TSTP Solution File: SWW473^2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW473^2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n003.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 00:21:04 EDT 2023
% Result : Theorem 1.25s 1.48s
% Output : Proof 1.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.22 % Problem : SWW473^2 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.23 % Command : do_cvc5 %s %d
% 0.23/0.44 % Computer : n003.cluster.edu
% 0.23/0.44 % Model : x86_64 x86_64
% 0.23/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.44 % Memory : 8042.1875MB
% 0.23/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.23/0.45 % CPULimit : 300
% 0.23/0.45 % WCLimit : 300
% 0.23/0.45 % DateTime : Sun Aug 27 18:46:55 EDT 2023
% 0.23/0.45 % CPUTime :
% 0.30/0.67 %----Proving TH0
% 0.30/0.68 %------------------------------------------------------------------------------
% 0.30/0.68 % File : SWW473^2 : TPTP v8.1.2. Released v5.3.0.
% 0.30/0.68 % Domain : Software Verification
% 0.30/0.68 % Problem : Hoare's Logic with Procedures line 383, 500 axioms selected
% 0.30/0.68 % Version : Especial.
% 0.30/0.68 % English :
% 0.30/0.68
% 0.30/0.68 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.30/0.68 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.30/0.68 % Source : [Bla11]
% 0.30/0.68 % Names : hoare_500_thf_l383 [Bla11]
% 0.30/0.68
% 0.30/0.68 % Status : Theorem
% 0.30/0.68 % Rating : 0.46 v8.1.0, 0.45 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.57 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v5.3.0
% 0.30/0.68 % Syntax : Number of formulae : 826 ( 137 unt; 107 typ; 0 def)
% 0.30/0.68 % Number of atoms : 2653 ( 494 equ; 85 cnn)
% 0.30/0.68 % Maximal formula atoms : 9 ( 3 avg)
% 0.30/0.68 % Number of connectives : 5606 ( 202 ~; 57 |; 185 &;4242 @)
% 0.30/0.68 % ( 137 <=>; 783 =>; 0 <=; 0 <~>)
% 0.30/0.68 % Maximal formula depth : 17 ( 7 avg)
% 0.30/0.68 % Number of types : 6 ( 5 usr)
% 0.30/0.68 % Number of type conns : 1635 (1635 >; 0 *; 0 +; 0 <<)
% 0.30/0.68 % Number of symbols : 108 ( 102 usr; 11 con; 0-3 aty)
% 0.30/0.68 % Number of variables : 1787 ( 105 ^;1617 !; 65 ?;1787 :)
% 0.30/0.68 % SPC : TH0_THM_EQU_NAR
% 0.30/0.68
% 0.30/0.68 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.30/0.68 % 2011-08-09 19:38:20
% 0.30/0.68 %------------------------------------------------------------------------------
% 0.30/0.68 %----Should-be-implicit typings (5)
% 0.30/0.68 thf(ty_ty_t__a,type,
% 0.30/0.68 x_a: $tType ).
% 0.30/0.68
% 0.30/0.68 thf(ty_ty_tc__Com__Ocom,type,
% 0.30/0.68 com: $tType ).
% 0.30/0.68
% 0.30/0.68 thf(ty_ty_tc__Com__Opname,type,
% 0.30/0.68 pname: $tType ).
% 0.30/0.68
% 0.30/0.68 thf(ty_ty_tc__Nat__Onat,type,
% 0.30/0.68 nat: $tType ).
% 0.30/0.68
% 0.30/0.68 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.30/0.68 option_com: $tType ).
% 0.30/0.68
% 0.30/0.68 %----Explicit typings (102)
% 0.30/0.68 thf(sy_c_Com_Obody,type,
% 0.30/0.68 body: pname > option_com ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ocard_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ocard_000t__a,type,
% 0.30/0.68 finite_card_a: ( x_a > $o ) > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ocard_000tc__Com__Opname,type,
% 0.30/0.68 finite_card_pname: ( pname > $o ) > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
% 0.30/0.68 finite_card_nat: ( nat > $o ) > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000t__a,type,
% 0.30/0.68 finite_finite_a: ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.30/0.68 finite_finite_pname: ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
% 0.30/0.68 finite_finite_nat: ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.30/0.68 minus_minus_nat: nat > nat > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.30/0.68 one_one_nat: nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.30/0.68 plus_plus_nat: nat > nat > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.30/0.68 zero_zero_nat: nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Nat_OSuc,type,
% 0.30/0.68 suc: nat > nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Nat_Onat_Onat__case_000_Eo,type,
% 0.30/0.68 nat_case_o: $o > ( nat > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.30/0.68 the_com: option_com > com ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 bot_bot_a_o_o: ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 bot_bot_pname_o_o: ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 bot_bot_nat_o_o: ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 bot_bot_a_o: x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 bot_bot_pname_o: pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 bot_bot_nat_o: nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.30/0.68 bot_bot_o: $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat,type,
% 0.30/0.68 bot_bot_nat: nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.30/0.68 ord_less_nat: nat > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 0.30/0.68 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
% 0.30/0.68 ord_less_eq_o: $o > $o > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.30/0.68 ord_less_eq_nat: nat > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.30/0.68 collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000t__a,type,
% 0.30/0.68 collect_a: ( x_a > $o ) > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.30/0.68 collect_pname: ( pname > $o ) > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
% 0.30/0.68 collect_nat: ( nat > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000t__a,type,
% 0.30/0.68 image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Com__Opname,type,
% 0.30/0.68 image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Nat__Onat,type,
% 0.30/0.68 image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000t__a,type,
% 0.30/0.68 image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 0.30/0.68 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat,type,
% 0.30/0.68 image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000t__a,type,
% 0.30/0.68 image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Com__Opname,type,
% 0.30/0.68 image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat,type,
% 0.30/0.68 image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000t__a_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 image_a_a_o: ( x_a > x_a > $o ) > ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 image_a_pname_o: ( x_a > pname > $o ) > ( x_a > $o ) > ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 image_a_nat_o: ( x_a > nat > $o ) > ( x_a > $o ) > ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000t__a_000t__a,type,
% 0.30/0.68 image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000t__a_000tc__Com__Opname,type,
% 0.30/0.68 image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000t__a_000tc__Nat__Onat,type,
% 0.30/0.68 image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000t__a,type,
% 0.30/0.68 image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.30/0.68 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat,type,
% 0.30/0.68 image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000t__a,type,
% 0.30/0.68 image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,type,
% 0.30/0.68 image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Nat__Onat,type,
% 0.30/0.68 image_nat_nat: ( nat > nat ) > ( nat > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oinsert_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oinsert_000t__a,type,
% 0.30/0.68 insert_a: x_a > ( x_a > $o ) > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.30/0.68 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_Set_Oinsert_000tc__Nat__Onat,type,
% 0.30/0.68 insert_nat: nat > ( nat > $o ) > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_fequal_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 fequal_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_fequal_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 fequal_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_fequal_000t__a,type,
% 0.30/0.68 fequal_a: x_a > x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_fequal_000tc__Com__Opname,type,
% 0.30/0.68 fequal_pname: pname > pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_fequal_000tc__Nat__Onat,type,
% 0.30/0.68 fequal_nat: nat > nat > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_member_000_062_It__a_M_Eo_J,type,
% 0.30/0.68 member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.30/0.68 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.30/0.68 member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_member_000t__a,type,
% 0.30/0.68 member_a: x_a > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_member_000tc__Com__Opname,type,
% 0.30/0.68 member_pname: pname > ( pname > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_c_member_000tc__Nat__Onat,type,
% 0.30/0.68 member_nat: nat > ( nat > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_v_G,type,
% 0.30/0.68 g: x_a > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_v_P,type,
% 0.30/0.68 p: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_v_U,type,
% 0.30/0.68 u: pname > $o ).
% 0.30/0.68
% 0.30/0.68 thf(sy_v_mgt,type,
% 0.30/0.68 mgt: com > x_a ).
% 0.30/0.68
% 0.30/0.68 thf(sy_v_mgt__call,type,
% 0.30/0.68 mgt_call: pname > x_a ).
% 0.30/0.68
% 0.30/0.68 thf(sy_v_na,type,
% 0.30/0.68 na: nat ).
% 0.30/0.68
% 0.30/0.68 thf(sy_v_pn,type,
% 0.30/0.68 pn: pname ).
% 0.30/0.68
% 0.30/0.68 thf(sy_v_wt,type,
% 0.30/0.68 wt: com > $o ).
% 0.30/0.68
% 0.30/0.68 %----Relevant facts (700)
% 0.30/0.68 thf(fact_0_assms_I1_J,axiom,
% 0.30/0.68 ! [Ts: x_a > $o,G: x_a > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o @ Ts @ G )
% 0.30/0.68 => ( p @ G @ Ts ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_1_finite__Collect__subsets,axiom,
% 0.30/0.68 ! [A_92: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_92 )
% 0.30/0.68 => ( finite1676163439at_o_o
% 0.30/0.68 @ ( collect_nat_o_o
% 0.30/0.68 @ ^ [B_47: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_2_finite__Collect__subsets,axiom,
% 0.30/0.68 ! [A_92: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_92 )
% 0.30/0.68 => ( finite1066544169me_o_o
% 0.30/0.68 @ ( collect_pname_o_o
% 0.30/0.68 @ ^ [B_47: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_3_finite__Collect__subsets,axiom,
% 0.30/0.68 ! [A_92: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_92 )
% 0.30/0.68 => ( finite_finite_a_o_o
% 0.30/0.68 @ ( collect_a_o_o
% 0.30/0.68 @ ^ [B_47: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_4_finite__Collect__subsets,axiom,
% 0.30/0.68 ! [A_92: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_92 )
% 0.30/0.68 => ( finite_finite_a_o
% 0.30/0.68 @ ( collect_a_o
% 0.30/0.68 @ ^ [B_47: x_a > $o] : ( ord_less_eq_a_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_5_finite__Collect__subsets,axiom,
% 0.30/0.68 ! [A_92: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_92 )
% 0.30/0.68 => ( finite297249702name_o
% 0.30/0.68 @ ( collect_pname_o
% 0.30/0.68 @ ^ [B_47: pname > $o] : ( ord_less_eq_pname_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_6_finite__Collect__subsets,axiom,
% 0.30/0.68 ! [A_92: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_92 )
% 0.30/0.68 => ( finite_finite_nat_o
% 0.30/0.68 @ ( collect_nat_o
% 0.30/0.68 @ ^ [B_47: nat > $o] : ( ord_less_eq_nat_o @ B_47 @ A_92 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_7_finite__imageI,axiom,
% 0.30/0.68 ! [H: pname > nat > $o,F_25: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ F_25 )
% 0.30/0.68 => ( finite_finite_nat_o @ ( image_pname_nat_o @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_8_finite__imageI,axiom,
% 0.30/0.68 ! [H: pname > pname > $o,F_25: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ F_25 )
% 0.30/0.68 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_9_finite__imageI,axiom,
% 0.30/0.68 ! [H: pname > x_a > $o,F_25: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ F_25 )
% 0.30/0.68 => ( finite_finite_a_o @ ( image_pname_a_o @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_10_finite__imageI,axiom,
% 0.30/0.68 ! [H: nat > x_a,F_25: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ F_25 )
% 0.30/0.68 => ( finite_finite_a @ ( image_nat_a @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_11_finite__imageI,axiom,
% 0.30/0.68 ! [H: nat > nat > $o,F_25: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ F_25 )
% 0.30/0.68 => ( finite_finite_nat_o @ ( image_nat_nat_o @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_12_finite__imageI,axiom,
% 0.30/0.68 ! [H: nat > pname > $o,F_25: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ F_25 )
% 0.30/0.68 => ( finite297249702name_o @ ( image_nat_pname_o @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_13_finite__imageI,axiom,
% 0.30/0.68 ! [H: nat > x_a > $o,F_25: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ F_25 )
% 0.30/0.68 => ( finite_finite_a_o @ ( image_nat_a_o @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_14_finite__imageI,axiom,
% 0.30/0.68 ! [H: x_a > pname,F_25: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ F_25 )
% 0.30/0.68 => ( finite_finite_pname @ ( image_a_pname @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_15_finite__imageI,axiom,
% 0.30/0.68 ! [H: ( nat > $o ) > pname,F_25: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ F_25 )
% 0.30/0.68 => ( finite_finite_pname @ ( image_nat_o_pname @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_16_finite__imageI,axiom,
% 0.30/0.68 ! [H: ( pname > $o ) > pname,F_25: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ F_25 )
% 0.30/0.68 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_17_finite__imageI,axiom,
% 0.30/0.68 ! [H: ( x_a > $o ) > pname,F_25: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ F_25 )
% 0.30/0.68 => ( finite_finite_pname @ ( image_a_o_pname @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_18_finite__imageI,axiom,
% 0.30/0.68 ! [H: x_a > nat,F_25: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ F_25 )
% 0.30/0.68 => ( finite_finite_nat @ ( image_a_nat @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_19_finite__imageI,axiom,
% 0.30/0.68 ! [H: ( nat > $o ) > nat,F_25: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ F_25 )
% 0.30/0.68 => ( finite_finite_nat @ ( image_nat_o_nat @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_20_finite__imageI,axiom,
% 0.30/0.68 ! [H: ( pname > $o ) > nat,F_25: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ F_25 )
% 0.30/0.68 => ( finite_finite_nat @ ( image_pname_o_nat @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_21_finite__imageI,axiom,
% 0.30/0.68 ! [H: ( x_a > $o ) > nat,F_25: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ F_25 )
% 0.30/0.68 => ( finite_finite_nat @ ( image_a_o_nat @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_22_finite__imageI,axiom,
% 0.30/0.68 ! [H: pname > x_a,F_25: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ F_25 )
% 0.30/0.68 => ( finite_finite_a @ ( image_pname_a @ H @ F_25 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_23_finite_OinsertI,axiom,
% 0.30/0.68 ! [A_91: nat > $o,A_90: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_90 )
% 0.30/0.68 => ( finite_finite_nat_o @ ( insert_nat_o @ A_91 @ A_90 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_24_finite_OinsertI,axiom,
% 0.30/0.68 ! [A_91: pname > $o,A_90: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_90 )
% 0.30/0.68 => ( finite297249702name_o @ ( insert_pname_o @ A_91 @ A_90 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_25_finite_OinsertI,axiom,
% 0.30/0.68 ! [A_91: x_a > $o,A_90: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_90 )
% 0.30/0.68 => ( finite_finite_a_o @ ( insert_a_o @ A_91 @ A_90 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_26_finite_OinsertI,axiom,
% 0.30/0.68 ! [A_91: pname,A_90: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_90 )
% 0.30/0.68 => ( finite_finite_pname @ ( insert_pname @ A_91 @ A_90 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_27_finite_OinsertI,axiom,
% 0.30/0.68 ! [A_91: nat,A_90: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_90 )
% 0.30/0.68 => ( finite_finite_nat @ ( insert_nat @ A_91 @ A_90 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_28_finite_OinsertI,axiom,
% 0.30/0.68 ! [A_91: x_a,A_90: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_90 )
% 0.30/0.68 => ( finite_finite_a @ ( insert_a @ A_91 @ A_90 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_29_card__image__le,axiom,
% 0.30/0.68 ! [F_24: pname > pname,A_89: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_30_card__image__le,axiom,
% 0.30/0.68 ! [F_24: x_a > x_a,A_89: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_31_card__image__le,axiom,
% 0.30/0.68 ! [F_24: ( nat > $o ) > x_a,A_89: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ F_24 @ A_89 ) ) @ ( finite_card_nat_o @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_32_card__image__le,axiom,
% 0.30/0.68 ! [F_24: ( pname > $o ) > x_a,A_89: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ F_24 @ A_89 ) ) @ ( finite_card_pname_o @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_33_card__image__le,axiom,
% 0.30/0.68 ! [F_24: ( x_a > $o ) > x_a,A_89: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ F_24 @ A_89 ) ) @ ( finite_card_a_o @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_34_card__image__le,axiom,
% 0.30/0.68 ! [F_24: pname > nat,A_89: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_35_card__image__le,axiom,
% 0.30/0.68 ! [F_24: x_a > nat,A_89: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_36_card__image__le,axiom,
% 0.30/0.68 ! [F_24: ( nat > $o ) > nat,A_89: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_nat_o @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_37_card__image__le,axiom,
% 0.30/0.68 ! [F_24: ( pname > $o ) > nat,A_89: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_pname_o @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_38_card__image__le,axiom,
% 0.30/0.68 ! [F_24: ( x_a > $o ) > nat,A_89: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ F_24 @ A_89 ) ) @ ( finite_card_a_o @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_39_card__image__le,axiom,
% 0.30/0.68 ! [F_24: x_a > pname,A_89: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ F_24 @ A_89 ) ) @ ( finite_card_a @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_40_card__image__le,axiom,
% 0.30/0.68 ! [F_24: nat > pname,A_89: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ F_24 @ A_89 ) ) @ ( finite_card_nat @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_41_card__image__le,axiom,
% 0.30/0.68 ! [F_24: pname > x_a,A_89: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_89 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ F_24 @ A_89 ) ) @ ( finite_card_pname @ A_89 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_42_card__mono,axiom,
% 0.30/0.68 ! [A_88: ( nat > $o ) > $o,B_46: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ B_46 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o_o @ A_88 @ B_46 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_88 ) @ ( finite_card_nat_o @ B_46 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_43_card__mono,axiom,
% 0.30/0.68 ! [A_88: ( pname > $o ) > $o,B_46: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ B_46 )
% 0.30/0.68 => ( ( ord_le1205211808me_o_o @ A_88 @ B_46 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_88 ) @ ( finite_card_pname_o @ B_46 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_44_card__mono,axiom,
% 0.30/0.68 ! [A_88: ( x_a > $o ) > $o,B_46: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ B_46 )
% 0.30/0.68 => ( ( ord_less_eq_a_o_o @ A_88 @ B_46 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_88 ) @ ( finite_card_a_o @ B_46 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_45_card__mono,axiom,
% 0.30/0.68 ! [A_88: pname > $o,B_46: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_46 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ A_88 @ B_46 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_pname @ A_88 ) @ ( finite_card_pname @ B_46 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_46_card__mono,axiom,
% 0.30/0.68 ! [A_88: x_a > $o,B_46: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_46 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ A_88 @ B_46 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a @ A_88 ) @ ( finite_card_a @ B_46 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_47_card__mono,axiom,
% 0.30/0.68 ! [A_88: nat > $o,B_46: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_46 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ A_88 @ B_46 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ A_88 ) @ ( finite_card_nat @ B_46 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_48_card__seteq,axiom,
% 0.30/0.68 ! [A_87: ( nat > $o ) > $o,B_45: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o_o @ A_87 @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B_45 ) @ ( finite_card_nat_o @ A_87 ) )
% 0.30/0.68 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_49_card__seteq,axiom,
% 0.30/0.68 ! [A_87: ( pname > $o ) > $o,B_45: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ B_45 )
% 0.30/0.68 => ( ( ord_le1205211808me_o_o @ A_87 @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B_45 ) @ ( finite_card_pname_o @ A_87 ) )
% 0.30/0.68 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_50_card__seteq,axiom,
% 0.30/0.68 ! [A_87: ( x_a > $o ) > $o,B_45: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_a_o_o @ A_87 @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_nat @ ( finite_card_a_o @ B_45 ) @ ( finite_card_a_o @ A_87 ) )
% 0.30/0.68 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_51_card__seteq,axiom,
% 0.30/0.68 ! [A_87: pname > $o,B_45: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ A_87 @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_nat @ ( finite_card_pname @ B_45 ) @ ( finite_card_pname @ A_87 ) )
% 0.30/0.68 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_52_card__seteq,axiom,
% 0.30/0.68 ! [A_87: x_a > $o,B_45: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ A_87 @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_nat @ ( finite_card_a @ B_45 ) @ ( finite_card_a @ A_87 ) )
% 0.30/0.68 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_53_card__seteq,axiom,
% 0.30/0.68 ! [A_87: nat > $o,B_45: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ A_87 @ B_45 )
% 0.30/0.68 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B_45 ) @ ( finite_card_nat @ A_87 ) )
% 0.30/0.68 => ( A_87 = B_45 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_54_card__insert__le,axiom,
% 0.30/0.68 ! [X_33: nat > $o,A_86: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_86 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_86 ) @ ( finite_card_nat_o @ ( insert_nat_o @ X_33 @ A_86 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_55_card__insert__le,axiom,
% 0.30/0.68 ! [X_33: pname > $o,A_86: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_86 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_86 ) @ ( finite_card_pname_o @ ( insert_pname_o @ X_33 @ A_86 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_56_card__insert__le,axiom,
% 0.30/0.68 ! [X_33: x_a > $o,A_86: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_86 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_86 ) @ ( finite_card_a_o @ ( insert_a_o @ X_33 @ A_86 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_57_card__insert__le,axiom,
% 0.30/0.68 ! [X_33: pname,A_86: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_86 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_pname @ A_86 ) @ ( finite_card_pname @ ( insert_pname @ X_33 @ A_86 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_58_card__insert__le,axiom,
% 0.30/0.68 ! [X_33: nat,A_86: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_86 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ A_86 ) @ ( finite_card_nat @ ( insert_nat @ X_33 @ A_86 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_59_card__insert__le,axiom,
% 0.30/0.68 ! [X_33: x_a,A_86: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_86 )
% 0.30/0.68 => ( ord_less_eq_nat @ ( finite_card_a @ A_86 ) @ ( finite_card_a @ ( insert_a @ X_33 @ A_86 ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_60_card__insert__if,axiom,
% 0.30/0.68 ! [X_32: nat > $o,A_85: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_85 )
% 0.30/0.68 => ( ( ( member_nat_o @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_32 @ A_85 ) )
% 0.30/0.68 = ( finite_card_nat_o @ A_85 ) ) )
% 0.30/0.68 & ( ~ ( member_nat_o @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_32 @ A_85 ) )
% 0.30/0.68 = ( suc @ ( finite_card_nat_o @ A_85 ) ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_61_card__insert__if,axiom,
% 0.30/0.68 ! [X_32: pname > $o,A_85: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_85 )
% 0.30/0.68 => ( ( ( member_pname_o @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_32 @ A_85 ) )
% 0.30/0.68 = ( finite_card_pname_o @ A_85 ) ) )
% 0.30/0.68 & ( ~ ( member_pname_o @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_32 @ A_85 ) )
% 0.30/0.68 = ( suc @ ( finite_card_pname_o @ A_85 ) ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_62_card__insert__if,axiom,
% 0.30/0.68 ! [X_32: x_a > $o,A_85: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_85 )
% 0.30/0.68 => ( ( ( member_a_o @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_a_o @ ( insert_a_o @ X_32 @ A_85 ) )
% 0.30/0.68 = ( finite_card_a_o @ A_85 ) ) )
% 0.30/0.68 & ( ~ ( member_a_o @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_a_o @ ( insert_a_o @ X_32 @ A_85 ) )
% 0.30/0.68 = ( suc @ ( finite_card_a_o @ A_85 ) ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_63_card__insert__if,axiom,
% 0.30/0.68 ! [X_32: nat,A_85: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_85 )
% 0.30/0.68 => ( ( ( member_nat @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_nat @ ( insert_nat @ X_32 @ A_85 ) )
% 0.30/0.68 = ( finite_card_nat @ A_85 ) ) )
% 0.30/0.68 & ( ~ ( member_nat @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_nat @ ( insert_nat @ X_32 @ A_85 ) )
% 0.30/0.68 = ( suc @ ( finite_card_nat @ A_85 ) ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_64_card__insert__if,axiom,
% 0.30/0.68 ! [X_32: pname,A_85: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_85 )
% 0.30/0.68 => ( ( ( member_pname @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_pname @ ( insert_pname @ X_32 @ A_85 ) )
% 0.30/0.68 = ( finite_card_pname @ A_85 ) ) )
% 0.30/0.68 & ( ~ ( member_pname @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_pname @ ( insert_pname @ X_32 @ A_85 ) )
% 0.30/0.68 = ( suc @ ( finite_card_pname @ A_85 ) ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_65_card__insert__if,axiom,
% 0.30/0.68 ! [X_32: x_a,A_85: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_85 )
% 0.30/0.68 => ( ( ( member_a @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_a @ ( insert_a @ X_32 @ A_85 ) )
% 0.30/0.68 = ( finite_card_a @ A_85 ) ) )
% 0.30/0.68 & ( ~ ( member_a @ X_32 @ A_85 )
% 0.30/0.68 => ( ( finite_card_a @ ( insert_a @ X_32 @ A_85 ) )
% 0.30/0.68 = ( suc @ ( finite_card_a @ A_85 ) ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_66_card__insert__disjoint,axiom,
% 0.30/0.68 ! [X_31: nat > $o,A_84: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_84 )
% 0.30/0.68 => ( ~ ( member_nat_o @ X_31 @ A_84 )
% 0.30/0.68 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_31 @ A_84 ) )
% 0.30/0.68 = ( suc @ ( finite_card_nat_o @ A_84 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_67_card__insert__disjoint,axiom,
% 0.30/0.68 ! [X_31: pname > $o,A_84: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_84 )
% 0.30/0.68 => ( ~ ( member_pname_o @ X_31 @ A_84 )
% 0.30/0.68 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_31 @ A_84 ) )
% 0.30/0.68 = ( suc @ ( finite_card_pname_o @ A_84 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_68_card__insert__disjoint,axiom,
% 0.30/0.68 ! [X_31: x_a > $o,A_84: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_84 )
% 0.30/0.68 => ( ~ ( member_a_o @ X_31 @ A_84 )
% 0.30/0.68 => ( ( finite_card_a_o @ ( insert_a_o @ X_31 @ A_84 ) )
% 0.30/0.68 = ( suc @ ( finite_card_a_o @ A_84 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_69_card__insert__disjoint,axiom,
% 0.30/0.68 ! [X_31: nat,A_84: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_84 )
% 0.30/0.68 => ( ~ ( member_nat @ X_31 @ A_84 )
% 0.30/0.68 => ( ( finite_card_nat @ ( insert_nat @ X_31 @ A_84 ) )
% 0.30/0.68 = ( suc @ ( finite_card_nat @ A_84 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_70_card__insert__disjoint,axiom,
% 0.30/0.68 ! [X_31: pname,A_84: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_84 )
% 0.30/0.68 => ( ~ ( member_pname @ X_31 @ A_84 )
% 0.30/0.68 => ( ( finite_card_pname @ ( insert_pname @ X_31 @ A_84 ) )
% 0.30/0.68 = ( suc @ ( finite_card_pname @ A_84 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_71_card__insert__disjoint,axiom,
% 0.30/0.68 ! [X_31: x_a,A_84: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_84 )
% 0.30/0.68 => ( ~ ( member_a @ X_31 @ A_84 )
% 0.30/0.68 => ( ( finite_card_a @ ( insert_a @ X_31 @ A_84 ) )
% 0.30/0.68 = ( suc @ ( finite_card_a @ A_84 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_72_finite__Collect__conjI,axiom,
% 0.30/0.68 ! [Q_1: x_a > $o,P_10: x_a > $o] :
% 0.30/0.68 ( ( ( finite_finite_a @ ( collect_a @ P_10 ) )
% 0.30/0.68 | ( finite_finite_a @ ( collect_a @ Q_1 ) ) )
% 0.30/0.68 => ( finite_finite_a
% 0.30/0.68 @ ( collect_a
% 0.30/0.68 @ ^ [X_1: x_a] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_73_finite__Collect__conjI,axiom,
% 0.30/0.68 ! [Q_1: ( nat > $o ) > $o,P_10: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( ( finite_finite_nat_o @ ( collect_nat_o @ P_10 ) )
% 0.30/0.68 | ( finite_finite_nat_o @ ( collect_nat_o @ Q_1 ) ) )
% 0.30/0.68 => ( finite_finite_nat_o
% 0.30/0.68 @ ( collect_nat_o
% 0.30/0.68 @ ^ [X_1: nat > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_74_finite__Collect__conjI,axiom,
% 0.30/0.68 ! [Q_1: ( pname > $o ) > $o,P_10: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_10 ) )
% 0.30/0.68 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 0.30/0.68 => ( finite297249702name_o
% 0.30/0.68 @ ( collect_pname_o
% 0.30/0.68 @ ^ [X_1: pname > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_75_finite__Collect__conjI,axiom,
% 0.30/0.68 ! [Q_1: ( x_a > $o ) > $o,P_10: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( ( finite_finite_a_o @ ( collect_a_o @ P_10 ) )
% 0.30/0.68 | ( finite_finite_a_o @ ( collect_a_o @ Q_1 ) ) )
% 0.30/0.68 => ( finite_finite_a_o
% 0.30/0.68 @ ( collect_a_o
% 0.30/0.68 @ ^ [X_1: x_a > $o] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_76_finite__Collect__conjI,axiom,
% 0.30/0.68 ! [Q_1: pname > $o,P_10: pname > $o] :
% 0.30/0.68 ( ( ( finite_finite_pname @ ( collect_pname @ P_10 ) )
% 0.30/0.68 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 0.30/0.68 => ( finite_finite_pname
% 0.30/0.68 @ ( collect_pname
% 0.30/0.68 @ ^ [X_1: pname] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_77_finite__Collect__conjI,axiom,
% 0.30/0.68 ! [Q_1: nat > $o,P_10: nat > $o] :
% 0.30/0.68 ( ( ( finite_finite_nat @ ( collect_nat @ P_10 ) )
% 0.30/0.68 | ( finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
% 0.30/0.68 => ( finite_finite_nat
% 0.30/0.68 @ ( collect_nat
% 0.30/0.68 @ ^ [X_1: nat] : ( (&) @ ( P_10 @ X_1 ) @ ( Q_1 @ X_1 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_78_Suc__diff__le,axiom,
% 0.30/0.68 ! [N: nat,M: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.68 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.30/0.68 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_79_finite__Collect__le__nat,axiom,
% 0.30/0.68 ! [K: nat] :
% 0.30/0.68 ( finite_finite_nat
% 0.30/0.68 @ ( collect_nat
% 0.30/0.68 @ ^ [N_2: nat] : ( ord_less_eq_nat @ N_2 @ K ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_80_card__Collect__le__nat,axiom,
% 0.30/0.68 ! [N: nat] :
% 0.30/0.68 ( ( finite_card_nat
% 0.30/0.68 @ ( collect_nat
% 0.30/0.68 @ ^ [I_1: nat] : ( ord_less_eq_nat @ I_1 @ N ) ) )
% 0.30/0.68 = ( suc @ N ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_81_Suc__inject,axiom,
% 0.30/0.68 ! [X: nat,Y: nat] :
% 0.30/0.68 ( ( ( suc @ X )
% 0.30/0.68 = ( suc @ Y ) )
% 0.30/0.68 => ( X = Y ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_82_nat_Oinject,axiom,
% 0.30/0.68 ! [Nat_2: nat,Nat: nat] :
% 0.30/0.68 ( ( ( suc @ Nat_2 )
% 0.30/0.68 = ( suc @ Nat ) )
% 0.30/0.68 <=> ( Nat_2 = Nat ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_83_Suc__n__not__n,axiom,
% 0.30/0.68 ! [N: nat] :
% 0.30/0.68 ( ( suc @ N )
% 0.30/0.68 != N ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_84_n__not__Suc__n,axiom,
% 0.30/0.68 ! [N: nat] :
% 0.30/0.68 ( N
% 0.30/0.68 != ( suc @ N ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_85_le__antisym,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.68 => ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.68 => ( M = N ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_86_le__trans,axiom,
% 0.30/0.68 ! [K: nat,I: nat,J_1: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/0.68 => ( ( ord_less_eq_nat @ J_1 @ K )
% 0.30/0.68 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_87_eq__imp__le,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ( M = N )
% 0.30/0.68 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_88_nat__le__linear,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.68 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_89_le__refl,axiom,
% 0.30/0.68 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_90_diff__commute,axiom,
% 0.30/0.68 ! [I: nat,J_1: nat,K: nat] :
% 0.30/0.68 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J_1 ) @ K )
% 0.30/0.68 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J_1 ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_91_finite__Collect__disjI,axiom,
% 0.30/0.68 ! [P_9: x_a > $o,Q: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a
% 0.30/0.68 @ ( collect_a
% 0.30/0.68 @ ^ [X_1: x_a] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/0.68 <=> ( ( finite_finite_a @ ( collect_a @ P_9 ) )
% 0.30/0.68 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_92_finite__Collect__disjI,axiom,
% 0.30/0.68 ! [P_9: ( nat > $o ) > $o,Q: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o
% 0.30/0.68 @ ( collect_nat_o
% 0.30/0.68 @ ^ [X_1: nat > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/0.68 <=> ( ( finite_finite_nat_o @ ( collect_nat_o @ P_9 ) )
% 0.30/0.68 & ( finite_finite_nat_o @ ( collect_nat_o @ Q ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_93_finite__Collect__disjI,axiom,
% 0.30/0.68 ! [P_9: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o
% 0.30/0.68 @ ( collect_pname_o
% 0.30/0.68 @ ^ [X_1: pname > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/0.68 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_9 ) )
% 0.30/0.68 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_94_finite__Collect__disjI,axiom,
% 0.30/0.68 ! [P_9: ( x_a > $o ) > $o,Q: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o
% 0.30/0.68 @ ( collect_a_o
% 0.30/0.68 @ ^ [X_1: x_a > $o] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/0.68 <=> ( ( finite_finite_a_o @ ( collect_a_o @ P_9 ) )
% 0.30/0.68 & ( finite_finite_a_o @ ( collect_a_o @ Q ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_95_finite__Collect__disjI,axiom,
% 0.30/0.68 ! [P_9: pname > $o,Q: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname
% 0.30/0.68 @ ( collect_pname
% 0.30/0.68 @ ^ [X_1: pname] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/0.68 <=> ( ( finite_finite_pname @ ( collect_pname @ P_9 ) )
% 0.30/0.68 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_96_finite__Collect__disjI,axiom,
% 0.30/0.68 ! [P_9: nat > $o,Q: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat
% 0.30/0.68 @ ( collect_nat
% 0.30/0.68 @ ^ [X_1: nat] : ( (|) @ ( P_9 @ X_1 ) @ ( Q @ X_1 ) ) ) )
% 0.30/0.68 <=> ( ( finite_finite_nat @ ( collect_nat @ P_9 ) )
% 0.30/0.68 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_97_finite__insert,axiom,
% 0.30/0.68 ! [A_83: nat > $o,A_82: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ ( insert_nat_o @ A_83 @ A_82 ) )
% 0.30/0.68 <=> ( finite_finite_nat_o @ A_82 ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_98_finite__insert,axiom,
% 0.30/0.68 ! [A_83: pname > $o,A_82: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ ( insert_pname_o @ A_83 @ A_82 ) )
% 0.30/0.68 <=> ( finite297249702name_o @ A_82 ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_99_finite__insert,axiom,
% 0.30/0.68 ! [A_83: x_a > $o,A_82: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ ( insert_a_o @ A_83 @ A_82 ) )
% 0.30/0.68 <=> ( finite_finite_a_o @ A_82 ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_100_finite__insert,axiom,
% 0.30/0.68 ! [A_83: pname,A_82: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ ( insert_pname @ A_83 @ A_82 ) )
% 0.30/0.68 <=> ( finite_finite_pname @ A_82 ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_101_finite__insert,axiom,
% 0.30/0.68 ! [A_83: nat,A_82: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ ( insert_nat @ A_83 @ A_82 ) )
% 0.30/0.68 <=> ( finite_finite_nat @ A_82 ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_102_finite__insert,axiom,
% 0.30/0.68 ! [A_83: x_a,A_82: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ ( insert_a @ A_83 @ A_82 ) )
% 0.30/0.68 <=> ( finite_finite_a @ A_82 ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_103_finite__subset,axiom,
% 0.30/0.68 ! [A_81: ( nat > $o ) > $o,B_44: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o_o @ A_81 @ B_44 )
% 0.30/0.68 => ( ( finite_finite_nat_o @ B_44 )
% 0.30/0.68 => ( finite_finite_nat_o @ A_81 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_104_finite__subset,axiom,
% 0.30/0.68 ! [A_81: ( pname > $o ) > $o,B_44: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( ord_le1205211808me_o_o @ A_81 @ B_44 )
% 0.30/0.68 => ( ( finite297249702name_o @ B_44 )
% 0.30/0.68 => ( finite297249702name_o @ A_81 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_105_finite__subset,axiom,
% 0.30/0.68 ! [A_81: ( x_a > $o ) > $o,B_44: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o_o @ A_81 @ B_44 )
% 0.30/0.68 => ( ( finite_finite_a_o @ B_44 )
% 0.30/0.68 => ( finite_finite_a_o @ A_81 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_106_finite__subset,axiom,
% 0.30/0.68 ! [A_81: x_a > $o,B_44: x_a > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o @ A_81 @ B_44 )
% 0.30/0.68 => ( ( finite_finite_a @ B_44 )
% 0.30/0.68 => ( finite_finite_a @ A_81 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_107_finite__subset,axiom,
% 0.30/0.68 ! [A_81: pname > $o,B_44: pname > $o] :
% 0.30/0.68 ( ( ord_less_eq_pname_o @ A_81 @ B_44 )
% 0.30/0.68 => ( ( finite_finite_pname @ B_44 )
% 0.30/0.68 => ( finite_finite_pname @ A_81 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_108_finite__subset,axiom,
% 0.30/0.68 ! [A_81: nat > $o,B_44: nat > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o @ A_81 @ B_44 )
% 0.30/0.68 => ( ( finite_finite_nat @ B_44 )
% 0.30/0.68 => ( finite_finite_nat @ A_81 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_109_rev__finite__subset,axiom,
% 0.30/0.68 ! [A_80: ( nat > $o ) > $o,B_43: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ B_43 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o_o @ A_80 @ B_43 )
% 0.30/0.68 => ( finite_finite_nat_o @ A_80 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_110_rev__finite__subset,axiom,
% 0.30/0.68 ! [A_80: ( pname > $o ) > $o,B_43: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ B_43 )
% 0.30/0.68 => ( ( ord_le1205211808me_o_o @ A_80 @ B_43 )
% 0.30/0.68 => ( finite297249702name_o @ A_80 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_111_rev__finite__subset,axiom,
% 0.30/0.68 ! [A_80: ( x_a > $o ) > $o,B_43: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ B_43 )
% 0.30/0.68 => ( ( ord_less_eq_a_o_o @ A_80 @ B_43 )
% 0.30/0.68 => ( finite_finite_a_o @ A_80 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_112_rev__finite__subset,axiom,
% 0.30/0.68 ! [A_80: x_a > $o,B_43: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_43 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ A_80 @ B_43 )
% 0.30/0.68 => ( finite_finite_a @ A_80 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_113_rev__finite__subset,axiom,
% 0.30/0.68 ! [A_80: pname > $o,B_43: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_43 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ A_80 @ B_43 )
% 0.30/0.68 => ( finite_finite_pname @ A_80 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_114_rev__finite__subset,axiom,
% 0.30/0.68 ! [A_80: nat > $o,B_43: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_43 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ A_80 @ B_43 )
% 0.30/0.68 => ( finite_finite_nat @ A_80 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_115_Suc__leD,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/0.68 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_116_le__SucE,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.68 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.30/0.68 => ( M
% 0.30/0.68 = ( suc @ N ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_117_le__SucI,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.68 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_118_Suc__le__mono,axiom,
% 0.30/0.68 ! [N: nat,M: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.30/0.68 <=> ( ord_less_eq_nat @ N @ M ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_119_le__Suc__eq,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.68 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.68 | ( M
% 0.30/0.68 = ( suc @ N ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_120_not__less__eq__eq,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ~ ( ord_less_eq_nat @ M @ N )
% 0.30/0.68 <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_121_Suc__n__not__le__n,axiom,
% 0.30/0.68 ! [N: nat] :
% 0.30/0.68 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_122_Suc__diff__diff,axiom,
% 0.30/0.68 ! [M: nat,N: nat,K: nat] :
% 0.30/0.68 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.30/0.68 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_123_diff__Suc__Suc,axiom,
% 0.30/0.68 ! [M: nat,N: nat] :
% 0.30/0.68 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/0.68 = ( minus_minus_nat @ M @ N ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_124_le__diff__iff,axiom,
% 0.30/0.68 ! [N: nat,K: nat,M: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ K @ M )
% 0.30/0.68 => ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.68 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.30/0.68 <=> ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_125_Nat_Odiff__diff__eq,axiom,
% 0.30/0.68 ! [N: nat,K: nat,M: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ K @ M )
% 0.30/0.68 => ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.68 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.30/0.68 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_126_eq__diff__iff,axiom,
% 0.30/0.68 ! [N: nat,K: nat,M: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ K @ M )
% 0.30/0.68 => ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.68 => ( ( ( minus_minus_nat @ M @ K )
% 0.30/0.68 = ( minus_minus_nat @ N @ K ) )
% 0.30/0.68 <=> ( M = N ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_127_diff__diff__cancel,axiom,
% 0.30/0.68 ! [I: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ I @ N )
% 0.30/0.68 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.30/0.68 = I ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_128_diff__le__mono,axiom,
% 0.30/0.68 ! [L: nat,M: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.68 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_129_diff__le__mono2,axiom,
% 0.30/0.68 ! [L: nat,M: nat,N: nat] :
% 0.30/0.68 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.68 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_130_diff__le__self,axiom,
% 0.30/0.68 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_131_finite__surj,axiom,
% 0.30/0.68 ! [B_42: x_a > $o,F_23: x_a > x_a,A_79: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_42 @ ( image_a_a @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_132_finite__surj,axiom,
% 0.30/0.68 ! [B_42: x_a > $o,F_23: ( nat > $o ) > x_a,A_79: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_42 @ ( image_nat_o_a @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_133_finite__surj,axiom,
% 0.30/0.68 ! [B_42: x_a > $o,F_23: ( pname > $o ) > x_a,A_79: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_42 @ ( image_pname_o_a @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_134_finite__surj,axiom,
% 0.30/0.68 ! [B_42: x_a > $o,F_23: ( x_a > $o ) > x_a,A_79: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_42 @ ( image_a_o_a @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_135_finite__surj,axiom,
% 0.30/0.68 ! [B_42: ( nat > $o ) > $o,F_23: pname > nat > $o,A_79: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o_o @ B_42 @ ( image_pname_nat_o @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_nat_o @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_136_finite__surj,axiom,
% 0.30/0.68 ! [B_42: ( pname > $o ) > $o,F_23: pname > pname > $o,A_79: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_79 )
% 0.30/0.68 => ( ( ord_le1205211808me_o_o @ B_42 @ ( image_pname_pname_o @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite297249702name_o @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_137_finite__surj,axiom,
% 0.30/0.68 ! [B_42: ( x_a > $o ) > $o,F_23: pname > x_a > $o,A_79: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_a_o_o @ B_42 @ ( image_pname_a_o @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_a_o @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_138_finite__surj,axiom,
% 0.30/0.68 ! [B_42: pname > $o,F_23: pname > pname,A_79: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_pname_pname @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_139_finite__surj,axiom,
% 0.30/0.68 ! [B_42: nat > $o,F_23: pname > nat,A_79: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_pname_nat @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_140_finite__surj,axiom,
% 0.30/0.68 ! [B_42: x_a > $o,F_23: nat > x_a,A_79: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_42 @ ( image_nat_a @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_141_finite__surj,axiom,
% 0.30/0.68 ! [B_42: ( nat > $o ) > $o,F_23: nat > nat > $o,A_79: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o_o @ B_42 @ ( image_nat_nat_o @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_nat_o @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_142_finite__surj,axiom,
% 0.30/0.68 ! [B_42: ( pname > $o ) > $o,F_23: nat > pname > $o,A_79: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_79 )
% 0.30/0.68 => ( ( ord_le1205211808me_o_o @ B_42 @ ( image_nat_pname_o @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite297249702name_o @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_143_finite__surj,axiom,
% 0.30/0.68 ! [B_42: ( x_a > $o ) > $o,F_23: nat > x_a > $o,A_79: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_a_o_o @ B_42 @ ( image_nat_a_o @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_a_o @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_144_finite__surj,axiom,
% 0.30/0.68 ! [B_42: pname > $o,F_23: nat > pname,A_79: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_nat_pname @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_145_finite__surj,axiom,
% 0.30/0.68 ! [B_42: nat > $o,F_23: nat > nat,A_79: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_nat_nat @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_146_finite__surj,axiom,
% 0.30/0.68 ! [B_42: pname > $o,F_23: x_a > pname,A_79: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_a_pname @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_147_finite__surj,axiom,
% 0.30/0.68 ! [B_42: pname > $o,F_23: ( nat > $o ) > pname,A_79: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_nat_o_pname @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_148_finite__surj,axiom,
% 0.30/0.68 ! [B_42: pname > $o,F_23: ( pname > $o ) > pname,A_79: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_pname_o_pname @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_149_finite__surj,axiom,
% 0.30/0.68 ! [B_42: pname > $o,F_23: ( x_a > $o ) > pname,A_79: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_42 @ ( image_a_o_pname @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_pname @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_150_finite__surj,axiom,
% 0.30/0.68 ! [B_42: nat > $o,F_23: x_a > nat,A_79: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_a_nat @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_151_finite__surj,axiom,
% 0.30/0.68 ! [B_42: nat > $o,F_23: ( nat > $o ) > nat,A_79: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_nat_o_nat @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_152_finite__surj,axiom,
% 0.30/0.68 ! [B_42: nat > $o,F_23: ( pname > $o ) > nat,A_79: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_pname_o_nat @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_153_finite__surj,axiom,
% 0.30/0.68 ! [B_42: nat > $o,F_23: ( x_a > $o ) > nat,A_79: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_42 @ ( image_a_o_nat @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_nat @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_154_finite__surj,axiom,
% 0.30/0.68 ! [B_42: x_a > $o,F_23: pname > x_a,A_79: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ A_79 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_42 @ ( image_pname_a @ F_23 @ A_79 ) )
% 0.30/0.68 => ( finite_finite_a @ B_42 ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_155_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( nat > $o ) > x_a,A_78: ( nat > $o ) > $o,B_41: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_41 @ ( image_nat_o_a @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_156_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( pname > $o ) > x_a,A_78: ( pname > $o ) > $o,B_41: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_41 @ ( image_pname_o_a @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite297249702name_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_157_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( x_a > $o ) > x_a,A_78: ( x_a > $o ) > $o,B_41: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_41 @ ( image_a_o_a @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_o_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_158_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: x_a > x_a,A_78: x_a > $o,B_41: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_41 @ ( image_a_a @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: x_a > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_159_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: x_a > nat > $o,A_78: x_a > $o,B_41: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_a_nat_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: x_a > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_160_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: x_a > pname > $o,A_78: x_a > $o,B_41: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ B_41 )
% 0.30/0.68 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_a_pname_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: x_a > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_161_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: x_a > x_a > $o,A_78: x_a > $o,B_41: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_a_a_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: x_a > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_162_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: x_a > pname,A_78: x_a > $o,B_41: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_a_pname @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: x_a > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_163_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( nat > $o ) > pname,A_78: ( nat > $o ) > $o,B_41: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_nat_o_pname @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_164_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( pname > $o ) > pname,A_78: ( pname > $o ) > $o,B_41: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_pname_o_pname @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite297249702name_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_165_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( x_a > $o ) > pname,A_78: ( x_a > $o ) > $o,B_41: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_a_o_pname @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_o_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_166_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: x_a > nat,A_78: x_a > $o,B_41: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_a_nat @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: x_a > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_167_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( nat > $o ) > nat,A_78: ( nat > $o ) > $o,B_41: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_nat_o_nat @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_168_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( pname > $o ) > nat,A_78: ( pname > $o ) > $o,B_41: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_pname_o_nat @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( ord_le1205211808me_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite297249702name_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_169_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: ( x_a > $o ) > nat,A_78: ( x_a > $o ) > $o,B_41: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_a_o_nat @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( ord_less_eq_a_o_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_a_o @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_a_o_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_170_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: pname > nat > $o,A_78: pname > $o,B_41: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_pname_nat_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: pname > $o] :
% 0.30/0.68 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_pname @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_171_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: pname > pname > $o,A_78: pname > $o,B_41: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ B_41 )
% 0.30/0.68 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_pname_pname_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: pname > $o] :
% 0.30/0.68 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_pname @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_172_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: pname > x_a > $o,A_78: pname > $o,B_41: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_pname_a_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: pname > $o] :
% 0.30/0.68 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_pname @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_173_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: pname > pname,A_78: pname > $o,B_41: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_pname_pname @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: pname > $o] :
% 0.30/0.68 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_pname @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_174_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: pname > nat,A_78: pname > $o,B_41: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_pname_nat @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: pname > $o] :
% 0.30/0.68 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_pname @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_175_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: nat > x_a,A_78: nat > $o,B_41: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_41 @ ( image_nat_a @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: nat > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_176_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: nat > nat > $o,A_78: nat > $o,B_41: ( nat > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_nat_o @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o_o @ B_41 @ ( image_nat_nat_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: nat > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_nat_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_177_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: nat > pname > $o,A_78: nat > $o,B_41: ( pname > $o ) > $o] :
% 0.30/0.68 ( ( finite297249702name_o @ B_41 )
% 0.30/0.68 => ( ( ord_le1205211808me_o_o @ B_41 @ ( image_nat_pname_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: nat > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_pname_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_178_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: nat > x_a > $o,A_78: nat > $o,B_41: ( x_a > $o ) > $o] :
% 0.30/0.68 ( ( finite_finite_a_o @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o_o @ B_41 @ ( image_nat_a_o @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: nat > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_a_o @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_179_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: nat > pname,A_78: nat > $o,B_41: pname > $o] :
% 0.30/0.68 ( ( finite_finite_pname @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_pname_o @ B_41 @ ( image_nat_pname @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: nat > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_pname @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_180_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: nat > nat,A_78: nat > $o,B_41: nat > $o] :
% 0.30/0.68 ( ( finite_finite_nat @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_nat_o @ B_41 @ ( image_nat_nat @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: nat > $o] :
% 0.30/0.68 ( ( ord_less_eq_nat_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_nat @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_nat_nat @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_181_finite__subset__image,axiom,
% 0.30/0.68 ! [F_22: pname > x_a,A_78: pname > $o,B_41: x_a > $o] :
% 0.30/0.68 ( ( finite_finite_a @ B_41 )
% 0.30/0.68 => ( ( ord_less_eq_a_o @ B_41 @ ( image_pname_a @ F_22 @ A_78 ) )
% 0.30/0.68 => ? [C_12: pname > $o] :
% 0.30/0.68 ( ( ord_less_eq_pname_o @ C_12 @ A_78 )
% 0.30/0.68 & ( finite_finite_pname @ C_12 )
% 0.30/0.68 & ( B_41
% 0.30/0.68 = ( image_pname_a @ F_22 @ C_12 ) ) ) ) ) ).
