,x7953),x7951))+P5(f158(f159(a199,x7951),x7952))+~P5(f158(f159(a199,x7953),x7952))+~P5(f158(f159(a199,f164(f213(x7951),x7953)),f164(f213(x7952),x7953)))
% 2.51/2.63 [805]~E(x8051,x8053)+~P4(x8053)+~P4(x8051)+P5(f107(f46(f37(f11(a44,f111(f19(a75),x8051)),f136(f20(a203),x8052))),x8053))
% 2.51/2.63 [806]~E(x8061,x8063)+~P8(x8063)+~P8(x8061)+P5(f167(f54(f38(f17(a44,f170(f21(a80),x8061)),f148(f22(a200),x8062))),x8063))
% 2.51/2.63 [817]~P4(x8171)+~P4(x8173)+~P5(f107(x8172,x8173))+P5(f107(f46(f37(f11(a44,f111(f19(a75),x8171)),f136(f20(a203),x8172))),x8173))
% 2.51/2.63 [818]~P8(x8181)+~P8(x8183)+~P5(f167(x8182,x8183))+P5(f167(f54(f38(f17(a44,f170(f21(a80),x8181)),f148(f22(a200),x8182))),x8183))
% 2.51/2.63 [633]~P1(x6332)+~P1(x6331)+E(x6331,x6332)+~P5(f154(f117(a212,x6332),x6331))+~P5(f154(f117(a212,x6331),x6332))
% 2.51/2.63 [635]~P7(x6352)+~P7(x6351)+E(x6351,x6352)+~P5(f102(f141(a216,x6352),x6351))+~P5(f102(f141(a216,x6351),x6352))
% 2.51/2.63 [838]~P4(x8382)+~P4(x8381)+E(x8381,x8382)+P5(f107(x8383,x8382))+~P5(f107(f46(f37(f11(a44,f111(f19(a75),x8381)),f136(f20(a203),x8383))),x8382))
% 2.51/2.63 [839]~P8(x8392)+~P8(x8391)+E(x8391,x8392)+P5(f167(x8393,x8392))+~P5(f167(f54(f38(f17(a44,f170(f21(a80),x8391)),f148(f22(a200),x8393))),x8392))
% 2.51/2.63 [845]~P4(x8452)+~P4(x8451)+E(x8451,x8452)+P5(f154(f108(a203,x8451),x8453))+~P5(f154(f108(a203,x8451),f46(f37(f11(a44,f111(f19(a75),x8452)),f136(f20(a203),x8453)))))
% 2.51/2.63 [847]~P8(x8472)+~P8(x8471)+E(x8471,x8472)+P5(f102(f165(a200,x8471),x8473))+~P5(f102(f165(a200,x8471),f54(f38(f17(a44,f170(f21(a80),x8472)),f148(f22(a200),x8473)))))
% 2.51/2.63 [644]~P1(x6441)+~P7(x6444)+~E(x6441,f201(x6442,x6444))+~P5(f102(f141(a216,x6444),x6443))+P5(f154(f117(a212,x6441),f201(x6442,x6443)))
% 2.51/2.63 [745]~P1(x7452)+~P1(x7451)+E(x7451,x7452)+~P5(f154(a2,x7452))+~P5(f154(f117(a212,x7451),x7452))+~P5(f158(f159(a199,f157(a43,x7452)),f157(a43,x7451)))
% 2.51/2.63 [746]~P7(x7462)+~P7(x7461)+E(x7461,x7462)+~P5(f102(a97,x7462))+~P5(f102(f141(a216,x7461),x7462))+~P5(f158(f159(a199,f153(a96,x7462)),f153(a96,x7461)))
% 2.51/2.63 [747]~P2(x7472)+~P2(x7471)+E(x7471,x7472)+~P5(f149(a81,x7472))+~P5(f149(f119(a218,x7471),x7472))+~P5(f158(f159(a199,f137(a86,x7472)),f137(a86,x7471)))
% 2.51/2.63 [748]~P3(x7482)+~P3(x7481)+E(x7481,x7482)+~P5(f132(a93,x7482))+~P5(f132(f142(a221,x7481),x7482))+~P5(f158(f159(a199,f147(a85,x7482)),f147(a85,x7481)))
% 2.51/2.63 [800]~P1(x8002)+~P1(x8001)+E(x8001,x8002)+P5(f154(f108(a203,x8003),x8001))+~E(f46(f37(f11(a44,f111(f19(a75),x8003)),f136(f20(a203),x8001))),f46(f37(f11(a44,f111(f19(a75),x8003)),f136(f20(a203),x8002))))+P5(f154(f108(a203,x8003),x8002))
% 2.51/2.63 [801]~P7(x8012)+~P7(x8011)+E(x8011,x8012)+P5(f102(f165(a200,x8013),x8011))+~E(f54(f38(f17(a44,f170(f21(a80),x8013)),f148(f22(a200),x8011))),f54(f38(f17(a44,f170(f21(a80),x8013)),f148(f22(a200),x8012))))+P5(f102(f165(a200,x8013),x8012))
% 2.51/2.63 %EqnAxiom
% 2.51/2.63 [1]E(x11,x11)
% 2.51/2.63 [2]E(x22,x21)+~E(x21,x22)
% 2.51/2.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 2.51/2.63 [4]~E(x41,x42)+E(f228(x41),f228(x42))
% 2.51/2.63 [5]~E(x51,x52)+E(f232(x51),f232(x52))
% 2.51/2.63 [6]~E(x61,x62)+E(f102(x61,x63),f102(x62,x63))
% 2.51/2.63 [7]~E(x71,x72)+E(f102(x73,x71),f102(x73,x72))
% 2.51/2.63 [8]~E(x81,x82)+E(f120(x81,x83),f120(x82,x83))
% 2.51/2.63 [9]~E(x91,x92)+E(f120(x93,x91),f120(x93,x92))
% 2.51/2.63 [10]~E(x101,x102)+E(f121(x101,x103),f121(x102,x103))
% 2.51/2.63 [11]~E(x111,x112)+E(f121(x113,x111),f121(x113,x112))
% 2.51/2.63 [12]~E(x121,x122)+E(f122(x121,x123),f122(x122,x123))
% 2.51/2.63 [13]~E(x131,x132)+E(f122(x133,x131),f122(x133,x132))
