TSTP Solution File: SWW473^1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW473^1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n008.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 00:21:03 EDT 2023
% Result : Theorem 0.75s 0.98s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.17 % Problem : SWW473^1 : TPTP v8.1.2. Released v5.3.0.
% 0.16/0.18 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n008.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 21:09:32 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.25/0.57 %----Proving TH0
% 0.25/0.57 %------------------------------------------------------------------------------
% 0.25/0.57 % File : SWW473^1 : TPTP v8.1.2. Released v5.3.0.
% 0.25/0.57 % Domain : Software Verification
% 0.25/0.57 % Problem : Hoare's Logic with Procedures line 383, 100 axioms selected
% 0.25/0.57 % Version : Especial.
% 0.25/0.57 % English :
% 0.25/0.57
% 0.25/0.57 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.25/0.57 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.25/0.57 % Source : [Bla11]
% 0.25/0.57 % Names : hoare_100_thf_l383 [Bla11]
% 0.25/0.57
% 0.25/0.57 % Status : ContradictoryAxioms
% 0.25/0.57 % Rating : 0.38 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.33 v7.3.0, 0.44 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v6.0.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v5.3.0
% 0.25/0.57 % Syntax : Number of formulae : 414 ( 50 unt; 107 typ; 0 def)
% 0.25/0.57 % Number of atoms : 1063 ( 137 equ; 37 cnn)
% 0.25/0.57 % Maximal formula atoms : 9 ( 3 avg)
% 0.25/0.57 % Number of connectives : 2278 ( 49 ~; 32 |; 30 &;1806 @)
% 0.25/0.57 % ( 42 <=>; 319 =>; 0 <=; 0 <~>)
% 0.25/0.57 % Maximal formula depth : 15 ( 7 avg)
% 0.25/0.57 % Number of types : 4 ( 3 usr)
% 0.25/0.57 % Number of type conns : 1252 (1252 >; 0 *; 0 +; 0 <<)
% 0.25/0.57 % Number of symbols : 109 ( 104 usr; 6 con; 0-3 aty)
% 0.25/0.57 % Number of variables : 706 ( 42 ^; 658 !; 6 ?; 706 :)
% 0.25/0.57 % SPC : TH0_CAX_EQU_NAR
% 0.25/0.57
% 0.25/0.57 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.25/0.57 % 2011-08-09 19:22:04
% 0.25/0.57 %------------------------------------------------------------------------------
% 0.25/0.57 %----Should-be-implicit typings (3)
% 0.25/0.57 thf(ty_ty_t__a,type,
% 0.25/0.57 x_a: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_ty_tc__Com__Opname,type,
% 0.25/0.57 pname: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_ty_tc__Nat__Onat,type,
% 0.25/0.57 nat: $tType ).
% 0.25/0.57
% 0.25/0.57 %----Explicit typings (104)
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 finite_card_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 finite221134632me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 finite_card_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000_062_It__a_M_Eo_J,type,
% 0.25/0.57 finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.57 finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.25/0.57 finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000t__a,type,
% 0.25/0.57 finite_card_a: ( x_a > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000tc__Com__Opname,type,
% 0.25/0.57 finite_card_pname: ( pname > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
% 0.25/0.57 finite_card_nat: ( nat > $o ) > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 finite1302365357_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo,type,
% 0.25/0.57 finite1648353812_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 finite1237261006_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_It__a_M_Eo_J,type,
% 0.25/0.57 finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.57 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.25/0.57 finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000t__a,type,
% 0.25/0.57 finite_finite_a: ( x_a > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.25/0.57 finite_finite_pname: ( pname > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
% 0.25/0.57 finite_finite_nat: ( nat > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.25/0.57 minus_minus_nat: nat > nat > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat_OSuc,type,
% 0.25/0.57 suc: nat > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_E,type,
% 0.25/0.57 ord_less_eq_a_o_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.57 ord_le1828183645_o_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M,type,
% 0.25/0.57 ord_le124054423_o_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 0.25/0.57 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_It__a_M_Eo_J,type,
% 0.25/0.57 ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.57 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.25/0.57 ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.25/0.57 ord_less_eq_nat: nat > nat > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Set_OCollect_000_062_I_062_I_062_It__a_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 collect_a_o_o_o: ( ( ( ( x_a > $o ) > $o ) > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 collect_pname_o_o_o: ( ( ( ( pname > $o ) > $o ) > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Set_OCollect_000_062_I_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 collect_nat_o_o_o: ( ( ( ( nat > $o ) > $o ) > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Set_OCollect_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.25/0.57 collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_000_062_It__a_M_Eo_J,type,
% 0.25/0.58 collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.58 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.25/0.58 collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_000t__a,type,
% 0.25/0.58 collect_a: ( x_a > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.25/0.58 collect_pname: ( pname > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
% 0.25/0.58 collect_nat: ( nat > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000t__a,type,
% 0.25/0.58 image_a_o_o_a: ( ( ( x_a > $o ) > $o ) > x_a ) > ( ( ( x_a > $o ) > $o ) > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 0.25/0.58 image_a_o_o_pname: ( ( ( x_a > $o ) > $o ) > pname ) > ( ( ( x_a > $o ) > $o ) > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_It__a_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 0.25/0.58 image_a_o_o_nat: ( ( ( x_a > $o ) > $o ) > nat ) > ( ( ( x_a > $o ) > $o ) > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000t__a,type,
% 0.25/0.58 image_pname_o_o_a: ( ( ( pname > $o ) > $o ) > x_a ) > ( ( ( pname > $o ) > $o ) > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 0.25/0.58 image_471733107_pname: ( ( ( pname > $o ) > $o ) > pname ) > ( ( ( pname > $o ) > $o ) > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 0.25/0.58 image_pname_o_o_nat: ( ( ( pname > $o ) > $o ) > nat ) > ( ( ( pname > $o ) > $o ) > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000t__a,type,
% 0.25/0.58 image_nat_o_o_a: ( ( ( nat > $o ) > $o ) > x_a ) > ( ( ( nat > $o ) > $o ) > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000tc__Com__Opname,type,
% 0.25/0.58 image_nat_o_o_pname: ( ( ( nat > $o ) > $o ) > pname ) > ( ( ( nat > $o ) > $o ) > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J_000tc__Nat__Onat,type,
% 0.25/0.58 image_nat_o_o_nat: ( ( ( nat > $o ) > $o ) > nat ) > ( ( ( nat > $o ) > $o ) > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000t__a,type,
% 0.25/0.58 image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Com__Opname,type,
% 0.25/0.58 image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Nat__Onat,type,
% 0.25/0.58 image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000t__a,type,
% 0.25/0.58 image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 0.25/0.58 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat,type,
% 0.25/0.58 image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000t__a,type,
% 0.25/0.58 image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Com__Opname,type,
% 0.25/0.58 image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat,type,
% 0.25/0.58 image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000t__a_000t__a,type,
% 0.25/0.58 image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000t__a_000tc__Com__Opname,type,
% 0.25/0.58 image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000t__a_000tc__Nat__Onat,type,
% 0.25/0.58 image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 image_pname_a_o_o: ( pname > ( x_a > $o ) > $o ) > ( pname > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 image_504089495me_o_o: ( pname > ( pname > $o ) > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 image_pname_nat_o_o: ( pname > ( nat > $o ) > $o ) > ( pname > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_It__a_M_Eo_J,type,
% 0.25/0.58 image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.58 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.25/0.58 image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000t__a,type,
% 0.25/0.58 image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.25/0.58 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat,type,
% 0.25/0.58 image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 image_nat_a_o_o: ( nat > ( x_a > $o ) > $o ) > ( nat > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 image_nat_pname_o_o: ( nat > ( pname > $o ) > $o ) > ( nat > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 image_nat_nat_o_o: ( nat > ( nat > $o ) > $o ) > ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_It__a_M_Eo_J,type,
% 0.25/0.58 image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.58 image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.25/0.58 image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000t__a,type,
% 0.25/0.58 image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,type,
% 0.25/0.58 image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 insert_a_o_o: ( ( x_a > $o ) > $o ) > ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 insert_pname_o_o: ( ( pname > $o ) > $o ) > ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.25/0.58 insert_nat_o_o: ( ( nat > $o ) > $o ) > ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000_062_It__a_M_Eo_J,type,
% 0.25/0.58 insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.58 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.25/0.58 insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000t__a,type,
% 0.25/0.58 insert_a: x_a > ( x_a > $o ) > x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.25/0.58 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_Oinsert_000tc__Nat__Onat,type,
% 0.25/0.58 insert_nat: nat > ( nat > $o ) > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_000_062_It__a_M_Eo_J,type,
% 0.25/0.58 member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.25/0.58 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.25/0.58 member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_000t__a,type,
% 0.25/0.58 member_a: x_a > ( x_a > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_000tc__Com__Opname,type,
% 0.25/0.58 member_pname: pname > ( pname > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_000tc__Nat__Onat,type,
% 0.25/0.58 member_nat: nat > ( nat > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_G,type,
% 0.25/0.58 g: x_a > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_P,type,
% 0.25/0.58 p: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_U,type,
% 0.25/0.58 u: pname > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_mgt__call,type,
% 0.25/0.58 mgt_call: pname > x_a ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_na,type,
% 0.25/0.58 na: nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_pn,type,
% 0.25/0.58 pn: pname ).
% 0.25/0.58
% 0.25/0.58 %----Relevant facts (300)
% 0.25/0.58 thf(fact_0_assms_I1_J,axiom,
% 0.25/0.58 ! [Ts: x_a > $o,G: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ Ts @ G )
% 0.25/0.58 => ( p @ G @ Ts ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_1_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_59 )
% 0.25/0.58 => ( finite_finite_nat_o
% 0.25/0.58 @ ( collect_nat_o
% 0.25/0.58 @ ^ [B_38: nat > $o] : ( ord_less_eq_nat_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_2_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_59 )
% 0.25/0.58 => ( finite297249702name_o
% 0.25/0.58 @ ( collect_pname_o
% 0.25/0.58 @ ^ [B_38: pname > $o] : ( ord_less_eq_pname_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_3_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ A_59 )
% 0.25/0.58 => ( finite_finite_a_o
% 0.25/0.58 @ ( collect_a_o
% 0.25/0.58 @ ^ [B_38: x_a > $o] : ( ord_less_eq_a_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_4_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: ( ( nat > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1676163439at_o_o @ A_59 )
% 0.25/0.58 => ( finite1237261006_o_o_o
% 0.25/0.58 @ ( collect_nat_o_o_o
% 0.25/0.58 @ ^ [B_38: ( ( nat > $o ) > $o ) > $o] : ( ord_le124054423_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_5_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1066544169me_o_o @ A_59 )
% 0.25/0.58 => ( finite1648353812_o_o_o
% 0.25/0.58 @ ( collect_pname_o_o_o
% 0.25/0.58 @ ^ [B_38: ( ( pname > $o ) > $o ) > $o] : ( ord_le1828183645_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_6_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: ( ( x_a > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o_o @ A_59 )
% 0.25/0.58 => ( finite1302365357_o_o_o
% 0.25/0.58 @ ( collect_a_o_o_o
% 0.25/0.58 @ ^ [B_38: ( ( x_a > $o ) > $o ) > $o] : ( ord_less_eq_a_o_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_7_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ A_59 )
% 0.25/0.58 => ( finite_finite_a_o_o
% 0.25/0.58 @ ( collect_a_o_o
% 0.25/0.58 @ ^ [B_38: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_8_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ A_59 )
% 0.25/0.58 => ( finite1066544169me_o_o
% 0.25/0.58 @ ( collect_pname_o_o
% 0.25/0.58 @ ^ [B_38: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_9_finite__Collect__subsets,axiom,
% 0.25/0.58 ! [A_59: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ A_59 )
% 0.25/0.58 => ( finite1676163439at_o_o
% 0.25/0.58 @ ( collect_nat_o_o
% 0.25/0.58 @ ^ [B_38: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B_38 @ A_59 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_10_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > x_a,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite_finite_a @ ( image_pname_a @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_11_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( ( nat > $o ) > $o ) > nat,F_15: ( ( nat > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1676163439at_o_o @ F_15 )
% 0.25/0.58 => ( finite_finite_nat @ ( image_nat_o_o_nat @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_12_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( ( pname > $o ) > $o ) > nat,F_15: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1066544169me_o_o @ F_15 )
% 0.25/0.58 => ( finite_finite_nat @ ( image_pname_o_o_nat @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_13_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( ( x_a > $o ) > $o ) > nat,F_15: ( ( x_a > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o_o @ F_15 )
% 0.25/0.58 => ( finite_finite_nat @ ( image_a_o_o_nat @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_14_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( x_a > $o ) > nat,F_15: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ F_15 )
% 0.25/0.58 => ( finite_finite_nat @ ( image_a_o_nat @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_15_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( pname > $o ) > nat,F_15: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ F_15 )
% 0.25/0.58 => ( finite_finite_nat @ ( image_pname_o_nat @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_16_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( nat > $o ) > nat,F_15: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ F_15 )
% 0.25/0.58 => ( finite_finite_nat @ ( image_nat_o_nat @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_17_finite__imageI,axiom,
% 0.25/0.58 ! [H: x_a > nat,F_15: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ F_15 )
% 0.25/0.58 => ( finite_finite_nat @ ( image_a_nat @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_18_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( ( nat > $o ) > $o ) > pname,F_15: ( ( nat > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1676163439at_o_o @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_nat_o_o_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_19_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( ( pname > $o ) > $o ) > pname,F_15: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1066544169me_o_o @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_471733107_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_20_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( ( x_a > $o ) > $o ) > pname,F_15: ( ( x_a > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o_o @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_a_o_o_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_21_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( x_a > $o ) > pname,F_15: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_a_o_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_22_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( pname > $o ) > pname,F_15: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_23_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( nat > $o ) > pname,F_15: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_nat_o_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_24_finite__imageI,axiom,
% 0.25/0.58 ! [H: x_a > pname,F_15: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_a_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_25_finite__imageI,axiom,
% 0.25/0.58 ! [H: nat > ( nat > $o ) > $o,F_15: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ F_15 )
% 0.25/0.58 => ( finite1676163439at_o_o @ ( image_nat_nat_o_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_26_finite__imageI,axiom,
% 0.25/0.58 ! [H: nat > ( pname > $o ) > $o,F_15: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ F_15 )
% 0.25/0.58 => ( finite1066544169me_o_o @ ( image_nat_pname_o_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_27_finite__imageI,axiom,
% 0.25/0.58 ! [H: nat > ( x_a > $o ) > $o,F_15: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ F_15 )
% 0.25/0.58 => ( finite_finite_a_o_o @ ( image_nat_a_o_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_28_finite__imageI,axiom,
% 0.25/0.58 ! [H: nat > x_a > $o,F_15: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ F_15 )
% 0.25/0.58 => ( finite_finite_a_o @ ( image_nat_a_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_29_finite__imageI,axiom,
% 0.25/0.58 ! [H: nat > pname > $o,F_15: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ F_15 )
% 0.25/0.58 => ( finite297249702name_o @ ( image_nat_pname_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_30_finite__imageI,axiom,
% 0.25/0.58 ! [H: nat > nat > $o,F_15: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ F_15 )
% 0.25/0.58 => ( finite_finite_nat_o @ ( image_nat_nat_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_31_finite__imageI,axiom,
% 0.25/0.58 ! [H: nat > x_a,F_15: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ F_15 )
% 0.25/0.58 => ( finite_finite_a @ ( image_nat_a @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_32_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > ( nat > $o ) > $o,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite1676163439at_o_o @ ( image_pname_nat_o_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_33_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > ( pname > $o ) > $o,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite1066544169me_o_o @ ( image_504089495me_o_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_34_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > ( x_a > $o ) > $o,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite_finite_a_o_o @ ( image_pname_a_o_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_35_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > x_a > $o,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite_finite_a_o @ ( image_pname_a_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_36_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > pname > $o,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_37_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > nat > $o,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite_finite_nat_o @ ( image_pname_nat_o @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_38_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > pname,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_pname_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_39_finite__imageI,axiom,
% 0.25/0.58 ! [H: x_a > x_a,F_15: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ F_15 )
% 0.25/0.58 => ( finite_finite_a @ ( image_a_a @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_40_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( nat > $o ) > x_a,F_15: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ F_15 )
% 0.25/0.58 => ( finite_finite_a @ ( image_nat_o_a @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_41_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( pname > $o ) > x_a,F_15: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ F_15 )
% 0.25/0.58 => ( finite_finite_a @ ( image_pname_o_a @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_42_finite__imageI,axiom,
% 0.25/0.58 ! [H: ( x_a > $o ) > x_a,F_15: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ F_15 )
% 0.25/0.58 => ( finite_finite_a @ ( image_a_o_a @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_43_finite__imageI,axiom,
% 0.25/0.58 ! [H: pname > nat,F_15: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ F_15 )
% 0.25/0.58 => ( finite_finite_nat @ ( image_pname_nat @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_44_finite__imageI,axiom,
% 0.25/0.58 ! [H: nat > pname,F_15: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ F_15 )
% 0.25/0.58 => ( finite_finite_pname @ ( image_nat_pname @ H @ F_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_45_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: x_a,A_57: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ A_57 )
% 0.25/0.58 => ( finite_finite_a @ ( insert_a @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_46_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: nat,A_57: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_57 )
% 0.25/0.58 => ( finite_finite_nat @ ( insert_nat @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_47_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: pname,A_57: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_57 )
% 0.25/0.58 => ( finite_finite_pname @ ( insert_pname @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_48_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: ( nat > $o ) > $o,A_57: ( ( nat > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1676163439at_o_o @ A_57 )
% 0.25/0.58 => ( finite1676163439at_o_o @ ( insert_nat_o_o @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_49_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: ( pname > $o ) > $o,A_57: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1066544169me_o_o @ A_57 )
% 0.25/0.58 => ( finite1066544169me_o_o @ ( insert_pname_o_o @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_50_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: ( x_a > $o ) > $o,A_57: ( ( x_a > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o_o @ A_57 )
% 0.25/0.58 => ( finite_finite_a_o_o @ ( insert_a_o_o @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_51_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: x_a > $o,A_57: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ A_57 )
% 0.25/0.58 => ( finite_finite_a_o @ ( insert_a_o @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_52_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: pname > $o,A_57: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ A_57 )
% 0.25/0.58 => ( finite297249702name_o @ ( insert_pname_o @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_53_finite_OinsertI,axiom,
% 0.25/0.58 ! [A_58: nat > $o,A_57: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ A_57 )
% 0.25/0.58 => ( finite_finite_nat_o @ ( insert_nat_o @ A_58 @ A_57 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_54_card__image__le,axiom,
% 0.25/0.58 ! [F_14: pname > nat,A_56: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_55_card__image__le,axiom,
% 0.25/0.58 ! [F_14: x_a > nat,A_56: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_56_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( nat > $o ) > nat,A_56: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_57_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( pname > $o ) > nat,A_56: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_58_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( x_a > $o ) > nat,A_56: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_59_card__image__le,axiom,
% 0.25/0.58 ! [F_14: x_a > pname,A_56: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_60_card__image__le,axiom,
% 0.25/0.58 ! [F_14: nat > pname,A_56: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_61_card__image__le,axiom,
% 0.25/0.58 ! [F_14: pname > x_a,A_56: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_62_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( ( nat > $o ) > $o ) > x_a,A_56: ( ( nat > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1676163439at_o_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_o_a @ F_14 @ A_56 ) ) @ ( finite_card_nat_o_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_63_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( ( pname > $o ) > $o ) > x_a,A_56: ( ( pname > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite1066544169me_o_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_o_a @ F_14 @ A_56 ) ) @ ( finite221134632me_o_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_64_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( ( x_a > $o ) > $o ) > x_a,A_56: ( ( x_a > $o ) > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_o_a @ F_14 @ A_56 ) ) @ ( finite_card_a_o_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_65_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( x_a > $o ) > x_a,A_56: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_66_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( pname > $o ) > x_a,A_56: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_67_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( nat > $o ) > x_a,A_56: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_68_card__image__le,axiom,