% 0.30/0.68
% 0.30/0.68 thf(fact_182_lift__Suc__mono__le,axiom,
% 0.30/0.68 ! [N_4: nat,N_3: nat,F_21: nat > $o] :
% 0.30/0.68 ( ! [N_2: nat] : ( ord_less_eq_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/0.69 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/0.69 => ( ord_less_eq_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_183_lift__Suc__mono__le,axiom,
% 0.30/0.69 ! [N_4: nat,N_3: nat,F_21: nat > pname > $o] :
% 0.30/0.69 ( ! [N_2: nat] : ( ord_less_eq_pname_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/0.69 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_184_lift__Suc__mono__le,axiom,
% 0.30/0.69 ! [N_4: nat,N_3: nat,F_21: nat > nat > $o] :
% 0.30/0.69 ( ! [N_2: nat] : ( ord_less_eq_nat_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/0.69 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_185_lift__Suc__mono__le,axiom,
% 0.30/0.69 ! [N_4: nat,N_3: nat,F_21: nat > x_a > $o] :
% 0.30/0.69 ( ! [N_2: nat] : ( ord_less_eq_a_o @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/0.69 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/0.69 => ( ord_less_eq_a_o @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_186_lift__Suc__mono__le,axiom,
% 0.30/0.69 ! [N_4: nat,N_3: nat,F_21: nat > nat] :
% 0.30/0.69 ( ! [N_2: nat] : ( ord_less_eq_nat @ ( F_21 @ N_2 ) @ ( F_21 @ ( suc @ N_2 ) ) )
% 0.30/0.69 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.30/0.69 => ( ord_less_eq_nat @ ( F_21 @ N_4 ) @ ( F_21 @ N_3 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_187_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: nat > pname,A_77: nat > $o] :
% 0.30/0.69 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/0.69 => ( ( finite_finite_pname @ ( image_nat_pname @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_nat
% 0.30/0.69 @ ( collect_nat
% 0.30/0.69 @ ^ [A_2: nat] :
% 0.30/0.69 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_188_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: x_a > pname,A_77: x_a > $o] :
% 0.30/0.69 ( ~ ( finite_finite_a @ A_77 )
% 0.30/0.69 => ( ( finite_finite_pname @ ( image_a_pname @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_a
% 0.30/0.69 @ ( collect_a
% 0.30/0.69 @ ^ [A_2: x_a] :
% 0.30/0.69 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_189_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: pname > pname,A_77: pname > $o] :
% 0.30/0.69 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/0.69 => ( ( finite_finite_pname @ ( image_pname_pname @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_pname
% 0.30/0.69 @ ( collect_pname
% 0.30/0.69 @ ^ [A_2: pname] :
% 0.30/0.69 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_190_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: ( nat > $o ) > pname,A_77: ( nat > $o ) > $o] :
% 0.30/0.69 ( ~ ( finite_finite_nat_o @ A_77 )
% 0.30/0.69 => ( ( finite_finite_pname @ ( image_nat_o_pname @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: nat > $o] :
% 0.30/0.69 ( ( member_nat_o @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_nat_o
% 0.30/0.69 @ ( collect_nat_o
% 0.30/0.69 @ ^ [A_2: nat > $o] :
% 0.30/0.69 ( (&) @ ( member_nat_o @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_191_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: ( pname > $o ) > pname,A_77: ( pname > $o ) > $o] :
% 0.30/0.69 ( ~ ( finite297249702name_o @ A_77 )
% 0.30/0.69 => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: pname > $o] :
% 0.30/0.69 ( ( member_pname_o @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite297249702name_o
% 0.30/0.69 @ ( collect_pname_o
% 0.30/0.69 @ ^ [A_2: pname > $o] :
% 0.30/0.69 ( (&) @ ( member_pname_o @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_192_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: ( x_a > $o ) > pname,A_77: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ~ ( finite_finite_a_o @ A_77 )
% 0.30/0.69 => ( ( finite_finite_pname @ ( image_a_o_pname @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: x_a > $o] :
% 0.30/0.69 ( ( member_a_o @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_a_o
% 0.30/0.69 @ ( collect_a_o
% 0.30/0.69 @ ^ [A_2: x_a > $o] :
% 0.30/0.69 ( (&) @ ( member_a_o @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_193_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: nat > nat,A_77: nat > $o] :
% 0.30/0.69 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat @ ( image_nat_nat @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_nat
% 0.30/0.69 @ ( collect_nat
% 0.30/0.69 @ ^ [A_2: nat] :
% 0.30/0.69 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_194_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: x_a > nat,A_77: x_a > $o] :
% 0.30/0.69 ( ~ ( finite_finite_a @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat @ ( image_a_nat @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_a
% 0.30/0.69 @ ( collect_a
% 0.30/0.69 @ ^ [A_2: x_a] :
% 0.30/0.69 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_195_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: pname > nat,A_77: pname > $o] :
% 0.30/0.69 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat @ ( image_pname_nat @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_pname
% 0.30/0.69 @ ( collect_pname
% 0.30/0.69 @ ^ [A_2: pname] :
% 0.30/0.69 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_196_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: ( nat > $o ) > nat,A_77: ( nat > $o ) > $o] :
% 0.30/0.69 ( ~ ( finite_finite_nat_o @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat @ ( image_nat_o_nat @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: nat > $o] :
% 0.30/0.69 ( ( member_nat_o @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_nat_o
% 0.30/0.69 @ ( collect_nat_o
% 0.30/0.69 @ ^ [A_2: nat > $o] :
% 0.30/0.69 ( (&) @ ( member_nat_o @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_197_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: ( pname > $o ) > nat,A_77: ( pname > $o ) > $o] :
% 0.30/0.69 ( ~ ( finite297249702name_o @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat @ ( image_pname_o_nat @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: pname > $o] :
% 0.30/0.69 ( ( member_pname_o @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite297249702name_o
% 0.30/0.69 @ ( collect_pname_o
% 0.30/0.69 @ ^ [A_2: pname > $o] :
% 0.30/0.69 ( (&) @ ( member_pname_o @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_198_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: ( x_a > $o ) > nat,A_77: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ~ ( finite_finite_a_o @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat @ ( image_a_o_nat @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: x_a > $o] :
% 0.30/0.69 ( ( member_a_o @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_a_o
% 0.30/0.69 @ ( collect_a_o
% 0.30/0.69 @ ^ [A_2: x_a > $o] :
% 0.30/0.69 ( (&) @ ( member_a_o @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_199_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: nat > x_a,A_77: nat > $o] :
% 0.30/0.69 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/0.69 => ( ( finite_finite_a @ ( image_nat_a @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_nat
% 0.30/0.69 @ ( collect_nat
% 0.30/0.69 @ ^ [A_2: nat] :
% 0.30/0.69 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_200_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: nat > nat > $o,A_77: nat > $o] :
% 0.30/0.69 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat_o @ ( image_nat_nat_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_nat
% 0.30/0.69 @ ( collect_nat
% 0.30/0.69 @ ^ [A_2: nat] :
% 0.30/0.69 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_201_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: nat > pname > $o,A_77: nat > $o] :
% 0.30/0.69 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/0.69 => ( ( finite297249702name_o @ ( image_nat_pname_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_nat
% 0.30/0.69 @ ( collect_nat
% 0.30/0.69 @ ^ [A_2: nat] :
% 0.30/0.69 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_202_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: nat > x_a > $o,A_77: nat > $o] :
% 0.30/0.69 ( ~ ( finite_finite_nat @ A_77 )
% 0.30/0.69 => ( ( finite_finite_a_o @ ( image_nat_a_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_nat
% 0.30/0.69 @ ( collect_nat
% 0.30/0.69 @ ^ [A_2: nat] :
% 0.30/0.69 ( (&) @ ( member_nat @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_203_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: pname > nat > $o,A_77: pname > $o] :
% 0.30/0.69 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat_o @ ( image_pname_nat_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_pname
% 0.30/0.69 @ ( collect_pname
% 0.30/0.69 @ ^ [A_2: pname] :
% 0.30/0.69 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_204_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: pname > pname > $o,A_77: pname > $o] :
% 0.30/0.69 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/0.69 => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_pname
% 0.30/0.69 @ ( collect_pname
% 0.30/0.69 @ ^ [A_2: pname] :
% 0.30/0.69 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_205_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: pname > x_a > $o,A_77: pname > $o] :
% 0.30/0.69 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/0.69 => ( ( finite_finite_a_o @ ( image_pname_a_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_pname
% 0.30/0.69 @ ( collect_pname
% 0.30/0.69 @ ^ [A_2: pname] :
% 0.30/0.69 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_206_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: x_a > x_a,A_77: x_a > $o] :
% 0.30/0.69 ( ~ ( finite_finite_a @ A_77 )
% 0.30/0.69 => ( ( finite_finite_a @ ( image_a_a @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_a
% 0.30/0.69 @ ( collect_a
% 0.30/0.69 @ ^ [A_2: x_a] :
% 0.30/0.69 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_207_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: x_a > nat > $o,A_77: x_a > $o] :
% 0.30/0.69 ( ~ ( finite_finite_a @ A_77 )
% 0.30/0.69 => ( ( finite_finite_nat_o @ ( image_a_nat_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_a
% 0.30/0.69 @ ( collect_a
% 0.30/0.69 @ ^ [A_2: x_a] :
% 0.30/0.69 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_208_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: x_a > pname > $o,A_77: x_a > $o] :
% 0.30/0.69 ( ~ ( finite_finite_a @ A_77 )
% 0.30/0.69 => ( ( finite297249702name_o @ ( image_a_pname_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_a
% 0.30/0.69 @ ( collect_a
% 0.30/0.69 @ ^ [A_2: x_a] :
% 0.30/0.69 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_209_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: x_a > x_a > $o,A_77: x_a > $o] :
% 0.30/0.69 ( ~ ( finite_finite_a @ A_77 )
% 0.30/0.69 => ( ( finite_finite_a_o @ ( image_a_a_o @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_a
% 0.30/0.69 @ ( collect_a
% 0.30/0.69 @ ^ [A_2: x_a] :
% 0.30/0.69 ( (&) @ ( member_a @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_210_pigeonhole__infinite,axiom,
% 0.30/0.69 ! [F_20: pname > x_a,A_77: pname > $o] :
% 0.30/0.69 ( ~ ( finite_finite_pname @ A_77 )
% 0.30/0.69 => ( ( finite_finite_a @ ( image_pname_a @ F_20 @ A_77 ) )
% 0.30/0.69 => ? [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_77 )
% 0.30/0.69 & ~ ( finite_finite_pname
% 0.30/0.69 @ ( collect_pname
% 0.30/0.69 @ ^ [A_2: pname] :
% 0.30/0.69 ( (&) @ ( member_pname @ A_2 @ A_77 )
% 0.30/0.69 @ ( ( F_20 @ A_2 )
% 0.30/0.69 = ( F_20 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_211_image__eqI,axiom,
% 0.30/0.69 ! [A_76: pname > $o,B_40: nat,F_19: pname > nat,X_30: pname] :
% 0.30/0.69 ( ( B_40
% 0.30/0.69 = ( F_19 @ X_30 ) )
% 0.30/0.69 => ( ( member_pname @ X_30 @ A_76 )
% 0.30/0.69 => ( member_nat @ B_40 @ ( image_pname_nat @ F_19 @ A_76 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_212_image__eqI,axiom,
% 0.30/0.69 ! [A_76: x_a > $o,B_40: nat,F_19: x_a > nat,X_30: x_a] :
% 0.30/0.69 ( ( B_40
% 0.30/0.69 = ( F_19 @ X_30 ) )
% 0.30/0.69 => ( ( member_a @ X_30 @ A_76 )
% 0.30/0.69 => ( member_nat @ B_40 @ ( image_a_nat @ F_19 @ A_76 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_213_image__eqI,axiom,
% 0.30/0.69 ! [A_76: nat > $o,B_40: pname,F_19: nat > pname,X_30: nat] :
% 0.30/0.69 ( ( B_40
% 0.30/0.69 = ( F_19 @ X_30 ) )
% 0.30/0.69 => ( ( member_nat @ X_30 @ A_76 )
% 0.30/0.69 => ( member_pname @ B_40 @ ( image_nat_pname @ F_19 @ A_76 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_214_image__eqI,axiom,
% 0.30/0.69 ! [A_76: nat > $o,B_40: x_a,F_19: nat > x_a,X_30: nat] :
% 0.30/0.69 ( ( B_40
% 0.30/0.69 = ( F_19 @ X_30 ) )
% 0.30/0.69 => ( ( member_nat @ X_30 @ A_76 )
% 0.30/0.69 => ( member_a @ B_40 @ ( image_nat_a @ F_19 @ A_76 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_215_image__eqI,axiom,
% 0.30/0.69 ! [A_76: pname > $o,B_40: x_a,F_19: pname > x_a,X_30: pname] :
% 0.30/0.69 ( ( B_40
% 0.30/0.69 = ( F_19 @ X_30 ) )
% 0.30/0.69 => ( ( member_pname @ X_30 @ A_76 )
% 0.30/0.69 => ( member_a @ B_40 @ ( image_pname_a @ F_19 @ A_76 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_216_equalityI,axiom,
% 0.30/0.69 ! [A_75: pname > $o,B_39: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_75 @ B_39 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ B_39 @ A_75 )
% 0.30/0.69 => ( A_75 = B_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_217_equalityI,axiom,
% 0.30/0.69 ! [A_75: nat > $o,B_39: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_75 @ B_39 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ B_39 @ A_75 )
% 0.30/0.69 => ( A_75 = B_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_218_equalityI,axiom,
% 0.30/0.69 ! [A_75: x_a > $o,B_39: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_75 @ B_39 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ B_39 @ A_75 )
% 0.30/0.69 => ( A_75 = B_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_219_subsetD,axiom,
% 0.30/0.69 ! [C_11: nat,A_74: nat > $o,B_38: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_74 @ B_38 )
% 0.30/0.69 => ( ( member_nat @ C_11 @ A_74 )
% 0.30/0.69 => ( member_nat @ C_11 @ B_38 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_220_subsetD,axiom,
% 0.30/0.69 ! [C_11: pname,A_74: pname > $o,B_38: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_74 @ B_38 )
% 0.30/0.69 => ( ( member_pname @ C_11 @ A_74 )
% 0.30/0.69 => ( member_pname @ C_11 @ B_38 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_221_subsetD,axiom,
% 0.30/0.69 ! [C_11: x_a,A_74: x_a > $o,B_38: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_74 @ B_38 )
% 0.30/0.69 => ( ( member_a @ C_11 @ A_74 )
% 0.30/0.69 => ( member_a @ C_11 @ B_38 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_222_insertCI,axiom,
% 0.30/0.69 ! [B_37: nat,A_73: nat,B_36: nat > $o] :
% 0.30/0.69 ( ( ~ ( member_nat @ A_73 @ B_36 )
% 0.30/0.69 => ( A_73 = B_37 ) )
% 0.30/0.69 => ( member_nat @ A_73 @ ( insert_nat @ B_37 @ B_36 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_223_insertCI,axiom,
% 0.30/0.69 ! [B_37: pname,A_73: pname,B_36: pname > $o] :
% 0.30/0.69 ( ( ~ ( member_pname @ A_73 @ B_36 )
% 0.30/0.69 => ( A_73 = B_37 ) )
% 0.30/0.69 => ( member_pname @ A_73 @ ( insert_pname @ B_37 @ B_36 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_224_insertCI,axiom,
% 0.30/0.69 ! [B_37: x_a,A_73: x_a,B_36: x_a > $o] :
% 0.30/0.69 ( ( ~ ( member_a @ A_73 @ B_36 )
% 0.30/0.69 => ( A_73 = B_37 ) )
% 0.30/0.69 => ( member_a @ A_73 @ ( insert_a @ B_37 @ B_36 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_225_insertE,axiom,
% 0.30/0.69 ! [A_72: nat,B_35: nat,A_71: nat > $o] :
% 0.30/0.69 ( ( member_nat @ A_72 @ ( insert_nat @ B_35 @ A_71 ) )
% 0.30/0.69 => ( ( A_72 != B_35 )
% 0.30/0.69 => ( member_nat @ A_72 @ A_71 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_226_insertE,axiom,
% 0.30/0.69 ! [A_72: pname,B_35: pname,A_71: pname > $o] :
% 0.30/0.69 ( ( member_pname @ A_72 @ ( insert_pname @ B_35 @ A_71 ) )
% 0.30/0.69 => ( ( A_72 != B_35 )
% 0.30/0.69 => ( member_pname @ A_72 @ A_71 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_227_insertE,axiom,
% 0.30/0.69 ! [A_72: x_a,B_35: x_a,A_71: x_a > $o] :
% 0.30/0.69 ( ( member_a @ A_72 @ ( insert_a @ B_35 @ A_71 ) )
% 0.30/0.69 => ( ( A_72 != B_35 )
% 0.30/0.69 => ( member_a @ A_72 @ A_71 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_228_zero__induct__lemma,axiom,
% 0.30/0.69 ! [I: nat,P: nat > $o,K: nat] :
% 0.30/0.69 ( ( P @ K )
% 0.30/0.69 => ( ! [N_2: nat] :
% 0.30/0.69 ( ( P @ ( suc @ N_2 ) )
% 0.30/0.69 => ( P @ N_2 ) )
% 0.30/0.69 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_229_Suc__le__D,axiom,
% 0.30/0.69 ! [N: nat,M_2: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ ( suc @ N ) @ M_2 )
% 0.30/0.69 => ? [M_1: nat] :
% 0.30/0.69 ( M_2
% 0.30/0.69 = ( suc @ M_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_230_insertI1,axiom,
% 0.30/0.69 ! [A_70: nat,B_34: nat > $o] : ( member_nat @ A_70 @ ( insert_nat @ A_70 @ B_34 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_231_insertI1,axiom,
% 0.30/0.69 ! [A_70: pname,B_34: pname > $o] : ( member_pname @ A_70 @ ( insert_pname @ A_70 @ B_34 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_232_insertI1,axiom,
% 0.30/0.69 ! [A_70: x_a,B_34: x_a > $o] : ( member_a @ A_70 @ ( insert_a @ A_70 @ B_34 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_233_insert__compr,axiom,
% 0.30/0.69 ! [A_69: nat > $o,B_33: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( insert_nat_o @ A_69 @ B_33 )
% 0.30/0.69 = ( collect_nat_o
% 0.30/0.69 @ ^ [X_1: nat > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_nat_o @ X_1 @ B_33 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_234_insert__compr,axiom,
% 0.30/0.69 ! [A_69: pname > $o,B_33: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( insert_pname_o @ A_69 @ B_33 )
% 0.30/0.69 = ( collect_pname_o
% 0.30/0.69 @ ^ [X_1: pname > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_pname_o @ X_1 @ B_33 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_235_insert__compr,axiom,
% 0.30/0.69 ! [A_69: x_a > $o,B_33: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( insert_a_o @ A_69 @ B_33 )
% 0.30/0.69 = ( collect_a_o
% 0.30/0.69 @ ^ [X_1: x_a > $o] : ( (|) @ ( X_1 = A_69 ) @ ( member_a_o @ X_1 @ B_33 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_236_insert__compr,axiom,
% 0.30/0.69 ! [A_69: nat,B_33: nat > $o] :
% 0.30/0.69 ( ( insert_nat @ A_69 @ B_33 )
% 0.30/0.69 = ( collect_nat
% 0.30/0.69 @ ^ [X_1: nat] : ( (|) @ ( X_1 = A_69 ) @ ( member_nat @ X_1 @ B_33 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_237_insert__compr,axiom,
% 0.30/0.69 ! [A_69: pname,B_33: pname > $o] :
% 0.30/0.69 ( ( insert_pname @ A_69 @ B_33 )
% 0.30/0.69 = ( collect_pname
% 0.30/0.69 @ ^ [X_1: pname] : ( (|) @ ( X_1 = A_69 ) @ ( member_pname @ X_1 @ B_33 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_238_insert__compr,axiom,
% 0.30/0.69 ! [A_69: x_a,B_33: x_a > $o] :
% 0.30/0.69 ( ( insert_a @ A_69 @ B_33 )
% 0.30/0.69 = ( collect_a
% 0.30/0.69 @ ^ [X_1: x_a] : ( (|) @ ( X_1 = A_69 ) @ ( member_a @ X_1 @ B_33 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_239_insert__Collect,axiom,
% 0.30/0.69 ! [A_68: pname,P_8: pname > $o] :
% 0.30/0.69 ( ( insert_pname @ A_68 @ ( collect_pname @ P_8 ) )
% 0.30/0.69 = ( collect_pname
% 0.30/0.69 @ ^ [U_1: pname] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_240_insert__Collect,axiom,
% 0.30/0.69 ! [A_68: nat > $o,P_8: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( insert_nat_o @ A_68 @ ( collect_nat_o @ P_8 ) )
% 0.30/0.69 = ( collect_nat_o
% 0.30/0.69 @ ^ [U_1: nat > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_241_insert__Collect,axiom,
% 0.30/0.69 ! [A_68: pname > $o,P_8: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( insert_pname_o @ A_68 @ ( collect_pname_o @ P_8 ) )
% 0.30/0.69 = ( collect_pname_o
% 0.30/0.69 @ ^ [U_1: pname > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_242_insert__Collect,axiom,
% 0.30/0.69 ! [A_68: x_a > $o,P_8: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( insert_a_o @ A_68 @ ( collect_a_o @ P_8 ) )
% 0.30/0.69 = ( collect_a_o
% 0.30/0.69 @ ^ [U_1: x_a > $o] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_243_insert__Collect,axiom,
% 0.30/0.69 ! [A_68: nat,P_8: nat > $o] :
% 0.30/0.69 ( ( insert_nat @ A_68 @ ( collect_nat @ P_8 ) )
% 0.30/0.69 = ( collect_nat
% 0.30/0.69 @ ^ [U_1: nat] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_244_insert__Collect,axiom,
% 0.30/0.69 ! [A_68: x_a,P_8: x_a > $o] :
% 0.30/0.69 ( ( insert_a @ A_68 @ ( collect_a @ P_8 ) )
% 0.30/0.69 = ( collect_a
% 0.30/0.69 @ ^ [U_1: x_a] : ( (=>) @ ( (~) @ ( U_1 = A_68 ) ) @ ( P_8 @ U_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_245_insert__absorb2,axiom,
% 0.30/0.69 ! [X_29: pname,A_67: pname > $o] :
% 0.30/0.69 ( ( insert_pname @ X_29 @ ( insert_pname @ X_29 @ A_67 ) )
% 0.30/0.69 = ( insert_pname @ X_29 @ A_67 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_246_insert__absorb2,axiom,
% 0.30/0.69 ! [X_29: nat,A_67: nat > $o] :
% 0.30/0.69 ( ( insert_nat @ X_29 @ ( insert_nat @ X_29 @ A_67 ) )
% 0.30/0.69 = ( insert_nat @ X_29 @ A_67 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_247_insert__absorb2,axiom,
% 0.30/0.69 ! [X_29: x_a,A_67: x_a > $o] :
% 0.30/0.69 ( ( insert_a @ X_29 @ ( insert_a @ X_29 @ A_67 ) )
% 0.30/0.69 = ( insert_a @ X_29 @ A_67 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_248_insert__commute,axiom,
% 0.30/0.69 ! [X_28: pname,Y_12: pname,A_66: pname > $o] :
% 0.30/0.69 ( ( insert_pname @ X_28 @ ( insert_pname @ Y_12 @ A_66 ) )
% 0.30/0.69 = ( insert_pname @ Y_12 @ ( insert_pname @ X_28 @ A_66 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_249_insert__commute,axiom,
% 0.30/0.69 ! [X_28: nat,Y_12: nat,A_66: nat > $o] :
% 0.30/0.69 ( ( insert_nat @ X_28 @ ( insert_nat @ Y_12 @ A_66 ) )
% 0.30/0.69 = ( insert_nat @ Y_12 @ ( insert_nat @ X_28 @ A_66 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_250_insert__commute,axiom,
% 0.30/0.69 ! [X_28: x_a,Y_12: x_a,A_66: x_a > $o] :
% 0.30/0.69 ( ( insert_a @ X_28 @ ( insert_a @ Y_12 @ A_66 ) )
% 0.30/0.69 = ( insert_a @ Y_12 @ ( insert_a @ X_28 @ A_66 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_251_insert__iff,axiom,
% 0.30/0.69 ! [A_65: nat,B_32: nat,A_64: nat > $o] :
% 0.30/0.69 ( ( member_nat @ A_65 @ ( insert_nat @ B_32 @ A_64 ) )
% 0.30/0.69 <=> ( ( A_65 = B_32 )
% 0.30/0.69 | ( member_nat @ A_65 @ A_64 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_252_insert__iff,axiom,
% 0.30/0.69 ! [A_65: pname,B_32: pname,A_64: pname > $o] :
% 0.30/0.69 ( ( member_pname @ A_65 @ ( insert_pname @ B_32 @ A_64 ) )
% 0.30/0.69 <=> ( ( A_65 = B_32 )
% 0.30/0.69 | ( member_pname @ A_65 @ A_64 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_253_insert__iff,axiom,
% 0.30/0.69 ! [A_65: x_a,B_32: x_a,A_64: x_a > $o] :
% 0.30/0.69 ( ( member_a @ A_65 @ ( insert_a @ B_32 @ A_64 ) )
% 0.30/0.69 <=> ( ( A_65 = B_32 )
% 0.30/0.69 | ( member_a @ A_65 @ A_64 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_254_insert__code,axiom,
% 0.30/0.69 ! [Y_11: pname,A_63: pname > $o,X_27: pname] :
% 0.30/0.69 ( ( insert_pname @ Y_11 @ A_63 @ X_27 )
% 0.30/0.69 <=> ( ( Y_11 = X_27 )
% 0.30/0.69 | ( A_63 @ X_27 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_255_insert__code,axiom,
% 0.30/0.69 ! [Y_11: nat,A_63: nat > $o,X_27: nat] :
% 0.30/0.69 ( ( insert_nat @ Y_11 @ A_63 @ X_27 )
% 0.30/0.69 <=> ( ( Y_11 = X_27 )
% 0.30/0.69 | ( A_63 @ X_27 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_256_insert__code,axiom,
% 0.30/0.69 ! [Y_11: x_a,A_63: x_a > $o,X_27: x_a] :
% 0.30/0.69 ( ( insert_a @ Y_11 @ A_63 @ X_27 )
% 0.30/0.69 <=> ( ( Y_11 = X_27 )
% 0.30/0.69 | ( A_63 @ X_27 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_257_insert__ident,axiom,
% 0.30/0.69 ! [B_31: nat > $o,X_26: nat,A_62: nat > $o] :
% 0.30/0.69 ( ~ ( member_nat @ X_26 @ A_62 )
% 0.30/0.69 => ( ~ ( member_nat @ X_26 @ B_31 )
% 0.30/0.69 => ( ( ( insert_nat @ X_26 @ A_62 )
% 0.30/0.69 = ( insert_nat @ X_26 @ B_31 ) )
% 0.30/0.69 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_258_insert__ident,axiom,
% 0.30/0.69 ! [B_31: pname > $o,X_26: pname,A_62: pname > $o] :
% 0.30/0.69 ( ~ ( member_pname @ X_26 @ A_62 )
% 0.30/0.69 => ( ~ ( member_pname @ X_26 @ B_31 )
% 0.30/0.69 => ( ( ( insert_pname @ X_26 @ A_62 )
% 0.30/0.69 = ( insert_pname @ X_26 @ B_31 ) )
% 0.30/0.69 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_259_insert__ident,axiom,
% 0.30/0.69 ! [B_31: x_a > $o,X_26: x_a,A_62: x_a > $o] :
% 0.30/0.69 ( ~ ( member_a @ X_26 @ A_62 )
% 0.30/0.69 => ( ~ ( member_a @ X_26 @ B_31 )
% 0.30/0.69 => ( ( ( insert_a @ X_26 @ A_62 )
% 0.30/0.69 = ( insert_a @ X_26 @ B_31 ) )
% 0.30/0.69 <=> ( A_62 = B_31 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_260_insertI2,axiom,
% 0.30/0.69 ! [B_30: nat,A_61: nat,B_29: nat > $o] :
% 0.30/0.69 ( ( member_nat @ A_61 @ B_29 )
% 0.30/0.69 => ( member_nat @ A_61 @ ( insert_nat @ B_30 @ B_29 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_261_insertI2,axiom,
% 0.30/0.69 ! [B_30: pname,A_61: pname,B_29: pname > $o] :
% 0.30/0.69 ( ( member_pname @ A_61 @ B_29 )
% 0.30/0.69 => ( member_pname @ A_61 @ ( insert_pname @ B_30 @ B_29 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_262_insertI2,axiom,
% 0.30/0.69 ! [B_30: x_a,A_61: x_a,B_29: x_a > $o] :
% 0.30/0.69 ( ( member_a @ A_61 @ B_29 )
% 0.30/0.69 => ( member_a @ A_61 @ ( insert_a @ B_30 @ B_29 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_263_insert__absorb,axiom,
% 0.30/0.69 ! [A_60: nat,A_59: nat > $o] :
% 0.30/0.69 ( ( member_nat @ A_60 @ A_59 )
% 0.30/0.69 => ( ( insert_nat @ A_60 @ A_59 )
% 0.30/0.69 = A_59 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_264_insert__absorb,axiom,
% 0.30/0.69 ! [A_60: pname,A_59: pname > $o] :
% 0.30/0.69 ( ( member_pname @ A_60 @ A_59 )
% 0.30/0.69 => ( ( insert_pname @ A_60 @ A_59 )
% 0.30/0.69 = A_59 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_265_insert__absorb,axiom,
% 0.30/0.69 ! [A_60: x_a,A_59: x_a > $o] :
% 0.30/0.69 ( ( member_a @ A_60 @ A_59 )
% 0.30/0.69 => ( ( insert_a @ A_60 @ A_59 )
% 0.30/0.69 = A_59 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_266_subset__refl,axiom,
% 0.30/0.69 ! [A_58: pname > $o] : ( ord_less_eq_pname_o @ A_58 @ A_58 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_267_subset__refl,axiom,
% 0.30/0.69 ! [A_58: nat > $o] : ( ord_less_eq_nat_o @ A_58 @ A_58 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_268_subset__refl,axiom,
% 0.30/0.69 ! [A_58: x_a > $o] : ( ord_less_eq_a_o @ A_58 @ A_58 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_269_set__eq__subset,axiom,
% 0.30/0.69 ! [A_57: pname > $o,B_28: pname > $o] :
% 0.30/0.69 ( ( A_57 = B_28 )
% 0.30/0.69 <=> ( ( ord_less_eq_pname_o @ A_57 @ B_28 )
% 0.30/0.69 & ( ord_less_eq_pname_o @ B_28 @ A_57 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_270_set__eq__subset,axiom,
% 0.30/0.69 ! [A_57: nat > $o,B_28: nat > $o] :
% 0.30/0.69 ( ( A_57 = B_28 )
% 0.30/0.69 <=> ( ( ord_less_eq_nat_o @ A_57 @ B_28 )
% 0.30/0.69 & ( ord_less_eq_nat_o @ B_28 @ A_57 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_271_set__eq__subset,axiom,
% 0.30/0.69 ! [A_57: x_a > $o,B_28: x_a > $o] :
% 0.30/0.69 ( ( A_57 = B_28 )
% 0.30/0.69 <=> ( ( ord_less_eq_a_o @ A_57 @ B_28 )
% 0.30/0.69 & ( ord_less_eq_a_o @ B_28 @ A_57 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_272_equalityD1,axiom,
% 0.30/0.69 ! [A_56: pname > $o,B_27: pname > $o] :
% 0.30/0.69 ( ( A_56 = B_27 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ A_56 @ B_27 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_273_equalityD1,axiom,
% 0.30/0.69 ! [A_56: nat > $o,B_27: nat > $o] :
% 0.30/0.69 ( ( A_56 = B_27 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ A_56 @ B_27 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_274_equalityD1,axiom,
% 0.30/0.69 ! [A_56: x_a > $o,B_27: x_a > $o] :
% 0.30/0.69 ( ( A_56 = B_27 )
% 0.30/0.69 => ( ord_less_eq_a_o @ A_56 @ B_27 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_275_equalityD2,axiom,
% 0.30/0.69 ! [A_55: pname > $o,B_26: pname > $o] :
% 0.30/0.69 ( ( A_55 = B_26 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ B_26 @ A_55 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_276_equalityD2,axiom,
% 0.30/0.69 ! [A_55: nat > $o,B_26: nat > $o] :
% 0.30/0.69 ( ( A_55 = B_26 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ B_26 @ A_55 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_277_equalityD2,axiom,
% 0.30/0.69 ! [A_55: x_a > $o,B_26: x_a > $o] :
% 0.30/0.69 ( ( A_55 = B_26 )
% 0.30/0.69 => ( ord_less_eq_a_o @ B_26 @ A_55 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_278_in__mono,axiom,
% 0.30/0.69 ! [X_25: nat,A_54: nat > $o,B_25: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_54 @ B_25 )
% 0.30/0.69 => ( ( member_nat @ X_25 @ A_54 )
% 0.30/0.69 => ( member_nat @ X_25 @ B_25 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_279_in__mono,axiom,
% 0.30/0.69 ! [X_25: pname,A_54: pname > $o,B_25: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_54 @ B_25 )
% 0.30/0.69 => ( ( member_pname @ X_25 @ A_54 )
% 0.30/0.69 => ( member_pname @ X_25 @ B_25 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_280_in__mono,axiom,
% 0.30/0.69 ! [X_25: x_a,A_54: x_a > $o,B_25: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_54 @ B_25 )
% 0.30/0.69 => ( ( member_a @ X_25 @ A_54 )
% 0.30/0.69 => ( member_a @ X_25 @ B_25 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_281_set__rev__mp,axiom,
% 0.30/0.69 ! [B_24: nat > $o,X_24: nat,A_53: nat > $o] :
% 0.30/0.69 ( ( member_nat @ X_24 @ A_53 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ A_53 @ B_24 )
% 0.30/0.69 => ( member_nat @ X_24 @ B_24 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_282_set__rev__mp,axiom,
% 0.30/0.69 ! [B_24: pname > $o,X_24: pname,A_53: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_24 @ A_53 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ A_53 @ B_24 )
% 0.30/0.69 => ( member_pname @ X_24 @ B_24 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_283_set__rev__mp,axiom,
% 0.30/0.69 ! [B_24: x_a > $o,X_24: x_a,A_53: x_a > $o] :
% 0.30/0.69 ( ( member_a @ X_24 @ A_53 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ A_53 @ B_24 )
% 0.30/0.69 => ( member_a @ X_24 @ B_24 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_284_set__mp,axiom,
% 0.30/0.69 ! [X_23: nat,A_52: nat > $o,B_23: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_52 @ B_23 )
% 0.30/0.69 => ( ( member_nat @ X_23 @ A_52 )
% 0.30/0.69 => ( member_nat @ X_23 @ B_23 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_285_set__mp,axiom,
% 0.30/0.69 ! [X_23: pname,A_52: pname > $o,B_23: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_52 @ B_23 )
% 0.30/0.69 => ( ( member_pname @ X_23 @ A_52 )
% 0.30/0.69 => ( member_pname @ X_23 @ B_23 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_286_set__mp,axiom,
% 0.30/0.69 ! [X_23: x_a,A_52: x_a > $o,B_23: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_52 @ B_23 )
% 0.30/0.69 => ( ( member_a @ X_23 @ A_52 )
% 0.30/0.69 => ( member_a @ X_23 @ B_23 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_287_mem__def,axiom,
% 0.30/0.69 ! [X_22: nat,A_51: nat > $o] :
% 0.30/0.69 ( ( member_nat @ X_22 @ A_51 )
% 0.30/0.69 <=> ( A_51 @ X_22 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_288_mem__def,axiom,
% 0.30/0.69 ! [X_22: pname,A_51: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_22 @ A_51 )
% 0.30/0.69 <=> ( A_51 @ X_22 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_289_mem__def,axiom,
% 0.30/0.69 ! [X_22: x_a,A_51: x_a > $o] :
% 0.30/0.69 ( ( member_a @ X_22 @ A_51 )
% 0.30/0.69 <=> ( A_51 @ X_22 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_290_Collect__def,axiom,
% 0.30/0.69 ! [P_7: x_a > $o] :
% 0.30/0.69 ( ( collect_a @ P_7 )
% 0.30/0.69 = P_7 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_291_Collect__def,axiom,
% 0.30/0.69 ! [P_7: pname > $o] :
% 0.30/0.69 ( ( collect_pname @ P_7 )
% 0.30/0.69 = P_7 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_292_Collect__def,axiom,
% 0.30/0.69 ! [P_7: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( collect_nat_o @ P_7 )
% 0.30/0.69 = P_7 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_293_Collect__def,axiom,
% 0.30/0.69 ! [P_7: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( collect_pname_o @ P_7 )
% 0.30/0.69 = P_7 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_294_Collect__def,axiom,
% 0.30/0.69 ! [P_7: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( collect_a_o @ P_7 )
% 0.30/0.69 = P_7 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_295_Collect__def,axiom,
% 0.30/0.69 ! [P_7: nat > $o] :
% 0.30/0.69 ( ( collect_nat @ P_7 )
% 0.30/0.69 = P_7 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_296_subset__trans,axiom,
% 0.30/0.69 ! [C_10: pname > $o,A_50: pname > $o,B_22: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_50 @ B_22 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ B_22 @ C_10 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ A_50 @ C_10 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_297_subset__trans,axiom,
% 0.30/0.69 ! [C_10: nat > $o,A_50: nat > $o,B_22: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_50 @ B_22 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ B_22 @ C_10 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ A_50 @ C_10 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_298_subset__trans,axiom,
% 0.30/0.69 ! [C_10: x_a > $o,A_50: x_a > $o,B_22: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_50 @ B_22 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ B_22 @ C_10 )
% 0.30/0.69 => ( ord_less_eq_a_o @ A_50 @ C_10 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_299_equalityE,axiom,
% 0.30/0.69 ! [A_49: pname > $o,B_21: pname > $o] :
% 0.30/0.69 ( ( A_49 = B_21 )
% 0.30/0.69 => ~ ( ( ord_less_eq_pname_o @ A_49 @ B_21 )
% 0.30/0.69 => ~ ( ord_less_eq_pname_o @ B_21 @ A_49 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_300_equalityE,axiom,
% 0.30/0.69 ! [A_49: nat > $o,B_21: nat > $o] :
% 0.30/0.69 ( ( A_49 = B_21 )
% 0.30/0.69 => ~ ( ( ord_less_eq_nat_o @ A_49 @ B_21 )
% 0.30/0.69 => ~ ( ord_less_eq_nat_o @ B_21 @ A_49 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_301_equalityE,axiom,
% 0.30/0.69 ! [A_49: x_a > $o,B_21: x_a > $o] :
% 0.30/0.69 ( ( A_49 = B_21 )
% 0.30/0.69 => ~ ( ( ord_less_eq_a_o @ A_49 @ B_21 )
% 0.30/0.69 => ~ ( ord_less_eq_a_o @ B_21 @ A_49 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_302_image__iff,axiom,
% 0.30/0.69 ! [Z_3: x_a,F_18: pname > x_a,A_48: pname > $o] :
% 0.30/0.69 ( ( member_a @ Z_3 @ ( image_pname_a @ F_18 @ A_48 ) )
% 0.30/0.69 <=> ? [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_48 )
% 0.30/0.69 & ( Z_3
% 0.30/0.69 = ( F_18 @ X_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_303_imageI,axiom,
% 0.30/0.69 ! [F_17: pname > nat,X_21: pname,A_47: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_21 @ A_47 )
% 0.30/0.69 => ( member_nat @ ( F_17 @ X_21 ) @ ( image_pname_nat @ F_17 @ A_47 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_304_imageI,axiom,
% 0.30/0.69 ! [F_17: x_a > nat,X_21: x_a,A_47: x_a > $o] :
% 0.30/0.69 ( ( member_a @ X_21 @ A_47 )
% 0.30/0.69 => ( member_nat @ ( F_17 @ X_21 ) @ ( image_a_nat @ F_17 @ A_47 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_305_imageI,axiom,
% 0.30/0.69 ! [F_17: nat > pname,X_21: nat,A_47: nat > $o] :
% 0.30/0.69 ( ( member_nat @ X_21 @ A_47 )
% 0.30/0.69 => ( member_pname @ ( F_17 @ X_21 ) @ ( image_nat_pname @ F_17 @ A_47 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_306_imageI,axiom,
% 0.30/0.69 ! [F_17: nat > x_a,X_21: nat,A_47: nat > $o] :
% 0.30/0.69 ( ( member_nat @ X_21 @ A_47 )
% 0.30/0.69 => ( member_a @ ( F_17 @ X_21 ) @ ( image_nat_a @ F_17 @ A_47 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_307_imageI,axiom,
% 0.30/0.69 ! [F_17: pname > x_a,X_21: pname,A_47: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_21 @ A_47 )
% 0.30/0.69 => ( member_a @ ( F_17 @ X_21 ) @ ( image_pname_a @ F_17 @ A_47 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_308_rev__image__eqI,axiom,
% 0.30/0.69 ! [B_20: nat,F_16: pname > nat,X_20: pname,A_46: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_20 @ A_46 )
% 0.30/0.69 => ( ( B_20
% 0.30/0.69 = ( F_16 @ X_20 ) )
% 0.30/0.69 => ( member_nat @ B_20 @ ( image_pname_nat @ F_16 @ A_46 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_309_rev__image__eqI,axiom,
% 0.30/0.69 ! [B_20: nat,F_16: x_a > nat,X_20: x_a,A_46: x_a > $o] :
% 0.30/0.69 ( ( member_a @ X_20 @ A_46 )
% 0.30/0.69 => ( ( B_20
% 0.30/0.69 = ( F_16 @ X_20 ) )
% 0.30/0.69 => ( member_nat @ B_20 @ ( image_a_nat @ F_16 @ A_46 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_310_rev__image__eqI,axiom,
% 0.30/0.69 ! [B_20: pname,F_16: nat > pname,X_20: nat,A_46: nat > $o] :
% 0.30/0.69 ( ( member_nat @ X_20 @ A_46 )
% 0.30/0.69 => ( ( B_20
% 0.30/0.69 = ( F_16 @ X_20 ) )
% 0.30/0.69 => ( member_pname @ B_20 @ ( image_nat_pname @ F_16 @ A_46 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_311_rev__image__eqI,axiom,
% 0.30/0.69 ! [B_20: x_a,F_16: nat > x_a,X_20: nat,A_46: nat > $o] :
% 0.30/0.69 ( ( member_nat @ X_20 @ A_46 )
% 0.30/0.69 => ( ( B_20
% 0.30/0.69 = ( F_16 @ X_20 ) )
% 0.30/0.69 => ( member_a @ B_20 @ ( image_nat_a @ F_16 @ A_46 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_312_rev__image__eqI,axiom,
% 0.30/0.69 ! [B_20: x_a,F_16: pname > x_a,X_20: pname,A_46: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_20 @ A_46 )
% 0.30/0.69 => ( ( B_20
% 0.30/0.69 = ( F_16 @ X_20 ) )
% 0.30/0.69 => ( member_a @ B_20 @ ( image_pname_a @ F_16 @ A_46 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_313_insert__compr__raw,axiom,
% 0.30/0.69 ! [X_1: nat > $o,Xa: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( insert_nat_o @ X_1 @ Xa )
% 0.30/0.69 = ( collect_nat_o
% 0.30/0.69 @ ^ [Y_10: nat > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_nat_o @ Y_10 @ Xa ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_314_insert__compr__raw,axiom,
% 0.30/0.69 ! [X_1: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( insert_pname_o @ X_1 @ Xa )
% 0.30/0.69 = ( collect_pname_o
% 0.30/0.69 @ ^ [Y_10: pname > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_pname_o @ Y_10 @ Xa ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_315_insert__compr__raw,axiom,
% 0.30/0.69 ! [X_1: x_a > $o,Xa: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( insert_a_o @ X_1 @ Xa )
% 0.30/0.69 = ( collect_a_o
% 0.30/0.69 @ ^ [Y_10: x_a > $o] : ( (|) @ ( Y_10 = X_1 ) @ ( member_a_o @ Y_10 @ Xa ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_316_insert__compr__raw,axiom,
% 0.30/0.69 ! [X_1: nat,Xa: nat > $o] :
% 0.30/0.69 ( ( insert_nat @ X_1 @ Xa )
% 0.30/0.69 = ( collect_nat
% 0.30/0.69 @ ^ [Y_10: nat] : ( (|) @ ( Y_10 = X_1 ) @ ( member_nat @ Y_10 @ Xa ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_317_insert__compr__raw,axiom,
% 0.30/0.69 ! [X_1: pname,Xa: pname > $o] :
% 0.30/0.69 ( ( insert_pname @ X_1 @ Xa )
% 0.30/0.69 = ( collect_pname
% 0.30/0.69 @ ^ [Y_10: pname] : ( (|) @ ( Y_10 = X_1 ) @ ( member_pname @ Y_10 @ Xa ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_318_insert__compr__raw,axiom,
% 0.30/0.69 ! [X_1: x_a,Xa: x_a > $o] :
% 0.30/0.69 ( ( insert_a @ X_1 @ Xa )
% 0.30/0.69 = ( collect_a
% 0.30/0.69 @ ^ [Y_10: x_a] : ( (|) @ ( Y_10 = X_1 ) @ ( member_a @ Y_10 @ Xa ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_319_subset__insertI,axiom,
% 0.30/0.69 ! [B_19: pname > $o,A_45: pname] : ( ord_less_eq_pname_o @ B_19 @ ( insert_pname @ A_45 @ B_19 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_320_subset__insertI,axiom,
% 0.30/0.69 ! [B_19: nat > $o,A_45: nat] : ( ord_less_eq_nat_o @ B_19 @ ( insert_nat @ A_45 @ B_19 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_321_subset__insertI,axiom,
% 0.30/0.69 ! [B_19: x_a > $o,A_45: x_a] : ( ord_less_eq_a_o @ B_19 @ ( insert_a @ A_45 @ B_19 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_322_insert__subset,axiom,
% 0.30/0.69 ! [X_19: nat,A_44: nat > $o,B_18: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ ( insert_nat @ X_19 @ A_44 ) @ B_18 )
% 0.30/0.69 <=> ( ( member_nat @ X_19 @ B_18 )
% 0.30/0.69 & ( ord_less_eq_nat_o @ A_44 @ B_18 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_323_insert__subset,axiom,
% 0.30/0.69 ! [X_19: pname,A_44: pname > $o,B_18: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_19 @ A_44 ) @ B_18 )
% 0.30/0.69 <=> ( ( member_pname @ X_19 @ B_18 )
% 0.30/0.69 & ( ord_less_eq_pname_o @ A_44 @ B_18 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_324_insert__subset,axiom,
% 0.30/0.69 ! [X_19: x_a,A_44: x_a > $o,B_18: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ ( insert_a @ X_19 @ A_44 ) @ B_18 )
% 0.30/0.69 <=> ( ( member_a @ X_19 @ B_18 )
% 0.30/0.69 & ( ord_less_eq_a_o @ A_44 @ B_18 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_325_subset__insert,axiom,
% 0.30/0.69 ! [B_17: nat > $o,X_18: nat,A_43: nat > $o] :
% 0.30/0.69 ( ~ ( member_nat @ X_18 @ A_43 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ A_43 @ ( insert_nat @ X_18 @ B_17 ) )
% 0.30/0.69 <=> ( ord_less_eq_nat_o @ A_43 @ B_17 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_326_subset__insert,axiom,
% 0.30/0.69 ! [B_17: pname > $o,X_18: pname,A_43: pname > $o] :
% 0.30/0.69 ( ~ ( member_pname @ X_18 @ A_43 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ A_43 @ ( insert_pname @ X_18 @ B_17 ) )
% 0.30/0.69 <=> ( ord_less_eq_pname_o @ A_43 @ B_17 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_327_subset__insert,axiom,
% 0.30/0.69 ! [B_17: x_a > $o,X_18: x_a,A_43: x_a > $o] :
% 0.30/0.69 ( ~ ( member_a @ X_18 @ A_43 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ A_43 @ ( insert_a @ X_18 @ B_17 ) )
% 0.30/0.69 <=> ( ord_less_eq_a_o @ A_43 @ B_17 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_328_subset__insertI2,axiom,
% 0.30/0.69 ! [B_16: pname,A_42: pname > $o,B_15: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_42 @ B_15 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_16 @ B_15 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_329_subset__insertI2,axiom,
% 0.30/0.69 ! [B_16: nat,A_42: nat > $o,B_15: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_42 @ B_15 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ A_42 @ ( insert_nat @ B_16 @ B_15 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_330_subset__insertI2,axiom,
% 0.30/0.69 ! [B_16: x_a,A_42: x_a > $o,B_15: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_42 @ B_15 )
% 0.30/0.69 => ( ord_less_eq_a_o @ A_42 @ ( insert_a @ B_16 @ B_15 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_331_insert__mono,axiom,
% 0.30/0.69 ! [A_41: pname,C_9: pname > $o,D_1: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ C_9 @ D_1 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ ( insert_pname @ A_41 @ C_9 ) @ ( insert_pname @ A_41 @ D_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_332_insert__mono,axiom,
% 0.30/0.69 ! [A_41: nat,C_9: nat > $o,D_1: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ C_9 @ D_1 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ ( insert_nat @ A_41 @ C_9 ) @ ( insert_nat @ A_41 @ D_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_333_insert__mono,axiom,
% 0.30/0.69 ! [A_41: x_a,C_9: x_a > $o,D_1: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ C_9 @ D_1 )
% 0.30/0.69 => ( ord_less_eq_a_o @ ( insert_a @ A_41 @ C_9 ) @ ( insert_a @ A_41 @ D_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_334_image__insert,axiom,
% 0.30/0.69 ! [F_15: x_a > pname,A_40: x_a,B_14: x_a > $o] :
% 0.30/0.69 ( ( image_a_pname @ F_15 @ ( insert_a @ A_40 @ B_14 ) )
% 0.30/0.69 = ( insert_pname @ ( F_15 @ A_40 ) @ ( image_a_pname @ F_15 @ B_14 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_335_image__insert,axiom,
% 0.30/0.69 ! [F_15: x_a > nat,A_40: x_a,B_14: x_a > $o] :
% 0.30/0.69 ( ( image_a_nat @ F_15 @ ( insert_a @ A_40 @ B_14 ) )
% 0.30/0.69 = ( insert_nat @ ( F_15 @ A_40 ) @ ( image_a_nat @ F_15 @ B_14 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_336_image__insert,axiom,
% 0.30/0.69 ! [F_15: nat > x_a,A_40: nat,B_14: nat > $o] :
% 0.30/0.69 ( ( image_nat_a @ F_15 @ ( insert_nat @ A_40 @ B_14 ) )
% 0.30/0.69 = ( insert_a @ ( F_15 @ A_40 ) @ ( image_nat_a @ F_15 @ B_14 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_337_image__insert,axiom,
% 0.30/0.69 ! [F_15: pname > x_a,A_40: pname,B_14: pname > $o] :
% 0.30/0.69 ( ( image_pname_a @ F_15 @ ( insert_pname @ A_40 @ B_14 ) )
% 0.30/0.69 = ( insert_a @ ( F_15 @ A_40 ) @ ( image_pname_a @ F_15 @ B_14 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_338_insert__image,axiom,
% 0.30/0.69 ! [F_14: pname > pname,X_17: pname,A_39: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_17 @ A_39 )
% 0.30/0.69 => ( ( insert_pname @ ( F_14 @ X_17 ) @ ( image_pname_pname @ F_14 @ A_39 ) )
% 0.30/0.69 = ( image_pname_pname @ F_14 @ A_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_339_insert__image,axiom,
% 0.30/0.69 ! [F_14: pname > nat,X_17: pname,A_39: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_17 @ A_39 )
% 0.30/0.69 => ( ( insert_nat @ ( F_14 @ X_17 ) @ ( image_pname_nat @ F_14 @ A_39 ) )
% 0.30/0.69 = ( image_pname_nat @ F_14 @ A_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_340_insert__image,axiom,
% 0.30/0.69 ! [F_14: x_a > pname,X_17: x_a,A_39: x_a > $o] :
% 0.30/0.69 ( ( member_a @ X_17 @ A_39 )
% 0.30/0.69 => ( ( insert_pname @ ( F_14 @ X_17 ) @ ( image_a_pname @ F_14 @ A_39 ) )
% 0.30/0.69 = ( image_a_pname @ F_14 @ A_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_341_insert__image,axiom,
% 0.30/0.69 ! [F_14: x_a > nat,X_17: x_a,A_39: x_a > $o] :
% 0.30/0.69 ( ( member_a @ X_17 @ A_39 )
% 0.30/0.69 => ( ( insert_nat @ ( F_14 @ X_17 ) @ ( image_a_nat @ F_14 @ A_39 ) )
% 0.30/0.69 = ( image_a_nat @ F_14 @ A_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_342_insert__image,axiom,
% 0.30/0.69 ! [F_14: nat > x_a,X_17: nat,A_39: nat > $o] :
% 0.30/0.69 ( ( member_nat @ X_17 @ A_39 )
% 0.30/0.69 => ( ( insert_a @ ( F_14 @ X_17 ) @ ( image_nat_a @ F_14 @ A_39 ) )
% 0.30/0.69 = ( image_nat_a @ F_14 @ A_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_343_insert__image,axiom,
% 0.30/0.69 ! [F_14: pname > x_a,X_17: pname,A_39: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_17 @ A_39 )
% 0.30/0.69 => ( ( insert_a @ ( F_14 @ X_17 ) @ ( image_pname_a @ F_14 @ A_39 ) )
% 0.30/0.69 = ( image_pname_a @ F_14 @ A_39 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_344_subset__image__iff,axiom,
% 0.30/0.69 ! [B_13: x_a > $o,F_13: nat > x_a,A_38: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ B_13 @ ( image_nat_a @ F_13 @ A_38 ) )
% 0.30/0.69 <=> ? [AA: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ AA @ A_38 )
% 0.30/0.69 & ( B_13
% 0.30/0.69 = ( image_nat_a @ F_13 @ AA ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_345_subset__image__iff,axiom,
% 0.30/0.69 ! [B_13: pname > $o,F_13: x_a > pname,A_38: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ B_13 @ ( image_a_pname @ F_13 @ A_38 ) )
% 0.30/0.69 <=> ? [AA: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ AA @ A_38 )
% 0.30/0.69 & ( B_13
% 0.30/0.69 = ( image_a_pname @ F_13 @ AA ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_346_subset__image__iff,axiom,
% 0.30/0.69 ! [B_13: nat > $o,F_13: x_a > nat,A_38: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ B_13 @ ( image_a_nat @ F_13 @ A_38 ) )
% 0.30/0.69 <=> ? [AA: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ AA @ A_38 )
% 0.30/0.69 & ( B_13
% 0.30/0.69 = ( image_a_nat @ F_13 @ AA ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_347_subset__image__iff,axiom,
% 0.30/0.69 ! [B_13: x_a > $o,F_13: pname > x_a,A_38: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ B_13 @ ( image_pname_a @ F_13 @ A_38 ) )
% 0.30/0.69 <=> ? [AA: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ AA @ A_38 )
% 0.30/0.69 & ( B_13
% 0.30/0.69 = ( image_pname_a @ F_13 @ AA ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_348_image__mono,axiom,
% 0.30/0.69 ! [F_12: x_a > pname,A_37: x_a > $o,B_12: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_37 @ B_12 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ ( image_a_pname @ F_12 @ A_37 ) @ ( image_a_pname @ F_12 @ B_12 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_349_image__mono,axiom,
% 0.30/0.69 ! [F_12: x_a > nat,A_37: x_a > $o,B_12: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_37 @ B_12 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ ( image_a_nat @ F_12 @ A_37 ) @ ( image_a_nat @ F_12 @ B_12 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_350_image__mono,axiom,
% 0.30/0.69 ! [F_12: nat > x_a,A_37: nat > $o,B_12: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_37 @ B_12 )
% 0.30/0.69 => ( ord_less_eq_a_o @ ( image_nat_a @ F_12 @ A_37 ) @ ( image_nat_a @ F_12 @ B_12 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_351_image__mono,axiom,
% 0.30/0.69 ! [F_12: pname > x_a,A_37: pname > $o,B_12: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_37 @ B_12 )
% 0.30/0.69 => ( ord_less_eq_a_o @ ( image_pname_a @ F_12 @ A_37 ) @ ( image_pname_a @ F_12 @ B_12 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_352_imageE,axiom,
% 0.30/0.69 ! [B_11: pname,F_11: nat > pname,A_36: nat > $o] :
% 0.30/0.69 ( ( member_pname @ B_11 @ ( image_nat_pname @ F_11 @ A_36 ) )
% 0.30/0.69 => ~ ! [X_1: nat] :
% 0.30/0.69 ( ( B_11
% 0.30/0.69 = ( F_11 @ X_1 ) )
% 0.30/0.69 => ~ ( member_nat @ X_1 @ A_36 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_353_imageE,axiom,
% 0.30/0.69 ! [B_11: x_a,F_11: nat > x_a,A_36: nat > $o] :
% 0.30/0.69 ( ( member_a @ B_11 @ ( image_nat_a @ F_11 @ A_36 ) )
% 0.30/0.69 => ~ ! [X_1: nat] :
% 0.30/0.69 ( ( B_11
% 0.30/0.69 = ( F_11 @ X_1 ) )
% 0.30/0.69 => ~ ( member_nat @ X_1 @ A_36 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_354_imageE,axiom,
% 0.30/0.69 ! [B_11: nat,F_11: pname > nat,A_36: pname > $o] :
% 0.30/0.69 ( ( member_nat @ B_11 @ ( image_pname_nat @ F_11 @ A_36 ) )
% 0.30/0.69 => ~ ! [X_1: pname] :
% 0.30/0.69 ( ( B_11
% 0.30/0.69 = ( F_11 @ X_1 ) )
% 0.30/0.69 => ~ ( member_pname @ X_1 @ A_36 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_355_imageE,axiom,
% 0.30/0.69 ! [B_11: nat,F_11: x_a > nat,A_36: x_a > $o] :
% 0.30/0.69 ( ( member_nat @ B_11 @ ( image_a_nat @ F_11 @ A_36 ) )
% 0.30/0.69 => ~ ! [X_1: x_a] :
% 0.30/0.69 ( ( B_11
% 0.30/0.69 = ( F_11 @ X_1 ) )
% 0.30/0.69 => ~ ( member_a @ X_1 @ A_36 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_356_imageE,axiom,
% 0.30/0.69 ! [B_11: x_a,F_11: pname > x_a,A_36: pname > $o] :
% 0.30/0.69 ( ( member_a @ B_11 @ ( image_pname_a @ F_11 @ A_36 ) )
% 0.30/0.69 => ~ ! [X_1: pname] :
% 0.30/0.69 ( ( B_11
% 0.30/0.69 = ( F_11 @ X_1 ) )
% 0.30/0.69 => ~ ( member_pname @ X_1 @ A_36 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_357_subsetI,axiom,
% 0.30/0.69 ! [B_10: nat > $o,A_35: nat > $o] :
% 0.30/0.69 ( ! [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_35 )
% 0.30/0.69 => ( member_nat @ X_1 @ B_10 ) )
% 0.30/0.69 => ( ord_less_eq_nat_o @ A_35 @ B_10 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_358_subsetI,axiom,
% 0.30/0.69 ! [B_10: pname > $o,A_35: pname > $o] :
% 0.30/0.69 ( ! [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_35 )
% 0.30/0.69 => ( member_pname @ X_1 @ B_10 ) )
% 0.30/0.69 => ( ord_less_eq_pname_o @ A_35 @ B_10 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_359_subsetI,axiom,
% 0.30/0.69 ! [B_10: x_a > $o,A_35: x_a > $o] :
% 0.30/0.69 ( ! [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_35 )
% 0.30/0.69 => ( member_a @ X_1 @ B_10 ) )
% 0.30/0.69 => ( ord_less_eq_a_o @ A_35 @ B_10 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_360_image__subsetI,axiom,
% 0.30/0.69 ! [F_10: pname > nat,B_9: nat > $o,A_34: pname > $o] :
% 0.30/0.69 ( ! [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_34 )
% 0.30/0.69 => ( member_nat @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/0.69 => ( ord_less_eq_nat_o @ ( image_pname_nat @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_361_image__subsetI,axiom,
% 0.30/0.69 ! [F_10: pname > pname,B_9: pname > $o,A_34: pname > $o] :
% 0.30/0.69 ( ! [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_34 )
% 0.30/0.69 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/0.69 => ( ord_less_eq_pname_o @ ( image_pname_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_362_image__subsetI,axiom,
% 0.30/0.69 ! [F_10: x_a > nat,B_9: nat > $o,A_34: x_a > $o] :
% 0.30/0.69 ( ! [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_34 )
% 0.30/0.69 => ( member_nat @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/0.69 => ( ord_less_eq_nat_o @ ( image_a_nat @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_363_image__subsetI,axiom,
% 0.30/0.69 ! [F_10: x_a > pname,B_9: pname > $o,A_34: x_a > $o] :
% 0.30/0.69 ( ! [X_1: x_a] :
% 0.30/0.69 ( ( member_a @ X_1 @ A_34 )
% 0.30/0.69 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/0.69 => ( ord_less_eq_pname_o @ ( image_a_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_364_image__subsetI,axiom,
% 0.30/0.69 ! [F_10: nat > pname,B_9: pname > $o,A_34: nat > $o] :
% 0.30/0.69 ( ! [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_34 )
% 0.30/0.69 => ( member_pname @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/0.69 => ( ord_less_eq_pname_o @ ( image_nat_pname @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_365_image__subsetI,axiom,
% 0.30/0.69 ! [F_10: nat > x_a,B_9: x_a > $o,A_34: nat > $o] :
% 0.30/0.69 ( ! [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ A_34 )
% 0.30/0.69 => ( member_a @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/0.69 => ( ord_less_eq_a_o @ ( image_nat_a @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_366_image__subsetI,axiom,
% 0.30/0.69 ! [F_10: pname > x_a,B_9: x_a > $o,A_34: pname > $o] :
% 0.30/0.69 ( ! [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ A_34 )
% 0.30/0.69 => ( member_a @ ( F_10 @ X_1 ) @ B_9 ) )
% 0.30/0.69 => ( ord_less_eq_a_o @ ( image_pname_a @ F_10 @ A_34 ) @ B_9 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_367_order__refl,axiom,
% 0.30/0.69 ! [X_16: $o] : ( ord_less_eq_o @ X_16 @ X_16 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_368_order__refl,axiom,
% 0.30/0.69 ! [X_16: pname > $o] : ( ord_less_eq_pname_o @ X_16 @ X_16 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_369_order__refl,axiom,
% 0.30/0.69 ! [X_16: nat > $o] : ( ord_less_eq_nat_o @ X_16 @ X_16 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_370_order__refl,axiom,
% 0.30/0.69 ! [X_16: x_a > $o] : ( ord_less_eq_a_o @ X_16 @ X_16 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_371_order__refl,axiom,
% 0.30/0.69 ! [X_16: nat] : ( ord_less_eq_nat @ X_16 @ X_16 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_372_finite__nat__set__iff__bounded__le,axiom,
% 0.30/0.69 ! [N_1: nat > $o] :
% 0.30/0.69 ( ( finite_finite_nat @ N_1 )
% 0.30/0.69 <=> ? [M_1: nat] :
% 0.30/0.69 ! [X_1: nat] :
% 0.30/0.69 ( ( member_nat @ X_1 @ N_1 )
% 0.30/0.69 => ( ord_less_eq_nat @ X_1 @ M_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_373_assms_I3_J,axiom,
% 0.30/0.69 ! [G: x_a > $o,C: com] :
% 0.30/0.69 ( ( wt @ C )
% 0.30/0.69 => ( ! [X_1: pname] :
% 0.30/0.69 ( ( member_pname @ X_1 @ u )
% 0.30/0.69 => ( p @ G @ ( insert_a @ ( mgt_call @ X_1 ) @ bot_bot_a_o ) ) )
% 0.30/0.69 => ( p @ G @ ( insert_a @ ( mgt @ C ) @ bot_bot_a_o ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_374_le__fun__def,axiom,
% 0.30/0.69 ! [F_9: pname > $o,G_3: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ F_9 @ G_3 )
% 0.30/0.69 <=> ! [X_1: pname] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_375_le__fun__def,axiom,
% 0.30/0.69 ! [F_9: nat > $o,G_3: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ F_9 @ G_3 )
% 0.30/0.69 <=> ! [X_1: nat] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_376_le__fun__def,axiom,
% 0.30/0.69 ! [F_9: x_a > $o,G_3: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ F_9 @ G_3 )
% 0.30/0.69 <=> ! [X_1: x_a] : ( ord_less_eq_o @ ( F_9 @ X_1 ) @ ( G_3 @ X_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_377_le__funD,axiom,
% 0.30/0.69 ! [X_15: pname,F_8: pname > $o,G_2: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ F_8 @ G_2 )
% 0.30/0.69 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_378_le__funD,axiom,
% 0.30/0.69 ! [X_15: nat,F_8: nat > $o,G_2: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ F_8 @ G_2 )
% 0.30/0.69 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_379_le__funD,axiom,
% 0.30/0.69 ! [X_15: x_a,F_8: x_a > $o,G_2: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ F_8 @ G_2 )
% 0.30/0.69 => ( ord_less_eq_o @ ( F_8 @ X_15 ) @ ( G_2 @ X_15 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_380_le__funE,axiom,
% 0.30/0.69 ! [X_14: pname,F_7: pname > $o,G_1: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ F_7 @ G_1 )
% 0.30/0.69 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_381_le__funE,axiom,
% 0.30/0.69 ! [X_14: nat,F_7: nat > $o,G_1: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ F_7 @ G_1 )
% 0.30/0.69 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_382_le__funE,axiom,
% 0.30/0.69 ! [X_14: x_a,F_7: x_a > $o,G_1: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ F_7 @ G_1 )
% 0.30/0.69 => ( ord_less_eq_o @ ( F_7 @ X_14 ) @ ( G_1 @ X_14 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_383_emptyE,axiom,
% 0.30/0.69 ! [A_33: nat] :
% 0.30/0.69 ~ ( member_nat @ A_33 @ bot_bot_nat_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_384_emptyE,axiom,
% 0.30/0.69 ! [A_33: pname] :
% 0.30/0.69 ~ ( member_pname @ A_33 @ bot_bot_pname_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_385_emptyE,axiom,
% 0.30/0.69 ! [A_33: x_a] :
% 0.30/0.69 ~ ( member_a @ A_33 @ bot_bot_a_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_386_finite_OemptyI,axiom,
% 0.30/0.69 finite_finite_nat_o @ bot_bot_nat_o_o ).