% 2.51/2.63 [14]~E(x141,x142)+E(f123(x141,x143),f123(x142,x143))
% 2.51/2.63 [15]~E(x151,x152)+E(f123(x153,x151),f123(x153,x152))
% 2.51/2.63 [16]~E(x161,x162)+E(f187(x161,x163),f187(x162,x163))
% 2.51/2.63 [17]~E(x171,x172)+E(f187(x173,x171),f187(x173,x172))
% 2.51/2.63 [18]~E(x181,x182)+E(f124(x181,x183),f124(x182,x183))
% 2.51/2.63 [19]~E(x191,x192)+E(f124(x193,x191),f124(x193,x192))
% 2.51/2.63 [20]~E(x201,x202)+E(f197(x201,x203),f197(x202,x203))
% 2.51/2.63 [21]~E(x211,x212)+E(f197(x213,x211),f197(x213,x212))
% 2.51/2.63 [22]~E(x221,x222)+E(f161(x221,x223),f161(x222,x223))
% 2.51/2.63 [23]~E(x231,x232)+E(f161(x233,x231),f161(x233,x232))
% 2.51/2.63 [24]~E(x241,x242)+E(f190(x241,x243),f190(x242,x243))
% 2.51/2.63 [25]~E(x251,x252)+E(f190(x253,x251),f190(x253,x252))
% 2.51/2.63 [26]~E(x261,x262)+E(f162(x261,x263),f162(x262,x263))
% 2.51/2.63 [27]~E(x271,x272)+E(f162(x273,x271),f162(x273,x272))
% 2.51/2.63 [28]~E(x281,x282)+E(f163(x281,x283),f163(x282,x283))
% 2.51/2.63 [29]~E(x291,x292)+E(f163(x293,x291),f163(x293,x292))
% 2.51/2.63 [30]~E(x301,x302)+E(f125(x301,x303),f125(x302,x303))
% 2.51/2.63 [31]~E(x311,x312)+E(f125(x313,x311),f125(x313,x312))
% 2.51/2.63 [32]~E(x321,x322)+E(f198(x321,x323),f198(x322,x323))
% 2.51/2.63 [33]~E(x331,x332)+E(f198(x333,x331),f198(x333,x332))
% 2.51/2.63 [34]~E(x341,x342)+E(f178(x341,x343),f178(x342,x343))
% 2.51/2.63 [35]~E(x351,x352)+E(f178(x353,x351),f178(x353,x352))
% 2.51/2.63 [36]~E(x361,x362)+E(f158(x361,x363),f158(x362,x363))
% 2.51/2.63 [37]~E(x371,x372)+E(f158(x373,x371),f158(x373,x372))
% 2.51/2.63 [38]~E(x381,x382)+E(f126(x381,x383),f126(x382,x383))
% 2.51/2.63 [39]~E(x391,x392)+E(f126(x393,x391),f126(x393,x392))
% 2.51/2.63 [40]~E(x401,x402)+E(f103(x401,x403),f103(x402,x403))
% 2.51/2.63 [41]~E(x411,x412)+E(f103(x413,x411),f103(x413,x412))
% 2.51/2.63 [42]~E(x421,x422)+E(f127(x421,x423),f127(x422,x423))
% 2.51/2.63 [43]~E(x431,x432)+E(f127(x433,x431),f127(x433,x432))
% 2.51/2.63 [44]~E(x441,x442)+E(f140(x441,x443),f140(x442,x443))
% 2.51/2.63 [45]~E(x451,x452)+E(f140(x453,x451),f140(x453,x452))
% 2.51/2.63 [46]~E(x461,x462)+E(f143(x461,x463),f143(x462,x463))
% 2.51/2.63 [47]~E(x471,x472)+E(f143(x473,x471),f143(x473,x472))
% 2.51/2.63 [48]~E(x481,x482)+E(f104(x481,x483),f104(x482,x483))
% 2.51/2.63 [49]~E(x491,x492)+E(f104(x493,x491),f104(x493,x492))
% 2.51/2.63 [50]~E(x501,x502)+E(f144(x501,x503),f144(x502,x503))
% 2.51/2.63 [51]~E(x511,x512)+E(f144(x513,x511),f144(x513,x512))
% 2.51/2.63 [52]~E(x521,x522)+E(f105(x521,x523),f105(x522,x523))
% 2.51/2.63 [53]~E(x531,x532)+E(f105(x533,x531),f105(x533,x532))
% 2.51/2.63 [54]~E(x541,x542)+E(f99(x541,x543),f99(x542,x543))
% 2.51/2.63 [55]~E(x551,x552)+E(f99(x553,x551),f99(x553,x552))
% 2.51/2.63 [56]~E(x561,x562)+E(f233(x561),f233(x562))
% 2.51/2.63 [57]~E(x571,x572)+E(f148(x571,x573),f148(x572,x573))
% 2.51/2.63 [58]~E(x581,x582)+E(f148(x583,x581),f148(x583,x582))
% 2.51/2.63 [59]~E(x591,x592)+E(f229(x591),f229(x592))
% 2.51/2.63 [60]~E(x601,x602)+E(f5(x601),f5(x602))
% 2.51/2.63 [61]~E(x611,x612)+E(f159(x611,x613),f159(x612,x613))
% 2.51/2.63 [62]~E(x621,x622)+E(f159(x623,x621),f159(x623,x622))
% 2.51/2.63 [63]~E(x631,x632)+E(f128(x631,x633),f128(x632,x633))
% 2.51/2.63 [64]~E(x641,x642)+E(f128(x643,x641),f128(x643,x642))
% 2.51/2.63 [65]~E(x651,x652)+E(f164(x651,x653),f164(x652,x653))
% 2.51/2.63 [66]~E(x661,x662)+E(f164(x663,x661),f164(x663,x662))
% 2.51/2.63 [67]~E(x671,x672)+E(f165(x671,x673),f165(x672,x673))
% 2.51/2.63 [68]~E(x681,x682)+E(f165(x683,x681),f165(x683,x682))
% 2.51/2.63 [69]~E(x691,x692)+E(f54(x691),f54(x692))