% 0.25/0.58 ! [F_14: x_a > x_a,A_56: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ F_14 @ A_56 ) ) @ ( finite_card_a @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_69_card__image__le,axiom,
% 0.25/0.58 ! [F_14: pname > pname,A_56: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_70_card__image__le,axiom,
% 0.25/0.58 ! [F_14: pname > nat > $o,A_56: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat_o @ ( image_pname_nat_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_71_card__image__le,axiom,
% 0.25/0.58 ! [F_14: pname > pname > $o,A_56: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname_o @ ( image_pname_pname_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_72_card__image__le,axiom,
% 0.25/0.58 ! [F_14: pname > x_a > $o,A_56: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a_o @ ( image_pname_a_o @ F_14 @ A_56 ) ) @ ( finite_card_pname @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_73_card__image__le,axiom,
% 0.25/0.58 ! [F_14: nat > x_a,A_56: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_a @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_74_card__image__le,axiom,
% 0.25/0.58 ! [F_14: nat > nat > $o,A_56: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat_o @ ( image_nat_nat_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_75_card__image__le,axiom,
% 0.25/0.58 ! [F_14: nat > pname > $o,A_56: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname_o @ ( image_nat_pname_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_76_card__image__le,axiom,
% 0.25/0.58 ! [F_14: nat > x_a > $o,A_56: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a_o @ ( image_nat_a_o @ F_14 @ A_56 ) ) @ ( finite_card_nat @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_77_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( nat > $o ) > pname,A_56: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_nat_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_78_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( pname > $o ) > pname,A_56: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_pname_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_79_card__image__le,axiom,
% 0.25/0.58 ! [F_14: ( x_a > $o ) > pname,A_56: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ A_56 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_o_pname @ F_14 @ A_56 ) ) @ ( finite_card_a_o @ A_56 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_80_card__mono,axiom,
% 0.25/0.58 ! [A_55: ( nat > $o ) > $o,B_37: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ B_37 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o_o @ A_55 @ B_37 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_55 ) @ ( finite_card_nat_o @ B_37 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_81_card__mono,axiom,
% 0.25/0.58 ! [A_55: ( pname > $o ) > $o,B_37: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ B_37 )
% 0.25/0.58 => ( ( ord_le1205211808me_o_o @ A_55 @ B_37 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_55 ) @ ( finite_card_pname_o @ B_37 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_82_card__mono,axiom,
% 0.25/0.58 ! [A_55: ( x_a > $o ) > $o,B_37: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ B_37 )
% 0.25/0.58 => ( ( ord_less_eq_a_o_o @ A_55 @ B_37 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_55 ) @ ( finite_card_a_o @ B_37 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_83_card__mono,axiom,
% 0.25/0.58 ! [A_55: pname > $o,B_37: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ B_37 )
% 0.25/0.58 => ( ( ord_less_eq_pname_o @ A_55 @ B_37 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname @ A_55 ) @ ( finite_card_pname @ B_37 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_84_card__mono,axiom,
% 0.25/0.58 ! [A_55: x_a > $o,B_37: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ B_37 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ A_55 @ B_37 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ A_55 ) @ ( finite_card_a @ B_37 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_85_card__mono,axiom,
% 0.25/0.58 ! [A_55: nat > $o,B_37: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ B_37 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o @ A_55 @ B_37 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat @ A_55 ) @ ( finite_card_nat @ B_37 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_86_card__seteq,axiom,
% 0.25/0.58 ! [A_54: ( nat > $o ) > $o,B_36: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o_o @ A_54 @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B_36 ) @ ( finite_card_nat_o @ A_54 ) )
% 0.25/0.58 => ( A_54 = B_36 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_87_card__seteq,axiom,
% 0.25/0.58 ! [A_54: ( pname > $o ) > $o,B_36: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ B_36 )
% 0.25/0.58 => ( ( ord_le1205211808me_o_o @ A_54 @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B_36 ) @ ( finite_card_pname_o @ A_54 ) )
% 0.25/0.58 => ( A_54 = B_36 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_88_card__seteq,axiom,
% 0.25/0.58 ! [A_54: ( x_a > $o ) > $o,B_36: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_a_o_o @ A_54 @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ ( finite_card_a_o @ B_36 ) @ ( finite_card_a_o @ A_54 ) )
% 0.25/0.58 => ( A_54 = B_36 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_89_card__seteq,axiom,
% 0.25/0.58 ! [A_54: pname > $o,B_36: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_pname_o @ A_54 @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ ( finite_card_pname @ B_36 ) @ ( finite_card_pname @ A_54 ) )
% 0.25/0.58 => ( A_54 = B_36 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_90_card__seteq,axiom,
% 0.25/0.58 ! [A_54: x_a > $o,B_36: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ A_54 @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ ( finite_card_a @ B_36 ) @ ( finite_card_a @ A_54 ) )
% 0.25/0.58 => ( A_54 = B_36 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_91_card__seteq,axiom,
% 0.25/0.58 ! [A_54: nat > $o,B_36: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o @ A_54 @ B_36 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B_36 ) @ ( finite_card_nat @ A_54 ) )
% 0.25/0.58 => ( A_54 = B_36 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_92_card__insert__le,axiom,
% 0.25/0.58 ! [X_19: nat > $o,A_53: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ A_53 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_53 ) @ ( finite_card_nat_o @ ( insert_nat_o @ X_19 @ A_53 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_93_card__insert__le,axiom,
% 0.25/0.58 ! [X_19: pname > $o,A_53: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ A_53 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_53 ) @ ( finite_card_pname_o @ ( insert_pname_o @ X_19 @ A_53 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_94_card__insert__le,axiom,
% 0.25/0.58 ! [X_19: x_a > $o,A_53: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ A_53 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_53 ) @ ( finite_card_a_o @ ( insert_a_o @ X_19 @ A_53 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_95_card__insert__le,axiom,
% 0.25/0.58 ! [X_19: pname,A_53: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_53 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_pname @ A_53 ) @ ( finite_card_pname @ ( insert_pname @ X_19 @ A_53 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_96_card__insert__le,axiom,
% 0.25/0.58 ! [X_19: nat,A_53: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_53 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_nat @ A_53 ) @ ( finite_card_nat @ ( insert_nat @ X_19 @ A_53 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_97_card__insert__le,axiom,
% 0.25/0.58 ! [X_19: x_a,A_53: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ A_53 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( finite_card_a @ A_53 ) @ ( finite_card_a @ ( insert_a @ X_19 @ A_53 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_98_card__insert__if,axiom,
% 0.25/0.58 ! [X_18: nat > $o,A_52: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ A_52 )
% 0.25/0.58 => ( ( ( member_nat_o @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_18 @ A_52 ) )
% 0.25/0.58 = ( finite_card_nat_o @ A_52 ) ) )
% 0.25/0.58 & ( ~ ( member_nat_o @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_18 @ A_52 ) )
% 0.25/0.58 = ( suc @ ( finite_card_nat_o @ A_52 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_99_card__insert__if,axiom,
% 0.25/0.58 ! [X_18: pname > $o,A_52: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ A_52 )
% 0.25/0.58 => ( ( ( member_pname_o @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_18 @ A_52 ) )
% 0.25/0.58 = ( finite_card_pname_o @ A_52 ) ) )
% 0.25/0.58 & ( ~ ( member_pname_o @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_18 @ A_52 ) )
% 0.25/0.58 = ( suc @ ( finite_card_pname_o @ A_52 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_100_card__insert__if,axiom,
% 0.25/0.58 ! [X_18: x_a > $o,A_52: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ A_52 )
% 0.25/0.58 => ( ( ( member_a_o @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_a_o @ ( insert_a_o @ X_18 @ A_52 ) )
% 0.25/0.58 = ( finite_card_a_o @ A_52 ) ) )
% 0.25/0.58 & ( ~ ( member_a_o @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_a_o @ ( insert_a_o @ X_18 @ A_52 ) )
% 0.25/0.58 = ( suc @ ( finite_card_a_o @ A_52 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_101_card__insert__if,axiom,
% 0.25/0.58 ! [X_18: nat,A_52: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_52 )
% 0.25/0.58 => ( ( ( member_nat @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_nat @ ( insert_nat @ X_18 @ A_52 ) )
% 0.25/0.58 = ( finite_card_nat @ A_52 ) ) )
% 0.25/0.58 & ( ~ ( member_nat @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_nat @ ( insert_nat @ X_18 @ A_52 ) )
% 0.25/0.58 = ( suc @ ( finite_card_nat @ A_52 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_102_card__insert__if,axiom,
% 0.25/0.58 ! [X_18: pname,A_52: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_52 )
% 0.25/0.58 => ( ( ( member_pname @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_pname @ ( insert_pname @ X_18 @ A_52 ) )
% 0.25/0.58 = ( finite_card_pname @ A_52 ) ) )
% 0.25/0.58 & ( ~ ( member_pname @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_pname @ ( insert_pname @ X_18 @ A_52 ) )
% 0.25/0.58 = ( suc @ ( finite_card_pname @ A_52 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_103_card__insert__if,axiom,
% 0.25/0.58 ! [X_18: x_a,A_52: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ A_52 )
% 0.25/0.58 => ( ( ( member_a @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_a @ ( insert_a @ X_18 @ A_52 ) )
% 0.25/0.58 = ( finite_card_a @ A_52 ) ) )
% 0.25/0.58 & ( ~ ( member_a @ X_18 @ A_52 )
% 0.25/0.58 => ( ( finite_card_a @ ( insert_a @ X_18 @ A_52 ) )
% 0.25/0.58 = ( suc @ ( finite_card_a @ A_52 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_104_card__insert__disjoint,axiom,
% 0.25/0.58 ! [X_17: nat > $o,A_51: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ A_51 )
% 0.25/0.58 => ( ~ ( member_nat_o @ X_17 @ A_51 )
% 0.25/0.58 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_17 @ A_51 ) )
% 0.25/0.58 = ( suc @ ( finite_card_nat_o @ A_51 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_105_card__insert__disjoint,axiom,
% 0.25/0.58 ! [X_17: pname > $o,A_51: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ A_51 )
% 0.25/0.58 => ( ~ ( member_pname_o @ X_17 @ A_51 )
% 0.25/0.58 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_17 @ A_51 ) )
% 0.25/0.58 = ( suc @ ( finite_card_pname_o @ A_51 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_106_card__insert__disjoint,axiom,
% 0.25/0.58 ! [X_17: x_a > $o,A_51: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ A_51 )
% 0.25/0.58 => ( ~ ( member_a_o @ X_17 @ A_51 )
% 0.25/0.58 => ( ( finite_card_a_o @ ( insert_a_o @ X_17 @ A_51 ) )
% 0.25/0.58 = ( suc @ ( finite_card_a_o @ A_51 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_107_card__insert__disjoint,axiom,
% 0.25/0.58 ! [X_17: nat,A_51: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ A_51 )
% 0.25/0.58 => ( ~ ( member_nat @ X_17 @ A_51 )
% 0.25/0.58 => ( ( finite_card_nat @ ( insert_nat @ X_17 @ A_51 ) )
% 0.25/0.58 = ( suc @ ( finite_card_nat @ A_51 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_108_card__insert__disjoint,axiom,
% 0.25/0.58 ! [X_17: pname,A_51: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_51 )
% 0.25/0.58 => ( ~ ( member_pname @ X_17 @ A_51 )
% 0.25/0.58 => ( ( finite_card_pname @ ( insert_pname @ X_17 @ A_51 ) )
% 0.25/0.58 = ( suc @ ( finite_card_pname @ A_51 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_109_card__insert__disjoint,axiom,
% 0.25/0.58 ! [X_17: x_a,A_51: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ A_51 )
% 0.25/0.58 => ( ~ ( member_a @ X_17 @ A_51 )
% 0.25/0.58 => ( ( finite_card_a @ ( insert_a @ X_17 @ A_51 ) )
% 0.25/0.58 = ( suc @ ( finite_card_a @ A_51 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_110_finite__Collect__conjI,axiom,
% 0.25/0.58 ! [Q_1: ( nat > $o ) > $o,P_4: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( ( finite_finite_nat_o @ ( collect_nat_o @ P_4 ) )
% 0.25/0.58 | ( finite_finite_nat_o @ ( collect_nat_o @ Q_1 ) ) )
% 0.25/0.58 => ( finite_finite_nat_o
% 0.25/0.58 @ ( collect_nat_o
% 0.25/0.58 @ ^ [X: nat > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_111_finite__Collect__conjI,axiom,
% 0.25/0.58 ! [Q_1: ( pname > $o ) > $o,P_4: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_4 ) )
% 0.25/0.58 | ( finite297249702name_o @ ( collect_pname_o @ Q_1 ) ) )
% 0.25/0.58 => ( finite297249702name_o
% 0.25/0.58 @ ( collect_pname_o
% 0.25/0.58 @ ^ [X: pname > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_112_finite__Collect__conjI,axiom,
% 0.25/0.58 ! [Q_1: ( x_a > $o ) > $o,P_4: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( ( finite_finite_a_o @ ( collect_a_o @ P_4 ) )
% 0.25/0.58 | ( finite_finite_a_o @ ( collect_a_o @ Q_1 ) ) )
% 0.25/0.58 => ( finite_finite_a_o
% 0.25/0.58 @ ( collect_a_o
% 0.25/0.58 @ ^ [X: x_a > $o] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_113_finite__Collect__conjI,axiom,
% 0.25/0.58 ! [Q_1: x_a > $o,P_4: x_a > $o] :
% 0.25/0.58 ( ( ( finite_finite_a @ ( collect_a @ P_4 ) )
% 0.25/0.58 | ( finite_finite_a @ ( collect_a @ Q_1 ) ) )
% 0.25/0.58 => ( finite_finite_a
% 0.25/0.58 @ ( collect_a
% 0.25/0.58 @ ^ [X: x_a] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_114_finite__Collect__conjI,axiom,
% 0.25/0.58 ! [Q_1: pname > $o,P_4: pname > $o] :
% 0.25/0.58 ( ( ( finite_finite_pname @ ( collect_pname @ P_4 ) )
% 0.25/0.58 | ( finite_finite_pname @ ( collect_pname @ Q_1 ) ) )
% 0.25/0.58 => ( finite_finite_pname
% 0.25/0.58 @ ( collect_pname
% 0.25/0.58 @ ^ [X: pname] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_115_finite__Collect__conjI,axiom,
% 0.25/0.58 ! [Q_1: nat > $o,P_4: nat > $o] :
% 0.25/0.58 ( ( ( finite_finite_nat @ ( collect_nat @ P_4 ) )
% 0.25/0.58 | ( finite_finite_nat @ ( collect_nat @ Q_1 ) ) )
% 0.25/0.58 => ( finite_finite_nat
% 0.25/0.58 @ ( collect_nat
% 0.25/0.58 @ ^ [X: nat] : ( (&) @ ( P_4 @ X ) @ ( Q_1 @ X ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_116_Suc__diff__le,axiom,
% 0.25/0.58 ! [N_1: nat,M_2: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ N_1 @ M_2 )
% 0.25/0.58 => ( ( minus_minus_nat @ ( suc @ M_2 ) @ N_1 )
% 0.25/0.58 = ( suc @ ( minus_minus_nat @ M_2 @ N_1 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_117_finite__Collect__le__nat,axiom,
% 0.25/0.58 ! [K: nat] :
% 0.25/0.58 ( finite_finite_nat
% 0.25/0.58 @ ( collect_nat
% 0.25/0.58 @ ^ [N_2: nat] : ( ord_less_eq_nat @ N_2 @ K ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_118_card__Collect__le__nat,axiom,
% 0.25/0.58 ! [N_1: nat] :
% 0.25/0.58 ( ( finite_card_nat
% 0.25/0.58 @ ( collect_nat
% 0.25/0.58 @ ^ [I_1: nat] : ( ord_less_eq_nat @ I_1 @ N_1 ) ) )
% 0.25/0.58 = ( suc @ N_1 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_119_Suc__inject,axiom,
% 0.25/0.58 ! [X_16: nat,Y_3: nat] :
% 0.25/0.58 ( ( ( suc @ X_16 )
% 0.25/0.58 = ( suc @ Y_3 ) )
% 0.25/0.58 => ( X_16 = Y_3 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_120_nat_Oinject,axiom,
% 0.25/0.58 ! [Nat_1: nat,Nat: nat] :
% 0.25/0.58 ( ( ( suc @ Nat_1 )
% 0.25/0.58 = ( suc @ Nat ) )
% 0.25/0.58 <=> ( Nat_1 = Nat ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_121_Suc__n__not__n,axiom,
% 0.25/0.58 ! [N_1: nat] :
% 0.25/0.58 ( ( suc @ N_1 )
% 0.25/0.58 != N_1 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_122_n__not__Suc__n,axiom,
% 0.25/0.58 ! [N_1: nat] :
% 0.25/0.58 ( N_1
% 0.25/0.58 != ( suc @ N_1 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_123_le__antisym,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ N_1 @ M_2 )
% 0.25/0.58 => ( M_2 = N_1 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_124_le__trans,axiom,
% 0.25/0.58 ! [K: nat,I: nat,J: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.58 => ( ( ord_less_eq_nat @ J @ K )
% 0.25/0.58 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_125_eq__imp__le,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( M_2 = N_1 )
% 0.25/0.58 => ( ord_less_eq_nat @ M_2 @ N_1 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_126_nat__le__linear,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.25/0.58 | ( ord_less_eq_nat @ N_1 @ M_2 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_127_le__refl,axiom,
% 0.25/0.58 ! [N_1: nat] : ( ord_less_eq_nat @ N_1 @ N_1 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_128_diff__commute,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat] :
% 0.25/0.58 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.25/0.58 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_129_finite__Collect__disjI,axiom,
% 0.25/0.58 ! [P_3: pname > $o,Q: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname
% 0.25/0.58 @ ( collect_pname
% 0.25/0.58 @ ^ [X: pname] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.25/0.58 <=> ( ( finite_finite_pname @ ( collect_pname @ P_3 ) )
% 0.25/0.58 & ( finite_finite_pname @ ( collect_pname @ Q ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_130_finite__Collect__disjI,axiom,
% 0.25/0.58 ! [P_3: ( nat > $o ) > $o,Q: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o
% 0.25/0.58 @ ( collect_nat_o
% 0.25/0.58 @ ^ [X: nat > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.25/0.58 <=> ( ( finite_finite_nat_o @ ( collect_nat_o @ P_3 ) )
% 0.25/0.58 & ( finite_finite_nat_o @ ( collect_nat_o @ Q ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_131_finite__Collect__disjI,axiom,
% 0.25/0.58 ! [P_3: ( pname > $o ) > $o,Q: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o
% 0.25/0.58 @ ( collect_pname_o
% 0.25/0.58 @ ^ [X: pname > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.25/0.58 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_3 ) )
% 0.25/0.58 & ( finite297249702name_o @ ( collect_pname_o @ Q ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_132_finite__Collect__disjI,axiom,
% 0.25/0.58 ! [P_3: ( x_a > $o ) > $o,Q: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o
% 0.25/0.58 @ ( collect_a_o
% 0.25/0.58 @ ^ [X: x_a > $o] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.25/0.58 <=> ( ( finite_finite_a_o @ ( collect_a_o @ P_3 ) )
% 0.25/0.58 & ( finite_finite_a_o @ ( collect_a_o @ Q ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_133_finite__Collect__disjI,axiom,
% 0.25/0.58 ! [P_3: nat > $o,Q: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat
% 0.25/0.58 @ ( collect_nat
% 0.25/0.58 @ ^ [X: nat] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.25/0.58 <=> ( ( finite_finite_nat @ ( collect_nat @ P_3 ) )
% 0.25/0.58 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_134_finite__Collect__disjI,axiom,
% 0.25/0.58 ! [P_3: x_a > $o,Q: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a
% 0.25/0.58 @ ( collect_a
% 0.25/0.58 @ ^ [X: x_a] : ( (|) @ ( P_3 @ X ) @ ( Q @ X ) ) ) )
% 0.25/0.58 <=> ( ( finite_finite_a @ ( collect_a @ P_3 ) )
% 0.25/0.58 & ( finite_finite_a @ ( collect_a @ Q ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_135_finite__insert,axiom,
% 0.25/0.58 ! [A_50: nat,A_49: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ ( insert_nat @ A_50 @ A_49 ) )
% 0.25/0.58 <=> ( finite_finite_nat @ A_49 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_136_finite__insert,axiom,
% 0.25/0.58 ! [A_50: pname,A_49: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ ( insert_pname @ A_50 @ A_49 ) )
% 0.25/0.58 <=> ( finite_finite_pname @ A_49 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_137_finite__insert,axiom,
% 0.25/0.58 ! [A_50: x_a,A_49: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ ( insert_a @ A_50 @ A_49 ) )
% 0.25/0.58 <=> ( finite_finite_a @ A_49 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_138_finite__insert,axiom,
% 0.25/0.58 ! [A_50: nat > $o,A_49: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ ( insert_nat_o @ A_50 @ A_49 ) )
% 0.25/0.58 <=> ( finite_finite_nat_o @ A_49 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_139_finite__insert,axiom,
% 0.25/0.58 ! [A_50: pname > $o,A_49: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ ( insert_pname_o @ A_50 @ A_49 ) )
% 0.25/0.58 <=> ( finite297249702name_o @ A_49 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_140_finite__insert,axiom,
% 0.25/0.58 ! [A_50: x_a > $o,A_49: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ ( insert_a_o @ A_50 @ A_49 ) )
% 0.25/0.58 <=> ( finite_finite_a_o @ A_49 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_141_finite__subset,axiom,
% 0.25/0.58 ! [A_48: ( nat > $o ) > $o,B_35: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o_o @ A_48 @ B_35 )
% 0.25/0.58 => ( ( finite_finite_nat_o @ B_35 )
% 0.25/0.58 => ( finite_finite_nat_o @ A_48 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_142_finite__subset,axiom,
% 0.25/0.58 ! [A_48: ( pname > $o ) > $o,B_35: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( ord_le1205211808me_o_o @ A_48 @ B_35 )
% 0.25/0.58 => ( ( finite297249702name_o @ B_35 )
% 0.25/0.58 => ( finite297249702name_o @ A_48 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_143_finite__subset,axiom,
% 0.25/0.58 ! [A_48: x_a > $o,B_35: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ A_48 @ B_35 )
% 0.25/0.58 => ( ( finite_finite_a @ B_35 )
% 0.25/0.58 => ( finite_finite_a @ A_48 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_144_finite__subset,axiom,
% 0.25/0.58 ! [A_48: ( x_a > $o ) > $o,B_35: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o_o @ A_48 @ B_35 )
% 0.25/0.58 => ( ( finite_finite_a_o @ B_35 )
% 0.25/0.58 => ( finite_finite_a_o @ A_48 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_145_finite__subset,axiom,
% 0.25/0.58 ! [A_48: nat > $o,B_35: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ A_48 @ B_35 )
% 0.25/0.58 => ( ( finite_finite_nat @ B_35 )
% 0.25/0.58 => ( finite_finite_nat @ A_48 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_146_finite__subset,axiom,
% 0.25/0.58 ! [A_48: pname > $o,B_35: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ A_48 @ B_35 )
% 0.25/0.58 => ( ( finite_finite_pname @ B_35 )
% 0.25/0.58 => ( finite_finite_pname @ A_48 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_147_rev__finite__subset,axiom,
% 0.25/0.58 ! [A_47: ( nat > $o ) > $o,B_34: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_nat_o @ B_34 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o_o @ A_47 @ B_34 )
% 0.25/0.58 => ( finite_finite_nat_o @ A_47 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_148_rev__finite__subset,axiom,
% 0.25/0.58 ! [A_47: ( pname > $o ) > $o,B_34: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( finite297249702name_o @ B_34 )
% 0.25/0.58 => ( ( ord_le1205211808me_o_o @ A_47 @ B_34 )
% 0.25/0.58 => ( finite297249702name_o @ A_47 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_149_rev__finite__subset,axiom,
% 0.25/0.58 ! [A_47: x_a > $o,B_34: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ B_34 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ A_47 @ B_34 )
% 0.25/0.58 => ( finite_finite_a @ A_47 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_150_rev__finite__subset,axiom,
% 0.25/0.58 ! [A_47: ( x_a > $o ) > $o,B_34: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( finite_finite_a_o @ B_34 )
% 0.25/0.58 => ( ( ord_less_eq_a_o_o @ A_47 @ B_34 )
% 0.25/0.58 => ( finite_finite_a_o @ A_47 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_151_rev__finite__subset,axiom,
% 0.25/0.58 ! [A_47: nat > $o,B_34: nat > $o] :
% 0.25/0.58 ( ( finite_finite_nat @ B_34 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o @ A_47 @ B_34 )
% 0.25/0.58 => ( finite_finite_nat @ A_47 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_152_rev__finite__subset,axiom,
% 0.25/0.58 ! [A_47: pname > $o,B_34: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ B_34 )
% 0.25/0.58 => ( ( ord_less_eq_pname_o @ A_47 @ B_34 )
% 0.25/0.58 => ( finite_finite_pname @ A_47 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_153_Suc__leD,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ ( suc @ M_2 ) @ N_1 )
% 0.25/0.58 => ( ord_less_eq_nat @ M_2 @ N_1 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_154_le__SucE,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) )
% 0.25/0.58 => ( ~ ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.25/0.58 => ( M_2
% 0.25/0.58 = ( suc @ N_1 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_155_le__SucI,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.25/0.58 => ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_156_Suc__le__mono,axiom,
% 0.25/0.58 ! [N_1: nat,M_2: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ ( suc @ M_2 ) )
% 0.25/0.58 <=> ( ord_less_eq_nat @ N_1 @ M_2 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_157_le__Suc__eq,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ M_2 @ ( suc @ N_1 ) )
% 0.25/0.58 <=> ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.25/0.58 | ( M_2
