TSTP Solution File: SWW473^3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWW473^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 00:21:05 EDT 2023
% Result : Theorem 1.73s 1.95s
% Output : Proof 1.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.28 % Problem : SWW473^3 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.29 % Command : do_cvc5 %s %d
% 0.29/0.50 % Computer : n010.cluster.edu
% 0.29/0.50 % Model : x86_64 x86_64
% 0.29/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.50 % Memory : 8042.1875MB
% 0.29/0.50 % OS : Linux 3.10.0-693.el7.x86_64
% 0.29/0.50 % CPULimit : 300
% 0.29/0.50 % WCLimit : 300
% 0.29/0.50 % DateTime : Sun Aug 27 22:04:34 EDT 2023
% 0.29/0.50 % CPUTime :
% 0.55/0.77 %----Proving TH0
% 0.55/0.78 %------------------------------------------------------------------------------
% 0.55/0.78 % File : SWW473^3 : TPTP v8.1.2. Released v5.3.0.
% 0.55/0.78 % Domain : Software Verification
% 0.55/0.78 % Problem : Hoare's Logic with Procedures line 383, 1000 axioms selected
% 0.55/0.78 % Version : Especial.
% 0.55/0.78 % English :
% 0.55/0.78
% 0.55/0.78 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.55/0.78 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.55/0.78 % Source : [Bla11]
% 0.55/0.78 % Names : hoare_1000_thf_l383 [Bla11]
% 0.55/0.78
% 0.55/0.78 % Status : ContradictoryAxioms
% 0.55/0.78 % Rating : 0.46 v8.1.0, 0.45 v7.5.0, 0.43 v7.4.0, 0.33 v7.3.0, 0.56 v7.2.0, 0.38 v7.1.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.57 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v5.3.0
% 0.55/0.78 % Syntax : Number of formulae : 1390 ( 234 unt; 175 typ; 0 def)
% 0.55/0.78 % Number of atoms : 4436 ( 862 equ; 70 cnn)
% 0.55/0.78 % Maximal formula atoms : 9 ( 3 avg)
% 0.55/0.78 % Number of connectives : 10367 ( 301 ~; 68 |; 270 &;8078 @)
% 0.55/0.78 % ( 253 <=>;1397 =>; 0 <=; 0 <~>)
% 0.55/0.78 % Maximal formula depth : 17 ( 7 avg)
% 0.55/0.78 % Number of types : 7 ( 6 usr)
% 0.55/0.78 % Number of type conns : 2454 (2454 >; 0 *; 0 +; 0 <<)
% 0.55/0.78 % Number of symbols : 176 ( 169 usr; 15 con; 0-3 aty)
% 0.55/0.78 % Number of variables : 2984 ( 93 ^;2786 !; 105 ?;2984 :)
% 0.55/0.78 % SPC : TH0_CAX_EQU_NAR
% 0.55/0.78
% 0.55/0.78 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.55/0.78 % 2011-08-09 19:59:45
% 0.55/0.78 %------------------------------------------------------------------------------
% 0.55/0.78 %----Should-be-implicit typings (6)
% 0.55/0.78 thf(ty_ty_t__a,type,
% 0.55/0.78 x_a: $tType ).
% 0.55/0.78
% 0.55/0.78 thf(ty_ty_tc__Com__Ocom,type,
% 0.55/0.78 com: $tType ).
% 0.55/0.78
% 0.55/0.78 thf(ty_ty_tc__Com__Opname,type,
% 0.55/0.78 pname: $tType ).
% 0.55/0.78
% 0.55/0.78 thf(ty_ty_tc__Int__Oint,type,
% 0.55/0.78 int: $tType ).
% 0.55/0.78
% 0.55/0.78 thf(ty_ty_tc__Nat__Onat,type,
% 0.55/0.78 nat: $tType ).
% 0.55/0.78
% 0.55/0.78 thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,
% 0.55/0.78 option_com: $tType ).
% 0.55/0.78
% 0.55/0.78 %----Explicit typings (169)
% 0.55/0.78 thf(sy_c_Com_Obody,type,
% 0.55/0.78 body: pname > option_com ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Ex,type,
% 0.55/0.78 ex: ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ocard_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 finite_card_a_o: ( ( x_a > $o ) > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 finite_card_pname_o: ( ( pname > $o ) > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 finite_card_int_o: ( ( int > $o ) > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ocard_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 finite_card_nat_o: ( ( nat > $o ) > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ocard_000t__a,type,
% 0.55/0.78 finite_card_a: ( x_a > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ocard_000tc__Com__Opname,type,
% 0.55/0.78 finite_card_pname: ( pname > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ocard_000tc__Int__Oint,type,
% 0.55/0.78 finite_card_int: ( int > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ocard_000tc__Nat__Onat,type,
% 0.55/0.78 finite_card_nat: ( nat > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 finite_finite_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Int__Oint_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 finite229719499nt_o_o: ( ( ( int > $o ) > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 finite1676163439at_o_o: ( ( ( nat > $o ) > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 finite_finite_a_o: ( ( x_a > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 finite297249702name_o: ( ( pname > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 finite_finite_int_o: ( ( int > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 finite_finite_nat_o: ( ( nat > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000t__a,type,
% 0.55/0.78 finite_finite_a: ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,
% 0.55/0.78 finite_finite_pname: ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000tc__Int__Oint,type,
% 0.55/0.78 finite_finite_int: ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofinite_000tc__Nat__Onat,type,
% 0.55/0.78 finite_finite_nat: ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofolding__one_000t__a,type,
% 0.55/0.78 finite_folding_one_a: ( x_a > x_a > x_a ) > ( ( x_a > $o ) > x_a ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,
% 0.55/0.78 finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Int__Oint,type,
% 0.55/0.78 finite1626084323ne_int: ( int > int > int ) > ( ( int > $o ) > int ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofolding__one_000tc__Nat__Onat,type,
% 0.55/0.78 finite988810631ne_nat: ( nat > nat > nat ) > ( ( nat > $o ) > nat ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000t__a,type,
% 0.55/0.78 finite1819937229idem_a: ( x_a > x_a > x_a ) > ( ( x_a > $o ) > x_a ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,
% 0.55/0.78 finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Int__Oint,type,
% 0.55/0.78 finite1432773856em_int: ( int > int > int ) > ( ( int > $o ) > int ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Nat__Onat,type,
% 0.55/0.78 finite795500164em_nat: ( nat > nat > nat ) > ( ( nat > $o ) > nat ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Oabs__class_Oabs_000tc__Int__Oint,type,
% 0.55/0.78 abs_abs_int: int > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 minus_minus_a_o: ( x_a > $o ) > ( x_a > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint,type,
% 0.55/0.78 minus_minus_int: int > int > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.55/0.78 minus_minus_nat: nat > nat > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Oone__class_Oone_000tc__Int__Oint,type,
% 0.55/0.78 one_one_int: int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.55/0.78 one_one_nat: nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,type,