% 2.51/2.63 [70]~E(x701,x702)+E(f136(x701,x703),f136(x702,x703))
% 2.51/2.63 [71]~E(x711,x712)+E(f136(x713,x711),f136(x713,x712))
% 2.51/2.63 [72]~E(x721,x722)+E(f47(x721),f47(x722))
% 2.51/2.63 [73]~E(x731,x732)+E(f27(x731),f27(x732))
% 2.51/2.63 [74]~E(x741,x742)+E(f40(x741,x743),f40(x742,x743))
% 2.51/2.63 [75]~E(x751,x752)+E(f40(x753,x751),f40(x753,x752))
% 2.51/2.63 [76]~E(x761,x762)+E(f117(x761,x763),f117(x762,x763))
% 2.51/2.63 [77]~E(x771,x772)+E(f117(x773,x771),f117(x773,x772))
% 2.51/2.63 [78]~E(x781,x782)+E(f154(x781,x783),f154(x782,x783))
% 2.51/2.63 [79]~E(x791,x792)+E(f154(x793,x791),f154(x793,x792))
% 2.51/2.63 [80]~E(x801,x802)+E(f22(x801),f22(x802))
% 2.51/2.63 [81]~E(x811,x812)+E(f111(x811,x813),f111(x812,x813))
% 2.51/2.63 [82]~E(x821,x822)+E(f111(x823,x821),f111(x823,x822))
% 2.51/2.63 [83]~E(x831,x832)+E(f141(x831,x833),f141(x832,x833))
% 2.51/2.63 [84]~E(x841,x842)+E(f141(x843,x841),f141(x843,x842))
% 2.51/2.63 [85]~E(x851,x852)+E(f38(x851,x853),f38(x852,x853))
% 2.51/2.63 [86]~E(x861,x862)+E(f38(x863,x861),f38(x863,x862))
% 2.51/2.63 [87]~E(x871,x872)+E(f149(x871,x873),f149(x872,x873))
% 2.51/2.63 [88]~E(x881,x882)+E(f149(x883,x881),f149(x883,x882))
% 2.51/2.63 [89]~E(x891,x892)+E(f109(x891,x893),f109(x892,x893))
% 2.51/2.63 [90]~E(x901,x902)+E(f109(x903,x901),f109(x903,x902))
% 2.51/2.63 [91]~E(x911,x912)+E(f106(x911,x913),f106(x912,x913))
% 2.51/2.63 [92]~E(x921,x922)+E(f106(x923,x921),f106(x923,x922))
% 2.51/2.63 [93]~E(x931,x932)+E(f62(x931,x933,x934),f62(x932,x933,x934))
% 2.51/2.63 [94]~E(x941,x942)+E(f62(x943,x941,x944),f62(x943,x942,x944))
% 2.51/2.63 [95]~E(x951,x952)+E(f62(x953,x954,x951),f62(x953,x954,x952))
% 2.51/2.63 [96]~E(x961,x962)+E(f147(x961,x963),f147(x962,x963))
% 2.51/2.63 [97]~E(x971,x972)+E(f147(x973,x971),f147(x973,x972))
% 2.51/2.63 [98]~E(x981,x982)+E(f19(x981),f19(x982))
% 2.51/2.63 [99]~E(x991,x992)+E(f107(x991,x993),f107(x992,x993))
% 2.51/2.63 [100]~E(x1001,x1002)+E(f107(x1003,x1001),f107(x1003,x1002))
% 2.51/2.63 [101]~E(x1011,x1012)+E(f110(x1011,x1013),f110(x1012,x1013))
% 2.51/2.63 [102]~E(x1021,x1022)+E(f110(x1023,x1021),f110(x1023,x1022))
% 2.51/2.63 [103]~E(x1031,x1032)+E(f6(x1031,x1033),f6(x1032,x1033))
% 2.51/2.63 [104]~E(x1041,x1042)+E(f6(x1043,x1041),f6(x1043,x1042))
% 2.51/2.63 [105]~E(x1051,x1052)+E(f58(x1051,x1053),f58(x1052,x1053))
% 2.51/2.63 [106]~E(x1061,x1062)+E(f58(x1063,x1061),f58(x1063,x1062))
% 2.51/2.63 [107]~E(x1071,x1072)+E(f7(x1071,x1073),f7(x1072,x1073))
% 2.51/2.63 [108]~E(x1081,x1082)+E(f7(x1083,x1081),f7(x1083,x1082))
% 2.51/2.63 [109]~E(x1091,x1092)+E(f167(x1091,x1093),f167(x1092,x1093))
% 2.51/2.63 [110]~E(x1101,x1102)+E(f167(x1103,x1101),f167(x1103,x1102))
% 2.51/2.63 [111]~E(x1111,x1112)+E(f11(x1111,x1113),f11(x1112,x1113))
% 2.51/2.63 [112]~E(x1121,x1122)+E(f11(x1123,x1121),f11(x1123,x1122))
% 2.51/2.63 [113]~E(x1131,x1132)+E(f108(x1131,x1133),f108(x1132,x1133))
% 2.51/2.63 [114]~E(x1141,x1142)+E(f108(x1143,x1141),f108(x1143,x1142))
% 2.51/2.63 [115]~E(x1151,x1152)+E(f168(x1151,x1153),f168(x1152,x1153))
% 2.51/2.63 [116]~E(x1161,x1162)+E(f168(x1163,x1161),f168(x1163,x1162))
% 2.51/2.63 [117]~E(x1171,x1172)+E(f145(x1171,x1173),f145(x1172,x1173))
% 2.51/2.63 [118]~E(x1181,x1182)+E(f145(x1183,x1181),f145(x1183,x1182))
% 2.51/2.63 [119]~E(x1191,x1192)+E(f8(x1191,x1193),f8(x1192,x1193))
% 2.51/2.63 [120]~E(x1201,x1202)+E(f8(x1203,x1201),f8(x1203,x1202))
% 2.51/2.63 [121]~E(x1211,x1212)+E(f166(x1211,x1213),f166(x1212,x1213))
% 2.51/2.63 [122]~E(x1221,x1222)+E(f166(x1223,x1221),f166(x1223,x1222))
% 2.51/2.63 [123]~E(x1231,x1232)+E(f139(x1231,x1233),f139(x1232,x1233))