% 0.25/0.58 = ( suc @ N_1 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_158_not__less__eq__eq,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ~ ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.25/0.58 <=> ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_2 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_159_Suc__n__not__le__n,axiom,
% 0.25/0.58 ! [N_1: nat] :
% 0.25/0.58 ~ ( ord_less_eq_nat @ ( suc @ N_1 ) @ N_1 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_160_Suc__diff__diff,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat,K: nat] :
% 0.25/0.58 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M_2 ) @ N_1 ) @ ( suc @ K ) )
% 0.25/0.58 = ( minus_minus_nat @ ( minus_minus_nat @ M_2 @ N_1 ) @ K ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_161_diff__Suc__Suc,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( minus_minus_nat @ ( suc @ M_2 ) @ ( suc @ N_1 ) )
% 0.25/0.58 = ( minus_minus_nat @ M_2 @ N_1 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_162_le__diff__iff,axiom,
% 0.25/0.58 ! [N_1: nat,K: nat,M_2: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ K @ M_2 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ K @ N_1 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ K ) @ ( minus_minus_nat @ N_1 @ K ) )
% 0.25/0.58 <=> ( ord_less_eq_nat @ M_2 @ N_1 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_163_Nat_Odiff__diff__eq,axiom,
% 0.25/0.58 ! [N_1: nat,K: nat,M_2: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ K @ M_2 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ K @ N_1 )
% 0.25/0.58 => ( ( minus_minus_nat @ ( minus_minus_nat @ M_2 @ K ) @ ( minus_minus_nat @ N_1 @ K ) )
% 0.25/0.58 = ( minus_minus_nat @ M_2 @ N_1 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_164_eq__diff__iff,axiom,
% 0.25/0.58 ! [N_1: nat,K: nat,M_2: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ K @ M_2 )
% 0.25/0.58 => ( ( ord_less_eq_nat @ K @ N_1 )
% 0.25/0.58 => ( ( ( minus_minus_nat @ M_2 @ K )
% 0.25/0.58 = ( minus_minus_nat @ N_1 @ K ) )
% 0.25/0.58 <=> ( M_2 = N_1 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_165_diff__diff__cancel,axiom,
% 0.25/0.58 ! [I: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ I @ N_1 )
% 0.25/0.58 => ( ( minus_minus_nat @ N_1 @ ( minus_minus_nat @ N_1 @ I ) )
% 0.25/0.58 = I ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_166_diff__le__mono,axiom,
% 0.25/0.58 ! [L: nat,M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ L ) @ ( minus_minus_nat @ N_1 @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_167_diff__le__mono2,axiom,
% 0.25/0.58 ! [L: nat,M_2: nat,N_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ M_2 @ N_1 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N_1 ) @ ( minus_minus_nat @ L @ M_2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_168_diff__le__self,axiom,
% 0.25/0.58 ! [M_2: nat,N_1: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M_2 @ N_1 ) @ M_2 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_169_finite__surj,axiom,
% 0.25/0.58 ! [B_33: x_a > $o,F_13: pname > x_a,A_46: pname > $o] :
% 0.25/0.58 ( ( finite_finite_pname @ A_46 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ B_33 @ ( image_pname_a @ F_13 @ A_46 ) )
% 0.25/0.58 => ( finite_finite_a @ B_33 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_170_finite__subset__image,axiom,
% 0.25/0.58 ! [F_12: pname > x_a,A_45: pname > $o,B_32: x_a > $o] :
% 0.25/0.58 ( ( finite_finite_a @ B_32 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ B_32 @ ( image_pname_a @ F_12 @ A_45 ) )
% 0.25/0.58 => ? [C_3: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ C_3 @ A_45 )
% 0.25/0.58 & ( finite_finite_pname @ C_3 )
% 0.25/0.58 & ( B_32
% 0.25/0.58 = ( image_pname_a @ F_12 @ C_3 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_171_lift__Suc__mono__le,axiom,
% 0.25/0.58 ! [N_4: nat,N_3: nat,F_11: nat > nat > $o] :
% 0.25/0.58 ( ! [N_2: nat] : ( ord_less_eq_nat_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 0.25/0.58 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.25/0.58 => ( ord_less_eq_nat_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_172_lift__Suc__mono__le,axiom,
% 0.25/0.58 ! [N_4: nat,N_3: nat,F_11: nat > pname > $o] :
% 0.25/0.58 ( ! [N_2: nat] : ( ord_less_eq_pname_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 0.25/0.58 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.25/0.58 => ( ord_less_eq_pname_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_173_lift__Suc__mono__le,axiom,
% 0.25/0.58 ! [N_4: nat,N_3: nat,F_11: nat > nat] :
% 0.25/0.58 ( ! [N_2: nat] : ( ord_less_eq_nat @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 0.25/0.58 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.25/0.58 => ( ord_less_eq_nat @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_174_lift__Suc__mono__le,axiom,
% 0.25/0.58 ! [N_4: nat,N_3: nat,F_11: nat > x_a > $o] :
% 0.25/0.58 ( ! [N_2: nat] : ( ord_less_eq_a_o @ ( F_11 @ N_2 ) @ ( F_11 @ ( suc @ N_2 ) ) )
% 0.25/0.58 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.25/0.58 => ( ord_less_eq_a_o @ ( F_11 @ N_4 ) @ ( F_11 @ N_3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_175_pigeonhole__infinite,axiom,
% 0.25/0.58 ! [F_10: pname > x_a,A_43: pname > $o] :
% 0.25/0.58 ( ~ ( finite_finite_pname @ A_43 )
% 0.25/0.58 => ( ( finite_finite_a @ ( image_pname_a @ F_10 @ A_43 ) )
% 0.25/0.58 => ? [X: pname] :
% 0.25/0.58 ( ( member_pname @ X @ A_43 )
% 0.25/0.58 & ~ ( finite_finite_pname
% 0.25/0.58 @ ( collect_pname
% 0.25/0.58 @ ^ [A_44: pname] :
% 0.25/0.58 ( (&) @ ( member_pname @ A_44 @ A_43 )
% 0.25/0.58 @ ( ( F_10 @ A_44 )
% 0.25/0.58 = ( F_10 @ X ) ) ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_176_image__eqI,axiom,
% 0.25/0.58 ! [A_42: pname > $o,B_31: x_a,F_9: pname > x_a,X_15: pname] :
% 0.25/0.58 ( ( B_31
% 0.25/0.58 = ( F_9 @ X_15 ) )
% 0.25/0.58 => ( ( member_pname @ X_15 @ A_42 )
% 0.25/0.58 => ( member_a @ B_31 @ ( image_pname_a @ F_9 @ A_42 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_177_equalityI,axiom,
% 0.25/0.58 ! [A_41: nat > $o,B_30: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ A_41 @ B_30 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o @ B_30 @ A_41 )
% 0.25/0.58 => ( A_41 = B_30 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_178_equalityI,axiom,
% 0.25/0.58 ! [A_41: pname > $o,B_30: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ A_41 @ B_30 )
% 0.25/0.58 => ( ( ord_less_eq_pname_o @ B_30 @ A_41 )
% 0.25/0.58 => ( A_41 = B_30 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_179_equalityI,axiom,
% 0.25/0.58 ! [A_41: x_a > $o,B_30: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ A_41 @ B_30 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ B_30 @ A_41 )
% 0.25/0.58 => ( A_41 = B_30 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_180_subsetD,axiom,
% 0.25/0.58 ! [C_2: nat,A_40: nat > $o,B_29: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ A_40 @ B_29 )
% 0.25/0.58 => ( ( member_nat @ C_2 @ A_40 )
% 0.25/0.58 => ( member_nat @ C_2 @ B_29 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_181_subsetD,axiom,
% 0.25/0.58 ! [C_2: x_a,A_40: x_a > $o,B_29: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ A_40 @ B_29 )
% 0.25/0.58 => ( ( member_a @ C_2 @ A_40 )
% 0.25/0.58 => ( member_a @ C_2 @ B_29 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_182_subsetD,axiom,
% 0.25/0.58 ! [C_2: pname,A_40: pname > $o,B_29: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ A_40 @ B_29 )
% 0.25/0.58 => ( ( member_pname @ C_2 @ A_40 )
% 0.25/0.58 => ( member_pname @ C_2 @ B_29 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_183_insertCI,axiom,
% 0.25/0.58 ! [B_28: nat,A_39: nat,B_27: nat > $o] :
% 0.25/0.58 ( ( ~ ( member_nat @ A_39 @ B_27 )
% 0.25/0.58 => ( A_39 = B_28 ) )
% 0.25/0.58 => ( member_nat @ A_39 @ ( insert_nat @ B_28 @ B_27 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_184_insertCI,axiom,
% 0.25/0.58 ! [B_28: pname,A_39: pname,B_27: pname > $o] :
% 0.25/0.58 ( ( ~ ( member_pname @ A_39 @ B_27 )
% 0.25/0.58 => ( A_39 = B_28 ) )
% 0.25/0.58 => ( member_pname @ A_39 @ ( insert_pname @ B_28 @ B_27 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_185_insertCI,axiom,
% 0.25/0.58 ! [B_28: x_a,A_39: x_a,B_27: x_a > $o] :
% 0.25/0.58 ( ( ~ ( member_a @ A_39 @ B_27 )
% 0.25/0.58 => ( A_39 = B_28 ) )
% 0.25/0.58 => ( member_a @ A_39 @ ( insert_a @ B_28 @ B_27 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_186_insertE,axiom,
% 0.25/0.58 ! [A_38: nat,B_26: nat,A_37: nat > $o] :
% 0.25/0.58 ( ( member_nat @ A_38 @ ( insert_nat @ B_26 @ A_37 ) )
% 0.25/0.58 => ( ( A_38 != B_26 )
% 0.25/0.58 => ( member_nat @ A_38 @ A_37 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_187_insertE,axiom,
% 0.25/0.58 ! [A_38: pname,B_26: pname,A_37: pname > $o] :
% 0.25/0.58 ( ( member_pname @ A_38 @ ( insert_pname @ B_26 @ A_37 ) )
% 0.25/0.58 => ( ( A_38 != B_26 )
% 0.25/0.58 => ( member_pname @ A_38 @ A_37 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_188_insertE,axiom,
% 0.25/0.58 ! [A_38: x_a,B_26: x_a,A_37: x_a > $o] :
% 0.25/0.58 ( ( member_a @ A_38 @ ( insert_a @ B_26 @ A_37 ) )
% 0.25/0.58 => ( ( A_38 != B_26 )
% 0.25/0.58 => ( member_a @ A_38 @ A_37 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_189_insertI1,axiom,
% 0.25/0.58 ! [A_36: nat,B_25: nat > $o] : ( member_nat @ A_36 @ ( insert_nat @ A_36 @ B_25 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_190_insertI1,axiom,
% 0.25/0.58 ! [A_36: pname,B_25: pname > $o] : ( member_pname @ A_36 @ ( insert_pname @ A_36 @ B_25 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_191_insertI1,axiom,
% 0.25/0.58 ! [A_36: x_a,B_25: x_a > $o] : ( member_a @ A_36 @ ( insert_a @ A_36 @ B_25 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_192_insert__compr,axiom,
% 0.25/0.58 ! [A_35: nat,B_24: nat > $o] :
% 0.25/0.58 ( ( insert_nat @ A_35 @ B_24 )
% 0.25/0.58 = ( collect_nat
% 0.25/0.58 @ ^ [X: nat] : ( (|) @ ( X = A_35 ) @ ( member_nat @ X @ B_24 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_193_insert__compr,axiom,
% 0.25/0.58 ! [A_35: pname,B_24: pname > $o] :
% 0.25/0.58 ( ( insert_pname @ A_35 @ B_24 )
% 0.25/0.58 = ( collect_pname
% 0.25/0.58 @ ^ [X: pname] : ( (|) @ ( X = A_35 ) @ ( member_pname @ X @ B_24 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_194_insert__compr,axiom,
% 0.25/0.58 ! [A_35: x_a,B_24: x_a > $o] :
% 0.25/0.58 ( ( insert_a @ A_35 @ B_24 )
% 0.25/0.58 = ( collect_a
% 0.25/0.58 @ ^ [X: x_a] : ( (|) @ ( X = A_35 ) @ ( member_a @ X @ B_24 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_195_insert__compr,axiom,
% 0.25/0.58 ! [A_35: nat > $o,B_24: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( insert_nat_o @ A_35 @ B_24 )
% 0.25/0.58 = ( collect_nat_o
% 0.25/0.58 @ ^ [X: nat > $o] : ( (|) @ ( X = A_35 ) @ ( member_nat_o @ X @ B_24 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_196_insert__compr,axiom,
% 0.25/0.58 ! [A_35: pname > $o,B_24: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( insert_pname_o @ A_35 @ B_24 )
% 0.25/0.58 = ( collect_pname_o
% 0.25/0.58 @ ^ [X: pname > $o] : ( (|) @ ( X = A_35 ) @ ( member_pname_o @ X @ B_24 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_197_insert__compr,axiom,
% 0.25/0.58 ! [A_35: x_a > $o,B_24: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( insert_a_o @ A_35 @ B_24 )
% 0.25/0.58 = ( collect_a_o
% 0.25/0.58 @ ^ [X: x_a > $o] : ( (|) @ ( X = A_35 ) @ ( member_a_o @ X @ B_24 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_198_insert__Collect,axiom,
% 0.25/0.58 ! [A_34: nat,P_2: nat > $o] :
% 0.25/0.58 ( ( insert_nat @ A_34 @ ( collect_nat @ P_2 ) )
% 0.25/0.58 = ( collect_nat
% 0.25/0.58 @ ^ [U: nat] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_199_insert__Collect,axiom,
% 0.25/0.58 ! [A_34: pname,P_2: pname > $o] :
% 0.25/0.58 ( ( insert_pname @ A_34 @ ( collect_pname @ P_2 ) )
% 0.25/0.58 = ( collect_pname
% 0.25/0.58 @ ^ [U: pname] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_200_insert__Collect,axiom,
% 0.25/0.58 ! [A_34: x_a,P_2: x_a > $o] :
% 0.25/0.58 ( ( insert_a @ A_34 @ ( collect_a @ P_2 ) )
% 0.25/0.58 = ( collect_a
% 0.25/0.58 @ ^ [U: x_a] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_201_insert__Collect,axiom,
% 0.25/0.58 ! [A_34: nat > $o,P_2: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( insert_nat_o @ A_34 @ ( collect_nat_o @ P_2 ) )
% 0.25/0.58 = ( collect_nat_o
% 0.25/0.58 @ ^ [U: nat > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_202_insert__Collect,axiom,
% 0.25/0.58 ! [A_34: pname > $o,P_2: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( insert_pname_o @ A_34 @ ( collect_pname_o @ P_2 ) )
% 0.25/0.58 = ( collect_pname_o
% 0.25/0.58 @ ^ [U: pname > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_203_insert__Collect,axiom,
% 0.25/0.58 ! [A_34: x_a > $o,P_2: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( insert_a_o @ A_34 @ ( collect_a_o @ P_2 ) )
% 0.25/0.58 = ( collect_a_o
% 0.25/0.58 @ ^ [U: x_a > $o] : ( (=>) @ ( (~) @ ( U = A_34 ) ) @ ( P_2 @ U ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_204_insert__absorb2,axiom,
% 0.25/0.58 ! [X_14: nat,A_33: nat > $o] :
% 0.25/0.58 ( ( insert_nat @ X_14 @ ( insert_nat @ X_14 @ A_33 ) )
% 0.25/0.58 = ( insert_nat @ X_14 @ A_33 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_205_insert__absorb2,axiom,
% 0.25/0.58 ! [X_14: pname,A_33: pname > $o] :
% 0.25/0.58 ( ( insert_pname @ X_14 @ ( insert_pname @ X_14 @ A_33 ) )
% 0.25/0.58 = ( insert_pname @ X_14 @ A_33 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_206_insert__absorb2,axiom,
% 0.25/0.58 ! [X_14: x_a,A_33: x_a > $o] :
% 0.25/0.58 ( ( insert_a @ X_14 @ ( insert_a @ X_14 @ A_33 ) )
% 0.25/0.58 = ( insert_a @ X_14 @ A_33 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_207_insert__commute,axiom,
% 0.25/0.58 ! [X_13: nat,Y_2: nat,A_32: nat > $o] :
% 0.25/0.58 ( ( insert_nat @ X_13 @ ( insert_nat @ Y_2 @ A_32 ) )
% 0.25/0.58 = ( insert_nat @ Y_2 @ ( insert_nat @ X_13 @ A_32 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_208_insert__commute,axiom,
% 0.25/0.58 ! [X_13: pname,Y_2: pname,A_32: pname > $o] :
% 0.25/0.58 ( ( insert_pname @ X_13 @ ( insert_pname @ Y_2 @ A_32 ) )
% 0.25/0.58 = ( insert_pname @ Y_2 @ ( insert_pname @ X_13 @ A_32 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_209_insert__commute,axiom,
% 0.25/0.58 ! [X_13: x_a,Y_2: x_a,A_32: x_a > $o] :
% 0.25/0.58 ( ( insert_a @ X_13 @ ( insert_a @ Y_2 @ A_32 ) )
% 0.25/0.58 = ( insert_a @ Y_2 @ ( insert_a @ X_13 @ A_32 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_210_insert__iff,axiom,
% 0.25/0.58 ! [A_31: nat,B_23: nat,A_30: nat > $o] :
% 0.25/0.58 ( ( member_nat @ A_31 @ ( insert_nat @ B_23 @ A_30 ) )
% 0.25/0.58 <=> ( ( A_31 = B_23 )
% 0.25/0.58 | ( member_nat @ A_31 @ A_30 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_211_insert__iff,axiom,
% 0.25/0.58 ! [A_31: pname,B_23: pname,A_30: pname > $o] :
% 0.25/0.58 ( ( member_pname @ A_31 @ ( insert_pname @ B_23 @ A_30 ) )
% 0.25/0.58 <=> ( ( A_31 = B_23 )
% 0.25/0.58 | ( member_pname @ A_31 @ A_30 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_212_insert__iff,axiom,
% 0.25/0.58 ! [A_31: x_a,B_23: x_a,A_30: x_a > $o] :
% 0.25/0.58 ( ( member_a @ A_31 @ ( insert_a @ B_23 @ A_30 ) )
% 0.25/0.58 <=> ( ( A_31 = B_23 )
% 0.25/0.58 | ( member_a @ A_31 @ A_30 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_213_insert__code,axiom,
% 0.25/0.58 ! [Y_1: nat,A_29: nat > $o,X_12: nat] :
% 0.25/0.58 ( ( insert_nat @ Y_1 @ A_29 @ X_12 )
% 0.25/0.58 <=> ( ( Y_1 = X_12 )
% 0.25/0.58 | ( A_29 @ X_12 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_214_insert__code,axiom,
% 0.25/0.58 ! [Y_1: pname,A_29: pname > $o,X_12: pname] :
% 0.25/0.58 ( ( insert_pname @ Y_1 @ A_29 @ X_12 )
% 0.25/0.58 <=> ( ( Y_1 = X_12 )
% 0.25/0.58 | ( A_29 @ X_12 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_215_insert__code,axiom,
% 0.25/0.58 ! [Y_1: x_a,A_29: x_a > $o,X_12: x_a] :
% 0.25/0.58 ( ( insert_a @ Y_1 @ A_29 @ X_12 )
% 0.25/0.58 <=> ( ( Y_1 = X_12 )
% 0.25/0.58 | ( A_29 @ X_12 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_216_insert__ident,axiom,
% 0.25/0.58 ! [B_22: nat > $o,X_11: nat,A_28: nat > $o] :
% 0.25/0.58 ( ~ ( member_nat @ X_11 @ A_28 )
% 0.25/0.58 => ( ~ ( member_nat @ X_11 @ B_22 )
% 0.25/0.58 => ( ( ( insert_nat @ X_11 @ A_28 )
% 0.25/0.58 = ( insert_nat @ X_11 @ B_22 ) )
% 0.25/0.58 <=> ( A_28 = B_22 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_217_insert__ident,axiom,
% 0.25/0.58 ! [B_22: pname > $o,X_11: pname,A_28: pname > $o] :
% 0.25/0.58 ( ~ ( member_pname @ X_11 @ A_28 )
% 0.25/0.58 => ( ~ ( member_pname @ X_11 @ B_22 )
% 0.25/0.58 => ( ( ( insert_pname @ X_11 @ A_28 )
% 0.25/0.58 = ( insert_pname @ X_11 @ B_22 ) )
% 0.25/0.58 <=> ( A_28 = B_22 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_218_insert__ident,axiom,
% 0.25/0.58 ! [B_22: x_a > $o,X_11: x_a,A_28: x_a > $o] :
% 0.25/0.58 ( ~ ( member_a @ X_11 @ A_28 )
% 0.25/0.58 => ( ~ ( member_a @ X_11 @ B_22 )
% 0.25/0.58 => ( ( ( insert_a @ X_11 @ A_28 )
% 0.25/0.58 = ( insert_a @ X_11 @ B_22 ) )
% 0.25/0.58 <=> ( A_28 = B_22 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_219_insertI2,axiom,
% 0.25/0.58 ! [B_21: nat,A_27: nat,B_20: nat > $o] :
% 0.25/0.58 ( ( member_nat @ A_27 @ B_20 )
% 0.25/0.58 => ( member_nat @ A_27 @ ( insert_nat @ B_21 @ B_20 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_220_insertI2,axiom,
% 0.25/0.58 ! [B_21: pname,A_27: pname,B_20: pname > $o] :
% 0.25/0.58 ( ( member_pname @ A_27 @ B_20 )
% 0.25/0.58 => ( member_pname @ A_27 @ ( insert_pname @ B_21 @ B_20 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_221_insertI2,axiom,
% 0.25/0.58 ! [B_21: x_a,A_27: x_a,B_20: x_a > $o] :
% 0.25/0.58 ( ( member_a @ A_27 @ B_20 )
% 0.25/0.58 => ( member_a @ A_27 @ ( insert_a @ B_21 @ B_20 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_222_insert__absorb,axiom,
% 0.25/0.58 ! [A_26: nat,A_25: nat > $o] :
% 0.25/0.58 ( ( member_nat @ A_26 @ A_25 )
% 0.25/0.58 => ( ( insert_nat @ A_26 @ A_25 )
% 0.25/0.58 = A_25 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_223_insert__absorb,axiom,
% 0.25/0.58 ! [A_26: pname,A_25: pname > $o] :
% 0.25/0.58 ( ( member_pname @ A_26 @ A_25 )
% 0.25/0.58 => ( ( insert_pname @ A_26 @ A_25 )
% 0.25/0.58 = A_25 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_224_insert__absorb,axiom,
% 0.25/0.58 ! [A_26: x_a,A_25: x_a > $o] :
% 0.25/0.58 ( ( member_a @ A_26 @ A_25 )
% 0.25/0.58 => ( ( insert_a @ A_26 @ A_25 )
% 0.25/0.58 = A_25 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_225_subset__refl,axiom,
% 0.25/0.58 ! [A_24: nat > $o] : ( ord_less_eq_nat_o @ A_24 @ A_24 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_226_subset__refl,axiom,
% 0.25/0.58 ! [A_24: pname > $o] : ( ord_less_eq_pname_o @ A_24 @ A_24 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_227_subset__refl,axiom,
% 0.25/0.58 ! [A_24: x_a > $o] : ( ord_less_eq_a_o @ A_24 @ A_24 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_228_set__eq__subset,axiom,
% 0.25/0.58 ! [A_23: nat > $o,B_19: nat > $o] :
% 0.25/0.58 ( ( A_23 = B_19 )
% 0.25/0.58 <=> ( ( ord_less_eq_nat_o @ A_23 @ B_19 )
% 0.25/0.58 & ( ord_less_eq_nat_o @ B_19 @ A_23 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_229_set__eq__subset,axiom,
% 0.25/0.58 ! [A_23: pname > $o,B_19: pname > $o] :
% 0.25/0.58 ( ( A_23 = B_19 )
% 0.25/0.58 <=> ( ( ord_less_eq_pname_o @ A_23 @ B_19 )
% 0.25/0.58 & ( ord_less_eq_pname_o @ B_19 @ A_23 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_230_set__eq__subset,axiom,
% 0.25/0.58 ! [A_23: x_a > $o,B_19: x_a > $o] :
% 0.25/0.58 ( ( A_23 = B_19 )
% 0.25/0.58 <=> ( ( ord_less_eq_a_o @ A_23 @ B_19 )
% 0.25/0.58 & ( ord_less_eq_a_o @ B_19 @ A_23 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_231_equalityD1,axiom,
% 0.25/0.58 ! [A_22: nat > $o,B_18: nat > $o] :
% 0.25/0.58 ( ( A_22 = B_18 )
% 0.25/0.58 => ( ord_less_eq_nat_o @ A_22 @ B_18 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_232_equalityD1,axiom,
% 0.25/0.58 ! [A_22: pname > $o,B_18: pname > $o] :
% 0.25/0.58 ( ( A_22 = B_18 )
% 0.25/0.58 => ( ord_less_eq_pname_o @ A_22 @ B_18 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_233_equalityD1,axiom,
% 0.25/0.58 ! [A_22: x_a > $o,B_18: x_a > $o] :
% 0.25/0.58 ( ( A_22 = B_18 )
% 0.25/0.58 => ( ord_less_eq_a_o @ A_22 @ B_18 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_234_equalityD2,axiom,
% 0.25/0.58 ! [A_21: nat > $o,B_17: nat > $o] :
% 0.25/0.58 ( ( A_21 = B_17 )
% 0.25/0.58 => ( ord_less_eq_nat_o @ B_17 @ A_21 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_235_equalityD2,axiom,
% 0.25/0.58 ! [A_21: pname > $o,B_17: pname > $o] :
% 0.25/0.58 ( ( A_21 = B_17 )
% 0.25/0.58 => ( ord_less_eq_pname_o @ B_17 @ A_21 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_236_equalityD2,axiom,
% 0.25/0.58 ! [A_21: x_a > $o,B_17: x_a > $o] :
% 0.25/0.58 ( ( A_21 = B_17 )
% 0.25/0.58 => ( ord_less_eq_a_o @ B_17 @ A_21 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_237_in__mono,axiom,
% 0.25/0.58 ! [X_10: nat,A_20: nat > $o,B_16: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ A_20 @ B_16 )
% 0.25/0.58 => ( ( member_nat @ X_10 @ A_20 )
% 0.25/0.58 => ( member_nat @ X_10 @ B_16 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_238_in__mono,axiom,
% 0.25/0.58 ! [X_10: x_a,A_20: x_a > $o,B_16: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ A_20 @ B_16 )
% 0.25/0.58 => ( ( member_a @ X_10 @ A_20 )
% 0.25/0.58 => ( member_a @ X_10 @ B_16 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_239_in__mono,axiom,
% 0.25/0.58 ! [X_10: pname,A_20: pname > $o,B_16: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ A_20 @ B_16 )
% 0.25/0.58 => ( ( member_pname @ X_10 @ A_20 )
% 0.25/0.58 => ( member_pname @ X_10 @ B_16 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_240_set__rev__mp,axiom,
% 0.25/0.58 ! [B_15: nat > $o,X_9: nat,A_19: nat > $o] :
% 0.25/0.58 ( ( member_nat @ X_9 @ A_19 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o @ A_19 @ B_15 )
% 0.25/0.58 => ( member_nat @ X_9 @ B_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_241_set__rev__mp,axiom,
% 0.25/0.58 ! [B_15: x_a > $o,X_9: x_a,A_19: x_a > $o] :
% 0.25/0.58 ( ( member_a @ X_9 @ A_19 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ A_19 @ B_15 )
% 0.25/0.58 => ( member_a @ X_9 @ B_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_242_set__rev__mp,axiom,
% 0.25/0.58 ! [B_15: pname > $o,X_9: pname,A_19: pname > $o] :
% 0.25/0.58 ( ( member_pname @ X_9 @ A_19 )
% 0.25/0.58 => ( ( ord_less_eq_pname_o @ A_19 @ B_15 )
% 0.25/0.58 => ( member_pname @ X_9 @ B_15 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_243_set__mp,axiom,
% 0.25/0.58 ! [X_8: nat,A_18: nat > $o,B_14: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ A_18 @ B_14 )
% 0.25/0.58 => ( ( member_nat @ X_8 @ A_18 )
% 0.25/0.58 => ( member_nat @ X_8 @ B_14 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_244_set__mp,axiom,
% 0.25/0.58 ! [X_8: x_a,A_18: x_a > $o,B_14: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ A_18 @ B_14 )
% 0.25/0.58 => ( ( member_a @ X_8 @ A_18 )
% 0.25/0.58 => ( member_a @ X_8 @ B_14 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_245_set__mp,axiom,
% 0.25/0.58 ! [X_8: pname,A_18: pname > $o,B_14: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ A_18 @ B_14 )
% 0.25/0.58 => ( ( member_pname @ X_8 @ A_18 )
% 0.25/0.58 => ( member_pname @ X_8 @ B_14 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_246_subset__trans,axiom,
% 0.25/0.58 ! [C_1: nat > $o,A_17: nat > $o,B_13: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ A_17 @ B_13 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o @ B_13 @ C_1 )
% 0.25/0.58 => ( ord_less_eq_nat_o @ A_17 @ C_1 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_247_subset__trans,axiom,
% 0.25/0.58 ! [C_1: pname > $o,A_17: pname > $o,B_13: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ A_17 @ B_13 )
% 0.25/0.58 => ( ( ord_less_eq_pname_o @ B_13 @ C_1 )
% 0.25/0.58 => ( ord_less_eq_pname_o @ A_17 @ C_1 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_248_subset__trans,axiom,
% 0.25/0.58 ! [C_1: x_a > $o,A_17: x_a > $o,B_13: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ A_17 @ B_13 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ B_13 @ C_1 )
% 0.25/0.58 => ( ord_less_eq_a_o @ A_17 @ C_1 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_249_equalityE,axiom,
% 0.25/0.58 ! [A_16: nat > $o,B_12: nat > $o] :
% 0.25/0.58 ( ( A_16 = B_12 )
% 0.25/0.58 => ~ ( ( ord_less_eq_nat_o @ A_16 @ B_12 )
% 0.25/0.58 => ~ ( ord_less_eq_nat_o @ B_12 @ A_16 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_250_equalityE,axiom,
% 0.25/0.58 ! [A_16: pname > $o,B_12: pname > $o] :
% 0.25/0.58 ( ( A_16 = B_12 )
% 0.25/0.58 => ~ ( ( ord_less_eq_pname_o @ A_16 @ B_12 )
% 0.25/0.58 => ~ ( ord_less_eq_pname_o @ B_12 @ A_16 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_251_equalityE,axiom,
% 0.25/0.58 ! [A_16: x_a > $o,B_12: x_a > $o] :
% 0.25/0.58 ( ( A_16 = B_12 )
% 0.25/0.58 => ~ ( ( ord_less_eq_a_o @ A_16 @ B_12 )
% 0.25/0.58 => ~ ( ord_less_eq_a_o @ B_12 @ A_16 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_252_mem__def,axiom,
% 0.25/0.58 ! [X_7: nat,A_15: nat > $o] :
% 0.25/0.58 ( ( member_nat @ X_7 @ A_15 )
% 0.25/0.58 <=> ( A_15 @ X_7 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_253_mem__def,axiom,
% 0.25/0.58 ! [X_7: x_a,A_15: x_a > $o] :
% 0.25/0.58 ( ( member_a @ X_7 @ A_15 )
% 0.25/0.58 <=> ( A_15 @ X_7 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_254_mem__def,axiom,
% 0.25/0.58 ! [X_7: pname,A_15: pname > $o] :
% 0.25/0.58 ( ( member_pname @ X_7 @ A_15 )
% 0.25/0.58 <=> ( A_15 @ X_7 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_255_Collect__def,axiom,
% 0.25/0.58 ! [P_1: pname > $o] :
% 0.25/0.58 ( ( collect_pname @ P_1 )
% 0.25/0.58 = P_1 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_256_Collect__def,axiom,
% 0.25/0.58 ! [P_1: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( collect_nat_o @ P_1 )
% 0.25/0.58 = P_1 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_257_Collect__def,axiom,
% 0.25/0.58 ! [P_1: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( collect_pname_o @ P_1 )
% 0.25/0.58 = P_1 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_258_Collect__def,axiom,
% 0.25/0.58 ! [P_1: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( collect_a_o @ P_1 )
% 0.25/0.58 = P_1 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_259_Collect__def,axiom,
% 0.25/0.58 ! [P_1: nat > $o] :
% 0.25/0.58 ( ( collect_nat @ P_1 )
% 0.25/0.58 = P_1 ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_260_image__iff,axiom,
% 0.25/0.58 ! [Z: x_a,F_8: pname > x_a,A_14: pname > $o] :
% 0.25/0.58 ( ( member_a @ Z @ ( image_pname_a @ F_8 @ A_14 ) )