% 0.30/0.69
% 0.30/0.69 thf(fact_387_finite_OemptyI,axiom,
% 0.30/0.69 finite297249702name_o @ bot_bot_pname_o_o ).
% 0.30/0.69
% 0.30/0.69 thf(fact_388_finite_OemptyI,axiom,
% 0.30/0.69 finite_finite_a_o @ bot_bot_a_o_o ).
% 0.30/0.69
% 0.30/0.69 thf(fact_389_finite_OemptyI,axiom,
% 0.30/0.69 finite_finite_a @ bot_bot_a_o ).
% 0.30/0.69
% 0.30/0.69 thf(fact_390_finite_OemptyI,axiom,
% 0.30/0.69 finite_finite_pname @ bot_bot_pname_o ).
% 0.30/0.69
% 0.30/0.69 thf(fact_391_finite_OemptyI,axiom,
% 0.30/0.69 finite_finite_nat @ bot_bot_nat_o ).
% 0.30/0.69
% 0.30/0.69 thf(fact_392_empty__subsetI,axiom,
% 0.30/0.69 ! [A_32: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_32 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_393_empty__subsetI,axiom,
% 0.30/0.69 ! [A_32: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A_32 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_394_empty__subsetI,axiom,
% 0.30/0.69 ! [A_32: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A_32 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_395_equals0D,axiom,
% 0.30/0.69 ! [A_31: nat,A_30: nat > $o] :
% 0.30/0.69 ( ( A_30 = bot_bot_nat_o )
% 0.30/0.69 => ~ ( member_nat @ A_31 @ A_30 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_396_equals0D,axiom,
% 0.30/0.69 ! [A_31: pname,A_30: pname > $o] :
% 0.30/0.69 ( ( A_30 = bot_bot_pname_o )
% 0.30/0.69 => ~ ( member_pname @ A_31 @ A_30 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_397_equals0D,axiom,
% 0.30/0.69 ! [A_31: x_a,A_30: x_a > $o] :
% 0.30/0.69 ( ( A_30 = bot_bot_a_o )
% 0.30/0.69 => ~ ( member_a @ A_31 @ A_30 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_398_Collect__empty__eq,axiom,
% 0.30/0.69 ! [P_6: pname > $o] :
% 0.30/0.69 ( ( ( collect_pname @ P_6 )
% 0.30/0.69 = bot_bot_pname_o )
% 0.30/0.69 <=> ! [X_1: pname] :
% 0.30/0.69 ~ ( P_6 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_399_Collect__empty__eq,axiom,
% 0.30/0.69 ! [P_6: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( ( collect_nat_o @ P_6 )
% 0.30/0.69 = bot_bot_nat_o_o )
% 0.30/0.69 <=> ! [X_1: nat > $o] :
% 0.30/0.69 ~ ( P_6 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_400_Collect__empty__eq,axiom,
% 0.30/0.69 ! [P_6: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( ( collect_pname_o @ P_6 )
% 0.30/0.69 = bot_bot_pname_o_o )
% 0.30/0.69 <=> ! [X_1: pname > $o] :
% 0.30/0.69 ~ ( P_6 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_401_Collect__empty__eq,axiom,
% 0.30/0.69 ! [P_6: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( ( collect_a_o @ P_6 )
% 0.30/0.69 = bot_bot_a_o_o )
% 0.30/0.69 <=> ! [X_1: x_a > $o] :
% 0.30/0.69 ~ ( P_6 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_402_Collect__empty__eq,axiom,
% 0.30/0.69 ! [P_6: x_a > $o] :
% 0.30/0.69 ( ( ( collect_a @ P_6 )
% 0.30/0.69 = bot_bot_a_o )
% 0.30/0.69 <=> ! [X_1: x_a] :
% 0.30/0.69 ~ ( P_6 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_403_Collect__empty__eq,axiom,
% 0.30/0.69 ! [P_6: nat > $o] :
% 0.30/0.69 ( ( ( collect_nat @ P_6 )
% 0.30/0.69 = bot_bot_nat_o )
% 0.30/0.69 <=> ! [X_1: nat] :
% 0.30/0.69 ~ ( P_6 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_404_empty__iff,axiom,
% 0.30/0.69 ! [C_8: nat] :
% 0.30/0.69 ~ ( member_nat @ C_8 @ bot_bot_nat_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_405_empty__iff,axiom,
% 0.30/0.69 ! [C_8: pname] :
% 0.30/0.69 ~ ( member_pname @ C_8 @ bot_bot_pname_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_406_empty__iff,axiom,
% 0.30/0.69 ! [C_8: x_a] :
% 0.30/0.69 ~ ( member_a @ C_8 @ bot_bot_a_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_407_empty__Collect__eq,axiom,
% 0.30/0.69 ! [P_5: pname > $o] :
% 0.30/0.69 ( ( bot_bot_pname_o
% 0.30/0.69 = ( collect_pname @ P_5 ) )
% 0.30/0.69 <=> ! [X_1: pname] :
% 0.30/0.69 ~ ( P_5 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_408_empty__Collect__eq,axiom,
% 0.30/0.69 ! [P_5: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( bot_bot_nat_o_o
% 0.30/0.69 = ( collect_nat_o @ P_5 ) )
% 0.30/0.69 <=> ! [X_1: nat > $o] :
% 0.30/0.69 ~ ( P_5 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_409_empty__Collect__eq,axiom,
% 0.30/0.69 ! [P_5: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( bot_bot_pname_o_o
% 0.30/0.69 = ( collect_pname_o @ P_5 ) )
% 0.30/0.69 <=> ! [X_1: pname > $o] :
% 0.30/0.69 ~ ( P_5 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_410_empty__Collect__eq,axiom,
% 0.30/0.69 ! [P_5: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( bot_bot_a_o_o
% 0.30/0.69 = ( collect_a_o @ P_5 ) )
% 0.30/0.69 <=> ! [X_1: x_a > $o] :
% 0.30/0.69 ~ ( P_5 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_411_empty__Collect__eq,axiom,
% 0.30/0.69 ! [P_5: x_a > $o] :
% 0.30/0.69 ( ( bot_bot_a_o
% 0.30/0.69 = ( collect_a @ P_5 ) )
% 0.30/0.69 <=> ! [X_1: x_a] :
% 0.30/0.69 ~ ( P_5 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_412_empty__Collect__eq,axiom,
% 0.30/0.69 ! [P_5: nat > $o] :
% 0.30/0.69 ( ( bot_bot_nat_o
% 0.30/0.69 = ( collect_nat @ P_5 ) )
% 0.30/0.69 <=> ! [X_1: nat] :
% 0.30/0.69 ~ ( P_5 @ X_1 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_413_ex__in__conv,axiom,
% 0.30/0.69 ! [A_29: nat > $o] :
% 0.30/0.69 ( ? [X_1: nat] : ( member_nat @ X_1 @ A_29 )
% 0.30/0.69 <=> ( A_29 != bot_bot_nat_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_414_ex__in__conv,axiom,
% 0.30/0.69 ! [A_29: pname > $o] :
% 0.30/0.69 ( ? [X_1: pname] : ( member_pname @ X_1 @ A_29 )
% 0.30/0.69 <=> ( A_29 != bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_415_ex__in__conv,axiom,
% 0.30/0.69 ! [A_29: x_a > $o] :
% 0.30/0.69 ( ? [X_1: x_a] : ( member_a @ X_1 @ A_29 )
% 0.30/0.69 <=> ( A_29 != bot_bot_a_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_416_all__not__in__conv,axiom,
% 0.30/0.69 ! [A_28: nat > $o] :
% 0.30/0.69 ( ! [X_1: nat] :
% 0.30/0.69 ~ ( member_nat @ X_1 @ A_28 )
% 0.30/0.69 <=> ( A_28 = bot_bot_nat_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_417_all__not__in__conv,axiom,
% 0.30/0.69 ! [A_28: pname > $o] :
% 0.30/0.69 ( ! [X_1: pname] :
% 0.30/0.69 ~ ( member_pname @ X_1 @ A_28 )
% 0.30/0.69 <=> ( A_28 = bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_418_all__not__in__conv,axiom,
% 0.30/0.69 ! [A_28: x_a > $o] :
% 0.30/0.69 ( ! [X_1: x_a] :
% 0.30/0.69 ~ ( member_a @ X_1 @ A_28 )
% 0.30/0.69 <=> ( A_28 = bot_bot_a_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_419_empty__def,axiom,
% 0.30/0.69 ( bot_bot_pname_o
% 0.30/0.69 = ( collect_pname
% 0.30/0.69 @ ^ [X_1: pname] : $false ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_420_empty__def,axiom,
% 0.30/0.69 ( bot_bot_nat_o_o
% 0.30/0.69 = ( collect_nat_o
% 0.30/0.69 @ ^ [X_1: nat > $o] : $false ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_421_empty__def,axiom,
% 0.30/0.69 ( bot_bot_pname_o_o
% 0.30/0.69 = ( collect_pname_o
% 0.30/0.69 @ ^ [X_1: pname > $o] : $false ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_422_empty__def,axiom,
% 0.30/0.69 ( bot_bot_a_o_o
% 0.30/0.69 = ( collect_a_o
% 0.30/0.69 @ ^ [X_1: x_a > $o] : $false ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_423_empty__def,axiom,
% 0.30/0.69 ( bot_bot_a_o
% 0.30/0.69 = ( collect_a
% 0.30/0.69 @ ^ [X_1: x_a] : $false ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_424_empty__def,axiom,
% 0.30/0.69 ( bot_bot_nat_o
% 0.30/0.69 = ( collect_nat
% 0.30/0.69 @ ^ [X_1: nat] : $false ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_425_bot__fun__def,axiom,
% 0.30/0.69 ! [X_1: pname] :
% 0.30/0.69 ( ( bot_bot_pname_o @ X_1 )
% 0.30/0.69 <=> bot_bot_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_426_bot__fun__def,axiom,
% 0.30/0.69 ! [X_1: nat] :
% 0.30/0.69 ( ( bot_bot_nat_o @ X_1 )
% 0.30/0.69 <=> bot_bot_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_427_bot__fun__def,axiom,
% 0.30/0.69 ! [X_1: x_a] :
% 0.30/0.69 ( ( bot_bot_a_o @ X_1 )
% 0.30/0.69 <=> bot_bot_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_428_bot__apply,axiom,
% 0.30/0.69 ! [X_13: pname] :
% 0.30/0.69 ( ( bot_bot_pname_o @ X_13 )
% 0.30/0.69 <=> bot_bot_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_429_bot__apply,axiom,
% 0.30/0.69 ! [X_13: nat] :
% 0.30/0.69 ( ( bot_bot_nat_o @ X_13 )
% 0.30/0.69 <=> bot_bot_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_430_bot__apply,axiom,
% 0.30/0.69 ! [X_13: x_a] :
% 0.30/0.69 ( ( bot_bot_a_o @ X_13 )
% 0.30/0.69 <=> bot_bot_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_431_le__bot,axiom,
% 0.30/0.69 ! [A_27: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_27 @ bot_bot_pname_o )
% 0.30/0.69 => ( A_27 = bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_432_le__bot,axiom,
% 0.30/0.69 ! [A_27: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ A_27 @ bot_bot_o )
% 0.30/0.69 => ( A_27
% 0.30/0.69 <=> bot_bot_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_433_le__bot,axiom,
% 0.30/0.69 ! [A_27: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_27 @ bot_bot_nat_o )
% 0.30/0.69 => ( A_27 = bot_bot_nat_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_434_le__bot,axiom,
% 0.30/0.69 ! [A_27: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_27 @ bot_bot_a_o )
% 0.30/0.69 => ( A_27 = bot_bot_a_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_435_le__bot,axiom,
% 0.30/0.69 ! [A_27: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ A_27 @ bot_bot_nat )
% 0.30/0.69 => ( A_27 = bot_bot_nat ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_436_bot__unique,axiom,
% 0.30/0.69 ! [A_26: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_26 @ bot_bot_pname_o )
% 0.30/0.69 <=> ( A_26 = bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_437_bot__unique,axiom,
% 0.30/0.69 ! [A_26: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ A_26 @ bot_bot_o )
% 0.30/0.69 <=> ( A_26
% 0.30/0.69 <=> bot_bot_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_438_bot__unique,axiom,
% 0.30/0.69 ! [A_26: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_26 @ bot_bot_nat_o )
% 0.30/0.69 <=> ( A_26 = bot_bot_nat_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_439_bot__unique,axiom,
% 0.30/0.69 ! [A_26: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_26 @ bot_bot_a_o )
% 0.30/0.69 <=> ( A_26 = bot_bot_a_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_440_bot__unique,axiom,
% 0.30/0.69 ! [A_26: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ A_26 @ bot_bot_nat )
% 0.30/0.69 <=> ( A_26 = bot_bot_nat ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_441_bot__least,axiom,
% 0.30/0.69 ! [A_25: pname > $o] : ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_25 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_442_bot__least,axiom,
% 0.30/0.69 ! [A_25: $o] : ( ord_less_eq_o @ bot_bot_o @ A_25 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_443_bot__least,axiom,
% 0.30/0.69 ! [A_25: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A_25 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_444_bot__least,axiom,
% 0.30/0.69 ! [A_25: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A_25 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_445_bot__least,axiom,
% 0.30/0.69 ! [A_25: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A_25 ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_446_singleton__inject,axiom,
% 0.30/0.69 ! [A_24: pname,B_8: pname] :
% 0.30/0.69 ( ( ( insert_pname @ A_24 @ bot_bot_pname_o )
% 0.30/0.69 = ( insert_pname @ B_8 @ bot_bot_pname_o ) )
% 0.30/0.69 => ( A_24 = B_8 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_447_singleton__inject,axiom,
% 0.30/0.69 ! [A_24: nat,B_8: nat] :
% 0.30/0.69 ( ( ( insert_nat @ A_24 @ bot_bot_nat_o )
% 0.30/0.69 = ( insert_nat @ B_8 @ bot_bot_nat_o ) )
% 0.30/0.69 => ( A_24 = B_8 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_448_singleton__inject,axiom,
% 0.30/0.69 ! [A_24: x_a,B_8: x_a] :
% 0.30/0.69 ( ( ( insert_a @ A_24 @ bot_bot_a_o )
% 0.30/0.69 = ( insert_a @ B_8 @ bot_bot_a_o ) )
% 0.30/0.69 => ( A_24 = B_8 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_449_singletonE,axiom,
% 0.30/0.69 ! [B_7: nat,A_23: nat] :
% 0.30/0.69 ( ( member_nat @ B_7 @ ( insert_nat @ A_23 @ bot_bot_nat_o ) )
% 0.30/0.69 => ( B_7 = A_23 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_450_singletonE,axiom,
% 0.30/0.69 ! [B_7: pname,A_23: pname] :
% 0.30/0.69 ( ( member_pname @ B_7 @ ( insert_pname @ A_23 @ bot_bot_pname_o ) )
% 0.30/0.69 => ( B_7 = A_23 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_451_singletonE,axiom,
% 0.30/0.69 ! [B_7: x_a,A_23: x_a] :
% 0.30/0.69 ( ( member_a @ B_7 @ ( insert_a @ A_23 @ bot_bot_a_o ) )
% 0.30/0.69 => ( B_7 = A_23 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_452_doubleton__eq__iff,axiom,
% 0.30/0.69 ! [A_22: pname,B_6: pname,C_7: pname,D: pname] :
% 0.30/0.69 ( ( ( insert_pname @ A_22 @ ( insert_pname @ B_6 @ bot_bot_pname_o ) )
% 0.30/0.69 = ( insert_pname @ C_7 @ ( insert_pname @ D @ bot_bot_pname_o ) ) )
% 0.30/0.69 <=> ( ( ( A_22 = C_7 )
% 0.30/0.69 & ( B_6 = D ) )
% 0.30/0.69 | ( ( A_22 = D )
% 0.30/0.69 & ( B_6 = C_7 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_453_doubleton__eq__iff,axiom,
% 0.30/0.69 ! [A_22: nat,B_6: nat,C_7: nat,D: nat] :
% 0.30/0.69 ( ( ( insert_nat @ A_22 @ ( insert_nat @ B_6 @ bot_bot_nat_o ) )
% 0.30/0.69 = ( insert_nat @ C_7 @ ( insert_nat @ D @ bot_bot_nat_o ) ) )
% 0.30/0.69 <=> ( ( ( A_22 = C_7 )
% 0.30/0.69 & ( B_6 = D ) )
% 0.30/0.69 | ( ( A_22 = D )
% 0.30/0.69 & ( B_6 = C_7 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_454_doubleton__eq__iff,axiom,
% 0.30/0.69 ! [A_22: x_a,B_6: x_a,C_7: x_a,D: x_a] :
% 0.30/0.69 ( ( ( insert_a @ A_22 @ ( insert_a @ B_6 @ bot_bot_a_o ) )
% 0.30/0.69 = ( insert_a @ C_7 @ ( insert_a @ D @ bot_bot_a_o ) ) )
% 0.30/0.69 <=> ( ( ( A_22 = C_7 )
% 0.30/0.69 & ( B_6 = D ) )
% 0.30/0.69 | ( ( A_22 = D )
% 0.30/0.69 & ( B_6 = C_7 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_455_singleton__iff,axiom,
% 0.30/0.69 ! [B_5: nat,A_21: nat] :
% 0.30/0.69 ( ( member_nat @ B_5 @ ( insert_nat @ A_21 @ bot_bot_nat_o ) )
% 0.30/0.69 <=> ( B_5 = A_21 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_456_singleton__iff,axiom,
% 0.30/0.69 ! [B_5: pname,A_21: pname] :
% 0.30/0.69 ( ( member_pname @ B_5 @ ( insert_pname @ A_21 @ bot_bot_pname_o ) )
% 0.30/0.69 <=> ( B_5 = A_21 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_457_singleton__iff,axiom,
% 0.30/0.69 ! [B_5: x_a,A_21: x_a] :
% 0.30/0.69 ( ( member_a @ B_5 @ ( insert_a @ A_21 @ bot_bot_a_o ) )
% 0.30/0.69 <=> ( B_5 = A_21 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_458_insert__not__empty,axiom,
% 0.30/0.69 ! [A_20: pname,A_19: pname > $o] :
% 0.30/0.69 ( ( insert_pname @ A_20 @ A_19 )
% 0.30/0.69 != bot_bot_pname_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_459_insert__not__empty,axiom,
% 0.30/0.69 ! [A_20: nat,A_19: nat > $o] :
% 0.30/0.69 ( ( insert_nat @ A_20 @ A_19 )
% 0.30/0.69 != bot_bot_nat_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_460_insert__not__empty,axiom,
% 0.30/0.69 ! [A_20: x_a,A_19: x_a > $o] :
% 0.30/0.69 ( ( insert_a @ A_20 @ A_19 )
% 0.30/0.69 != bot_bot_a_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_461_empty__not__insert,axiom,
% 0.30/0.69 ! [A_18: pname,A_17: pname > $o] :
% 0.30/0.69 ( bot_bot_pname_o
% 0.30/0.69 != ( insert_pname @ A_18 @ A_17 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_462_empty__not__insert,axiom,
% 0.30/0.69 ! [A_18: nat,A_17: nat > $o] :
% 0.30/0.69 ( bot_bot_nat_o
% 0.30/0.69 != ( insert_nat @ A_18 @ A_17 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_463_empty__not__insert,axiom,
% 0.30/0.69 ! [A_18: x_a,A_17: x_a > $o] :
% 0.30/0.69 ( bot_bot_a_o
% 0.30/0.69 != ( insert_a @ A_18 @ A_17 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_464_subset__empty,axiom,
% 0.30/0.69 ! [A_16: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_16 @ bot_bot_nat_o )
% 0.30/0.69 <=> ( A_16 = bot_bot_nat_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_465_subset__empty,axiom,
% 0.30/0.69 ! [A_16: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_16 @ bot_bot_pname_o )
% 0.30/0.69 <=> ( A_16 = bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_466_subset__empty,axiom,
% 0.30/0.69 ! [A_16: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_16 @ bot_bot_a_o )
% 0.30/0.69 <=> ( A_16 = bot_bot_a_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_467_image__is__empty,axiom,
% 0.30/0.69 ! [F_6: pname > x_a,A_15: pname > $o] :
% 0.30/0.69 ( ( ( image_pname_a @ F_6 @ A_15 )
% 0.30/0.69 = bot_bot_a_o )
% 0.30/0.69 <=> ( A_15 = bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_468_image__empty,axiom,
% 0.30/0.69 ! [F_5: pname > x_a] :
% 0.30/0.69 ( ( image_pname_a @ F_5 @ bot_bot_pname_o )
% 0.30/0.69 = bot_bot_a_o ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_469_empty__is__image,axiom,
% 0.30/0.69 ! [F_4: pname > x_a,A_14: pname > $o] :
% 0.30/0.69 ( ( bot_bot_a_o
% 0.30/0.69 = ( image_pname_a @ F_4 @ A_14 ) )
% 0.30/0.69 <=> ( A_14 = bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_470_Collect__conv__if,axiom,
% 0.30/0.69 ! [P_4: nat > $o,A_13: nat] :
% 0.30/0.69 ( ( ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_nat
% 0.30/0.69 @ ^ [X_1: nat] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = ( insert_nat @ A_13 @ bot_bot_nat_o ) ) )
% 0.30/0.69 & ( ~ ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_nat
% 0.30/0.69 @ ^ [X_1: nat] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_nat_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_471_Collect__conv__if,axiom,
% 0.30/0.69 ! [P_4: pname > $o,A_13: pname] :
% 0.30/0.69 ( ( ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_pname
% 0.30/0.69 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = ( insert_pname @ A_13 @ bot_bot_pname_o ) ) )
% 0.30/0.69 & ( ~ ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_pname
% 0.30/0.69 @ ^ [X_1: pname] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_pname_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_472_Collect__conv__if,axiom,
% 0.30/0.69 ! [P_4: x_a > $o,A_13: x_a] :
% 0.30/0.69 ( ( ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_a
% 0.30/0.69 @ ^ [X_1: x_a] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = ( insert_a @ A_13 @ bot_bot_a_o ) ) )
% 0.30/0.69 & ( ~ ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_a
% 0.30/0.69 @ ^ [X_1: x_a] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_a_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_473_Collect__conv__if,axiom,
% 0.30/0.69 ! [P_4: ( nat > $o ) > $o,A_13: nat > $o] :
% 0.30/0.69 ( ( ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_nat_o
% 0.30/0.69 @ ^ [X_1: nat > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = ( insert_nat_o @ A_13 @ bot_bot_nat_o_o ) ) )
% 0.30/0.69 & ( ~ ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_nat_o
% 0.30/0.69 @ ^ [X_1: nat > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_nat_o_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_474_Collect__conv__if,axiom,
% 0.30/0.69 ! [P_4: ( pname > $o ) > $o,A_13: pname > $o] :
% 0.30/0.69 ( ( ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_pname_o
% 0.30/0.69 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = ( insert_pname_o @ A_13 @ bot_bot_pname_o_o ) ) )
% 0.30/0.69 & ( ~ ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_pname_o
% 0.30/0.69 @ ^ [X_1: pname > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_pname_o_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_475_Collect__conv__if,axiom,
% 0.30/0.69 ! [P_4: ( x_a > $o ) > $o,A_13: x_a > $o] :
% 0.30/0.69 ( ( ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_a_o
% 0.30/0.69 @ ^ [X_1: x_a > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = ( insert_a_o @ A_13 @ bot_bot_a_o_o ) ) )
% 0.30/0.69 & ( ~ ( P_4 @ A_13 )
% 0.30/0.69 => ( ( collect_a_o
% 0.30/0.69 @ ^ [X_1: x_a > $o] : ( (&) @ ( X_1 = A_13 ) @ ( P_4 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_a_o_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_476_Collect__conv__if2,axiom,
% 0.30/0.69 ! [P_3: nat > $o,A_12: nat] :
% 0.30/0.69 ( ( ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_nat
% 0.30/0.69 @ ^ [X_1: nat] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = ( insert_nat @ A_12 @ bot_bot_nat_o ) ) )
% 0.30/0.69 & ( ~ ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_nat
% 0.30/0.69 @ ^ [X_1: nat] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_nat_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_477_Collect__conv__if2,axiom,
% 0.30/0.69 ! [P_3: pname > $o,A_12: pname] :
% 0.30/0.69 ( ( ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_pname
% 0.30/0.69 @ ^ [X_1: pname] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = ( insert_pname @ A_12 @ bot_bot_pname_o ) ) )
% 0.30/0.69 & ( ~ ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_pname
% 0.30/0.69 @ ^ [X_1: pname] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_pname_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_478_Collect__conv__if2,axiom,
% 0.30/0.69 ! [P_3: x_a > $o,A_12: x_a] :
% 0.30/0.69 ( ( ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_a
% 0.30/0.69 @ ^ [X_1: x_a] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = ( insert_a @ A_12 @ bot_bot_a_o ) ) )
% 0.30/0.69 & ( ~ ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_a
% 0.30/0.69 @ ^ [X_1: x_a] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_a_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_479_Collect__conv__if2,axiom,
% 0.30/0.69 ! [P_3: ( nat > $o ) > $o,A_12: nat > $o] :
% 0.30/0.69 ( ( ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_nat_o
% 0.30/0.69 @ ^ [X_1: nat > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = ( insert_nat_o @ A_12 @ bot_bot_nat_o_o ) ) )
% 0.30/0.69 & ( ~ ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_nat_o
% 0.30/0.69 @ ^ [X_1: nat > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_nat_o_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_480_Collect__conv__if2,axiom,
% 0.30/0.69 ! [P_3: ( pname > $o ) > $o,A_12: pname > $o] :
% 0.30/0.69 ( ( ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_pname_o
% 0.30/0.69 @ ^ [X_1: pname > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = ( insert_pname_o @ A_12 @ bot_bot_pname_o_o ) ) )
% 0.30/0.69 & ( ~ ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_pname_o
% 0.30/0.69 @ ^ [X_1: pname > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_pname_o_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_481_Collect__conv__if2,axiom,
% 0.30/0.69 ! [P_3: ( x_a > $o ) > $o,A_12: x_a > $o] :
% 0.30/0.69 ( ( ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_a_o
% 0.30/0.69 @ ^ [X_1: x_a > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = ( insert_a_o @ A_12 @ bot_bot_a_o_o ) ) )
% 0.30/0.69 & ( ~ ( P_3 @ A_12 )
% 0.30/0.69 => ( ( collect_a_o
% 0.30/0.69 @ ^ [X_1: x_a > $o] : ( (&) @ ( A_12 = X_1 ) @ ( P_3 @ X_1 ) ) )
% 0.30/0.69 = bot_bot_a_o_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_482_singleton__conv,axiom,
% 0.30/0.69 ! [A_11: nat] :
% 0.30/0.69 ( ( collect_nat
% 0.30/0.69 @ ^ [X_1: nat] : ( X_1 = A_11 ) )
% 0.30/0.69 = ( insert_nat @ A_11 @ bot_bot_nat_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_483_singleton__conv,axiom,
% 0.30/0.69 ! [A_11: pname] :
% 0.30/0.69 ( ( collect_pname
% 0.30/0.69 @ ^ [X_1: pname] : ( X_1 = A_11 ) )
% 0.30/0.69 = ( insert_pname @ A_11 @ bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_484_singleton__conv,axiom,
% 0.30/0.69 ! [A_11: x_a] :
% 0.30/0.69 ( ( collect_a
% 0.30/0.69 @ ^ [X_1: x_a] : ( X_1 = A_11 ) )
% 0.30/0.69 = ( insert_a @ A_11 @ bot_bot_a_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_485_singleton__conv,axiom,
% 0.30/0.69 ! [A_11: nat > $o] :
% 0.30/0.69 ( ( collect_nat_o
% 0.30/0.69 @ ^ [X_1: nat > $o] : ( X_1 = A_11 ) )
% 0.30/0.69 = ( insert_nat_o @ A_11 @ bot_bot_nat_o_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_486_singleton__conv,axiom,
% 0.30/0.69 ! [A_11: pname > $o] :
% 0.30/0.69 ( ( collect_pname_o
% 0.30/0.69 @ ^ [X_1: pname > $o] : ( X_1 = A_11 ) )
% 0.30/0.69 = ( insert_pname_o @ A_11 @ bot_bot_pname_o_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_487_singleton__conv,axiom,
% 0.30/0.69 ! [A_11: x_a > $o] :
% 0.30/0.69 ( ( collect_a_o
% 0.30/0.69 @ ^ [X_1: x_a > $o] : ( X_1 = A_11 ) )
% 0.30/0.69 = ( insert_a_o @ A_11 @ bot_bot_a_o_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_488_singleton__conv2,axiom,
% 0.30/0.69 ! [A_10: nat] :
% 0.30/0.69 ( ( collect_nat @ ( fequal_nat @ A_10 ) )
% 0.30/0.69 = ( insert_nat @ A_10 @ bot_bot_nat_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_489_singleton__conv2,axiom,
% 0.30/0.69 ! [A_10: pname] :
% 0.30/0.69 ( ( collect_pname @ ( fequal_pname @ A_10 ) )
% 0.30/0.69 = ( insert_pname @ A_10 @ bot_bot_pname_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_490_singleton__conv2,axiom,
% 0.30/0.69 ! [A_10: x_a] :
% 0.30/0.69 ( ( collect_a @ ( fequal_a @ A_10 ) )
% 0.30/0.69 = ( insert_a @ A_10 @ bot_bot_a_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_491_singleton__conv2,axiom,
% 0.30/0.69 ! [A_10: nat > $o] :
% 0.30/0.69 ( ( collect_nat_o @ ( fequal_nat_o @ A_10 ) )
% 0.30/0.69 = ( insert_nat_o @ A_10 @ bot_bot_nat_o_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_492_singleton__conv2,axiom,
% 0.30/0.69 ! [A_10: pname > $o] :
% 0.30/0.69 ( ( collect_pname_o @ ( fequal_pname_o @ A_10 ) )
% 0.30/0.69 = ( insert_pname_o @ A_10 @ bot_bot_pname_o_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_493_singleton__conv2,axiom,
% 0.30/0.69 ! [A_10: x_a > $o] :
% 0.30/0.69 ( ( collect_a_o @ ( fequal_a_o @ A_10 ) )
% 0.30/0.69 = ( insert_a_o @ A_10 @ bot_bot_a_o_o ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_494_subset__singletonD,axiom,
% 0.30/0.69 ! [A_9: nat > $o,X_12: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_9 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) )
% 0.30/0.69 => ( ( A_9 = bot_bot_nat_o )
% 0.30/0.69 | ( A_9
% 0.30/0.69 = ( insert_nat @ X_12 @ bot_bot_nat_o ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_495_subset__singletonD,axiom,
% 0.30/0.69 ! [A_9: pname > $o,X_12: pname] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_9 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 0.30/0.69 => ( ( A_9 = bot_bot_pname_o )
% 0.30/0.69 | ( A_9
% 0.30/0.69 = ( insert_pname @ X_12 @ bot_bot_pname_o ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_496_subset__singletonD,axiom,
% 0.30/0.69 ! [A_9: x_a > $o,X_12: x_a] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_9 @ ( insert_a @ X_12 @ bot_bot_a_o ) )
% 0.30/0.69 => ( ( A_9 = bot_bot_a_o )
% 0.30/0.69 | ( A_9
% 0.30/0.69 = ( insert_a @ X_12 @ bot_bot_a_o ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_497_image__constant,axiom,
% 0.30/0.69 ! [C_6: x_a,X_11: pname,A_8: pname > $o] :
% 0.30/0.69 ( ( member_pname @ X_11 @ A_8 )
% 0.30/0.69 => ( ( image_pname_a
% 0.30/0.69 @ ^ [X_1: pname] : C_6
% 0.30/0.69 @ A_8 )
% 0.30/0.69 = ( insert_a @ C_6 @ bot_bot_a_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_498_image__constant__conv,axiom,
% 0.30/0.69 ! [C_5: x_a,A_7: pname > $o] :
% 0.30/0.69 ( ( ( A_7 = bot_bot_pname_o )
% 0.30/0.69 => ( ( image_pname_a
% 0.30/0.69 @ ^ [X_1: pname] : C_5
% 0.30/0.69 @ A_7 )
% 0.30/0.69 = bot_bot_a_o ) )
% 0.30/0.69 & ( ( A_7 != bot_bot_pname_o )
% 0.30/0.69 => ( ( image_pname_a
% 0.30/0.69 @ ^ [X_1: pname] : C_5
% 0.30/0.69 @ A_7 )
% 0.30/0.69 = ( insert_a @ C_5 @ bot_bot_a_o ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_499_linorder__le__cases,axiom,
% 0.30/0.69 ! [X_10: nat,Y_9: nat] :
% 0.30/0.69 ( ~ ( ord_less_eq_nat @ X_10 @ Y_9 )
% 0.30/0.69 => ( ord_less_eq_nat @ Y_9 @ X_10 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_500_xt1_I6_J,axiom,
% 0.30/0.69 ! [Z_2: $o,Y_8: $o,X_9: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ Y_8 @ X_9 )
% 0.30/0.69 => ( ( ord_less_eq_o @ Z_2 @ Y_8 )
% 0.30/0.69 => ( ord_less_eq_o @ Z_2 @ X_9 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_501_xt1_I6_J,axiom,
% 0.30/0.69 ! [Z_2: nat > $o,Y_8: nat > $o,X_9: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ Y_8 @ X_9 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ Z_2 @ Y_8 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ Z_2 @ X_9 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_502_xt1_I6_J,axiom,
% 0.30/0.69 ! [Z_2: pname > $o,Y_8: pname > $o,X_9: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ Y_8 @ X_9 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ Z_2 @ Y_8 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ Z_2 @ X_9 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_503_xt1_I6_J,axiom,
% 0.30/0.69 ! [Z_2: nat,Y_8: nat,X_9: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ Y_8 @ X_9 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ Z_2 @ Y_8 )
% 0.30/0.69 => ( ord_less_eq_nat @ Z_2 @ X_9 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_504_xt1_I6_J,axiom,
% 0.30/0.69 ! [Z_2: x_a > $o,Y_8: x_a > $o,X_9: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ Y_8 @ X_9 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ Z_2 @ Y_8 )
% 0.30/0.69 => ( ord_less_eq_a_o @ Z_2 @ X_9 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_505_xt1_I5_J,axiom,
% 0.30/0.69 ! [Y_7: $o,X_8: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ Y_7 @ X_8 )
% 0.30/0.69 => ( ( ord_less_eq_o @ X_8 @ Y_7 )
% 0.30/0.69 => ( X_8
% 0.30/0.69 <=> Y_7 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_506_xt1_I5_J,axiom,
% 0.30/0.69 ! [Y_7: nat > $o,X_8: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ Y_7 @ X_8 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ X_8 @ Y_7 )
% 0.30/0.69 => ( X_8 = Y_7 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_507_xt1_I5_J,axiom,
% 0.30/0.69 ! [Y_7: pname > $o,X_8: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ Y_7 @ X_8 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ X_8 @ Y_7 )
% 0.30/0.69 => ( X_8 = Y_7 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_508_xt1_I5_J,axiom,
% 0.30/0.69 ! [Y_7: nat,X_8: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ Y_7 @ X_8 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ X_8 @ Y_7 )
% 0.30/0.69 => ( X_8 = Y_7 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_509_xt1_I5_J,axiom,
% 0.30/0.69 ! [Y_7: x_a > $o,X_8: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ Y_7 @ X_8 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ X_8 @ Y_7 )
% 0.30/0.69 => ( X_8 = Y_7 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_510_order__trans,axiom,
% 0.30/0.69 ! [Z_1: $o,X_7: $o,Y_6: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ X_7 @ Y_6 )
% 0.30/0.69 => ( ( ord_less_eq_o @ Y_6 @ Z_1 )
% 0.30/0.69 => ( ord_less_eq_o @ X_7 @ Z_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_511_order__trans,axiom,
% 0.30/0.69 ! [Z_1: nat > $o,X_7: nat > $o,Y_6: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ X_7 @ Y_6 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ Y_6 @ Z_1 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ X_7 @ Z_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_512_order__trans,axiom,
% 0.30/0.69 ! [Z_1: pname > $o,X_7: pname > $o,Y_6: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ X_7 @ Y_6 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ Y_6 @ Z_1 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ X_7 @ Z_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_513_order__trans,axiom,
% 0.30/0.69 ! [Z_1: nat,X_7: nat,Y_6: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ X_7 @ Y_6 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ Y_6 @ Z_1 )
% 0.30/0.69 => ( ord_less_eq_nat @ X_7 @ Z_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_514_order__trans,axiom,
% 0.30/0.69 ! [Z_1: x_a > $o,X_7: x_a > $o,Y_6: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ X_7 @ Y_6 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ Y_6 @ Z_1 )
% 0.30/0.69 => ( ord_less_eq_a_o @ X_7 @ Z_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_515_order__antisym,axiom,
% 0.30/0.69 ! [X_6: $o,Y_5: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ X_6 @ Y_5 )
% 0.30/0.69 => ( ( ord_less_eq_o @ Y_5 @ X_6 )
% 0.30/0.69 => ( X_6
% 0.30/0.69 <=> Y_5 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_516_order__antisym,axiom,
% 0.30/0.69 ! [X_6: nat > $o,Y_5: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ X_6 @ Y_5 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ Y_5 @ X_6 )
% 0.30/0.69 => ( X_6 = Y_5 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_517_order__antisym,axiom,
% 0.30/0.69 ! [X_6: pname > $o,Y_5: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ X_6 @ Y_5 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ Y_5 @ X_6 )
% 0.30/0.69 => ( X_6 = Y_5 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_518_order__antisym,axiom,
% 0.30/0.69 ! [X_6: nat,Y_5: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ X_6 @ Y_5 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ Y_5 @ X_6 )
% 0.30/0.69 => ( X_6 = Y_5 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_519_order__antisym,axiom,
% 0.30/0.69 ! [X_6: x_a > $o,Y_5: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ X_6 @ Y_5 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ Y_5 @ X_6 )
% 0.30/0.69 => ( X_6 = Y_5 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_520_xt1_I4_J,axiom,
% 0.30/0.69 ! [C_4: $o,B_4: $o,A_6: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ B_4 @ A_6 )
% 0.30/0.69 => ( ( B_4
% 0.30/0.69 <=> C_4 )
% 0.30/0.69 => ( ord_less_eq_o @ C_4 @ A_6 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_521_xt1_I4_J,axiom,
% 0.30/0.69 ! [C_4: nat > $o,B_4: nat > $o,A_6: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ B_4 @ A_6 )
% 0.30/0.69 => ( ( B_4 = C_4 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ C_4 @ A_6 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_522_xt1_I4_J,axiom,
% 0.30/0.69 ! [C_4: pname > $o,B_4: pname > $o,A_6: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ B_4 @ A_6 )
% 0.30/0.69 => ( ( B_4 = C_4 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ C_4 @ A_6 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_523_xt1_I4_J,axiom,
% 0.30/0.69 ! [C_4: nat,B_4: nat,A_6: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ B_4 @ A_6 )
% 0.30/0.69 => ( ( B_4 = C_4 )
% 0.30/0.69 => ( ord_less_eq_nat @ C_4 @ A_6 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_524_xt1_I4_J,axiom,
% 0.30/0.69 ! [C_4: x_a > $o,B_4: x_a > $o,A_6: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ B_4 @ A_6 )
% 0.30/0.69 => ( ( B_4 = C_4 )
% 0.30/0.69 => ( ord_less_eq_a_o @ C_4 @ A_6 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_525_ord__le__eq__trans,axiom,
% 0.30/0.69 ! [C_3: $o,A_5: $o,B_3: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ A_5 @ B_3 )
% 0.30/0.69 => ( ( B_3
% 0.30/0.69 <=> C_3 )
% 0.30/0.69 => ( ord_less_eq_o @ A_5 @ C_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_526_ord__le__eq__trans,axiom,
% 0.30/0.69 ! [C_3: nat > $o,A_5: nat > $o,B_3: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ A_5 @ B_3 )
% 0.30/0.69 => ( ( B_3 = C_3 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ A_5 @ C_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_527_ord__le__eq__trans,axiom,
% 0.30/0.69 ! [C_3: pname > $o,A_5: pname > $o,B_3: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ A_5 @ B_3 )
% 0.30/0.69 => ( ( B_3 = C_3 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ A_5 @ C_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_528_ord__le__eq__trans,axiom,
% 0.30/0.69 ! [C_3: nat,A_5: nat,B_3: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ A_5 @ B_3 )
% 0.30/0.69 => ( ( B_3 = C_3 )
% 0.30/0.69 => ( ord_less_eq_nat @ A_5 @ C_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_529_ord__le__eq__trans,axiom,
% 0.30/0.69 ! [C_3: x_a > $o,A_5: x_a > $o,B_3: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ A_5 @ B_3 )
% 0.30/0.69 => ( ( B_3 = C_3 )
% 0.30/0.69 => ( ord_less_eq_a_o @ A_5 @ C_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_530_xt1_I3_J,axiom,
% 0.30/0.69 ! [C_2: $o,B_2: $o,A_4: $o] :
% 0.30/0.69 ( ( A_4
% 0.30/0.69 <=> B_2 )
% 0.30/0.69 => ( ( ord_less_eq_o @ C_2 @ B_2 )
% 0.30/0.69 => ( ord_less_eq_o @ C_2 @ A_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_531_xt1_I3_J,axiom,
% 0.30/0.69 ! [C_2: nat > $o,A_4: nat > $o,B_2: nat > $o] :
% 0.30/0.69 ( ( A_4 = B_2 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ C_2 @ B_2 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ C_2 @ A_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_532_xt1_I3_J,axiom,
% 0.30/0.69 ! [C_2: pname > $o,A_4: pname > $o,B_2: pname > $o] :
% 0.30/0.69 ( ( A_4 = B_2 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ C_2 @ B_2 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ C_2 @ A_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_533_xt1_I3_J,axiom,
% 0.30/0.69 ! [C_2: nat,A_4: nat,B_2: nat] :
% 0.30/0.69 ( ( A_4 = B_2 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ C_2 @ B_2 )
% 0.30/0.69 => ( ord_less_eq_nat @ C_2 @ A_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_534_xt1_I3_J,axiom,
% 0.30/0.69 ! [C_2: x_a > $o,A_4: x_a > $o,B_2: x_a > $o] :
% 0.30/0.69 ( ( A_4 = B_2 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ C_2 @ B_2 )
% 0.30/0.69 => ( ord_less_eq_a_o @ C_2 @ A_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_535_ord__eq__le__trans,axiom,
% 0.30/0.69 ! [C_1: $o,B_1: $o,A_3: $o] :
% 0.30/0.69 ( ( A_3
% 0.30/0.69 <=> B_1 )
% 0.30/0.69 => ( ( ord_less_eq_o @ B_1 @ C_1 )
% 0.30/0.69 => ( ord_less_eq_o @ A_3 @ C_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_536_ord__eq__le__trans,axiom,
% 0.30/0.69 ! [C_1: nat > $o,A_3: nat > $o,B_1: nat > $o] :
% 0.30/0.69 ( ( A_3 = B_1 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ B_1 @ C_1 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ A_3 @ C_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_537_ord__eq__le__trans,axiom,
% 0.30/0.69 ! [C_1: pname > $o,A_3: pname > $o,B_1: pname > $o] :
% 0.30/0.69 ( ( A_3 = B_1 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ B_1 @ C_1 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ A_3 @ C_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_538_ord__eq__le__trans,axiom,
% 0.30/0.69 ! [C_1: nat,A_3: nat,B_1: nat] :
% 0.30/0.69 ( ( A_3 = B_1 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ B_1 @ C_1 )
% 0.30/0.69 => ( ord_less_eq_nat @ A_3 @ C_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_539_ord__eq__le__trans,axiom,
% 0.30/0.69 ! [C_1: x_a > $o,A_3: x_a > $o,B_1: x_a > $o] :
% 0.30/0.69 ( ( A_3 = B_1 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ B_1 @ C_1 )
% 0.30/0.69 => ( ord_less_eq_a_o @ A_3 @ C_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_540_order__antisym__conv,axiom,
% 0.30/0.69 ! [Y_4: $o,X_5: $o] :
% 0.30/0.69 ( ( ord_less_eq_o @ Y_4 @ X_5 )
% 0.30/0.69 => ( ( ord_less_eq_o @ X_5 @ Y_4 )
% 0.30/0.69 <=> ( X_5
% 0.30/0.69 <=> Y_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_541_order__antisym__conv,axiom,
% 0.30/0.69 ! [Y_4: nat > $o,X_5: nat > $o] :
% 0.30/0.69 ( ( ord_less_eq_nat_o @ Y_4 @ X_5 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ X_5 @ Y_4 )
% 0.30/0.69 <=> ( X_5 = Y_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_542_order__antisym__conv,axiom,
% 0.30/0.69 ! [Y_4: pname > $o,X_5: pname > $o] :
% 0.30/0.69 ( ( ord_less_eq_pname_o @ Y_4 @ X_5 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ X_5 @ Y_4 )
% 0.30/0.69 <=> ( X_5 = Y_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_543_order__antisym__conv,axiom,
% 0.30/0.69 ! [Y_4: nat,X_5: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ Y_4 @ X_5 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ X_5 @ Y_4 )
% 0.30/0.69 <=> ( X_5 = Y_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_544_order__antisym__conv,axiom,
% 0.30/0.69 ! [Y_4: x_a > $o,X_5: x_a > $o] :
% 0.30/0.69 ( ( ord_less_eq_a_o @ Y_4 @ X_5 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ X_5 @ Y_4 )
% 0.30/0.69 <=> ( X_5 = Y_4 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_545_order__eq__refl,axiom,
% 0.30/0.69 ! [Y_3: $o,X_4: $o] :
% 0.30/0.69 ( ( X_4
% 0.30/0.69 <=> Y_3 )
% 0.30/0.69 => ( ord_less_eq_o @ X_4 @ Y_3 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_546_order__eq__refl,axiom,
% 0.30/0.69 ! [X_4: nat > $o,Y_3: nat > $o] :
% 0.30/0.69 ( ( X_4 = Y_3 )
% 0.30/0.69 => ( ord_less_eq_nat_o @ X_4 @ Y_3 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_547_order__eq__refl,axiom,
% 0.30/0.69 ! [X_4: pname > $o,Y_3: pname > $o] :
% 0.30/0.69 ( ( X_4 = Y_3 )
% 0.30/0.69 => ( ord_less_eq_pname_o @ X_4 @ Y_3 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_548_order__eq__refl,axiom,
% 0.30/0.69 ! [X_4: nat,Y_3: nat] :
% 0.30/0.69 ( ( X_4 = Y_3 )
% 0.30/0.69 => ( ord_less_eq_nat @ X_4 @ Y_3 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_549_order__eq__refl,axiom,
% 0.30/0.69 ! [X_4: x_a > $o,Y_3: x_a > $o] :
% 0.30/0.69 ( ( X_4 = Y_3 )
% 0.30/0.69 => ( ord_less_eq_a_o @ X_4 @ Y_3 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_550_order__eq__iff,axiom,
% 0.30/0.69 ! [Y_2: $o,X_3: $o] :
% 0.30/0.69 ( ( X_3
% 0.30/0.69 <=> Y_2 )
% 0.30/0.69 <=> ( ( ord_less_eq_o @ X_3 @ Y_2 )
% 0.30/0.69 & ( ord_less_eq_o @ Y_2 @ X_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_551_order__eq__iff,axiom,
% 0.30/0.69 ! [X_3: nat > $o,Y_2: nat > $o] :
% 0.30/0.69 ( ( X_3 = Y_2 )
% 0.30/0.69 <=> ( ( ord_less_eq_nat_o @ X_3 @ Y_2 )
% 0.30/0.69 & ( ord_less_eq_nat_o @ Y_2 @ X_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_552_order__eq__iff,axiom,
% 0.30/0.69 ! [X_3: pname > $o,Y_2: pname > $o] :
% 0.30/0.69 ( ( X_3 = Y_2 )
% 0.30/0.69 <=> ( ( ord_less_eq_pname_o @ X_3 @ Y_2 )
% 0.30/0.69 & ( ord_less_eq_pname_o @ Y_2 @ X_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_553_order__eq__iff,axiom,
% 0.30/0.69 ! [X_3: nat,Y_2: nat] :
% 0.30/0.69 ( ( X_3 = Y_2 )
% 0.30/0.69 <=> ( ( ord_less_eq_nat @ X_3 @ Y_2 )
% 0.30/0.69 & ( ord_less_eq_nat @ Y_2 @ X_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_554_order__eq__iff,axiom,
% 0.30/0.69 ! [X_3: x_a > $o,Y_2: x_a > $o] :
% 0.30/0.69 ( ( X_3 = Y_2 )
% 0.30/0.69 <=> ( ( ord_less_eq_a_o @ X_3 @ Y_2 )
% 0.30/0.69 & ( ord_less_eq_a_o @ Y_2 @ X_3 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_555_linorder__linear,axiom,
% 0.30/0.69 ! [X_2: nat,Y_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ X_2 @ Y_1 )
% 0.30/0.69 | ( ord_less_eq_nat @ Y_1 @ X_2 ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_556_finite__subset__induct,axiom,
% 0.30/0.69 ! [P_2: ( nat > $o ) > $o,A_1: nat > $o,F_3: nat > $o] :
% 0.30/0.69 ( ( finite_finite_nat @ F_3 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o @ F_3 @ A_1 )
% 0.30/0.69 => ( ( P_2 @ bot_bot_nat_o )
% 0.30/0.69 => ( ! [A_2: nat,F_2: nat > $o] :
% 0.30/0.69 ( ( finite_finite_nat @ F_2 )
% 0.30/0.69 => ( ( member_nat @ A_2 @ A_1 )
% 0.30/0.69 => ( ~ ( member_nat @ A_2 @ F_2 )
% 0.30/0.69 => ( ( P_2 @ F_2 )
% 0.30/0.69 => ( P_2 @ ( insert_nat @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/0.69 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_557_finite__subset__induct,axiom,
% 0.30/0.69 ! [P_2: ( pname > $o ) > $o,A_1: pname > $o,F_3: pname > $o] :
% 0.30/0.69 ( ( finite_finite_pname @ F_3 )
% 0.30/0.69 => ( ( ord_less_eq_pname_o @ F_3 @ A_1 )
% 0.30/0.69 => ( ( P_2 @ bot_bot_pname_o )
% 0.30/0.69 => ( ! [A_2: pname,F_2: pname > $o] :
% 0.30/0.69 ( ( finite_finite_pname @ F_2 )
% 0.30/0.69 => ( ( member_pname @ A_2 @ A_1 )
% 0.30/0.69 => ( ~ ( member_pname @ A_2 @ F_2 )
% 0.30/0.69 => ( ( P_2 @ F_2 )
% 0.30/0.69 => ( P_2 @ ( insert_pname @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/0.69 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_558_finite__subset__induct,axiom,
% 0.30/0.69 ! [P_2: ( x_a > $o ) > $o,A_1: x_a > $o,F_3: x_a > $o] :
% 0.30/0.69 ( ( finite_finite_a @ F_3 )
% 0.30/0.69 => ( ( ord_less_eq_a_o @ F_3 @ A_1 )
% 0.30/0.69 => ( ( P_2 @ bot_bot_a_o )
% 0.30/0.69 => ( ! [A_2: x_a,F_2: x_a > $o] :
% 0.30/0.69 ( ( finite_finite_a @ F_2 )
% 0.30/0.69 => ( ( member_a @ A_2 @ A_1 )
% 0.30/0.69 => ( ~ ( member_a @ A_2 @ F_2 )
% 0.30/0.69 => ( ( P_2 @ F_2 )
% 0.30/0.69 => ( P_2 @ ( insert_a @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/0.69 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_559_finite__subset__induct,axiom,
% 0.30/0.69 ! [P_2: ( ( nat > $o ) > $o ) > $o,A_1: ( nat > $o ) > $o,F_3: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( finite_finite_nat_o @ F_3 )
% 0.30/0.69 => ( ( ord_less_eq_nat_o_o @ F_3 @ A_1 )
% 0.30/0.69 => ( ( P_2 @ bot_bot_nat_o_o )
% 0.30/0.69 => ( ! [A_2: nat > $o,F_2: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( finite_finite_nat_o @ F_2 )
% 0.30/0.69 => ( ( member_nat_o @ A_2 @ A_1 )
% 0.30/0.69 => ( ~ ( member_nat_o @ A_2 @ F_2 )
% 0.30/0.69 => ( ( P_2 @ F_2 )
% 0.30/0.69 => ( P_2 @ ( insert_nat_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/0.69 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_560_finite__subset__induct,axiom,
% 0.30/0.69 ! [P_2: ( ( pname > $o ) > $o ) > $o,A_1: ( pname > $o ) > $o,F_3: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( finite297249702name_o @ F_3 )
% 0.30/0.69 => ( ( ord_le1205211808me_o_o @ F_3 @ A_1 )
% 0.30/0.69 => ( ( P_2 @ bot_bot_pname_o_o )
% 0.30/0.69 => ( ! [A_2: pname > $o,F_2: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( finite297249702name_o @ F_2 )
% 0.30/0.69 => ( ( member_pname_o @ A_2 @ A_1 )
% 0.30/0.69 => ( ~ ( member_pname_o @ A_2 @ F_2 )
% 0.30/0.69 => ( ( P_2 @ F_2 )
% 0.30/0.69 => ( P_2 @ ( insert_pname_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/0.69 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_561_finite__subset__induct,axiom,
% 0.30/0.69 ! [P_2: ( ( x_a > $o ) > $o ) > $o,A_1: ( x_a > $o ) > $o,F_3: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( finite_finite_a_o @ F_3 )
% 0.30/0.69 => ( ( ord_less_eq_a_o_o @ F_3 @ A_1 )
% 0.30/0.69 => ( ( P_2 @ bot_bot_a_o_o )
% 0.30/0.69 => ( ! [A_2: x_a > $o,F_2: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( finite_finite_a_o @ F_2 )
% 0.30/0.69 => ( ( member_a_o @ A_2 @ A_1 )
% 0.30/0.69 => ( ~ ( member_a_o @ A_2 @ F_2 )
% 0.30/0.69 => ( ( P_2 @ F_2 )
% 0.30/0.69 => ( P_2 @ ( insert_a_o @ A_2 @ F_2 ) ) ) ) ) )
% 0.30/0.69 => ( P_2 @ F_3 ) ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_562_assms_I2_J,axiom,
% 0.30/0.69 ! [Pn: pname,G: x_a > $o] :
% 0.30/0.69 ( ( p @ ( insert_a @ ( mgt_call @ Pn ) @ G ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ Pn ) ) ) @ bot_bot_a_o ) )
% 0.30/0.69 => ( p @ G @ ( insert_a @ ( mgt_call @ Pn ) @ bot_bot_a_o ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_563_finite__induct,axiom,
% 0.30/0.69 ! [P_1: ( ( nat > $o ) > $o ) > $o,F_1: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( finite_finite_nat_o @ F_1 )
% 0.30/0.69 => ( ( P_1 @ bot_bot_nat_o_o )
% 0.30/0.69 => ( ! [X_1: nat > $o,F_2: ( nat > $o ) > $o] :
% 0.30/0.69 ( ( finite_finite_nat_o @ F_2 )
% 0.30/0.69 => ( ~ ( member_nat_o @ X_1 @ F_2 )
% 0.30/0.69 => ( ( P_1 @ F_2 )
% 0.30/0.69 => ( P_1 @ ( insert_nat_o @ X_1 @ F_2 ) ) ) ) )
% 0.30/0.69 => ( P_1 @ F_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_564_finite__induct,axiom,
% 0.30/0.69 ! [P_1: ( ( pname > $o ) > $o ) > $o,F_1: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( finite297249702name_o @ F_1 )
% 0.30/0.69 => ( ( P_1 @ bot_bot_pname_o_o )
% 0.30/0.69 => ( ! [X_1: pname > $o,F_2: ( pname > $o ) > $o] :
% 0.30/0.69 ( ( finite297249702name_o @ F_2 )
% 0.30/0.69 => ( ~ ( member_pname_o @ X_1 @ F_2 )
% 0.30/0.69 => ( ( P_1 @ F_2 )
% 0.30/0.69 => ( P_1 @ ( insert_pname_o @ X_1 @ F_2 ) ) ) ) )
% 0.30/0.69 => ( P_1 @ F_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_565_finite__induct,axiom,
% 0.30/0.69 ! [P_1: ( ( x_a > $o ) > $o ) > $o,F_1: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( finite_finite_a_o @ F_1 )
% 0.30/0.69 => ( ( P_1 @ bot_bot_a_o_o )
% 0.30/0.69 => ( ! [X_1: x_a > $o,F_2: ( x_a > $o ) > $o] :
% 0.30/0.69 ( ( finite_finite_a_o @ F_2 )
% 0.30/0.69 => ( ~ ( member_a_o @ X_1 @ F_2 )
% 0.30/0.69 => ( ( P_1 @ F_2 )
% 0.30/0.69 => ( P_1 @ ( insert_a_o @ X_1 @ F_2 ) ) ) ) )
% 0.30/0.69 => ( P_1 @ F_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_566_finite__less__ub,axiom,
% 0.30/0.69 ! [U: nat,F: nat > nat] :
% 0.30/0.69 ( ! [N_2: nat] : ( ord_less_eq_nat @ N_2 @ ( F @ N_2 ) )
% 0.30/0.69 => ( finite_finite_nat
% 0.30/0.69 @ ( collect_nat
% 0.30/0.69 @ ^ [N_2: nat] : ( ord_less_eq_nat @ ( F @ N_2 ) @ U ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_567_assms_I4_J,axiom,
% 0.30/0.69 ! [Pn: pname] :
% 0.30/0.69 ( ( member_pname @ Pn @ u )
% 0.30/0.69 => ( wt @ ( the_com @ ( body @ Pn ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_568_diff__Suc__eq__diff__pred,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.30/0.69 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_569_diff__Suc__1,axiom,
% 0.30/0.69 ! [N: nat] :
% 0.30/0.69 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.30/0.69 = N ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_570_less__eq__nat_Osimps_I2_J,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/0.69 <=> ( nat_case_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_571_add__Suc__right,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.30/0.69 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_572_add__Suc,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.30/0.69 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_573_add__Suc__shift,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.30/0.69 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_574_nat__add__right__cancel,axiom,
% 0.30/0.69 ! [M: nat,K: nat,N: nat] :
% 0.30/0.69 ( ( ( plus_plus_nat @ M @ K )
% 0.30/0.69 = ( plus_plus_nat @ N @ K ) )
% 0.30/0.69 <=> ( M = N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_575_nat__add__left__cancel,axiom,
% 0.30/0.69 ! [K: nat,M: nat,N: nat] :
% 0.30/0.69 ( ( ( plus_plus_nat @ K @ M )
% 0.30/0.69 = ( plus_plus_nat @ K @ N ) )
% 0.30/0.69 <=> ( M = N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_576_nat__add__assoc,axiom,
% 0.30/0.69 ! [M: nat,N: nat,K: nat] :
% 0.30/0.69 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.30/0.69 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_577_nat__add__left__commute,axiom,
% 0.30/0.69 ! [X: nat,Y: nat,Z: nat] :
% 0.30/0.69 ( ( plus_plus_nat @ X @ ( plus_plus_nat @ Y @ Z ) )
% 0.30/0.69 = ( plus_plus_nat @ Y @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_578_nat__add__commute,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( plus_plus_nat @ M @ N )
% 0.30/0.69 = ( plus_plus_nat @ N @ M ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_579_diff__add__inverse2,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.30/0.69 = M ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_580_diff__add__inverse,axiom,
% 0.30/0.69 ! [N: nat,M: nat] :
% 0.30/0.69 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.30/0.69 = M ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_581_diff__diff__left,axiom,
% 0.30/0.69 ! [I: nat,J_1: nat,K: nat] :
% 0.30/0.69 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J_1 ) @ K )
% 0.30/0.69 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_582_diff__cancel,axiom,
% 0.30/0.69 ! [K: nat,M: nat,N: nat] :
% 0.30/0.69 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.30/0.69 = ( minus_minus_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_583_diff__cancel2,axiom,
% 0.30/0.69 ! [M: nat,K: nat,N: nat] :
% 0.30/0.69 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.30/0.69 = ( minus_minus_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_584_le__add2,axiom,
% 0.30/0.69 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_585_le__add1,axiom,
% 0.30/0.69 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_586_le__iff__add,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.69 <=> ? [K_1: nat] :
% 0.30/0.69 ( N