% 2.51/2.63 [124]~E(x1241,x1242)+E(f139(x1243,x1241),f139(x1243,x1242))
% 2.51/2.63 [125]~E(x1251,x1252)+E(f151(x1251,x1253),f151(x1252,x1253))
% 2.51/2.63 [126]~E(x1261,x1262)+E(f151(x1263,x1261),f151(x1263,x1262))
% 2.51/2.63 [127]~E(x1271,x1272)+E(f18(x1271,x1273),f18(x1272,x1273))
% 2.51/2.63 [128]~E(x1281,x1282)+E(f18(x1283,x1281),f18(x1283,x1282))
% 2.51/2.63 [129]~E(x1291,x1292)+E(f30(x1291),f30(x1292))
% 2.51/2.63 [130]~E(x1301,x1302)+E(f132(x1301,x1303),f132(x1302,x1303))
% 2.51/2.63 [131]~E(x1311,x1312)+E(f132(x1313,x1311),f132(x1313,x1312))
% 2.51/2.63 [132]~E(x1321,x1322)+E(f160(x1321,x1323),f160(x1322,x1323))
% 2.51/2.63 [133]~E(x1331,x1332)+E(f160(x1333,x1331),f160(x1333,x1332))
% 2.51/2.63 [134]~E(x1341,x1342)+E(f10(x1341,x1343),f10(x1342,x1343))
% 2.51/2.63 [135]~E(x1351,x1352)+E(f10(x1353,x1351),f10(x1353,x1352))
% 2.51/2.63 [136]~E(x1361,x1362)+E(f26(x1361),f26(x1362))
% 2.51/2.63 [137]~E(x1371,x1372)+E(f60(x1371,x1373),f60(x1372,x1373))
% 2.51/2.63 [138]~E(x1381,x1382)+E(f60(x1383,x1381),f60(x1383,x1382))
% 2.51/2.63 [139]~E(x1391,x1392)+E(f42(x1391,x1393),f42(x1392,x1393))
% 2.51/2.63 [140]~E(x1401,x1402)+E(f42(x1403,x1401),f42(x1403,x1402))
% 2.51/2.63 [141]~E(x1411,x1412)+E(f13(x1411,x1413),f13(x1412,x1413))
% 2.51/2.63 [142]~E(x1421,x1422)+E(f13(x1423,x1421),f13(x1423,x1422))
% 2.51/2.63 [143]~E(x1431,x1432)+E(f59(x1431,x1433),f59(x1432,x1433))
% 2.51/2.63 [144]~E(x1441,x1442)+E(f59(x1443,x1441),f59(x1443,x1442))
% 2.51/2.63 [145]~E(x1451,x1452)+E(f21(x1451),f21(x1452))
% 2.51/2.63 [146]~E(x1461,x1462)+E(f29(x1461),f29(x1462))
% 2.51/2.63 [147]~E(x1471,x1472)+E(f14(x1471,x1473),f14(x1472,x1473))
% 2.51/2.63 [148]~E(x1481,x1482)+E(f14(x1483,x1481),f14(x1483,x1482))
% 2.51/2.63 [149]~E(x1491,x1492)+E(f201(x1491,x1493),f201(x1492,x1493))
% 2.51/2.63 [150]~E(x1501,x1502)+E(f201(x1503,x1501),f201(x1503,x1502))
% 2.51/2.63 [151]~E(x1511,x1512)+E(f69(x1511,x1513,x1514),f69(x1512,x1513,x1514))
% 2.51/2.63 [152]~E(x1521,x1522)+E(f69(x1523,x1521,x1524),f69(x1523,x1522,x1524))
% 2.51/2.63 [153]~E(x1531,x1532)+E(f69(x1533,x1534,x1531),f69(x1533,x1534,x1532))
% 2.51/2.63 [154]~E(x1541,x1542)+E(f112(x1541,x1543),f112(x1542,x1543))
% 2.51/2.63 [155]~E(x1551,x1552)+E(f112(x1553,x1551),f112(x1553,x1552))
% 2.51/2.63 [156]~E(x1561,x1562)+E(f12(x1561,x1563),f12(x1562,x1563))
% 2.51/2.63 [157]~E(x1571,x1572)+E(f12(x1573,x1571),f12(x1573,x1572))
% 2.51/2.63 [158]~E(x1581,x1582)+E(f113(x1581,x1583),f113(x1582,x1583))
% 2.51/2.63 [159]~E(x1591,x1592)+E(f113(x1593,x1591),f113(x1593,x1592))
% 2.51/2.63 [160]~E(x1601,x1602)+E(f9(x1601,x1603),f9(x1602,x1603))
% 2.51/2.63 [161]~E(x1611,x1612)+E(f9(x1613,x1611),f9(x1613,x1612))
% 2.51/2.63 [162]~E(x1621,x1622)+E(f156(x1621,x1623),f156(x1622,x1623))
% 2.51/2.63 [163]~E(x1631,x1632)+E(f156(x1633,x1631),f156(x1633,x1632))
% 2.51/2.63 [164]~E(x1641,x1642)+E(f17(x1641,x1643),f17(x1642,x1643))
% 2.51/2.63 [165]~E(x1651,x1652)+E(f17(x1653,x1651),f17(x1653,x1652))
% 2.51/2.63 [166]~E(x1661,x1662)+E(f37(x1661,x1663),f37(x1662,x1663))
% 2.51/2.63 [167]~E(x1671,x1672)+E(f37(x1673,x1671),f37(x1673,x1672))
% 2.51/2.63 [168]~E(x1681,x1682)+E(f20(x1681),f20(x1682))
% 2.51/2.63 [169]~E(x1691,x1692)+E(f169(x1691,x1693),f169(x1692,x1693))
% 2.51/2.63 [170]~E(x1701,x1702)+E(f169(x1703,x1701),f169(x1703,x1702))
% 2.51/2.63 [171]~E(x1711,x1712)+E(f171(x1711,x1713),f171(x1712,x1713))
% 2.51/2.63 [172]~E(x1721,x1722)+E(f171(x1723,x1721),f171(x1723,x1722))
% 2.51/2.63 [173]~E(x1731,x1732)+E(f180(x1731,x1733),f180(x1732,x1733))
% 2.51/2.63 [174]~E(x1741,x1742)+E(f180(x1743,x1741),f180(x1743,x1742))