% 0.25/0.58 <=> ? [X: pname] :
% 0.25/0.58 ( ( member_pname @ X @ A_14 )
% 0.25/0.58 & ( Z
% 0.25/0.58 = ( F_8 @ X ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_261_imageI,axiom,
% 0.25/0.58 ! [F_7: pname > x_a,X_6: pname,A_13: pname > $o] :
% 0.25/0.58 ( ( member_pname @ X_6 @ A_13 )
% 0.25/0.58 => ( member_a @ ( F_7 @ X_6 ) @ ( image_pname_a @ F_7 @ A_13 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_262_rev__image__eqI,axiom,
% 0.25/0.58 ! [B_11: x_a,F_6: pname > x_a,X_5: pname,A_12: pname > $o] :
% 0.25/0.58 ( ( member_pname @ X_5 @ A_12 )
% 0.25/0.58 => ( ( B_11
% 0.25/0.58 = ( F_6 @ X_5 ) )
% 0.25/0.58 => ( member_a @ B_11 @ ( image_pname_a @ F_6 @ A_12 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_263_insert__compr__raw,axiom,
% 0.25/0.58 ! [X: nat,Xa: nat > $o] :
% 0.25/0.58 ( ( insert_nat @ X @ Xa )
% 0.25/0.58 = ( collect_nat
% 0.25/0.58 @ ^ [Y: nat] : ( (|) @ ( Y = X ) @ ( member_nat @ Y @ Xa ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_264_insert__compr__raw,axiom,
% 0.25/0.58 ! [X: pname,Xa: pname > $o] :
% 0.25/0.58 ( ( insert_pname @ X @ Xa )
% 0.25/0.58 = ( collect_pname
% 0.25/0.58 @ ^ [Y: pname] : ( (|) @ ( Y = X ) @ ( member_pname @ Y @ Xa ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_265_insert__compr__raw,axiom,
% 0.25/0.58 ! [X: x_a,Xa: x_a > $o] :
% 0.25/0.58 ( ( insert_a @ X @ Xa )
% 0.25/0.58 = ( collect_a
% 0.25/0.58 @ ^ [Y: x_a] : ( (|) @ ( Y = X ) @ ( member_a @ Y @ Xa ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_266_insert__compr__raw,axiom,
% 0.25/0.58 ! [X: nat > $o,Xa: ( nat > $o ) > $o] :
% 0.25/0.58 ( ( insert_nat_o @ X @ Xa )
% 0.25/0.58 = ( collect_nat_o
% 0.25/0.58 @ ^ [Y: nat > $o] : ( (|) @ ( Y = X ) @ ( member_nat_o @ Y @ Xa ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_267_insert__compr__raw,axiom,
% 0.25/0.58 ! [X: pname > $o,Xa: ( pname > $o ) > $o] :
% 0.25/0.58 ( ( insert_pname_o @ X @ Xa )
% 0.25/0.58 = ( collect_pname_o
% 0.25/0.58 @ ^ [Y: pname > $o] : ( (|) @ ( Y = X ) @ ( member_pname_o @ Y @ Xa ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_268_insert__compr__raw,axiom,
% 0.25/0.58 ! [X: x_a > $o,Xa: ( x_a > $o ) > $o] :
% 0.25/0.58 ( ( insert_a_o @ X @ Xa )
% 0.25/0.58 = ( collect_a_o
% 0.25/0.58 @ ^ [Y: x_a > $o] : ( (|) @ ( Y = X ) @ ( member_a_o @ Y @ Xa ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_269_subset__insertI,axiom,
% 0.25/0.58 ! [B_10: nat > $o,A_11: nat] : ( ord_less_eq_nat_o @ B_10 @ ( insert_nat @ A_11 @ B_10 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_270_subset__insertI,axiom,
% 0.25/0.58 ! [B_10: pname > $o,A_11: pname] : ( ord_less_eq_pname_o @ B_10 @ ( insert_pname @ A_11 @ B_10 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_271_subset__insertI,axiom,
% 0.25/0.58 ! [B_10: x_a > $o,A_11: x_a] : ( ord_less_eq_a_o @ B_10 @ ( insert_a @ A_11 @ B_10 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_272_insert__subset,axiom,
% 0.25/0.58 ! [X_4: nat,A_10: nat > $o,B_9: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ ( insert_nat @ X_4 @ A_10 ) @ B_9 )
% 0.25/0.58 <=> ( ( member_nat @ X_4 @ B_9 )
% 0.25/0.58 & ( ord_less_eq_nat_o @ A_10 @ B_9 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_273_insert__subset,axiom,
% 0.25/0.58 ! [X_4: pname,A_10: pname > $o,B_9: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_4 @ A_10 ) @ B_9 )
% 0.25/0.58 <=> ( ( member_pname @ X_4 @ B_9 )
% 0.25/0.58 & ( ord_less_eq_pname_o @ A_10 @ B_9 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_274_insert__subset,axiom,
% 0.25/0.58 ! [X_4: x_a,A_10: x_a > $o,B_9: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ ( insert_a @ X_4 @ A_10 ) @ B_9 )
% 0.25/0.58 <=> ( ( member_a @ X_4 @ B_9 )
% 0.25/0.58 & ( ord_less_eq_a_o @ A_10 @ B_9 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_275_subset__insert,axiom,
% 0.25/0.58 ! [B_8: nat > $o,X_3: nat,A_9: nat > $o] :
% 0.25/0.58 ( ~ ( member_nat @ X_3 @ A_9 )
% 0.25/0.58 => ( ( ord_less_eq_nat_o @ A_9 @ ( insert_nat @ X_3 @ B_8 ) )
% 0.25/0.58 <=> ( ord_less_eq_nat_o @ A_9 @ B_8 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_276_subset__insert,axiom,
% 0.25/0.58 ! [B_8: pname > $o,X_3: pname,A_9: pname > $o] :
% 0.25/0.58 ( ~ ( member_pname @ X_3 @ A_9 )
% 0.25/0.58 => ( ( ord_less_eq_pname_o @ A_9 @ ( insert_pname @ X_3 @ B_8 ) )
% 0.25/0.58 <=> ( ord_less_eq_pname_o @ A_9 @ B_8 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_277_subset__insert,axiom,
% 0.25/0.58 ! [B_8: x_a > $o,X_3: x_a,A_9: x_a > $o] :
% 0.25/0.58 ( ~ ( member_a @ X_3 @ A_9 )
% 0.25/0.58 => ( ( ord_less_eq_a_o @ A_9 @ ( insert_a @ X_3 @ B_8 ) )
% 0.25/0.58 <=> ( ord_less_eq_a_o @ A_9 @ B_8 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_278_subset__insertI2,axiom,
% 0.25/0.58 ! [B_7: nat,A_8: nat > $o,B_6: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ A_8 @ B_6 )
% 0.25/0.58 => ( ord_less_eq_nat_o @ A_8 @ ( insert_nat @ B_7 @ B_6 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_279_subset__insertI2,axiom,
% 0.25/0.58 ! [B_7: pname,A_8: pname > $o,B_6: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ A_8 @ B_6 )
% 0.25/0.58 => ( ord_less_eq_pname_o @ A_8 @ ( insert_pname @ B_7 @ B_6 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_280_subset__insertI2,axiom,
% 0.25/0.58 ! [B_7: x_a,A_8: x_a > $o,B_6: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ A_8 @ B_6 )
% 0.25/0.58 => ( ord_less_eq_a_o @ A_8 @ ( insert_a @ B_7 @ B_6 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_281_insert__mono,axiom,
% 0.25/0.58 ! [A_7: nat,C: nat > $o,D: nat > $o] :
% 0.25/0.58 ( ( ord_less_eq_nat_o @ C @ D )
% 0.25/0.58 => ( ord_less_eq_nat_o @ ( insert_nat @ A_7 @ C ) @ ( insert_nat @ A_7 @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_282_insert__mono,axiom,
% 0.25/0.58 ! [A_7: pname,C: pname > $o,D: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ C @ D )
% 0.25/0.58 => ( ord_less_eq_pname_o @ ( insert_pname @ A_7 @ C ) @ ( insert_pname @ A_7 @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_283_insert__mono,axiom,
% 0.25/0.58 ! [A_7: x_a,C: x_a > $o,D: x_a > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ C @ D )
% 0.25/0.58 => ( ord_less_eq_a_o @ ( insert_a @ A_7 @ C ) @ ( insert_a @ A_7 @ D ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_284_image__insert,axiom,
% 0.25/0.58 ! [F_5: pname > x_a,A_6: pname,B_5: pname > $o] :
% 0.25/0.58 ( ( image_pname_a @ F_5 @ ( insert_pname @ A_6 @ B_5 ) )
% 0.25/0.58 = ( insert_a @ ( F_5 @ A_6 ) @ ( image_pname_a @ F_5 @ B_5 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_285_insert__image,axiom,
% 0.25/0.58 ! [F_4: pname > x_a,X_2: pname,A_5: pname > $o] :
% 0.25/0.58 ( ( member_pname @ X_2 @ A_5 )
% 0.25/0.58 => ( ( insert_a @ ( F_4 @ X_2 ) @ ( image_pname_a @ F_4 @ A_5 ) )
% 0.25/0.58 = ( image_pname_a @ F_4 @ A_5 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_286_subset__image__iff,axiom,
% 0.25/0.58 ! [B_4: x_a > $o,F_3: pname > x_a,A_4: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_a_o @ B_4 @ ( image_pname_a @ F_3 @ A_4 ) )
% 0.25/0.58 <=> ? [AA: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ AA @ A_4 )
% 0.25/0.58 & ( B_4
% 0.25/0.58 = ( image_pname_a @ F_3 @ AA ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_287_image__mono,axiom,
% 0.25/0.58 ! [F_2: pname > x_a,A_3: pname > $o,B_3: pname > $o] :
% 0.25/0.58 ( ( ord_less_eq_pname_o @ A_3 @ B_3 )
% 0.25/0.58 => ( ord_less_eq_a_o @ ( image_pname_a @ F_2 @ A_3 ) @ ( image_pname_a @ F_2 @ B_3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_288_imageE,axiom,
% 0.25/0.58 ! [B_2: x_a,F_1: pname > x_a,A_2: pname > $o] :
% 0.25/0.58 ( ( member_a @ B_2 @ ( image_pname_a @ F_1 @ A_2 ) )
% 0.25/0.58 => ~ ! [X: pname] :
% 0.25/0.58 ( ( B_2
% 0.25/0.58 = ( F_1 @ X ) )
% 0.25/0.58 => ~ ( member_pname @ X @ A_2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_289_subsetI,axiom,
% 0.25/0.58 ! [B_1: nat > $o,A_1: nat > $o] :
% 0.25/0.58 ( ! [X: nat] :
% 0.25/0.58 ( ( member_nat @ X @ A_1 )
% 0.25/0.58 => ( member_nat @ X @ B_1 ) )
% 0.25/0.58 => ( ord_less_eq_nat_o @ A_1 @ B_1 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_290_subsetI,axiom,
% 0.25/0.58 ! [B_1: x_a > $o,A_1: x_a > $o] :
% 0.25/0.58 ( ! [X: x_a] :
% 0.25/0.58 ( ( member_a @ X @ A_1 )
% 0.25/0.58 => ( member_a @ X @ B_1 ) )
% 0.25/0.58 => ( ord_less_eq_a_o @ A_1 @ B_1 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_291_subsetI,axiom,
% 0.25/0.58 ! [B_1: pname > $o,A_1: pname > $o] :
% 0.25/0.58 ( ! [X: pname] :
% 0.25/0.58 ( ( member_pname @ X @ A_1 )
% 0.25/0.58 => ( member_pname @ X @ B_1 ) )
% 0.25/0.58 => ( ord_less_eq_pname_o @ A_1 @ B_1 ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_292_zero__induct__lemma,axiom,
% 0.25/0.58 ! [I: nat,P: nat > $o,K: nat] :
% 0.25/0.58 ( ( P @ K )
% 0.25/0.58 => ( ! [N_2: nat] :
% 0.25/0.58 ( ( P @ ( suc @ N_2 ) )
% 0.25/0.58 => ( P @ N_2 ) )
% 0.25/0.58 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_293_Suc__le__D,axiom,
% 0.25/0.58 ! [N_1: nat,M_1: nat] :
% 0.25/0.58 ( ( ord_less_eq_nat @ ( suc @ N_1 ) @ M_1 )
% 0.25/0.58 => ? [M: nat] :
% 0.25/0.58 ( M_1
% 0.25/0.58 = ( suc @ M ) ) ) ).
% 0.25/0.58
% 0.25/0.58 thf(fact_294_image__subsetI,axiom,
% 0.25/0.58 ! [F: pname > x_a,B: x_a > $o,A: pname > $o] :
% 0.25/0.58 ( ! [X: pname] :
% 0.25/0.58 ( ( member_pname @ X @ A )
% 0.25/0.58 => ( member_a @ ( F @ X ) @ B ) )
% 0.25/0.58 => ( ord_less_eq_a_o @ ( image_pname_a @ F @ A ) @ B ) ) ).
% 0.25/0.65
% 0.25/0.65 thf(fact_295_order__refl,axiom,
% 0.25/0.65 ! [X_1: nat > $o] : ( ord_less_eq_nat_o @ X_1 @ X_1 ) ).
% 0.25/0.65
% 0.25/0.65 thf(fact_296_order__refl,axiom,
% 0.25/0.65 ! [X_1: pname > $o] : ( ord_less_eq_pname_o @ X_1 @ X_1 ) ).
% 0.25/0.65
% 0.25/0.65 thf(fact_297_order__refl,axiom,
% 0.25/0.65 ! [X_1: nat] : ( ord_less_eq_nat @ X_1 @ X_1 ) ).
% 0.25/0.65
% 0.25/0.65 thf(fact_298_order__refl,axiom,
% 0.25/0.65 ! [X_1: x_a > $o] : ( ord_less_eq_a_o @ X_1 @ X_1 ) ).
% 0.25/0.65
% 0.25/0.65 thf(fact_299_finite__nat__set__iff__bounded__le,axiom,
% 0.25/0.65 ! [N: nat > $o] :
% 0.25/0.65 ( ( finite_finite_nat @ N )
% 0.25/0.65 <=> ? [M: nat] :
% 0.25/0.65 ! [X: nat] :
% 0.25/0.65 ( ( member_nat @ X @ N )
% 0.25/0.65 => ( ord_less_eq_nat @ X @ M ) ) ) ).
% 0.25/0.65
% 0.25/0.65 %----Conjectures (7)
% 0.25/0.65 thf(conj_0,hypothesis,
% 0.25/0.65 finite_finite_pname @ u ).
% 0.25/0.65
% 0.25/0.65 thf(conj_1,hypothesis,
% 0.25/0.65 ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ).
% 0.25/0.65
% 0.25/0.65 thf(conj_2,hypothesis,
% 0.25/0.65 ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ).
% 0.25/0.65
% 0.25/0.65 thf(conj_3,hypothesis,
% 0.25/0.65 ( ( finite_card_a @ g )
% 0.25/0.65 = ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ) ).
% 0.25/0.65
% 0.25/0.65 thf(conj_4,hypothesis,
% 0.25/0.65 member_pname @ pn @ u ).
% 0.25/0.65
% 0.25/0.65 thf(conj_5,hypothesis,
% 0.25/0.65 ~ ( member_a @ ( mgt_call @ pn ) @ g ) ).
% 0.25/0.65
% 0.25/0.65 thf(conj_6,conjecture,
% 0.25/0.65 ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ).
% 0.25/0.65
% 0.25/0.65 %------------------------------------------------------------------------------
% 0.25/0.65 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.7eLCWVQvOk/cvc5---1.0.5_11477.p...
% 0.25/0.65 (declare-sort $$unsorted 0)
% 0.25/0.65 (declare-sort tptp.x_a 0)
% 0.25/0.65 (declare-sort tptp.pname 0)
% 0.25/0.65 (declare-sort tptp.nat 0)
% 0.25/0.65 (declare-fun tptp.finite_card_a_o_o ((-> (-> (-> tptp.x_a Bool) Bool) Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite221134632me_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite_card_nat_o_o ((-> (-> (-> tptp.nat Bool) Bool) Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite_card_a_o ((-> (-> tptp.x_a Bool) Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite_card_pname_o ((-> (-> tptp.pname Bool) Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite_card_nat_o ((-> (-> tptp.nat Bool) Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite_card_a ((-> tptp.x_a Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite_card_pname ((-> tptp.pname Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite_card_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.25/0.65 (declare-fun tptp.finite1302365357_o_o_o ((-> (-> (-> (-> tptp.x_a Bool) Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite1648353812_o_o_o ((-> (-> (-> (-> tptp.pname Bool) Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite1237261006_o_o_o ((-> (-> (-> (-> tptp.nat Bool) Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite_finite_a_o_o ((-> (-> (-> tptp.x_a Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite1066544169me_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite1676163439at_o_o ((-> (-> (-> tptp.nat Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite_finite_a_o ((-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite297249702name_o ((-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite_finite_nat_o ((-> (-> tptp.nat Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite_finite_a ((-> tptp.x_a Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite_finite_pname ((-> tptp.pname Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.finite_finite_nat ((-> tptp.nat Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.25/0.65 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.25/0.65 (declare-fun tptp.ord_less_eq_a_o_o_o ((-> (-> (-> tptp.x_a Bool) Bool) Bool) (-> (-> (-> tptp.x_a Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_le1828183645_o_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool) (-> (-> (-> tptp.pname Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_le124054423_o_o_o ((-> (-> (-> tptp.nat Bool) Bool) Bool) (-> (-> (-> tptp.nat Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_less_eq_a_o_o ((-> (-> tptp.x_a Bool) Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_le1205211808me_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_less_eq_nat_o_o ((-> (-> tptp.nat Bool) Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_less_eq_a_o ((-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_less_eq_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.collect_a_o_o_o ((-> (-> (-> (-> tptp.x_a Bool) Bool) Bool) Bool) (-> (-> (-> tptp.x_a Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_pname_o_o_o ((-> (-> (-> (-> tptp.pname Bool) Bool) Bool) Bool) (-> (-> (-> tptp.pname Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_nat_o_o_o ((-> (-> (-> (-> tptp.nat Bool) Bool) Bool) Bool) (-> (-> (-> tptp.nat Bool) Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_a_o_o ((-> (-> (-> tptp.x_a Bool) Bool) Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_pname_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_nat_o_o ((-> (-> (-> tptp.nat Bool) Bool) Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_a_o ((-> (-> tptp.x_a Bool) Bool) (-> tptp.x_a Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_pname_o ((-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_nat_o ((-> (-> tptp.nat Bool) Bool) (-> tptp.nat Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.collect_a ((-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.collect_pname ((-> tptp.pname Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.collect_nat ((-> tptp.nat Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_o_o_a ((-> (-> (-> tptp.x_a Bool) Bool) tptp.x_a) (-> (-> (-> tptp.x_a Bool) Bool) Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_o_o_pname ((-> (-> (-> tptp.x_a Bool) Bool) tptp.pname) (-> (-> (-> tptp.x_a Bool) Bool) Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_o_o_nat ((-> (-> (-> tptp.x_a Bool) Bool) tptp.nat) (-> (-> (-> tptp.x_a Bool) Bool) Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_o_o_a ((-> (-> (-> tptp.pname Bool) Bool) tptp.x_a) (-> (-> (-> tptp.pname Bool) Bool) Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_471733107_pname ((-> (-> (-> tptp.pname Bool) Bool) tptp.pname) (-> (-> (-> tptp.pname Bool) Bool) Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_o_o_nat ((-> (-> (-> tptp.pname Bool) Bool) tptp.nat) (-> (-> (-> tptp.pname Bool) Bool) Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_o_o_a ((-> (-> (-> tptp.nat Bool) Bool) tptp.x_a) (-> (-> (-> tptp.nat Bool) Bool) Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_o_o_pname ((-> (-> (-> tptp.nat Bool) Bool) tptp.pname) (-> (-> (-> tptp.nat Bool) Bool) Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_o_o_nat ((-> (-> (-> tptp.nat Bool) Bool) tptp.nat) (-> (-> (-> tptp.nat Bool) Bool) Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_o_a ((-> (-> tptp.x_a Bool) tptp.x_a) (-> (-> tptp.x_a Bool) Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_o_pname ((-> (-> tptp.x_a Bool) tptp.pname) (-> (-> tptp.x_a Bool) Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_o_nat ((-> (-> tptp.x_a Bool) tptp.nat) (-> (-> tptp.x_a Bool) Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_o_a ((-> (-> tptp.pname Bool) tptp.x_a) (-> (-> tptp.pname Bool) Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_o_pname ((-> (-> tptp.pname Bool) tptp.pname) (-> (-> tptp.pname Bool) Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_o_nat ((-> (-> tptp.pname Bool) tptp.nat) (-> (-> tptp.pname Bool) Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_o_a ((-> (-> tptp.nat Bool) tptp.x_a) (-> (-> tptp.nat Bool) Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_o_pname ((-> (-> tptp.nat Bool) tptp.pname) (-> (-> tptp.nat Bool) Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_o_nat ((-> (-> tptp.nat Bool) tptp.nat) (-> (-> tptp.nat Bool) Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_a ((-> tptp.x_a tptp.x_a) (-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_pname ((-> tptp.x_a tptp.pname) (-> tptp.x_a Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.image_a_nat ((-> tptp.x_a tptp.nat) (-> tptp.x_a Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_a_o_o ((-> tptp.pname (-> tptp.x_a Bool) Bool) (-> tptp.pname Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_504089495me_o_o ((-> tptp.pname (-> tptp.pname Bool) Bool) (-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_nat_o_o ((-> tptp.pname (-> tptp.nat Bool) Bool) (-> tptp.pname Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_a_o ((-> tptp.pname tptp.x_a Bool) (-> tptp.pname Bool) (-> tptp.x_a Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_pname_o ((-> tptp.pname tptp.pname Bool) (-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_nat_o ((-> tptp.pname tptp.nat Bool) (-> tptp.pname Bool) (-> tptp.nat Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_a ((-> tptp.pname tptp.x_a) (-> tptp.pname Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_pname ((-> tptp.pname tptp.pname) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.image_pname_nat ((-> tptp.pname tptp.nat) (-> tptp.pname Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_a_o_o ((-> tptp.nat (-> tptp.x_a Bool) Bool) (-> tptp.nat Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_pname_o_o ((-> tptp.nat (-> tptp.pname Bool) Bool) (-> tptp.nat Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_nat_o_o ((-> tptp.nat (-> tptp.nat Bool) Bool) (-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_a_o ((-> tptp.nat tptp.x_a Bool) (-> tptp.nat Bool) (-> tptp.x_a Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_pname_o ((-> tptp.nat tptp.pname Bool) (-> tptp.nat Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_a ((-> tptp.nat tptp.x_a) (-> tptp.nat Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.image_nat_pname ((-> tptp.nat tptp.pname) (-> tptp.nat Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.insert_a_o_o ((-> (-> tptp.x_a Bool) Bool) (-> (-> (-> tptp.x_a Bool) Bool) Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.insert_pname_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> (-> tptp.pname Bool) Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.insert_nat_o_o ((-> (-> tptp.nat Bool) Bool) (-> (-> (-> tptp.nat Bool) Bool) Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.insert_a_o ((-> tptp.x_a Bool) (-> (-> tptp.x_a Bool) Bool) (-> tptp.x_a Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.insert_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.insert_nat_o ((-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool) (-> tptp.nat Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.insert_a (tptp.x_a (-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.insert_pname (tptp.pname (-> tptp.pname Bool) tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.insert_nat (tptp.nat (-> tptp.nat Bool) tptp.nat) Bool)
% 0.25/0.65 (declare-fun tptp.member_a_o ((-> tptp.x_a Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.member_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.member_nat_o ((-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.member_a (tptp.x_a (-> tptp.x_a Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.member_pname (tptp.pname (-> tptp.pname Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.member_nat (tptp.nat (-> tptp.nat Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.g (tptp.x_a) Bool)
% 0.25/0.65 (declare-fun tptp.p ((-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.25/0.65 (declare-fun tptp.u (tptp.pname) Bool)
% 0.25/0.65 (declare-fun tptp.mgt_call (tptp.pname) tptp.x_a)
% 0.25/0.65 (declare-fun tptp.na () tptp.nat)
% 0.25/0.65 (declare-fun tptp.pn () tptp.pname)
% 0.25/0.65 (assert (forall ((Ts (-> tptp.x_a Bool)) (G (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Ts) G) (@ (@ tptp.p G) Ts))))
% 0.25/0.65 (assert (forall ((A_59 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_59) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((B_38 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((A_59 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_59) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((B_38 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((A_59 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_59) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((B_38 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((A_59 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o A_59) (@ tptp.finite1237261006_o_o_o (@ tptp.collect_nat_o_o_o (lambda ((B_38 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (@ (@ tptp.ord_le124054423_o_o_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((A_59 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_59) (@ tptp.finite1648353812_o_o_o (@ tptp.collect_pname_o_o_o (lambda ((B_38 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (@ (@ tptp.ord_le1828183645_o_o_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((A_59 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o A_59) (@ tptp.finite1302365357_o_o_o (@ tptp.collect_a_o_o_o (lambda ((B_38 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (@ (@ tptp.ord_less_eq_a_o_o_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((A_59 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_59) (@ tptp.finite_finite_a_o_o (@ tptp.collect_a_o_o (lambda ((B_38 (-> (-> tptp.x_a Bool) Bool))) (@ (@ tptp.ord_less_eq_a_o_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((A_59 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_59) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((B_38 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((A_59 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_59) (@ tptp.finite1676163439at_o_o (@ tptp.collect_nat_o_o (lambda ((B_38 (-> (-> tptp.nat Bool) Bool))) (@ (@ tptp.ord_less_eq_nat_o_o B_38) A_59)))))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname tptp.x_a)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> (-> tptp.nat Bool) Bool) tptp.nat)) (F_15 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_o_nat H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> (-> tptp.pname Bool) Bool) tptp.nat)) (F_15 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_o_nat H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> (-> tptp.x_a Bool) Bool) tptp.nat)) (F_15 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_o_nat H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.x_a Bool) tptp.nat)) (F_15 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_nat H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.nat)) (F_15 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_nat H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.nat Bool) tptp.nat)) (F_15 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_nat H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.x_a tptp.nat)) (F_15 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_nat H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> (-> tptp.nat Bool) Bool) tptp.pname)) (F_15 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_o_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> (-> tptp.pname Bool) Bool) tptp.pname)) (F_15 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_471733107_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> (-> tptp.x_a Bool) Bool) tptp.pname)) (F_15 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_o_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.x_a Bool) tptp.pname)) (F_15 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.pname)) (F_15 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.nat Bool) tptp.pname)) (F_15 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.x_a tptp.pname)) (F_15 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.nat (-> tptp.nat Bool) Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite1676163439at_o_o (@ (@ tptp.image_nat_nat_o_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.nat (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite1066544169me_o_o (@ (@ tptp.image_nat_pname_o_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.nat (-> tptp.x_a Bool) Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_a_o_o (@ (@ tptp.image_nat_a_o_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.nat tptp.x_a Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.nat tptp.pname Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.nat tptp.nat Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.nat tptp.x_a)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_a (@ (@ tptp.image_nat_a H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname (-> tptp.nat Bool) Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite1676163439at_o_o (@ (@ tptp.image_pname_nat_o_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite1066544169me_o_o (@ (@ tptp.image_504089495me_o_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname (-> tptp.x_a Bool) Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_a_o_o (@ (@ tptp.image_pname_a_o_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname tptp.x_a Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_a_o (@ (@ tptp.image_pname_a_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname tptp.pname Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname tptp.nat Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_pname_nat_o H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname tptp.pname)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.x_a tptp.x_a)) (F_15 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_15) (@ tptp.finite_finite_a (@ (@ tptp.image_a_a H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.nat Bool) tptp.x_a)) (F_15 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_15) (@ tptp.finite_finite_a (@ (@ tptp.image_nat_o_a H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.x_a)) (F_15 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_15) (@ tptp.finite_finite_a (@ (@ tptp.image_pname_o_a H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> (-> tptp.x_a Bool) tptp.x_a)) (F_15 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_15) (@ tptp.finite_finite_a (@ (@ tptp.image_a_o_a H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.pname tptp.nat)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_nat H) F_15)))))