% 0.55/0.78 plus_plus_int: int > int > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.55/0.78 plus_plus_nat: nat > nat > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint,type,
% 0.55/0.78 times_times_int: int > int > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat,type,
% 0.55/0.78 times_times_nat: nat > nat > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,type,
% 0.55/0.78 zero_zero_int: int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.55/0.78 zero_zero_nat: nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_HOL_OThe_000t__a,type,
% 0.55/0.78 the_a: ( x_a > $o ) > x_a ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_HOL_OThe_000tc__Int__Oint,type,
% 0.55/0.78 the_int: ( int > $o ) > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_HOL_OThe_000tc__Nat__Onat,type,
% 0.55/0.78 the_nat: ( nat > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_If_000tc__Nat__Onat,type,
% 0.55/0.78 if_nat: $o > nat > nat > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Int_OBit1,type,
% 0.55/0.78 bit1: int > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Int_OPls,type,
% 0.55/0.78 pls: int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint,type,
% 0.55/0.78 number_number_of_int: int > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat,type,
% 0.55/0.78 number_number_of_nat: int > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Int_Osucc,type,
% 0.55/0.78 succ: int > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Nat_OSuc,type,
% 0.55/0.78 suc: nat > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Nat_Onat_Onat__case_000_Eo,type,
% 0.55/0.78 nat_case_o: $o > ( nat > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Nat_Onat_Onat__case_000tc__Nat__Onat,type,
% 0.55/0.78 nat_case_nat: nat > ( nat > nat ) > nat > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Int__Oint,type,
% 0.55/0.78 semiri1621563631at_int: nat > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Nat__Numeral_Oneg,type,
% 0.55/0.78 nat_neg: int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Nat__Transfer_Otsub,type,
% 0.55/0.78 nat_tsub: int > int > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Option_Othe_000tc__Com__Ocom,type,
% 0.55/0.78 the_com: option_com > com ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 bot_bot_a_o: x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 bot_bot_pname_o: pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 bot_bot_int_o: int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 bot_bot_nat_o: nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,
% 0.55/0.78 bot_bot_o: $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Obot__class_Obot_000tc__Nat__Onat,type,
% 0.55/0.78 bot_bot_nat: nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 ord_less_int_o: ( int > $o ) > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint,type,
% 0.55/0.78 ord_less_int: int > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.55/0.78 ord_less_nat: nat > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 ord_less_eq_a_o_o: ( ( x_a > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,
% 0.55/0.78 ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Int__Oint_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 ord_less_eq_int_o_o: ( ( int > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 ord_less_eq_nat_o_o: ( ( nat > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 ord_less_eq_a_o: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,
% 0.55/0.78 ord_less_eq_o: $o > $o > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint,type,
% 0.55/0.78 ord_less_eq_int: int > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.55/0.78 ord_less_eq_nat: nat > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000_062_I_062_It__a_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 collect_a_o_o: ( ( ( x_a > $o ) > $o ) > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Int__Oint_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 collect_int_o_o: ( ( ( int > $o ) > $o ) > $o ) > ( ( int > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000_062_I_062_Itc__Nat__Onat_M_Eo_J_M_Eo_J,type,
% 0.55/0.78 collect_nat_o_o: ( ( ( nat > $o ) > $o ) > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 collect_a_o: ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 collect_int_o: ( ( int > $o ) > $o ) > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 collect_nat_o: ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000t__a,type,
% 0.55/0.78 collect_a: ( x_a > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000tc__Com__Opname,type,
% 0.55/0.78 collect_pname: ( pname > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000tc__Int__Oint,type,
% 0.55/0.78 collect_int: ( int > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_OCollect_000tc__Nat__Onat,type,
% 0.55/0.78 collect_nat: ( nat > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000t__a,type,
% 0.55/0.78 image_a_o_a: ( ( x_a > $o ) > x_a ) > ( ( x_a > $o ) > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Com__Opname,type,
% 0.55/0.78 image_a_o_pname: ( ( x_a > $o ) > pname ) > ( ( x_a > $o ) > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Int__Oint,type,
% 0.55/0.78 image_a_o_int: ( ( x_a > $o ) > int ) > ( ( x_a > $o ) > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_It__a_M_Eo_J_000tc__Nat__Onat,type,
% 0.55/0.78 image_a_o_nat: ( ( x_a > $o ) > nat ) > ( ( x_a > $o ) > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000t__a,type,
% 0.55/0.78 image_pname_o_a: ( ( pname > $o ) > x_a ) > ( ( pname > $o ) > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,
% 0.55/0.78 image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Int__Oint,type,
% 0.55/0.78 image_pname_o_int: ( ( pname > $o ) > int ) > ( ( pname > $o ) > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Nat__Onat,type,
% 0.55/0.78 image_pname_o_nat: ( ( pname > $o ) > nat ) > ( ( pname > $o ) > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Int__Oint_M_Eo_J_000t__a,type,
% 0.55/0.78 image_int_o_a: ( ( int > $o ) > x_a ) > ( ( int > $o ) > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Int__Oint_M_Eo_J_000tc__Com__Opname,type,
% 0.55/0.78 image_int_o_pname: ( ( int > $o ) > pname ) > ( ( int > $o ) > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Int__Oint_M_Eo_J_000tc__Int__Oint,type,
% 0.55/0.78 image_int_o_int: ( ( int > $o ) > int ) > ( ( int > $o ) > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Int__Oint_M_Eo_J_000tc__Nat__Onat,type,
% 0.55/0.78 image_int_o_nat: ( ( int > $o ) > nat ) > ( ( int > $o ) > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000t__a,type,
% 0.55/0.78 image_nat_o_a: ( ( nat > $o ) > x_a ) > ( ( nat > $o ) > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Com__Opname,type,
% 0.55/0.78 image_nat_o_pname: ( ( nat > $o ) > pname ) > ( ( nat > $o ) > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Int__Oint,type,