% 2.51/2.63 [175]~E(x1751,x1752)+E(f15(x1751,x1753),f15(x1752,x1753))
% 2.51/2.63 [176]~E(x1761,x1762)+E(f15(x1763,x1761),f15(x1763,x1762))
% 2.51/2.63 [177]~E(x1771,x1772)+E(f129(x1771,x1773),f129(x1772,x1773))
% 2.51/2.63 [178]~E(x1781,x1782)+E(f129(x1783,x1781),f129(x1783,x1782))
% 2.51/2.63 [179]~E(x1791,x1792)+E(f213(x1791),f213(x1792))
% 2.51/2.63 [180]~E(x1801,x1802)+E(f46(x1801),f46(x1802))
% 2.51/2.63 [181]~E(x1811,x1812)+E(f16(x1811,x1813),f16(x1812,x1813))
% 2.51/2.63 [182]~E(x1821,x1822)+E(f16(x1823,x1821),f16(x1823,x1822))
% 2.51/2.63 [183]~E(x1831,x1832)+E(f130(x1831,x1833),f130(x1832,x1833))
% 2.51/2.63 [184]~E(x1841,x1842)+E(f130(x1843,x1841),f130(x1843,x1842))
% 2.51/2.63 [185]~E(x1851,x1852)+E(f170(x1851,x1853),f170(x1852,x1853))
% 2.51/2.63 [186]~E(x1861,x1862)+E(f170(x1863,x1861),f170(x1863,x1862))
% 2.51/2.63 [187]~E(x1871,x1872)+E(f28(x1871),f28(x1872))
% 2.51/2.63 [188]~E(x1881,x1882)+E(f177(x1881,x1883),f177(x1882,x1883))
% 2.51/2.63 [189]~E(x1891,x1892)+E(f177(x1893,x1891),f177(x1893,x1892))
% 2.51/2.63 [190]~E(x1901,x1902)+E(f118(x1901,x1903),f118(x1902,x1903))
% 2.51/2.63 [191]~E(x1911,x1912)+E(f118(x1913,x1911),f118(x1913,x1912))
% 2.51/2.63 [192]~E(x1921,x1922)+E(f36(x1921),f36(x1922))
% 2.51/2.63 [193]~E(x1931,x1932)+E(f208(x1931,x1933),f208(x1932,x1933))
% 2.51/2.63 [194]~E(x1941,x1942)+E(f208(x1943,x1941),f208(x1943,x1942))
% 2.51/2.63 [195]~E(x1951,x1952)+E(f153(x1951,x1953),f153(x1952,x1953))
% 2.51/2.63 [196]~E(x1961,x1962)+E(f153(x1963,x1961),f153(x1963,x1962))
% 2.51/2.63 [197]~E(x1971,x1972)+E(f135(x1971,x1973),f135(x1972,x1973))
% 2.51/2.63 [198]~E(x1981,x1982)+E(f135(x1983,x1981),f135(x1983,x1982))
% 2.51/2.63 [199]~E(x1991,x1992)+E(f33(x1991),f33(x1992))
% 2.51/2.63 [200]~E(x2001,x2002)+E(f119(x2001,x2003),f119(x2002,x2003))
% 2.51/2.63 [201]~E(x2011,x2012)+E(f119(x2013,x2011),f119(x2013,x2012))
% 2.51/2.63 [202]~E(x2021,x2022)+E(f192(x2021,x2023),f192(x2022,x2023))
% 2.51/2.63 [203]~E(x2031,x2032)+E(f192(x2033,x2031),f192(x2033,x2032))
% 2.51/2.63 [204]~E(x2041,x2042)+E(f67(x2041,x2043,x2044),f67(x2042,x2043,x2044))
% 2.51/2.63 [205]~E(x2051,x2052)+E(f67(x2053,x2051,x2054),f67(x2053,x2052,x2054))
% 2.51/2.63 [206]~E(x2061,x2062)+E(f67(x2063,x2064,x2061),f67(x2063,x2064,x2062))
% 2.51/2.63 [207]~E(x2071,x2072)+E(f137(x2071,x2073),f137(x2072,x2073))
% 2.51/2.63 [208]~E(x2081,x2082)+E(f137(x2083,x2081),f137(x2083,x2082))
% 2.51/2.63 [209]~E(x2091,x2092)+E(f150(x2091,x2093),f150(x2092,x2093))
% 2.51/2.63 [210]~E(x2101,x2102)+E(f150(x2103,x2101),f150(x2103,x2102))
% 2.51/2.63 [211]~E(x2111,x2112)+E(f65(x2111,x2113,x2114),f65(x2112,x2113,x2114))
% 2.51/2.63 [212]~E(x2121,x2122)+E(f65(x2123,x2121,x2124),f65(x2123,x2122,x2124))
% 2.51/2.63 [213]~E(x2131,x2132)+E(f65(x2133,x2134,x2131),f65(x2133,x2134,x2132))
% 2.51/2.63 [214]~E(x2141,x2142)+E(f188(x2141,x2143),f188(x2142,x2143))
% 2.51/2.63 [215]~E(x2151,x2152)+E(f188(x2153,x2151),f188(x2153,x2152))
% 2.51/2.63 [216]~E(x2161,x2162)+E(f55(x2161),f55(x2162))
% 2.51/2.63 [217]~E(x2171,x2172)+E(f115(x2171,x2173),f115(x2172,x2173))
% 2.51/2.63 [218]~E(x2181,x2182)+E(f115(x2183,x2181),f115(x2183,x2182))
% 2.51/2.63 [219]~E(x2191,x2192)+E(f224(x2191),f224(x2192))
% 2.51/2.63 [220]~E(x2201,x2202)+E(f138(x2201,x2203),f138(x2202,x2203))
% 2.51/2.63 [221]~E(x2211,x2212)+E(f138(x2213,x2211),f138(x2213,x2212))
% 2.51/2.63 [222]~E(x2221,x2222)+E(f23(x2221),f23(x2222))
% 2.51/2.63 [223]~E(x2231,x2232)+E(f133(x2231,x2233),f133(x2232,x2233))
% 2.51/2.63 [224]~E(x2241,x2242)+E(f133(x2243,x2241),f133(x2243,x2242))
% 2.51/2.63 [225]~E(x2251,x2252)+E(f57(x2251,x2253),f57(x2252,x2253))