% 0.25/0.65 (assert (forall ((H (-> tptp.nat tptp.pname)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_pname H) F_15)))))
% 0.25/0.65 (assert (forall ((A_58 tptp.x_a) (A_57 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_57) (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_58) A_57)))))
% 0.25/0.65 (assert (forall ((A_58 tptp.nat) (A_57 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_57) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_58) A_57)))))
% 0.25/0.65 (assert (forall ((A_58 tptp.pname) (A_57 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_57) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_58) A_57)))))
% 0.25/0.65 (assert (forall ((A_58 (-> (-> tptp.nat Bool) Bool)) (A_57 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o A_57) (@ tptp.finite1676163439at_o_o (@ (@ tptp.insert_nat_o_o A_58) A_57)))))
% 0.25/0.65 (assert (forall ((A_58 (-> (-> tptp.pname Bool) Bool)) (A_57 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_57) (@ tptp.finite1066544169me_o_o (@ (@ tptp.insert_pname_o_o A_58) A_57)))))
% 0.25/0.65 (assert (forall ((A_58 (-> (-> tptp.x_a Bool) Bool)) (A_57 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o A_57) (@ tptp.finite_finite_a_o_o (@ (@ tptp.insert_a_o_o A_58) A_57)))))
% 0.25/0.65 (assert (forall ((A_58 (-> tptp.x_a Bool)) (A_57 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_57) (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_58) A_57)))))
% 0.25/0.65 (assert (forall ((A_58 (-> tptp.pname Bool)) (A_57 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_57) (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_58) A_57)))))
% 0.25/0.65 (assert (forall ((A_58 (-> tptp.nat Bool)) (A_57 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_57) (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_58) A_57)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.pname tptp.nat)) (A_56 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_nat F_14) A_56))) (@ tptp.finite_card_pname A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.x_a tptp.nat)) (A_56 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_nat F_14) A_56))) (@ tptp.finite_card_a A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.nat Bool) tptp.nat)) (A_56 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_nat_o_nat F_14) A_56))) (@ tptp.finite_card_nat_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.pname Bool) tptp.nat)) (A_56 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_o_nat F_14) A_56))) (@ tptp.finite_card_pname_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.x_a Bool) tptp.nat)) (A_56 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_o_nat F_14) A_56))) (@ tptp.finite_card_a_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.x_a tptp.pname)) (A_56 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_a_pname F_14) A_56))) (@ tptp.finite_card_a A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.nat tptp.pname)) (A_56 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_nat_pname F_14) A_56))) (@ tptp.finite_card_nat A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.pname tptp.x_a)) (A_56 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_a F_14) A_56))) (@ tptp.finite_card_pname A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> (-> tptp.nat Bool) Bool) tptp.x_a)) (A_56 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_o_o_a F_14) A_56))) (@ tptp.finite_card_nat_o_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> (-> tptp.pname Bool) Bool) tptp.x_a)) (A_56 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_o_o_a F_14) A_56))) (@ tptp.finite221134632me_o_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> (-> tptp.x_a Bool) Bool) tptp.x_a)) (A_56 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_o_o_a F_14) A_56))) (@ tptp.finite_card_a_o_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_56 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_o_a F_14) A_56))) (@ tptp.finite_card_a_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.pname Bool) tptp.x_a)) (A_56 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_o_a F_14) A_56))) (@ tptp.finite_card_pname_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.nat Bool) tptp.x_a)) (A_56 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_o_a F_14) A_56))) (@ tptp.finite_card_nat_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.x_a tptp.x_a)) (A_56 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_a F_14) A_56))) (@ tptp.finite_card_a A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.pname tptp.pname)) (A_56 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_pname_pname F_14) A_56))) (@ tptp.finite_card_pname A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.pname tptp.nat Bool)) (A_56 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o (@ (@ tptp.image_pname_nat_o F_14) A_56))) (@ tptp.finite_card_pname A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.pname tptp.pname Bool)) (A_56 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o (@ (@ tptp.image_pname_pname_o F_14) A_56))) (@ tptp.finite_card_pname A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.pname tptp.x_a Bool)) (A_56 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o (@ (@ tptp.image_pname_a_o F_14) A_56))) (@ tptp.finite_card_pname A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.nat tptp.x_a)) (A_56 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_a F_14) A_56))) (@ tptp.finite_card_nat A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.nat tptp.nat Bool)) (A_56 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o (@ (@ tptp.image_nat_nat_o F_14) A_56))) (@ tptp.finite_card_nat A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.nat tptp.pname Bool)) (A_56 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o (@ (@ tptp.image_nat_pname_o F_14) A_56))) (@ tptp.finite_card_nat A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> tptp.nat tptp.x_a Bool)) (A_56 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o (@ (@ tptp.image_nat_a_o F_14) A_56))) (@ tptp.finite_card_nat A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.nat Bool) tptp.pname)) (A_56 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_nat_o_pname F_14) A_56))) (@ tptp.finite_card_nat_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.pname Bool) tptp.pname)) (A_56 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_pname_o_pname F_14) A_56))) (@ tptp.finite_card_pname_o A_56)))))
% 0.25/0.65 (assert (forall ((F_14 (-> (-> tptp.x_a Bool) tptp.pname)) (A_56 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_a_o_pname F_14) A_56))) (@ tptp.finite_card_a_o A_56)))))
% 0.25/0.65 (assert (forall ((A_55 (-> (-> tptp.nat Bool) Bool)) (B_37 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_37) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_55)) (@ tptp.finite_card_nat_o B_37))))))
% 0.25/0.65 (assert (forall ((A_55 (-> (-> tptp.pname Bool) Bool)) (B_37 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_37) (=> (@ (@ tptp.ord_le1205211808me_o_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_55)) (@ tptp.finite_card_pname_o B_37))))))
% 0.25/0.65 (assert (forall ((A_55 (-> (-> tptp.x_a Bool) Bool)) (B_37 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_37) (=> (@ (@ tptp.ord_less_eq_a_o_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_55)) (@ tptp.finite_card_a_o B_37))))))
% 0.25/0.65 (assert (forall ((A_55 (-> tptp.pname Bool)) (B_37 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_37) (=> (@ (@ tptp.ord_less_eq_pname_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_55)) (@ tptp.finite_card_pname B_37))))))
% 0.25/0.65 (assert (forall ((A_55 (-> tptp.x_a Bool)) (B_37 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_37) (=> (@ (@ tptp.ord_less_eq_a_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_55)) (@ tptp.finite_card_a B_37))))))
% 0.25/0.65 (assert (forall ((A_55 (-> tptp.nat Bool)) (B_37 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_37) (=> (@ (@ tptp.ord_less_eq_nat_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_55)) (@ tptp.finite_card_nat B_37))))))
% 0.25/0.65 (assert (forall ((A_54 (-> (-> tptp.nat Bool) Bool)) (B_36 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_36) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_54) B_36) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o B_36)) (@ tptp.finite_card_nat_o A_54)) (= A_54 B_36))))))
% 0.25/0.65 (assert (forall ((A_54 (-> (-> tptp.pname Bool) Bool)) (B_36 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_36) (=> (@ (@ tptp.ord_le1205211808me_o_o A_54) B_36) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o B_36)) (@ tptp.finite_card_pname_o A_54)) (= A_54 B_36))))))
% 0.25/0.65 (assert (forall ((A_54 (-> (-> tptp.x_a Bool) Bool)) (B_36 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_36) (=> (@ (@ tptp.ord_less_eq_a_o_o A_54) B_36) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o B_36)) (@ tptp.finite_card_a_o A_54)) (= A_54 B_36))))))
% 0.25/0.65 (assert (forall ((A_54 (-> tptp.pname Bool)) (B_36 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_36) (=> (@ (@ tptp.ord_less_eq_pname_o A_54) B_36) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname B_36)) (@ tptp.finite_card_pname A_54)) (= A_54 B_36))))))
% 0.25/0.65 (assert (forall ((A_54 (-> tptp.x_a Bool)) (B_36 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_36) (=> (@ (@ tptp.ord_less_eq_a_o A_54) B_36) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a B_36)) (@ tptp.finite_card_a A_54)) (= A_54 B_36))))))
% 0.25/0.65 (assert (forall ((A_54 (-> tptp.nat Bool)) (B_36 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_36) (=> (@ (@ tptp.ord_less_eq_nat_o A_54) B_36) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B_36)) (@ tptp.finite_card_nat A_54)) (= A_54 B_36))))))
% 0.25/0.65 (assert (forall ((X_19 (-> tptp.nat Bool)) (A_53 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_53)) (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_19) A_53))))))
% 0.25/0.65 (assert (forall ((X_19 (-> tptp.pname Bool)) (A_53 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_53)) (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_19) A_53))))))
% 0.25/0.65 (assert (forall ((X_19 (-> tptp.x_a Bool)) (A_53 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_53)) (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_19) A_53))))))
% 0.25/0.65 (assert (forall ((X_19 tptp.pname) (A_53 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_53)) (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_19) A_53))))))
% 0.25/0.65 (assert (forall ((X_19 tptp.nat) (A_53 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_53)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_19) A_53))))))
% 0.25/0.65 (assert (forall ((X_19 tptp.x_a) (A_53 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_53)) (@ tptp.finite_card_a (@ (@ tptp.insert_a X_19) A_53))))))
% 0.25/0.65 (assert (forall ((X_18 (-> tptp.nat Bool)) (A_52 (-> (-> tptp.nat Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_nat_o A_52))) (let ((_let_2 (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_nat_o X_18) A_52))) (=> (@ tptp.finite_finite_nat_o A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.25/0.65 (assert (forall ((X_18 (-> tptp.pname Bool)) (A_52 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_pname_o A_52))) (let ((_let_2 (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_pname_o X_18) A_52))) (=> (@ tptp.finite297249702name_o A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.25/0.65 (assert (forall ((X_18 (-> tptp.x_a Bool)) (A_52 (-> (-> tptp.x_a Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_a_o A_52))) (let ((_let_2 (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_a_o X_18) A_52))) (=> (@ tptp.finite_finite_a_o A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.25/0.65 (assert (forall ((X_18 tptp.nat) (A_52 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_card_nat A_52))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_nat X_18) A_52))) (=> (@ tptp.finite_finite_nat A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.25/0.65 (assert (forall ((X_18 tptp.pname) (A_52 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.finite_card_pname A_52))) (let ((_let_2 (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_pname X_18) A_52))) (=> (@ tptp.finite_finite_pname A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.25/0.65 (assert (forall ((X_18 tptp.x_a) (A_52 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.finite_card_a A_52))) (let ((_let_2 (@ tptp.finite_card_a (@ (@ tptp.insert_a X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_a X_18) A_52))) (=> (@ tptp.finite_finite_a A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.25/0.65 (assert (forall ((X_17 (-> tptp.nat Bool)) (A_51 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_51) (=> (not (@ (@ tptp.member_nat_o X_17) A_51)) (= (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_nat_o A_51)))))))
% 0.25/0.65 (assert (forall ((X_17 (-> tptp.pname Bool)) (A_51 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_51) (=> (not (@ (@ tptp.member_pname_o X_17) A_51)) (= (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_pname_o A_51)))))))
% 0.25/0.65 (assert (forall ((X_17 (-> tptp.x_a Bool)) (A_51 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_51) (=> (not (@ (@ tptp.member_a_o X_17) A_51)) (= (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_a_o A_51)))))))
% 0.25/0.65 (assert (forall ((X_17 tptp.nat) (A_51 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_51) (=> (not (@ (@ tptp.member_nat X_17) A_51)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_nat A_51)))))))
% 0.25/0.65 (assert (forall ((X_17 tptp.pname) (A_51 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_51) (=> (not (@ (@ tptp.member_pname X_17) A_51)) (= (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_pname A_51)))))))
% 0.25/0.65 (assert (forall ((X_17 tptp.x_a) (A_51 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_51) (=> (not (@ (@ tptp.member_a X_17) A_51)) (= (@ tptp.finite_card_a (@ (@ tptp.insert_a X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_a A_51)))))))
% 0.25/0.65 (assert (forall ((Q_1 (-> (-> tptp.nat Bool) Bool)) (P_4 (-> (-> tptp.nat Bool) Bool))) (=> (or (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_4)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q_1))) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X (-> tptp.nat Bool))) (and (@ P_4 X) (@ Q_1 X))))))))
% 0.25/0.65 (assert (forall ((Q_1 (-> (-> tptp.pname Bool) Bool)) (P_4 (-> (-> tptp.pname Bool) Bool))) (=> (or (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_4)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_1))) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X (-> tptp.pname Bool))) (and (@ P_4 X) (@ Q_1 X))))))))
% 0.25/0.65 (assert (forall ((Q_1 (-> (-> tptp.x_a Bool) Bool)) (P_4 (-> (-> tptp.x_a Bool) Bool))) (=> (or (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_4)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q_1))) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X (-> tptp.x_a Bool))) (and (@ P_4 X) (@ Q_1 X))))))))
% 0.25/0.65 (assert (forall ((Q_1 (-> tptp.x_a Bool)) (P_4 (-> tptp.x_a Bool))) (=> (or (@ tptp.finite_finite_a (@ tptp.collect_a P_4)) (@ tptp.finite_finite_a (@ tptp.collect_a Q_1))) (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X tptp.x_a)) (and (@ P_4 X) (@ Q_1 X))))))))
% 0.25/0.65 (assert (forall ((Q_1 (-> tptp.pname Bool)) (P_4 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_4)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_1))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (@ P_4 X) (@ Q_1 X))))))))
% 0.25/0.65 (assert (forall ((Q_1 (-> tptp.nat Bool)) (P_4 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P_4)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_1))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P_4 X) (@ Q_1 X))))))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat) (M_2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N_1) M_2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M_2)) N_1) (@ tptp.suc (@ (@ tptp.minus_minus_nat M_2) N_1))))))
% 0.25/0.65 (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))))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I_1) N_1)))) (@ tptp.suc N_1))))
% 0.25/0.65 (assert (forall ((X_16 tptp.nat) (Y_3 tptp.nat)) (=> (= (@ tptp.suc X_16) (@ tptp.suc Y_3)) (= X_16 Y_3))))
% 0.25/0.65 (assert (forall ((Nat_1 tptp.nat) (Nat tptp.nat)) (= (= (@ tptp.suc Nat_1) (@ tptp.suc Nat)) (= Nat_1 Nat))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat)) (not (= (@ tptp.suc N_1) N_1))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat)) (not (= N_1 (@ tptp.suc N_1)))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M_2) N_1) (=> (@ (@ tptp.ord_less_eq_nat N_1) M_2) (= M_2 N_1)))))
% 0.25/0.65 (assert (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (= M_2 N_1) (@ (@ tptp.ord_less_eq_nat M_2) N_1))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M_2) N_1) (@ (@ tptp.ord_less_eq_nat N_1) M_2))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) N_1)))
% 0.25/0.65 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 0.25/0.65 (assert (forall ((P_3 (-> tptp.pname Bool)) (Q (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_3)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q))))))
% 0.25/0.65 (assert (forall ((P_3 (-> (-> tptp.nat Bool) Bool)) (Q (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X (-> tptp.nat Bool))) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_3)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q))))))
% 0.25/0.65 (assert (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (Q (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X (-> tptp.pname Bool))) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_3)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q))))))
% 0.25/0.65 (assert (forall ((P_3 (-> (-> tptp.x_a Bool) Bool)) (Q (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X (-> tptp.x_a Bool))) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_3)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q))))))
% 0.25/0.65 (assert (forall ((P_3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P_3)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 0.25/0.65 (assert (forall ((P_3 (-> tptp.x_a Bool)) (Q (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X tptp.x_a)) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_a (@ tptp.collect_a P_3)) (@ tptp.finite_finite_a (@ tptp.collect_a Q))))))
% 0.25/0.65 (assert (forall ((A_50 tptp.nat) (A_49 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_50) A_49)) (@ tptp.finite_finite_nat A_49))))
% 0.25/0.65 (assert (forall ((A_50 tptp.pname) (A_49 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_50) A_49)) (@ tptp.finite_finite_pname A_49))))
% 0.25/0.65 (assert (forall ((A_50 tptp.x_a) (A_49 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_50) A_49)) (@ tptp.finite_finite_a A_49))))
% 0.25/0.65 (assert (forall ((A_50 (-> tptp.nat Bool)) (A_49 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_50) A_49)) (@ tptp.finite_finite_nat_o A_49))))
% 0.25/0.65 (assert (forall ((A_50 (-> tptp.pname Bool)) (A_49 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_50) A_49)) (@ tptp.finite297249702name_o A_49))))
% 0.25/0.65 (assert (forall ((A_50 (-> tptp.x_a Bool)) (A_49 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_50) A_49)) (@ tptp.finite_finite_a_o A_49))))
% 0.25/0.65 (assert (forall ((A_48 (-> (-> tptp.nat Bool) Bool)) (B_35 (-> (-> tptp.nat Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_48) B_35) (=> (@ tptp.finite_finite_nat_o B_35) (@ tptp.finite_finite_nat_o A_48)))))
% 0.25/0.65 (assert (forall ((A_48 (-> (-> tptp.pname Bool) Bool)) (B_35 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_48) B_35) (=> (@ tptp.finite297249702name_o B_35) (@ tptp.finite297249702name_o A_48)))))
% 0.25/0.65 (assert (forall ((A_48 (-> tptp.x_a Bool)) (B_35 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_48) B_35) (=> (@ tptp.finite_finite_a B_35) (@ tptp.finite_finite_a A_48)))))
% 0.25/0.65 (assert (forall ((A_48 (-> (-> tptp.x_a Bool) Bool)) (B_35 (-> (-> tptp.x_a Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_a_o_o A_48) B_35) (=> (@ tptp.finite_finite_a_o B_35) (@ tptp.finite_finite_a_o A_48)))))
% 0.25/0.65 (assert (forall ((A_48 (-> tptp.nat Bool)) (B_35 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_48) B_35) (=> (@ tptp.finite_finite_nat B_35) (@ tptp.finite_finite_nat A_48)))))
% 0.25/0.65 (assert (forall ((A_48 (-> tptp.pname Bool)) (B_35 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_48) B_35) (=> (@ tptp.finite_finite_pname B_35) (@ tptp.finite_finite_pname A_48)))))
% 0.25/0.65 (assert (forall ((A_47 (-> (-> tptp.nat Bool) Bool)) (B_34 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_34) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_47) B_34) (@ tptp.finite_finite_nat_o A_47)))))
% 0.25/0.65 (assert (forall ((A_47 (-> (-> tptp.pname Bool) Bool)) (B_34 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_34) (=> (@ (@ tptp.ord_le1205211808me_o_o A_47) B_34) (@ tptp.finite297249702name_o A_47)))))
% 0.25/0.65 (assert (forall ((A_47 (-> tptp.x_a Bool)) (B_34 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_34) (=> (@ (@ tptp.ord_less_eq_a_o A_47) B_34) (@ tptp.finite_finite_a A_47)))))
% 0.25/0.65 (assert (forall ((A_47 (-> (-> tptp.x_a Bool) Bool)) (B_34 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_34) (=> (@ (@ tptp.ord_less_eq_a_o_o A_47) B_34) (@ tptp.finite_finite_a_o A_47)))))
% 0.25/0.65 (assert (forall ((A_47 (-> tptp.nat Bool)) (B_34 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_34) (=> (@ (@ tptp.ord_less_eq_nat_o A_47) B_34) (@ tptp.finite_finite_nat A_47)))))
% 0.25/0.65 (assert (forall ((A_47 (-> tptp.pname Bool)) (B_34 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_34) (=> (@ (@ tptp.ord_less_eq_pname_o A_47) B_34) (@ tptp.finite_finite_pname A_47)))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M_2)) N_1) (@ (@ tptp.ord_less_eq_nat M_2) N_1))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc N_1))) (let ((_let_2 (@ tptp.ord_less_eq_nat M_2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N_1)) (= M_2 _let_1)))))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M_2))) (=> (@ _let_1 N_1) (@ _let_1 (@ tptp.suc N_1))))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat) (M_2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) (@ tptp.suc M_2)) (@ (@ tptp.ord_less_eq_nat N_1) M_2))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc N_1))) (let ((_let_2 (@ tptp.ord_less_eq_nat M_2))) (= (@ _let_2 _let_1) (or (@ _let_2 N_1) (= M_2 _let_1)))))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M_2) N_1)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) M_2))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) N_1))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M_2)) N_1)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M_2) N_1)) K))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M_2)) (@ tptp.suc N_1)) (@ (@ tptp.minus_minus_nat M_2) N_1))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat) (K tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M_2) (=> (@ _let_1 N_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M_2) K)) (@ (@ tptp.minus_minus_nat N_1) K)) (@ (@ tptp.ord_less_eq_nat M_2) N_1)))))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat) (K tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M_2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M_2) (=> (@ _let_2 N_1) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N_1) K)) (@ _let_1 N_1))))))))
% 0.25/0.65 (assert (forall ((N_1 tptp.nat) (K tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M_2) (=> (@ _let_1 N_1) (= (= (@ (@ tptp.minus_minus_nat M_2) K) (@ (@ tptp.minus_minus_nat N_1) K)) (= M_2 N_1)))))))
% 0.25/0.65 (assert (forall ((I tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N_1))) (=> (@ (@ tptp.ord_less_eq_nat I) N_1) (= (@ _let_1 (@ _let_1 I)) I)))))
% 0.25/0.65 (assert (forall ((L tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M_2) N_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M_2) L)) (@ (@ tptp.minus_minus_nat N_1) L)))))
% 0.25/0.65 (assert (forall ((L tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M_2) N_1) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_1)) (@ _let_1 M_2))))))
% 0.25/0.65 (assert (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M_2) N_1)) M_2)))
% 0.25/0.65 (assert (forall ((B_33 (-> tptp.x_a Bool)) (F_13 (-> tptp.pname tptp.x_a)) (A_46 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_46) (=> (@ (@ tptp.ord_less_eq_a_o B_33) (@ (@ tptp.image_pname_a F_13) A_46)) (@ tptp.finite_finite_a B_33)))))
% 0.25/0.65 (assert (forall ((F_12 (-> tptp.pname tptp.x_a)) (A_45 (-> tptp.pname Bool)) (B_32 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_32) (=> (@ (@ tptp.ord_less_eq_a_o B_32) (@ (@ tptp.image_pname_a F_12) A_45)) (exists ((C_3 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_3) A_45) (@ tptp.finite_finite_pname C_3) (= B_32 (@ (@ tptp.image_pname_a F_12) C_3))))))))