% 0.55/0.78 image_nat_o_int: ( ( nat > $o ) > int ) > ( ( nat > $o ) > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000_062_Itc__Nat__Onat_M_Eo_J_000tc__Nat__Onat,type,
% 0.55/0.78 image_nat_o_nat: ( ( nat > $o ) > nat ) > ( ( nat > $o ) > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000t__a_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 image_a_a_o: ( x_a > x_a > $o ) > ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 image_a_pname_o: ( x_a > pname > $o ) > ( x_a > $o ) > ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 image_a_int_o: ( x_a > int > $o ) > ( x_a > $o ) > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000t__a_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 image_a_nat_o: ( x_a > nat > $o ) > ( x_a > $o ) > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000t__a_000t__a,type,
% 0.55/0.78 image_a_a: ( x_a > x_a ) > ( x_a > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000t__a_000tc__Com__Opname,type,
% 0.55/0.78 image_a_pname: ( x_a > pname ) > ( x_a > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000t__a_000tc__Int__Oint,type,
% 0.55/0.78 image_a_int: ( x_a > int ) > ( x_a > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000t__a_000tc__Nat__Onat,type,
% 0.55/0.78 image_a_nat: ( x_a > nat ) > ( x_a > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 image_pname_a_o: ( pname > x_a > $o ) > ( pname > $o ) > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 image_pname_int_o: ( pname > int > $o ) > ( pname > $o ) > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 image_pname_nat_o: ( pname > nat > $o ) > ( pname > $o ) > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000t__a,type,
% 0.55/0.78 image_pname_a: ( pname > x_a ) > ( pname > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,
% 0.55/0.78 image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Int__Oint,type,
% 0.55/0.78 image_pname_int: ( pname > int ) > ( pname > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Nat__Onat,type,
% 0.55/0.78 image_pname_nat: ( pname > nat ) > ( pname > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Int__Oint_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 image_int_a_o: ( int > x_a > $o ) > ( int > $o ) > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Int__Oint_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 image_int_pname_o: ( int > pname > $o ) > ( int > $o ) > ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Int__Oint_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 image_int_int_o: ( int > int > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Int__Oint_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 image_int_nat_o: ( int > nat > $o ) > ( int > $o ) > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Int__Oint_000t__a,type,
% 0.55/0.78 image_int_a: ( int > x_a ) > ( int > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Int__Oint_000tc__Com__Opname,type,
% 0.55/0.78 image_int_pname: ( int > pname ) > ( int > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 image_nat_a_o: ( nat > x_a > $o ) > ( nat > $o ) > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 image_nat_pname_o: ( nat > pname > $o ) > ( nat > $o ) > ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 image_nat_int_o: ( nat > int > $o ) > ( nat > $o ) > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 image_nat_nat_o: ( nat > nat > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000t__a,type,
% 0.55/0.78 image_nat_a: ( nat > x_a ) > ( nat > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Com__Opname,type,
% 0.55/0.78 image_nat_pname: ( nat > pname ) > ( nat > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oimage_000tc__Nat__Onat_000tc__Int__Oint,type,
% 0.55/0.78 image_nat_int: ( nat > int ) > ( nat > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oinsert_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 insert_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oinsert_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 insert_int_o: ( int > $o ) > ( ( int > $o ) > $o ) > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oinsert_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 insert_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oinsert_000t__a,type,
% 0.55/0.78 insert_a: x_a > ( x_a > $o ) > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,
% 0.55/0.78 insert_pname: pname > ( pname > $o ) > pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oinsert_000tc__Int__Oint,type,
% 0.55/0.78 insert_int: int > ( int > $o ) > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Oinsert_000tc__Nat__Onat,type,
% 0.55/0.78 insert_nat: nat > ( nat > $o ) > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Othe__elem_000t__a,type,
% 0.55/0.78 the_elem_a: ( x_a > $o ) > x_a ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Othe__elem_000tc__Int__Oint,type,
% 0.55/0.78 the_elem_int: ( int > $o ) > int ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_Set_Othe__elem_000tc__Nat__Onat,type,
% 0.55/0.78 the_elem_nat: ( nat > $o ) > nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_fequal_000t__a,type,
% 0.55/0.78 fequal_a: x_a > x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_fequal_000tc__Int__Oint,type,
% 0.55/0.78 fequal_int: int > int > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_fequal_000tc__Nat__Onat,type,
% 0.55/0.78 fequal_nat: nat > nat > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_member_000_062_It__a_M_Eo_J,type,
% 0.55/0.78 member_a_o: ( x_a > $o ) > ( ( x_a > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,
% 0.55/0.78 member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_member_000_062_Itc__Int__Oint_M_Eo_J,type,
% 0.55/0.78 member_int_o: ( int > $o ) > ( ( int > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_member_000_062_Itc__Nat__Onat_M_Eo_J,type,
% 0.55/0.78 member_nat_o: ( nat > $o ) > ( ( nat > $o ) > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_member_000t__a,type,
% 0.55/0.78 member_a: x_a > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_member_000tc__Com__Opname,type,
% 0.55/0.78 member_pname: pname > ( pname > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_member_000tc__Int__Oint,type,
% 0.55/0.78 member_int: int > ( int > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_c_member_000tc__Nat__Onat,type,
% 0.55/0.78 member_nat: nat > ( nat > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_v_G,type,
% 0.55/0.78 g: x_a > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_v_P,type,
% 0.55/0.78 p: ( x_a > $o ) > ( x_a > $o ) > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_v_U,type,
% 0.55/0.78 u: pname > $o ).
% 0.55/0.78
% 0.55/0.78 thf(sy_v_mgt,type,
% 0.55/0.78 mgt: com > x_a ).
% 0.55/0.78
% 0.55/0.78 thf(sy_v_mgt__call,type,
% 0.55/0.78 mgt_call: pname > x_a ).
% 0.55/0.78
% 0.55/0.78 thf(sy_v_na,type,
% 0.55/0.78 na: nat ).
% 0.55/0.78
% 0.55/0.78 thf(sy_v_pn,type,
% 0.55/0.78 pn: pname ).
% 0.55/0.78
% 0.55/0.78 thf(sy_v_wt,type,
% 0.55/0.78 wt: com > $o ).