% 2.51/2.63 [226]~E(x2261,x2262)+E(f57(x2263,x2261),f57(x2263,x2262))
% 2.51/2.63 [227]~E(x2271,x2272)+E(f56(x2271,x2273),f56(x2272,x2273))
% 2.51/2.63 [228]~E(x2281,x2282)+E(f56(x2283,x2281),f56(x2283,x2282))
% 2.51/2.63 [229]~E(x2291,x2292)+E(f70(x2291,x2293,x2294),f70(x2292,x2293,x2294))
% 2.51/2.63 [230]~E(x2301,x2302)+E(f70(x2303,x2301,x2304),f70(x2303,x2302,x2304))
% 2.51/2.63 [231]~E(x2311,x2312)+E(f70(x2313,x2314,x2311),f70(x2313,x2314,x2312))
% 2.51/2.63 [232]~E(x2321,x2322)+E(f39(x2321,x2323),f39(x2322,x2323))
% 2.51/2.63 [233]~E(x2331,x2332)+E(f39(x2333,x2331),f39(x2333,x2332))
% 2.51/2.63 [234]~E(x2341,x2342)+E(f72(x2341,x2343,x2344),f72(x2342,x2343,x2344))
% 2.51/2.63 [235]~E(x2351,x2352)+E(f72(x2353,x2351,x2354),f72(x2353,x2352,x2354))
% 2.51/2.64 [236]~E(x2361,x2362)+E(f72(x2363,x2364,x2361),f72(x2363,x2364,x2362))
% 2.51/2.64 [237]~E(x2371,x2372)+E(f172(x2371,x2373),f172(x2372,x2373))
% 2.51/2.64 [238]~E(x2381,x2382)+E(f172(x2383,x2381),f172(x2383,x2382))
% 2.51/2.64 [239]~E(x2391,x2392)+E(f114(x2391,x2393),f114(x2392,x2393))
% 2.51/2.64 [240]~E(x2401,x2402)+E(f114(x2403,x2401),f114(x2403,x2402))
% 2.51/2.64 [241]~E(x2411,x2412)+E(f157(x2411,x2413),f157(x2412,x2413))
% 2.51/2.64 [242]~E(x2421,x2422)+E(f157(x2423,x2421),f157(x2423,x2422))
% 2.51/2.64 [243]~E(x2431,x2432)+E(f64(x2431,x2433,x2434),f64(x2432,x2433,x2434))
% 2.51/2.64 [244]~E(x2441,x2442)+E(f64(x2443,x2441,x2444),f64(x2443,x2442,x2444))
% 2.51/2.64 [245]~E(x2451,x2452)+E(f64(x2453,x2454,x2451),f64(x2453,x2454,x2452))
% 2.51/2.64 [246]~E(x2461,x2462)+E(f41(x2461,x2463),f41(x2462,x2463))
% 2.51/2.64 [247]~E(x2471,x2472)+E(f41(x2473,x2471),f41(x2473,x2472))
% 2.51/2.64 [248]~E(x2481,x2482)+E(f191(x2481,x2483),f191(x2482,x2483))
% 2.51/2.64 [249]~E(x2491,x2492)+E(f191(x2493,x2491),f191(x2493,x2492))
% 2.51/2.64 [250]~E(x2501,x2502)+E(f206(x2501,x2503),f206(x2502,x2503))
% 2.51/2.64 [251]~E(x2511,x2512)+E(f206(x2513,x2511),f206(x2513,x2512))
% 2.51/2.64 [252]~E(x2521,x2522)+E(f142(x2521,x2523),f142(x2522,x2523))
% 2.51/2.64 [253]~E(x2531,x2532)+E(f142(x2533,x2531),f142(x2533,x2532))
% 2.51/2.64 [254]~E(x2541,x2542)+E(f152(x2541,x2543),f152(x2542,x2543))
% 2.51/2.64 [255]~E(x2551,x2552)+E(f152(x2553,x2551),f152(x2553,x2552))
% 2.51/2.64 [256]~E(x2561,x2562)+E(f176(x2561,x2563),f176(x2562,x2563))
% 2.51/2.64 [257]~E(x2571,x2572)+E(f176(x2573,x2571),f176(x2573,x2572))
% 2.51/2.64 [258]~E(x2581,x2582)+E(f194(x2581,x2583),f194(x2582,x2583))
% 2.51/2.64 [259]~E(x2591,x2592)+E(f194(x2593,x2591),f194(x2593,x2592))
% 2.51/2.64 [260]~E(x2601,x2602)+E(f24(x2601),f24(x2602))
% 2.51/2.64 [261]~E(x2611,x2612)+E(f71(x2611,x2613,x2614),f71(x2612,x2613,x2614))
% 2.51/2.64 [262]~E(x2621,x2622)+E(f71(x2623,x2621,x2624),f71(x2623,x2622,x2624))
% 2.51/2.64 [263]~E(x2631,x2632)+E(f71(x2633,x2634,x2631),f71(x2633,x2634,x2632))
% 2.51/2.64 [264]~E(x2641,x2642)+E(f181(x2641,x2643),f181(x2642,x2643))
% 2.51/2.64 [265]~E(x2651,x2652)+E(f181(x2653,x2651),f181(x2653,x2652))
% 2.51/2.64 [266]~E(x2661,x2662)+E(f51(x2661),f51(x2662))
% 2.51/2.64 [267]~E(x2671,x2672)+E(f189(x2671,x2673),f189(x2672,x2673))
% 2.51/2.64 [268]~E(x2681,x2682)+E(f189(x2683,x2681),f189(x2683,x2682))
% 2.51/2.64 [269]~E(x2691,x2692)+E(f195(x2691,x2693),f195(x2692,x2693))
% 2.51/2.64 [270]~E(x2701,x2702)+E(f195(x2703,x2701),f195(x2703,x2702))
% 2.51/2.64 [271]~E(x2711,x2712)+E(f146(x2711,x2713),f146(x2712,x2713))
% 2.51/2.64 [272]~E(x2721,x2722)+E(f146(x2723,x2721),f146(x2723,x2722))
% 2.51/2.64 [273]~E(x2731,x2732)+E(f209(x2731,x2733),f209(x2732,x2733))
% 2.51/2.64 [274]~E(x2741,x2742)+E(f209(x2743,x2741),f209(x2743,x2742))