% 0.25/0.65 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_11 (-> tptp.nat tptp.nat Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o (@ F_11 N_2)) (@ F_11 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat_o (@ F_11 N_4)) (@ F_11 N_3))))))
% 0.25/0.65 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_11 (-> tptp.nat tptp.pname Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_pname_o (@ F_11 N_2)) (@ F_11 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_pname_o (@ F_11 N_4)) (@ F_11 N_3))))))
% 0.25/0.65 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_11 (-> tptp.nat tptp.nat))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F_11 N_2)) (@ F_11 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat (@ F_11 N_4)) (@ F_11 N_3))))))
% 0.25/0.65 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_11 (-> tptp.nat tptp.x_a Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_a_o (@ F_11 N_2)) (@ F_11 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_a_o (@ F_11 N_4)) (@ F_11 N_3))))))
% 0.25/0.65 (assert (forall ((F_10 (-> tptp.pname tptp.x_a)) (A_43 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_43)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a F_10) A_43)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_43) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_44 tptp.pname)) (and (@ (@ tptp.member_pname A_44) A_43) (= (@ F_10 A_44) (@ F_10 X)))))))))))))
% 0.25/0.65 (assert (forall ((A_42 (-> tptp.pname Bool)) (B_31 tptp.x_a) (F_9 (-> tptp.pname tptp.x_a)) (X_15 tptp.pname)) (=> (= B_31 (@ F_9 X_15)) (=> (@ (@ tptp.member_pname X_15) A_42) (@ (@ tptp.member_a B_31) (@ (@ tptp.image_pname_a F_9) A_42))))))
% 0.25/0.65 (assert (forall ((A_41 (-> tptp.nat Bool)) (B_30 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_41) B_30) (=> (@ (@ tptp.ord_less_eq_nat_o B_30) A_41) (= A_41 B_30)))))
% 0.25/0.65 (assert (forall ((A_41 (-> tptp.pname Bool)) (B_30 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_41) B_30) (=> (@ (@ tptp.ord_less_eq_pname_o B_30) A_41) (= A_41 B_30)))))
% 0.25/0.65 (assert (forall ((A_41 (-> tptp.x_a Bool)) (B_30 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_41) B_30) (=> (@ (@ tptp.ord_less_eq_a_o B_30) A_41) (= A_41 B_30)))))
% 0.25/0.65 (assert (forall ((C_2 tptp.nat) (A_40 (-> tptp.nat Bool)) (B_29 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_2))) (=> (@ (@ tptp.ord_less_eq_nat_o A_40) B_29) (=> (@ _let_1 A_40) (@ _let_1 B_29))))))
% 0.25/0.65 (assert (forall ((C_2 tptp.x_a) (A_40 (-> tptp.x_a Bool)) (B_29 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_2))) (=> (@ (@ tptp.ord_less_eq_a_o A_40) B_29) (=> (@ _let_1 A_40) (@ _let_1 B_29))))))
% 0.25/0.65 (assert (forall ((C_2 tptp.pname) (A_40 (-> tptp.pname Bool)) (B_29 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_2))) (=> (@ (@ tptp.ord_less_eq_pname_o A_40) B_29) (=> (@ _let_1 A_40) (@ _let_1 B_29))))))
% 0.25/0.65 (assert (forall ((B_28 tptp.nat) (A_39 tptp.nat) (B_27 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_39))) (=> (=> (not (@ _let_1 B_27)) (= A_39 B_28)) (@ _let_1 (@ (@ tptp.insert_nat B_28) B_27))))))
% 0.25/0.65 (assert (forall ((B_28 tptp.pname) (A_39 tptp.pname) (B_27 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_39))) (=> (=> (not (@ _let_1 B_27)) (= A_39 B_28)) (@ _let_1 (@ (@ tptp.insert_pname B_28) B_27))))))
% 0.25/0.65 (assert (forall ((B_28 tptp.x_a) (A_39 tptp.x_a) (B_27 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_39))) (=> (=> (not (@ _let_1 B_27)) (= A_39 B_28)) (@ _let_1 (@ (@ tptp.insert_a B_28) B_27))))))
% 0.25/0.65 (assert (forall ((A_38 tptp.nat) (B_26 tptp.nat) (A_37 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_38))) (=> (@ _let_1 (@ (@ tptp.insert_nat B_26) A_37)) (=> (not (= A_38 B_26)) (@ _let_1 A_37))))))
% 0.25/0.65 (assert (forall ((A_38 tptp.pname) (B_26 tptp.pname) (A_37 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_38))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_26) A_37)) (=> (not (= A_38 B_26)) (@ _let_1 A_37))))))
% 0.25/0.65 (assert (forall ((A_38 tptp.x_a) (B_26 tptp.x_a) (A_37 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_38))) (=> (@ _let_1 (@ (@ tptp.insert_a B_26) A_37)) (=> (not (= A_38 B_26)) (@ _let_1 A_37))))))
% 0.25/0.65 (assert (forall ((A_36 tptp.nat) (B_25 (-> tptp.nat Bool))) (@ (@ tptp.member_nat A_36) (@ (@ tptp.insert_nat A_36) B_25))))
% 0.25/0.65 (assert (forall ((A_36 tptp.pname) (B_25 (-> tptp.pname Bool))) (@ (@ tptp.member_pname A_36) (@ (@ tptp.insert_pname A_36) B_25))))
% 0.25/0.65 (assert (forall ((A_36 tptp.x_a) (B_25 (-> tptp.x_a Bool))) (@ (@ tptp.member_a A_36) (@ (@ tptp.insert_a A_36) B_25))))
% 0.25/0.65 (assert (forall ((A_35 tptp.nat) (B_24 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_35) B_24) (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (= X A_35) (@ (@ tptp.member_nat X) B_24)))))))
% 0.25/0.65 (assert (forall ((A_35 tptp.pname) (B_24 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_35) B_24) (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (= X A_35) (@ (@ tptp.member_pname X) B_24)))))))
% 0.25/0.65 (assert (forall ((A_35 tptp.x_a) (B_24 (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a A_35) B_24) (@ tptp.collect_a (lambda ((X tptp.x_a)) (or (= X A_35) (@ (@ tptp.member_a X) B_24)))))))
% 0.25/0.65 (assert (forall ((A_35 (-> tptp.nat Bool)) (B_24 (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o A_35) B_24) (@ tptp.collect_nat_o (lambda ((X (-> tptp.nat Bool))) (or (= X A_35) (@ (@ tptp.member_nat_o X) B_24)))))))
% 0.25/0.65 (assert (forall ((A_35 (-> tptp.pname Bool)) (B_24 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_35) B_24) (@ tptp.collect_pname_o (lambda ((X (-> tptp.pname Bool))) (or (= X A_35) (@ (@ tptp.member_pname_o X) B_24)))))))
% 0.25/0.65 (assert (forall ((A_35 (-> tptp.x_a Bool)) (B_24 (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o A_35) B_24) (@ tptp.collect_a_o (lambda ((X (-> tptp.x_a Bool))) (or (= X A_35) (@ (@ tptp.member_a_o X) B_24)))))))
% 0.25/0.65 (assert (forall ((A_34 tptp.nat) (P_2 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_34) (@ tptp.collect_nat P_2)) (@ tptp.collect_nat (lambda ((U tptp.nat)) (=> (not (= U A_34)) (@ P_2 U)))))))
% 0.25/0.65 (assert (forall ((A_34 tptp.pname) (P_2 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_34) (@ tptp.collect_pname P_2)) (@ tptp.collect_pname (lambda ((U tptp.pname)) (=> (not (= U A_34)) (@ P_2 U)))))))
% 0.25/0.65 (assert (forall ((A_34 tptp.x_a) (P_2 (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a A_34) (@ tptp.collect_a P_2)) (@ tptp.collect_a (lambda ((U tptp.x_a)) (=> (not (= U A_34)) (@ P_2 U)))))))
% 0.25/0.65 (assert (forall ((A_34 (-> tptp.nat Bool)) (P_2 (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o A_34) (@ tptp.collect_nat_o P_2)) (@ tptp.collect_nat_o (lambda ((U (-> tptp.nat Bool))) (=> (not (= U A_34)) (@ P_2 U)))))))
% 0.25/0.65 (assert (forall ((A_34 (-> tptp.pname Bool)) (P_2 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_34) (@ tptp.collect_pname_o P_2)) (@ tptp.collect_pname_o (lambda ((U (-> tptp.pname Bool))) (=> (not (= U A_34)) (@ P_2 U)))))))
% 0.25/0.65 (assert (forall ((A_34 (-> tptp.x_a Bool)) (P_2 (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o A_34) (@ tptp.collect_a_o P_2)) (@ tptp.collect_a_o (lambda ((U (-> tptp.x_a Bool))) (=> (not (= U A_34)) (@ P_2 U)))))))
% 0.25/0.65 (assert (forall ((X_14 tptp.nat) (A_33 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_14))) (let ((_let_2 (@ _let_1 A_33))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.65 (assert (forall ((X_14 tptp.pname) (A_33 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_14))) (let ((_let_2 (@ _let_1 A_33))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.65 (assert (forall ((X_14 tptp.x_a) (A_33 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_14))) (let ((_let_2 (@ _let_1 A_33))) (= (@ _let_1 _let_2) _let_2)))))
% 0.25/0.65 (assert (forall ((X_13 tptp.nat) (Y_2 tptp.nat) (A_32 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_13))) (let ((_let_2 (@ tptp.insert_nat Y_2))) (= (@ _let_1 (@ _let_2 A_32)) (@ _let_2 (@ _let_1 A_32)))))))
% 0.25/0.65 (assert (forall ((X_13 tptp.pname) (Y_2 tptp.pname) (A_32 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_13))) (let ((_let_2 (@ tptp.insert_pname Y_2))) (= (@ _let_1 (@ _let_2 A_32)) (@ _let_2 (@ _let_1 A_32)))))))
% 0.25/0.65 (assert (forall ((X_13 tptp.x_a) (Y_2 tptp.x_a) (A_32 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_13))) (let ((_let_2 (@ tptp.insert_a Y_2))) (= (@ _let_1 (@ _let_2 A_32)) (@ _let_2 (@ _let_1 A_32)))))))
% 0.25/0.65 (assert (forall ((A_31 tptp.nat) (B_23 tptp.nat) (A_30 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_31))) (= (@ _let_1 (@ (@ tptp.insert_nat B_23) A_30)) (or (= A_31 B_23) (@ _let_1 A_30))))))
% 0.25/0.65 (assert (forall ((A_31 tptp.pname) (B_23 tptp.pname) (A_30 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_31))) (= (@ _let_1 (@ (@ tptp.insert_pname B_23) A_30)) (or (= A_31 B_23) (@ _let_1 A_30))))))
% 0.25/0.65 (assert (forall ((A_31 tptp.x_a) (B_23 tptp.x_a) (A_30 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_31))) (= (@ _let_1 (@ (@ tptp.insert_a B_23) A_30)) (or (= A_31 B_23) (@ _let_1 A_30))))))
% 0.25/0.65 (assert (forall ((Y_1 tptp.nat) (A_29 (-> tptp.nat Bool)) (X_12 tptp.nat)) (= (@ (@ (@ tptp.insert_nat Y_1) A_29) X_12) (or (= Y_1 X_12) (@ A_29 X_12)))))
% 0.25/0.65 (assert (forall ((Y_1 tptp.pname) (A_29 (-> tptp.pname Bool)) (X_12 tptp.pname)) (= (@ (@ (@ tptp.insert_pname Y_1) A_29) X_12) (or (= Y_1 X_12) (@ A_29 X_12)))))
% 0.25/0.65 (assert (forall ((Y_1 tptp.x_a) (A_29 (-> tptp.x_a Bool)) (X_12 tptp.x_a)) (= (@ (@ (@ tptp.insert_a Y_1) A_29) X_12) (or (= Y_1 X_12) (@ A_29 X_12)))))
% 0.25/0.65 (assert (forall ((B_22 (-> tptp.nat Bool)) (X_11 tptp.nat) (A_28 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_11))) (let ((_let_2 (@ tptp.member_nat X_11))) (=> (not (@ _let_2 A_28)) (=> (not (@ _let_2 B_22)) (= (= (@ _let_1 A_28) (@ _let_1 B_22)) (= A_28 B_22))))))))
% 0.25/0.65 (assert (forall ((B_22 (-> tptp.pname Bool)) (X_11 tptp.pname) (A_28 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_11))) (let ((_let_2 (@ tptp.member_pname X_11))) (=> (not (@ _let_2 A_28)) (=> (not (@ _let_2 B_22)) (= (= (@ _let_1 A_28) (@ _let_1 B_22)) (= A_28 B_22))))))))
% 0.25/0.65 (assert (forall ((B_22 (-> tptp.x_a Bool)) (X_11 tptp.x_a) (A_28 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_11))) (let ((_let_2 (@ tptp.member_a X_11))) (=> (not (@ _let_2 A_28)) (=> (not (@ _let_2 B_22)) (= (= (@ _let_1 A_28) (@ _let_1 B_22)) (= A_28 B_22))))))))
% 0.25/0.65 (assert (forall ((B_21 tptp.nat) (A_27 tptp.nat) (B_20 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_27))) (=> (@ _let_1 B_20) (@ _let_1 (@ (@ tptp.insert_nat B_21) B_20))))))
% 0.25/0.65 (assert (forall ((B_21 tptp.pname) (A_27 tptp.pname) (B_20 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_27))) (=> (@ _let_1 B_20) (@ _let_1 (@ (@ tptp.insert_pname B_21) B_20))))))
% 0.25/0.65 (assert (forall ((B_21 tptp.x_a) (A_27 tptp.x_a) (B_20 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_27))) (=> (@ _let_1 B_20) (@ _let_1 (@ (@ tptp.insert_a B_21) B_20))))))
% 0.25/0.65 (assert (forall ((A_26 tptp.nat) (A_25 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat A_26) A_25) (= (@ (@ tptp.insert_nat A_26) A_25) A_25))))
% 0.25/0.65 (assert (forall ((A_26 tptp.pname) (A_25 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_26) A_25) (= (@ (@ tptp.insert_pname A_26) A_25) A_25))))
% 0.25/0.65 (assert (forall ((A_26 tptp.x_a) (A_25 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a A_26) A_25) (= (@ (@ tptp.insert_a A_26) A_25) A_25))))
% 0.25/0.65 (assert (forall ((A_24 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o A_24) A_24)))
% 0.25/0.65 (assert (forall ((A_24 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o A_24) A_24)))
% 0.25/0.65 (assert (forall ((A_24 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o A_24) A_24)))
% 0.25/0.65 (assert (forall ((A_23 (-> tptp.nat Bool)) (B_19 (-> tptp.nat Bool))) (= (= A_23 B_19) (and (@ (@ tptp.ord_less_eq_nat_o A_23) B_19) (@ (@ tptp.ord_less_eq_nat_o B_19) A_23)))))
% 0.25/0.65 (assert (forall ((A_23 (-> tptp.pname Bool)) (B_19 (-> tptp.pname Bool))) (= (= A_23 B_19) (and (@ (@ tptp.ord_less_eq_pname_o A_23) B_19) (@ (@ tptp.ord_less_eq_pname_o B_19) A_23)))))
% 0.25/0.65 (assert (forall ((A_23 (-> tptp.x_a Bool)) (B_19 (-> tptp.x_a Bool))) (= (= A_23 B_19) (and (@ (@ tptp.ord_less_eq_a_o A_23) B_19) (@ (@ tptp.ord_less_eq_a_o B_19) A_23)))))
% 0.25/0.65 (assert (forall ((A_22 (-> tptp.nat Bool)) (B_18 (-> tptp.nat Bool))) (=> (= A_22 B_18) (@ (@ tptp.ord_less_eq_nat_o A_22) B_18))))
% 0.25/0.65 (assert (forall ((A_22 (-> tptp.pname Bool)) (B_18 (-> tptp.pname Bool))) (=> (= A_22 B_18) (@ (@ tptp.ord_less_eq_pname_o A_22) B_18))))
% 0.25/0.65 (assert (forall ((A_22 (-> tptp.x_a Bool)) (B_18 (-> tptp.x_a Bool))) (=> (= A_22 B_18) (@ (@ tptp.ord_less_eq_a_o A_22) B_18))))
% 0.25/0.65 (assert (forall ((A_21 (-> tptp.nat Bool)) (B_17 (-> tptp.nat Bool))) (=> (= A_21 B_17) (@ (@ tptp.ord_less_eq_nat_o B_17) A_21))))
% 0.25/0.65 (assert (forall ((A_21 (-> tptp.pname Bool)) (B_17 (-> tptp.pname Bool))) (=> (= A_21 B_17) (@ (@ tptp.ord_less_eq_pname_o B_17) A_21))))
% 0.25/0.65 (assert (forall ((A_21 (-> tptp.x_a Bool)) (B_17 (-> tptp.x_a Bool))) (=> (= A_21 B_17) (@ (@ tptp.ord_less_eq_a_o B_17) A_21))))
% 0.25/0.65 (assert (forall ((X_10 tptp.nat) (A_20 (-> tptp.nat Bool)) (B_16 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_10))) (=> (@ (@ tptp.ord_less_eq_nat_o A_20) B_16) (=> (@ _let_1 A_20) (@ _let_1 B_16))))))
% 0.25/0.65 (assert (forall ((X_10 tptp.x_a) (A_20 (-> tptp.x_a Bool)) (B_16 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_10))) (=> (@ (@ tptp.ord_less_eq_a_o A_20) B_16) (=> (@ _let_1 A_20) (@ _let_1 B_16))))))
% 0.25/0.65 (assert (forall ((X_10 tptp.pname) (A_20 (-> tptp.pname Bool)) (B_16 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_10))) (=> (@ (@ tptp.ord_less_eq_pname_o A_20) B_16) (=> (@ _let_1 A_20) (@ _let_1 B_16))))))
% 0.25/0.65 (assert (forall ((B_15 (-> tptp.nat Bool)) (X_9 tptp.nat) (A_19 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_9))) (=> (@ _let_1 A_19) (=> (@ (@ tptp.ord_less_eq_nat_o A_19) B_15) (@ _let_1 B_15))))))
% 0.25/0.65 (assert (forall ((B_15 (-> tptp.x_a Bool)) (X_9 tptp.x_a) (A_19 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_9))) (=> (@ _let_1 A_19) (=> (@ (@ tptp.ord_less_eq_a_o A_19) B_15) (@ _let_1 B_15))))))
% 0.25/0.65 (assert (forall ((B_15 (-> tptp.pname Bool)) (X_9 tptp.pname) (A_19 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_9))) (=> (@ _let_1 A_19) (=> (@ (@ tptp.ord_less_eq_pname_o A_19) B_15) (@ _let_1 B_15))))))
% 0.25/0.65 (assert (forall ((X_8 tptp.nat) (A_18 (-> tptp.nat Bool)) (B_14 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_8))) (=> (@ (@ tptp.ord_less_eq_nat_o A_18) B_14) (=> (@ _let_1 A_18) (@ _let_1 B_14))))))
% 0.25/0.65 (assert (forall ((X_8 tptp.x_a) (A_18 (-> tptp.x_a Bool)) (B_14 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_8))) (=> (@ (@ tptp.ord_less_eq_a_o A_18) B_14) (=> (@ _let_1 A_18) (@ _let_1 B_14))))))
% 0.25/0.65 (assert (forall ((X_8 tptp.pname) (A_18 (-> tptp.pname Bool)) (B_14 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_8))) (=> (@ (@ tptp.ord_less_eq_pname_o A_18) B_14) (=> (@ _let_1 A_18) (@ _let_1 B_14))))))
% 0.25/0.65 (assert (forall ((C_1 (-> tptp.nat Bool)) (A_17 (-> tptp.nat Bool)) (B_13 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_17))) (=> (@ _let_1 B_13) (=> (@ (@ tptp.ord_less_eq_nat_o B_13) C_1) (@ _let_1 C_1))))))
% 0.25/0.65 (assert (forall ((C_1 (-> tptp.pname Bool)) (A_17 (-> tptp.pname Bool)) (B_13 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_17))) (=> (@ _let_1 B_13) (=> (@ (@ tptp.ord_less_eq_pname_o B_13) C_1) (@ _let_1 C_1))))))
% 0.25/0.65 (assert (forall ((C_1 (-> tptp.x_a Bool)) (A_17 (-> tptp.x_a Bool)) (B_13 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_17))) (=> (@ _let_1 B_13) (=> (@ (@ tptp.ord_less_eq_a_o B_13) C_1) (@ _let_1 C_1))))))
% 0.25/0.65 (assert (forall ((A_16 (-> tptp.nat Bool)) (B_12 (-> tptp.nat Bool))) (=> (= A_16 B_12) (not (=> (@ (@ tptp.ord_less_eq_nat_o A_16) B_12) (not (@ (@ tptp.ord_less_eq_nat_o B_12) A_16)))))))
% 0.25/0.65 (assert (forall ((A_16 (-> tptp.pname Bool)) (B_12 (-> tptp.pname Bool))) (=> (= A_16 B_12) (not (=> (@ (@ tptp.ord_less_eq_pname_o A_16) B_12) (not (@ (@ tptp.ord_less_eq_pname_o B_12) A_16)))))))
% 0.25/0.65 (assert (forall ((A_16 (-> tptp.x_a Bool)) (B_12 (-> tptp.x_a Bool))) (=> (= A_16 B_12) (not (=> (@ (@ tptp.ord_less_eq_a_o A_16) B_12) (not (@ (@ tptp.ord_less_eq_a_o B_12) A_16)))))))
% 0.25/0.65 (assert (forall ((X_7 tptp.nat) (A_15 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X_7) A_15) (@ A_15 X_7))))
% 0.25/0.65 (assert (forall ((X_7 tptp.x_a) (A_15 (-> tptp.x_a Bool))) (= (@ (@ tptp.member_a X_7) A_15) (@ A_15 X_7))))
% 0.25/0.65 (assert (forall ((X_7 tptp.pname) (A_15 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_7) A_15) (@ A_15 X_7))))
% 0.25/0.65 (assert (forall ((P_1 (-> tptp.pname Bool))) (= (@ tptp.collect_pname P_1) P_1)))
% 0.25/0.65 (assert (forall ((P_1 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.collect_nat_o P_1) P_1)))
% 0.25/0.65 (assert (forall ((P_1 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.collect_pname_o P_1) P_1)))
% 0.25/0.65 (assert (forall ((P_1 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.collect_a_o P_1) P_1)))
% 0.25/0.65 (assert (forall ((P_1 (-> tptp.nat Bool))) (= (@ tptp.collect_nat P_1) P_1)))
% 0.25/0.65 (assert (forall ((Z tptp.x_a) (F_8 (-> tptp.pname tptp.x_a)) (A_14 (-> tptp.pname Bool))) (= (@ (@ tptp.member_a Z) (@ (@ tptp.image_pname_a F_8) A_14)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_14) (= Z (@ F_8 X)))))))
% 0.25/0.65 (assert (forall ((F_7 (-> tptp.pname tptp.x_a)) (X_6 tptp.pname) (A_13 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_6) A_13) (@ (@ tptp.member_a (@ F_7 X_6)) (@ (@ tptp.image_pname_a F_7) A_13)))))
% 0.25/0.65 (assert (forall ((B_11 tptp.x_a) (F_6 (-> tptp.pname tptp.x_a)) (X_5 tptp.pname) (A_12 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_5) A_12) (=> (= B_11 (@ F_6 X_5)) (@ (@ tptp.member_a B_11) (@ (@ tptp.image_pname_a F_6) A_12))))))
% 0.25/0.65 (assert (forall ((X tptp.nat) (Xa (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat X) Xa) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (or (= Y X) (@ (@ tptp.member_nat Y) Xa)))))))
% 0.25/0.65 (assert (forall ((X tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X) Xa) (@ tptp.collect_pname (lambda ((Y tptp.pname)) (or (= Y X) (@ (@ tptp.member_pname Y) Xa)))))))
% 0.25/0.65 (assert (forall ((X tptp.x_a) (Xa (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a X) Xa) (@ tptp.collect_a (lambda ((Y tptp.x_a)) (or (= Y X) (@ (@ tptp.member_a Y) Xa)))))))
% 0.25/0.65 (assert (forall ((X (-> tptp.nat Bool)) (Xa (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o X) Xa) (@ tptp.collect_nat_o (lambda ((Y (-> tptp.nat Bool))) (or (= Y X) (@ (@ tptp.member_nat_o Y) Xa)))))))
% 0.25/0.65 (assert (forall ((X (-> tptp.pname Bool)) (Xa (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o X) Xa) (@ tptp.collect_pname_o (lambda ((Y (-> tptp.pname Bool))) (or (= Y X) (@ (@ tptp.member_pname_o Y) Xa)))))))
% 0.25/0.65 (assert (forall ((X (-> tptp.x_a Bool)) (Xa (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o X) Xa) (@ tptp.collect_a_o (lambda ((Y (-> tptp.x_a Bool))) (or (= Y X) (@ (@ tptp.member_a_o Y) Xa)))))))
% 0.25/0.65 (assert (forall ((B_10 (-> tptp.nat Bool)) (A_11 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o B_10) (@ (@ tptp.insert_nat A_11) B_10))))
% 0.25/0.65 (assert (forall ((B_10 (-> tptp.pname Bool)) (A_11 tptp.pname)) (@ (@ tptp.ord_less_eq_pname_o B_10) (@ (@ tptp.insert_pname A_11) B_10))))
% 0.25/0.65 (assert (forall ((B_10 (-> tptp.x_a Bool)) (A_11 tptp.x_a)) (@ (@ tptp.ord_less_eq_a_o B_10) (@ (@ tptp.insert_a A_11) B_10))))
% 0.25/0.65 (assert (forall ((X_4 tptp.nat) (A_10 (-> tptp.nat Bool)) (B_9 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.insert_nat X_4) A_10)) B_9) (and (@ (@ tptp.member_nat X_4) B_9) (@ (@ tptp.ord_less_eq_nat_o A_10) B_9)))))
% 0.25/0.65 (assert (forall ((X_4 tptp.pname) (A_10 (-> tptp.pname Bool)) (B_9 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.insert_pname X_4) A_10)) B_9) (and (@ (@ tptp.member_pname X_4) B_9) (@ (@ tptp.ord_less_eq_pname_o A_10) B_9)))))
% 0.25/0.65 (assert (forall ((X_4 tptp.x_a) (A_10 (-> tptp.x_a Bool)) (B_9 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a X_4) A_10)) B_9) (and (@ (@ tptp.member_a X_4) B_9) (@ (@ tptp.ord_less_eq_a_o A_10) B_9)))))
% 0.25/0.65 (assert (forall ((B_8 (-> tptp.nat Bool)) (X_3 tptp.nat) (A_9 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_9))) (=> (not (@ (@ tptp.member_nat X_3) A_9)) (= (@ _let_1 (@ (@ tptp.insert_nat X_3) B_8)) (@ _let_1 B_8))))))
% 0.25/0.65 (assert (forall ((B_8 (-> tptp.pname Bool)) (X_3 tptp.pname) (A_9 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_9))) (=> (not (@ (@ tptp.member_pname X_3) A_9)) (= (@ _let_1 (@ (@ tptp.insert_pname X_3) B_8)) (@ _let_1 B_8))))))
% 0.25/0.65 (assert (forall ((B_8 (-> tptp.x_a Bool)) (X_3 tptp.x_a) (A_9 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_9))) (=> (not (@ (@ tptp.member_a X_3) A_9)) (= (@ _let_1 (@ (@ tptp.insert_a X_3) B_8)) (@ _let_1 B_8))))))
% 0.25/0.65 (assert (forall ((B_7 tptp.nat) (A_8 (-> tptp.nat Bool)) (B_6 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_8))) (=> (@ _let_1 B_6) (@ _let_1 (@ (@ tptp.insert_nat B_7) B_6))))))
% 0.25/0.65 (assert (forall ((B_7 tptp.pname) (A_8 (-> tptp.pname Bool)) (B_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_8))) (=> (@ _let_1 B_6) (@ _let_1 (@ (@ tptp.insert_pname B_7) B_6))))))
% 0.25/0.65 (assert (forall ((B_7 tptp.x_a) (A_8 (-> tptp.x_a Bool)) (B_6 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_8))) (=> (@ _let_1 B_6) (@ _let_1 (@ (@ tptp.insert_a B_7) B_6))))))
% 0.25/0.65 (assert (forall ((A_7 tptp.nat) (C (-> tptp.nat Bool)) (D (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_7))) (=> (@ (@ tptp.ord_less_eq_nat_o C) D) (@ (@ tptp.ord_less_eq_nat_o (@ _let_1 C)) (@ _let_1 D))))))
% 0.25/0.65 (assert (forall ((A_7 tptp.pname) (C (-> tptp.pname Bool)) (D (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_7))) (=> (@ (@ tptp.ord_less_eq_pname_o C) D) (@ (@ tptp.ord_less_eq_pname_o (@ _let_1 C)) (@ _let_1 D))))))
% 0.25/0.65 (assert (forall ((A_7 tptp.x_a) (C (-> tptp.x_a Bool)) (D (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_7))) (=> (@ (@ tptp.ord_less_eq_a_o C) D) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 C)) (@ _let_1 D))))))
% 0.25/0.65 (assert (forall ((F_5 (-> tptp.pname tptp.x_a)) (A_6 tptp.pname) (B_5 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_5))) (= (@ _let_1 (@ (@ tptp.insert_pname A_6) B_5)) (@ (@ tptp.insert_a (@ F_5 A_6)) (@ _let_1 B_5))))))
% 0.25/0.65 (assert (forall ((F_4 (-> tptp.pname tptp.x_a)) (X_2 tptp.pname) (A_5 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_a F_4) A_5))) (=> (@ (@ tptp.member_pname X_2) A_5) (= (@ (@ tptp.insert_a (@ F_4 X_2)) _let_1) _let_1)))))
% 0.25/0.65 (assert (forall ((B_4 (-> tptp.x_a Bool)) (F_3 (-> tptp.pname tptp.x_a)) (A_4 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_a_o B_4) (@ (@ tptp.image_pname_a F_3) A_4)) (exists ((AA (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o AA) A_4) (= B_4 (@ (@ tptp.image_pname_a F_3) AA)))))))
% 0.25/0.65 (assert (forall ((F_2 (-> tptp.pname tptp.x_a)) (A_3 (-> tptp.pname Bool)) (B_3 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_2))) (=> (@ (@ tptp.ord_less_eq_pname_o A_3) B_3) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 A_3)) (@ _let_1 B_3))))))
% 0.25/0.65 (assert (forall ((B_2 tptp.x_a) (F_1 (-> tptp.pname tptp.x_a)) (A_2 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_a B_2) (@ (@ tptp.image_pname_a F_1) A_2)) (not (forall ((X tptp.pname)) (=> (= B_2 (@ F_1 X)) (not (@ (@ tptp.member_pname X) A_2))))))))
% 0.25/0.65 (assert (forall ((B_1 (-> tptp.nat Bool)) (A_1 (-> tptp.nat Bool))) (=> (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_less_eq_nat_o A_1) B_1))))
% 0.25/0.65 (assert (forall ((B_1 (-> tptp.x_a Bool)) (A_1 (-> tptp.x_a Bool))) (=> (forall ((X tptp.x_a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_less_eq_a_o A_1) B_1))))
% 0.25/0.65 (assert (forall ((B_1 (-> tptp.pname Bool)) (A_1 (-> tptp.pname Bool))) (=> (forall ((X tptp.pname)) (let ((_let_1 (@ tptp.member_pname X))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_less_eq_pname_o A_1) B_1))))
% 0.25/0.65 (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))))))
% 0.75/0.98 (assert (forall ((N_1 tptp.nat) (M_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) M_1) (exists ((M tptp.nat)) (= M_1 (@ tptp.suc M))))))
% 0.75/0.98 (assert (forall ((F (-> tptp.pname tptp.x_a)) (B (-> tptp.x_a Bool)) (A (-> tptp.pname Bool))) (=> (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) A) (@ (@ tptp.member_a (@ F X)) B))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.image_pname_a F) A)) B))))
% 0.75/0.98 (assert (forall ((X_1 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o X_1) X_1)))
% 0.75/0.98 (assert (forall ((X_1 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o X_1) X_1)))
% 0.75/0.98 (assert (forall ((X_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X_1) X_1)))
% 0.75/0.98 (assert (forall ((X_1 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o X_1) X_1)))
% 0.75/0.98 (assert (forall ((N (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N) (exists ((M tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N) (@ (@ tptp.ord_less_eq_nat X) M)))))))
% 0.75/0.98 (assert (@ tptp.finite_finite_pname tptp.u))
% 0.75/0.98 (assert (@ (@ tptp.ord_less_eq_a_o tptp.g) (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u)))
% 0.75/0.98 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.na)) (@ tptp.finite_card_a (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u))))
% 0.75/0.98 (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))))
% 0.75/0.98 (assert (@ (@ tptp.member_pname tptp.pn) tptp.u))
% 0.75/0.98 (assert (not (@ (@ tptp.member_a (@ tptp.mgt_call tptp.pn)) tptp.g)))
% 0.75/0.98 (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))))
% 0.75/0.98 (set-info :filename cvc5---1.0.5_11477)
% 0.75/0.98 (check-sat-assuming ( true ))
% 0.75/0.98 ------- get file name : TPTP file name is SWW473^1
% 0.75/0.98 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_11477.smt2...