% 0.55/0.78
% 0.55/0.78 %----Relevant facts (1199)
% 0.55/0.78 thf(fact_0_assms_I1_J,axiom,
% 0.55/0.78 ! [Ts: x_a > $o,G: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ Ts @ G )
% 0.55/0.78 => ( p @ G @ Ts ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_1_finite__Collect__subsets,axiom,
% 0.55/0.78 ! [A_161: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_161 )
% 0.55/0.78 => ( finite229719499nt_o_o
% 0.55/0.78 @ ( collect_int_o_o
% 0.55/0.78 @ ^ [B_26: ( int > $o ) > $o] : ( ord_less_eq_int_o_o @ B_26 @ A_161 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_2_finite__Collect__subsets,axiom,
% 0.55/0.78 ! [A_161: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_161 )
% 0.55/0.78 => ( finite1676163439at_o_o
% 0.55/0.78 @ ( collect_nat_o_o
% 0.55/0.78 @ ^ [B_26: ( nat > $o ) > $o] : ( ord_less_eq_nat_o_o @ B_26 @ A_161 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_3_finite__Collect__subsets,axiom,
% 0.55/0.78 ! [A_161: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_161 )
% 0.55/0.78 => ( finite1066544169me_o_o
% 0.55/0.78 @ ( collect_pname_o_o
% 0.55/0.78 @ ^ [B_26: ( pname > $o ) > $o] : ( ord_le1205211808me_o_o @ B_26 @ A_161 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_4_finite__Collect__subsets,axiom,
% 0.55/0.78 ! [A_161: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_161 )
% 0.55/0.78 => ( finite_finite_a_o_o
% 0.55/0.78 @ ( collect_a_o_o
% 0.55/0.78 @ ^ [B_26: ( x_a > $o ) > $o] : ( ord_less_eq_a_o_o @ B_26 @ A_161 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_5_finite__Collect__subsets,axiom,
% 0.55/0.78 ! [A_161: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_161 )
% 0.55/0.78 => ( finite_finite_a_o
% 0.55/0.78 @ ( collect_a_o
% 0.55/0.78 @ ^ [B_26: x_a > $o] : ( ord_less_eq_a_o @ B_26 @ A_161 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_6_finite__Collect__subsets,axiom,
% 0.55/0.78 ! [A_161: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_161 )
% 0.55/0.78 => ( finite297249702name_o
% 0.55/0.78 @ ( collect_pname_o
% 0.55/0.78 @ ^ [B_26: pname > $o] : ( ord_less_eq_pname_o @ B_26 @ A_161 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_7_finite__Collect__subsets,axiom,
% 0.55/0.78 ! [A_161: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_161 )
% 0.55/0.78 => ( finite_finite_nat_o
% 0.55/0.78 @ ( collect_nat_o
% 0.55/0.78 @ ^ [B_26: nat > $o] : ( ord_less_eq_nat_o @ B_26 @ A_161 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_8_finite__Collect__subsets,axiom,
% 0.55/0.78 ! [A_161: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_161 )
% 0.55/0.78 => ( finite_finite_int_o
% 0.55/0.78 @ ( collect_int_o
% 0.55/0.78 @ ^ [B_26: int > $o] : ( ord_less_eq_int_o @ B_26 @ A_161 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_9_finite__imageI,axiom,
% 0.55/0.78 ! [H: pname > int > $o,F_42: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ F_42 )
% 0.55/0.78 => ( finite_finite_int_o @ ( image_pname_int_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_10_finite__imageI,axiom,
% 0.55/0.78 ! [H: pname > nat > $o,F_42: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ F_42 )
% 0.55/0.78 => ( finite_finite_nat_o @ ( image_pname_nat_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_11_finite__imageI,axiom,
% 0.55/0.78 ! [H: pname > pname > $o,F_42: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ F_42 )
% 0.55/0.78 => ( finite297249702name_o @ ( image_pname_pname_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_12_finite__imageI,axiom,
% 0.55/0.78 ! [H: pname > x_a > $o,F_42: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ F_42 )
% 0.55/0.78 => ( finite_finite_a_o @ ( image_pname_a_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_13_finite__imageI,axiom,
% 0.55/0.78 ! [H: nat > x_a,F_42: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ F_42 )
% 0.55/0.78 => ( finite_finite_a @ ( image_nat_a @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_14_finite__imageI,axiom,
% 0.55/0.78 ! [H: nat > int > $o,F_42: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ F_42 )
% 0.55/0.78 => ( finite_finite_int_o @ ( image_nat_int_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_15_finite__imageI,axiom,
% 0.55/0.78 ! [H: nat > nat > $o,F_42: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ F_42 )
% 0.55/0.78 => ( finite_finite_nat_o @ ( image_nat_nat_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_16_finite__imageI,axiom,
% 0.55/0.78 ! [H: nat > pname > $o,F_42: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ F_42 )
% 0.55/0.78 => ( finite297249702name_o @ ( image_nat_pname_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_17_finite__imageI,axiom,
% 0.55/0.78 ! [H: nat > x_a > $o,F_42: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ F_42 )
% 0.55/0.78 => ( finite_finite_a_o @ ( image_nat_a_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_18_finite__imageI,axiom,
% 0.55/0.78 ! [H: int > x_a,F_42: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ F_42 )
% 0.55/0.78 => ( finite_finite_a @ ( image_int_a @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_19_finite__imageI,axiom,
% 0.55/0.78 ! [H: int > int > $o,F_42: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ F_42 )
% 0.55/0.78 => ( finite_finite_int_o @ ( image_int_int_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_20_finite__imageI,axiom,
% 0.55/0.78 ! [H: int > nat > $o,F_42: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ F_42 )
% 0.55/0.78 => ( finite_finite_nat_o @ ( image_int_nat_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_21_finite__imageI,axiom,
% 0.55/0.78 ! [H: int > pname > $o,F_42: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ F_42 )
% 0.55/0.78 => ( finite297249702name_o @ ( image_int_pname_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_22_finite__imageI,axiom,
% 0.55/0.78 ! [H: int > x_a > $o,F_42: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ F_42 )
% 0.55/0.78 => ( finite_finite_a_o @ ( image_int_a_o @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_23_finite__imageI,axiom,
% 0.55/0.78 ! [H: x_a > pname,F_42: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ F_42 )
% 0.55/0.78 => ( finite_finite_pname @ ( image_a_pname @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_24_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( int > $o ) > pname,F_42: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ F_42 )
% 0.55/0.78 => ( finite_finite_pname @ ( image_int_o_pname @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_25_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( nat > $o ) > pname,F_42: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ F_42 )
% 0.55/0.78 => ( finite_finite_pname @ ( image_nat_o_pname @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_26_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( pname > $o ) > pname,F_42: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ F_42 )