% 2.51/2.64 [275]~E(x2751,x2752)+E(f66(x2751,x2753,x2754),f66(x2752,x2753,x2754))
% 2.51/2.64 [276]~E(x2761,x2762)+E(f66(x2763,x2761,x2764),f66(x2763,x2762,x2764))
% 2.51/2.64 [277]~E(x2771,x2772)+E(f66(x2773,x2774,x2771),f66(x2773,x2774,x2772))
% 2.51/2.64 [278]~E(x2781,x2782)+E(f193(x2781,x2783),f193(x2782,x2783))
% 2.51/2.64 [279]~E(x2791,x2792)+E(f193(x2793,x2791),f193(x2793,x2792))
% 2.51/2.64 [280]~E(x2801,x2802)+E(f173(x2801,x2803),f173(x2802,x2803))
% 2.51/2.64 [281]~E(x2811,x2812)+E(f173(x2813,x2811),f173(x2813,x2812))
% 2.51/2.64 [282]~E(x2821,x2822)+E(f205(x2821,x2823),f205(x2822,x2823))
% 2.51/2.64 [283]~E(x2831,x2832)+E(f205(x2833,x2831),f205(x2833,x2832))
% 2.51/2.64 [284]~E(x2841,x2842)+E(f49(x2841),f49(x2842))
% 2.51/2.64 [285]~E(x2851,x2852)+E(f131(x2851,x2853),f131(x2852,x2853))
% 2.51/2.64 [286]~E(x2861,x2862)+E(f131(x2863,x2861),f131(x2863,x2862))
% 2.51/2.64 [287]~E(x2871,x2872)+E(f34(x2871),f34(x2872))
% 2.51/2.64 [288]~E(x2881,x2882)+E(f185(x2881,x2883),f185(x2882,x2883))
% 2.51/2.64 [289]~E(x2891,x2892)+E(f185(x2893,x2891),f185(x2893,x2892))
% 2.51/2.64 [290]~E(x2901,x2902)+E(f186(x2901,x2903),f186(x2902,x2903))
% 2.51/2.64 [291]~E(x2911,x2912)+E(f186(x2913,x2911),f186(x2913,x2912))
% 2.51/2.64 [292]~E(x2921,x2922)+E(f35(x2921),f35(x2922))
% 2.51/2.64 [293]~E(x2931,x2932)+E(f61(x2931),f61(x2932))
% 2.51/2.64 [294]~E(x2941,x2942)+E(f32(x2941),f32(x2942))
% 2.51/2.64 [295]~E(x2951,x2952)+E(f25(x2951),f25(x2952))
% 2.51/2.64 [296]~E(x2961,x2962)+E(f50(x2961),f50(x2962))
% 2.51/2.64 [297]~E(x2971,x2972)+E(f63(x2971,x2973),f63(x2972,x2973))
% 2.51/2.64 [298]~E(x2981,x2982)+E(f63(x2983,x2981),f63(x2983,x2982))
% 2.51/2.64 [299]~E(x2991,x2992)+E(f31(x2991),f31(x2992))
% 2.51/2.64 [300]~E(x3001,x3002)+E(f134(x3001,x3003),f134(x3002,x3003))
% 2.51/2.64 [301]~E(x3011,x3012)+E(f134(x3013,x3011),f134(x3013,x3012))
% 2.51/2.64 [302]~E(x3021,x3022)+E(f175(x3021,x3023),f175(x3022,x3023))
% 2.51/2.64 [303]~E(x3031,x3032)+E(f175(x3033,x3031),f175(x3033,x3032))
% 2.51/2.64 [304]~E(x3041,x3042)+E(f183(x3041,x3043),f183(x3042,x3043))
% 2.51/2.64 [305]~E(x3051,x3052)+E(f183(x3053,x3051),f183(x3053,x3052))
% 2.51/2.64 [306]~E(x3061,x3062)+E(f68(x3061,x3063,x3064),f68(x3062,x3063,x3064))
% 2.51/2.64 [307]~E(x3071,x3072)+E(f68(x3073,x3071,x3074),f68(x3073,x3072,x3074))
% 2.51/2.64 [308]~E(x3081,x3082)+E(f68(x3083,x3084,x3081),f68(x3083,x3084,x3082))
% 2.51/2.64 [309]~E(x3091,x3092)+E(f116(x3091,x3093),f116(x3092,x3093))
% 2.51/2.64 [310]~E(x3101,x3102)+E(f116(x3103,x3101),f116(x3103,x3102))
% 2.51/2.64 [311]~E(x3111,x3112)+E(f155(x3111,x3113),f155(x3112,x3113))
% 2.51/2.64 [312]~E(x3121,x3122)+E(f155(x3123,x3121),f155(x3123,x3122))
% 2.51/2.64 [313]~E(x3131,x3132)+E(f174(x3131,x3133),f174(x3132,x3133))
% 2.51/2.64 [314]~E(x3141,x3142)+E(f174(x3143,x3141),f174(x3143,x3142))
% 2.51/2.64 [315]~E(x3151,x3152)+E(f48(x3151),f48(x3152))
% 2.51/2.64 [316]~E(x3161,x3162)+E(f230(x3161),f230(x3162))
% 2.51/2.64 [317]~E(x3171,x3172)+E(f196(x3171,x3173),f196(x3172,x3173))
% 2.51/2.64 [318]~E(x3181,x3182)+E(f196(x3183,x3181),f196(x3183,x3182))
% 2.51/2.64 [319]~E(x3191,x3192)+E(f207(x3191,x3193),f207(x3192,x3193))
% 2.51/2.64 [320]~E(x3201,x3202)+E(f207(x3203,x3201),f207(x3203,x3202))
% 2.51/2.64 [321]~E(x3211,x3212)+E(f53(x3211),f53(x3212))
% 2.51/2.64 [322]~E(x3221,x3222)+E(f184(x3221,x3223),f184(x3222,x3223))
% 2.51/2.64 [323]~E(x3231,x3232)+E(f184(x3233,x3231),f184(x3233,x3232))
% 2.51/2.64 [324]~E(x3241,x3242)+E(f52(x3241),f52(x3242))
% 2.51/2.64 [325]~E(x3251,x3252)+E(f182(x3251,x3253),f182(x3252,x3253))
% 2.51/2.64 [326]~E(x3261,x3262)+E(f182(x3263,x3261),f182(x3263,x3262))