% 0.30/0.69 = ( plus_plus_nat @ M @ K_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_587_nat__add__left__cancel__le,axiom,
% 0.30/0.69 ! [K: nat,M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.30/0.69 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_588_trans__le__add1,axiom,
% 0.30/0.69 ! [M: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/0.69 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_589_trans__le__add2,axiom,
% 0.30/0.69 ! [M: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/0.69 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_590_add__le__mono1,axiom,
% 0.30/0.69 ! [K: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/0.69 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_591_add__le__mono,axiom,
% 0.30/0.69 ! [K: nat,L: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ K @ L )
% 0.30/0.69 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_592_add__leD2,axiom,
% 0.30/0.69 ! [M: nat,K: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.30/0.69 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_593_add__leD1,axiom,
% 0.30/0.69 ! [M: nat,K: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.30/0.69 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_594_add__leE,axiom,
% 0.30/0.69 ! [M: nat,K: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.30/0.69 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.69 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_595_diff__add__assoc2,axiom,
% 0.30/0.69 ! [I: nat,K: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/0.69 => ( ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I ) @ K )
% 0.30/0.69 = ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K ) @ I ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_596_add__diff__assoc2,axiom,
% 0.30/0.69 ! [I: nat,K: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/0.69 => ( ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K ) @ I )
% 0.30/0.69 = ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I ) @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_597_diff__add__assoc,axiom,
% 0.30/0.69 ! [I: nat,K: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/0.69 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J_1 ) @ K )
% 0.30/0.69 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_598_le__imp__diff__is__add,axiom,
% 0.30/0.69 ! [K: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/0.69 => ( ( ( minus_minus_nat @ J_1 @ I )
% 0.30/0.69 = K )
% 0.30/0.69 <=> ( J_1
% 0.30/0.69 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_599_le__add__diff__inverse2,axiom,
% 0.30/0.69 ! [N: nat,M: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.69 => ( ( plus_plus_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.30/0.69 = M ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_600_le__diff__conv2,axiom,
% 0.30/0.69 ! [I: nat,K: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/0.69 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.30/0.69 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_601_add__diff__assoc,axiom,
% 0.30/0.69 ! [I: nat,K: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/0.69 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.30/0.69 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J_1 ) @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_602_le__add__diff__inverse,axiom,
% 0.30/0.69 ! [N: nat,M: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.69 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.30/0.69 = M ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_603_le__add__diff,axiom,
% 0.30/0.69 ! [M: nat,K: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.69 => ( ord_less_eq_nat @ M @ ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_604_le__diff__conv,axiom,
% 0.30/0.69 ! [J_1: nat,K: nat,I: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J_1 @ K ) @ I )
% 0.30/0.69 <=> ( ord_less_eq_nat @ J_1 @ ( plus_plus_nat @ I @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_605_diff__diff__right,axiom,
% 0.30/0.69 ! [I: nat,K: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/0.69 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.30/0.69 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_606_Suc__eq__plus1,axiom,
% 0.30/0.69 ! [N: nat] :
% 0.30/0.69 ( ( suc @ N )
% 0.30/0.69 = ( plus_plus_nat @ N @ one_one_nat ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_607_Suc__eq__plus1__left,axiom,
% 0.30/0.69 ! [N: nat] :
% 0.30/0.69 ( ( suc @ N )
% 0.30/0.69 = ( plus_plus_nat @ one_one_nat @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_608_diff__Suc__diff__eq2,axiom,
% 0.30/0.69 ! [M: nat,K: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/0.69 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J_1 @ K ) ) @ M )
% 0.30/0.69 = ( minus_minus_nat @ ( suc @ J_1 ) @ ( plus_plus_nat @ K @ M ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_609_diff__Suc__diff__eq1,axiom,
% 0.30/0.69 ! [M: nat,K: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.30/0.69 => ( ( minus_minus_nat @ M @ ( suc @ ( minus_minus_nat @ J_1 @ K ) ) )
% 0.30/0.69 = ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( suc @ J_1 ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_610_termination__basic__simps_I3_J,axiom,
% 0.30/0.69 ! [Z: nat,X: nat,Y: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.69 => ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_611_termination__basic__simps_I4_J,axiom,
% 0.30/0.69 ! [Y: nat,X: nat,Z: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ X @ Z )
% 0.30/0.69 => ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_612_lessI,axiom,
% 0.30/0.69 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_613_Suc__mono,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ M @ N )
% 0.30/0.69 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_614_finite__Collect__less__nat,axiom,
% 0.30/0.69 ! [K: nat] :
% 0.30/0.69 ( finite_finite_nat
% 0.30/0.69 @ ( collect_nat
% 0.30/0.69 @ ^ [N_2: nat] : ( ord_less_nat @ N_2 @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_615_termination__basic__simps_I1_J,axiom,
% 0.30/0.69 ! [Z: nat,X: nat,Y: nat] :
% 0.30/0.69 ( ( ord_less_nat @ X @ Y )
% 0.30/0.69 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_616_termination__basic__simps_I2_J,axiom,
% 0.30/0.69 ! [Y: nat,X: nat,Z: nat] :
% 0.30/0.69 ( ( ord_less_nat @ X @ Z )
% 0.30/0.69 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_617_add__lessD1,axiom,
% 0.30/0.69 ! [I: nat,J_1: nat,K: nat] :
% 0.30/0.69 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J_1 ) @ K )
% 0.30/0.69 => ( ord_less_nat @ I @ K ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_618_less__add__eq__less,axiom,
% 0.30/0.69 ! [M: nat,N: nat,K: nat,L: nat] :
% 0.30/0.69 ( ( ord_less_nat @ K @ L )
% 0.30/0.69 => ( ( ( plus_plus_nat @ M @ L )
% 0.30/0.69 = ( plus_plus_nat @ K @ N ) )
% 0.30/0.69 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_619_add__less__mono,axiom,
% 0.30/0.69 ! [K: nat,L: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_nat @ I @ J_1 )
% 0.30/0.69 => ( ( ord_less_nat @ K @ L )
% 0.30/0.69 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_620_add__less__mono1,axiom,
% 0.30/0.69 ! [K: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_nat @ I @ J_1 )
% 0.30/0.69 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_621_trans__less__add2,axiom,
% 0.30/0.69 ! [M: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_nat @ I @ J_1 )
% 0.30/0.69 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_622_trans__less__add1,axiom,
% 0.30/0.69 ! [M: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_nat @ I @ J_1 )
% 0.30/0.69 => ( ord_less_nat @ I @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_623_nat__add__left__cancel__less,axiom,
% 0.30/0.69 ! [K: nat,M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.30/0.69 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_624_not__add__less2,axiom,
% 0.30/0.69 ! [J_1: nat,I: nat] :
% 0.30/0.69 ~ ( ord_less_nat @ ( plus_plus_nat @ J_1 @ I ) @ I ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_625_not__add__less1,axiom,
% 0.30/0.69 ! [I: nat,J_1: nat] :
% 0.30/0.69 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J_1 ) @ I ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_626_Suc__less__SucD,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/0.69 => ( ord_less_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_627_Suc__lessD,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.30/0.69 => ( ord_less_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_628_less__SucE,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.30/0.69 => ( ~ ( ord_less_nat @ M @ N )
% 0.30/0.69 => ( M = N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_629_less__trans__Suc,axiom,
% 0.30/0.69 ! [K: nat,I: nat,J_1: nat] :
% 0.30/0.69 ( ( ord_less_nat @ I @ J_1 )
% 0.30/0.69 => ( ( ord_less_nat @ J_1 @ K )
% 0.30/0.69 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_630_Suc__lessI,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ M @ N )
% 0.30/0.69 => ( ( ( suc @ M )
% 0.30/0.69 != N )
% 0.30/0.69 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_631_less__SucI,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ M @ N )
% 0.30/0.69 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_632_less__antisym,axiom,
% 0.30/0.69 ! [N: nat,M: nat] :
% 0.30/0.69 ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.69 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.30/0.69 => ( M = N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_633_not__less__less__Suc__eq,axiom,
% 0.30/0.69 ! [N: nat,M: nat] :
% 0.30/0.69 ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.69 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.30/0.69 <=> ( N = M ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_634_Suc__less__eq,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/0.69 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_635_less__Suc__eq,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.30/0.69 <=> ( ( ord_less_nat @ M @ N )
% 0.30/0.69 | ( M = N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_636_not__less__eq,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ~ ( ord_less_nat @ M @ N )
% 0.30/0.69 <=> ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_637_less__or__eq__imp__le,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ( ord_less_nat @ M @ N )
% 0.30/0.69 | ( M = N ) )
% 0.30/0.69 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_638_le__neq__implies__less,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.69 => ( ( M != N )
% 0.30/0.69 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_639_less__imp__le__nat,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ M @ N )
% 0.30/0.69 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_640_le__eq__less__or__eq,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.69 <=> ( ( ord_less_nat @ M @ N )
% 0.30/0.69 | ( M = N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_641_nat__less__le,axiom,
% 0.30/0.69 ! [M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ M @ N )
% 0.30/0.69 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.69 & ( M != N ) ) ) ).
% 0.30/0.69
% 0.30/0.69 thf(fact_642_diff__less__mono2,axiom,
% 0.30/0.69 ! [L: nat,M: nat,N: nat] :
% 0.30/0.69 ( ( ord_less_nat @ M @ N )
% 0.30/0.69 => ( ( ord_less_nat @ M @ L )
% 0.30/0.70 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_643_less__imp__diff__less,axiom,
% 0.30/0.70 ! [N: nat,J_1: nat,K: nat] :
% 0.30/0.70 ( ( ord_less_nat @ J_1 @ K )
% 0.30/0.70 => ( ord_less_nat @ ( minus_minus_nat @ J_1 @ N ) @ K ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_644_termination__basic__simps_I5_J,axiom,
% 0.30/0.70 ! [X: nat,Y: nat] :
% 0.30/0.70 ( ( ord_less_nat @ X @ Y )
% 0.30/0.70 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_645_less__not__refl,axiom,
% 0.30/0.70 ! [N: nat] :
% 0.30/0.70 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_646_nat__neq__iff,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( M != N )
% 0.30/0.70 <=> ( ( ord_less_nat @ M @ N )
% 0.30/0.70 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_647_linorder__neqE__nat,axiom,
% 0.30/0.70 ! [X: nat,Y: nat] :
% 0.30/0.70 ( ( X != Y )
% 0.30/0.70 => ( ~ ( ord_less_nat @ X @ Y )
% 0.30/0.70 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_648_less__irrefl__nat,axiom,
% 0.30/0.70 ! [N: nat] :
% 0.30/0.70 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_649_less__not__refl2,axiom,
% 0.30/0.70 ! [N: nat,M: nat] :
% 0.30/0.70 ( ( ord_less_nat @ N @ M )
% 0.30/0.70 => ( M != N ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_650_less__not__refl3,axiom,
% 0.30/0.70 ! [S: nat,T: nat] :
% 0.30/0.70 ( ( ord_less_nat @ S @ T )
% 0.30/0.70 => ( S != T ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_651_nat__less__cases,axiom,
% 0.30/0.70 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.30/0.70 ( ( ( ord_less_nat @ M @ N )
% 0.30/0.70 => ( P @ N @ M ) )
% 0.30/0.70 => ( ( ( M = N )
% 0.30/0.70 => ( P @ N @ M ) )
% 0.30/0.70 => ( ( ( ord_less_nat @ N @ M )
% 0.30/0.70 => ( P @ N @ M ) )
% 0.30/0.70 => ( P @ N @ M ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_652_finite__nat__set__iff__bounded,axiom,
% 0.30/0.70 ! [N_1: nat > $o] :
% 0.30/0.70 ( ( finite_finite_nat @ N_1 )
% 0.30/0.70 <=> ? [M_1: nat] :
% 0.30/0.70 ! [X_1: nat] :
% 0.30/0.70 ( ( member_nat @ X_1 @ N_1 )
% 0.30/0.70 => ( ord_less_nat @ X_1 @ M_1 ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_653_card__Collect__less__nat,axiom,
% 0.30/0.70 ! [N: nat] :
% 0.30/0.70 ( ( finite_card_nat
% 0.30/0.70 @ ( collect_nat
% 0.30/0.70 @ ^ [I_1: nat] : ( ord_less_nat @ I_1 @ N ) ) )
% 0.30/0.70 = N ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_654_finite__M__bounded__by__nat,axiom,
% 0.30/0.70 ! [P: nat > $o,I: nat] :
% 0.30/0.70 ( finite_finite_nat
% 0.30/0.70 @ ( collect_nat
% 0.30/0.70 @ ^ [K_1: nat] : ( (&) @ ( P @ K_1 ) @ ( ord_less_nat @ K_1 @ I ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_655_less__add__Suc1,axiom,
% 0.30/0.70 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_656_less__add__Suc2,axiom,
% 0.30/0.70 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_657_less__iff__Suc__add,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_nat @ M @ N )
% 0.30/0.70 <=> ? [K_1: nat] :
% 0.30/0.70 ( N
% 0.30/0.70 = ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_658_less__eq__Suc__le,axiom,
% 0.30/0.70 ! [N: nat,M: nat] :
% 0.30/0.70 ( ( ord_less_nat @ N @ M )
% 0.30/0.70 <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_659_less__Suc__eq__le,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.30/0.70 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_660_Suc__le__eq,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/0.70 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_661_le__imp__less__Suc,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.70 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_662_Suc__leI,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_nat @ M @ N )
% 0.30/0.70 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_663_le__less__Suc__eq,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.70 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.30/0.70 <=> ( N = M ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_664_Suc__le__lessD,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/0.70 => ( ord_less_nat @ M @ N ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_665_diff__less__Suc,axiom,
% 0.30/0.70 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_666_add__diff__inverse,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ~ ( ord_less_nat @ M @ N )
% 0.30/0.70 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.30/0.70 = M ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_667_less__diff__conv,axiom,
% 0.30/0.70 ! [I: nat,J_1: nat,K: nat] :
% 0.30/0.70 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J_1 @ K ) )
% 0.30/0.70 <=> ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J_1 ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_668_diff__less__mono,axiom,
% 0.30/0.70 ! [C: nat,A: nat,B: nat] :
% 0.30/0.70 ( ( ord_less_nat @ A @ B )
% 0.30/0.70 => ( ( ord_less_eq_nat @ C @ A )
% 0.30/0.70 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_669_less__diff__iff,axiom,
% 0.30/0.70 ! [N: nat,K: nat,M: nat] :
% 0.30/0.70 ( ( ord_less_eq_nat @ K @ M )
% 0.30/0.70 => ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.70 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.30/0.70 <=> ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_670_less__eq__Suc__le__raw,axiom,
% 0.30/0.70 ! [X_1: nat] :
% 0.30/0.70 ( ( ord_less_nat @ X_1 )
% 0.30/0.70 = ( ord_less_eq_nat @ ( suc @ X_1 ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_671_mono__nat__linear__lb,axiom,
% 0.30/0.70 ! [M: nat,K: nat,F: nat > nat] :
% 0.30/0.70 ( ! [M_1: nat,N_2: nat] :
% 0.30/0.70 ( ( ord_less_nat @ M_1 @ N_2 )
% 0.30/0.70 => ( ord_less_nat @ ( F @ M_1 ) @ ( F @ N_2 ) ) )
% 0.30/0.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_672_inc__induct,axiom,
% 0.30/0.70 ! [P: nat > $o,I: nat,J_1: nat] :
% 0.30/0.70 ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/0.70 => ( ( P @ J_1 )
% 0.30/0.70 => ( ! [I_1: nat] :
% 0.30/0.70 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.30/0.70 => ( ( P @ ( suc @ I_1 ) )
% 0.30/0.70 => ( P @ I_1 ) ) )
% 0.30/0.70 => ( P @ I ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_673_less__imp__Suc__add,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_nat @ M @ N )
% 0.30/0.70 => ? [K_1: nat] :
% 0.30/0.70 ( N
% 0.30/0.70 = ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_674_bounded__nat__set__is__finite,axiom,
% 0.30/0.70 ! [N: nat,N_1: nat > $o] :
% 0.30/0.70 ( ! [X_1: nat] :
% 0.30/0.70 ( ( member_nat @ X_1 @ N_1 )
% 0.30/0.70 => ( ord_less_nat @ X_1 @ N ) )
% 0.30/0.70 => ( finite_finite_nat @ N_1 ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_675_less__mono__imp__le__mono,axiom,
% 0.30/0.70 ! [I: nat,J_1: nat,F: nat > nat] :
% 0.30/0.70 ( ! [I_1: nat,J: nat] :
% 0.30/0.70 ( ( ord_less_nat @ I_1 @ J )
% 0.30/0.70 => ( ord_less_nat @ ( F @ I_1 ) @ ( F @ J ) ) )
% 0.30/0.70 => ( ( ord_less_eq_nat @ I @ J_1 )
% 0.30/0.70 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J_1 ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_676_Suc__lessE,axiom,
% 0.30/0.70 ! [I: nat,K: nat] :
% 0.30/0.70 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.30/0.70 => ~ ! [J: nat] :
% 0.30/0.70 ( ( ord_less_nat @ I @ J )
% 0.30/0.70 => ( K
% 0.30/0.70 != ( suc @ J ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_677_lessE,axiom,
% 0.30/0.70 ! [I: nat,K: nat] :
% 0.30/0.70 ( ( ord_less_nat @ I @ K )
% 0.30/0.70 => ( ( K
% 0.30/0.70 != ( suc @ I ) )
% 0.30/0.70 => ~ ! [J: nat] :
% 0.30/0.70 ( ( ord_less_nat @ I @ J )
% 0.30/0.70 => ( K
% 0.30/0.70 != ( suc @ J ) ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_678_less__zeroE,axiom,
% 0.30/0.70 ! [N: nat] :
% 0.30/0.70 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_679_le0,axiom,
% 0.30/0.70 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_680_zero__less__Suc,axiom,
% 0.30/0.70 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_681_add__is__1,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ( plus_plus_nat @ M @ N )
% 0.30/0.70 = ( suc @ zero_zero_nat ) )
% 0.30/0.70 <=> ( ( ( M
% 0.30/0.70 = ( suc @ zero_zero_nat ) )
% 0.30/0.70 & ( N = zero_zero_nat ) )
% 0.30/0.70 | ( ( M = zero_zero_nat )
% 0.30/0.70 & ( N
% 0.30/0.70 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_682_one__is__add,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ( suc @ zero_zero_nat )
% 0.30/0.70 = ( plus_plus_nat @ M @ N ) )
% 0.30/0.70 <=> ( ( ( M
% 0.30/0.70 = ( suc @ zero_zero_nat ) )
% 0.30/0.70 & ( N = zero_zero_nat ) )
% 0.30/0.70 | ( ( M = zero_zero_nat )
% 0.30/0.70 & ( N
% 0.30/0.70 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_683_diff__add__0,axiom,
% 0.30/0.70 ! [N: nat,M: nat] :
% 0.30/0.70 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.30/0.70 = zero_zero_nat ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_684_diff__is__0__eq_H,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.70 => ( ( minus_minus_nat @ M @ N )
% 0.30/0.70 = zero_zero_nat ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_685_diff__is__0__eq,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ( minus_minus_nat @ M @ N )
% 0.30/0.70 = zero_zero_nat )
% 0.30/0.70 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_686_One__nat__def,axiom,
% 0.30/0.70 ( one_one_nat
% 0.30/0.70 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.70
% 0.30/0.70 thf(fact_687_diffs0__imp__equal,axiom,
% 0.30/0.70 ! [M: nat,N: nat] :
% 0.30/0.70 ( ( ( minus_minus_nat @ M @ N )
% 0.30/0.70 = zero_zero_nat )
% 0.51/0.83 => ( ( ( minus_minus_nat @ N @ M )
% 0.51/0.83 = zero_zero_nat )
% 0.51/0.83 => ( M = N ) ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_688_diff__self__eq__0,axiom,
% 0.51/0.83 ! [M: nat] :
% 0.51/0.83 ( ( minus_minus_nat @ M @ M )
% 0.51/0.83 = zero_zero_nat ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_689_minus__nat_Odiff__0,axiom,
% 0.51/0.83 ! [M: nat] :
% 0.51/0.83 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.51/0.83 = M ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_690_diff__0__eq__0,axiom,
% 0.51/0.83 ! [N: nat] :
% 0.51/0.83 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.51/0.83 = zero_zero_nat ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_691_Suc__neq__Zero,axiom,
% 0.51/0.83 ! [M: nat] :
% 0.51/0.83 ( ( suc @ M )
% 0.51/0.83 != zero_zero_nat ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_692_Zero__neq__Suc,axiom,
% 0.51/0.83 ! [M: nat] :
% 0.51/0.83 ( zero_zero_nat
% 0.51/0.83 != ( suc @ M ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_693_nat_Osimps_I3_J,axiom,
% 0.51/0.83 ! [Nat_1: nat] :
% 0.51/0.83 ( ( suc @ Nat_1 )
% 0.51/0.83 != zero_zero_nat ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_694_Suc__not__Zero,axiom,
% 0.51/0.83 ! [M: nat] :
% 0.51/0.83 ( ( suc @ M )
% 0.51/0.83 != zero_zero_nat ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_695_nat_Osimps_I2_J,axiom,
% 0.51/0.83 ! [Nat: nat] :
% 0.51/0.83 ( zero_zero_nat
% 0.51/0.83 != ( suc @ Nat ) ) ).
% 0.51/0.83
% 0.51/0.83 thf(fact_696_Zero__not__Suc,axiom,
% 0.51/0.83 ! [M: nat] :
% 0.51/0.84 ( zero_zero_nat
% 0.51/0.84 != ( suc @ M ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(fact_697_bot__nat__def,axiom,
% 0.51/0.84 bot_bot_nat = zero_zero_nat ).
% 0.51/0.84
% 0.51/0.84 thf(fact_698_le__0__eq,axiom,
% 0.51/0.84 ! [N: nat] :
% 0.51/0.84 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.51/0.84 <=> ( N = zero_zero_nat ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(fact_699_less__eq__nat_Osimps_I1_J,axiom,
% 0.51/0.84 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.51/0.84
% 0.51/0.84 %----Helper facts (12)
% 0.51/0.84 thf(help_fequal_1_1_fequal_000t__a_T,axiom,
% 0.51/0.84 ! [X: x_a,Y: x_a] :
% 0.51/0.84 ( ~ ( fequal_a @ X @ Y )
% 0.51/0.84 | ( X = Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_2_1_fequal_000t__a_T,axiom,
% 0.51/0.84 ! [X: x_a,Y: x_a] :
% 0.51/0.84 ( ( X != Y )
% 0.51/0.84 | ( fequal_a @ X @ Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.51/0.84 ! [X: nat,Y: nat] :
% 0.51/0.84 ( ~ ( fequal_nat @ X @ Y )
% 0.51/0.84 | ( X = Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.51/0.84 ! [X: nat,Y: nat] :
% 0.51/0.84 ( ( X != Y )
% 0.51/0.84 | ( fequal_nat @ X @ Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,
% 0.51/0.84 ! [X: pname,Y: pname] :
% 0.51/0.84 ( ~ ( fequal_pname @ X @ Y )
% 0.51/0.84 | ( X = Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,
% 0.51/0.84 ! [X: pname,Y: pname] :
% 0.51/0.84 ( ( X != Y )
% 0.51/0.84 | ( fequal_pname @ X @ Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_1_1_fequal_000_062_It__a_M_Eo_J_T,axiom,
% 0.51/0.84 ! [X: x_a > $o,Y: x_a > $o] :
% 0.51/0.84 ( ~ ( fequal_a_o @ X @ Y )
% 0.51/0.84 | ( X = Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_2_1_fequal_000_062_It__a_M_Eo_J_T,axiom,
% 0.51/0.84 ! [X: x_a > $o,Y: x_a > $o] :
% 0.51/0.84 ( ( X != Y )
% 0.51/0.84 | ( fequal_a_o @ X @ Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_1_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T,axiom,
% 0.51/0.84 ! [X: nat > $o,Y: nat > $o] :
% 0.51/0.84 ( ~ ( fequal_nat_o @ X @ Y )
% 0.51/0.84 | ( X = Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_2_1_fequal_000_062_Itc__Nat__Onat_M_Eo_J_T,axiom,
% 0.51/0.84 ! [X: nat > $o,Y: nat > $o] :
% 0.51/0.84 ( ( X != Y )
% 0.51/0.84 | ( fequal_nat_o @ X @ Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.51/0.84 ! [X: pname > $o,Y: pname > $o] :
% 0.51/0.84 ( ~ ( fequal_pname_o @ X @ Y )
% 0.51/0.84 | ( X = Y ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,
% 0.51/0.84 ! [X: pname > $o,Y: pname > $o] :
% 0.51/0.84 ( ( X != Y )
% 0.51/0.84 | ( fequal_pname_o @ X @ Y ) ) ).
% 0.51/0.84
% 0.51/0.84 %----Conjectures (7)
% 0.51/0.84 thf(conj_0,hypothesis,
% 0.51/0.84 finite_finite_pname @ u ).
% 0.51/0.84
% 0.51/0.84 thf(conj_1,hypothesis,
% 0.51/0.84 ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ).
% 0.51/0.84
% 0.51/0.84 thf(conj_2,hypothesis,
% 0.51/0.84 ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(conj_3,hypothesis,
% 0.51/0.84 ( ( finite_card_a @ g )
% 0.51/0.84 = ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ) ).
% 0.51/0.84
% 0.51/0.84 thf(conj_4,hypothesis,
% 0.51/0.84 member_pname @ pn @ u ).
% 0.51/0.84
% 0.51/0.84 thf(conj_5,hypothesis,
% 0.51/0.84 ~ ( member_a @ ( mgt_call @ pn ) @ g ) ).
% 0.51/0.84
% 0.51/0.84 thf(conj_6,conjecture,
% 0.51/0.84 ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ).
% 0.51/0.84
% 0.51/0.84 %------------------------------------------------------------------------------
% 0.51/0.84 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.6nYbxvKDqQ/cvc5---1.0.5_11101.p...
% 0.51/0.84 (declare-sort $$unsorted 0)
% 0.51/0.84 (declare-sort tptp.x_a 0)
% 0.51/0.84 (declare-sort tptp.com 0)
% 0.51/0.84 (declare-sort tptp.pname 0)
% 0.51/0.84 (declare-sort tptp.nat 0)
% 0.51/0.84 (declare-sort tptp.option_com 0)
% 0.51/0.84 (declare-fun tptp.body (tptp.pname) tptp.option_com)
% 0.51/0.84 (declare-fun tptp.finite_card_a_o ((-> (-> tptp.x_a Bool) Bool)) tptp.nat)
% 0.51/0.84 (declare-fun tptp.finite_card_pname_o ((-> (-> tptp.pname Bool) Bool)) tptp.nat)
% 0.51/0.84 (declare-fun tptp.finite_card_nat_o ((-> (-> tptp.nat Bool) Bool)) tptp.nat)
% 0.51/0.84 (declare-fun tptp.finite_card_a ((-> tptp.x_a Bool)) tptp.nat)
% 0.51/0.84 (declare-fun tptp.finite_card_pname ((-> tptp.pname Bool)) tptp.nat)
% 0.51/0.84 (declare-fun tptp.finite_card_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.51/0.84 (declare-fun tptp.finite_finite_a_o_o ((-> (-> (-> tptp.x_a Bool) Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.finite1066544169me_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.finite1676163439at_o_o ((-> (-> (-> tptp.nat Bool) Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.finite_finite_a_o ((-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.finite297249702name_o ((-> (-> tptp.pname Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.finite_finite_nat_o ((-> (-> tptp.nat Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.finite_finite_a ((-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.finite_finite_pname ((-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.finite_finite_nat ((-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.51/0.84 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.51/0.84 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.51/0.84 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.51/0.84 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.51/0.84 (declare-fun tptp.nat_case_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.the_com (tptp.option_com) tptp.com)
% 0.51/0.84 (declare-fun tptp.bot_bot_a_o_o ((-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.bot_bot_pname_o_o ((-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.bot_bot_nat_o_o ((-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.bot_bot_a_o (tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.bot_bot_pname_o (tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.bot_bot_o () Bool)
% 0.51/0.84 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 0.51/0.84 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.ord_less_eq_a_o_o ((-> (-> tptp.x_a Bool) Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.ord_le1205211808me_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.ord_less_eq_nat_o_o ((-> (-> tptp.nat Bool) Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.ord_less_eq_a_o ((-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.ord_less_eq_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 0.51/0.84 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.collect_a_o_o ((-> (-> (-> tptp.x_a Bool) Bool) Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.collect_pname_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.collect_nat_o_o ((-> (-> (-> tptp.nat Bool) Bool) Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.collect_a_o ((-> (-> tptp.x_a Bool) Bool) (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.collect_pname_o ((-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.collect_nat_o ((-> (-> tptp.nat Bool) Bool) (-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.collect_a ((-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.collect_pname ((-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.collect_nat ((-> tptp.nat Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_o_a ((-> (-> tptp.x_a Bool) tptp.x_a) (-> (-> tptp.x_a Bool) Bool) tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_o_pname ((-> (-> tptp.x_a Bool) tptp.pname) (-> (-> tptp.x_a Bool) Bool) tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_o_nat ((-> (-> tptp.x_a Bool) tptp.nat) (-> (-> tptp.x_a Bool) Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_o_a ((-> (-> tptp.pname Bool) tptp.x_a) (-> (-> tptp.pname Bool) Bool) tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_o_pname ((-> (-> tptp.pname Bool) tptp.pname) (-> (-> tptp.pname Bool) Bool) tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_o_nat ((-> (-> tptp.pname Bool) tptp.nat) (-> (-> tptp.pname Bool) Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_o_a ((-> (-> tptp.nat Bool) tptp.x_a) (-> (-> tptp.nat Bool) Bool) tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_o_pname ((-> (-> tptp.nat Bool) tptp.pname) (-> (-> tptp.nat Bool) Bool) tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_o_nat ((-> (-> tptp.nat Bool) tptp.nat) (-> (-> tptp.nat Bool) Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_a_o ((-> tptp.x_a tptp.x_a Bool) (-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_pname_o ((-> tptp.x_a tptp.pname Bool) (-> tptp.x_a Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_nat_o ((-> tptp.x_a tptp.nat Bool) (-> tptp.x_a Bool) (-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_a ((-> tptp.x_a tptp.x_a) (-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_pname ((-> tptp.x_a tptp.pname) (-> tptp.x_a Bool) tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.image_a_nat ((-> tptp.x_a tptp.nat) (-> tptp.x_a Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_a_o ((-> tptp.pname tptp.x_a Bool) (-> tptp.pname Bool) (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_pname_o ((-> tptp.pname tptp.pname Bool) (-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_nat_o ((-> tptp.pname tptp.nat Bool) (-> tptp.pname Bool) (-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_a ((-> tptp.pname tptp.x_a) (-> tptp.pname Bool) tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_pname ((-> tptp.pname tptp.pname) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.image_pname_nat ((-> tptp.pname tptp.nat) (-> tptp.pname Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_a_o ((-> tptp.nat tptp.x_a Bool) (-> tptp.nat Bool) (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_pname_o ((-> tptp.nat tptp.pname Bool) (-> tptp.nat Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_a ((-> tptp.nat tptp.x_a) (-> tptp.nat Bool) tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_pname ((-> tptp.nat tptp.pname) (-> tptp.nat Bool) tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.insert_a_o ((-> tptp.x_a Bool) (-> (-> tptp.x_a Bool) Bool) (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.insert_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.insert_nat_o ((-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool) (-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.insert_a (tptp.x_a (-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.insert_pname (tptp.pname (-> tptp.pname Bool) tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.insert_nat (tptp.nat (-> tptp.nat Bool) tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.fequal_a_o ((-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.fequal_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.fequal_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.fequal_a (tptp.x_a tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.fequal_pname (tptp.pname tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.fequal_nat (tptp.nat tptp.nat) Bool)
% 0.51/0.84 (declare-fun tptp.member_a_o ((-> tptp.x_a Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.member_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.member_nat_o ((-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.member_a (tptp.x_a (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.member_pname (tptp.pname (-> tptp.pname Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.member_nat (tptp.nat (-> tptp.nat Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.g (tptp.x_a) Bool)
% 0.51/0.84 (declare-fun tptp.p ((-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.51/0.84 (declare-fun tptp.u (tptp.pname) Bool)
% 0.51/0.84 (declare-fun tptp.mgt (tptp.com) tptp.x_a)
% 0.51/0.84 (declare-fun tptp.mgt_call (tptp.pname) tptp.x_a)
% 0.51/0.84 (declare-fun tptp.na () tptp.nat)
% 0.51/0.84 (declare-fun tptp.pn () tptp.pname)
% 0.51/0.84 (declare-fun tptp.wt (tptp.com) Bool)
% 0.51/0.84 (assert (forall ((Ts (-> tptp.x_a Bool)) (G (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Ts) G) (@ (@ tptp.p G) Ts))))
% 0.51/0.84 (assert (forall ((A_92 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_92) (@ tptp.finite1676163439at_o_o (@ tptp.collect_nat_o_o (lambda ((B_47 (-> (-> tptp.nat Bool) Bool))) (@ (@ tptp.ord_less_eq_nat_o_o B_47) A_92)))))))
% 0.51/0.84 (assert (forall ((A_92 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_92) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((B_47 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o B_47) A_92)))))))
% 0.51/0.84 (assert (forall ((A_92 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_92) (@ tptp.finite_finite_a_o_o (@ tptp.collect_a_o_o (lambda ((B_47 (-> (-> tptp.x_a Bool) Bool))) (@ (@ tptp.ord_less_eq_a_o_o B_47) A_92)))))))
% 0.51/0.84 (assert (forall ((A_92 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_92) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((B_47 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o B_47) A_92)))))))
% 0.51/0.84 (assert (forall ((A_92 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_92) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((B_47 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o B_47) A_92)))))))
% 0.51/0.84 (assert (forall ((A_92 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_92) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((B_47 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o B_47) A_92)))))))
% 0.51/0.84 (assert (forall ((H (-> tptp.pname tptp.nat Bool)) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_pname_nat_o H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.pname tptp.pname Bool)) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.pname tptp.x_a Bool)) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (@ tptp.finite_finite_a_o (@ (@ tptp.image_pname_a_o H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.nat tptp.x_a)) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (@ tptp.finite_finite_a (@ (@ tptp.image_nat_a H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.nat tptp.nat Bool)) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.nat tptp.pname Bool)) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.nat tptp.x_a Bool)) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.x_a tptp.pname)) (F_25 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_25) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_pname H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> (-> tptp.nat Bool) tptp.pname)) (F_25 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_25) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_pname H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.pname)) (F_25 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_25) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> (-> tptp.x_a Bool) tptp.pname)) (F_25 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_25) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_pname H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.x_a tptp.nat)) (F_25 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_25) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_nat H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> (-> tptp.nat Bool) tptp.nat)) (F_25 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_25) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_nat H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.nat)) (F_25 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_25) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_nat H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> (-> tptp.x_a Bool) tptp.nat)) (F_25 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_25) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_nat H) F_25)))))
% 0.51/0.84 (assert (forall ((H (-> tptp.pname tptp.x_a)) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a H) F_25)))))
% 0.51/0.84 (assert (forall ((A_91 (-> tptp.nat Bool)) (A_90 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_90) (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_91) A_90)))))
% 0.51/0.84 (assert (forall ((A_91 (-> tptp.pname Bool)) (A_90 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_90) (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_91) A_90)))))
% 0.51/0.84 (assert (forall ((A_91 (-> tptp.x_a Bool)) (A_90 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_90) (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_91) A_90)))))
% 0.51/0.84 (assert (forall ((A_91 tptp.pname) (A_90 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_90) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_91) A_90)))))
% 0.51/0.84 (assert (forall ((A_91 tptp.nat) (A_90 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_90) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_91) A_90)))))
% 0.51/0.84 (assert (forall ((A_91 tptp.x_a) (A_90 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_90) (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_91) A_90)))))
% 0.51/0.84 (assert (forall ((F_24 (-> tptp.pname tptp.pname)) (A_89 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_pname_pname F_24) A_89))) (@ tptp.finite_card_pname A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> tptp.x_a tptp.x_a)) (A_89 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_a F_24) A_89))) (@ tptp.finite_card_a A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> (-> tptp.nat Bool) tptp.x_a)) (A_89 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_o_a F_24) A_89))) (@ tptp.finite_card_nat_o A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> (-> tptp.pname Bool) tptp.x_a)) (A_89 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_o_a F_24) A_89))) (@ tptp.finite_card_pname_o A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_89 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_o_a F_24) A_89))) (@ tptp.finite_card_a_o A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> tptp.pname tptp.nat)) (A_89 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_nat F_24) A_89))) (@ tptp.finite_card_pname A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> tptp.x_a tptp.nat)) (A_89 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_nat F_24) A_89))) (@ tptp.finite_card_a A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> (-> tptp.nat Bool) tptp.nat)) (A_89 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_nat_o_nat F_24) A_89))) (@ tptp.finite_card_nat_o A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> (-> tptp.pname Bool) tptp.nat)) (A_89 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_o_nat F_24) A_89))) (@ tptp.finite_card_pname_o A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> (-> tptp.x_a Bool) tptp.nat)) (A_89 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_o_nat F_24) A_89))) (@ tptp.finite_card_a_o A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> tptp.x_a tptp.pname)) (A_89 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_a_pname F_24) A_89))) (@ tptp.finite_card_a A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> tptp.nat tptp.pname)) (A_89 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_nat_pname F_24) A_89))) (@ tptp.finite_card_nat A_89)))))
% 0.51/0.84 (assert (forall ((F_24 (-> tptp.pname tptp.x_a)) (A_89 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_a F_24) A_89))) (@ tptp.finite_card_pname A_89)))))
% 0.51/0.84 (assert (forall ((A_88 (-> (-> tptp.nat Bool) Bool)) (B_46 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_46) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_88)) (@ tptp.finite_card_nat_o B_46))))))
% 0.51/0.84 (assert (forall ((A_88 (-> (-> tptp.pname Bool) Bool)) (B_46 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_46) (=> (@ (@ tptp.ord_le1205211808me_o_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_88)) (@ tptp.finite_card_pname_o B_46))))))
% 0.51/0.84 (assert (forall ((A_88 (-> (-> tptp.x_a Bool) Bool)) (B_46 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_46) (=> (@ (@ tptp.ord_less_eq_a_o_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_88)) (@ tptp.finite_card_a_o B_46))))))
% 0.51/0.84 (assert (forall ((A_88 (-> tptp.pname Bool)) (B_46 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_46) (=> (@ (@ tptp.ord_less_eq_pname_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_88)) (@ tptp.finite_card_pname B_46))))))
% 0.51/0.84 (assert (forall ((A_88 (-> tptp.x_a Bool)) (B_46 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_46) (=> (@ (@ tptp.ord_less_eq_a_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_88)) (@ tptp.finite_card_a B_46))))))
% 0.51/0.84 (assert (forall ((A_88 (-> tptp.nat Bool)) (B_46 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_46) (=> (@ (@ tptp.ord_less_eq_nat_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_88)) (@ tptp.finite_card_nat B_46))))))
% 0.51/0.84 (assert (forall ((A_87 (-> (-> tptp.nat Bool) Bool)) (B_45 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_45) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o B_45)) (@ tptp.finite_card_nat_o A_87)) (= A_87 B_45))))))
% 0.51/0.84 (assert (forall ((A_87 (-> (-> tptp.pname Bool) Bool)) (B_45 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_45) (=> (@ (@ tptp.ord_le1205211808me_o_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o B_45)) (@ tptp.finite_card_pname_o A_87)) (= A_87 B_45))))))
% 0.51/0.84 (assert (forall ((A_87 (-> (-> tptp.x_a Bool) Bool)) (B_45 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_45) (=> (@ (@ tptp.ord_less_eq_a_o_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o B_45)) (@ tptp.finite_card_a_o A_87)) (= A_87 B_45))))))
% 0.51/0.84 (assert (forall ((A_87 (-> tptp.pname Bool)) (B_45 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_45) (=> (@ (@ tptp.ord_less_eq_pname_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname B_45)) (@ tptp.finite_card_pname A_87)) (= A_87 B_45))))))
% 0.51/0.84 (assert (forall ((A_87 (-> tptp.x_a Bool)) (B_45 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_45) (=> (@ (@ tptp.ord_less_eq_a_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a B_45)) (@ tptp.finite_card_a A_87)) (= A_87 B_45))))))
% 0.51/0.84 (assert (forall ((A_87 (-> tptp.nat Bool)) (B_45 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_45) (=> (@ (@ tptp.ord_less_eq_nat_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B_45)) (@ tptp.finite_card_nat A_87)) (= A_87 B_45))))))
% 0.51/0.84 (assert (forall ((X_33 (-> tptp.nat Bool)) (A_86 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_86)) (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_33) A_86))))))
% 0.51/0.84 (assert (forall ((X_33 (-> tptp.pname Bool)) (A_86 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_86)) (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_33) A_86))))))
% 0.51/0.84 (assert (forall ((X_33 (-> tptp.x_a Bool)) (A_86 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_86)) (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_33) A_86))))))
% 0.51/0.84 (assert (forall ((X_33 tptp.pname) (A_86 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_86)) (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_33) A_86))))))
% 0.51/0.84 (assert (forall ((X_33 tptp.nat) (A_86 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_86)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_33) A_86))))))
% 0.51/0.84 (assert (forall ((X_33 tptp.x_a) (A_86 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_86)) (@ tptp.finite_card_a (@ (@ tptp.insert_a X_33) A_86))))))
% 0.51/0.84 (assert (forall ((X_32 (-> tptp.nat Bool)) (A_85 (-> (-> tptp.nat Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_nat_o A_85))) (let ((_let_2 (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_nat_o X_32) A_85))) (=> (@ tptp.finite_finite_nat_o A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.51/0.84 (assert (forall ((X_32 (-> tptp.pname Bool)) (A_85 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_pname_o A_85))) (let ((_let_2 (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_pname_o X_32) A_85))) (=> (@ tptp.finite297249702name_o A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.51/0.84 (assert (forall ((X_32 (-> tptp.x_a Bool)) (A_85 (-> (-> tptp.x_a Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_a_o A_85))) (let ((_let_2 (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_a_o X_32) A_85))) (=> (@ tptp.finite_finite_a_o A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.51/0.84 (assert (forall ((X_32 tptp.nat) (A_85 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_card_nat A_85))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_nat X_32) A_85))) (=> (@ tptp.finite_finite_nat A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.51/0.84 (assert (forall ((X_32 tptp.pname) (A_85 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.finite_card_pname A_85))) (let ((_let_2 (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_pname X_32) A_85))) (=> (@ tptp.finite_finite_pname A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.51/0.84 (assert (forall ((X_32 tptp.x_a) (A_85 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.finite_card_a A_85))) (let ((_let_2 (@ tptp.finite_card_a (@ (@ tptp.insert_a X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_a X_32) A_85))) (=> (@ tptp.finite_finite_a A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.51/0.84 (assert (forall ((X_31 (-> tptp.nat Bool)) (A_84 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_84) (=> (not (@ (@ tptp.member_nat_o X_31) A_84)) (= (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_nat_o A_84)))))))
% 0.51/0.84 (assert (forall ((X_31 (-> tptp.pname Bool)) (A_84 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_84) (=> (not (@ (@ tptp.member_pname_o X_31) A_84)) (= (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_pname_o A_84)))))))
% 0.51/0.84 (assert (forall ((X_31 (-> tptp.x_a Bool)) (A_84 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_84) (=> (not (@ (@ tptp.member_a_o X_31) A_84)) (= (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_a_o A_84)))))))
% 0.51/0.84 (assert (forall ((X_31 tptp.nat) (A_84 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_84) (=> (not (@ (@ tptp.member_nat X_31) A_84)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_nat A_84)))))))
% 0.51/0.84 (assert (forall ((X_31 tptp.pname) (A_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_84) (=> (not (@ (@ tptp.member_pname X_31) A_84)) (= (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_pname A_84)))))))
% 0.51/0.84 (assert (forall ((X_31 tptp.x_a) (A_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_84) (=> (not (@ (@ tptp.member_a X_31) A_84)) (= (@ tptp.finite_card_a (@ (@ tptp.insert_a X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_a A_84)))))))
% 0.51/0.84 (assert (forall ((Q_1 (-> tptp.x_a Bool)) (P_10 (-> tptp.x_a Bool))) (=> (or (@ tptp.finite_finite_a (@ tptp.collect_a P_10)) (@ tptp.finite_finite_a (@ tptp.collect_a Q_1))) (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (@ P_10 X_1) (@ Q_1 X_1))))))))
% 0.51/0.84 (assert (forall ((Q_1 (-> (-> tptp.nat Bool) Bool)) (P_10 (-> (-> tptp.nat Bool) Bool))) (=> (or (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_10)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q_1))) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (@ P_10 X_1) (@ Q_1 X_1))))))))
% 0.51/0.84 (assert (forall ((Q_1 (-> (-> tptp.pname Bool) Bool)) (P_10 (-> (-> tptp.pname Bool) Bool))) (=> (or (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_10)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_1))) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (@ P_10 X_1) (@ Q_1 X_1))))))))
% 0.51/0.84 (assert (forall ((Q_1 (-> (-> tptp.x_a Bool) Bool)) (P_10 (-> (-> tptp.x_a Bool) Bool))) (=> (or (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_10)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q_1))) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (@ P_10 X_1) (@ Q_1 X_1))))))))
% 0.51/0.84 (assert (forall ((Q_1 (-> tptp.pname Bool)) (P_10 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_10)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_1))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (@ P_10 X_1) (@ Q_1 X_1))))))))
% 0.51/0.84 (assert (forall ((Q_1 (-> tptp.nat Bool)) (P_10 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P_10)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_1))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (@ P_10 X_1) (@ Q_1 X_1))))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 0.51/0.84 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_2) K))))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I_1) N)))) (@ tptp.suc N))))
% 0.51/0.84 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 0.51/0.84 (assert (forall ((Nat_2 tptp.nat) (Nat tptp.nat)) (= (= (@ tptp.suc Nat_2) (@ tptp.suc Nat)) (= Nat_2 Nat))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (not (= (@ tptp.suc N) N))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_nat J_1) K) (@ _let_1 K))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.51/0.84 (assert (forall ((I tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J_1)))))
% 0.51/0.84 (assert (forall ((P_9 (-> tptp.x_a Bool)) (Q (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_a (@ tptp.collect_a P_9)) (@ tptp.finite_finite_a (@ tptp.collect_a Q))))))
% 0.51/0.84 (assert (forall ((P_9 (-> (-> tptp.nat Bool) Bool)) (Q (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_9)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q))))))
% 0.51/0.84 (assert (forall ((P_9 (-> (-> tptp.pname Bool) Bool)) (Q (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_9)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q))))))