% 0.55/0.78 => ( finite_finite_pname @ ( image_pname_o_pname @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_27_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( x_a > $o ) > pname,F_42: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ F_42 )
% 0.55/0.78 => ( finite_finite_pname @ ( image_a_o_pname @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_28_finite__imageI,axiom,
% 0.55/0.78 ! [H: x_a > nat,F_42: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ F_42 )
% 0.55/0.78 => ( finite_finite_nat @ ( image_a_nat @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_29_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( int > $o ) > nat,F_42: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ F_42 )
% 0.55/0.78 => ( finite_finite_nat @ ( image_int_o_nat @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_30_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( nat > $o ) > nat,F_42: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ F_42 )
% 0.55/0.78 => ( finite_finite_nat @ ( image_nat_o_nat @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_31_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( pname > $o ) > nat,F_42: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ F_42 )
% 0.55/0.78 => ( finite_finite_nat @ ( image_pname_o_nat @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_32_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( x_a > $o ) > nat,F_42: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ F_42 )
% 0.55/0.78 => ( finite_finite_nat @ ( image_a_o_nat @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_33_finite__imageI,axiom,
% 0.55/0.78 ! [H: x_a > int,F_42: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ F_42 )
% 0.55/0.78 => ( finite_finite_int @ ( image_a_int @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_34_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( int > $o ) > int,F_42: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ F_42 )
% 0.55/0.78 => ( finite_finite_int @ ( image_int_o_int @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_35_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( nat > $o ) > int,F_42: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ F_42 )
% 0.55/0.78 => ( finite_finite_int @ ( image_nat_o_int @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_36_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( pname > $o ) > int,F_42: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ F_42 )
% 0.55/0.78 => ( finite_finite_int @ ( image_pname_o_int @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_37_finite__imageI,axiom,
% 0.55/0.78 ! [H: ( x_a > $o ) > int,F_42: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ F_42 )
% 0.55/0.78 => ( finite_finite_int @ ( image_a_o_int @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_38_finite__imageI,axiom,
% 0.55/0.78 ! [H: pname > x_a,F_42: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ F_42 )
% 0.55/0.78 => ( finite_finite_a @ ( image_pname_a @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_39_finite__imageI,axiom,
% 0.55/0.78 ! [H: nat > int,F_42: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ F_42 )
% 0.55/0.78 => ( finite_finite_int @ ( image_nat_int @ H @ F_42 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_40_finite_OinsertI,axiom,
% 0.55/0.78 ! [A_160: int > $o,A_159: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_159 )
% 0.55/0.78 => ( finite_finite_int_o @ ( insert_int_o @ A_160 @ A_159 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_41_finite_OinsertI,axiom,
% 0.55/0.78 ! [A_160: nat > $o,A_159: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_159 )
% 0.55/0.78 => ( finite_finite_nat_o @ ( insert_nat_o @ A_160 @ A_159 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_42_finite_OinsertI,axiom,
% 0.55/0.78 ! [A_160: pname > $o,A_159: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_159 )
% 0.55/0.78 => ( finite297249702name_o @ ( insert_pname_o @ A_160 @ A_159 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_43_finite_OinsertI,axiom,
% 0.55/0.78 ! [A_160: x_a > $o,A_159: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_159 )
% 0.55/0.78 => ( finite_finite_a_o @ ( insert_a_o @ A_160 @ A_159 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_44_finite_OinsertI,axiom,
% 0.55/0.78 ! [A_160: pname,A_159: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_159 )
% 0.55/0.78 => ( finite_finite_pname @ ( insert_pname @ A_160 @ A_159 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_45_finite_OinsertI,axiom,
% 0.55/0.78 ! [A_160: nat,A_159: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_159 )
% 0.55/0.78 => ( finite_finite_nat @ ( insert_nat @ A_160 @ A_159 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_46_finite_OinsertI,axiom,
% 0.55/0.78 ! [A_160: int,A_159: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_159 )
% 0.55/0.78 => ( finite_finite_int @ ( insert_int @ A_160 @ A_159 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_47_finite_OinsertI,axiom,
% 0.55/0.78 ! [A_160: x_a,A_159: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_159 )
% 0.55/0.78 => ( finite_finite_a @ ( insert_a @ A_160 @ A_159 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_48_card__image__le,axiom,
% 0.55/0.78 ! [F_41: pname > pname,A_158: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_pname_pname @ F_41 @ A_158 ) ) @ ( finite_card_pname @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_49_card__image__le,axiom,
% 0.55/0.78 ! [F_41: x_a > x_a,A_158: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_a @ F_41 @ A_158 ) ) @ ( finite_card_a @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_50_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( int > $o ) > x_a,A_158: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_int_o_a @ F_41 @ A_158 ) ) @ ( finite_card_int_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_51_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( nat > $o ) > x_a,A_158: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_nat_o_a @ F_41 @ A_158 ) ) @ ( finite_card_nat_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_52_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( pname > $o ) > x_a,A_158: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_o_a @ F_41 @ A_158 ) ) @ ( finite_card_pname_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_53_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( x_a > $o ) > x_a,A_158: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_a_o_a @ F_41 @ A_158 ) ) @ ( finite_card_a_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_54_card__image__le,axiom,
% 0.55/0.78 ! [F_41: pname > nat,A_158: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_nat @ F_41 @ A_158 ) ) @ ( finite_card_pname @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_55_card__image__le,axiom,