% 2.51/2.64 [327]~E(x3271,x3272)+E(f231(x3271),f231(x3272))
% 2.51/2.64 [328]~E(x3281,x3282)+E(f179(x3281,x3283),f179(x3282,x3283))
% 2.51/2.64 [329]~E(x3291,x3292)+E(f179(x3293,x3291),f179(x3293,x3292))
% 2.51/2.64 [330]~P1(x3301)+P1(x3302)+~E(x3301,x3302)
% 2.51/2.64 [331]~P7(x3311)+P7(x3312)+~E(x3311,x3312)
% 2.51/2.64 [332]~P2(x3321)+P2(x3322)+~E(x3321,x3322)
% 2.51/2.64 [333]~P3(x3331)+P3(x3332)+~E(x3331,x3332)
% 2.51/2.64 [334]~P8(x3341)+P8(x3342)+~E(x3341,x3342)
% 2.51/2.64 [335]~P4(x3351)+P4(x3352)+~E(x3351,x3352)
% 2.51/2.64 [336]~P5(x3361)+P5(x3362)+~E(x3361,x3362)
% 2.51/2.64 [337]~P6(x3371)+P6(x3372)+~E(x3371,x3372)
% 2.51/2.64
% 2.51/2.64 %-------------------------------------------
% 2.65/2.64 cnf(873,plain,
% 2.65/2.64 (P5(f102(f141(a216,x8731),f54(f38(f17(a44,f170(f21(a80),x8732)),f148(f22(a200),x8731)))))),
% 2.65/2.64 inference(rename_variables,[],[442])).
% 2.65/2.64 cnf(876,plain,
% 2.65/2.64 (P5(f102(f141(a216,x8761),f54(f38(f17(a44,f170(f21(a80),x8762)),f148(f22(a200),x8761)))))),
% 2.65/2.64 inference(rename_variables,[],[442])).
% 2.65/2.64 cnf(879,plain,
% 2.65/2.64 (P5(f154(f117(a212,x8791),f46(f37(f11(a44,f111(f19(a75),x8792)),f136(f20(a203),x8791)))))),
% 2.65/2.64 inference(rename_variables,[],[440])).
% 2.65/2.64 cnf(882,plain,
% 2.65/2.64 (P5(f154(f117(a212,x8821),f46(f37(f11(a44,f111(f19(a75),x8822)),f136(f20(a203),x8821)))))),
% 2.65/2.64 inference(rename_variables,[],[440])).
% 2.65/2.64 cnf(885,plain,
% 2.65/2.64 (P5(f126(f106(a217,x8851),f42(f9(a44,f159(f5(a79),x8852)),f151(f26(a211),x8851))))),
% 2.65/2.64 inference(rename_variables,[],[431])).
% 2.65/2.64 cnf(888,plain,
% 2.65/2.64 (P5(f126(f106(a217,x8881),f42(f9(a44,f159(f5(a79),x8882)),f151(f26(a211),x8881))))),
% 2.65/2.64 inference(rename_variables,[],[431])).
% 2.65/2.64 cnf(899,plain,
% 2.65/2.64 (~P5(f158(f159(a199,f164(a226,x8991)),x8991))),
% 2.65/2.64 inference(rename_variables,[],[451])).
% 2.65/2.64 cnf(924,plain,
% 2.65/2.64 (~E(f164(a226,x9241),x9241)),
% 2.65/2.64 inference(rename_variables,[],[449])).
% 2.65/2.64 cnf(1598,plain,
% 2.65/2.64 ($false),
% 2.65/2.64 inference(scs_inference,[],[452,338,339,340,341,342,343,345,372,421,450,427,424,449,924,360,451,899,394,396,431,885,888,432,439,440,879,882,442,873,876,2,510,507,865,864,863,862,843,842,691,677,650,628,622,592,591,590,589,588,575,533,785,593,620,336,3,640,702,668,658,653,669,627,672,854,700,683,684,579,578,527,526,525,524,502,495,494,493,492,491,490,489,488,487,486,485,484,483,482,481,480,479,478,477,476,475,474,473,472,471,470,469,468,467,466,465,464,463,462,461,460,459,458,457,456,455,454,453,329,328,327,326,325,324,323,322,321,320,319,318,317,316,315,314,313,312,311,310,309,308,307,306,305,304,303,302,301,300,299,298,297,296,295,294,293,292,291,290,289,288,287,286,285,284,283,282,281,280,279,278,277,276,275,274,273,272,271,270,269,268,267,266,265,264,263,262,261,260,259,258,257,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,816,815,810,808,770,765,762,695,694,693,692,617,616,609,608,582,573,572,570,569,567,566,565,564,563,562,561,560,559,558,557,556,555,554,553,552,551,550,549,548,547,546,545,544,543,542,541,540,539,538,537,536,535,523,522,517,516,515,512,511,506,505,504,503,497,853,852,851,850,830,829,741,740,739,738,737,736,735,734,733,732,731,730,729,728,727,726,725,724,723,722,721,720,719,718,717,716,857,856,840,826,825,823,822,793,790,768,705,704,703,679,678]),
% 2.65/2.64 ['proof']).
% 2.67/2.64 % SZS output end Proof
% 2.67/2.64 % Total time :1.740000s
%------------------------------------------------------------------------------