% 0.51/0.84 (assert (forall ((P_9 (-> (-> tptp.x_a Bool) Bool)) (Q (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_9)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q))))))
% 0.51/0.84 (assert (forall ((P_9 (-> tptp.pname Bool)) (Q (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_9)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q))))))
% 0.51/0.84 (assert (forall ((P_9 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P_9)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 0.51/0.84 (assert (forall ((A_83 (-> tptp.nat Bool)) (A_82 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_83) A_82)) (@ tptp.finite_finite_nat_o A_82))))
% 0.51/0.84 (assert (forall ((A_83 (-> tptp.pname Bool)) (A_82 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_83) A_82)) (@ tptp.finite297249702name_o A_82))))
% 0.51/0.84 (assert (forall ((A_83 (-> tptp.x_a Bool)) (A_82 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_83) A_82)) (@ tptp.finite_finite_a_o A_82))))
% 0.51/0.84 (assert (forall ((A_83 tptp.pname) (A_82 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_83) A_82)) (@ tptp.finite_finite_pname A_82))))
% 0.51/0.84 (assert (forall ((A_83 tptp.nat) (A_82 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_83) A_82)) (@ tptp.finite_finite_nat A_82))))
% 0.51/0.84 (assert (forall ((A_83 tptp.x_a) (A_82 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_83) A_82)) (@ tptp.finite_finite_a A_82))))
% 0.51/0.84 (assert (forall ((A_81 (-> (-> tptp.nat Bool) Bool)) (B_44 (-> (-> tptp.nat Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_81) B_44) (=> (@ tptp.finite_finite_nat_o B_44) (@ tptp.finite_finite_nat_o A_81)))))
% 0.51/0.84 (assert (forall ((A_81 (-> (-> tptp.pname Bool) Bool)) (B_44 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_81) B_44) (=> (@ tptp.finite297249702name_o B_44) (@ tptp.finite297249702name_o A_81)))))
% 0.51/0.84 (assert (forall ((A_81 (-> (-> tptp.x_a Bool) Bool)) (B_44 (-> (-> tptp.x_a Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_a_o_o A_81) B_44) (=> (@ tptp.finite_finite_a_o B_44) (@ tptp.finite_finite_a_o A_81)))))
% 0.51/0.84 (assert (forall ((A_81 (-> tptp.x_a Bool)) (B_44 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_81) B_44) (=> (@ tptp.finite_finite_a B_44) (@ tptp.finite_finite_a A_81)))))
% 0.51/0.84 (assert (forall ((A_81 (-> tptp.pname Bool)) (B_44 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_81) B_44) (=> (@ tptp.finite_finite_pname B_44) (@ tptp.finite_finite_pname A_81)))))
% 0.51/0.84 (assert (forall ((A_81 (-> tptp.nat Bool)) (B_44 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_81) B_44) (=> (@ tptp.finite_finite_nat B_44) (@ tptp.finite_finite_nat A_81)))))
% 0.51/0.84 (assert (forall ((A_80 (-> (-> tptp.nat Bool) Bool)) (B_43 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_43) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_80) B_43) (@ tptp.finite_finite_nat_o A_80)))))
% 0.51/0.84 (assert (forall ((A_80 (-> (-> tptp.pname Bool) Bool)) (B_43 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_43) (=> (@ (@ tptp.ord_le1205211808me_o_o A_80) B_43) (@ tptp.finite297249702name_o A_80)))))
% 0.51/0.84 (assert (forall ((A_80 (-> (-> tptp.x_a Bool) Bool)) (B_43 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_43) (=> (@ (@ tptp.ord_less_eq_a_o_o A_80) B_43) (@ tptp.finite_finite_a_o A_80)))))
% 0.51/0.84 (assert (forall ((A_80 (-> tptp.x_a Bool)) (B_43 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_43) (=> (@ (@ tptp.ord_less_eq_a_o A_80) B_43) (@ tptp.finite_finite_a A_80)))))
% 0.51/0.84 (assert (forall ((A_80 (-> tptp.pname Bool)) (B_43 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_43) (=> (@ (@ tptp.ord_less_eq_pname_o A_80) B_43) (@ tptp.finite_finite_pname A_80)))))
% 0.51/0.84 (assert (forall ((A_80 (-> tptp.nat Bool)) (B_43 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_43) (=> (@ (@ tptp.ord_less_eq_nat_o A_80) B_43) (@ tptp.finite_finite_nat A_80)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 0.51/0.84 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 0.51/0.84 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> tptp.x_a tptp.x_a)) (A_79 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_a_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> (-> tptp.nat Bool) tptp.x_a)) (A_79 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_nat_o_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> (-> tptp.pname Bool) tptp.x_a)) (A_79 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_pname_o_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_79 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_a_o_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> (-> tptp.nat Bool) Bool)) (F_23 (-> tptp.pname tptp.nat Bool)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_42) (@ (@ tptp.image_pname_nat_o F_23) A_79)) (@ tptp.finite_finite_nat_o B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> (-> tptp.pname Bool) Bool)) (F_23 (-> tptp.pname tptp.pname Bool)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_le1205211808me_o_o B_42) (@ (@ tptp.image_pname_pname_o F_23) A_79)) (@ tptp.finite297249702name_o B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> (-> tptp.x_a Bool) Bool)) (F_23 (-> tptp.pname tptp.x_a Bool)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_a_o_o B_42) (@ (@ tptp.image_pname_a_o F_23) A_79)) (@ tptp.finite_finite_a_o B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> tptp.pname tptp.pname)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_pname_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> tptp.pname tptp.nat)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_pname_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> tptp.nat tptp.x_a)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_nat_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> (-> tptp.nat Bool) Bool)) (F_23 (-> tptp.nat tptp.nat Bool)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_42) (@ (@ tptp.image_nat_nat_o F_23) A_79)) (@ tptp.finite_finite_nat_o B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> (-> tptp.pname Bool) Bool)) (F_23 (-> tptp.nat tptp.pname Bool)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_le1205211808me_o_o B_42) (@ (@ tptp.image_nat_pname_o F_23) A_79)) (@ tptp.finite297249702name_o B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> (-> tptp.x_a Bool) Bool)) (F_23 (-> tptp.nat tptp.x_a Bool)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_a_o_o B_42) (@ (@ tptp.image_nat_a_o F_23) A_79)) (@ tptp.finite_finite_a_o B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> tptp.nat tptp.pname)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_nat_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> tptp.nat tptp.nat)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_nat_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> tptp.x_a tptp.pname)) (A_79 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_a_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> (-> tptp.nat Bool) tptp.pname)) (A_79 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_nat_o_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> (-> tptp.pname Bool) tptp.pname)) (A_79 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_pname_o_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> (-> tptp.x_a Bool) tptp.pname)) (A_79 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_a_o_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> tptp.x_a tptp.nat)) (A_79 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_a_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> (-> tptp.nat Bool) tptp.nat)) (A_79 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_nat_o_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> (-> tptp.pname Bool) tptp.nat)) (A_79 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_pname_o_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> (-> tptp.x_a Bool) tptp.nat)) (A_79 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_a_o_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))))
% 0.51/0.84 (assert (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> tptp.pname tptp.x_a)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_pname_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.nat Bool) tptp.x_a)) (A_78 (-> (-> tptp.nat Bool) Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_nat_o_a F_22) A_78)) (exists ((C_12 (-> (-> tptp.nat Bool) Bool))) (and (@ (@ tptp.ord_less_eq_nat_o_o C_12) A_78) (@ tptp.finite_finite_nat_o C_12) (= B_41 (@ (@ tptp.image_nat_o_a F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.pname Bool) tptp.x_a)) (A_78 (-> (-> tptp.pname Bool) Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_pname_o_a F_22) A_78)) (exists ((C_12 (-> (-> tptp.pname Bool) Bool))) (and (@ (@ tptp.ord_le1205211808me_o_o C_12) A_78) (@ tptp.finite297249702name_o C_12) (= B_41 (@ (@ tptp.image_pname_o_a F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_78 (-> (-> tptp.x_a Bool) Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_a_o_a F_22) A_78)) (exists ((C_12 (-> (-> tptp.x_a Bool) Bool))) (and (@ (@ tptp.ord_less_eq_a_o_o C_12) A_78) (@ tptp.finite_finite_a_o C_12) (= B_41 (@ (@ tptp.image_a_o_a F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.x_a tptp.x_a)) (A_78 (-> tptp.x_a Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_a_a F_22) A_78)) (exists ((C_12 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_12) A_78) (@ tptp.finite_finite_a C_12) (= B_41 (@ (@ tptp.image_a_a F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.x_a tptp.nat Bool)) (A_78 (-> tptp.x_a Bool)) (B_41 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_41) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_41) (@ (@ tptp.image_a_nat_o F_22) A_78)) (exists ((C_12 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_12) A_78) (@ tptp.finite_finite_a C_12) (= B_41 (@ (@ tptp.image_a_nat_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.x_a tptp.pname Bool)) (A_78 (-> tptp.x_a Bool)) (B_41 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_41) (=> (@ (@ tptp.ord_le1205211808me_o_o B_41) (@ (@ tptp.image_a_pname_o F_22) A_78)) (exists ((C_12 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_12) A_78) (@ tptp.finite_finite_a C_12) (= B_41 (@ (@ tptp.image_a_pname_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.x_a tptp.x_a Bool)) (A_78 (-> tptp.x_a Bool)) (B_41 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_41) (=> (@ (@ tptp.ord_less_eq_a_o_o B_41) (@ (@ tptp.image_a_a_o F_22) A_78)) (exists ((C_12 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_12) A_78) (@ tptp.finite_finite_a C_12) (= B_41 (@ (@ tptp.image_a_a_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.x_a tptp.pname)) (A_78 (-> tptp.x_a Bool)) (B_41 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_41) (=> (@ (@ tptp.ord_less_eq_pname_o B_41) (@ (@ tptp.image_a_pname F_22) A_78)) (exists ((C_12 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_12) A_78) (@ tptp.finite_finite_a C_12) (= B_41 (@ (@ tptp.image_a_pname F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.nat Bool) tptp.pname)) (A_78 (-> (-> tptp.nat Bool) Bool)) (B_41 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_41) (=> (@ (@ tptp.ord_less_eq_pname_o B_41) (@ (@ tptp.image_nat_o_pname F_22) A_78)) (exists ((C_12 (-> (-> tptp.nat Bool) Bool))) (and (@ (@ tptp.ord_less_eq_nat_o_o C_12) A_78) (@ tptp.finite_finite_nat_o C_12) (= B_41 (@ (@ tptp.image_nat_o_pname F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.pname Bool) tptp.pname)) (A_78 (-> (-> tptp.pname Bool) Bool)) (B_41 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_41) (=> (@ (@ tptp.ord_less_eq_pname_o B_41) (@ (@ tptp.image_pname_o_pname F_22) A_78)) (exists ((C_12 (-> (-> tptp.pname Bool) Bool))) (and (@ (@ tptp.ord_le1205211808me_o_o C_12) A_78) (@ tptp.finite297249702name_o C_12) (= B_41 (@ (@ tptp.image_pname_o_pname F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.x_a Bool) tptp.pname)) (A_78 (-> (-> tptp.x_a Bool) Bool)) (B_41 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_41) (=> (@ (@ tptp.ord_less_eq_pname_o B_41) (@ (@ tptp.image_a_o_pname F_22) A_78)) (exists ((C_12 (-> (-> tptp.x_a Bool) Bool))) (and (@ (@ tptp.ord_less_eq_a_o_o C_12) A_78) (@ tptp.finite_finite_a_o C_12) (= B_41 (@ (@ tptp.image_a_o_pname F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.x_a tptp.nat)) (A_78 (-> tptp.x_a Bool)) (B_41 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_41) (=> (@ (@ tptp.ord_less_eq_nat_o B_41) (@ (@ tptp.image_a_nat F_22) A_78)) (exists ((C_12 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_12) A_78) (@ tptp.finite_finite_a C_12) (= B_41 (@ (@ tptp.image_a_nat F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.nat Bool) tptp.nat)) (A_78 (-> (-> tptp.nat Bool) Bool)) (B_41 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_41) (=> (@ (@ tptp.ord_less_eq_nat_o B_41) (@ (@ tptp.image_nat_o_nat F_22) A_78)) (exists ((C_12 (-> (-> tptp.nat Bool) Bool))) (and (@ (@ tptp.ord_less_eq_nat_o_o C_12) A_78) (@ tptp.finite_finite_nat_o C_12) (= B_41 (@ (@ tptp.image_nat_o_nat F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.pname Bool) tptp.nat)) (A_78 (-> (-> tptp.pname Bool) Bool)) (B_41 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_41) (=> (@ (@ tptp.ord_less_eq_nat_o B_41) (@ (@ tptp.image_pname_o_nat F_22) A_78)) (exists ((C_12 (-> (-> tptp.pname Bool) Bool))) (and (@ (@ tptp.ord_le1205211808me_o_o C_12) A_78) (@ tptp.finite297249702name_o C_12) (= B_41 (@ (@ tptp.image_pname_o_nat F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> (-> tptp.x_a Bool) tptp.nat)) (A_78 (-> (-> tptp.x_a Bool) Bool)) (B_41 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_41) (=> (@ (@ tptp.ord_less_eq_nat_o B_41) (@ (@ tptp.image_a_o_nat F_22) A_78)) (exists ((C_12 (-> (-> tptp.x_a Bool) Bool))) (and (@ (@ tptp.ord_less_eq_a_o_o C_12) A_78) (@ tptp.finite_finite_a_o C_12) (= B_41 (@ (@ tptp.image_a_o_nat F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.pname tptp.nat Bool)) (A_78 (-> tptp.pname Bool)) (B_41 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_41) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_41) (@ (@ tptp.image_pname_nat_o F_22) A_78)) (exists ((C_12 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_12) A_78) (@ tptp.finite_finite_pname C_12) (= B_41 (@ (@ tptp.image_pname_nat_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.pname tptp.pname Bool)) (A_78 (-> tptp.pname Bool)) (B_41 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_41) (=> (@ (@ tptp.ord_le1205211808me_o_o B_41) (@ (@ tptp.image_pname_pname_o F_22) A_78)) (exists ((C_12 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_12) A_78) (@ tptp.finite_finite_pname C_12) (= B_41 (@ (@ tptp.image_pname_pname_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.pname tptp.x_a Bool)) (A_78 (-> tptp.pname Bool)) (B_41 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_41) (=> (@ (@ tptp.ord_less_eq_a_o_o B_41) (@ (@ tptp.image_pname_a_o F_22) A_78)) (exists ((C_12 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_12) A_78) (@ tptp.finite_finite_pname C_12) (= B_41 (@ (@ tptp.image_pname_a_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.pname tptp.pname)) (A_78 (-> tptp.pname Bool)) (B_41 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_41) (=> (@ (@ tptp.ord_less_eq_pname_o B_41) (@ (@ tptp.image_pname_pname F_22) A_78)) (exists ((C_12 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_12) A_78) (@ tptp.finite_finite_pname C_12) (= B_41 (@ (@ tptp.image_pname_pname F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.pname tptp.nat)) (A_78 (-> tptp.pname Bool)) (B_41 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_41) (=> (@ (@ tptp.ord_less_eq_nat_o B_41) (@ (@ tptp.image_pname_nat F_22) A_78)) (exists ((C_12 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_12) A_78) (@ tptp.finite_finite_pname C_12) (= B_41 (@ (@ tptp.image_pname_nat F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.nat tptp.x_a)) (A_78 (-> tptp.nat Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_nat_a F_22) A_78)) (exists ((C_12 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_12) A_78) (@ tptp.finite_finite_nat C_12) (= B_41 (@ (@ tptp.image_nat_a F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.nat tptp.nat Bool)) (A_78 (-> tptp.nat Bool)) (B_41 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_41) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_41) (@ (@ tptp.image_nat_nat_o F_22) A_78)) (exists ((C_12 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_12) A_78) (@ tptp.finite_finite_nat C_12) (= B_41 (@ (@ tptp.image_nat_nat_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.nat tptp.pname Bool)) (A_78 (-> tptp.nat Bool)) (B_41 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_41) (=> (@ (@ tptp.ord_le1205211808me_o_o B_41) (@ (@ tptp.image_nat_pname_o F_22) A_78)) (exists ((C_12 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_12) A_78) (@ tptp.finite_finite_nat C_12) (= B_41 (@ (@ tptp.image_nat_pname_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.nat tptp.x_a Bool)) (A_78 (-> tptp.nat Bool)) (B_41 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_41) (=> (@ (@ tptp.ord_less_eq_a_o_o B_41) (@ (@ tptp.image_nat_a_o F_22) A_78)) (exists ((C_12 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_12) A_78) (@ tptp.finite_finite_nat C_12) (= B_41 (@ (@ tptp.image_nat_a_o F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.nat tptp.pname)) (A_78 (-> tptp.nat Bool)) (B_41 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_41) (=> (@ (@ tptp.ord_less_eq_pname_o B_41) (@ (@ tptp.image_nat_pname F_22) A_78)) (exists ((C_12 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_12) A_78) (@ tptp.finite_finite_nat C_12) (= B_41 (@ (@ tptp.image_nat_pname F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.nat tptp.nat)) (A_78 (-> tptp.nat Bool)) (B_41 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_41) (=> (@ (@ tptp.ord_less_eq_nat_o B_41) (@ (@ tptp.image_nat_nat F_22) A_78)) (exists ((C_12 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_12) A_78) (@ tptp.finite_finite_nat C_12) (= B_41 (@ (@ tptp.image_nat_nat F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((F_22 (-> tptp.pname tptp.x_a)) (A_78 (-> tptp.pname Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_pname_a F_22) A_78)) (exists ((C_12 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_12) A_78) (@ tptp.finite_finite_pname C_12) (= B_41 (@ (@ tptp.image_pname_a F_22) C_12))))))))
% 0.51/0.84 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_21 (-> tptp.nat Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_o (@ F_21 N_2)) (@ F_21 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_o (@ F_21 N_4)) (@ F_21 N_3))))))
% 0.51/0.84 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_21 (-> tptp.nat tptp.pname Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_pname_o (@ F_21 N_2)) (@ F_21 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_pname_o (@ F_21 N_4)) (@ F_21 N_3))))))
% 0.51/0.84 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_21 (-> tptp.nat tptp.nat Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o (@ F_21 N_2)) (@ F_21 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat_o (@ F_21 N_4)) (@ F_21 N_3))))))
% 0.51/0.84 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_21 (-> tptp.nat tptp.x_a Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_a_o (@ F_21 N_2)) (@ F_21 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_a_o (@ F_21 N_4)) (@ F_21 N_3))))))
% 0.51/0.84 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_21 (-> tptp.nat tptp.nat))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F_21 N_2)) (@ F_21 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat (@ F_21 N_4)) (@ F_21 N_3))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.nat tptp.pname)) (A_77 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_77)) (=> (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_pname F_20) A_77)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_77) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_2 tptp.nat)) (and (@ (@ tptp.member_nat A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.x_a tptp.pname)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite_finite_pname (@ (@ tptp.image_a_pname F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.pname tptp.pname)) (A_77 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_pname F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> (-> tptp.nat Bool) tptp.pname)) (A_77 (-> (-> tptp.nat Bool) Bool))) (=> (not (@ tptp.finite_finite_nat_o A_77)) (=> (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_pname F_20) A_77)) (exists ((X_1 (-> tptp.nat Bool))) (and (@ (@ tptp.member_nat_o X_1) A_77) (not (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((A_2 (-> tptp.nat Bool))) (and (@ (@ tptp.member_nat_o A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> (-> tptp.pname Bool) tptp.pname)) (A_77 (-> (-> tptp.pname Bool) Bool))) (=> (not (@ tptp.finite297249702name_o A_77)) (=> (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname F_20) A_77)) (exists ((X_1 (-> tptp.pname Bool))) (and (@ (@ tptp.member_pname_o X_1) A_77) (not (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((A_2 (-> tptp.pname Bool))) (and (@ (@ tptp.member_pname_o A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> (-> tptp.x_a Bool) tptp.pname)) (A_77 (-> (-> tptp.x_a Bool) Bool))) (=> (not (@ tptp.finite_finite_a_o A_77)) (=> (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_pname F_20) A_77)) (exists ((X_1 (-> tptp.x_a Bool))) (and (@ (@ tptp.member_a_o X_1) A_77) (not (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((A_2 (-> tptp.x_a Bool))) (and (@ (@ tptp.member_a_o A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.nat tptp.nat)) (A_77 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_77)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat F_20) A_77)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_77) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_2 tptp.nat)) (and (@ (@ tptp.member_nat A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.x_a tptp.nat)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_a_nat F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.pname tptp.nat)) (A_77 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_nat F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> (-> tptp.nat Bool) tptp.nat)) (A_77 (-> (-> tptp.nat Bool) Bool))) (=> (not (@ tptp.finite_finite_nat_o A_77)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_nat F_20) A_77)) (exists ((X_1 (-> tptp.nat Bool))) (and (@ (@ tptp.member_nat_o X_1) A_77) (not (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((A_2 (-> tptp.nat Bool))) (and (@ (@ tptp.member_nat_o A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> (-> tptp.pname Bool) tptp.nat)) (A_77 (-> (-> tptp.pname Bool) Bool))) (=> (not (@ tptp.finite297249702name_o A_77)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_nat F_20) A_77)) (exists ((X_1 (-> tptp.pname Bool))) (and (@ (@ tptp.member_pname_o X_1) A_77) (not (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((A_2 (-> tptp.pname Bool))) (and (@ (@ tptp.member_pname_o A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> (-> tptp.x_a Bool) tptp.nat)) (A_77 (-> (-> tptp.x_a Bool) Bool))) (=> (not (@ tptp.finite_finite_a_o A_77)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_nat F_20) A_77)) (exists ((X_1 (-> tptp.x_a Bool))) (and (@ (@ tptp.member_a_o X_1) A_77) (not (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((A_2 (-> tptp.x_a Bool))) (and (@ (@ tptp.member_a_o A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.nat tptp.x_a)) (A_77 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_77)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_nat_a F_20) A_77)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_77) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_2 tptp.nat)) (and (@ (@ tptp.member_nat A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.nat tptp.nat Bool)) (A_77 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_77)) (=> (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o F_20) A_77)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_77) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_2 tptp.nat)) (and (@ (@ tptp.member_nat A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.nat tptp.pname Bool)) (A_77 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_77)) (=> (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o F_20) A_77)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_77) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_2 tptp.nat)) (and (@ (@ tptp.member_nat A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.nat tptp.x_a Bool)) (A_77 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_77)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o F_20) A_77)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_77) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_2 tptp.nat)) (and (@ (@ tptp.member_nat A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.pname tptp.nat Bool)) (A_77 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite_finite_nat_o (@ (@ tptp.image_pname_nat_o F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.pname tptp.pname Bool)) (A_77 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.pname tptp.x_a Bool)) (A_77 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_pname_a_o F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.x_a tptp.x_a)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_a_a F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.x_a tptp.nat Bool)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite_finite_nat_o (@ (@ tptp.image_a_nat_o F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.x_a tptp.pname Bool)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite297249702name_o (@ (@ tptp.image_a_pname_o F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.x_a tptp.x_a Bool)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_a_a_o F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((F_20 (-> tptp.pname tptp.x_a)) (A_77 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))))
% 0.51/0.84 (assert (forall ((A_76 (-> tptp.pname Bool)) (B_40 tptp.nat) (F_19 (-> tptp.pname tptp.nat)) (X_30 tptp.pname)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_pname X_30) A_76) (@ (@ tptp.member_nat B_40) (@ (@ tptp.image_pname_nat F_19) A_76))))))
% 0.51/0.84 (assert (forall ((A_76 (-> tptp.x_a Bool)) (B_40 tptp.nat) (F_19 (-> tptp.x_a tptp.nat)) (X_30 tptp.x_a)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_a X_30) A_76) (@ (@ tptp.member_nat B_40) (@ (@ tptp.image_a_nat F_19) A_76))))))
% 0.51/0.84 (assert (forall ((A_76 (-> tptp.nat Bool)) (B_40 tptp.pname) (F_19 (-> tptp.nat tptp.pname)) (X_30 tptp.nat)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_nat X_30) A_76) (@ (@ tptp.member_pname B_40) (@ (@ tptp.image_nat_pname F_19) A_76))))))
% 0.51/0.84 (assert (forall ((A_76 (-> tptp.nat Bool)) (B_40 tptp.x_a) (F_19 (-> tptp.nat tptp.x_a)) (X_30 tptp.nat)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_nat X_30) A_76) (@ (@ tptp.member_a B_40) (@ (@ tptp.image_nat_a F_19) A_76))))))
% 0.51/0.84 (assert (forall ((A_76 (-> tptp.pname Bool)) (B_40 tptp.x_a) (F_19 (-> tptp.pname tptp.x_a)) (X_30 tptp.pname)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_pname X_30) A_76) (@ (@ tptp.member_a B_40) (@ (@ tptp.image_pname_a F_19) A_76))))))
% 0.51/0.84 (assert (forall ((A_75 (-> tptp.pname Bool)) (B_39 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_75) B_39) (=> (@ (@ tptp.ord_less_eq_pname_o B_39) A_75) (= A_75 B_39)))))
% 0.51/0.84 (assert (forall ((A_75 (-> tptp.nat Bool)) (B_39 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_75) B_39) (=> (@ (@ tptp.ord_less_eq_nat_o B_39) A_75) (= A_75 B_39)))))
% 0.51/0.84 (assert (forall ((A_75 (-> tptp.x_a Bool)) (B_39 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_75) B_39) (=> (@ (@ tptp.ord_less_eq_a_o B_39) A_75) (= A_75 B_39)))))
% 0.51/0.84 (assert (forall ((C_11 tptp.nat) (A_74 (-> tptp.nat Bool)) (B_38 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_11))) (=> (@ (@ tptp.ord_less_eq_nat_o A_74) B_38) (=> (@ _let_1 A_74) (@ _let_1 B_38))))))
% 0.51/0.84 (assert (forall ((C_11 tptp.pname) (A_74 (-> tptp.pname Bool)) (B_38 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_11))) (=> (@ (@ tptp.ord_less_eq_pname_o A_74) B_38) (=> (@ _let_1 A_74) (@ _let_1 B_38))))))
% 0.51/0.84 (assert (forall ((C_11 tptp.x_a) (A_74 (-> tptp.x_a Bool)) (B_38 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_11))) (=> (@ (@ tptp.ord_less_eq_a_o A_74) B_38) (=> (@ _let_1 A_74) (@ _let_1 B_38))))))
% 0.51/0.84 (assert (forall ((B_37 tptp.nat) (A_73 tptp.nat) (B_36 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_73))) (=> (=> (not (@ _let_1 B_36)) (= A_73 B_37)) (@ _let_1 (@ (@ tptp.insert_nat B_37) B_36))))))
% 0.51/0.84 (assert (forall ((B_37 tptp.pname) (A_73 tptp.pname) (B_36 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_73))) (=> (=> (not (@ _let_1 B_36)) (= A_73 B_37)) (@ _let_1 (@ (@ tptp.insert_pname B_37) B_36))))))
% 0.51/0.84 (assert (forall ((B_37 tptp.x_a) (A_73 tptp.x_a) (B_36 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_73))) (=> (=> (not (@ _let_1 B_36)) (= A_73 B_37)) (@ _let_1 (@ (@ tptp.insert_a B_37) B_36))))))
% 0.51/0.84 (assert (forall ((A_72 tptp.nat) (B_35 tptp.nat) (A_71 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_72))) (=> (@ _let_1 (@ (@ tptp.insert_nat B_35) A_71)) (=> (not (= A_72 B_35)) (@ _let_1 A_71))))))
% 0.51/0.84 (assert (forall ((A_72 tptp.pname) (B_35 tptp.pname) (A_71 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_72))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_35) A_71)) (=> (not (= A_72 B_35)) (@ _let_1 A_71))))))
% 0.51/0.84 (assert (forall ((A_72 tptp.x_a) (B_35 tptp.x_a) (A_71 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_72))) (=> (@ _let_1 (@ (@ tptp.insert_a B_35) A_71)) (=> (not (= A_72 B_35)) (@ _let_1 A_71))))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N_2 tptp.nat)) (=> (@ P (@ tptp.suc N_2)) (@ P N_2))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M_2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M_2) (exists ((M_1 tptp.nat)) (= M_2 (@ tptp.suc M_1))))))
% 0.51/0.84 (assert (forall ((A_70 tptp.nat) (B_34 (-> tptp.nat Bool))) (@ (@ tptp.member_nat A_70) (@ (@ tptp.insert_nat A_70) B_34))))
% 0.51/0.84 (assert (forall ((A_70 tptp.pname) (B_34 (-> tptp.pname Bool))) (@ (@ tptp.member_pname A_70) (@ (@ tptp.insert_pname A_70) B_34))))
% 0.51/0.84 (assert (forall ((A_70 tptp.x_a) (B_34 (-> tptp.x_a Bool))) (@ (@ tptp.member_a A_70) (@ (@ tptp.insert_a A_70) B_34))))
% 0.51/0.84 (assert (forall ((A_69 (-> tptp.nat Bool)) (B_33 (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o A_69) B_33) (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (or (= X_1 A_69) (@ (@ tptp.member_nat_o X_1) B_33)))))))
% 0.51/0.84 (assert (forall ((A_69 (-> tptp.pname Bool)) (B_33 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_69) B_33) (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (= X_1 A_69) (@ (@ tptp.member_pname_o X_1) B_33)))))))
% 0.51/0.84 (assert (forall ((A_69 (-> tptp.x_a Bool)) (B_33 (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o A_69) B_33) (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (or (= X_1 A_69) (@ (@ tptp.member_a_o X_1) B_33)))))))
% 0.51/0.84 (assert (forall ((A_69 tptp.nat) (B_33 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_69) B_33) (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (or (= X_1 A_69) (@ (@ tptp.member_nat X_1) B_33)))))))
% 0.51/0.84 (assert (forall ((A_69 tptp.pname) (B_33 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_69) B_33) (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (= X_1 A_69) (@ (@ tptp.member_pname X_1) B_33)))))))
% 0.51/0.84 (assert (forall ((A_69 tptp.x_a) (B_33 (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a A_69) B_33) (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (or (= X_1 A_69) (@ (@ tptp.member_a X_1) B_33)))))))
% 0.51/0.84 (assert (forall ((A_68 tptp.pname) (P_8 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_68) (@ tptp.collect_pname P_8)) (@ tptp.collect_pname (lambda ((U_1 tptp.pname)) (=> (not (= U_1 A_68)) (@ P_8 U_1)))))))
% 0.51/0.84 (assert (forall ((A_68 (-> tptp.nat Bool)) (P_8 (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o A_68) (@ tptp.collect_nat_o P_8)) (@ tptp.collect_nat_o (lambda ((U_1 (-> tptp.nat Bool))) (=> (not (= U_1 A_68)) (@ P_8 U_1)))))))
% 0.51/0.84 (assert (forall ((A_68 (-> tptp.pname Bool)) (P_8 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_68) (@ tptp.collect_pname_o P_8)) (@ tptp.collect_pname_o (lambda ((U_1 (-> tptp.pname Bool))) (=> (not (= U_1 A_68)) (@ P_8 U_1)))))))
% 0.51/0.84 (assert (forall ((A_68 (-> tptp.x_a Bool)) (P_8 (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o A_68) (@ tptp.collect_a_o P_8)) (@ tptp.collect_a_o (lambda ((U_1 (-> tptp.x_a Bool))) (=> (not (= U_1 A_68)) (@ P_8 U_1)))))))
% 0.51/0.84 (assert (forall ((A_68 tptp.nat) (P_8 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_68) (@ tptp.collect_nat P_8)) (@ tptp.collect_nat (lambda ((U_1 tptp.nat)) (=> (not (= U_1 A_68)) (@ P_8 U_1)))))))
% 0.51/0.84 (assert (forall ((A_68 tptp.x_a) (P_8 (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a A_68) (@ tptp.collect_a P_8)) (@ tptp.collect_a (lambda ((U_1 tptp.x_a)) (=> (not (= U_1 A_68)) (@ P_8 U_1)))))))
% 0.51/0.84 (assert (forall ((X_29 tptp.pname) (A_67 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_29))) (let ((_let_2 (@ _let_1 A_67))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.84 (assert (forall ((X_29 tptp.nat) (A_67 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_29))) (let ((_let_2 (@ _let_1 A_67))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.84 (assert (forall ((X_29 tptp.x_a) (A_67 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_29))) (let ((_let_2 (@ _let_1 A_67))) (= (@ _let_1 _let_2) _let_2)))))
% 0.51/0.84 (assert (forall ((X_28 tptp.pname) (Y_12 tptp.pname) (A_66 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_28))) (let ((_let_2 (@ tptp.insert_pname Y_12))) (= (@ _let_1 (@ _let_2 A_66)) (@ _let_2 (@ _let_1 A_66)))))))
% 0.51/0.84 (assert (forall ((X_28 tptp.nat) (Y_12 tptp.nat) (A_66 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_28))) (let ((_let_2 (@ tptp.insert_nat Y_12))) (= (@ _let_1 (@ _let_2 A_66)) (@ _let_2 (@ _let_1 A_66)))))))
% 0.51/0.84 (assert (forall ((X_28 tptp.x_a) (Y_12 tptp.x_a) (A_66 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_28))) (let ((_let_2 (@ tptp.insert_a Y_12))) (= (@ _let_1 (@ _let_2 A_66)) (@ _let_2 (@ _let_1 A_66)))))))
% 0.51/0.84 (assert (forall ((A_65 tptp.nat) (B_32 tptp.nat) (A_64 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_65))) (= (@ _let_1 (@ (@ tptp.insert_nat B_32) A_64)) (or (= A_65 B_32) (@ _let_1 A_64))))))
% 0.51/0.84 (assert (forall ((A_65 tptp.pname) (B_32 tptp.pname) (A_64 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_65))) (= (@ _let_1 (@ (@ tptp.insert_pname B_32) A_64)) (or (= A_65 B_32) (@ _let_1 A_64))))))
% 0.51/0.84 (assert (forall ((A_65 tptp.x_a) (B_32 tptp.x_a) (A_64 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_65))) (= (@ _let_1 (@ (@ tptp.insert_a B_32) A_64)) (or (= A_65 B_32) (@ _let_1 A_64))))))
% 0.51/0.84 (assert (forall ((Y_11 tptp.pname) (A_63 (-> tptp.pname Bool)) (X_27 tptp.pname)) (= (@ (@ (@ tptp.insert_pname Y_11) A_63) X_27) (or (= Y_11 X_27) (@ A_63 X_27)))))
% 0.51/0.84 (assert (forall ((Y_11 tptp.nat) (A_63 (-> tptp.nat Bool)) (X_27 tptp.nat)) (= (@ (@ (@ tptp.insert_nat Y_11) A_63) X_27) (or (= Y_11 X_27) (@ A_63 X_27)))))
% 0.51/0.84 (assert (forall ((Y_11 tptp.x_a) (A_63 (-> tptp.x_a Bool)) (X_27 tptp.x_a)) (= (@ (@ (@ tptp.insert_a Y_11) A_63) X_27) (or (= Y_11 X_27) (@ A_63 X_27)))))
% 0.51/0.84 (assert (forall ((B_31 (-> tptp.nat Bool)) (X_26 tptp.nat) (A_62 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_26))) (let ((_let_2 (@ tptp.member_nat X_26))) (=> (not (@ _let_2 A_62)) (=> (not (@ _let_2 B_31)) (= (= (@ _let_1 A_62) (@ _let_1 B_31)) (= A_62 B_31))))))))
% 0.51/0.84 (assert (forall ((B_31 (-> tptp.pname Bool)) (X_26 tptp.pname) (A_62 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_26))) (let ((_let_2 (@ tptp.member_pname X_26))) (=> (not (@ _let_2 A_62)) (=> (not (@ _let_2 B_31)) (= (= (@ _let_1 A_62) (@ _let_1 B_31)) (= A_62 B_31))))))))
% 0.51/0.84 (assert (forall ((B_31 (-> tptp.x_a Bool)) (X_26 tptp.x_a) (A_62 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_26))) (let ((_let_2 (@ tptp.member_a X_26))) (=> (not (@ _let_2 A_62)) (=> (not (@ _let_2 B_31)) (= (= (@ _let_1 A_62) (@ _let_1 B_31)) (= A_62 B_31))))))))
% 0.51/0.84 (assert (forall ((B_30 tptp.nat) (A_61 tptp.nat) (B_29 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_61))) (=> (@ _let_1 B_29) (@ _let_1 (@ (@ tptp.insert_nat B_30) B_29))))))
% 0.51/0.84 (assert (forall ((B_30 tptp.pname) (A_61 tptp.pname) (B_29 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_61))) (=> (@ _let_1 B_29) (@ _let_1 (@ (@ tptp.insert_pname B_30) B_29))))))
% 0.51/0.84 (assert (forall ((B_30 tptp.x_a) (A_61 tptp.x_a) (B_29 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_61))) (=> (@ _let_1 B_29) (@ _let_1 (@ (@ tptp.insert_a B_30) B_29))))))
% 0.51/0.84 (assert (forall ((A_60 tptp.nat) (A_59 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat A_60) A_59) (= (@ (@ tptp.insert_nat A_60) A_59) A_59))))
% 0.51/0.84 (assert (forall ((A_60 tptp.pname) (A_59 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_60) A_59) (= (@ (@ tptp.insert_pname A_60) A_59) A_59))))
% 0.51/0.84 (assert (forall ((A_60 tptp.x_a) (A_59 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a A_60) A_59) (= (@ (@ tptp.insert_a A_60) A_59) A_59))))
% 0.51/0.84 (assert (forall ((A_58 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o A_58) A_58)))
% 0.51/0.84 (assert (forall ((A_58 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o A_58) A_58)))
% 0.51/0.84 (assert (forall ((A_58 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o A_58) A_58)))
% 0.51/0.84 (assert (forall ((A_57 (-> tptp.pname Bool)) (B_28 (-> tptp.pname Bool))) (= (= A_57 B_28) (and (@ (@ tptp.ord_less_eq_pname_o A_57) B_28) (@ (@ tptp.ord_less_eq_pname_o B_28) A_57)))))
% 0.51/0.84 (assert (forall ((A_57 (-> tptp.nat Bool)) (B_28 (-> tptp.nat Bool))) (= (= A_57 B_28) (and (@ (@ tptp.ord_less_eq_nat_o A_57) B_28) (@ (@ tptp.ord_less_eq_nat_o B_28) A_57)))))
% 0.51/0.84 (assert (forall ((A_57 (-> tptp.x_a Bool)) (B_28 (-> tptp.x_a Bool))) (= (= A_57 B_28) (and (@ (@ tptp.ord_less_eq_a_o A_57) B_28) (@ (@ tptp.ord_less_eq_a_o B_28) A_57)))))
% 0.51/0.84 (assert (forall ((A_56 (-> tptp.pname Bool)) (B_27 (-> tptp.pname Bool))) (=> (= A_56 B_27) (@ (@ tptp.ord_less_eq_pname_o A_56) B_27))))
% 0.51/0.84 (assert (forall ((A_56 (-> tptp.nat Bool)) (B_27 (-> tptp.nat Bool))) (=> (= A_56 B_27) (@ (@ tptp.ord_less_eq_nat_o A_56) B_27))))
% 0.51/0.84 (assert (forall ((A_56 (-> tptp.x_a Bool)) (B_27 (-> tptp.x_a Bool))) (=> (= A_56 B_27) (@ (@ tptp.ord_less_eq_a_o A_56) B_27))))
% 0.51/0.84 (assert (forall ((A_55 (-> tptp.pname Bool)) (B_26 (-> tptp.pname Bool))) (=> (= A_55 B_26) (@ (@ tptp.ord_less_eq_pname_o B_26) A_55))))
% 0.51/0.84 (assert (forall ((A_55 (-> tptp.nat Bool)) (B_26 (-> tptp.nat Bool))) (=> (= A_55 B_26) (@ (@ tptp.ord_less_eq_nat_o B_26) A_55))))
% 0.51/0.84 (assert (forall ((A_55 (-> tptp.x_a Bool)) (B_26 (-> tptp.x_a Bool))) (=> (= A_55 B_26) (@ (@ tptp.ord_less_eq_a_o B_26) A_55))))
% 0.51/0.84 (assert (forall ((X_25 tptp.nat) (A_54 (-> tptp.nat Bool)) (B_25 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_25))) (=> (@ (@ tptp.ord_less_eq_nat_o A_54) B_25) (=> (@ _let_1 A_54) (@ _let_1 B_25))))))
% 0.51/0.84 (assert (forall ((X_25 tptp.pname) (A_54 (-> tptp.pname Bool)) (B_25 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_25))) (=> (@ (@ tptp.ord_less_eq_pname_o A_54) B_25) (=> (@ _let_1 A_54) (@ _let_1 B_25))))))
% 0.51/0.84 (assert (forall ((X_25 tptp.x_a) (A_54 (-> tptp.x_a Bool)) (B_25 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_25))) (=> (@ (@ tptp.ord_less_eq_a_o A_54) B_25) (=> (@ _let_1 A_54) (@ _let_1 B_25))))))
% 0.51/0.84 (assert (forall ((B_24 (-> tptp.nat Bool)) (X_24 tptp.nat) (A_53 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_24))) (=> (@ _let_1 A_53) (=> (@ (@ tptp.ord_less_eq_nat_o A_53) B_24) (@ _let_1 B_24))))))
% 0.51/0.84 (assert (forall ((B_24 (-> tptp.pname Bool)) (X_24 tptp.pname) (A_53 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_24))) (=> (@ _let_1 A_53) (=> (@ (@ tptp.ord_less_eq_pname_o A_53) B_24) (@ _let_1 B_24))))))
% 0.51/0.84 (assert (forall ((B_24 (-> tptp.x_a Bool)) (X_24 tptp.x_a) (A_53 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_24))) (=> (@ _let_1 A_53) (=> (@ (@ tptp.ord_less_eq_a_o A_53) B_24) (@ _let_1 B_24))))))
% 0.51/0.84 (assert (forall ((X_23 tptp.nat) (A_52 (-> tptp.nat Bool)) (B_23 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_23))) (=> (@ (@ tptp.ord_less_eq_nat_o A_52) B_23) (=> (@ _let_1 A_52) (@ _let_1 B_23))))))
% 0.51/0.84 (assert (forall ((X_23 tptp.pname) (A_52 (-> tptp.pname Bool)) (B_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_23))) (=> (@ (@ tptp.ord_less_eq_pname_o A_52) B_23) (=> (@ _let_1 A_52) (@ _let_1 B_23))))))
% 0.51/0.84 (assert (forall ((X_23 tptp.x_a) (A_52 (-> tptp.x_a Bool)) (B_23 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_23))) (=> (@ (@ tptp.ord_less_eq_a_o A_52) B_23) (=> (@ _let_1 A_52) (@ _let_1 B_23))))))
% 0.51/0.84 (assert (forall ((X_22 tptp.nat) (A_51 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X_22) A_51) (@ A_51 X_22))))
% 0.51/0.84 (assert (forall ((X_22 tptp.pname) (A_51 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_22) A_51) (@ A_51 X_22))))
% 0.51/0.84 (assert (forall ((X_22 tptp.x_a) (A_51 (-> tptp.x_a Bool))) (= (@ (@ tptp.member_a X_22) A_51) (@ A_51 X_22))))
% 0.51/0.84 (assert (forall ((P_7 (-> tptp.x_a Bool))) (= (@ tptp.collect_a P_7) P_7)))
% 0.51/0.84 (assert (forall ((P_7 (-> tptp.pname Bool))) (= (@ tptp.collect_pname P_7) P_7)))
% 0.51/0.84 (assert (forall ((P_7 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.collect_nat_o P_7) P_7)))
% 0.51/0.84 (assert (forall ((P_7 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.collect_pname_o P_7) P_7)))
% 0.51/0.84 (assert (forall ((P_7 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.collect_a_o P_7) P_7)))
% 0.51/0.84 (assert (forall ((P_7 (-> tptp.nat Bool))) (= (@ tptp.collect_nat P_7) P_7)))
% 0.51/0.84 (assert (forall ((C_10 (-> tptp.pname Bool)) (A_50 (-> tptp.pname Bool)) (B_22 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_50))) (=> (@ _let_1 B_22) (=> (@ (@ tptp.ord_less_eq_pname_o B_22) C_10) (@ _let_1 C_10))))))
% 0.51/0.84 (assert (forall ((C_10 (-> tptp.nat Bool)) (A_50 (-> tptp.nat Bool)) (B_22 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_50))) (=> (@ _let_1 B_22) (=> (@ (@ tptp.ord_less_eq_nat_o B_22) C_10) (@ _let_1 C_10))))))
% 0.51/0.84 (assert (forall ((C_10 (-> tptp.x_a Bool)) (A_50 (-> tptp.x_a Bool)) (B_22 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_50))) (=> (@ _let_1 B_22) (=> (@ (@ tptp.ord_less_eq_a_o B_22) C_10) (@ _let_1 C_10))))))
% 0.51/0.84 (assert (forall ((A_49 (-> tptp.pname Bool)) (B_21 (-> tptp.pname Bool))) (=> (= A_49 B_21) (not (=> (@ (@ tptp.ord_less_eq_pname_o A_49) B_21) (not (@ (@ tptp.ord_less_eq_pname_o B_21) A_49)))))))
% 0.51/0.84 (assert (forall ((A_49 (-> tptp.nat Bool)) (B_21 (-> tptp.nat Bool))) (=> (= A_49 B_21) (not (=> (@ (@ tptp.ord_less_eq_nat_o A_49) B_21) (not (@ (@ tptp.ord_less_eq_nat_o B_21) A_49)))))))
% 0.51/0.84 (assert (forall ((A_49 (-> tptp.x_a Bool)) (B_21 (-> tptp.x_a Bool))) (=> (= A_49 B_21) (not (=> (@ (@ tptp.ord_less_eq_a_o A_49) B_21) (not (@ (@ tptp.ord_less_eq_a_o B_21) A_49)))))))
% 0.51/0.84 (assert (forall ((Z_3 tptp.x_a) (F_18 (-> tptp.pname tptp.x_a)) (A_48 (-> tptp.pname Bool))) (= (@ (@ tptp.member_a Z_3) (@ (@ tptp.image_pname_a F_18) A_48)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_48) (= Z_3 (@ F_18 X_1)))))))
% 0.51/0.84 (assert (forall ((F_17 (-> tptp.pname tptp.nat)) (X_21 tptp.pname) (A_47 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_21) A_47) (@ (@ tptp.member_nat (@ F_17 X_21)) (@ (@ tptp.image_pname_nat F_17) A_47)))))
% 0.51/0.84 (assert (forall ((F_17 (-> tptp.x_a tptp.nat)) (X_21 tptp.x_a) (A_47 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a X_21) A_47) (@ (@ tptp.member_nat (@ F_17 X_21)) (@ (@ tptp.image_a_nat F_17) A_47)))))
% 0.51/0.84 (assert (forall ((F_17 (-> tptp.nat tptp.pname)) (X_21 tptp.nat) (A_47 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_21) A_47) (@ (@ tptp.member_pname (@ F_17 X_21)) (@ (@ tptp.image_nat_pname F_17) A_47)))))
% 0.51/0.84 (assert (forall ((F_17 (-> tptp.nat tptp.x_a)) (X_21 tptp.nat) (A_47 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_21) A_47) (@ (@ tptp.member_a (@ F_17 X_21)) (@ (@ tptp.image_nat_a F_17) A_47)))))
% 0.51/0.84 (assert (forall ((F_17 (-> tptp.pname tptp.x_a)) (X_21 tptp.pname) (A_47 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_21) A_47) (@ (@ tptp.member_a (@ F_17 X_21)) (@ (@ tptp.image_pname_a F_17) A_47)))))
% 0.51/0.84 (assert (forall ((B_20 tptp.nat) (F_16 (-> tptp.pname tptp.nat)) (X_20 tptp.pname) (A_46 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_nat B_20) (@ (@ tptp.image_pname_nat F_16) A_46))))))
% 0.51/0.84 (assert (forall ((B_20 tptp.nat) (F_16 (-> tptp.x_a tptp.nat)) (X_20 tptp.x_a) (A_46 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_nat B_20) (@ (@ tptp.image_a_nat F_16) A_46))))))
% 0.51/0.84 (assert (forall ((B_20 tptp.pname) (F_16 (-> tptp.nat tptp.pname)) (X_20 tptp.nat) (A_46 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_pname B_20) (@ (@ tptp.image_nat_pname F_16) A_46))))))
% 0.51/0.84 (assert (forall ((B_20 tptp.x_a) (F_16 (-> tptp.nat tptp.x_a)) (X_20 tptp.nat) (A_46 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_a B_20) (@ (@ tptp.image_nat_a F_16) A_46))))))
% 0.51/0.84 (assert (forall ((B_20 tptp.x_a) (F_16 (-> tptp.pname tptp.x_a)) (X_20 tptp.pname) (A_46 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_a B_20) (@ (@ tptp.image_pname_a F_16) A_46))))))
% 0.51/0.84 (assert (forall ((X_1 (-> tptp.nat Bool)) (Xa (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o X_1) Xa) (@ tptp.collect_nat_o (lambda ((Y_10 (-> tptp.nat Bool))) (or (= Y_10 X_1) (@ (@ tptp.member_nat_o Y_10) Xa)))))))
% 0.51/0.84 (assert (forall ((X_1 (-> tptp.pname Bool)) (Xa (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o X_1) Xa) (@ tptp.collect_pname_o (lambda ((Y_10 (-> tptp.pname Bool))) (or (= Y_10 X_1) (@ (@ tptp.member_pname_o Y_10) Xa)))))))
% 0.51/0.84 (assert (forall ((X_1 (-> tptp.x_a Bool)) (Xa (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o X_1) Xa) (@ tptp.collect_a_o (lambda ((Y_10 (-> tptp.x_a Bool))) (or (= Y_10 X_1) (@ (@ tptp.member_a_o Y_10) Xa)))))))
% 0.51/0.84 (assert (forall ((X_1 tptp.nat) (Xa (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat X_1) Xa) (@ tptp.collect_nat (lambda ((Y_10 tptp.nat)) (or (= Y_10 X_1) (@ (@ tptp.member_nat Y_10) Xa)))))))
% 0.51/0.84 (assert (forall ((X_1 tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X_1) Xa) (@ tptp.collect_pname (lambda ((Y_10 tptp.pname)) (or (= Y_10 X_1) (@ (@ tptp.member_pname Y_10) Xa)))))))
% 0.51/0.84 (assert (forall ((X_1 tptp.x_a) (Xa (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a X_1) Xa) (@ tptp.collect_a (lambda ((Y_10 tptp.x_a)) (or (= Y_10 X_1) (@ (@ tptp.member_a Y_10) Xa)))))))
% 0.51/0.84 (assert (forall ((B_19 (-> tptp.pname Bool)) (A_45 tptp.pname)) (@ (@ tptp.ord_less_eq_pname_o B_19) (@ (@ tptp.insert_pname A_45) B_19))))
% 0.51/0.84 (assert (forall ((B_19 (-> tptp.nat Bool)) (A_45 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o B_19) (@ (@ tptp.insert_nat A_45) B_19))))
% 0.51/0.84 (assert (forall ((B_19 (-> tptp.x_a Bool)) (A_45 tptp.x_a)) (@ (@ tptp.ord_less_eq_a_o B_19) (@ (@ tptp.insert_a A_45) B_19))))
% 0.51/0.84 (assert (forall ((X_19 tptp.nat) (A_44 (-> tptp.nat Bool)) (B_18 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.insert_nat X_19) A_44)) B_18) (and (@ (@ tptp.member_nat X_19) B_18) (@ (@ tptp.ord_less_eq_nat_o A_44) B_18)))))
% 0.51/0.84 (assert (forall ((X_19 tptp.pname) (A_44 (-> tptp.pname Bool)) (B_18 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.insert_pname X_19) A_44)) B_18) (and (@ (@ tptp.member_pname X_19) B_18) (@ (@ tptp.ord_less_eq_pname_o A_44) B_18)))))
% 0.51/0.84 (assert (forall ((X_19 tptp.x_a) (A_44 (-> tptp.x_a Bool)) (B_18 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a X_19) A_44)) B_18) (and (@ (@ tptp.member_a X_19) B_18) (@ (@ tptp.ord_less_eq_a_o A_44) B_18)))))
% 0.51/0.84 (assert (forall ((B_17 (-> tptp.nat Bool)) (X_18 tptp.nat) (A_43 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_43))) (=> (not (@ (@ tptp.member_nat X_18) A_43)) (= (@ _let_1 (@ (@ tptp.insert_nat X_18) B_17)) (@ _let_1 B_17))))))
% 0.51/0.84 (assert (forall ((B_17 (-> tptp.pname Bool)) (X_18 tptp.pname) (A_43 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_43))) (=> (not (@ (@ tptp.member_pname X_18) A_43)) (= (@ _let_1 (@ (@ tptp.insert_pname X_18) B_17)) (@ _let_1 B_17))))))
% 0.51/0.84 (assert (forall ((B_17 (-> tptp.x_a Bool)) (X_18 tptp.x_a) (A_43 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_43))) (=> (not (@ (@ tptp.member_a X_18) A_43)) (= (@ _let_1 (@ (@ tptp.insert_a X_18) B_17)) (@ _let_1 B_17))))))
% 0.51/0.84 (assert (forall ((B_16 tptp.pname) (A_42 (-> tptp.pname Bool)) (B_15 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_42))) (=> (@ _let_1 B_15) (@ _let_1 (@ (@ tptp.insert_pname B_16) B_15))))))
% 0.51/0.84 (assert (forall ((B_16 tptp.nat) (A_42 (-> tptp.nat Bool)) (B_15 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_42))) (=> (@ _let_1 B_15) (@ _let_1 (@ (@ tptp.insert_nat B_16) B_15))))))
% 0.51/0.84 (assert (forall ((B_16 tptp.x_a) (A_42 (-> tptp.x_a Bool)) (B_15 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_42))) (=> (@ _let_1 B_15) (@ _let_1 (@ (@ tptp.insert_a B_16) B_15))))))
% 0.51/0.84 (assert (forall ((A_41 tptp.pname) (C_9 (-> tptp.pname Bool)) (D_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_41))) (=> (@ (@ tptp.ord_less_eq_pname_o C_9) D_1) (@ (@ tptp.ord_less_eq_pname_o (@ _let_1 C_9)) (@ _let_1 D_1))))))
% 0.51/0.84 (assert (forall ((A_41 tptp.nat) (C_9 (-> tptp.nat Bool)) (D_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_41))) (=> (@ (@ tptp.ord_less_eq_nat_o C_9) D_1) (@ (@ tptp.ord_less_eq_nat_o (@ _let_1 C_9)) (@ _let_1 D_1))))))
% 0.51/0.84 (assert (forall ((A_41 tptp.x_a) (C_9 (-> tptp.x_a Bool)) (D_1 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_41))) (=> (@ (@ tptp.ord_less_eq_a_o C_9) D_1) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 C_9)) (@ _let_1 D_1))))))
% 0.51/0.84 (assert (forall ((F_15 (-> tptp.x_a tptp.pname)) (A_40 tptp.x_a) (B_14 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.image_a_pname F_15))) (= (@ _let_1 (@ (@ tptp.insert_a A_40) B_14)) (@ (@ tptp.insert_pname (@ F_15 A_40)) (@ _let_1 B_14))))))
% 0.51/0.84 (assert (forall ((F_15 (-> tptp.x_a tptp.nat)) (A_40 tptp.x_a) (B_14 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.image_a_nat F_15))) (= (@ _let_1 (@ (@ tptp.insert_a A_40) B_14)) (@ (@ tptp.insert_nat (@ F_15 A_40)) (@ _let_1 B_14))))))
% 0.51/0.84 (assert (forall ((F_15 (-> tptp.nat tptp.x_a)) (A_40 tptp.nat) (B_14 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_a F_15))) (= (@ _let_1 (@ (@ tptp.insert_nat A_40) B_14)) (@ (@ tptp.insert_a (@ F_15 A_40)) (@ _let_1 B_14))))))
% 0.51/0.84 (assert (forall ((F_15 (-> tptp.pname tptp.x_a)) (A_40 tptp.pname) (B_14 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_15))) (= (@ _let_1 (@ (@ tptp.insert_pname A_40) B_14)) (@ (@ tptp.insert_a (@ F_15 A_40)) (@ _let_1 B_14))))))