% 0.55/0.78 ! [F_41: x_a > nat,A_158: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_nat @ F_41 @ A_158 ) ) @ ( finite_card_a @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_56_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( int > $o ) > nat,A_158: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_int_o_nat @ F_41 @ A_158 ) ) @ ( finite_card_int_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_57_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( nat > $o ) > nat,A_158: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_o_nat @ F_41 @ A_158 ) ) @ ( finite_card_nat_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_58_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( pname > $o ) > nat,A_158: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_pname_o_nat @ F_41 @ A_158 ) ) @ ( finite_card_pname_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_59_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( x_a > $o ) > nat,A_158: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_a_o_nat @ F_41 @ A_158 ) ) @ ( finite_card_a_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_60_card__image__le,axiom,
% 0.55/0.78 ! [F_41: pname > int,A_158: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_pname_int @ F_41 @ A_158 ) ) @ ( finite_card_pname @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_61_card__image__le,axiom,
% 0.55/0.78 ! [F_41: x_a > int,A_158: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_a_int @ F_41 @ A_158 ) ) @ ( finite_card_a @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_62_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( int > $o ) > int,A_158: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_int_o_int @ F_41 @ A_158 ) ) @ ( finite_card_int_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_63_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( nat > $o ) > int,A_158: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_nat_o_int @ F_41 @ A_158 ) ) @ ( finite_card_nat_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_64_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( pname > $o ) > int,A_158: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_pname_o_int @ F_41 @ A_158 ) ) @ ( finite_card_pname_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_65_card__image__le,axiom,
% 0.55/0.78 ! [F_41: ( x_a > $o ) > int,A_158: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_a_o_int @ F_41 @ A_158 ) ) @ ( finite_card_a_o @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_66_card__image__le,axiom,
% 0.55/0.78 ! [F_41: x_a > pname,A_158: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_a_pname @ F_41 @ A_158 ) ) @ ( finite_card_a @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_67_card__image__le,axiom,
% 0.55/0.78 ! [F_41: nat > pname,A_158: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_nat_pname @ F_41 @ A_158 ) ) @ ( finite_card_nat @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_68_card__image__le,axiom,
% 0.55/0.78 ! [F_41: int > pname,A_158: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_pname @ ( image_int_pname @ F_41 @ A_158 ) ) @ ( finite_card_int @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_69_card__image__le,axiom,
% 0.55/0.78 ! [F_41: pname > x_a,A_158: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a @ ( image_pname_a @ F_41 @ A_158 ) ) @ ( finite_card_pname @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_70_card__image__le,axiom,
% 0.55/0.78 ! [F_41: nat > int,A_158: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_158 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_nat_int @ F_41 @ A_158 ) ) @ ( finite_card_nat @ A_158 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_71_card__mono,axiom,
% 0.55/0.78 ! [A_157: ( int > $o ) > $o,B_89: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ B_89 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ A_157 @ B_89 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int_o @ A_157 ) @ ( finite_card_int_o @ B_89 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_72_card__mono,axiom,
% 0.55/0.78 ! [A_157: ( nat > $o ) > $o,B_89: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ B_89 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ A_157 @ B_89 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_157 ) @ ( finite_card_nat_o @ B_89 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_73_card__mono,axiom,
% 0.55/0.78 ! [A_157: ( pname > $o ) > $o,B_89: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ B_89 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ A_157 @ B_89 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_157 ) @ ( finite_card_pname_o @ B_89 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_74_card__mono,axiom,
% 0.55/0.78 ! [A_157: ( x_a > $o ) > $o,B_89: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ B_89 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ A_157 @ B_89 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_157 ) @ ( finite_card_a_o @ B_89 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_75_card__mono,axiom,
% 0.55/0.78 ! [A_157: pname > $o,B_89: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_89 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ A_157 @ B_89 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_pname @ A_157 ) @ ( finite_card_pname @ B_89 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_76_card__mono,axiom,
% 0.55/0.78 ! [A_157: x_a > $o,B_89: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_89 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ A_157 @ B_89 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a @ A_157 ) @ ( finite_card_a @ B_89 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_77_card__mono,axiom,
% 0.55/0.78 ! [A_157: nat > $o,B_89: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_89 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ A_157 @ B_89 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat @ A_157 ) @ ( finite_card_nat @ B_89 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_78_card__mono,axiom,
% 0.55/0.78 ! [A_157: int > $o,B_89: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_89 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ A_157 @ B_89 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ A_157 ) @ ( finite_card_int @ B_89 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_79_card__seteq,axiom,
% 0.55/0.78 ! [A_156: ( int > $o ) > $o,B_88: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ A_156 @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( finite_card_int_o @ B_88 ) @ ( finite_card_int_o @ A_156 ) )
% 0.55/0.78 => ( A_156 = B_88 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_80_card__seteq,axiom,
% 0.55/0.78 ! [A_156: ( nat > $o ) > $o,B_88: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ A_156 @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( finite_card_nat_o @ B_88 ) @ ( finite_card_nat_o @ A_156 ) )
% 0.55/0.78 => ( A_156 = B_88 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_81_card__seteq,axiom,