% 0.75/0.98 --- Run --ho-elim --full-saturate-quant at 10...
% 0.75/0.98 % SZS status Theorem for SWW473^1
% 0.75/0.98 % SZS output start Proof for SWW473^1
% 0.75/0.98 (
% 0.75/0.98 (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_4 tptp.x_a) (A_10 (-> tptp.x_a Bool)) (B_9 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a X_4) A_10)) B_9) (and (@ (@ tptp.member_a X_4) B_9) (@ (@ tptp.ord_less_eq_a_o A_10) B_9)))))) (let ((_let_9 (forall ((A_42 (-> tptp.pname Bool)) (B_31 tptp.x_a) (F_9 (-> tptp.pname tptp.x_a)) (X_15 tptp.pname)) (=> (= B_31 (@ F_9 X_15)) (=> (@ (@ tptp.member_pname X_15) A_42) (@ (@ tptp.member_a B_31) (@ (@ tptp.image_pname_a F_9) A_42))))))) (let ((_let_10 (forall ((BOUND_VARIABLE_11060 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_11061 |u_(-> tptp.pname tptp.x_a)|) (X_15 tptp.pname)) (or (not (ho_53 (ho_77 k_76 X_15) BOUND_VARIABLE_11060)) (ho_45 (ho_72 k_71 (ho_95 BOUND_VARIABLE_11061 X_15)) (ho_185 (ho_184 k_183 BOUND_VARIABLE_11061) BOUND_VARIABLE_11060)))))) (let ((_let_11 (ho_185 (ho_184 k_183 k_356) k_355))) (let ((_let_12 (ho_95 k_356 tptp.pn))) (let ((_let_13 (ho_45 (ho_72 k_71 _let_12) _let_11))) (let ((_let_14 (ho_53 (ho_77 k_76 tptp.pn) k_355))) (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_42 (-> tptp.pname Bool)) (F_9 (-> tptp.pname tptp.x_a)) (X_15 tptp.pname)) (or (not (@ (@ tptp.member_pname X_15) A_42)) (@ (@ tptp.member_a (@ F_9 X_15)) (@ (@ tptp.image_pname_a F_9) A_42)))) _let_10))))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (ho_45 (ho_144 k_145 k_357) _let_11))) (let ((_let_20 (and _let_13 _let_19))) (let ((_let_21 (not _let_13))) (let ((_let_22 (ho_45 (ho_144 k_145 (ho_70 (ho_69 k_312 _let_12) k_357)) _let_11))) (let ((_let_23 (= _let_22 _let_20))) (let ((_let_24 (not _let_20))) (let ((_let_25 (forall ((X_4 tptp.x_a) (BOUND_VARIABLE_12214 |u_(-> tptp.x_a Bool)|) (BOUND_VARIABLE_12213 |u_(-> tptp.x_a Bool)|)) (= (and (ho_45 (ho_72 k_71 X_4) BOUND_VARIABLE_12213) (ho_45 (ho_144 k_145 BOUND_VARIABLE_12214) BOUND_VARIABLE_12213)) (ho_45 (ho_144 k_145 (ho_70 (ho_69 k_312 X_4) BOUND_VARIABLE_12214)) BOUND_VARIABLE_12213))))) (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_355 k_356 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_357 _let_11 QUANTIFIERS_INST_E_MATCHING ((ho_45 (ho_144 k_145 (ho_70 (ho_69 k_312 X_4) BOUND_VARIABLE_12214)) BOUND_VARIABLE_12213)))) :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_59 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_59) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((B_38 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o B_38) A_59)))))) (forall ((A_59 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_59) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((B_38 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o B_38) A_59)))))) (forall ((A_59 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_59) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((B_38 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o B_38) A_59)))))) (forall ((A_59 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o A_59) (@ tptp.finite1237261006_o_o_o (@ tptp.collect_nat_o_o_o (lambda ((B_38 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (@ (@ tptp.ord_le124054423_o_o_o B_38) A_59)))))) (forall ((A_59 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_59) (@ tptp.finite1648353812_o_o_o (@ tptp.collect_pname_o_o_o (lambda ((B_38 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (@ (@ tptp.ord_le1828183645_o_o_o B_38) A_59)))))) (forall ((A_59 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o A_59) (@ tptp.finite1302365357_o_o_o (@ tptp.collect_a_o_o_o (lambda ((B_38 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (@ (@ tptp.ord_less_eq_a_o_o_o B_38) A_59)))))) (forall ((A_59 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_59) (@ tptp.finite_finite_a_o_o (@ tptp.collect_a_o_o (lambda ((B_38 (-> (-> tptp.x_a Bool) Bool))) (@ (@ tptp.ord_less_eq_a_o_o B_38) A_59)))))) (forall ((A_59 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_59) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((B_38 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o B_38) A_59)))))) (forall ((A_59 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_59) (@ tptp.finite1676163439at_o_o (@ tptp.collect_nat_o_o (lambda ((B_38 (-> (-> tptp.nat Bool) Bool))) (@ (@ tptp.ord_less_eq_nat_o_o B_38) A_59)))))) (forall ((H (-> tptp.pname tptp.x_a)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a H) F_15)))) (forall ((H (-> (-> (-> tptp.nat Bool) Bool) tptp.nat)) (F_15 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_o_nat H) F_15)))) (forall ((H (-> (-> (-> tptp.pname Bool) Bool) tptp.nat)) (F_15 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_o_nat H) F_15)))) (forall ((H (-> (-> (-> tptp.x_a Bool) Bool) tptp.nat)) (F_15 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_o_nat H) F_15)))) (forall ((H (-> (-> tptp.x_a Bool) tptp.nat)) (F_15 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_nat H) F_15)))) (forall ((H (-> (-> tptp.pname Bool) tptp.nat)) (F_15 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_nat H) F_15)))) (forall ((H (-> (-> tptp.nat Bool) tptp.nat)) (F_15 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_nat H) F_15)))) (forall ((H (-> tptp.x_a tptp.nat)) (F_15 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_15) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_nat H) F_15)))) (forall ((H (-> (-> (-> tptp.nat Bool) Bool) tptp.pname)) (F_15 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_o_pname H) F_15)))) (forall ((H (-> (-> (-> tptp.pname Bool) Bool) tptp.pname)) (F_15 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_471733107_pname H) F_15)))) (forall ((H (-> (-> (-> tptp.x_a Bool) Bool) tptp.pname)) (F_15 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_o_pname H) F_15)))) (forall ((H (-> (-> tptp.x_a Bool) tptp.pname)) (F_15 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_pname H) F_15)))) (forall ((H (-> (-> tptp.pname Bool) tptp.pname)) (F_15 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname H) F_15)))) (forall ((H (-> (-> tptp.nat Bool) tptp.pname)) (F_15 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_pname H) F_15)))) (forall ((H (-> tptp.x_a tptp.pname)) (F_15 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_15) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_pname H) F_15)))) (forall ((H (-> tptp.nat (-> tptp.nat Bool) Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite1676163439at_o_o (@ (@ tptp.image_nat_nat_o_o H) F_15)))) (forall ((H (-> tptp.nat (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite1066544169me_o_o (@ (@ tptp.image_nat_pname_o_o H) F_15)))) (forall ((H (-> tptp.nat (-> tptp.x_a Bool) Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_a_o_o (@ (@ tptp.image_nat_a_o_o H) F_15)))) (forall ((H (-> tptp.nat tptp.x_a Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o H) F_15)))) (forall ((H (-> tptp.nat tptp.pname Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o H) F_15)))) (forall ((H (-> tptp.nat tptp.nat Bool)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o H) F_15)))) (forall ((H (-> tptp.nat tptp.x_a)) (F_15 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_15) (@ tptp.finite_finite_a (@ (@ tptp.image_nat_a H) F_15)))) (forall ((H (-> tptp.pname (-> tptp.nat Bool) Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite1676163439at_o_o (@ (@ tptp.image_pname_nat_o_o H) F_15)))) (forall ((H (-> tptp.pname (-> tptp.pname Bool) Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite1066544169me_o_o (@ (@ tptp.image_504089495me_o_o H) F_15)))) (forall ((H (-> tptp.pname (-> tptp.x_a Bool) Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_a_o_o (@ (@ tptp.image_pname_a_o_o H) F_15)))) (forall ((H (-> tptp.pname tptp.x_a Bool)) (F_15 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_15) (@ tptp.finite_finite_a_o (@ (@ tptp.image_pname_a_o H) F_15)))) (forall ((H (-> 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A_57)))) (forall ((A_58 (-> tptp.nat Bool)) (A_57 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_57) (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_58) A_57)))) (forall ((F_14 (-> tptp.pname tptp.nat)) (A_56 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_nat F_14) A_56))) (@ tptp.finite_card_pname A_56)))) (forall ((F_14 (-> tptp.x_a tptp.nat)) (A_56 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_nat F_14) A_56))) (@ tptp.finite_card_a A_56)))) (forall ((F_14 (-> (-> tptp.nat Bool) tptp.nat)) (A_56 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_nat_o_nat F_14) A_56))) (@ tptp.finite_card_nat_o A_56)))) (forall ((F_14 (-> (-> tptp.pname Bool) tptp.nat)) (A_56 (-> (-> tptp.pname Bool) Bool))) (=> (@ 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(@ tptp.finite_card_a (@ (@ tptp.image_pname_a F_14) A_56))) (@ tptp.finite_card_pname A_56)))) (forall ((F_14 (-> (-> (-> tptp.nat Bool) Bool) tptp.x_a)) (A_56 (-> (-> (-> tptp.nat Bool) Bool) Bool))) (=> (@ tptp.finite1676163439at_o_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_o_o_a F_14) A_56))) (@ tptp.finite_card_nat_o_o A_56)))) (forall ((F_14 (-> (-> (-> tptp.pname Bool) Bool) tptp.x_a)) (A_56 (-> (-> (-> tptp.pname Bool) Bool) Bool))) (=> (@ tptp.finite1066544169me_o_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_o_o_a F_14) A_56))) (@ tptp.finite221134632me_o_o A_56)))) (forall ((F_14 (-> (-> (-> tptp.x_a Bool) Bool) tptp.x_a)) (A_56 (-> (-> (-> tptp.x_a Bool) Bool) Bool))) (=> (@ tptp.finite_finite_a_o_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_o_o_a F_14) A_56))) (@ tptp.finite_card_a_o_o A_56)))) (forall ((F_14 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_56 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_o_a F_14) A_56))) (@ tptp.finite_card_a_o A_56)))) (forall ((F_14 (-> (-> tptp.pname Bool) tptp.x_a)) (A_56 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_o_a F_14) A_56))) (@ tptp.finite_card_pname_o A_56)))) (forall ((F_14 (-> (-> tptp.nat Bool) tptp.x_a)) (A_56 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_o_a F_14) A_56))) (@ tptp.finite_card_nat_o A_56)))) (forall ((F_14 (-> tptp.x_a tptp.x_a)) (A_56 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_56) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_a F_14) A_56))) (@ tptp.finite_card_a A_56)))) (forall ((F_14 (-> tptp.pname tptp.pname)) (A_56 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_56) (@ (@ 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B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_55)) (@ tptp.finite_card_pname_o B_37))))) (forall ((A_55 (-> (-> tptp.x_a Bool) Bool)) (B_37 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_37) (=> (@ (@ tptp.ord_less_eq_a_o_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_55)) (@ tptp.finite_card_a_o B_37))))) (forall ((A_55 (-> tptp.pname Bool)) (B_37 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_37) (=> (@ (@ tptp.ord_less_eq_pname_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_55)) (@ tptp.finite_card_pname B_37))))) (forall ((A_55 (-> tptp.x_a Bool)) (B_37 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_37) (=> (@ (@ tptp.ord_less_eq_a_o A_55) B_37) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_55)) (@ tptp.finite_card_a B_37))))) (forall ((A_55 (-> tptp.nat Bool)) (B_37 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_37) (=> (@ (@ tptp.ord_less_eq_nat_o A_55) B_37) (@ (@ 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tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_53)) (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_19) A_53))))) (forall ((X_19 (-> tptp.x_a Bool)) (A_53 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_53)) (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_19) A_53))))) (forall ((X_19 tptp.pname) (A_53 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_53)) (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_19) A_53))))) (forall ((X_19 tptp.nat) (A_53 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_53)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_19) A_53))))) (forall ((X_19 tptp.x_a) (A_53 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_53) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_53)) (@ 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tptp.insert_a_o X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_a_o X_18) A_52))) (=> (@ tptp.finite_finite_a_o A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_18 tptp.nat) (A_52 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_card_nat A_52))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_nat X_18) A_52))) (=> (@ tptp.finite_finite_nat A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_18 tptp.pname) (A_52 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.finite_card_pname A_52))) (let ((_let_2 (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_pname X_18) A_52))) (=> (@ tptp.finite_finite_pname A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_18 tptp.x_a) (A_52 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.finite_card_a A_52))) (let ((_let_2 (@ tptp.finite_card_a (@ (@ tptp.insert_a X_18) A_52)))) (let ((_let_3 (@ (@ tptp.member_a X_18) A_52))) (=> (@ tptp.finite_finite_a A_52) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_17 (-> tptp.nat Bool)) (A_51 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_51) (=> (not (@ (@ tptp.member_nat_o X_17) A_51)) (= (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_nat_o A_51)))))) (forall ((X_17 (-> tptp.pname Bool)) (A_51 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_51) (=> (not (@ (@ tptp.member_pname_o X_17) A_51)) (= (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_pname_o A_51)))))) (forall ((X_17 (-> tptp.x_a Bool)) (A_51 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_51) (=> (not (@ (@ tptp.member_a_o X_17) A_51)) (= (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_a_o A_51)))))) (forall ((X_17 tptp.nat) (A_51 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_51) (=> (not (@ (@ tptp.member_nat X_17) A_51)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_nat A_51)))))) (forall ((X_17 tptp.pname) (A_51 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_51) (=> (not (@ (@ tptp.member_pname X_17) A_51)) (= (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_pname A_51)))))) (forall ((X_17 tptp.x_a) (A_51 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_51) (=> (not (@ (@ tptp.member_a X_17) A_51)) (= (@ tptp.finite_card_a (@ (@ tptp.insert_a X_17) A_51)) (@ tptp.suc (@ tptp.finite_card_a A_51)))))) (forall ((Q_1 (-> (-> tptp.nat Bool) Bool)) (P_4 (-> (-> tptp.nat Bool) Bool))) (=> (or (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_4)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q_1))) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X (-> tptp.nat Bool))) (and (@ P_4 X) (@ Q_1 X))))))) (forall ((Q_1 (-> (-> tptp.pname Bool) Bool)) (P_4 (-> (-> tptp.pname Bool) Bool))) (=> (or (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_4)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_1))) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X (-> tptp.pname Bool))) (and (@ P_4 X) (@ Q_1 X))))))) (forall ((Q_1 (-> (-> tptp.x_a Bool) Bool)) (P_4 (-> (-> tptp.x_a Bool) Bool))) (=> (or (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_4)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q_1))) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X (-> tptp.x_a Bool))) (and (@ P_4 X) (@ Q_1 X))))))) (forall ((Q_1 (-> tptp.x_a Bool)) (P_4 (-> tptp.x_a Bool))) (=> (or (@ tptp.finite_finite_a (@ tptp.collect_a P_4)) (@ tptp.finite_finite_a (@ tptp.collect_a Q_1))) (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X tptp.x_a)) (and (@ P_4 X) (@ Q_1 X))))))) (forall ((Q_1 (-> tptp.pname Bool)) (P_4 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_4)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_1))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X tptp.pname)) (and (@ P_4 X) (@ Q_1 X))))))) (forall ((Q_1 (-> tptp.nat Bool)) (P_4 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P_4)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_1))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ P_4 X) (@ Q_1 X))))))) (forall ((N_1 tptp.nat) (M_2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N_1) M_2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M_2)) N_1) (@ tptp.suc (@ (@ tptp.minus_minus_nat M_2) N_1))))) (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_1 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I_1) N_1)))) (@ tptp.suc N_1))) (forall ((X_16 tptp.nat) (Y_3 tptp.nat)) (=> (= (@ tptp.suc X_16) (@ tptp.suc Y_3)) (= X_16 Y_3))) (forall ((Nat_1 tptp.nat) (Nat tptp.nat)) (= (= (@ tptp.suc Nat_1) (@ tptp.suc Nat)) (= Nat_1 Nat))) (forall ((N_1 tptp.nat)) (not (= (@ tptp.suc N_1) N_1))) (forall ((N_1 tptp.nat)) (not (= N_1 (@ tptp.suc N_1)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M_2) N_1) (=> (@ (@ tptp.ord_less_eq_nat N_1) M_2) (= M_2 N_1)))) (forall ((K tptp.nat) (I tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (= M_2 N_1) (@ (@ tptp.ord_less_eq_nat M_2) N_1))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M_2) N_1) (@ (@ tptp.ord_less_eq_nat N_1) M_2))) (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) N_1)) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))) (forall ((P_3 (-> tptp.pname Bool)) (Q (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_3)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q))))) (forall ((P_3 (-> (-> tptp.nat Bool) Bool)) (Q (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X (-> tptp.nat Bool))) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_3)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q))))) (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (Q (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X (-> tptp.pname Bool))) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_3)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q))))) (forall ((P_3 (-> (-> tptp.x_a Bool) Bool)) (Q (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X (-> tptp.x_a Bool))) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_3)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q))))) (forall ((P_3 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P_3)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))) (forall ((P_3 (-> tptp.x_a Bool)) (Q (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X tptp.x_a)) (or (@ P_3 X) (@ Q X))))) (and (@ tptp.finite_finite_a (@ tptp.collect_a P_3)) (@ tptp.finite_finite_a (@ tptp.collect_a Q))))) (forall ((A_50 tptp.nat) (A_49 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_50) A_49)) (@ tptp.finite_finite_nat A_49))) (forall ((A_50 tptp.pname) (A_49 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_50) A_49)) (@ tptp.finite_finite_pname A_49))) (forall ((A_50 tptp.x_a) (A_49 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_50) A_49)) (@ tptp.finite_finite_a A_49))) (forall ((A_50 (-> tptp.nat Bool)) (A_49 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_50) A_49)) (@ tptp.finite_finite_nat_o A_49))) (forall ((A_50 (-> tptp.pname Bool)) (A_49 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_50) A_49)) (@ tptp.finite297249702name_o A_49))) (forall ((A_50 (-> tptp.x_a Bool)) (A_49 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_50) A_49)) (@ tptp.finite_finite_a_o A_49))) (forall ((A_48 (-> (-> tptp.nat Bool) Bool)) (B_35 (-> (-> tptp.nat Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_48) B_35) (=> (@ tptp.finite_finite_nat_o B_35) (@ tptp.finite_finite_nat_o A_48)))) (forall ((A_48 (-> (-> tptp.pname Bool) Bool)) (B_35 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_48) B_35) (=> (@ tptp.finite297249702name_o B_35) (@ tptp.finite297249702name_o A_48)))) (forall ((A_48 (-> tptp.x_a Bool)) (B_35 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_48) B_35) (=> (@ tptp.finite_finite_a B_35) (@ tptp.finite_finite_a A_48)))) (forall ((A_48 (-> (-> tptp.x_a Bool) Bool)) (B_35 (-> (-> tptp.x_a Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_a_o_o A_48) B_35) (=> (@ tptp.finite_finite_a_o B_35) (@ tptp.finite_finite_a_o A_48)))) (forall ((A_48 (-> tptp.nat Bool)) (B_35 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_48) B_35) (=> (@ tptp.finite_finite_nat B_35) (@ tptp.finite_finite_nat A_48)))) (forall ((A_48 (-> tptp.pname Bool)) (B_35 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_48) B_35) (=> (@ tptp.finite_finite_pname B_35) (@ tptp.finite_finite_pname A_48)))) (forall ((A_47 (-> (-> tptp.nat Bool) Bool)) (B_34 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_34) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_47) B_34) (@ tptp.finite_finite_nat_o A_47)))) (forall ((A_47 (-> (-> tptp.pname Bool) Bool)) (B_34 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_34) (=> (@ (@ tptp.ord_le1205211808me_o_o A_47) B_34) (@ tptp.finite297249702name_o A_47)))) (forall ((A_47 (-> tptp.x_a Bool)) (B_34 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_34) (=> (@ (@ tptp.ord_less_eq_a_o A_47) B_34) (@ tptp.finite_finite_a A_47)))) (forall ((A_47 (-> (-> tptp.x_a Bool) Bool)) (B_34 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_34) (=> (@ (@ tptp.ord_less_eq_a_o_o A_47) B_34) (@ tptp.finite_finite_a_o A_47)))) (forall ((A_47 (-> tptp.nat Bool)) (B_34 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_34) (=> (@ (@ tptp.ord_less_eq_nat_o A_47) B_34) (@ tptp.finite_finite_nat A_47)))) (forall ((A_47 (-> tptp.pname Bool)) (B_34 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_34) (=> (@ (@ tptp.ord_less_eq_pname_o A_47) B_34) (@ tptp.finite_finite_pname A_47)))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M_2)) N_1) (@ (@ tptp.ord_less_eq_nat M_2) N_1))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc N_1))) (let ((_let_2 (@ tptp.ord_less_eq_nat M_2))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N_1)) (= M_2 _let_1)))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M_2))) (=> (@ _let_1 N_1) (@ _let_1 (@ tptp.suc N_1))))) (forall ((N_1 tptp.nat) (M_2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) (@ tptp.suc M_2)) (@ (@ tptp.ord_less_eq_nat N_1) M_2))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.suc N_1))) (let ((_let_2 (@ tptp.ord_less_eq_nat M_2))) (= (@ _let_2 _let_1) (or (@ _let_2 N_1) (= M_2 _let_1)))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M_2) N_1)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) M_2))) (forall ((N_1 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) N_1))) (forall ((M_2 tptp.nat) (N_1 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M_2)) N_1)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M_2) N_1)) K))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M_2)) (@ tptp.suc N_1)) (@ (@ tptp.minus_minus_nat M_2) N_1))) (forall ((N_1 tptp.nat) (K tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M_2) (=> (@ _let_1 N_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M_2) K)) (@ (@ tptp.minus_minus_nat N_1) K)) (@ (@ tptp.ord_less_eq_nat M_2) N_1)))))) (forall ((N_1 tptp.nat) (K tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M_2))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M_2) (=> (@ _let_2 N_1) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N_1) K)) (@ _let_1 N_1))))))) (forall ((N_1 tptp.nat) (K tptp.nat) (M_2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M_2) (=> (@ _let_1 N_1) (= (= (@ (@ tptp.minus_minus_nat M_2) K) (@ (@ tptp.minus_minus_nat N_1) K)) (= M_2 N_1)))))) (forall ((I tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N_1))) (=> (@ (@ tptp.ord_less_eq_nat I) N_1) (= (@ _let_1 (@ _let_1 I)) I)))) (forall ((L tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M_2) N_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M_2) L)) (@ (@ tptp.minus_minus_nat N_1) L)))) (forall ((L tptp.nat) (M_2 tptp.nat) (N_1 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M_2) N_1) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_1)) (@ _let_1 M_2))))) (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M_2) N_1)) M_2)) (forall ((B_33 (-> tptp.x_a Bool)) (F_13 (-> tptp.pname tptp.x_a)) (A_46 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_46) (=> (@ (@ tptp.ord_less_eq_a_o B_33) (@ (@ tptp.image_pname_a F_13) A_46)) (@ tptp.finite_finite_a B_33)))) (forall ((F_12 (-> tptp.pname tptp.x_a)) (A_45 (-> tptp.pname Bool)) (B_32 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_32) (=> (@ (@ tptp.ord_less_eq_a_o B_32) (@ (@ tptp.image_pname_a F_12) A_45)) (exists ((C_3 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_3) A_45) (@ tptp.finite_finite_pname C_3) (= B_32 (@ (@ tptp.image_pname_a F_12) C_3))))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_11 (-> tptp.nat tptp.nat Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o (@ F_11 N_2)) (@ F_11 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat_o (@ F_11 N_4)) (@ F_11 N_3))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_11 (-> tptp.nat tptp.pname Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_pname_o (@ F_11 N_2)) (@ F_11 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_pname_o (@ F_11 N_4)) (@ F_11 N_3))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_11 (-> tptp.nat tptp.nat))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F_11 N_2)) (@ F_11 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat (@ F_11 N_4)) (@ F_11 N_3))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_11 (-> tptp.nat tptp.x_a Bool))) (=> (forall ((N_2 tptp.nat)) (@ (@ tptp.ord_less_eq_a_o (@ F_11 N_2)) (@ F_11 (@ tptp.suc N_2)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_a_o (@ F_11 N_4)) (@ F_11 N_3))))) (forall ((F_10 (-> tptp.pname tptp.x_a)) (A_43 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_43)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a F_10) A_43)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_43) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_44 tptp.pname)) (and (@ (@ tptp.member_pname A_44) A_43) (= (@ F_10 A_44) (@ F_10 X)))))))))))) _let_9 (forall ((A_41 (-> tptp.nat Bool)) (B_30 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_41) B_30) (=> (@ (@ tptp.ord_less_eq_nat_o B_30) A_41) (= A_41 B_30)))) (forall ((A_41 (-> tptp.pname Bool)) (B_30 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_41) B_30) (=> (@ (@ tptp.ord_less_eq_pname_o B_30) A_41) (= A_41 B_30)))) (forall ((A_41 (-> tptp.x_a Bool)) (B_30 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_41) B_30) (=> (@ (@ tptp.ord_less_eq_a_o B_30) A_41) (= A_41 B_30)))) (forall ((C_2 tptp.nat) (A_40 (-> tptp.nat Bool)) (B_29 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_2))) (=> (@ (@ tptp.ord_less_eq_nat_o A_40) B_29) (=> (@ _let_1 A_40) (@ _let_1 B_29))))) (forall ((C_2 tptp.x_a) (A_40 (-> tptp.x_a Bool)) (B_29 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_2))) (=> (@ (@ tptp.ord_less_eq_a_o A_40) B_29) (=> (@ _let_1 A_40) (@ _let_1 B_29))))) (forall ((C_2 tptp.pname) (A_40 (-> tptp.pname Bool)) (B_29 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_2))) (=> (@ (@ tptp.ord_less_eq_pname_o A_40) B_29) (=> (@ _let_1 A_40) (@ _let_1 B_29))))) (forall ((B_28 tptp.nat) (A_39 tptp.nat) (B_27 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_39))) (=> (=> (not (@ _let_1 B_27)) (= A_39 B_28)) (@ _let_1 (@ (@ tptp.insert_nat B_28) B_27))))) (forall ((B_28 tptp.pname) (A_39 tptp.pname) (B_27 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_39))) (=> (=> (not (@ _let_1 B_27)) (= A_39 B_28)) (@ _let_1 (@ (@ tptp.insert_pname B_28) B_27))))) (forall ((B_28 tptp.x_a) (A_39 tptp.x_a) (B_27 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_39))) (=> (=> (not (@ _let_1 B_27)) (= A_39 B_28)) (@ _let_1 (@ (@ tptp.insert_a B_28) B_27))))) (forall ((A_38 tptp.nat) (B_26 tptp.nat) (A_37 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_38))) (=> (@ _let_1 (@ (@ tptp.insert_nat B_26) A_37)) (=> (not (= A_38 B_26)) (@ _let_1 A_37))))) (forall ((A_38 tptp.pname) (B_26 tptp.pname) (A_37 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_38))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_26) A_37)) (=> (not (= A_38 B_26)) (@ _let_1 A_37))))) (forall ((A_38 tptp.x_a) (B_26 tptp.x_a) (A_37 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_38))) (=> (@ _let_1 (@ (@ tptp.insert_a B_26) A_37)) (=> (not (= A_38 B_26)) (@ _let_1 A_37))))) (forall ((A_36 tptp.nat) (B_25 (-> tptp.nat Bool))) (@ (@ tptp.member_nat A_36) (@ (@ tptp.insert_nat A_36) B_25))) (forall ((A_36 tptp.pname) (B_25 (-> tptp.pname Bool))) (@ (@ tptp.member_pname A_36) (@ (@ tptp.insert_pname A_36) B_25))) (forall ((A_36 tptp.x_a) (B_25 (-> tptp.x_a Bool))) (@ (@ tptp.member_a A_36) (@ (@ tptp.insert_a A_36) B_25))) (forall ((A_35 tptp.nat) (B_24 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_35) B_24) (@ tptp.collect_nat (lambda ((X tptp.nat)) (or (= X A_35) (@ (@ tptp.member_nat X) B_24)))))) (forall ((A_35 tptp.pname) (B_24 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_35) B_24) (@ tptp.collect_pname (lambda ((X tptp.pname)) (or (= X A_35) (@ (@ tptp.member_pname X) B_24)))))) (forall ((A_35 tptp.x_a) (B_24 (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a A_35) B_24) (@ tptp.collect_a (lambda ((X tptp.x_a)) (or (= X A_35) (@ (@ tptp.member_a X) B_24)))))) (forall ((A_35 (-> tptp.nat Bool)) (B_24 (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o A_35) B_24) (@ tptp.collect_nat_o (lambda ((X (-> tptp.nat Bool))) (or (= X A_35) (@ (@ tptp.member_nat_o X) B_24)))))) (forall ((A_35 (-> tptp.pname Bool)) (B_24 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_35) B_24) (@ tptp.collect_pname_o (lambda ((X (-> tptp.pname Bool))) (or (= X A_35) (@ (@ tptp.member_pname_o X) B_24)))))) (forall ((A_35 (-> tptp.x_a Bool)) (B_24 (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o A_35) B_24) (@ tptp.collect_a_o (lambda ((X (-> tptp.x_a Bool))) (or (= X A_35) (@ (@ tptp.member_a_o X) B_24)))))) (forall ((A_34 tptp.nat) (P_2 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_34) (@ tptp.collect_nat P_2)) (@ tptp.collect_nat (lambda ((U tptp.nat)) (=> (not (= U A_34)) (@ P_2 U)))))) (forall ((A_34 tptp.pname) (P_2 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_34) (@ tptp.collect_pname P_2)) (@ tptp.collect_pname (lambda ((U tptp.pname)) (=> (not (= U A_34)) (@ P_2 U)))))) (forall ((A_34 tptp.x_a) (P_2 (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a A_34) (@ tptp.collect_a P_2)) (@ tptp.collect_a (lambda ((U tptp.x_a)) (=> (not (= U A_34)) (@ P_2 U)))))) (forall ((A_34 (-> tptp.nat Bool)) (P_2 (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o A_34) (@ tptp.collect_nat_o P_2)) (@ tptp.collect_nat_o (lambda ((U (-> tptp.nat Bool))) (=> (not (= U A_34)) (@ P_2 U)))))) (forall ((A_34 (-> tptp.pname Bool)) (P_2 (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o A_34) (@ tptp.collect_pname_o P_2)) (@ tptp.collect_pname_o (lambda ((U (-> tptp.pname Bool))) (=> (not (= U A_34)) (@ P_2 U)))))) (forall ((A_34 (-> tptp.x_a Bool)) (P_2 (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o A_34) (@ tptp.collect_a_o P_2)) (@ tptp.collect_a_o (lambda ((U (-> tptp.x_a Bool))) (=> (not (= U A_34)) (@ P_2 U)))))) (forall ((X_14 tptp.nat) (A_33 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_14))) (let ((_let_2 (@ _let_1 A_33))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X_14 tptp.pname) (A_33 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_14))) (let ((_let_2 (@ _let_1 A_33))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X_14 tptp.x_a) (A_33 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_14))) (let ((_let_2 (@ _let_1 A_33))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X_13 tptp.nat) (Y_2 tptp.nat) (A_32 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_13))) (let ((_let_2 (@ tptp.insert_nat Y_2))) (= (@ _let_1 (@ _let_2 A_32)) (@ _let_2 (@ _let_1 A_32)))))) (forall ((X_13 tptp.pname) (Y_2 tptp.pname) (A_32 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_13))) (let ((_let_2 (@ tptp.insert_pname Y_2))) (= (@ _let_1 (@ _let_2 A_32)) (@ _let_2 (@ _let_1 A_32)))))) (forall ((X_13 tptp.x_a) (Y_2 tptp.x_a) (A_32 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_13))) (let ((_let_2 (@ tptp.insert_a Y_2))) (= (@ _let_1 (@ _let_2 A_32)) (@ _let_2 (@ _let_1 A_32)))))) (forall ((A_31 tptp.nat) (B_23 tptp.nat) (A_30 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_31))) (= (@ _let_1 (@ (@ tptp.insert_nat B_23) A_30)) (or (= A_31 B_23) (@ _let_1 A_30))))) (forall ((A_31 tptp.pname) (B_23 tptp.pname) (A_30 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_31))) (= (@ _let_1 (@ (@ tptp.insert_pname B_23) A_30)) (or (= A_31 B_23) (@ _let_1 A_30))))) (forall ((A_31 tptp.x_a) (B_23 tptp.x_a) (A_30 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_31))) (= (@ _let_1 (@ (@ tptp.insert_a B_23) A_30)) (or (= A_31 B_23) (@ _let_1 A_30))))) (forall ((Y_1 tptp.nat) (A_29 (-> tptp.nat Bool)) (X_12 tptp.nat)) (= (@ (@ (@ tptp.insert_nat Y_1) A_29) X_12) (or (= Y_1 X_12) (@ A_29 X_12)))) (forall ((Y_1 tptp.pname) (A_29 (-> tptp.pname Bool)) (X_12 tptp.pname)) (= (@ (@ (@ tptp.insert_pname Y_1) A_29) X_12) (or (= Y_1 X_12) (@ A_29 X_12)))) (forall ((Y_1 tptp.x_a) (A_29 (-> tptp.x_a Bool)) (X_12 tptp.x_a)) (= (@ (@ (@ tptp.insert_a Y_1) A_29) X_12) (or (= Y_1 X_12) (@ A_29 X_12)))) (forall ((B_22 (-> tptp.nat Bool)) (X_11 tptp.nat) (A_28 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_11))) (let ((_let_2 (@ tptp.member_nat X_11))) (=> (not (@ _let_2 A_28)) (=> (not (@ _let_2 B_22)) (= (= (@ _let_1 A_28) (@ _let_1 B_22)) (= A_28 B_22))))))) (forall ((B_22 (-> tptp.pname Bool)) (X_11 tptp.pname) (A_28 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_11))) (let ((_let_2 (@ tptp.member_pname X_11))) (=> (not (@ _let_2 A_28)) (=> (not (@ _let_2 B_22)) (= (= (@ _let_1 A_28) (@ _let_1 B_22)) (= A_28 B_22))))))) (forall ((B_22 (-> tptp.x_a Bool)) (X_11 tptp.x_a) (A_28 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_11))) (let ((_let_2 (@ tptp.member_a X_11))) (=> (not (@ _let_2 A_28)) (=> (not (@ _let_2 B_22)) (= (= (@ _let_1 A_28) (@ _let_1 B_22)) (= A_28 B_22))))))) (forall ((B_21 tptp.nat) (A_27 tptp.nat) (B_20 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_27))) (=> (@ _let_1 B_20) (@ _let_1 (@ (@ tptp.insert_nat B_21) B_20))))) (forall ((B_21 tptp.pname) (A_27 tptp.pname) (B_20 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_27))) (=> (@ _let_1 B_20) (@ _let_1 (@ (@ tptp.insert_pname B_21) B_20))))) (forall ((B_21 tptp.x_a) (A_27 tptp.x_a) (B_20 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_27))) (=> (@ _let_1 B_20) (@ _let_1 (@ (@ tptp.insert_a B_21) B_20))))) (forall ((A_26 tptp.nat) (A_25 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat A_26) A_25) (= (@ (@ tptp.insert_nat A_26) A_25) A_25))) (forall ((A_26 tptp.pname) (A_25 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_26) A_25) (= (@ (@ tptp.insert_pname A_26) A_25) A_25))) (forall ((A_26 tptp.x_a) (A_25 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a A_26) A_25) (= (@ (@ tptp.insert_a A_26) A_25) A_25))) (forall ((A_24 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o A_24) A_24)) (forall ((A_24 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o A_24) A_24)) (forall ((A_24 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o A_24) A_24)) (forall ((A_23 (-> tptp.nat Bool)) (B_19 (-> tptp.nat Bool))) (= (= A_23 B_19) (and (@ (@ tptp.ord_less_eq_nat_o A_23) B_19) (@ (@ tptp.ord_less_eq_nat_o B_19) A_23)))) (forall ((A_23 (-> tptp.pname Bool)) (B_19 (-> tptp.pname Bool))) (= (= A_23 B_19) (and (@ (@ tptp.ord_less_eq_pname_o A_23) B_19) (@ (@ tptp.ord_less_eq_pname_o B_19) A_23)))) (forall ((A_23 (-> tptp.x_a Bool)) (B_19 (-> tptp.x_a Bool))) (= (= A_23 B_19) (and (@ (@ tptp.ord_less_eq_a_o A_23) B_19) (@ (@ tptp.ord_less_eq_a_o B_19) A_23)))) (forall ((A_22 (-> tptp.nat Bool)) (B_18 (-> tptp.nat Bool))) (=> (= A_22 B_18) (@ (@ tptp.ord_less_eq_nat_o A_22) B_18))) (forall ((A_22 (-> tptp.pname Bool)) (B_18 (-> tptp.pname Bool))) (=> (= A_22 B_18) (@ (@ tptp.ord_less_eq_pname_o A_22) B_18))) (forall ((A_22 (-> tptp.x_a Bool)) (B_18 (-> tptp.x_a Bool))) (=> (= A_22 B_18) (@ (@ tptp.ord_less_eq_a_o A_22) B_18))) (forall ((A_21 (-> tptp.nat Bool)) (B_17 (-> tptp.nat Bool))) (=> (= A_21 B_17) (@ (@ tptp.ord_less_eq_nat_o B_17) A_21))) (forall ((A_21 (-> tptp.pname Bool)) (B_17 (-> tptp.pname Bool))) (=> (= A_21 B_17) (@ (@ tptp.ord_less_eq_pname_o B_17) A_21))) (forall ((A_21 (-> tptp.x_a Bool)) (B_17 (-> tptp.x_a Bool))) (=> (= A_21 B_17) (@ (@ tptp.ord_less_eq_a_o B_17) A_21))) (forall ((X_10 tptp.nat) (A_20 (-> tptp.nat Bool)) (B_16 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_10))) (=> (@ (@ tptp.ord_less_eq_nat_o A_20) B_16) (=> (@ _let_1 A_20) (@ _let_1 B_16))))) (forall ((X_10 tptp.x_a) (A_20 (-> tptp.x_a Bool)) (B_16 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_10))) (=> (@ (@ tptp.ord_less_eq_a_o A_20) B_16) (=> (@ _let_1 A_20) (@ _let_1 B_16))))) (forall ((X_10 tptp.pname) (A_20 (-> tptp.pname Bool)) (B_16 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_10))) (=> (@ (@ tptp.ord_less_eq_pname_o A_20) B_16) (=> (@ _let_1 A_20) (@ _let_1 B_16))))) (forall ((B_15 (-> tptp.nat Bool)) (X_9 tptp.nat) (A_19 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_9))) (=> (@ _let_1 A_19) (=> (@ (@ tptp.ord_less_eq_nat_o A_19) B_15) (@ _let_1 B_15))))) (forall ((B_15 (-> tptp.x_a Bool)) (X_9 tptp.x_a) (A_19 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_9))) (=> (@ _let_1 A_19) (=> (@ (@ tptp.ord_less_eq_a_o A_19) B_15) (@ _let_1 B_15))))) (forall ((B_15 (-> tptp.pname Bool)) (X_9 tptp.pname) (A_19 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_9))) (=> (@ _let_1 A_19) (=> (@ (@ tptp.ord_less_eq_pname_o A_19) B_15) (@ _let_1 B_15))))) (forall ((X_8 tptp.nat) (A_18 (-> tptp.nat Bool)) (B_14 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_8))) (=> (@ (@ tptp.ord_less_eq_nat_o A_18) B_14) (=> (@ _let_1 A_18) (@ _let_1 B_14))))) (forall ((X_8 tptp.x_a) (A_18 (-> tptp.x_a Bool)) (B_14 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_8))) (=> (@ (@ tptp.ord_less_eq_a_o A_18) B_14) (=> (@ _let_1 A_18) (@ _let_1 B_14))))) (forall ((X_8 tptp.pname) (A_18 (-> tptp.pname Bool)) (B_14 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_8))) (=> (@ (@ tptp.ord_less_eq_pname_o A_18) B_14) (=> (@ _let_1 A_18) (@ _let_1 B_14))))) (forall ((C_1 (-> tptp.nat Bool)) (A_17 (-> tptp.nat Bool)) (B_13 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_17))) (=> (@ _let_1 B_13) (=> (@ (@ tptp.ord_less_eq_nat_o B_13) C_1) (@ _let_1 C_1))))) (forall ((C_1 (-> tptp.pname Bool)) (A_17 (-> tptp.pname Bool)) (B_13 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_17))) (=> (@ _let_1 B_13) (=> (@ (@ tptp.ord_less_eq_pname_o B_13) C_1) (@ _let_1 C_1))))) (forall ((C_1 (-> tptp.x_a Bool)) (A_17 (-> tptp.x_a Bool)) (B_13 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_17))) (=> (@ _let_1 B_13) (=> (@ (@ tptp.ord_less_eq_a_o B_13) C_1) (@ _let_1 C_1))))) (forall ((A_16 (-> tptp.nat Bool)) (B_12 (-> tptp.nat Bool))) (=> (= A_16 B_12) (not (=> (@ (@ tptp.ord_less_eq_nat_o A_16) B_12) (not (@ (@ tptp.ord_less_eq_nat_o B_12) A_16)))))) (forall ((A_16 (-> tptp.pname Bool)) (B_12 (-> tptp.pname Bool))) (=> (= A_16 B_12) (not (=> (@ (@ tptp.ord_less_eq_pname_o A_16) B_12) (not (@ (@ tptp.ord_less_eq_pname_o B_12) A_16)))))) (forall ((A_16 (-> tptp.x_a Bool)) (B_12 (-> tptp.x_a Bool))) (=> (= A_16 B_12) (not (=> (@ (@ tptp.ord_less_eq_a_o A_16) B_12) (not (@ (@ tptp.ord_less_eq_a_o B_12) A_16)))))) (forall ((X_7 tptp.nat) (A_15 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X_7) A_15) (@ A_15 X_7))) (forall ((X_7 tptp.x_a) (A_15 (-> tptp.x_a Bool))) (= (@ (@ tptp.member_a X_7) A_15) (@ A_15 X_7))) (forall ((X_7 tptp.pname) (A_15 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_7) A_15) (@ A_15 X_7))) (forall ((P_1 (-> tptp.pname Bool))) (= (@ tptp.collect_pname P_1) P_1)) (forall ((P_1 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.collect_nat_o P_1) P_1)) (forall ((P_1 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.collect_pname_o P_1) P_1)) (forall ((P_1 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.collect_a_o P_1) P_1)) (forall ((P_1 (-> tptp.nat Bool))) (= (@ tptp.collect_nat P_1) P_1)) (forall ((Z tptp.x_a) (F_8 (-> tptp.pname tptp.x_a)) (A_14 (-> tptp.pname Bool))) (= (@ (@ tptp.member_a Z) (@ (@ tptp.image_pname_a F_8) A_14)) (exists ((X tptp.pname)) (and (@ (@ tptp.member_pname X) A_14) (= Z (@ F_8 X)))))) (forall ((F_7 (-> tptp.pname tptp.x_a)) (X_6 tptp.pname) (A_13 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_6) A_13) (@ (@ tptp.member_a (@ F_7 X_6)) (@ (@ tptp.image_pname_a F_7) A_13)))) (forall ((B_11 tptp.x_a) (F_6 (-> tptp.pname tptp.x_a)) (X_5 tptp.pname) (A_12 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_5) A_12) (=> (= B_11 (@ F_6 X_5)) (@ (@ tptp.member_a B_11) (@ (@ tptp.image_pname_a F_6) A_12))))) (forall ((X tptp.nat) (Xa (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat X) Xa) (@ tptp.collect_nat (lambda ((Y tptp.nat)) (or (= Y X) (@ (@ tptp.member_nat Y) Xa)))))) (forall ((X tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X) Xa) (@ tptp.collect_pname (lambda ((Y tptp.pname)) (or (= Y X) (@ (@ tptp.member_pname Y) Xa)))))) (forall ((X tptp.x_a) (Xa (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a X) Xa) (@ tptp.collect_a (lambda ((Y tptp.x_a)) (or (= Y X) (@ (@ tptp.member_a Y) Xa)))))) (forall ((X (-> tptp.nat Bool)) (Xa (-> (-> tptp.nat Bool) Bool))) (= (@ (@ tptp.insert_nat_o X) Xa) (@ tptp.collect_nat_o (lambda ((Y (-> tptp.nat Bool))) (or (= Y X) (@ (@ tptp.member_nat_o Y) Xa)))))) (forall ((X (-> tptp.pname Bool)) (Xa (-> (-> tptp.pname Bool) Bool))) (= (@ (@ tptp.insert_pname_o X) Xa) (@ tptp.collect_pname_o (lambda ((Y (-> tptp.pname Bool))) (or (= Y X) (@ (@ tptp.member_pname_o Y) Xa)))))) (forall ((X (-> tptp.x_a Bool)) (Xa (-> (-> tptp.x_a Bool) Bool))) (= (@ (@ tptp.insert_a_o X) Xa) (@ tptp.collect_a_o (lambda ((Y (-> tptp.x_a Bool))) (or (= Y X) (@ (@ tptp.member_a_o Y) Xa)))))) (forall ((B_10 (-> tptp.nat Bool)) (A_11 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o B_10) (@ (@ tptp.insert_nat A_11) B_10))) (forall ((B_10 (-> tptp.pname Bool)) (A_11 tptp.pname)) (@ (@ tptp.ord_less_eq_pname_o B_10) (@ (@ tptp.insert_pname A_11) B_10))) (forall ((B_10 (-> tptp.x_a Bool)) (A_11 tptp.x_a)) (@ (@ tptp.ord_less_eq_a_o B_10) (@ (@ tptp.insert_a A_11) B_10))) (forall ((X_4 tptp.nat) (A_10 (-> tptp.nat Bool)) (B_9 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.insert_nat X_4) A_10)) B_9) (and (@ (@ tptp.member_nat X_4) B_9) (@ (@ tptp.ord_less_eq_nat_o A_10) B_9)))) (forall ((X_4 tptp.pname) (A_10 (-> tptp.pname Bool)) (B_9 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.insert_pname X_4) A_10)) B_9) (and (@ (@ tptp.member_pname X_4) B_9) (@ (@ tptp.ord_less_eq_pname_o A_10) B_9)))) _let_8 (forall ((B_8 (-> tptp.nat Bool)) (X_3 tptp.nat) (A_9 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_9))) (=> (not (@ (@ tptp.member_nat X_3) A_9)) (= (@ _let_1 (@ (@ tptp.insert_nat X_3) B_8)) (@ _let_1 B_8))))) (forall ((B_8 (-> tptp.pname Bool)) (X_3 tptp.pname) (A_9 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_9))) (=> (not (@ (@ tptp.member_pname X_3) A_9)) (= (@ _let_1 (@ (@ tptp.insert_pname X_3) B_8)) (@ _let_1 B_8))))) (forall ((B_8 (-> tptp.x_a Bool)) (X_3 tptp.x_a) (A_9 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_9))) (=> (not (@ (@ tptp.member_a X_3) A_9)) (= (@ _let_1 (@ (@ tptp.insert_a X_3) B_8)) (@ _let_1 B_8))))) (forall ((B_7 tptp.nat) (A_8 (-> tptp.nat Bool)) (B_6 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_8))) (=> (@ _let_1 B_6) (@ _let_1 (@ (@ tptp.insert_nat B_7) B_6))))) (forall ((B_7 tptp.pname) (A_8 (-> tptp.pname Bool)) (B_6 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_8))) (=> (@ _let_1 B_6) (@ _let_1 (@ (@ tptp.insert_pname B_7) B_6))))) (forall ((B_7 tptp.x_a) (A_8 (-> tptp.x_a Bool)) (B_6 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_8))) (=> (@ _let_1 B_6) (@ _let_1 (@ (@ tptp.insert_a B_7) B_6))))) (forall ((A_7 tptp.nat) (C (-> tptp.nat Bool)) (D (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_7))) (=> (@ (@ tptp.ord_less_eq_nat_o C) D) (@ (@ tptp.ord_less_eq_nat_o (@ _let_1 C)) (@ _let_1 D))))) (forall ((A_7 tptp.pname) (C (-> tptp.pname Bool)) (D (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_7))) (=> (@ (@ tptp.ord_less_eq_pname_o C) D) (@ (@ tptp.ord_less_eq_pname_o (@ _let_1 C)) (@ _let_1 D))))) (forall ((A_7 tptp.x_a) (C (-> tptp.x_a Bool)) (D (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_7))) (=> (@ (@ tptp.ord_less_eq_a_o C) D) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 C)) (@ _let_1 D))))) (forall ((F_5 (-> tptp.pname tptp.x_a)) (A_6 tptp.pname) (B_5 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_5))) (= (@ _let_1 (@ (@ tptp.insert_pname A_6) B_5)) (@ (@ tptp.insert_a (@ F_5 A_6)) (@ _let_1 B_5))))) (forall ((F_4 (-> tptp.pname tptp.x_a)) (X_2 tptp.pname) (A_5 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_a F_4) A_5))) (=> (@ (@ tptp.member_pname X_2) A_5) (= (@ (@ tptp.insert_a (@ F_4 X_2)) _let_1) _let_1)))) (forall ((B_4 (-> tptp.x_a Bool)) (F_3 (-> tptp.pname tptp.x_a)) (A_4 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_a_o B_4) (@ (@ tptp.image_pname_a F_3) A_4)) (exists ((AA (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o AA) A_4) (= B_4 (@ (@ tptp.image_pname_a F_3) AA)))))) (forall ((F_2 (-> tptp.pname tptp.x_a)) (A_3 (-> tptp.pname Bool)) (B_3 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_2))) (=> (@ (@ tptp.ord_less_eq_pname_o A_3) B_3) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 A_3)) (@ _let_1 B_3))))) (forall ((B_2 tptp.x_a) (F_1 (-> tptp.pname tptp.x_a)) (A_2 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_a B_2) (@ (@ tptp.image_pname_a F_1) A_2)) (not (forall ((X tptp.pname)) (=> (= B_2 (@ F_1 X)) (not (@ (@ tptp.member_pname X) A_2))))))) (forall ((B_1 (-> tptp.nat Bool)) (A_1 (-> tptp.nat Bool))) (=> (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_less_eq_nat_o A_1) B_1))) (forall ((B_1 (-> tptp.x_a Bool)) (A_1 (-> tptp.x_a Bool))) (=> (forall ((X tptp.x_a)) (let ((_let_1 (@ tptp.member_a X))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_less_eq_a_o A_1) B_1))) (forall ((B_1 (-> tptp.pname Bool)) (A_1 (-> tptp.pname Bool))) (=> (forall ((X tptp.pname)) (let ((_let_1 (@ tptp.member_pname X))) (=> (@ _let_1 A_1) (@ _let_1 B_1)))) (@ (@ tptp.ord_less_eq_pname_o A_1) B_1))) (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))))) (forall ((N_1 tptp.nat) (M_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N_1)) M_1) (exists ((M tptp.nat)) (= M_1 (@ tptp.suc M))))) (forall ((F (-> tptp.pname tptp.x_a)) (B (-> tptp.x_a Bool)) (A (-> tptp.pname Bool))) (=> (forall ((X tptp.pname)) (=> (@ (@ tptp.member_pname X) A) (@ (@ tptp.member_a (@ F X)) B))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.image_pname_a F) A)) B))) (forall ((X_1 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o X_1) X_1)) (forall ((X_1 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o X_1) X_1)) (forall ((X_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X_1) X_1)) (forall ((X_1 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o X_1) X_1)) (forall ((N (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N) (exists ((M tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N) (@ (@ tptp.ord_less_eq_nat X) M)))))) (@ 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)))))))))))))))))))))))))))))
% 0.75/0.99 )
% 0.75/0.99 % SZS output end Proof for SWW473^1
% 0.75/0.99 % cvc5---1.0.5 exiting
% 0.75/0.99 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------