% 0.51/0.84 (assert (forall ((F_14 (-> tptp.pname tptp.pname)) (X_17 tptp.pname) (A_39 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_pname F_14) A_39))) (=> (@ (@ tptp.member_pname X_17) A_39) (= (@ (@ tptp.insert_pname (@ F_14 X_17)) _let_1) _let_1)))))
% 0.51/0.84 (assert (forall ((F_14 (-> tptp.pname tptp.nat)) (X_17 tptp.pname) (A_39 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_nat F_14) A_39))) (=> (@ (@ tptp.member_pname X_17) A_39) (= (@ (@ tptp.insert_nat (@ F_14 X_17)) _let_1) _let_1)))))
% 0.51/0.84 (assert (forall ((F_14 (-> tptp.x_a tptp.pname)) (X_17 tptp.x_a) (A_39 (-> tptp.x_a Bool))) (let ((_let_1 (@ (@ tptp.image_a_pname F_14) A_39))) (=> (@ (@ tptp.member_a X_17) A_39) (= (@ (@ tptp.insert_pname (@ F_14 X_17)) _let_1) _let_1)))))
% 0.51/0.84 (assert (forall ((F_14 (-> tptp.x_a tptp.nat)) (X_17 tptp.x_a) (A_39 (-> tptp.x_a Bool))) (let ((_let_1 (@ (@ tptp.image_a_nat F_14) A_39))) (=> (@ (@ tptp.member_a X_17) A_39) (= (@ (@ tptp.insert_nat (@ F_14 X_17)) _let_1) _let_1)))))
% 0.51/0.84 (assert (forall ((F_14 (-> tptp.nat tptp.x_a)) (X_17 tptp.nat) (A_39 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.image_nat_a F_14) A_39))) (=> (@ (@ tptp.member_nat X_17) A_39) (= (@ (@ tptp.insert_a (@ F_14 X_17)) _let_1) _let_1)))))
% 0.51/0.84 (assert (forall ((F_14 (-> tptp.pname tptp.x_a)) (X_17 tptp.pname) (A_39 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_a F_14) A_39))) (=> (@ (@ tptp.member_pname X_17) A_39) (= (@ (@ tptp.insert_a (@ F_14 X_17)) _let_1) _let_1)))))
% 0.51/0.84 (assert (forall ((B_13 (-> tptp.x_a Bool)) (F_13 (-> tptp.nat tptp.x_a)) (A_38 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_a_o B_13) (@ (@ tptp.image_nat_a F_13) A_38)) (exists ((AA (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o AA) A_38) (= B_13 (@ (@ tptp.image_nat_a F_13) AA)))))))
% 0.51/0.84 (assert (forall ((B_13 (-> tptp.pname Bool)) (F_13 (-> tptp.x_a tptp.pname)) (A_38 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_pname_o B_13) (@ (@ tptp.image_a_pname F_13) A_38)) (exists ((AA (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o AA) A_38) (= B_13 (@ (@ tptp.image_a_pname F_13) AA)))))))
% 0.51/0.84 (assert (forall ((B_13 (-> tptp.nat Bool)) (F_13 (-> tptp.x_a tptp.nat)) (A_38 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_nat_o B_13) (@ (@ tptp.image_a_nat F_13) A_38)) (exists ((AA (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o AA) A_38) (= B_13 (@ (@ tptp.image_a_nat F_13) AA)))))))
% 0.51/0.84 (assert (forall ((B_13 (-> tptp.x_a Bool)) (F_13 (-> tptp.pname tptp.x_a)) (A_38 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_a_o B_13) (@ (@ tptp.image_pname_a F_13) A_38)) (exists ((AA (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o AA) A_38) (= B_13 (@ (@ tptp.image_pname_a F_13) AA)))))))
% 0.51/0.84 (assert (forall ((F_12 (-> tptp.x_a tptp.pname)) (A_37 (-> tptp.x_a Bool)) (B_12 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.image_a_pname F_12))) (=> (@ (@ tptp.ord_less_eq_a_o A_37) B_12) (@ (@ tptp.ord_less_eq_pname_o (@ _let_1 A_37)) (@ _let_1 B_12))))))
% 0.51/0.84 (assert (forall ((F_12 (-> tptp.x_a tptp.nat)) (A_37 (-> tptp.x_a Bool)) (B_12 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.image_a_nat F_12))) (=> (@ (@ tptp.ord_less_eq_a_o A_37) B_12) (@ (@ tptp.ord_less_eq_nat_o (@ _let_1 A_37)) (@ _let_1 B_12))))))
% 0.51/0.84 (assert (forall ((F_12 (-> tptp.nat tptp.x_a)) (A_37 (-> tptp.nat Bool)) (B_12 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_a F_12))) (=> (@ (@ tptp.ord_less_eq_nat_o A_37) B_12) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 A_37)) (@ _let_1 B_12))))))
% 0.51/0.84 (assert (forall ((F_12 (-> tptp.pname tptp.x_a)) (A_37 (-> tptp.pname Bool)) (B_12 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_12))) (=> (@ (@ tptp.ord_less_eq_pname_o A_37) B_12) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 A_37)) (@ _let_1 B_12))))))
% 0.51/0.84 (assert (forall ((B_11 tptp.pname) (F_11 (-> tptp.nat tptp.pname)) (A_36 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_pname B_11) (@ (@ tptp.image_nat_pname F_11) A_36)) (not (forall ((X_1 tptp.nat)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_nat X_1) A_36))))))))
% 0.51/0.84 (assert (forall ((B_11 tptp.x_a) (F_11 (-> tptp.nat tptp.x_a)) (A_36 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_a B_11) (@ (@ tptp.image_nat_a F_11) A_36)) (not (forall ((X_1 tptp.nat)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_nat X_1) A_36))))))))
% 0.51/0.84 (assert (forall ((B_11 tptp.nat) (F_11 (-> tptp.pname tptp.nat)) (A_36 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_nat B_11) (@ (@ tptp.image_pname_nat F_11) A_36)) (not (forall ((X_1 tptp.pname)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_pname X_1) A_36))))))))
% 0.51/0.84 (assert (forall ((B_11 tptp.nat) (F_11 (-> tptp.x_a tptp.nat)) (A_36 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_nat B_11) (@ (@ tptp.image_a_nat F_11) A_36)) (not (forall ((X_1 tptp.x_a)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_a X_1) A_36))))))))
% 0.51/0.84 (assert (forall ((B_11 tptp.x_a) (F_11 (-> tptp.pname tptp.x_a)) (A_36 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_a B_11) (@ (@ tptp.image_pname_a F_11) A_36)) (not (forall ((X_1 tptp.pname)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_pname X_1) A_36))))))))
% 0.51/0.84 (assert (forall ((B_10 (-> tptp.nat Bool)) (A_35 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X_1))) (=> (@ _let_1 A_35) (@ _let_1 B_10)))) (@ (@ tptp.ord_less_eq_nat_o A_35) B_10))))
% 0.51/0.84 (assert (forall ((B_10 (-> tptp.pname Bool)) (A_35 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (let ((_let_1 (@ tptp.member_pname X_1))) (=> (@ _let_1 A_35) (@ _let_1 B_10)))) (@ (@ tptp.ord_less_eq_pname_o A_35) B_10))))
% 0.51/0.84 (assert (forall ((B_10 (-> tptp.x_a Bool)) (A_35 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (let ((_let_1 (@ tptp.member_a X_1))) (=> (@ _let_1 A_35) (@ _let_1 B_10)))) (@ (@ tptp.ord_less_eq_a_o A_35) B_10))))
% 0.51/0.84 (assert (forall ((F_10 (-> tptp.pname tptp.nat)) (B_9 (-> tptp.nat Bool)) (A_34 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) A_34) (@ (@ tptp.member_nat (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.image_pname_nat F_10) A_34)) B_9))))
% 0.51/0.84 (assert (forall ((F_10 (-> tptp.pname tptp.pname)) (B_9 (-> tptp.pname Bool)) (A_34 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) A_34) (@ (@ tptp.member_pname (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.image_pname_pname F_10) A_34)) B_9))))
% 0.51/0.84 (assert (forall ((F_10 (-> tptp.x_a tptp.nat)) (B_9 (-> tptp.nat Bool)) (A_34 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (=> (@ (@ tptp.member_a X_1) A_34) (@ (@ tptp.member_nat (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.image_a_nat F_10) A_34)) B_9))))
% 0.51/0.84 (assert (forall ((F_10 (-> tptp.x_a tptp.pname)) (B_9 (-> tptp.pname Bool)) (A_34 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (=> (@ (@ tptp.member_a X_1) A_34) (@ (@ tptp.member_pname (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.image_a_pname F_10) A_34)) B_9))))
% 0.51/0.84 (assert (forall ((F_10 (-> tptp.nat tptp.pname)) (B_9 (-> tptp.pname Bool)) (A_34 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) A_34) (@ (@ tptp.member_pname (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.image_nat_pname F_10) A_34)) B_9))))
% 0.51/0.84 (assert (forall ((F_10 (-> tptp.nat tptp.x_a)) (B_9 (-> tptp.x_a Bool)) (A_34 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) A_34) (@ (@ tptp.member_a (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.image_nat_a F_10) A_34)) B_9))))
% 0.51/0.84 (assert (forall ((F_10 (-> tptp.pname tptp.x_a)) (B_9 (-> tptp.x_a Bool)) (A_34 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) A_34) (@ (@ tptp.member_a (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.image_pname_a F_10) A_34)) B_9))))
% 0.51/0.84 (assert (forall ((X_16 Bool)) (@ (@ tptp.ord_less_eq_o X_16) X_16)))
% 0.51/0.84 (assert (forall ((X_16 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o X_16) X_16)))
% 0.51/0.84 (assert (forall ((X_16 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o X_16) X_16)))
% 0.51/0.84 (assert (forall ((X_16 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o X_16) X_16)))
% 0.51/0.84 (assert (forall ((X_16 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X_16) X_16)))
% 0.51/0.84 (assert (forall ((N_1 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_1) (exists ((M_1 tptp.nat)) (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_1) (@ (@ tptp.ord_less_eq_nat X_1) M_1)))))))
% 0.51/0.84 (assert (forall ((G (-> tptp.x_a Bool)) (C tptp.com)) (=> (@ tptp.wt C) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) tptp.u) (@ (@ tptp.p G) (@ (@ tptp.insert_a (@ tptp.mgt_call X_1)) tptp.bot_bot_a_o)))) (@ (@ tptp.p G) (@ (@ tptp.insert_a (@ tptp.mgt C)) tptp.bot_bot_a_o))))))
% 0.51/0.84 (assert (forall ((F_9 (-> tptp.pname Bool)) (G_3 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o F_9) G_3) (forall ((X_1 tptp.pname)) (@ (@ tptp.ord_less_eq_o (@ F_9 X_1)) (@ G_3 X_1))))))
% 0.51/0.84 (assert (forall ((F_9 (-> tptp.nat Bool)) (G_3 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o F_9) G_3) (forall ((X_1 tptp.nat)) (@ (@ tptp.ord_less_eq_o (@ F_9 X_1)) (@ G_3 X_1))))))
% 0.51/0.84 (assert (forall ((F_9 (-> tptp.x_a Bool)) (G_3 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o F_9) G_3) (forall ((X_1 tptp.x_a)) (@ (@ tptp.ord_less_eq_o (@ F_9 X_1)) (@ G_3 X_1))))))
% 0.51/0.84 (assert (forall ((X_15 tptp.pname) (F_8 (-> tptp.pname Bool)) (G_2 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o F_8) G_2) (@ (@ tptp.ord_less_eq_o (@ F_8 X_15)) (@ G_2 X_15)))))
% 0.51/0.84 (assert (forall ((X_15 tptp.nat) (F_8 (-> tptp.nat Bool)) (G_2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o F_8) G_2) (@ (@ tptp.ord_less_eq_o (@ F_8 X_15)) (@ G_2 X_15)))))
% 0.51/0.84 (assert (forall ((X_15 tptp.x_a) (F_8 (-> tptp.x_a Bool)) (G_2 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o F_8) G_2) (@ (@ tptp.ord_less_eq_o (@ F_8 X_15)) (@ G_2 X_15)))))
% 0.51/0.84 (assert (forall ((X_14 tptp.pname) (F_7 (-> tptp.pname Bool)) (G_1 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o F_7) G_1) (@ (@ tptp.ord_less_eq_o (@ F_7 X_14)) (@ G_1 X_14)))))
% 0.51/0.84 (assert (forall ((X_14 tptp.nat) (F_7 (-> tptp.nat Bool)) (G_1 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o F_7) G_1) (@ (@ tptp.ord_less_eq_o (@ F_7 X_14)) (@ G_1 X_14)))))
% 0.51/0.84 (assert (forall ((X_14 tptp.x_a) (F_7 (-> tptp.x_a Bool)) (G_1 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o F_7) G_1) (@ (@ tptp.ord_less_eq_o (@ F_7 X_14)) (@ G_1 X_14)))))
% 0.51/0.84 (assert (forall ((A_33 tptp.nat)) (not (@ (@ tptp.member_nat A_33) tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((A_33 tptp.pname)) (not (@ (@ tptp.member_pname A_33) tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((A_33 tptp.x_a)) (not (@ (@ tptp.member_a A_33) tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (@ tptp.finite_finite_nat_o tptp.bot_bot_nat_o_o))
% 0.51/0.84 (assert (@ tptp.finite297249702name_o tptp.bot_bot_pname_o_o))
% 0.51/0.84 (assert (@ tptp.finite_finite_a_o tptp.bot_bot_a_o_o))
% 0.51/0.84 (assert (@ tptp.finite_finite_a tptp.bot_bot_a_o))
% 0.51/0.84 (assert (@ tptp.finite_finite_pname tptp.bot_bot_pname_o))
% 0.51/0.84 (assert (@ tptp.finite_finite_nat tptp.bot_bot_nat_o))
% 0.51/0.84 (assert (forall ((A_32 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o tptp.bot_bot_pname_o) A_32)))
% 0.51/0.84 (assert (forall ((A_32 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o tptp.bot_bot_nat_o) A_32)))
% 0.51/0.84 (assert (forall ((A_32 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o tptp.bot_bot_a_o) A_32)))
% 0.51/0.84 (assert (forall ((A_31 tptp.nat) (A_30 (-> tptp.nat Bool))) (=> (= A_30 tptp.bot_bot_nat_o) (not (@ (@ tptp.member_nat A_31) A_30)))))
% 0.51/0.84 (assert (forall ((A_31 tptp.pname) (A_30 (-> tptp.pname Bool))) (=> (= A_30 tptp.bot_bot_pname_o) (not (@ (@ tptp.member_pname A_31) A_30)))))
% 0.51/0.84 (assert (forall ((A_31 tptp.x_a) (A_30 (-> tptp.x_a Bool))) (=> (= A_30 tptp.bot_bot_a_o) (not (@ (@ tptp.member_a A_31) A_30)))))
% 0.51/0.84 (assert (forall ((P_6 (-> tptp.pname Bool))) (= (= (@ tptp.collect_pname P_6) tptp.bot_bot_pname_o) (forall ((X_1 tptp.pname)) (not (@ P_6 X_1))))))
% 0.51/0.84 (assert (forall ((P_6 (-> (-> tptp.nat Bool) Bool))) (= (= (@ tptp.collect_nat_o P_6) tptp.bot_bot_nat_o_o) (forall ((X_1 (-> tptp.nat Bool))) (not (@ P_6 X_1))))))
% 0.51/0.84 (assert (forall ((P_6 (-> (-> tptp.pname Bool) Bool))) (= (= (@ tptp.collect_pname_o P_6) tptp.bot_bot_pname_o_o) (forall ((X_1 (-> tptp.pname Bool))) (not (@ P_6 X_1))))))
% 0.51/0.84 (assert (forall ((P_6 (-> (-> tptp.x_a Bool) Bool))) (= (= (@ tptp.collect_a_o P_6) tptp.bot_bot_a_o_o) (forall ((X_1 (-> tptp.x_a Bool))) (not (@ P_6 X_1))))))
% 0.51/0.84 (assert (forall ((P_6 (-> tptp.x_a Bool))) (= (= (@ tptp.collect_a P_6) tptp.bot_bot_a_o) (forall ((X_1 tptp.x_a)) (not (@ P_6 X_1))))))
% 0.51/0.84 (assert (forall ((P_6 (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P_6) tptp.bot_bot_nat_o) (forall ((X_1 tptp.nat)) (not (@ P_6 X_1))))))
% 0.51/0.84 (assert (forall ((C_8 tptp.nat)) (not (@ (@ tptp.member_nat C_8) tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((C_8 tptp.pname)) (not (@ (@ tptp.member_pname C_8) tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((C_8 tptp.x_a)) (not (@ (@ tptp.member_a C_8) tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (forall ((P_5 (-> tptp.pname Bool))) (= (= tptp.bot_bot_pname_o (@ tptp.collect_pname P_5)) (forall ((X_1 tptp.pname)) (not (@ P_5 X_1))))))
% 0.51/0.84 (assert (forall ((P_5 (-> (-> tptp.nat Bool) Bool))) (= (= tptp.bot_bot_nat_o_o (@ tptp.collect_nat_o P_5)) (forall ((X_1 (-> tptp.nat Bool))) (not (@ P_5 X_1))))))
% 0.51/0.84 (assert (forall ((P_5 (-> (-> tptp.pname Bool) Bool))) (= (= tptp.bot_bot_pname_o_o (@ tptp.collect_pname_o P_5)) (forall ((X_1 (-> tptp.pname Bool))) (not (@ P_5 X_1))))))
% 0.51/0.84 (assert (forall ((P_5 (-> (-> tptp.x_a Bool) Bool))) (= (= tptp.bot_bot_a_o_o (@ tptp.collect_a_o P_5)) (forall ((X_1 (-> tptp.x_a Bool))) (not (@ P_5 X_1))))))
% 0.51/0.84 (assert (forall ((P_5 (-> tptp.x_a Bool))) (= (= tptp.bot_bot_a_o (@ tptp.collect_a P_5)) (forall ((X_1 tptp.x_a)) (not (@ P_5 X_1))))))
% 0.51/0.84 (assert (forall ((P_5 (-> tptp.nat Bool))) (= (= tptp.bot_bot_nat_o (@ tptp.collect_nat P_5)) (forall ((X_1 tptp.nat)) (not (@ P_5 X_1))))))
% 0.51/0.84 (assert (forall ((A_29 (-> tptp.nat Bool))) (= (exists ((X_1 tptp.nat)) (@ (@ tptp.member_nat X_1) A_29)) (not (= A_29 tptp.bot_bot_nat_o)))))
% 0.51/0.84 (assert (forall ((A_29 (-> tptp.pname Bool))) (= (exists ((X_1 tptp.pname)) (@ (@ tptp.member_pname X_1) A_29)) (not (= A_29 tptp.bot_bot_pname_o)))))
% 0.51/0.84 (assert (forall ((A_29 (-> tptp.x_a Bool))) (= (exists ((X_1 tptp.x_a)) (@ (@ tptp.member_a X_1) A_29)) (not (= A_29 tptp.bot_bot_a_o)))))
% 0.51/0.84 (assert (forall ((A_28 (-> tptp.nat Bool))) (= (forall ((X_1 tptp.nat)) (not (@ (@ tptp.member_nat X_1) A_28))) (= A_28 tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((A_28 (-> tptp.pname Bool))) (= (forall ((X_1 tptp.pname)) (not (@ (@ tptp.member_pname X_1) A_28))) (= A_28 tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((A_28 (-> tptp.x_a Bool))) (= (forall ((X_1 tptp.x_a)) (not (@ (@ tptp.member_a X_1) A_28))) (= A_28 tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (= tptp.bot_bot_pname_o (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) false))))
% 0.51/0.84 (assert (= tptp.bot_bot_nat_o_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) false))))
% 0.51/0.84 (assert (= tptp.bot_bot_pname_o_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) false))))
% 0.51/0.84 (assert (= tptp.bot_bot_a_o_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) false))))
% 0.51/0.84 (assert (= tptp.bot_bot_a_o (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) false))))
% 0.51/0.84 (assert (= tptp.bot_bot_nat_o (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) false))))
% 0.51/0.84 (assert (forall ((X_1 tptp.pname)) (= (@ tptp.bot_bot_pname_o X_1) tptp.bot_bot_o)))
% 0.51/0.84 (assert (forall ((X_1 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_1) tptp.bot_bot_o)))
% 0.51/0.84 (assert (forall ((X_1 tptp.x_a)) (= (@ tptp.bot_bot_a_o X_1) tptp.bot_bot_o)))
% 0.51/0.84 (assert (forall ((X_13 tptp.pname)) (= (@ tptp.bot_bot_pname_o X_13) tptp.bot_bot_o)))
% 0.51/0.84 (assert (forall ((X_13 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_13) tptp.bot_bot_o)))
% 0.51/0.84 (assert (forall ((X_13 tptp.x_a)) (= (@ tptp.bot_bot_a_o X_13) tptp.bot_bot_o)))
% 0.51/0.84 (assert (forall ((A_27 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_27) tptp.bot_bot_pname_o) (= A_27 tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((A_27 Bool)) (=> (@ (@ tptp.ord_less_eq_o A_27) tptp.bot_bot_o) (= A_27 tptp.bot_bot_o))))
% 0.51/0.84 (assert (forall ((A_27 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_27) tptp.bot_bot_nat_o) (= A_27 tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((A_27 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_27) tptp.bot_bot_a_o) (= A_27 tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (forall ((A_27 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_27) tptp.bot_bot_nat) (= A_27 tptp.bot_bot_nat))))
% 0.51/0.84 (assert (forall ((A_26 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o A_26) tptp.bot_bot_pname_o) (= A_26 tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((A_26 Bool)) (= (@ (@ tptp.ord_less_eq_o A_26) tptp.bot_bot_o) (= A_26 tptp.bot_bot_o))))
% 0.51/0.84 (assert (forall ((A_26 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o A_26) tptp.bot_bot_nat_o) (= A_26 tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((A_26 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o A_26) tptp.bot_bot_a_o) (= A_26 tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (forall ((A_26 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A_26) tptp.bot_bot_nat) (= A_26 tptp.bot_bot_nat))))
% 0.51/0.84 (assert (forall ((A_25 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o tptp.bot_bot_pname_o) A_25)))
% 0.51/0.84 (assert (forall ((A_25 Bool)) (@ (@ tptp.ord_less_eq_o tptp.bot_bot_o) A_25)))
% 0.51/0.84 (assert (forall ((A_25 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o tptp.bot_bot_nat_o) A_25)))
% 0.51/0.84 (assert (forall ((A_25 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o tptp.bot_bot_a_o) A_25)))
% 0.51/0.84 (assert (forall ((A_25 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A_25)))
% 0.51/0.84 (assert (forall ((A_24 tptp.pname) (B_8 tptp.pname)) (=> (= (@ (@ tptp.insert_pname A_24) tptp.bot_bot_pname_o) (@ (@ tptp.insert_pname B_8) tptp.bot_bot_pname_o)) (= A_24 B_8))))
% 0.51/0.84 (assert (forall ((A_24 tptp.nat) (B_8 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A_24) tptp.bot_bot_nat_o) (@ (@ tptp.insert_nat B_8) tptp.bot_bot_nat_o)) (= A_24 B_8))))
% 0.51/0.84 (assert (forall ((A_24 tptp.x_a) (B_8 tptp.x_a)) (=> (= (@ (@ tptp.insert_a A_24) tptp.bot_bot_a_o) (@ (@ tptp.insert_a B_8) tptp.bot_bot_a_o)) (= A_24 B_8))))
% 0.51/0.84 (assert (forall ((B_7 tptp.nat) (A_23 tptp.nat)) (=> (@ (@ tptp.member_nat B_7) (@ (@ tptp.insert_nat A_23) tptp.bot_bot_nat_o)) (= B_7 A_23))))
% 0.51/0.84 (assert (forall ((B_7 tptp.pname) (A_23 tptp.pname)) (=> (@ (@ tptp.member_pname B_7) (@ (@ tptp.insert_pname A_23) tptp.bot_bot_pname_o)) (= B_7 A_23))))
% 0.51/0.84 (assert (forall ((B_7 tptp.x_a) (A_23 tptp.x_a)) (=> (@ (@ tptp.member_a B_7) (@ (@ tptp.insert_a A_23) tptp.bot_bot_a_o)) (= B_7 A_23))))
% 0.51/0.84 (assert (forall ((A_22 tptp.pname) (B_6 tptp.pname) (C_7 tptp.pname) (D tptp.pname)) (= (= (@ (@ tptp.insert_pname A_22) (@ (@ tptp.insert_pname B_6) tptp.bot_bot_pname_o)) (@ (@ tptp.insert_pname C_7) (@ (@ tptp.insert_pname D) tptp.bot_bot_pname_o))) (or (and (= A_22 C_7) (= B_6 D)) (and (= A_22 D) (= B_6 C_7))))))
% 0.51/0.84 (assert (forall ((A_22 tptp.nat) (B_6 tptp.nat) (C_7 tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.insert_nat A_22) (@ (@ tptp.insert_nat B_6) tptp.bot_bot_nat_o)) (@ (@ tptp.insert_nat C_7) (@ (@ tptp.insert_nat D) tptp.bot_bot_nat_o))) (or (and (= A_22 C_7) (= B_6 D)) (and (= A_22 D) (= B_6 C_7))))))
% 0.51/0.84 (assert (forall ((A_22 tptp.x_a) (B_6 tptp.x_a) (C_7 tptp.x_a) (D tptp.x_a)) (= (= (@ (@ tptp.insert_a A_22) (@ (@ tptp.insert_a B_6) tptp.bot_bot_a_o)) (@ (@ tptp.insert_a C_7) (@ (@ tptp.insert_a D) tptp.bot_bot_a_o))) (or (and (= A_22 C_7) (= B_6 D)) (and (= A_22 D) (= B_6 C_7))))))
% 0.51/0.84 (assert (forall ((B_5 tptp.nat) (A_21 tptp.nat)) (= (@ (@ tptp.member_nat B_5) (@ (@ tptp.insert_nat A_21) tptp.bot_bot_nat_o)) (= B_5 A_21))))
% 0.51/0.84 (assert (forall ((B_5 tptp.pname) (A_21 tptp.pname)) (= (@ (@ tptp.member_pname B_5) (@ (@ tptp.insert_pname A_21) tptp.bot_bot_pname_o)) (= B_5 A_21))))
% 0.51/0.84 (assert (forall ((B_5 tptp.x_a) (A_21 tptp.x_a)) (= (@ (@ tptp.member_a B_5) (@ (@ tptp.insert_a A_21) tptp.bot_bot_a_o)) (= B_5 A_21))))
% 0.51/0.84 (assert (forall ((A_20 tptp.pname) (A_19 (-> tptp.pname Bool))) (not (= (@ (@ tptp.insert_pname A_20) A_19) tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((A_20 tptp.nat) (A_19 (-> tptp.nat Bool))) (not (= (@ (@ tptp.insert_nat A_20) A_19) tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((A_20 tptp.x_a) (A_19 (-> tptp.x_a Bool))) (not (= (@ (@ tptp.insert_a A_20) A_19) tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (forall ((A_18 tptp.pname) (A_17 (-> tptp.pname Bool))) (not (= tptp.bot_bot_pname_o (@ (@ tptp.insert_pname A_18) A_17)))))
% 0.51/0.84 (assert (forall ((A_18 tptp.nat) (A_17 (-> tptp.nat Bool))) (not (= tptp.bot_bot_nat_o (@ (@ tptp.insert_nat A_18) A_17)))))
% 0.51/0.84 (assert (forall ((A_18 tptp.x_a) (A_17 (-> tptp.x_a Bool))) (not (= tptp.bot_bot_a_o (@ (@ tptp.insert_a A_18) A_17)))))
% 0.51/0.84 (assert (forall ((A_16 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o A_16) tptp.bot_bot_nat_o) (= A_16 tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((A_16 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o A_16) tptp.bot_bot_pname_o) (= A_16 tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((A_16 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o A_16) tptp.bot_bot_a_o) (= A_16 tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (forall ((F_6 (-> tptp.pname tptp.x_a)) (A_15 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_pname_a F_6) A_15) tptp.bot_bot_a_o) (= A_15 tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((F_5 (-> tptp.pname tptp.x_a))) (= (@ (@ tptp.image_pname_a F_5) tptp.bot_bot_pname_o) tptp.bot_bot_a_o)))
% 0.51/0.84 (assert (forall ((F_4 (-> tptp.pname tptp.x_a)) (A_14 (-> tptp.pname Bool))) (= (= tptp.bot_bot_a_o (@ (@ tptp.image_pname_a F_4) A_14)) (= A_14 tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((P_4 (-> tptp.nat Bool)) (A_13 tptp.nat)) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_nat A_13) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_nat_o))))))
% 0.51/0.84 (assert (forall ((P_4 (-> tptp.pname Bool)) (A_13 tptp.pname)) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_pname A_13) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_pname_o))))))
% 0.51/0.84 (assert (forall ((P_4 (-> tptp.x_a Bool)) (A_13 tptp.x_a)) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_a A_13) tptp.bot_bot_a_o))) (=> (not _let_1) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_a_o))))))
% 0.51/0.84 (assert (forall ((P_4 (-> (-> tptp.nat Bool) Bool)) (A_13 (-> tptp.nat Bool))) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_nat_o A_13) tptp.bot_bot_nat_o_o))) (=> (not _let_1) (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_nat_o_o))))))
% 0.51/0.84 (assert (forall ((P_4 (-> (-> tptp.pname Bool) Bool)) (A_13 (-> tptp.pname Bool))) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_pname_o A_13) tptp.bot_bot_pname_o_o))) (=> (not _let_1) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_pname_o_o))))))
% 0.51/0.84 (assert (forall ((P_4 (-> (-> tptp.x_a Bool) Bool)) (A_13 (-> tptp.x_a Bool))) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_a_o A_13) tptp.bot_bot_a_o_o))) (=> (not _let_1) (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_a_o_o))))))
% 0.51/0.84 (assert (forall ((P_3 (-> tptp.nat Bool)) (A_12 tptp.nat)) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_nat A_12) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_nat_o))))))
% 0.51/0.84 (assert (forall ((P_3 (-> tptp.pname Bool)) (A_12 tptp.pname)) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_pname A_12) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_pname_o))))))
% 0.51/0.84 (assert (forall ((P_3 (-> tptp.x_a Bool)) (A_12 tptp.x_a)) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_a A_12) tptp.bot_bot_a_o))) (=> (not _let_1) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_a_o))))))
% 0.51/0.84 (assert (forall ((P_3 (-> (-> tptp.nat Bool) Bool)) (A_12 (-> tptp.nat Bool))) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_nat_o A_12) tptp.bot_bot_nat_o_o))) (=> (not _let_1) (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_nat_o_o))))))
% 0.51/0.84 (assert (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (A_12 (-> tptp.pname Bool))) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_pname_o A_12) tptp.bot_bot_pname_o_o))) (=> (not _let_1) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_pname_o_o))))))
% 0.51/0.84 (assert (forall ((P_3 (-> (-> tptp.x_a Bool) Bool)) (A_12 (-> tptp.x_a Bool))) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_a_o A_12) tptp.bot_bot_a_o_o))) (=> (not _let_1) (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_a_o_o))))))
% 0.51/0.84 (assert (forall ((A_11 tptp.nat)) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (= X_1 A_11))) (@ (@ tptp.insert_nat A_11) tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((A_11 tptp.pname)) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (= X_1 A_11))) (@ (@ tptp.insert_pname A_11) tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((A_11 tptp.x_a)) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (= X_1 A_11))) (@ (@ tptp.insert_a A_11) tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (forall ((A_11 (-> tptp.nat Bool))) (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (= X_1 A_11))) (@ (@ tptp.insert_nat_o A_11) tptp.bot_bot_nat_o_o))))
% 0.51/0.84 (assert (forall ((A_11 (-> tptp.pname Bool))) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (= X_1 A_11))) (@ (@ tptp.insert_pname_o A_11) tptp.bot_bot_pname_o_o))))
% 0.51/0.84 (assert (forall ((A_11 (-> tptp.x_a Bool))) (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (= X_1 A_11))) (@ (@ tptp.insert_a_o A_11) tptp.bot_bot_a_o_o))))
% 0.51/0.84 (assert (forall ((A_10 tptp.nat)) (= (@ tptp.collect_nat (@ tptp.fequal_nat A_10)) (@ (@ tptp.insert_nat A_10) tptp.bot_bot_nat_o))))
% 0.51/0.84 (assert (forall ((A_10 tptp.pname)) (= (@ tptp.collect_pname (@ tptp.fequal_pname A_10)) (@ (@ tptp.insert_pname A_10) tptp.bot_bot_pname_o))))
% 0.51/0.84 (assert (forall ((A_10 tptp.x_a)) (= (@ tptp.collect_a (@ tptp.fequal_a A_10)) (@ (@ tptp.insert_a A_10) tptp.bot_bot_a_o))))
% 0.51/0.84 (assert (forall ((A_10 (-> tptp.nat Bool))) (= (@ tptp.collect_nat_o (@ tptp.fequal_nat_o A_10)) (@ (@ tptp.insert_nat_o A_10) tptp.bot_bot_nat_o_o))))
% 0.51/0.84 (assert (forall ((A_10 (-> tptp.pname Bool))) (= (@ tptp.collect_pname_o (@ tptp.fequal_pname_o A_10)) (@ (@ tptp.insert_pname_o A_10) tptp.bot_bot_pname_o_o))))
% 0.51/0.84 (assert (forall ((A_10 (-> tptp.x_a Bool))) (= (@ tptp.collect_a_o (@ tptp.fequal_a_o A_10)) (@ (@ tptp.insert_a_o A_10) tptp.bot_bot_a_o_o))))
% 0.51/0.84 (assert (forall ((A_9 (-> tptp.nat Bool)) (X_12 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X_12) tptp.bot_bot_nat_o))) (=> (@ (@ tptp.ord_less_eq_nat_o A_9) _let_1) (or (= A_9 tptp.bot_bot_nat_o) (= A_9 _let_1))))))
% 0.51/0.84 (assert (forall ((A_9 (-> tptp.pname Bool)) (X_12 tptp.pname)) (let ((_let_1 (@ (@ tptp.insert_pname X_12) tptp.bot_bot_pname_o))) (=> (@ (@ tptp.ord_less_eq_pname_o A_9) _let_1) (or (= A_9 tptp.bot_bot_pname_o) (= A_9 _let_1))))))
% 0.51/0.84 (assert (forall ((A_9 (-> tptp.x_a Bool)) (X_12 tptp.x_a)) (let ((_let_1 (@ (@ tptp.insert_a X_12) tptp.bot_bot_a_o))) (=> (@ (@ tptp.ord_less_eq_a_o A_9) _let_1) (or (= A_9 tptp.bot_bot_a_o) (= A_9 _let_1))))))
% 0.51/0.84 (assert (forall ((C_6 tptp.x_a) (X_11 tptp.pname) (A_8 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_11) A_8) (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_6)) A_8) (@ (@ tptp.insert_a C_6) tptp.bot_bot_a_o)))))
% 0.51/0.84 (assert (forall ((C_5 tptp.x_a) (A_7 (-> tptp.pname Bool))) (let ((_let_1 (= A_7 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_5)) A_7) tptp.bot_bot_a_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_5)) A_7) (@ (@ tptp.insert_a C_5) tptp.bot_bot_a_o)))))))
% 0.51/0.84 (assert (forall ((X_10 tptp.nat) (Y_9 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X_10) Y_9)) (@ (@ tptp.ord_less_eq_nat Y_9) X_10))))
% 0.51/0.84 (assert (forall ((Z_2 Bool) (Y_8 Bool) (X_9 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o Z_2))) (=> (@ (@ tptp.ord_less_eq_o Y_8) X_9) (=> (@ _let_1 Y_8) (@ _let_1 X_9))))))
% 0.51/0.84 (assert (forall ((Z_2 (-> tptp.nat Bool)) (Y_8 (-> tptp.nat Bool)) (X_9 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o Z_2))) (=> (@ (@ tptp.ord_less_eq_nat_o Y_8) X_9) (=> (@ _let_1 Y_8) (@ _let_1 X_9))))))
% 0.51/0.84 (assert (forall ((Z_2 (-> tptp.pname Bool)) (Y_8 (-> tptp.pname Bool)) (X_9 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o Z_2))) (=> (@ (@ tptp.ord_less_eq_pname_o Y_8) X_9) (=> (@ _let_1 Y_8) (@ _let_1 X_9))))))
% 0.51/0.84 (assert (forall ((Z_2 tptp.nat) (Y_8 tptp.nat) (X_9 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z_2))) (=> (@ (@ tptp.ord_less_eq_nat Y_8) X_9) (=> (@ _let_1 Y_8) (@ _let_1 X_9))))))
% 0.51/0.84 (assert (forall ((Z_2 (-> tptp.x_a Bool)) (Y_8 (-> tptp.x_a Bool)) (X_9 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o Z_2))) (=> (@ (@ tptp.ord_less_eq_a_o Y_8) X_9) (=> (@ _let_1 Y_8) (@ _let_1 X_9))))))
% 0.51/0.84 (assert (forall ((Y_7 Bool) (X_8 Bool)) (=> (@ (@ tptp.ord_less_eq_o Y_7) X_8) (=> (@ (@ tptp.ord_less_eq_o X_8) Y_7) (= X_8 Y_7)))))
% 0.51/0.84 (assert (forall ((Y_7 (-> tptp.nat Bool)) (X_8 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o Y_7) X_8) (=> (@ (@ tptp.ord_less_eq_nat_o X_8) Y_7) (= X_8 Y_7)))))
% 0.51/0.84 (assert (forall ((Y_7 (-> tptp.pname Bool)) (X_8 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o Y_7) X_8) (=> (@ (@ tptp.ord_less_eq_pname_o X_8) Y_7) (= X_8 Y_7)))))
% 0.51/0.84 (assert (forall ((Y_7 tptp.nat) (X_8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y_7) X_8) (=> (@ (@ tptp.ord_less_eq_nat X_8) Y_7) (= X_8 Y_7)))))
% 0.51/0.84 (assert (forall ((Y_7 (-> tptp.x_a Bool)) (X_8 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Y_7) X_8) (=> (@ (@ tptp.ord_less_eq_a_o X_8) Y_7) (= X_8 Y_7)))))
% 0.51/0.84 (assert (forall ((Z_1 Bool) (X_7 Bool) (Y_6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o X_7))) (=> (@ _let_1 Y_6) (=> (@ (@ tptp.ord_less_eq_o Y_6) Z_1) (@ _let_1 Z_1))))))
% 0.51/0.84 (assert (forall ((Z_1 (-> tptp.nat Bool)) (X_7 (-> tptp.nat Bool)) (Y_6 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o X_7))) (=> (@ _let_1 Y_6) (=> (@ (@ tptp.ord_less_eq_nat_o Y_6) Z_1) (@ _let_1 Z_1))))))
% 0.51/0.84 (assert (forall ((Z_1 (-> tptp.pname Bool)) (X_7 (-> tptp.pname Bool)) (Y_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o X_7))) (=> (@ _let_1 Y_6) (=> (@ (@ tptp.ord_less_eq_pname_o Y_6) Z_1) (@ _let_1 Z_1))))))
% 0.51/0.84 (assert (forall ((Z_1 tptp.nat) (X_7 tptp.nat) (Y_6 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X_7))) (=> (@ _let_1 Y_6) (=> (@ (@ tptp.ord_less_eq_nat Y_6) Z_1) (@ _let_1 Z_1))))))
% 0.51/0.84 (assert (forall ((Z_1 (-> tptp.x_a Bool)) (X_7 (-> tptp.x_a Bool)) (Y_6 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o X_7))) (=> (@ _let_1 Y_6) (=> (@ (@ tptp.ord_less_eq_a_o Y_6) Z_1) (@ _let_1 Z_1))))))
% 0.51/0.84 (assert (forall ((X_6 Bool) (Y_5 Bool)) (=> (@ (@ tptp.ord_less_eq_o X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_o Y_5) X_6) (= X_6 Y_5)))))
% 0.51/0.84 (assert (forall ((X_6 (-> tptp.nat Bool)) (Y_5 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_nat_o Y_5) X_6) (= X_6 Y_5)))))
% 0.51/0.84 (assert (forall ((X_6 (-> tptp.pname Bool)) (Y_5 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_pname_o Y_5) X_6) (= X_6 Y_5)))))
% 0.51/0.84 (assert (forall ((X_6 tptp.nat) (Y_5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_nat Y_5) X_6) (= X_6 Y_5)))))
% 0.51/0.84 (assert (forall ((X_6 (-> tptp.x_a Bool)) (Y_5 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_a_o Y_5) X_6) (= X_6 Y_5)))))
% 0.51/0.84 (assert (forall ((C_4 Bool) (B_4 Bool) (A_6 Bool)) (=> (@ (@ tptp.ord_less_eq_o B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_o C_4) A_6)))))
% 0.51/0.84 (assert (forall ((C_4 (-> tptp.nat Bool)) (B_4 (-> tptp.nat Bool)) (A_6 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_nat_o C_4) A_6)))))
% 0.51/0.84 (assert (forall ((C_4 (-> tptp.pname Bool)) (B_4 (-> tptp.pname Bool)) (A_6 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_pname_o C_4) A_6)))))
% 0.51/0.84 (assert (forall ((C_4 tptp.nat) (B_4 tptp.nat) (A_6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_nat C_4) A_6)))))
% 0.51/0.84 (assert (forall ((C_4 (-> tptp.x_a Bool)) (B_4 (-> tptp.x_a Bool)) (A_6 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_a_o C_4) A_6)))))
% 0.51/0.84 (assert (forall ((C_3 Bool) (A_5 Bool) (B_3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))))
% 0.51/0.84 (assert (forall ((C_3 (-> tptp.nat Bool)) (A_5 (-> tptp.nat Bool)) (B_3 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))))
% 0.51/0.84 (assert (forall ((C_3 (-> tptp.pname Bool)) (A_5 (-> tptp.pname Bool)) (B_3 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))))
% 0.51/0.84 (assert (forall ((C_3 tptp.nat) (A_5 tptp.nat) (B_3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))))
% 0.51/0.84 (assert (forall ((C_3 (-> tptp.x_a Bool)) (A_5 (-> tptp.x_a Bool)) (B_3 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))))
% 0.51/0.84 (assert (forall ((C_2 Bool) (B_2 Bool) (A_4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))))
% 0.51/0.84 (assert (forall ((C_2 (-> tptp.nat Bool)) (A_4 (-> tptp.nat Bool)) (B_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))))
% 0.51/0.84 (assert (forall ((C_2 (-> tptp.pname Bool)) (A_4 (-> tptp.pname Bool)) (B_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))))
% 0.51/0.84 (assert (forall ((C_2 tptp.nat) (A_4 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))))
% 0.51/0.84 (assert (forall ((C_2 (-> tptp.x_a Bool)) (A_4 (-> tptp.x_a Bool)) (B_2 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))))
% 0.51/0.84 (assert (forall ((C_1 Bool) (B_1 Bool) (A_3 Bool)) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_o B_1) C_1) (@ (@ tptp.ord_less_eq_o A_3) C_1)))))
% 0.51/0.84 (assert (forall ((C_1 (-> tptp.nat Bool)) (A_3 (-> tptp.nat Bool)) (B_1 (-> tptp.nat Bool))) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_nat_o B_1) C_1) (@ (@ tptp.ord_less_eq_nat_o A_3) C_1)))))
% 0.51/0.84 (assert (forall ((C_1 (-> tptp.pname Bool)) (A_3 (-> tptp.pname Bool)) (B_1 (-> tptp.pname Bool))) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_pname_o B_1) C_1) (@ (@ tptp.ord_less_eq_pname_o A_3) C_1)))))
% 0.51/0.84 (assert (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_1 tptp.nat)) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_nat B_1) C_1) (@ (@ tptp.ord_less_eq_nat A_3) C_1)))))
% 0.51/0.84 (assert (forall ((C_1 (-> tptp.x_a Bool)) (A_3 (-> tptp.x_a Bool)) (B_1 (-> tptp.x_a Bool))) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_a_o B_1) C_1) (@ (@ tptp.ord_less_eq_a_o A_3) C_1)))))
% 0.51/0.84 (assert (forall ((Y_4 Bool) (X_5 Bool)) (=> (@ (@ tptp.ord_less_eq_o Y_4) X_5) (= (@ (@ tptp.ord_less_eq_o X_5) Y_4) (= X_5 Y_4)))))
% 0.51/0.84 (assert (forall ((Y_4 (-> tptp.nat Bool)) (X_5 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o Y_4) X_5) (= (@ (@ tptp.ord_less_eq_nat_o X_5) Y_4) (= X_5 Y_4)))))
% 0.51/0.84 (assert (forall ((Y_4 (-> tptp.pname Bool)) (X_5 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o Y_4) X_5) (= (@ (@ tptp.ord_less_eq_pname_o X_5) Y_4) (= X_5 Y_4)))))
% 0.51/0.84 (assert (forall ((Y_4 tptp.nat) (X_5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y_4) X_5) (= (@ (@ tptp.ord_less_eq_nat X_5) Y_4) (= X_5 Y_4)))))
% 0.51/0.84 (assert (forall ((Y_4 (-> tptp.x_a Bool)) (X_5 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Y_4) X_5) (= (@ (@ tptp.ord_less_eq_a_o X_5) Y_4) (= X_5 Y_4)))))
% 0.51/0.84 (assert (forall ((Y_3 Bool) (X_4 Bool)) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_o X_4) Y_3))))
% 0.51/0.84 (assert (forall ((X_4 (-> tptp.nat Bool)) (Y_3 (-> tptp.nat Bool))) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_nat_o X_4) Y_3))))
% 0.51/0.84 (assert (forall ((X_4 (-> tptp.pname Bool)) (Y_3 (-> tptp.pname Bool))) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_pname_o X_4) Y_3))))
% 0.51/0.84 (assert (forall ((X_4 tptp.nat) (Y_3 tptp.nat)) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_nat X_4) Y_3))))
% 0.51/0.84 (assert (forall ((X_4 (-> tptp.x_a Bool)) (Y_3 (-> tptp.x_a Bool))) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_a_o X_4) Y_3))))
% 0.51/0.84 (assert (forall ((Y_2 Bool) (X_3 Bool)) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_o X_3) Y_2) (@ (@ tptp.ord_less_eq_o Y_2) X_3)))))
% 0.51/0.84 (assert (forall ((X_3 (-> tptp.nat Bool)) (Y_2 (-> tptp.nat Bool))) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_nat_o X_3) Y_2) (@ (@ tptp.ord_less_eq_nat_o Y_2) X_3)))))
% 0.51/0.84 (assert (forall ((X_3 (-> tptp.pname Bool)) (Y_2 (-> tptp.pname Bool))) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_pname_o X_3) Y_2) (@ (@ tptp.ord_less_eq_pname_o Y_2) X_3)))))
% 0.51/0.84 (assert (forall ((X_3 tptp.nat) (Y_2 tptp.nat)) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_nat X_3) Y_2) (@ (@ tptp.ord_less_eq_nat Y_2) X_3)))))
% 0.51/0.84 (assert (forall ((X_3 (-> tptp.x_a Bool)) (Y_2 (-> tptp.x_a Bool))) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_a_o X_3) Y_2) (@ (@ tptp.ord_less_eq_a_o Y_2) X_3)))))
% 0.51/0.84 (assert (forall ((X_2 tptp.nat) (Y_1 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X_2) Y_1) (@ (@ tptp.ord_less_eq_nat Y_1) X_2))))
% 0.51/0.84 (assert (forall ((P_2 (-> (-> tptp.nat Bool) Bool)) (A_1 (-> tptp.nat Bool)) (F_3 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_3) (=> (@ (@ tptp.ord_less_eq_nat_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_nat_o) (=> (forall ((A_2 tptp.nat) (F_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_2))) (=> (@ tptp.finite_finite_nat F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_nat A_2) F_2)))))))) (@ P_2 F_3)))))))
% 0.51/0.84 (assert (forall ((P_2 (-> (-> tptp.pname Bool) Bool)) (A_1 (-> tptp.pname Bool)) (F_3 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_3) (=> (@ (@ tptp.ord_less_eq_pname_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_pname_o) (=> (forall ((A_2 tptp.pname) (F_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_2))) (=> (@ tptp.finite_finite_pname F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_pname A_2) F_2)))))))) (@ P_2 F_3)))))))
% 0.51/0.84 (assert (forall ((P_2 (-> (-> tptp.x_a Bool) Bool)) (A_1 (-> tptp.x_a Bool)) (F_3 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_3) (=> (@ (@ tptp.ord_less_eq_a_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_a_o) (=> (forall ((A_2 tptp.x_a) (F_2 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_2))) (=> (@ tptp.finite_finite_a F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_a A_2) F_2)))))))) (@ P_2 F_3)))))))
% 0.51/0.84 (assert (forall ((P_2 (-> (-> (-> tptp.nat Bool) Bool) Bool)) (A_1 (-> (-> tptp.nat Bool) Bool)) (F_3 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_3) (=> (@ (@ tptp.ord_less_eq_nat_o_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_nat_o_o) (=> (forall ((A_2 (-> tptp.nat Bool)) (F_2 (-> (-> tptp.nat Bool) Bool))) (let ((_let_1 (@ tptp.member_nat_o A_2))) (=> (@ tptp.finite_finite_nat_o F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_nat_o A_2) F_2)))))))) (@ P_2 F_3)))))))
% 0.51/0.84 (assert (forall ((P_2 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (A_1 (-> (-> tptp.pname Bool) Bool)) (F_3 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_3) (=> (@ (@ tptp.ord_le1205211808me_o_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_pname_o_o) (=> (forall ((A_2 (-> tptp.pname Bool)) (F_2 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o A_2))) (=> (@ tptp.finite297249702name_o F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_pname_o A_2) F_2)))))))) (@ P_2 F_3)))))))
% 0.51/0.84 (assert (forall ((P_2 (-> (-> (-> tptp.x_a Bool) Bool) Bool)) (A_1 (-> (-> tptp.x_a Bool) Bool)) (F_3 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_3) (=> (@ (@ tptp.ord_less_eq_a_o_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_a_o_o) (=> (forall ((A_2 (-> tptp.x_a Bool)) (F_2 (-> (-> tptp.x_a Bool) Bool))) (let ((_let_1 (@ tptp.member_a_o A_2))) (=> (@ tptp.finite_finite_a_o F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_a_o A_2) F_2)))))))) (@ P_2 F_3)))))))
% 0.51/0.84 (assert (forall ((Pn tptp.pname) (G (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a (@ tptp.mgt_call Pn)))) (=> (@ (@ tptp.p (@ _let_1 G)) (@ (@ tptp.insert_a (@ tptp.mgt (@ tptp.the_com (@ tptp.body Pn)))) tptp.bot_bot_a_o)) (@ (@ tptp.p G) (@ _let_1 tptp.bot_bot_a_o))))))
% 0.51/0.84 (assert (forall ((P_1 (-> (-> (-> tptp.nat Bool) Bool) Bool)) (F_1 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_1) (=> (@ P_1 tptp.bot_bot_nat_o_o) (=> (forall ((X_1 (-> tptp.nat Bool)) (F_2 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_2) (=> (not (@ (@ tptp.member_nat_o X_1) F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_nat_o X_1) F_2)))))) (@ P_1 F_1))))))
% 0.51/0.84 (assert (forall ((P_1 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (F_1 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_1) (=> (@ P_1 tptp.bot_bot_pname_o_o) (=> (forall ((X_1 (-> tptp.pname Bool)) (F_2 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_2) (=> (not (@ (@ tptp.member_pname_o X_1) F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_pname_o X_1) F_2)))))) (@ P_1 F_1))))))
% 0.51/0.84 (assert (forall ((P_1 (-> (-> (-> tptp.x_a Bool) Bool) Bool)) (F_1 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_1) (=> (@ P_1 tptp.bot_bot_a_o_o) (=> (forall ((X_1 (-> tptp.x_a Bool)) (F_2 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_2) (=> (not (@ (@ tptp.member_a_o X_1) F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_a_o X_1) F_2)))))) (@ P_1 F_1))))))
% 0.51/0.84 (assert (forall ((U tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_2) (@ F N_2))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N_2)) U)))))))
% 0.51/0.84 (assert (forall ((Pn tptp.pname)) (=> (@ (@ tptp.member_pname Pn) tptp.u) (@ tptp.wt (@ tptp.the_com (@ tptp.body Pn))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.nat_case_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K) (@ (@ tptp.plus_plus_nat N) K)) (= M N))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) K))))))
% 0.51/0.84 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 0.51/0.84 (assert (forall ((I tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) K))))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M) K_1))))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J_1) K)))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (L tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J_1) L))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K)) I)))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I)) K)))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K)))))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (= (= (@ (@ tptp.minus_minus_nat J_1) I) K) (= J_1 (@ (@ tptp.plus_plus_nat K) I))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) N)) N) M))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J_1)))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) K)))))
% 0.51/0.84 (assert (forall ((J_1 tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J_1) K)) I) (@ (@ tptp.ord_less_eq_nat J_1) (@ (@ tptp.plus_plus_nat I) K)))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J_1)))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (= (@ tptp.suc N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (= (@ tptp.suc N) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J_1) K))) M) (@ (@ tptp.minus_minus_nat (@ tptp.suc J_1)) (@ (@ tptp.plus_plus_nat K) M))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat M) (@ tptp.suc (@ (@ tptp.minus_minus_nat J_1) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ tptp.suc J_1))))))
% 0.51/0.84 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.51/0.84 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 0.51/0.84 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_2 tptp.nat)) (@ (@ tptp.ord_less_nat N_2) K))))))
% 0.51/0.84 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.51/0.84 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J_1)) K) (@ (@ tptp.ord_less_nat I) K))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (L tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_1) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J_1) L))))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J_1) K)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.51/0.84 (assert (forall ((J_1 tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J_1) I)) I))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (J_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J_1)) I))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 0.51/0.84 (assert (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_1) (=> (@ (@ tptp.ord_less_nat J_1) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (not (= M N))))))
% 0.51/0.84 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat J_1) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J_1) N)) K))))
% 0.51/0.84 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.51/0.84 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.51/0.84 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.51/0.84 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ P N) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N) _let_1) (=> (=> (= M N) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N) M) _let_1) _let_1))))))
% 0.51/0.84 (assert (forall ((N_1 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_1) (exists ((M_1 tptp.nat)) (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_1) (@ (@ tptp.ord_less_nat X_1) M_1)))))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I_1 tptp.nat)) (@ (@ tptp.ord_less_nat I_1) N)))) N)))
% 0.51/0.84 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ P K_1) (@ (@ tptp.ord_less_nat K_1) I)))))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_1)))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J_1))))
% 0.51/0.84 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 0.51/0.84 (assert (forall ((X_1 tptp.nat)) (= (@ tptp.ord_less_nat X_1) (@ tptp.ord_less_eq_nat (@ tptp.suc X_1)))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (K tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_1) N_2) (@ (@ tptp.ord_less_nat (@ F M_1)) (@ F N_2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 0.51/0.84 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (=> (@ P J_1) (=> (forall ((I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ P (@ tptp.suc I_1)) (@ P I_1)))) (@ P I))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_1)))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (N_1 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_1) (@ (@ tptp.ord_less_nat X_1) N))) (@ tptp.finite_finite_nat N_1))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (J_1 tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (@ (@ tptp.ord_less_nat (@ F I_1)) (@ F J)))) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J_1))))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (not (= K (@ tptp.suc J)))))))))
% 0.51/0.84 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (not (= K (@ tptp.suc J))))))))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 0.51/0.84 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.51/0.84 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 0.51/0.84 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 0.51/0.84 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.51/0.84 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.51/0.84 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.51/0.84 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.51/0.84 (assert (forall ((Nat_1 tptp.nat)) (not (= (@ tptp.suc Nat_1) tptp.zero_zero_nat))))
% 0.51/0.84 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.51/0.84 (assert (forall ((Nat tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat)))))
% 0.51/0.84 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.51/0.84 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.51/0.84 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.51/0.84 (assert (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (@ (@ tptp.fequal_a X) Y)) (= X Y))))
% 0.51/0.84 (assert (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (= X Y)) (@ (@ tptp.fequal_a X) Y))))
% 0.51/0.84 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (not (@ (@ tptp.fequal_nat X) Y)) (= X Y))))
% 0.51/0.84 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (@ (@ tptp.fequal_nat X) Y))))
% 0.51/0.84 (assert (forall ((X tptp.pname) (Y tptp.pname)) (or (not (@ (@ tptp.fequal_pname X) Y)) (= X Y))))
% 0.51/0.84 (assert (forall ((X tptp.pname) (Y tptp.pname)) (or (not (= X Y)) (@ (@ tptp.fequal_pname X) Y))))
% 0.51/0.84 (assert (forall ((X (-> tptp.x_a Bool)) (Y (-> tptp.x_a Bool))) (or (not (@ (@ tptp.fequal_a_o X) Y)) (= X Y))))
% 0.51/0.84 (assert (forall ((X (-> tptp.x_a Bool)) (Y (-> tptp.x_a Bool))) (or (not (= X Y)) (@ (@ tptp.fequal_a_o X) Y))))
% 0.51/0.84 (assert (forall ((X (-> tptp.nat Bool)) (Y (-> tptp.nat Bool))) (or (not (@ (@ tptp.fequal_nat_o X) Y)) (= X Y))))
% 0.51/0.84 (assert (forall ((X (-> tptp.nat Bool)) (Y (-> tptp.nat Bool))) (or (not (= X Y)) (@ (@ tptp.fequal_nat_o X) Y))))
% 0.51/0.84 (assert (forall ((X (-> tptp.pname Bool)) (Y (-> tptp.pname Bool))) (or (not (@ (@ tptp.fequal_pname_o X) Y)) (= X Y))))
% 0.51/0.84 (assert (forall ((X (-> tptp.pname Bool)) (Y (-> tptp.pname Bool))) (or (not (= X Y)) (@ (@ tptp.fequal_pname_o X) Y))))
% 0.51/0.84 (assert (@ tptp.finite_finite_pname tptp.u))
% 0.51/0.84 (assert (@ (@ tptp.ord_less_eq_a_o tptp.g) (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u)))
% 1.25/1.48 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.na)) (@ tptp.finite_card_a (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u))))
% 1.25/1.48 (assert (= (@ tptp.finite_card_a tptp.g) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u))) (@ tptp.suc tptp.na))))
% 1.25/1.48 (assert (@ (@ tptp.member_pname tptp.pn) tptp.u))
% 1.25/1.48 (assert (not (@ (@ tptp.member_a (@ tptp.mgt_call tptp.pn)) tptp.g)))
% 1.25/1.48 (assert (not (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a (@ tptp.mgt_call tptp.pn)) tptp.g)) (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u))))
% 1.25/1.48 (set-info :filename cvc5---1.0.5_11101)
% 1.25/1.48 (check-sat-assuming ( true ))
% 1.25/1.48 ------- get file name : TPTP file name is SWW473^2
% 1.25/1.48 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11101.smt2...