% 0.55/0.78 ! [A_156: ( pname > $o ) > $o,B_88: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ B_88 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ A_156 @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( finite_card_pname_o @ B_88 ) @ ( finite_card_pname_o @ A_156 ) )
% 0.55/0.78 => ( A_156 = B_88 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_82_card__seteq,axiom,
% 0.55/0.78 ! [A_156: ( x_a > $o ) > $o,B_88: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ A_156 @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( finite_card_a_o @ B_88 ) @ ( finite_card_a_o @ A_156 ) )
% 0.55/0.78 => ( A_156 = B_88 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_83_card__seteq,axiom,
% 0.55/0.78 ! [A_156: pname > $o,B_88: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ A_156 @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( finite_card_pname @ B_88 ) @ ( finite_card_pname @ A_156 ) )
% 0.55/0.78 => ( A_156 = B_88 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_84_card__seteq,axiom,
% 0.55/0.78 ! [A_156: x_a > $o,B_88: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ A_156 @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( finite_card_a @ B_88 ) @ ( finite_card_a @ A_156 ) )
% 0.55/0.78 => ( A_156 = B_88 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_85_card__seteq,axiom,
% 0.55/0.78 ! [A_156: nat > $o,B_88: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ A_156 @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B_88 ) @ ( finite_card_nat @ A_156 ) )
% 0.55/0.78 => ( A_156 = B_88 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_86_card__seteq,axiom,
% 0.55/0.78 ! [A_156: int > $o,B_88: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ A_156 @ B_88 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( finite_card_int @ B_88 ) @ ( finite_card_int @ A_156 ) )
% 0.55/0.78 => ( A_156 = B_88 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_87_card__insert__le,axiom,
% 0.55/0.78 ! [X_53: int > $o,A_155: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_155 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int_o @ A_155 ) @ ( finite_card_int_o @ ( insert_int_o @ X_53 @ A_155 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_88_card__insert__le,axiom,
% 0.55/0.78 ! [X_53: nat > $o,A_155: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_155 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat_o @ A_155 ) @ ( finite_card_nat_o @ ( insert_nat_o @ X_53 @ A_155 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_89_card__insert__le,axiom,
% 0.55/0.78 ! [X_53: pname > $o,A_155: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_155 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_pname_o @ A_155 ) @ ( finite_card_pname_o @ ( insert_pname_o @ X_53 @ A_155 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_90_card__insert__le,axiom,
% 0.55/0.78 ! [X_53: x_a > $o,A_155: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_155 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a_o @ A_155 ) @ ( finite_card_a_o @ ( insert_a_o @ X_53 @ A_155 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_91_card__insert__le,axiom,
% 0.55/0.78 ! [X_53: pname,A_155: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_155 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_pname @ A_155 ) @ ( finite_card_pname @ ( insert_pname @ X_53 @ A_155 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_92_card__insert__le,axiom,
% 0.55/0.78 ! [X_53: nat,A_155: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_155 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_nat @ A_155 ) @ ( finite_card_nat @ ( insert_nat @ X_53 @ A_155 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_93_card__insert__le,axiom,
% 0.55/0.78 ! [X_53: int,A_155: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_155 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_int @ A_155 ) @ ( finite_card_int @ ( insert_int @ X_53 @ A_155 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_94_card__insert__le,axiom,
% 0.55/0.78 ! [X_53: x_a,A_155: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_155 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( finite_card_a @ A_155 ) @ ( finite_card_a @ ( insert_a @ X_53 @ A_155 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_95_card__insert__if,axiom,
% 0.55/0.78 ! [X_52: int > $o,A_154: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_154 )
% 0.55/0.78 => ( ( ( member_int_o @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_int_o @ ( insert_int_o @ X_52 @ A_154 ) )
% 0.55/0.78 = ( finite_card_int_o @ A_154 ) ) )
% 0.55/0.78 & ( ~ ( member_int_o @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_int_o @ ( insert_int_o @ X_52 @ A_154 ) )
% 0.55/0.78 = ( suc @ ( finite_card_int_o @ A_154 ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_96_card__insert__if,axiom,
% 0.55/0.78 ! [X_52: nat > $o,A_154: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_154 )
% 0.55/0.78 => ( ( ( member_nat_o @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_52 @ A_154 ) )
% 0.55/0.78 = ( finite_card_nat_o @ A_154 ) ) )
% 0.55/0.78 & ( ~ ( member_nat_o @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_52 @ A_154 ) )
% 0.55/0.78 = ( suc @ ( finite_card_nat_o @ A_154 ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_97_card__insert__if,axiom,
% 0.55/0.78 ! [X_52: pname > $o,A_154: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_154 )
% 0.55/0.78 => ( ( ( member_pname_o @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_52 @ A_154 ) )
% 0.55/0.78 = ( finite_card_pname_o @ A_154 ) ) )
% 0.55/0.78 & ( ~ ( member_pname_o @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_52 @ A_154 ) )
% 0.55/0.78 = ( suc @ ( finite_card_pname_o @ A_154 ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_98_card__insert__if,axiom,
% 0.55/0.78 ! [X_52: x_a > $o,A_154: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_154 )
% 0.55/0.78 => ( ( ( member_a_o @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_a_o @ ( insert_a_o @ X_52 @ A_154 ) )
% 0.55/0.78 = ( finite_card_a_o @ A_154 ) ) )
% 0.55/0.78 & ( ~ ( member_a_o @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_a_o @ ( insert_a_o @ X_52 @ A_154 ) )
% 0.55/0.78 = ( suc @ ( finite_card_a_o @ A_154 ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_99_card__insert__if,axiom,
% 0.55/0.78 ! [X_52: pname,A_154: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_154 )
% 0.55/0.78 => ( ( ( member_pname @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_pname @ ( insert_pname @ X_52 @ A_154 ) )
% 0.55/0.78 = ( finite_card_pname @ A_154 ) ) )
% 0.55/0.78 & ( ~ ( member_pname @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_pname @ ( insert_pname @ X_52 @ A_154 ) )
% 0.55/0.78 = ( suc @ ( finite_card_pname @ A_154 ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_100_card__insert__if,axiom,
% 0.55/0.78 ! [X_52: nat,A_154: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_154 )