% 1.25/1.48 --- Run --ho-elim --full-saturate-quant at 10...
% 1.25/1.48 % SZS status Theorem for SWW473^2
% 1.25/1.48 % SZS output start Proof for SWW473^2
% 1.25/1.48 (
% 1.25/1.48 (let ((_let_1 (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u))) (let ((_let_2 (@ tptp.mgt_call tptp.pn))) (let ((_let_3 (not (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a _let_2) tptp.g)) _let_1)))) (let ((_let_4 (@ (@ tptp.member_pname tptp.pn) tptp.u))) (let ((_let_5 (@ tptp.suc tptp.na))) (let ((_let_6 (@ tptp.finite_card_a _let_1))) (let ((_let_7 (@ (@ tptp.ord_less_eq_a_o tptp.g) _let_1))) (let ((_let_8 (forall ((X_19 tptp.x_a) (A_44 (-> tptp.x_a Bool)) (B_18 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a X_19) A_44)) B_18) (and (@ (@ tptp.member_a X_19) B_18) (@ (@ tptp.ord_less_eq_a_o A_44) B_18)))))) (let ((_let_9 (forall ((A_76 (-> tptp.pname Bool)) (B_40 tptp.x_a) (F_19 (-> tptp.pname tptp.x_a)) (X_30 tptp.pname)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_pname X_30) A_76) (@ (@ tptp.member_a B_40) (@ (@ tptp.image_pname_a F_19) A_76))))))) (let ((_let_10 (forall ((BOUND_VARIABLE_26457 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_26458 |u_(-> tptp.pname tptp.x_a)|) (X_30 tptp.pname)) (or (not (ho_130 (ho_186 k_185 X_30) BOUND_VARIABLE_26457)) (ho_126 (ho_183 k_182 (ho_120 BOUND_VARIABLE_26458 X_30)) (ho_406 (ho_405 k_404 BOUND_VARIABLE_26458) BOUND_VARIABLE_26457)))))) (let ((_let_11 (ho_406 (ho_405 k_404 k_465) k_466))) (let ((_let_12 (ho_120 k_465 tptp.pn))) (let ((_let_13 (ho_126 (ho_183 k_182 _let_12) _let_11))) (let ((_let_14 (ho_130 (ho_186 k_185 tptp.pn) k_466))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13))) (let ((_let_17 (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_76 (-> tptp.pname Bool)) (F_19 (-> tptp.pname tptp.x_a)) (X_30 tptp.pname)) (or (not (@ (@ tptp.member_pname X_30) A_76)) (@ (@ tptp.member_a (@ F_19 X_30)) (@ (@ tptp.image_pname_a F_19) A_76)))) _let_10))))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (ho_126 (ho_125 k_329 k_482) _let_11))) (let ((_let_20 (and _let_13 _let_19))) (let ((_let_21 (not _let_13))) (let ((_let_22 (ho_126 (ho_125 k_329 (ho_153 (ho_152 k_412 _let_12) k_482)) _let_11))) (let ((_let_23 (= _let_22 _let_20))) (let ((_let_24 (not _let_20))) (let ((_let_25 (forall ((X_19 tptp.x_a) (BOUND_VARIABLE_27758 |u_(-> tptp.x_a Bool)|) (BOUND_VARIABLE_27757 |u_(-> tptp.x_a Bool)|)) (= (and (ho_126 (ho_183 k_182 X_19) BOUND_VARIABLE_27757) (ho_126 (ho_125 k_329 BOUND_VARIABLE_27758) BOUND_VARIABLE_27757)) (ho_126 (ho_125 k_329 (ho_153 (ho_152 k_412 X_19) BOUND_VARIABLE_27758)) BOUND_VARIABLE_27757))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_8)) (PREPROCESS :args ((= _let_8 _let_25)))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (k_466 k_465 tptp.pn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_10))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_13 _let_18))) (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_20)) :args ((or (not _let_19) _let_20 _let_21))) (EQ_RESOLVE (ASSUME :args (_let_7)) (PREPROCESS :args ((= _let_7 _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_23)) :args ((or _let_22 _let_24 (not _let_23)))) (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 (not _let_22))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_26 :args (_let_12 k_482 _let_11 QUANTIFIERS_INST_E_MATCHING ((ho_126 (ho_125 k_329 (ho_153 (ho_152 k_412 X_19) BOUND_VARIABLE_27758)) BOUND_VARIABLE_27757)))) :args (_let_25)))) _let_26 :args (_let_23 false _let_25)) :args (_let_24 true _let_22 false _let_23)) :args (_let_21 false _let_19 true _let_20)) :args (_let_18 false _let_14 true _let_13)) _let_17 :args (false true _let_16 false _let_10)) :args ((forall ((Ts (-> tptp.x_a Bool)) (G (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Ts) G) (@ (@ tptp.p G) Ts))) (forall ((A_92 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_92) (@ tptp.finite1676163439at_o_o (@ tptp.collect_nat_o_o (lambda ((B_47 (-> (-> tptp.nat Bool) Bool))) (@ (@ tptp.ord_less_eq_nat_o_o B_47) A_92)))))) (forall ((A_92 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_92) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((B_47 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o B_47) A_92)))))) (forall ((A_92 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_92) (@ tptp.finite_finite_a_o_o (@ tptp.collect_a_o_o (lambda ((B_47 (-> (-> tptp.x_a Bool) Bool))) (@ (@ tptp.ord_less_eq_a_o_o B_47) A_92)))))) (forall ((A_92 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_92) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((B_47 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o B_47) A_92)))))) (forall ((A_92 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_92) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((B_47 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o B_47) A_92)))))) (forall ((A_92 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_92) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((B_47 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o B_47) A_92)))))) (forall ((H (-> tptp.pname tptp.nat Bool)) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_pname_nat_o H) F_25)))) (forall ((H (-> tptp.pname tptp.pname Bool)) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o H) F_25)))) (forall ((H (-> tptp.pname tptp.x_a Bool)) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (@ tptp.finite_finite_a_o (@ (@ tptp.image_pname_a_o H) F_25)))) (forall ((H (-> tptp.nat tptp.x_a)) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (@ tptp.finite_finite_a (@ (@ tptp.image_nat_a H) F_25)))) (forall ((H (-> tptp.nat tptp.nat Bool)) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o H) F_25)))) (forall ((H (-> tptp.nat tptp.pname Bool)) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o H) F_25)))) (forall ((H (-> tptp.nat tptp.x_a Bool)) (F_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_25) (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o H) F_25)))) (forall ((H (-> tptp.x_a tptp.pname)) (F_25 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_25) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_pname H) F_25)))) (forall ((H (-> (-> tptp.nat Bool) tptp.pname)) (F_25 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_25) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_pname H) F_25)))) (forall ((H (-> (-> tptp.pname Bool) tptp.pname)) (F_25 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_25) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname H) F_25)))) (forall ((H (-> (-> tptp.x_a Bool) tptp.pname)) (F_25 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_25) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_pname H) F_25)))) (forall ((H (-> tptp.x_a tptp.nat)) (F_25 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_25) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_nat H) F_25)))) (forall ((H (-> (-> tptp.nat Bool) tptp.nat)) (F_25 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_25) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_nat H) F_25)))) (forall ((H (-> (-> tptp.pname Bool) tptp.nat)) (F_25 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_25) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_nat H) F_25)))) (forall ((H (-> (-> tptp.x_a Bool) tptp.nat)) (F_25 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_25) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_nat H) F_25)))) (forall ((H (-> tptp.pname tptp.x_a)) (F_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_25) (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a H) F_25)))) (forall ((A_91 (-> tptp.nat Bool)) (A_90 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_90) (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_91) A_90)))) (forall ((A_91 (-> tptp.pname Bool)) (A_90 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_90) (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_91) A_90)))) (forall ((A_91 (-> tptp.x_a Bool)) (A_90 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_90) (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_91) A_90)))) (forall ((A_91 tptp.pname) (A_90 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_90) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_91) A_90)))) (forall ((A_91 tptp.nat) (A_90 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_90) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_91) A_90)))) (forall ((A_91 tptp.x_a) (A_90 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_90) (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_91) A_90)))) (forall ((F_24 (-> tptp.pname tptp.pname)) (A_89 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_pname_pname F_24) A_89))) (@ tptp.finite_card_pname A_89)))) (forall ((F_24 (-> tptp.x_a tptp.x_a)) (A_89 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_a F_24) A_89))) (@ tptp.finite_card_a A_89)))) (forall ((F_24 (-> (-> tptp.nat Bool) tptp.x_a)) (A_89 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_o_a F_24) A_89))) (@ tptp.finite_card_nat_o A_89)))) (forall ((F_24 (-> (-> tptp.pname Bool) tptp.x_a)) (A_89 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_o_a F_24) A_89))) (@ tptp.finite_card_pname_o A_89)))) (forall ((F_24 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_89 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_o_a F_24) A_89))) (@ tptp.finite_card_a_o A_89)))) (forall ((F_24 (-> tptp.pname tptp.nat)) (A_89 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_nat F_24) A_89))) (@ tptp.finite_card_pname A_89)))) (forall ((F_24 (-> tptp.x_a tptp.nat)) (A_89 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_nat F_24) A_89))) (@ tptp.finite_card_a A_89)))) (forall ((F_24 (-> (-> tptp.nat Bool) tptp.nat)) (A_89 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_nat_o_nat F_24) A_89))) (@ tptp.finite_card_nat_o A_89)))) (forall ((F_24 (-> (-> tptp.pname Bool) tptp.nat)) (A_89 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_o_nat F_24) A_89))) (@ tptp.finite_card_pname_o A_89)))) (forall ((F_24 (-> (-> tptp.x_a Bool) tptp.nat)) (A_89 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_o_nat F_24) A_89))) (@ tptp.finite_card_a_o A_89)))) (forall ((F_24 (-> tptp.x_a tptp.pname)) (A_89 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_a_pname F_24) A_89))) (@ tptp.finite_card_a A_89)))) (forall ((F_24 (-> tptp.nat tptp.pname)) (A_89 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_nat_pname F_24) A_89))) (@ tptp.finite_card_nat A_89)))) (forall ((F_24 (-> tptp.pname tptp.x_a)) (A_89 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_a F_24) A_89))) (@ tptp.finite_card_pname A_89)))) (forall ((A_88 (-> (-> tptp.nat Bool) Bool)) (B_46 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_46) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_88)) (@ tptp.finite_card_nat_o B_46))))) (forall ((A_88 (-> (-> tptp.pname Bool) Bool)) (B_46 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_46) (=> (@ (@ tptp.ord_le1205211808me_o_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_88)) (@ tptp.finite_card_pname_o B_46))))) (forall ((A_88 (-> (-> tptp.x_a Bool) Bool)) (B_46 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_46) (=> (@ (@ tptp.ord_less_eq_a_o_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_88)) (@ tptp.finite_card_a_o B_46))))) (forall ((A_88 (-> tptp.pname Bool)) (B_46 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_46) (=> (@ (@ tptp.ord_less_eq_pname_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_88)) (@ tptp.finite_card_pname B_46))))) (forall ((A_88 (-> tptp.x_a Bool)) (B_46 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_46) (=> (@ (@ tptp.ord_less_eq_a_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_88)) (@ tptp.finite_card_a B_46))))) (forall ((A_88 (-> tptp.nat Bool)) (B_46 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_46) (=> (@ (@ tptp.ord_less_eq_nat_o A_88) B_46) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_88)) (@ tptp.finite_card_nat B_46))))) (forall ((A_87 (-> (-> tptp.nat Bool) Bool)) (B_45 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_45) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o B_45)) (@ tptp.finite_card_nat_o A_87)) (= A_87 B_45))))) (forall ((A_87 (-> (-> tptp.pname Bool) Bool)) (B_45 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_45) (=> (@ (@ tptp.ord_le1205211808me_o_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o B_45)) (@ tptp.finite_card_pname_o A_87)) (= A_87 B_45))))) (forall ((A_87 (-> (-> tptp.x_a Bool) Bool)) (B_45 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_45) (=> (@ (@ tptp.ord_less_eq_a_o_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o B_45)) (@ tptp.finite_card_a_o A_87)) (= A_87 B_45))))) (forall ((A_87 (-> tptp.pname Bool)) (B_45 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_45) (=> (@ (@ tptp.ord_less_eq_pname_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname B_45)) (@ tptp.finite_card_pname A_87)) (= A_87 B_45))))) (forall ((A_87 (-> tptp.x_a Bool)) (B_45 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_45) (=> (@ (@ tptp.ord_less_eq_a_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a B_45)) (@ tptp.finite_card_a A_87)) (= A_87 B_45))))) (forall ((A_87 (-> tptp.nat Bool)) (B_45 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_45) (=> (@ (@ tptp.ord_less_eq_nat_o A_87) B_45) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B_45)) (@ tptp.finite_card_nat A_87)) (= A_87 B_45))))) (forall ((X_33 (-> tptp.nat Bool)) (A_86 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_86)) (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_33) A_86))))) (forall ((X_33 (-> tptp.pname Bool)) (A_86 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_86)) (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_33) A_86))))) (forall ((X_33 (-> tptp.x_a Bool)) (A_86 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_86)) (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_33) A_86))))) (forall ((X_33 tptp.pname) (A_86 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_86)) (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_33) A_86))))) (forall ((X_33 tptp.nat) (A_86 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_86)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_33) A_86))))) (forall ((X_33 tptp.x_a) (A_86 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_86) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_86)) (@ tptp.finite_card_a (@ (@ tptp.insert_a X_33) A_86))))) (forall ((X_32 (-> tptp.nat Bool)) (A_85 (-> (-> tptp.nat Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_nat_o A_85))) (let ((_let_2 (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_nat_o X_32) A_85))) (=> (@ tptp.finite_finite_nat_o A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_32 (-> tptp.pname Bool)) (A_85 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_pname_o A_85))) (let ((_let_2 (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_pname_o X_32) A_85))) (=> (@ tptp.finite297249702name_o A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_32 (-> tptp.x_a Bool)) (A_85 (-> (-> tptp.x_a Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_a_o A_85))) (let ((_let_2 (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_a_o X_32) A_85))) (=> (@ tptp.finite_finite_a_o A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_32 tptp.nat) (A_85 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_card_nat A_85))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_nat X_32) A_85))) (=> (@ tptp.finite_finite_nat A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_32 tptp.pname) (A_85 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.finite_card_pname A_85))) (let ((_let_2 (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_pname X_32) A_85))) (=> (@ tptp.finite_finite_pname A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_32 tptp.x_a) (A_85 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.finite_card_a A_85))) (let ((_let_2 (@ tptp.finite_card_a (@ (@ tptp.insert_a X_32) A_85)))) (let ((_let_3 (@ (@ tptp.member_a X_32) A_85))) (=> (@ tptp.finite_finite_a A_85) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_31 (-> tptp.nat Bool)) (A_84 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_84) (=> (not (@ (@ tptp.member_nat_o X_31) A_84)) (= (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_nat_o A_84)))))) (forall ((X_31 (-> tptp.pname Bool)) (A_84 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_84) (=> (not (@ (@ tptp.member_pname_o X_31) A_84)) (= (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_pname_o A_84)))))) (forall ((X_31 (-> tptp.x_a Bool)) (A_84 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_84) (=> (not (@ (@ tptp.member_a_o X_31) A_84)) (= (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_a_o A_84)))))) (forall ((X_31 tptp.nat) (A_84 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_84) (=> (not (@ (@ tptp.member_nat X_31) A_84)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_nat A_84)))))) (forall ((X_31 tptp.pname) (A_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_84) (=> (not (@ (@ tptp.member_pname X_31) A_84)) (= (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_pname A_84)))))) (forall ((X_31 tptp.x_a) (A_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_84) (=> (not (@ (@ tptp.member_a X_31) A_84)) (= (@ tptp.finite_card_a (@ (@ tptp.insert_a X_31) A_84)) (@ tptp.suc (@ tptp.finite_card_a A_84)))))) (forall ((Q_1 (-> tptp.x_a Bool)) (P_10 (-> tptp.x_a Bool))) (=> (or (@ tptp.finite_finite_a (@ tptp.collect_a P_10)) (@ tptp.finite_finite_a (@ tptp.collect_a Q_1))) (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (@ P_10 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> (-> tptp.nat Bool) Bool)) (P_10 (-> (-> tptp.nat Bool) Bool))) (=> (or (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_10)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q_1))) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (@ P_10 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> (-> tptp.pname Bool) Bool)) (P_10 (-> (-> tptp.pname Bool) Bool))) (=> (or (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_10)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_1))) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (@ P_10 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> (-> tptp.x_a Bool) Bool)) (P_10 (-> (-> tptp.x_a Bool) Bool))) (=> (or (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_10)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q_1))) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (@ P_10 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> tptp.pname Bool)) (P_10 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_10)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_1))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (@ P_10 X_1) (@ Q_1 X_1))))))) (forall ((Q_1 (-> tptp.nat Bool)) (P_10 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P_10)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_1))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (@ P_10 X_1) (@ Q_1 X_1))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_2) K))))) (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I_1) N)))) (@ tptp.suc N))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))) (forall ((Nat_2 tptp.nat) (Nat tptp.nat)) (= (= (@ tptp.suc Nat_2) (@ tptp.suc Nat)) (= Nat_2 Nat))) (forall ((N tptp.nat)) (not (= (@ tptp.suc N) N))) (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_nat J_1) K) (@ _let_1 K))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (forall ((I tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J_1)))) (forall ((P_9 (-> tptp.x_a Bool)) (Q (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_a (@ tptp.collect_a P_9)) (@ tptp.finite_finite_a (@ tptp.collect_a Q))))) (forall ((P_9 (-> (-> tptp.nat Bool) Bool)) (Q (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_9)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q))))) (forall ((P_9 (-> (-> tptp.pname Bool) Bool)) (Q (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_9)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q))))) (forall ((P_9 (-> (-> tptp.x_a Bool) Bool)) (Q (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_9)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q))))) (forall ((P_9 (-> tptp.pname Bool)) (Q (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_9)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q))))) (forall ((P_9 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (or (@ P_9 X_1) (@ Q X_1))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P_9)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))) (forall ((A_83 (-> tptp.nat Bool)) (A_82 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_83) A_82)) (@ tptp.finite_finite_nat_o A_82))) (forall ((A_83 (-> tptp.pname Bool)) (A_82 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_83) A_82)) (@ tptp.finite297249702name_o A_82))) (forall ((A_83 (-> tptp.x_a Bool)) (A_82 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_83) A_82)) (@ tptp.finite_finite_a_o A_82))) (forall ((A_83 tptp.pname) (A_82 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_83) A_82)) (@ tptp.finite_finite_pname A_82))) (forall ((A_83 tptp.nat) (A_82 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_83) A_82)) (@ tptp.finite_finite_nat A_82))) (forall ((A_83 tptp.x_a) (A_82 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_83) A_82)) (@ tptp.finite_finite_a A_82))) (forall ((A_81 (-> (-> tptp.nat Bool) Bool)) (B_44 (-> (-> tptp.nat Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_81) B_44) (=> (@ tptp.finite_finite_nat_o B_44) (@ tptp.finite_finite_nat_o A_81)))) (forall ((A_81 (-> (-> tptp.pname Bool) Bool)) (B_44 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_81) B_44) (=> (@ tptp.finite297249702name_o B_44) (@ tptp.finite297249702name_o A_81)))) (forall ((A_81 (-> (-> tptp.x_a Bool) Bool)) (B_44 (-> (-> tptp.x_a Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_a_o_o A_81) B_44) (=> (@ tptp.finite_finite_a_o B_44) (@ tptp.finite_finite_a_o A_81)))) (forall ((A_81 (-> tptp.x_a Bool)) (B_44 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_81) B_44) (=> (@ tptp.finite_finite_a B_44) (@ tptp.finite_finite_a A_81)))) (forall ((A_81 (-> tptp.pname Bool)) (B_44 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_81) B_44) (=> (@ tptp.finite_finite_pname B_44) (@ tptp.finite_finite_pname A_81)))) (forall ((A_81 (-> tptp.nat Bool)) (B_44 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_81) B_44) (=> (@ tptp.finite_finite_nat B_44) (@ tptp.finite_finite_nat A_81)))) (forall ((A_80 (-> (-> tptp.nat Bool) Bool)) (B_43 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_43) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_80) B_43) (@ tptp.finite_finite_nat_o A_80)))) (forall ((A_80 (-> (-> tptp.pname Bool) Bool)) (B_43 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_43) (=> (@ (@ tptp.ord_le1205211808me_o_o A_80) B_43) (@ tptp.finite297249702name_o A_80)))) (forall ((A_80 (-> (-> tptp.x_a Bool) Bool)) (B_43 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_43) (=> (@ (@ tptp.ord_less_eq_a_o_o A_80) B_43) (@ tptp.finite_finite_a_o A_80)))) (forall ((A_80 (-> tptp.x_a Bool)) (B_43 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_43) (=> (@ (@ tptp.ord_less_eq_a_o A_80) B_43) (@ tptp.finite_finite_a A_80)))) (forall ((A_80 (-> tptp.pname Bool)) (B_43 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_43) (=> (@ (@ tptp.ord_less_eq_pname_o A_80) B_43) (@ tptp.finite_finite_pname A_80)))) (forall ((A_80 (-> tptp.nat Bool)) (B_43 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_43) (=> (@ (@ tptp.ord_less_eq_nat_o A_80) B_43) (@ tptp.finite_finite_nat A_80)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))) (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)) (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> tptp.x_a tptp.x_a)) (A_79 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_a_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))) (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> (-> tptp.nat Bool) tptp.x_a)) (A_79 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_nat_o_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))) (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> (-> tptp.pname Bool) tptp.x_a)) (A_79 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_pname_o_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))) (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_79 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_a_o_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))) (forall ((B_42 (-> (-> tptp.nat Bool) Bool)) (F_23 (-> tptp.pname tptp.nat Bool)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_42) (@ (@ tptp.image_pname_nat_o F_23) A_79)) (@ tptp.finite_finite_nat_o B_42)))) (forall ((B_42 (-> (-> tptp.pname Bool) Bool)) (F_23 (-> tptp.pname tptp.pname Bool)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_le1205211808me_o_o B_42) (@ (@ tptp.image_pname_pname_o F_23) A_79)) (@ tptp.finite297249702name_o B_42)))) (forall ((B_42 (-> (-> tptp.x_a Bool) Bool)) (F_23 (-> tptp.pname tptp.x_a Bool)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_a_o_o B_42) (@ (@ tptp.image_pname_a_o F_23) A_79)) (@ tptp.finite_finite_a_o B_42)))) (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> tptp.pname tptp.pname)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_pname_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))) (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> tptp.pname tptp.nat)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_pname_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))) (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> tptp.nat tptp.x_a)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_nat_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))) (forall ((B_42 (-> (-> tptp.nat Bool) Bool)) (F_23 (-> tptp.nat tptp.nat Bool)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_42) (@ (@ tptp.image_nat_nat_o F_23) A_79)) (@ tptp.finite_finite_nat_o B_42)))) (forall ((B_42 (-> (-> tptp.pname Bool) Bool)) (F_23 (-> tptp.nat tptp.pname Bool)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_le1205211808me_o_o B_42) (@ (@ tptp.image_nat_pname_o F_23) A_79)) (@ tptp.finite297249702name_o B_42)))) (forall ((B_42 (-> (-> tptp.x_a Bool) Bool)) (F_23 (-> tptp.nat tptp.x_a Bool)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_a_o_o B_42) (@ (@ tptp.image_nat_a_o F_23) A_79)) (@ tptp.finite_finite_a_o B_42)))) (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> tptp.nat tptp.pname)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_nat_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))) (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> tptp.nat tptp.nat)) (A_79 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_nat_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))) (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> tptp.x_a tptp.pname)) (A_79 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_a_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))) (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> (-> tptp.nat Bool) tptp.pname)) (A_79 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_79) (=> (@ (@ tptp.ord_less_eq_pname_o B_42) (@ (@ tptp.image_nat_o_pname F_23) A_79)) (@ tptp.finite_finite_pname B_42)))) (forall ((B_42 (-> tptp.pname Bool)) (F_23 (-> (-> tptp.pname 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((B_42 (-> tptp.nat Bool)) (F_23 (-> (-> tptp.pname Bool) tptp.nat)) (A_79 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_pname_o_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))) (forall ((B_42 (-> tptp.nat Bool)) (F_23 (-> (-> tptp.x_a Bool) tptp.nat)) (A_79 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_79) (=> (@ (@ tptp.ord_less_eq_nat_o B_42) (@ (@ tptp.image_a_o_nat F_23) A_79)) (@ tptp.finite_finite_nat B_42)))) (forall ((B_42 (-> tptp.x_a Bool)) (F_23 (-> tptp.pname tptp.x_a)) (A_79 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_79) (=> (@ (@ tptp.ord_less_eq_a_o B_42) (@ (@ tptp.image_pname_a F_23) A_79)) (@ tptp.finite_finite_a B_42)))) (forall ((F_22 (-> (-> tptp.nat Bool) tptp.x_a)) (A_78 (-> (-> tptp.nat Bool) Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_nat_o_a F_22) A_78)) (exists ((C_12 (-> (-> tptp.nat Bool) Bool))) (and (@ (@ tptp.ord_less_eq_nat_o_o C_12) A_78) (@ tptp.finite_finite_nat_o C_12) (= B_41 (@ (@ tptp.image_nat_o_a F_22) C_12))))))) (forall ((F_22 (-> (-> tptp.pname Bool) tptp.x_a)) (A_78 (-> (-> tptp.pname Bool) Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_pname_o_a F_22) A_78)) (exists ((C_12 (-> (-> tptp.pname Bool) Bool))) (and (@ (@ tptp.ord_le1205211808me_o_o C_12) A_78) (@ tptp.finite297249702name_o C_12) (= B_41 (@ (@ tptp.image_pname_o_a F_22) C_12))))))) (forall ((F_22 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_78 (-> (-> tptp.x_a Bool) Bool)) (B_41 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_41) (=> (@ (@ tptp.ord_less_eq_a_o B_41) (@ (@ tptp.image_a_o_a F_22) A_78)) (exists ((C_12 (-> (-> tptp.x_a Bool) Bool))) (and (@ (@ tptp.ord_less_eq_a_o_o C_12) A_78) (@ tptp.finite_finite_a_o C_12) (= B_41 (@ (@ tptp.image_a_o_a F_22) C_12))))))) (forall ((F_22 (-> 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(=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))) (forall ((F_20 (-> tptp.pname tptp.x_a Bool)) (A_77 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_pname_a_o F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))) (forall ((F_20 (-> tptp.x_a tptp.x_a)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_a_a F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))) (forall ((F_20 (-> tptp.x_a tptp.nat Bool)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite_finite_nat_o (@ (@ tptp.image_a_nat_o F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))) (forall ((F_20 (-> tptp.x_a tptp.pname Bool)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite297249702name_o (@ (@ tptp.image_a_pname_o F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))) (forall ((F_20 (-> tptp.x_a tptp.x_a Bool)) (A_77 (-> tptp.x_a Bool))) (=> (not (@ tptp.finite_finite_a A_77)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_a_a_o F_20) A_77)) (exists ((X_1 tptp.x_a)) (and (@ (@ tptp.member_a X_1) A_77) (not (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((A_2 tptp.x_a)) (and (@ (@ tptp.member_a A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))) (forall ((F_20 (-> tptp.pname tptp.x_a)) (A_77 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_77)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a F_20) A_77)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_77) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_2 tptp.pname)) (and (@ (@ tptp.member_pname A_2) A_77) (= (@ F_20 A_2) (@ F_20 X_1)))))))))))) (forall ((A_76 (-> tptp.pname Bool)) (B_40 tptp.nat) (F_19 (-> tptp.pname tptp.nat)) (X_30 tptp.pname)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_pname X_30) A_76) (@ (@ tptp.member_nat B_40) (@ (@ tptp.image_pname_nat F_19) A_76))))) (forall ((A_76 (-> tptp.x_a Bool)) (B_40 tptp.nat) (F_19 (-> tptp.x_a tptp.nat)) (X_30 tptp.x_a)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_a X_30) A_76) (@ (@ tptp.member_nat B_40) (@ (@ tptp.image_a_nat F_19) A_76))))) (forall ((A_76 (-> tptp.nat Bool)) (B_40 tptp.pname) (F_19 (-> tptp.nat tptp.pname)) (X_30 tptp.nat)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_nat X_30) A_76) (@ (@ tptp.member_pname B_40) (@ (@ tptp.image_nat_pname F_19) A_76))))) (forall ((A_76 (-> tptp.nat Bool)) (B_40 tptp.x_a) (F_19 (-> tptp.nat tptp.x_a)) (X_30 tptp.nat)) (=> (= B_40 (@ F_19 X_30)) (=> (@ (@ tptp.member_nat X_30) A_76) (@ (@ tptp.member_a B_40) (@ (@ tptp.image_nat_a F_19) A_76))))) _let_9 (forall ((A_75 (-> tptp.pname Bool)) (B_39 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_75) B_39) (=> (@ (@ tptp.ord_less_eq_pname_o B_39) A_75) (= A_75 B_39)))) (forall ((A_75 (-> tptp.nat Bool)) (B_39 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_75) B_39) (=> (@ (@ tptp.ord_less_eq_nat_o B_39) A_75) (= A_75 B_39)))) (forall ((A_75 (-> tptp.x_a Bool)) (B_39 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_75) B_39) (=> (@ (@ tptp.ord_less_eq_a_o B_39) A_75) (= A_75 B_39)))) (forall ((C_11 tptp.nat) (A_74 (-> tptp.nat Bool)) (B_38 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_11))) (=> (@ (@ tptp.ord_less_eq_nat_o A_74) B_38) (=> (@ _let_1 A_74) (@ _let_1 B_38))))) (forall ((C_11 tptp.pname) (A_74 (-> tptp.pname Bool)) (B_38 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_11))) (=> (@ (@ tptp.ord_less_eq_pname_o A_74) B_38) (=> (@ _let_1 A_74) (@ _let_1 B_38))))) (forall ((C_11 tptp.x_a) (A_74 (-> tptp.x_a Bool)) (B_38 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_11))) (=> (@ (@ tptp.ord_less_eq_a_o A_74) B_38) (=> (@ _let_1 A_74) (@ _let_1 B_38))))) (forall ((B_37 tptp.nat) (A_73 tptp.nat) (B_36 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_73))) (=> (=> (not (@ _let_1 B_36)) (= A_73 B_37)) (@ _let_1 (@ (@ tptp.insert_nat B_37) B_36))))) (forall ((B_37 tptp.pname) (A_73 tptp.pname) (B_36 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_73))) (=> (=> (not (@ _let_1 B_36)) (= A_73 B_37)) (@ _let_1 (@ (@ tptp.insert_pname B_37) B_36))))) (forall ((B_37 tptp.x_a) (A_73 tptp.x_a) (B_36 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_73))) (=> (=> (not (@ _let_1 B_36)) (= A_73 B_37)) (@ _let_1 (@ (@ tptp.insert_a B_37) B_36))))) (forall ((A_72 tptp.nat) (B_35 tptp.nat) (A_71 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_72))) (=> (@ _let_1 (@ (@ tptp.insert_nat B_35) A_71)) (=> (not (= A_72 B_35)) (@ _let_1 A_71))))) (forall ((A_72 tptp.pname) (B_35 tptp.pname) (A_71 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_72))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_35) A_71)) (=> (not (= A_72 B_35)) (@ _let_1 A_71))))) (forall ((A_72 tptp.x_a) (B_35 tptp.x_a) (A_71 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_72))) (=> (@ _let_1 (@ (@ tptp.insert_a B_35) A_71)) (=> 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tptp.pname) (A_63 (-> tptp.pname Bool)) (X_27 tptp.pname)) (= (@ (@ (@ tptp.insert_pname Y_11) A_63) X_27) (or (= Y_11 X_27) (@ A_63 X_27)))) (forall ((Y_11 tptp.nat) (A_63 (-> tptp.nat Bool)) (X_27 tptp.nat)) (= (@ (@ (@ tptp.insert_nat Y_11) A_63) X_27) (or (= Y_11 X_27) (@ A_63 X_27)))) (forall ((Y_11 tptp.x_a) (A_63 (-> tptp.x_a Bool)) (X_27 tptp.x_a)) (= (@ (@ (@ tptp.insert_a Y_11) A_63) X_27) (or (= Y_11 X_27) (@ A_63 X_27)))) (forall ((B_31 (-> tptp.nat Bool)) (X_26 tptp.nat) (A_62 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_26))) (let ((_let_2 (@ tptp.member_nat X_26))) (=> (not (@ _let_2 A_62)) (=> (not (@ _let_2 B_31)) (= (= (@ _let_1 A_62) (@ _let_1 B_31)) (= A_62 B_31))))))) (forall ((B_31 (-> tptp.pname Bool)) (X_26 tptp.pname) (A_62 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_26))) (let ((_let_2 (@ tptp.member_pname X_26))) (=> (not (@ _let_2 A_62)) (=> (not (@ _let_2 B_31)) (= (= (@ _let_1 A_62) (@ _let_1 B_31)) (= A_62 B_31))))))) (forall ((B_31 (-> tptp.x_a Bool)) (X_26 tptp.x_a) (A_62 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_26))) (let ((_let_2 (@ tptp.member_a X_26))) (=> (not (@ _let_2 A_62)) (=> (not (@ _let_2 B_31)) (= (= (@ _let_1 A_62) (@ _let_1 B_31)) (= A_62 B_31))))))) (forall ((B_30 tptp.nat) (A_61 tptp.nat) (B_29 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_61))) (=> (@ _let_1 B_29) (@ _let_1 (@ (@ tptp.insert_nat B_30) B_29))))) (forall ((B_30 tptp.pname) (A_61 tptp.pname) (B_29 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_61))) (=> (@ _let_1 B_29) (@ _let_1 (@ (@ tptp.insert_pname B_30) B_29))))) (forall ((B_30 tptp.x_a) (A_61 tptp.x_a) (B_29 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_61))) (=> (@ _let_1 B_29) (@ _let_1 (@ (@ tptp.insert_a B_30) B_29))))) (forall ((A_60 tptp.nat) (A_59 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat A_60) A_59) (= (@ (@ tptp.insert_nat A_60) A_59) A_59))) (forall ((A_60 tptp.pname) (A_59 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_60) A_59) (= (@ (@ tptp.insert_pname A_60) A_59) A_59))) (forall ((A_60 tptp.x_a) (A_59 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a A_60) A_59) (= (@ (@ tptp.insert_a A_60) A_59) A_59))) (forall ((A_58 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o A_58) A_58)) (forall ((A_58 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o A_58) A_58)) (forall ((A_58 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o A_58) A_58)) (forall ((A_57 (-> tptp.pname Bool)) (B_28 (-> tptp.pname Bool))) (= (= A_57 B_28) (and (@ (@ tptp.ord_less_eq_pname_o A_57) B_28) (@ (@ tptp.ord_less_eq_pname_o B_28) A_57)))) (forall ((A_57 (-> tptp.nat Bool)) (B_28 (-> tptp.nat Bool))) (= (= A_57 B_28) (and (@ (@ tptp.ord_less_eq_nat_o A_57) B_28) (@ (@ tptp.ord_less_eq_nat_o B_28) A_57)))) (forall ((A_57 (-> tptp.x_a Bool)) (B_28 (-> tptp.x_a Bool))) (= (= A_57 B_28) (and (@ (@ tptp.ord_less_eq_a_o A_57) B_28) (@ (@ tptp.ord_less_eq_a_o B_28) A_57)))) (forall ((A_56 (-> tptp.pname Bool)) (B_27 (-> tptp.pname Bool))) (=> (= A_56 B_27) (@ (@ tptp.ord_less_eq_pname_o A_56) B_27))) (forall ((A_56 (-> tptp.nat Bool)) (B_27 (-> tptp.nat Bool))) (=> (= A_56 B_27) (@ (@ tptp.ord_less_eq_nat_o A_56) B_27))) (forall ((A_56 (-> tptp.x_a Bool)) (B_27 (-> tptp.x_a Bool))) (=> (= A_56 B_27) (@ (@ tptp.ord_less_eq_a_o A_56) B_27))) (forall ((A_55 (-> tptp.pname Bool)) (B_26 (-> tptp.pname Bool))) (=> (= A_55 B_26) (@ (@ tptp.ord_less_eq_pname_o B_26) A_55))) (forall ((A_55 (-> tptp.nat Bool)) (B_26 (-> tptp.nat Bool))) (=> (= A_55 B_26) (@ (@ tptp.ord_less_eq_nat_o B_26) A_55))) (forall ((A_55 (-> tptp.x_a Bool)) (B_26 (-> tptp.x_a Bool))) (=> (= A_55 B_26) (@ (@ tptp.ord_less_eq_a_o B_26) A_55))) (forall ((X_25 tptp.nat) (A_54 (-> tptp.nat Bool)) (B_25 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_25))) (=> (@ (@ tptp.ord_less_eq_nat_o A_54) B_25) (=> (@ _let_1 A_54) (@ _let_1 B_25))))) (forall ((X_25 tptp.pname) (A_54 (-> tptp.pname Bool)) (B_25 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_25))) (=> (@ (@ tptp.ord_less_eq_pname_o A_54) B_25) (=> (@ _let_1 A_54) (@ _let_1 B_25))))) (forall ((X_25 tptp.x_a) (A_54 (-> tptp.x_a Bool)) (B_25 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_25))) (=> (@ (@ tptp.ord_less_eq_a_o A_54) B_25) (=> (@ _let_1 A_54) (@ _let_1 B_25))))) (forall ((B_24 (-> tptp.nat Bool)) (X_24 tptp.nat) (A_53 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_24))) (=> (@ _let_1 A_53) (=> (@ (@ tptp.ord_less_eq_nat_o A_53) B_24) (@ _let_1 B_24))))) (forall ((B_24 (-> tptp.pname Bool)) (X_24 tptp.pname) (A_53 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_24))) (=> (@ _let_1 A_53) (=> (@ (@ tptp.ord_less_eq_pname_o A_53) B_24) (@ _let_1 B_24))))) (forall ((B_24 (-> tptp.x_a Bool)) (X_24 tptp.x_a) (A_53 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_24))) (=> (@ _let_1 A_53) (=> (@ (@ tptp.ord_less_eq_a_o A_53) B_24) (@ _let_1 B_24))))) (forall ((X_23 tptp.nat) (A_52 (-> tptp.nat Bool)) (B_23 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_23))) (=> (@ (@ tptp.ord_less_eq_nat_o A_52) B_23) (=> (@ _let_1 A_52) (@ _let_1 B_23))))) (forall ((X_23 tptp.pname) (A_52 (-> tptp.pname Bool)) (B_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_23))) (=> (@ (@ tptp.ord_less_eq_pname_o A_52) B_23) (=> (@ _let_1 A_52) (@ _let_1 B_23))))) (forall ((X_23 tptp.x_a) (A_52 (-> tptp.x_a Bool)) (B_23 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_23))) (=> (@ (@ tptp.ord_less_eq_a_o A_52) B_23) (=> (@ _let_1 A_52) (@ _let_1 B_23))))) (forall ((X_22 tptp.nat) (A_51 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X_22) A_51) (@ A_51 X_22))) (forall ((X_22 tptp.pname) (A_51 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_22) A_51) (@ A_51 X_22))) (forall ((X_22 tptp.x_a) (A_51 (-> tptp.x_a Bool))) (= (@ (@ tptp.member_a X_22) A_51) (@ A_51 X_22))) (forall ((P_7 (-> tptp.x_a Bool))) (= (@ tptp.collect_a P_7) P_7)) (forall ((P_7 (-> tptp.pname Bool))) (= (@ tptp.collect_pname P_7) P_7)) (forall ((P_7 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.collect_nat_o P_7) P_7)) (forall ((P_7 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.collect_pname_o P_7) P_7)) (forall ((P_7 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.collect_a_o P_7) P_7)) (forall ((P_7 (-> tptp.nat Bool))) (= (@ tptp.collect_nat P_7) P_7)) (forall ((C_10 (-> tptp.pname Bool)) (A_50 (-> tptp.pname Bool)) (B_22 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_50))) (=> (@ _let_1 B_22) (=> (@ (@ tptp.ord_less_eq_pname_o B_22) C_10) (@ _let_1 C_10))))) (forall ((C_10 (-> tptp.nat Bool)) (A_50 (-> tptp.nat Bool)) (B_22 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_50))) (=> (@ _let_1 B_22) (=> (@ (@ tptp.ord_less_eq_nat_o B_22) C_10) (@ _let_1 C_10))))) (forall ((C_10 (-> tptp.x_a Bool)) (A_50 (-> tptp.x_a Bool)) (B_22 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_50))) (=> (@ _let_1 B_22) (=> (@ (@ tptp.ord_less_eq_a_o B_22) C_10) (@ _let_1 C_10))))) (forall ((A_49 (-> tptp.pname Bool)) (B_21 (-> tptp.pname Bool))) (=> (= A_49 B_21) (not (=> (@ (@ tptp.ord_less_eq_pname_o A_49) B_21) (not (@ (@ tptp.ord_less_eq_pname_o B_21) A_49)))))) (forall ((A_49 (-> tptp.nat Bool)) (B_21 (-> tptp.nat Bool))) (=> (= A_49 B_21) (not (=> (@ (@ tptp.ord_less_eq_nat_o A_49) B_21) (not (@ (@ tptp.ord_less_eq_nat_o B_21) A_49)))))) (forall ((A_49 (-> tptp.x_a Bool)) (B_21 (-> tptp.x_a Bool))) (=> (= A_49 B_21) (not (=> (@ (@ tptp.ord_less_eq_a_o A_49) B_21) (not (@ (@ tptp.ord_less_eq_a_o B_21) A_49)))))) (forall ((Z_3 tptp.x_a) (F_18 (-> tptp.pname tptp.x_a)) (A_48 (-> tptp.pname Bool))) (= (@ (@ tptp.member_a Z_3) (@ (@ tptp.image_pname_a F_18) A_48)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_48) (= Z_3 (@ F_18 X_1)))))) (forall ((F_17 (-> tptp.pname tptp.nat)) (X_21 tptp.pname) (A_47 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_21) A_47) (@ (@ tptp.member_nat (@ F_17 X_21)) (@ (@ tptp.image_pname_nat F_17) A_47)))) (forall ((F_17 (-> tptp.x_a tptp.nat)) (X_21 tptp.x_a) (A_47 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a X_21) A_47) (@ (@ tptp.member_nat (@ F_17 X_21)) (@ (@ tptp.image_a_nat F_17) A_47)))) (forall ((F_17 (-> tptp.nat tptp.pname)) (X_21 tptp.nat) (A_47 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_21) A_47) (@ (@ tptp.member_pname (@ F_17 X_21)) (@ (@ tptp.image_nat_pname F_17) A_47)))) (forall ((F_17 (-> tptp.nat tptp.x_a)) (X_21 tptp.nat) (A_47 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_21) A_47) (@ (@ tptp.member_a (@ F_17 X_21)) (@ (@ tptp.image_nat_a F_17) A_47)))) (forall ((F_17 (-> tptp.pname tptp.x_a)) (X_21 tptp.pname) (A_47 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_21) A_47) (@ (@ tptp.member_a (@ F_17 X_21)) (@ (@ tptp.image_pname_a F_17) A_47)))) (forall ((B_20 tptp.nat) (F_16 (-> tptp.pname tptp.nat)) (X_20 tptp.pname) (A_46 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_nat B_20) (@ (@ tptp.image_pname_nat F_16) A_46))))) (forall ((B_20 tptp.nat) (F_16 (-> tptp.x_a tptp.nat)) (X_20 tptp.x_a) (A_46 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_nat B_20) (@ (@ tptp.image_a_nat F_16) A_46))))) (forall ((B_20 tptp.pname) (F_16 (-> tptp.nat tptp.pname)) (X_20 tptp.nat) (A_46 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_pname B_20) (@ (@ tptp.image_nat_pname F_16) A_46))))) (forall ((B_20 tptp.x_a) (F_16 (-> tptp.nat tptp.x_a)) (X_20 tptp.nat) (A_46 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_a B_20) (@ (@ tptp.image_nat_a F_16) A_46))))) (forall ((B_20 tptp.x_a) (F_16 (-> tptp.pname tptp.x_a)) (X_20 tptp.pname) (A_46 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_20) A_46) (=> (= B_20 (@ F_16 X_20)) (@ (@ tptp.member_a B_20) (@ (@ tptp.image_pname_a F_16) A_46))))) (forall ((X_1 (-> tptp.nat Bool)) (Xa (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o X_1) Xa) (@ tptp.collect_nat_o (lambda ((Y_10 (-> tptp.nat Bool))) (or (= Y_10 X_1) (@ (@ tptp.member_nat_o Y_10) Xa)))))) (forall ((X_1 (-> tptp.pname Bool)) (Xa (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o X_1) Xa) (@ tptp.collect_pname_o (lambda ((Y_10 (-> tptp.pname Bool))) (or (= Y_10 X_1) (@ (@ tptp.member_pname_o Y_10) Xa)))))) (forall ((X_1 (-> tptp.x_a Bool)) (Xa (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o X_1) Xa) (@ tptp.collect_a_o (lambda ((Y_10 (-> tptp.x_a Bool))) (or (= Y_10 X_1) (@ (@ tptp.member_a_o Y_10) Xa)))))) (forall ((X_1 tptp.nat) (Xa (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat X_1) Xa) (@ tptp.collect_nat (lambda ((Y_10 tptp.nat)) (or (= Y_10 X_1) (@ (@ tptp.member_nat Y_10) Xa)))))) (forall ((X_1 tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X_1) Xa) (@ tptp.collect_pname (lambda ((Y_10 tptp.pname)) (or (= Y_10 X_1) (@ (@ tptp.member_pname Y_10) Xa)))))) (forall ((X_1 tptp.x_a) (Xa (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a X_1) Xa) (@ tptp.collect_a (lambda ((Y_10 tptp.x_a)) (or (= Y_10 X_1) (@ (@ tptp.member_a Y_10) Xa)))))) (forall ((B_19 (-> tptp.pname Bool)) (A_45 tptp.pname)) (@ (@ tptp.ord_less_eq_pname_o B_19) (@ (@ tptp.insert_pname A_45) B_19))) (forall ((B_19 (-> tptp.nat Bool)) (A_45 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o B_19) (@ (@ tptp.insert_nat A_45) B_19))) (forall ((B_19 (-> tptp.x_a Bool)) (A_45 tptp.x_a)) (@ (@ tptp.ord_less_eq_a_o B_19) (@ (@ tptp.insert_a A_45) B_19))) (forall ((X_19 tptp.nat) (A_44 (-> tptp.nat Bool)) (B_18 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.insert_nat X_19) A_44)) B_18) (and (@ (@ tptp.member_nat X_19) B_18) (@ (@ tptp.ord_less_eq_nat_o A_44) B_18)))) (forall ((X_19 tptp.pname) (A_44 (-> tptp.pname Bool)) (B_18 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.insert_pname X_19) A_44)) B_18) (and (@ (@ tptp.member_pname X_19) B_18) (@ (@ tptp.ord_less_eq_pname_o A_44) B_18)))) _let_8 (forall ((B_17 (-> tptp.nat Bool)) (X_18 tptp.nat) (A_43 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_43))) (=> (not (@ (@ tptp.member_nat X_18) A_43)) (= (@ _let_1 (@ (@ tptp.insert_nat X_18) B_17)) (@ _let_1 B_17))))) (forall ((B_17 (-> tptp.pname Bool)) (X_18 tptp.pname) (A_43 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_43))) (=> (not (@ (@ tptp.member_pname X_18) A_43)) (= (@ _let_1 (@ (@ tptp.insert_pname X_18) B_17)) (@ _let_1 B_17))))) (forall ((B_17 (-> tptp.x_a Bool)) (X_18 tptp.x_a) (A_43 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_43))) (=> (not (@ (@ tptp.member_a X_18) A_43)) (= (@ _let_1 (@ (@ tptp.insert_a X_18) B_17)) (@ _let_1 B_17))))) (forall ((B_16 tptp.pname) (A_42 (-> tptp.pname Bool)) (B_15 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_42))) (=> (@ _let_1 B_15) (@ _let_1 (@ (@ tptp.insert_pname B_16) B_15))))) (forall ((B_16 tptp.nat) (A_42 (-> tptp.nat Bool)) (B_15 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_42))) (=> (@ _let_1 B_15) (@ _let_1 (@ (@ tptp.insert_nat B_16) B_15))))) (forall ((B_16 tptp.x_a) (A_42 (-> tptp.x_a Bool)) (B_15 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_42))) (=> (@ _let_1 B_15) (@ _let_1 (@ (@ tptp.insert_a B_16) B_15))))) (forall ((A_41 tptp.pname) (C_9 (-> tptp.pname Bool)) (D_1 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_41))) (=> (@ (@ tptp.ord_less_eq_pname_o C_9) D_1) (@ (@ tptp.ord_less_eq_pname_o (@ _let_1 C_9)) (@ _let_1 D_1))))) (forall ((A_41 tptp.nat) (C_9 (-> tptp.nat Bool)) (D_1 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_41))) (=> (@ (@ tptp.ord_less_eq_nat_o C_9) D_1) (@ (@ tptp.ord_less_eq_nat_o (@ _let_1 C_9)) (@ _let_1 D_1))))) (forall ((A_41 tptp.x_a) (C_9 (-> tptp.x_a Bool)) (D_1 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_41))) (=> (@ (@ tptp.ord_less_eq_a_o C_9) D_1) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 C_9)) (@ _let_1 D_1))))) (forall ((F_15 (-> tptp.x_a tptp.pname)) (A_40 tptp.x_a) (B_14 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.image_a_pname F_15))) (= (@ _let_1 (@ (@ tptp.insert_a A_40) B_14)) (@ (@ tptp.insert_pname (@ F_15 A_40)) (@ _let_1 B_14))))) (forall ((F_15 (-> tptp.x_a tptp.nat)) (A_40 tptp.x_a) (B_14 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.image_a_nat F_15))) (= (@ _let_1 (@ (@ tptp.insert_a A_40) B_14)) (@ (@ tptp.insert_nat (@ F_15 A_40)) (@ _let_1 B_14))))) (forall ((F_15 (-> tptp.nat tptp.x_a)) (A_40 tptp.nat) (B_14 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_a F_15))) (= (@ _let_1 (@ (@ tptp.insert_nat A_40) B_14)) (@ (@ tptp.insert_a (@ F_15 A_40)) (@ _let_1 B_14))))) (forall ((F_15 (-> tptp.pname tptp.x_a)) (A_40 tptp.pname) (B_14 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_15))) (= (@ _let_1 (@ (@ tptp.insert_pname A_40) B_14)) (@ (@ tptp.insert_a (@ F_15 A_40)) (@ _let_1 B_14))))) (forall ((F_14 (-> tptp.pname tptp.pname)) (X_17 tptp.pname) (A_39 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_pname F_14) A_39))) (=> (@ (@ tptp.member_pname X_17) A_39) (= (@ (@ tptp.insert_pname (@ F_14 X_17)) _let_1) _let_1)))) (forall ((F_14 (-> tptp.pname tptp.nat)) (X_17 tptp.pname) (A_39 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_nat F_14) A_39))) (=> (@ (@ tptp.member_pname X_17) A_39) (= (@ (@ tptp.insert_nat (@ F_14 X_17)) _let_1) _let_1)))) (forall ((F_14 (-> tptp.x_a tptp.pname)) (X_17 tptp.x_a) (A_39 (-> tptp.x_a Bool))) (let ((_let_1 (@ (@ tptp.image_a_pname F_14) A_39))) (=> (@ (@ tptp.member_a X_17) A_39) (= (@ (@ tptp.insert_pname (@ F_14 X_17)) _let_1) _let_1)))) (forall ((F_14 (-> tptp.x_a tptp.nat)) (X_17 tptp.x_a) (A_39 (-> tptp.x_a Bool))) (let ((_let_1 (@ (@ tptp.image_a_nat F_14) A_39))) (=> (@ (@ tptp.member_a X_17) A_39) (= (@ (@ tptp.insert_nat (@ F_14 X_17)) _let_1) _let_1)))) (forall ((F_14 (-> tptp.nat tptp.x_a)) (X_17 tptp.nat) (A_39 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.image_nat_a F_14) A_39))) (=> (@ (@ tptp.member_nat X_17) A_39) (= (@ (@ tptp.insert_a (@ F_14 X_17)) _let_1) _let_1)))) (forall ((F_14 (-> tptp.pname tptp.x_a)) (X_17 tptp.pname) (A_39 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_a F_14) A_39))) (=> (@ (@ tptp.member_pname X_17) A_39) (= (@ (@ tptp.insert_a (@ F_14 X_17)) _let_1) _let_1)))) (forall ((B_13 (-> tptp.x_a Bool)) (F_13 (-> tptp.nat tptp.x_a)) (A_38 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_a_o B_13) (@ (@ tptp.image_nat_a F_13) A_38)) (exists ((AA (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o AA) A_38) (= B_13 (@ (@ tptp.image_nat_a F_13) AA)))))) (forall ((B_13 (-> tptp.pname Bool)) (F_13 (-> tptp.x_a tptp.pname)) (A_38 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_pname_o B_13) (@ (@ tptp.image_a_pname F_13) A_38)) (exists ((AA (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o AA) A_38) (= B_13 (@ (@ tptp.image_a_pname F_13) AA)))))) (forall ((B_13 (-> tptp.nat Bool)) (F_13 (-> tptp.x_a tptp.nat)) (A_38 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_nat_o B_13) (@ (@ tptp.image_a_nat F_13) A_38)) (exists ((AA (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o AA) A_38) (= B_13 (@ (@ tptp.image_a_nat F_13) AA)))))) (forall ((B_13 (-> tptp.x_a Bool)) (F_13 (-> tptp.pname tptp.x_a)) (A_38 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_a_o B_13) (@ (@ tptp.image_pname_a F_13) A_38)) (exists ((AA (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o AA) A_38) (= B_13 (@ (@ tptp.image_pname_a F_13) AA)))))) (forall ((F_12 (-> tptp.x_a tptp.pname)) (A_37 (-> tptp.x_a Bool)) (B_12 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.image_a_pname F_12))) (=> (@ (@ tptp.ord_less_eq_a_o A_37) B_12) (@ (@ tptp.ord_less_eq_pname_o (@ _let_1 A_37)) (@ _let_1 B_12))))) (forall ((F_12 (-> tptp.x_a tptp.nat)) (A_37 (-> tptp.x_a Bool)) (B_12 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.image_a_nat F_12))) (=> (@ (@ tptp.ord_less_eq_a_o A_37) B_12) (@ (@ tptp.ord_less_eq_nat_o (@ _let_1 A_37)) (@ _let_1 B_12))))) (forall ((F_12 (-> tptp.nat tptp.x_a)) (A_37 (-> tptp.nat Bool)) (B_12 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_a F_12))) (=> (@ (@ tptp.ord_less_eq_nat_o A_37) B_12) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 A_37)) (@ _let_1 B_12))))) (forall ((F_12 (-> tptp.pname tptp.x_a)) (A_37 (-> tptp.pname Bool)) (B_12 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_12))) (=> (@ (@ tptp.ord_less_eq_pname_o A_37) B_12) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 A_37)) (@ _let_1 B_12))))) (forall ((B_11 tptp.pname) (F_11 (-> tptp.nat tptp.pname)) (A_36 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_pname B_11) (@ (@ tptp.image_nat_pname F_11) A_36)) (not (forall ((X_1 tptp.nat)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_nat X_1) A_36))))))) (forall ((B_11 tptp.x_a) (F_11 (-> tptp.nat tptp.x_a)) (A_36 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_a B_11) (@ (@ tptp.image_nat_a F_11) A_36)) (not (forall ((X_1 tptp.nat)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_nat X_1) A_36))))))) (forall ((B_11 tptp.nat) (F_11 (-> tptp.pname tptp.nat)) (A_36 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_nat B_11) (@ (@ tptp.image_pname_nat F_11) A_36)) (not (forall ((X_1 tptp.pname)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_pname X_1) A_36))))))) (forall ((B_11 tptp.nat) (F_11 (-> tptp.x_a tptp.nat)) (A_36 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_nat B_11) (@ (@ tptp.image_a_nat F_11) A_36)) (not (forall ((X_1 tptp.x_a)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_a X_1) A_36))))))) (forall ((B_11 tptp.x_a) (F_11 (-> tptp.pname tptp.x_a)) (A_36 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_a B_11) (@ (@ tptp.image_pname_a F_11) A_36)) (not (forall ((X_1 tptp.pname)) (=> (= B_11 (@ F_11 X_1)) (not (@ (@ tptp.member_pname X_1) A_36))))))) (forall ((B_10 (-> tptp.nat Bool)) (A_35 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X_1))) (=> (@ _let_1 A_35) (@ _let_1 B_10)))) (@ (@ tptp.ord_less_eq_nat_o A_35) B_10))) (forall ((B_10 (-> tptp.pname Bool)) (A_35 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (let ((_let_1 (@ tptp.member_pname X_1))) (=> (@ _let_1 A_35) (@ _let_1 B_10)))) (@ (@ tptp.ord_less_eq_pname_o A_35) B_10))) (forall ((B_10 (-> tptp.x_a Bool)) (A_35 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (let ((_let_1 (@ tptp.member_a X_1))) (=> (@ _let_1 A_35) (@ _let_1 B_10)))) (@ (@ tptp.ord_less_eq_a_o A_35) B_10))) (forall ((F_10 (-> tptp.pname tptp.nat)) (B_9 (-> tptp.nat Bool)) (A_34 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) A_34) (@ (@ tptp.member_nat (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.image_pname_nat F_10) A_34)) B_9))) (forall ((F_10 (-> tptp.pname tptp.pname)) (B_9 (-> tptp.pname Bool)) (A_34 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) A_34) (@ (@ tptp.member_pname (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.image_pname_pname F_10) A_34)) B_9))) (forall ((F_10 (-> tptp.x_a tptp.nat)) (B_9 (-> tptp.nat Bool)) (A_34 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (=> (@ (@ tptp.member_a X_1) A_34) (@ (@ tptp.member_nat (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.image_a_nat F_10) A_34)) B_9))) (forall ((F_10 (-> tptp.x_a tptp.pname)) (B_9 (-> tptp.pname Bool)) (A_34 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (=> (@ (@ tptp.member_a X_1) A_34) (@ (@ tptp.member_pname (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.image_a_pname F_10) A_34)) B_9))) (forall ((F_10 (-> tptp.nat tptp.pname)) (B_9 (-> tptp.pname Bool)) (A_34 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) A_34) (@ (@ tptp.member_pname (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.image_nat_pname F_10) A_34)) B_9))) (forall ((F_10 (-> tptp.nat tptp.x_a)) (B_9 (-> tptp.x_a Bool)) (A_34 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) A_34) (@ (@ tptp.member_a (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.image_nat_a F_10) A_34)) B_9))) (forall ((F_10 (-> tptp.pname tptp.x_a)) (B_9 (-> tptp.x_a Bool)) (A_34 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) A_34) (@ (@ tptp.member_a (@ F_10 X_1)) B_9))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.image_pname_a F_10) A_34)) B_9))) (forall ((X_16 Bool)) (@ (@ tptp.ord_less_eq_o X_16) X_16)) (forall ((X_16 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o X_16) X_16)) (forall ((X_16 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o X_16) X_16)) (forall ((X_16 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o X_16) X_16)) (forall ((X_16 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X_16) X_16)) (forall ((N_1 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_1) (exists ((M_1 tptp.nat)) (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_1) (@ (@ tptp.ord_less_eq_nat X_1) M_1)))))) (forall ((G (-> tptp.x_a Bool)) (C tptp.com)) (=> (@ tptp.wt C) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) tptp.u) (@ (@ tptp.p G) (@ (@ tptp.insert_a (@ tptp.mgt_call X_1)) tptp.bot_bot_a_o)))) (@ (@ tptp.p G) (@ (@ tptp.insert_a (@ tptp.mgt C)) tptp.bot_bot_a_o))))) (forall ((F_9 (-> tptp.pname Bool)) (G_3 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o F_9) G_3) (forall ((X_1 tptp.pname)) (@ (@ tptp.ord_less_eq_o (@ F_9 X_1)) (@ G_3 X_1))))) (forall ((F_9 (-> tptp.nat Bool)) (G_3 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o F_9) G_3) (forall ((X_1 tptp.nat)) (@ (@ tptp.ord_less_eq_o (@ F_9 X_1)) (@ G_3 X_1))))) (forall ((F_9 (-> tptp.x_a Bool)) (G_3 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o F_9) G_3) (forall ((X_1 tptp.x_a)) (@ (@ tptp.ord_less_eq_o (@ F_9 X_1)) (@ G_3 X_1))))) (forall ((X_15 tptp.pname) (F_8 (-> tptp.pname Bool)) (G_2 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o F_8) G_2) (@ (@ tptp.ord_less_eq_o (@ F_8 X_15)) (@ G_2 X_15)))) (forall ((X_15 tptp.nat) (F_8 (-> tptp.nat Bool)) (G_2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o F_8) G_2) (@ (@ tptp.ord_less_eq_o (@ F_8 X_15)) (@ G_2 X_15)))) (forall ((X_15 tptp.x_a) (F_8 (-> tptp.x_a Bool)) (G_2 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o F_8) G_2) (@ (@ tptp.ord_less_eq_o (@ F_8 X_15)) (@ G_2 X_15)))) (forall ((X_14 tptp.pname) (F_7 (-> tptp.pname Bool)) (G_1 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o F_7) G_1) (@ (@ tptp.ord_less_eq_o (@ F_7 X_14)) (@ G_1 X_14)))) (forall ((X_14 tptp.nat) (F_7 (-> tptp.nat Bool)) (G_1 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o F_7) G_1) (@ (@ tptp.ord_less_eq_o (@ F_7 X_14)) (@ G_1 X_14)))) (forall ((X_14 tptp.x_a) (F_7 (-> tptp.x_a Bool)) (G_1 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o F_7) G_1) (@ (@ tptp.ord_less_eq_o (@ F_7 X_14)) (@ G_1 X_14)))) (forall ((A_33 tptp.nat)) (not (@ (@ tptp.member_nat A_33) tptp.bot_bot_nat_o))) (forall ((A_33 tptp.pname)) (not (@ (@ tptp.member_pname A_33) tptp.bot_bot_pname_o))) (forall ((A_33 tptp.x_a)) (not (@ (@ tptp.member_a A_33) tptp.bot_bot_a_o))) (@ tptp.finite_finite_nat_o tptp.bot_bot_nat_o_o) (@ tptp.finite297249702name_o tptp.bot_bot_pname_o_o) (@ tptp.finite_finite_a_o tptp.bot_bot_a_o_o) (@ tptp.finite_finite_a tptp.bot_bot_a_o) (@ tptp.finite_finite_pname tptp.bot_bot_pname_o) (@ tptp.finite_finite_nat tptp.bot_bot_nat_o) (forall ((A_32 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o tptp.bot_bot_pname_o) A_32)) (forall ((A_32 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o tptp.bot_bot_nat_o) A_32)) (forall ((A_32 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o tptp.bot_bot_a_o) A_32)) (forall ((A_31 tptp.nat) (A_30 (-> tptp.nat Bool))) (=> (= A_30 tptp.bot_bot_nat_o) (not (@ (@ tptp.member_nat A_31) A_30)))) (forall ((A_31 tptp.pname) (A_30 (-> tptp.pname Bool))) (=> (= A_30 tptp.bot_bot_pname_o) (not (@ (@ tptp.member_pname A_31) A_30)))) (forall ((A_31 tptp.x_a) (A_30 (-> tptp.x_a Bool))) (=> (= A_30 tptp.bot_bot_a_o) (not (@ (@ tptp.member_a A_31) A_30)))) (forall ((P_6 (-> tptp.pname Bool))) (= (= (@ tptp.collect_pname P_6) tptp.bot_bot_pname_o) (forall ((X_1 tptp.pname)) (not (@ P_6 X_1))))) (forall ((P_6 (-> (-> tptp.nat Bool) Bool))) (= (= (@ tptp.collect_nat_o P_6) tptp.bot_bot_nat_o_o) (forall ((X_1 (-> tptp.nat Bool))) (not (@ P_6 X_1))))) (forall ((P_6 (-> (-> tptp.pname Bool) Bool))) (= (= (@ tptp.collect_pname_o P_6) tptp.bot_bot_pname_o_o) (forall ((X_1 (-> tptp.pname Bool))) (not (@ P_6 X_1))))) (forall ((P_6 (-> (-> tptp.x_a Bool) Bool))) (= (= (@ tptp.collect_a_o P_6) tptp.bot_bot_a_o_o) (forall ((X_1 (-> tptp.x_a Bool))) (not (@ P_6 X_1))))) (forall ((P_6 (-> tptp.x_a Bool))) (= (= (@ tptp.collect_a P_6) tptp.bot_bot_a_o) (forall ((X_1 tptp.x_a)) (not (@ P_6 X_1))))) (forall ((P_6 (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P_6) tptp.bot_bot_nat_o) (forall ((X_1 tptp.nat)) (not (@ P_6 X_1))))) (forall ((C_8 tptp.nat)) (not (@ (@ tptp.member_nat C_8) tptp.bot_bot_nat_o))) (forall ((C_8 tptp.pname)) (not (@ (@ tptp.member_pname C_8) tptp.bot_bot_pname_o))) (forall ((C_8 tptp.x_a)) (not (@ (@ tptp.member_a C_8) tptp.bot_bot_a_o))) (forall ((P_5 (-> tptp.pname Bool))) (= (= tptp.bot_bot_pname_o (@ tptp.collect_pname P_5)) (forall ((X_1 tptp.pname)) (not (@ P_5 X_1))))) (forall ((P_5 (-> (-> tptp.nat Bool) Bool))) (= (= tptp.bot_bot_nat_o_o (@ tptp.collect_nat_o P_5)) (forall ((X_1 (-> tptp.nat Bool))) (not (@ P_5 X_1))))) (forall ((P_5 (-> (-> tptp.pname Bool) Bool))) (= (= tptp.bot_bot_pname_o_o (@ tptp.collect_pname_o P_5)) (forall ((X_1 (-> tptp.pname Bool))) (not (@ P_5 X_1))))) (forall ((P_5 (-> (-> tptp.x_a Bool) Bool))) (= (= tptp.bot_bot_a_o_o (@ tptp.collect_a_o P_5)) (forall ((X_1 (-> tptp.x_a Bool))) (not (@ P_5 X_1))))) (forall ((P_5 (-> tptp.x_a Bool))) (= (= tptp.bot_bot_a_o (@ tptp.collect_a P_5)) (forall ((X_1 tptp.x_a)) (not (@ P_5 X_1))))) (forall ((P_5 (-> tptp.nat Bool))) (= (= tptp.bot_bot_nat_o (@ tptp.collect_nat P_5)) (forall ((X_1 tptp.nat)) (not (@ P_5 X_1))))) (forall ((A_29 (-> tptp.nat Bool))) (= (exists ((X_1 tptp.nat)) (@ (@ tptp.member_nat X_1) A_29)) (not (= A_29 tptp.bot_bot_nat_o)))) (forall ((A_29 (-> tptp.pname Bool))) (= (exists ((X_1 tptp.pname)) (@ (@ tptp.member_pname X_1) A_29)) (not (= A_29 tptp.bot_bot_pname_o)))) (forall ((A_29 (-> tptp.x_a Bool))) (= (exists ((X_1 tptp.x_a)) (@ (@ tptp.member_a X_1) A_29)) (not (= A_29 tptp.bot_bot_a_o)))) (forall ((A_28 (-> tptp.nat Bool))) (= (forall ((X_1 tptp.nat)) (not (@ (@ tptp.member_nat X_1) A_28))) (= A_28 tptp.bot_bot_nat_o))) (forall ((A_28 (-> tptp.pname Bool))) (= (forall ((X_1 tptp.pname)) (not (@ (@ tptp.member_pname X_1) A_28))) (= A_28 tptp.bot_bot_pname_o))) (forall ((A_28 (-> tptp.x_a Bool))) (= (forall ((X_1 tptp.x_a)) (not (@ (@ tptp.member_a X_1) A_28))) (= A_28 tptp.bot_bot_a_o))) (= tptp.bot_bot_pname_o (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) false))) (= tptp.bot_bot_nat_o_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) false))) (= tptp.bot_bot_pname_o_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) false))) (= tptp.bot_bot_a_o_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) false))) (= tptp.bot_bot_a_o (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) false))) (= tptp.bot_bot_nat_o (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) false))) (forall ((X_1 tptp.pname)) (= (@ tptp.bot_bot_pname_o X_1) tptp.bot_bot_o)) (forall ((X_1 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_1) tptp.bot_bot_o)) (forall ((X_1 tptp.x_a)) (= (@ tptp.bot_bot_a_o X_1) tptp.bot_bot_o)) (forall ((X_13 tptp.pname)) (= (@ tptp.bot_bot_pname_o X_13) tptp.bot_bot_o)) (forall ((X_13 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_13) tptp.bot_bot_o)) (forall ((X_13 tptp.x_a)) (= (@ tptp.bot_bot_a_o X_13) tptp.bot_bot_o)) (forall ((A_27 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_27) tptp.bot_bot_pname_o) (= A_27 tptp.bot_bot_pname_o))) (forall ((A_27 Bool)) (=> (@ (@ tptp.ord_less_eq_o A_27) tptp.bot_bot_o) (= A_27 tptp.bot_bot_o))) (forall ((A_27 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_27) tptp.bot_bot_nat_o) (= A_27 tptp.bot_bot_nat_o))) (forall ((A_27 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_27) tptp.bot_bot_a_o) (= A_27 tptp.bot_bot_a_o))) (forall ((A_27 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_27) tptp.bot_bot_nat) (= A_27 tptp.bot_bot_nat))) (forall ((A_26 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o A_26) tptp.bot_bot_pname_o) (= A_26 tptp.bot_bot_pname_o))) (forall ((A_26 Bool)) (= (@ (@ tptp.ord_less_eq_o A_26) tptp.bot_bot_o) (= A_26 tptp.bot_bot_o))) (forall ((A_26 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o A_26) tptp.bot_bot_nat_o) (= A_26 tptp.bot_bot_nat_o))) (forall ((A_26 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o A_26) tptp.bot_bot_a_o) (= A_26 tptp.bot_bot_a_o))) (forall ((A_26 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A_26) tptp.bot_bot_nat) (= A_26 tptp.bot_bot_nat))) (forall ((A_25 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o tptp.bot_bot_pname_o) A_25)) (forall ((A_25 Bool)) (@ (@ tptp.ord_less_eq_o tptp.bot_bot_o) A_25)) (forall ((A_25 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o tptp.bot_bot_nat_o) A_25)) (forall ((A_25 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o tptp.bot_bot_a_o) A_25)) (forall ((A_25 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A_25)) (forall ((A_24 tptp.pname) (B_8 tptp.pname)) (=> (= (@ (@ tptp.insert_pname A_24) tptp.bot_bot_pname_o) (@ (@ tptp.insert_pname B_8) tptp.bot_bot_pname_o)) (= A_24 B_8))) (forall ((A_24 tptp.nat) (B_8 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A_24) tptp.bot_bot_nat_o) (@ (@ tptp.insert_nat B_8) tptp.bot_bot_nat_o)) (= A_24 B_8))) (forall ((A_24 tptp.x_a) (B_8 tptp.x_a)) (=> (= (@ (@ tptp.insert_a A_24) tptp.bot_bot_a_o) (@ (@ tptp.insert_a B_8) tptp.bot_bot_a_o)) (= A_24 B_8))) (forall ((B_7 tptp.nat) (A_23 tptp.nat)) (=> (@ (@ tptp.member_nat B_7) (@ (@ tptp.insert_nat A_23) tptp.bot_bot_nat_o)) (= B_7 A_23))) (forall ((B_7 tptp.pname) (A_23 tptp.pname)) (=> (@ (@ tptp.member_pname B_7) (@ (@ tptp.insert_pname A_23) tptp.bot_bot_pname_o)) (= B_7 A_23))) (forall ((B_7 tptp.x_a) (A_23 tptp.x_a)) (=> (@ (@ tptp.member_a B_7) (@ (@ tptp.insert_a A_23) tptp.bot_bot_a_o)) (= B_7 A_23))) (forall ((A_22 tptp.pname) (B_6 tptp.pname) (C_7 tptp.pname) (D tptp.pname)) (= (= (@ (@ tptp.insert_pname A_22) (@ (@ tptp.insert_pname B_6) tptp.bot_bot_pname_o)) (@ (@ tptp.insert_pname C_7) (@ (@ tptp.insert_pname D) tptp.bot_bot_pname_o))) (or (and (= A_22 C_7) (= B_6 D)) (and (= A_22 D) (= B_6 C_7))))) (forall ((A_22 tptp.nat) (B_6 tptp.nat) (C_7 tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.insert_nat A_22) (@ (@ tptp.insert_nat B_6) tptp.bot_bot_nat_o)) (@ (@ tptp.insert_nat C_7) (@ (@ tptp.insert_nat D) tptp.bot_bot_nat_o))) (or (and (= A_22 C_7) (= B_6 D)) (and (= A_22 D) (= B_6 C_7))))) (forall ((A_22 tptp.x_a) (B_6 tptp.x_a) (C_7 tptp.x_a) (D tptp.x_a)) (= (= (@ (@ tptp.insert_a A_22) (@ (@ tptp.insert_a B_6) tptp.bot_bot_a_o)) (@ (@ tptp.insert_a C_7) (@ (@ tptp.insert_a D) tptp.bot_bot_a_o))) (or (and (= A_22 C_7) (= B_6 D)) (and (= A_22 D) (= B_6 C_7))))) (forall ((B_5 tptp.nat) (A_21 tptp.nat)) (= (@ (@ tptp.member_nat B_5) (@ (@ tptp.insert_nat A_21) tptp.bot_bot_nat_o)) (= B_5 A_21))) (forall ((B_5 tptp.pname) (A_21 tptp.pname)) (= (@ (@ tptp.member_pname B_5) (@ (@ tptp.insert_pname A_21) tptp.bot_bot_pname_o)) (= B_5 A_21))) (forall ((B_5 tptp.x_a) (A_21 tptp.x_a)) (= (@ (@ tptp.member_a B_5) (@ (@ tptp.insert_a A_21) tptp.bot_bot_a_o)) (= B_5 A_21))) (forall ((A_20 tptp.pname) (A_19 (-> tptp.pname Bool))) (not (= (@ (@ tptp.insert_pname A_20) A_19) tptp.bot_bot_pname_o))) (forall ((A_20 tptp.nat) (A_19 (-> tptp.nat Bool))) (not (= (@ (@ tptp.insert_nat A_20) A_19) tptp.bot_bot_nat_o))) (forall ((A_20 tptp.x_a) (A_19 (-> tptp.x_a Bool))) (not (= (@ (@ tptp.insert_a A_20) A_19) tptp.bot_bot_a_o))) (forall ((A_18 tptp.pname) (A_17 (-> tptp.pname Bool))) (not (= tptp.bot_bot_pname_o (@ (@ tptp.insert_pname A_18) A_17)))) (forall ((A_18 tptp.nat) (A_17 (-> tptp.nat Bool))) (not (= tptp.bot_bot_nat_o (@ (@ tptp.insert_nat A_18) A_17)))) (forall ((A_18 tptp.x_a) (A_17 (-> tptp.x_a Bool))) (not (= tptp.bot_bot_a_o (@ (@ tptp.insert_a A_18) A_17)))) (forall ((A_16 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o A_16) tptp.bot_bot_nat_o) (= A_16 tptp.bot_bot_nat_o))) (forall ((A_16 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o A_16) tptp.bot_bot_pname_o) (= A_16 tptp.bot_bot_pname_o))) (forall ((A_16 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o A_16) tptp.bot_bot_a_o) (= A_16 tptp.bot_bot_a_o))) (forall ((F_6 (-> tptp.pname tptp.x_a)) (A_15 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_pname_a F_6) A_15) tptp.bot_bot_a_o) (= A_15 tptp.bot_bot_pname_o))) (forall ((F_5 (-> tptp.pname tptp.x_a))) (= (@ (@ tptp.image_pname_a F_5) tptp.bot_bot_pname_o) tptp.bot_bot_a_o)) (forall ((F_4 (-> tptp.pname tptp.x_a)) (A_14 (-> tptp.pname Bool))) (= (= tptp.bot_bot_a_o (@ (@ tptp.image_pname_a F_4) A_14)) (= A_14 tptp.bot_bot_pname_o))) (forall ((P_4 (-> tptp.nat Bool)) (A_13 tptp.nat)) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_nat A_13) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_nat_o))))) (forall ((P_4 (-> tptp.pname Bool)) (A_13 tptp.pname)) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_pname A_13) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_pname_o))))) (forall ((P_4 (-> tptp.x_a Bool)) (A_13 tptp.x_a)) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_a A_13) tptp.bot_bot_a_o))) (=> (not _let_1) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_a_o))))) (forall ((P_4 (-> (-> tptp.nat Bool) Bool)) (A_13 (-> tptp.nat Bool))) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_nat_o A_13) tptp.bot_bot_nat_o_o))) (=> (not _let_1) (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_nat_o_o))))) (forall ((P_4 (-> (-> tptp.pname Bool) Bool)) (A_13 (-> tptp.pname Bool))) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_pname_o A_13) tptp.bot_bot_pname_o_o))) (=> (not _let_1) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_pname_o_o))))) (forall ((P_4 (-> (-> tptp.x_a Bool) Bool)) (A_13 (-> tptp.x_a Bool))) (let ((_let_1 (@ P_4 A_13))) (and (=> _let_1 (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) (@ (@ tptp.insert_a_o A_13) tptp.bot_bot_a_o_o))) (=> (not _let_1) (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (= X_1 A_13) (@ P_4 X_1)))) tptp.bot_bot_a_o_o))))) (forall ((P_3 (-> tptp.nat Bool)) (A_12 tptp.nat)) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_nat A_12) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_nat_o))))) (forall ((P_3 (-> tptp.pname Bool)) (A_12 tptp.pname)) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_pname A_12) tptp.bot_bot_pname_o))) (=> (not _let_1) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_pname_o))))) (forall ((P_3 (-> tptp.x_a Bool)) (A_12 tptp.x_a)) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_a A_12) tptp.bot_bot_a_o))) (=> (not _let_1) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_a_o))))) (forall ((P_3 (-> (-> tptp.nat Bool) Bool)) (A_12 (-> tptp.nat Bool))) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_nat_o A_12) tptp.bot_bot_nat_o_o))) (=> (not _let_1) (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_nat_o_o))))) (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (A_12 (-> tptp.pname Bool))) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_pname_o A_12) tptp.bot_bot_pname_o_o))) (=> (not _let_1) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_pname_o_o))))) (forall ((P_3 (-> (-> tptp.x_a Bool) Bool)) (A_12 (-> tptp.x_a Bool))) (let ((_let_1 (@ P_3 A_12))) (and (=> _let_1 (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) (@ (@ tptp.insert_a_o A_12) tptp.bot_bot_a_o_o))) (=> (not _let_1) (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (= A_12 X_1) (@ P_3 X_1)))) tptp.bot_bot_a_o_o))))) (forall ((A_11 tptp.nat)) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (= X_1 A_11))) (@ (@ tptp.insert_nat A_11) tptp.bot_bot_nat_o))) (forall ((A_11 tptp.pname)) (= (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (= X_1 A_11))) (@ (@ tptp.insert_pname A_11) tptp.bot_bot_pname_o))) (forall ((A_11 tptp.x_a)) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (= X_1 A_11))) (@ (@ tptp.insert_a A_11) tptp.bot_bot_a_o))) (forall ((A_11 (-> tptp.nat Bool))) (= (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (= X_1 A_11))) (@ (@ tptp.insert_nat_o A_11) tptp.bot_bot_nat_o_o))) (forall ((A_11 (-> tptp.pname Bool))) (= (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (= X_1 A_11))) (@ (@ tptp.insert_pname_o A_11) tptp.bot_bot_pname_o_o))) (forall ((A_11 (-> tptp.x_a Bool))) (= (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (= X_1 A_11))) (@ (@ tptp.insert_a_o A_11) tptp.bot_bot_a_o_o))) (forall ((A_10 tptp.nat)) (= (@ tptp.collect_nat (@ tptp.fequal_nat A_10)) (@ (@ tptp.insert_nat A_10) tptp.bot_bot_nat_o))) (forall ((A_10 tptp.pname)) (= (@ tptp.collect_pname (@ tptp.fequal_pname A_10)) (@ (@ tptp.insert_pname A_10) tptp.bot_bot_pname_o))) (forall ((A_10 tptp.x_a)) (= (@ tptp.collect_a (@ tptp.fequal_a A_10)) (@ (@ tptp.insert_a A_10) tptp.bot_bot_a_o))) (forall ((A_10 (-> tptp.nat Bool))) (= (@ tptp.collect_nat_o (@ tptp.fequal_nat_o A_10)) (@ (@ tptp.insert_nat_o A_10) tptp.bot_bot_nat_o_o))) (forall ((A_10 (-> tptp.pname Bool))) (= (@ tptp.collect_pname_o (@ tptp.fequal_pname_o A_10)) (@ (@ tptp.insert_pname_o A_10) tptp.bot_bot_pname_o_o))) (forall ((A_10 (-> tptp.x_a Bool))) (= (@ tptp.collect_a_o (@ tptp.fequal_a_o A_10)) (@ (@ tptp.insert_a_o A_10) tptp.bot_bot_a_o_o))) (forall ((A_9 (-> tptp.nat Bool)) (X_12 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X_12) tptp.bot_bot_nat_o))) (=> (@ (@ tptp.ord_less_eq_nat_o A_9) _let_1) (or (= A_9 tptp.bot_bot_nat_o) (= A_9 _let_1))))) (forall ((A_9 (-> tptp.pname Bool)) (X_12 tptp.pname)) (let ((_let_1 (@ (@ tptp.insert_pname X_12) tptp.bot_bot_pname_o))) (=> (@ (@ tptp.ord_less_eq_pname_o A_9) _let_1) (or (= A_9 tptp.bot_bot_pname_o) (= A_9 _let_1))))) (forall ((A_9 (-> tptp.x_a Bool)) (X_12 tptp.x_a)) (let ((_let_1 (@ (@ tptp.insert_a X_12) tptp.bot_bot_a_o))) (=> (@ (@ tptp.ord_less_eq_a_o A_9) _let_1) (or (= A_9 tptp.bot_bot_a_o) (= A_9 _let_1))))) (forall ((C_6 tptp.x_a) (X_11 tptp.pname) (A_8 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_11) A_8) (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_6)) A_8) (@ (@ tptp.insert_a C_6) tptp.bot_bot_a_o)))) (forall ((C_5 tptp.x_a) (A_7 (-> tptp.pname Bool))) (let ((_let_1 (= A_7 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_5)) A_7) tptp.bot_bot_a_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_5)) A_7) (@ (@ tptp.insert_a C_5) tptp.bot_bot_a_o)))))) (forall ((X_10 tptp.nat) (Y_9 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X_10) Y_9)) (@ (@ tptp.ord_less_eq_nat Y_9) X_10))) (forall ((Z_2 Bool) (Y_8 Bool) (X_9 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o Z_2))) (=> (@ (@ tptp.ord_less_eq_o Y_8) X_9) (=> (@ _let_1 Y_8) (@ _let_1 X_9))))) (forall ((Z_2 (-> 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(-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o X_7))) (=> (@ _let_1 Y_6) (=> (@ (@ tptp.ord_less_eq_pname_o Y_6) Z_1) (@ _let_1 Z_1))))) (forall ((Z_1 tptp.nat) (X_7 tptp.nat) (Y_6 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X_7))) (=> (@ _let_1 Y_6) (=> (@ (@ tptp.ord_less_eq_nat Y_6) Z_1) (@ _let_1 Z_1))))) (forall ((Z_1 (-> tptp.x_a Bool)) (X_7 (-> tptp.x_a Bool)) (Y_6 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o X_7))) (=> (@ _let_1 Y_6) (=> (@ (@ tptp.ord_less_eq_a_o Y_6) Z_1) (@ _let_1 Z_1))))) (forall ((X_6 Bool) (Y_5 Bool)) (=> (@ (@ tptp.ord_less_eq_o X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_o Y_5) X_6) (= X_6 Y_5)))) (forall ((X_6 (-> tptp.nat Bool)) (Y_5 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_nat_o Y_5) X_6) (= X_6 Y_5)))) (forall ((X_6 (-> tptp.pname Bool)) (Y_5 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_pname_o Y_5) X_6) (= X_6 Y_5)))) (forall ((X_6 tptp.nat) (Y_5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_nat Y_5) X_6) (= X_6 Y_5)))) (forall ((X_6 (-> tptp.x_a Bool)) (Y_5 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o X_6) Y_5) (=> (@ (@ tptp.ord_less_eq_a_o Y_5) X_6) (= X_6 Y_5)))) (forall ((C_4 Bool) (B_4 Bool) (A_6 Bool)) (=> (@ (@ tptp.ord_less_eq_o B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_o C_4) A_6)))) (forall ((C_4 (-> tptp.nat Bool)) (B_4 (-> tptp.nat Bool)) (A_6 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_nat_o C_4) A_6)))) (forall ((C_4 (-> tptp.pname Bool)) (B_4 (-> tptp.pname Bool)) (A_6 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_pname_o C_4) A_6)))) (forall ((C_4 tptp.nat) (B_4 tptp.nat) (A_6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_nat C_4) A_6)))) (forall ((C_4 (-> tptp.x_a Bool)) (B_4 (-> tptp.x_a Bool)) (A_6 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o B_4) A_6) (=> (= B_4 C_4) (@ (@ tptp.ord_less_eq_a_o C_4) A_6)))) (forall ((C_3 Bool) (A_5 Bool) (B_3 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))) (forall ((C_3 (-> tptp.nat Bool)) (A_5 (-> tptp.nat Bool)) (B_3 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))) (forall ((C_3 (-> tptp.pname Bool)) (A_5 (-> tptp.pname Bool)) (B_3 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))) (forall ((C_3 tptp.nat) (A_5 tptp.nat) (B_3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))) (forall ((C_3 (-> tptp.x_a Bool)) (A_5 (-> tptp.x_a Bool)) (B_3 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_5))) (=> (@ _let_1 B_3) (=> (= B_3 C_3) (@ _let_1 C_3))))) (forall ((C_2 Bool) (B_2 Bool) (A_4 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_o C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))) (forall ((C_2 (-> tptp.nat Bool)) (A_4 (-> tptp.nat Bool)) (B_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))) (forall ((C_2 (-> tptp.pname Bool)) (A_4 (-> tptp.pname Bool)) (B_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))) (forall ((C_2 tptp.nat) (A_4 tptp.nat) (B_2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))) (forall ((C_2 (-> tptp.x_a Bool)) (A_4 (-> tptp.x_a Bool)) (B_2 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o C_2))) (=> (= A_4 B_2) (=> (@ _let_1 B_2) (@ _let_1 A_4))))) (forall ((C_1 Bool) (B_1 Bool) (A_3 Bool)) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_o B_1) C_1) (@ (@ tptp.ord_less_eq_o A_3) C_1)))) (forall ((C_1 (-> tptp.nat Bool)) (A_3 (-> tptp.nat Bool)) (B_1 (-> tptp.nat Bool))) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_nat_o B_1) C_1) (@ (@ tptp.ord_less_eq_nat_o A_3) C_1)))) (forall ((C_1 (-> tptp.pname Bool)) (A_3 (-> tptp.pname Bool)) (B_1 (-> tptp.pname Bool))) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_pname_o B_1) C_1) (@ (@ tptp.ord_less_eq_pname_o A_3) C_1)))) (forall ((C_1 tptp.nat) (A_3 tptp.nat) (B_1 tptp.nat)) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_nat B_1) C_1) (@ (@ tptp.ord_less_eq_nat A_3) C_1)))) (forall ((C_1 (-> tptp.x_a Bool)) (A_3 (-> tptp.x_a Bool)) (B_1 (-> tptp.x_a Bool))) (=> (= A_3 B_1) (=> (@ (@ tptp.ord_less_eq_a_o B_1) C_1) (@ (@ tptp.ord_less_eq_a_o A_3) C_1)))) (forall ((Y_4 Bool) (X_5 Bool)) (=> (@ (@ tptp.ord_less_eq_o Y_4) X_5) (= (@ (@ tptp.ord_less_eq_o X_5) Y_4) (= X_5 Y_4)))) (forall ((Y_4 (-> tptp.nat Bool)) (X_5 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o Y_4) X_5) (= (@ (@ tptp.ord_less_eq_nat_o X_5) Y_4) (= X_5 Y_4)))) (forall ((Y_4 (-> tptp.pname Bool)) (X_5 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o Y_4) X_5) (= (@ (@ tptp.ord_less_eq_pname_o X_5) Y_4) (= X_5 Y_4)))) (forall ((Y_4 tptp.nat) (X_5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y_4) X_5) (= (@ (@ tptp.ord_less_eq_nat X_5) Y_4) (= X_5 Y_4)))) (forall ((Y_4 (-> tptp.x_a Bool)) (X_5 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Y_4) X_5) (= (@ (@ tptp.ord_less_eq_a_o X_5) Y_4) (= X_5 Y_4)))) (forall ((Y_3 Bool) (X_4 Bool)) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_o X_4) Y_3))) (forall ((X_4 (-> tptp.nat Bool)) (Y_3 (-> tptp.nat Bool))) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_nat_o X_4) Y_3))) (forall ((X_4 (-> tptp.pname Bool)) (Y_3 (-> tptp.pname Bool))) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_pname_o X_4) Y_3))) (forall ((X_4 tptp.nat) (Y_3 tptp.nat)) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_nat X_4) Y_3))) (forall ((X_4 (-> tptp.x_a Bool)) (Y_3 (-> tptp.x_a Bool))) (=> (= X_4 Y_3) (@ (@ tptp.ord_less_eq_a_o X_4) Y_3))) (forall ((Y_2 Bool) (X_3 Bool)) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_o X_3) Y_2) (@ (@ tptp.ord_less_eq_o Y_2) X_3)))) (forall ((X_3 (-> tptp.nat Bool)) (Y_2 (-> tptp.nat Bool))) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_nat_o X_3) Y_2) (@ (@ tptp.ord_less_eq_nat_o Y_2) X_3)))) (forall ((X_3 (-> tptp.pname Bool)) (Y_2 (-> tptp.pname Bool))) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_pname_o X_3) Y_2) (@ (@ tptp.ord_less_eq_pname_o Y_2) X_3)))) (forall ((X_3 tptp.nat) (Y_2 tptp.nat)) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_nat X_3) Y_2) (@ (@ tptp.ord_less_eq_nat Y_2) X_3)))) (forall ((X_3 (-> tptp.x_a Bool)) (Y_2 (-> tptp.x_a Bool))) (= (= X_3 Y_2) (and (@ (@ tptp.ord_less_eq_a_o X_3) Y_2) (@ (@ tptp.ord_less_eq_a_o Y_2) X_3)))) (forall ((X_2 tptp.nat) (Y_1 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X_2) Y_1) (@ (@ tptp.ord_less_eq_nat Y_1) X_2))) (forall ((P_2 (-> (-> tptp.nat Bool) Bool)) (A_1 (-> tptp.nat Bool)) (F_3 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_3) (=> (@ (@ tptp.ord_less_eq_nat_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_nat_o) (=> (forall ((A_2 tptp.nat) (F_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_2))) (=> (@ tptp.finite_finite_nat F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_nat A_2) F_2)))))))) (@ P_2 F_3)))))) (forall ((P_2 (-> (-> tptp.pname Bool) Bool)) (A_1 (-> tptp.pname Bool)) (F_3 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_3) (=> (@ (@ tptp.ord_less_eq_pname_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_pname_o) (=> (forall ((A_2 tptp.pname) (F_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_2))) (=> (@ tptp.finite_finite_pname F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_pname A_2) F_2)))))))) (@ P_2 F_3)))))) (forall ((P_2 (-> (-> tptp.x_a Bool) Bool)) (A_1 (-> tptp.x_a Bool)) (F_3 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_3) (=> (@ (@ tptp.ord_less_eq_a_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_a_o) (=> (forall ((A_2 tptp.x_a) (F_2 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_2))) (=> (@ tptp.finite_finite_a F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_a A_2) F_2)))))))) (@ P_2 F_3)))))) (forall ((P_2 (-> (-> (-> tptp.nat Bool) Bool) Bool)) (A_1 (-> (-> tptp.nat Bool) Bool)) (F_3 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_3) (=> (@ (@ tptp.ord_less_eq_nat_o_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_nat_o_o) (=> (forall ((A_2 (-> tptp.nat Bool)) (F_2 (-> (-> tptp.nat Bool) Bool))) (let ((_let_1 (@ tptp.member_nat_o A_2))) (=> (@ tptp.finite_finite_nat_o F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_nat_o A_2) F_2)))))))) (@ P_2 F_3)))))) (forall ((P_2 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (A_1 (-> (-> tptp.pname Bool) Bool)) (F_3 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_3) (=> (@ (@ tptp.ord_le1205211808me_o_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_pname_o_o) (=> (forall ((A_2 (-> tptp.pname Bool)) (F_2 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.member_pname_o A_2))) (=> (@ tptp.finite297249702name_o F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_pname_o A_2) F_2)))))))) (@ P_2 F_3)))))) (forall ((P_2 (-> (-> (-> tptp.x_a Bool) Bool) Bool)) (A_1 (-> (-> tptp.x_a Bool) Bool)) (F_3 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_3) (=> (@ (@ tptp.ord_less_eq_a_o_o F_3) A_1) (=> (@ P_2 tptp.bot_bot_a_o_o) (=> (forall ((A_2 (-> tptp.x_a Bool)) (F_2 (-> (-> tptp.x_a Bool) Bool))) (let ((_let_1 (@ tptp.member_a_o A_2))) (=> (@ tptp.finite_finite_a_o F_2) (=> (@ _let_1 A_1) (=> (not (@ _let_1 F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_a_o A_2) F_2)))))))) (@ P_2 F_3)))))) (forall ((Pn tptp.pname) (G (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a (@ tptp.mgt_call Pn)))) (=> (@ (@ tptp.p (@ _let_1 G)) (@ (@ tptp.insert_a (@ tptp.mgt (@ tptp.the_com (@ tptp.body Pn)))) tptp.bot_bot_a_o)) (@ (@ tptp.p G) (@ _let_1 tptp.bot_bot_a_o))))) (forall ((P_1 (-> (-> (-> tptp.nat Bool) Bool) Bool)) (F_1 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_1) (=> (@ P_1 tptp.bot_bot_nat_o_o) (=> (forall ((X_1 (-> tptp.nat Bool)) (F_2 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_2) (=> (not (@ (@ tptp.member_nat_o X_1) F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_nat_o X_1) F_2)))))) (@ P_1 F_1))))) (forall ((P_1 (-> (-> (-> tptp.pname Bool) Bool) Bool)) (F_1 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_1) (=> (@ P_1 tptp.bot_bot_pname_o_o) (=> (forall ((X_1 (-> tptp.pname Bool)) (F_2 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_2) (=> (not (@ (@ tptp.member_pname_o X_1) F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_pname_o X_1) F_2)))))) (@ P_1 F_1))))) (forall ((P_1 (-> (-> (-> tptp.x_a Bool) Bool) Bool)) (F_1 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_1) (=> (@ P_1 tptp.bot_bot_a_o_o) (=> (forall ((X_1 (-> tptp.x_a Bool)) (F_2 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_2) (=> (not (@ (@ tptp.member_a_o X_1) F_2)) (=> (@ P_1 F_2) (@ P_1 (@ (@ tptp.insert_a_o X_1) F_2)))))) (@ P_1 F_1))))) (forall ((U tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_2) (@ F N_2))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N_2)) U)))))) (forall ((Pn tptp.pname)) (=> (@ (@ tptp.member_pname Pn) tptp.u) (@ tptp.wt (@ tptp.the_com (@ tptp.body Pn))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.nat_case_o false) (@ tptp.ord_less_eq_nat M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K) (@ (@ tptp.plus_plus_nat N) K)) (= M N))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) K))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)) (forall ((I tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) K))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ 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tptp.nat) (L tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J_1) L))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))) (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K)) I)))) (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K)) I) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I)) K)))) (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K)))))) (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (= (= (@ (@ tptp.minus_minus_nat J_1) I) K) (= J_1 (@ (@ tptp.plus_plus_nat K) I))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) N)) N) M))) (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) J_1)))) (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I))) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) K)))) (forall ((J_1 tptp.nat) (K tptp.nat) (I tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J_1) K)) I) (@ (@ tptp.ord_less_eq_nat J_1) (@ (@ tptp.plus_plus_nat I) K)))) (forall ((I tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat I) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I) K)) J_1)))) (forall ((N tptp.nat)) (= (@ tptp.suc N) (@ (@ tptp.plus_plus_nat N) 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tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_2 tptp.nat)) (@ (@ tptp.ord_less_nat N_2) K))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))) (forall ((I tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J_1)) K) (@ (@ tptp.ord_less_nat I) K))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((K tptp.nat) (L tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_1) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J_1) L))))) (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J_1) K)))) (forall ((M tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))) (forall ((M tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((J_1 tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J_1) I)) I))) (forall ((I tptp.nat) (J_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J_1)) I))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))) (forall ((K tptp.nat) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_1) (=> (@ (@ tptp.ord_less_nat J_1) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (not (= M N))))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))) (forall ((N tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat J_1) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J_1) N)) K))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ P N) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N) _let_1) (=> (=> (= M N) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N) M) _let_1) _let_1))))) (forall ((N_1 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_1) (exists ((M_1 tptp.nat)) (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_1) (@ (@ tptp.ord_less_nat X_1) M_1)))))) (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I_1 tptp.nat)) (@ (@ tptp.ord_less_nat I_1) N)))) N)) (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ P K_1) (@ (@ tptp.ord_less_nat K_1) I)))))) (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))) (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_1)))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))) (forall ((I tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) J_1))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))) (forall ((X_1 tptp.nat)) (= (@ tptp.ord_less_nat X_1) (@ tptp.ord_less_eq_nat (@ tptp.suc X_1)))) (forall ((M tptp.nat) (K tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((M_1 tptp.nat) (N_2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_1) N_2) (@ (@ tptp.ord_less_nat (@ F M_1)) (@ F N_2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))) (forall ((P (-> tptp.nat Bool)) (I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (=> (@ P J_1) (=> (forall ((I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ P (@ tptp.suc I_1)) (@ P I_1)))) (@ P I))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_1)))))) (forall ((N tptp.nat) (N_1 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_1) (@ (@ tptp.ord_less_nat X_1) N))) (@ tptp.finite_finite_nat N_1))) (forall ((I tptp.nat) (J_1 tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (@ (@ tptp.ord_less_nat (@ F I_1)) (@ F J)))) (=> (@ (@ tptp.ord_less_eq_nat I) J_1) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J_1))))) (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (not (= K (@ tptp.suc J)))))))) (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (not (= K (@ tptp.suc J))))))))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))) (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((Nat_1 tptp.nat)) (not (= (@ tptp.suc Nat_1) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((Nat tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (= tptp.bot_bot_nat tptp.zero_zero_nat) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (@ (@ tptp.fequal_a X) Y)) (= X Y))) (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (= X Y)) (@ (@ tptp.fequal_a X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (@ (@ tptp.fequal_nat X) Y)) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (@ (@ tptp.fequal_nat X) Y))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (@ (@ tptp.fequal_pname X) Y)) (= X Y))) (forall ((X tptp.pname) (Y tptp.pname)) (or (not (= X Y)) (@ (@ tptp.fequal_pname X) Y))) (forall ((X (-> tptp.x_a Bool)) (Y (-> tptp.x_a Bool))) (or (not (@ (@ tptp.fequal_a_o X) Y)) (= X Y))) (forall ((X (-> tptp.x_a Bool)) (Y (-> tptp.x_a Bool))) (or (not (= X Y)) (@ (@ tptp.fequal_a_o X) Y))) (forall ((X (-> tptp.nat Bool)) (Y (-> tptp.nat Bool))) (or (not (@ (@ tptp.fequal_nat_o X) Y)) (= X Y))) (forall ((X (-> tptp.nat Bool)) (Y (-> tptp.nat Bool))) (or (not (= X Y)) (@ (@ tptp.fequal_nat_o X) Y))) (forall ((X (-> tptp.pname Bool)) (Y (-> tptp.pname Bool))) (or (not (@ (@ tptp.fequal_pname_o X) Y)) (= X Y))) (forall ((X (-> tptp.pname Bool)) (Y (-> tptp.pname Bool))) (or (not (= X Y)) (@ (@ tptp.fequal_pname_o X) Y))) (@ tptp.finite_finite_pname tptp.u) _let_7 (@ (@ tptp.ord_less_eq_nat _let_5) _let_6) (= (@ tptp.finite_card_a tptp.g) (@ (@ tptp.minus_minus_nat _let_6) _let_5)) _let_4 (not (@ (@ tptp.member_a _let_2) tptp.g)) _let_3 true)))))))))))))))))))))))))))))
% 1.25/1.49 )
% 1.25/1.49 % SZS output end Proof for SWW473^2
% 1.25/1.49 % cvc5---1.0.5 exiting
% 1.25/1.50 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------