% 0.55/0.78 => ( ( ( member_nat @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_nat @ ( insert_nat @ X_52 @ A_154 ) )
% 0.55/0.78 = ( finite_card_nat @ A_154 ) ) )
% 0.55/0.78 & ( ~ ( member_nat @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_nat @ ( insert_nat @ X_52 @ A_154 ) )
% 0.55/0.78 = ( suc @ ( finite_card_nat @ A_154 ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_101_card__insert__if,axiom,
% 0.55/0.78 ! [X_52: int,A_154: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_154 )
% 0.55/0.78 => ( ( ( member_int @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_int @ ( insert_int @ X_52 @ A_154 ) )
% 0.55/0.78 = ( finite_card_int @ A_154 ) ) )
% 0.55/0.78 & ( ~ ( member_int @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_int @ ( insert_int @ X_52 @ A_154 ) )
% 0.55/0.78 = ( suc @ ( finite_card_int @ A_154 ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_102_card__insert__if,axiom,
% 0.55/0.78 ! [X_52: x_a,A_154: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_154 )
% 0.55/0.78 => ( ( ( member_a @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_a @ ( insert_a @ X_52 @ A_154 ) )
% 0.55/0.78 = ( finite_card_a @ A_154 ) ) )
% 0.55/0.78 & ( ~ ( member_a @ X_52 @ A_154 )
% 0.55/0.78 => ( ( finite_card_a @ ( insert_a @ X_52 @ A_154 ) )
% 0.55/0.78 = ( suc @ ( finite_card_a @ A_154 ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_103_card__insert__disjoint,axiom,
% 0.55/0.78 ! [X_51: int > $o,A_153: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_153 )
% 0.55/0.78 => ( ~ ( member_int_o @ X_51 @ A_153 )
% 0.55/0.78 => ( ( finite_card_int_o @ ( insert_int_o @ X_51 @ A_153 ) )
% 0.55/0.78 = ( suc @ ( finite_card_int_o @ A_153 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_104_card__insert__disjoint,axiom,
% 0.55/0.78 ! [X_51: nat > $o,A_153: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_153 )
% 0.55/0.78 => ( ~ ( member_nat_o @ X_51 @ A_153 )
% 0.55/0.78 => ( ( finite_card_nat_o @ ( insert_nat_o @ X_51 @ A_153 ) )
% 0.55/0.78 = ( suc @ ( finite_card_nat_o @ A_153 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_105_card__insert__disjoint,axiom,
% 0.55/0.78 ! [X_51: pname > $o,A_153: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_153 )
% 0.55/0.78 => ( ~ ( member_pname_o @ X_51 @ A_153 )
% 0.55/0.78 => ( ( finite_card_pname_o @ ( insert_pname_o @ X_51 @ A_153 ) )
% 0.55/0.78 = ( suc @ ( finite_card_pname_o @ A_153 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_106_card__insert__disjoint,axiom,
% 0.55/0.78 ! [X_51: x_a > $o,A_153: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_153 )
% 0.55/0.78 => ( ~ ( member_a_o @ X_51 @ A_153 )
% 0.55/0.78 => ( ( finite_card_a_o @ ( insert_a_o @ X_51 @ A_153 ) )
% 0.55/0.78 = ( suc @ ( finite_card_a_o @ A_153 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_107_card__insert__disjoint,axiom,
% 0.55/0.78 ! [X_51: pname,A_153: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_153 )
% 0.55/0.78 => ( ~ ( member_pname @ X_51 @ A_153 )
% 0.55/0.78 => ( ( finite_card_pname @ ( insert_pname @ X_51 @ A_153 ) )
% 0.55/0.78 = ( suc @ ( finite_card_pname @ A_153 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_108_card__insert__disjoint,axiom,
% 0.55/0.78 ! [X_51: nat,A_153: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_153 )
% 0.55/0.78 => ( ~ ( member_nat @ X_51 @ A_153 )
% 0.55/0.78 => ( ( finite_card_nat @ ( insert_nat @ X_51 @ A_153 ) )
% 0.55/0.78 = ( suc @ ( finite_card_nat @ A_153 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_109_card__insert__disjoint,axiom,
% 0.55/0.78 ! [X_51: int,A_153: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_153 )
% 0.55/0.78 => ( ~ ( member_int @ X_51 @ A_153 )
% 0.55/0.78 => ( ( finite_card_int @ ( insert_int @ X_51 @ A_153 ) )
% 0.55/0.78 = ( suc @ ( finite_card_int @ A_153 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_110_card__insert__disjoint,axiom,
% 0.55/0.78 ! [X_51: x_a,A_153: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_153 )
% 0.55/0.78 => ( ~ ( member_a @ X_51 @ A_153 )
% 0.55/0.78 => ( ( finite_card_a @ ( insert_a @ X_51 @ A_153 ) )
% 0.55/0.78 = ( suc @ ( finite_card_a @ A_153 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_111_finite__Collect__conjI,axiom,
% 0.55/0.78 ! [Q_3: x_a > $o,P_13: x_a > $o] :
% 0.55/0.78 ( ( ( finite_finite_a @ ( collect_a @ P_13 ) )
% 0.55/0.78 | ( finite_finite_a @ ( collect_a @ Q_3 ) ) )
% 0.55/0.78 => ( finite_finite_a
% 0.55/0.78 @ ( collect_a
% 0.55/0.78 @ ^ [X_1: x_a] : ( (&) @ ( P_13 @ X_1 ) @ ( Q_3 @ X_1 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_112_finite__Collect__conjI,axiom,
% 0.55/0.78 ! [Q_3: ( int > $o ) > $o,P_13: ( int > $o ) > $o] :
% 0.55/0.78 ( ( ( finite_finite_int_o @ ( collect_int_o @ P_13 ) )
% 0.55/0.78 | ( finite_finite_int_o @ ( collect_int_o @ Q_3 ) ) )
% 0.55/0.78 => ( finite_finite_int_o
% 0.55/0.78 @ ( collect_int_o
% 0.55/0.78 @ ^ [X_1: int > $o] : ( (&) @ ( P_13 @ X_1 ) @ ( Q_3 @ X_1 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_113_finite__Collect__conjI,axiom,
% 0.55/0.78 ! [Q_3: ( nat > $o ) > $o,P_13: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( ( finite_finite_nat_o @ ( collect_nat_o @ P_13 ) )
% 0.55/0.78 | ( finite_finite_nat_o @ ( collect_nat_o @ Q_3 ) ) )
% 0.55/0.78 => ( finite_finite_nat_o
% 0.55/0.78 @ ( collect_nat_o
% 0.55/0.78 @ ^ [X_1: nat > $o] : ( (&) @ ( P_13 @ X_1 ) @ ( Q_3 @ X_1 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_114_finite__Collect__conjI,axiom,
% 0.55/0.78 ! [Q_3: ( pname > $o ) > $o,P_13: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( ( finite297249702name_o @ ( collect_pname_o @ P_13 ) )
% 0.55/0.78 | ( finite297249702name_o @ ( collect_pname_o @ Q_3 ) ) )
% 0.55/0.78 => ( finite297249702name_o
% 0.55/0.78 @ ( collect_pname_o
% 0.55/0.78 @ ^ [X_1: pname > $o] : ( (&) @ ( P_13 @ X_1 ) @ ( Q_3 @ X_1 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_115_finite__Collect__conjI,axiom,
% 0.55/0.78 ! [Q_3: ( x_a > $o ) > $o,P_13: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( ( finite_finite_a_o @ ( collect_a_o @ P_13 ) )
% 0.55/0.78 | ( finite_finite_a_o @ ( collect_a_o @ Q_3 ) ) )
% 0.55/0.78 => ( finite_finite_a_o
% 0.55/0.78 @ ( collect_a_o
% 0.55/0.78 @ ^ [X_1: x_a > $o] : ( (&) @ ( P_13 @ X_1 ) @ ( Q_3 @ X_1 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_116_finite__Collect__conjI,axiom,
% 0.55/0.78 ! [Q_3: pname > $o,P_13: pname > $o] :
% 0.55/0.78 ( ( ( finite_finite_pname @ ( collect_pname @ P_13 ) )
% 0.55/0.78 | ( finite_finite_pname @ ( collect_pname @ Q_3 ) ) )
% 0.55/0.78 => ( finite_finite_pname
% 0.55/0.78 @ ( collect_pname
% 0.55/0.78 @ ^ [X_1: pname] : ( (&) @ ( P_13 @ X_1 ) @ ( Q_3 @ X_1 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_117_finite__Collect__conjI,axiom,
% 0.55/0.78 ! [Q_3: nat > $o,P_13: nat > $o] :
% 0.55/0.78 ( ( ( finite_finite_nat @ ( collect_nat @ P_13 ) )
% 0.55/0.78 | ( finite_finite_nat @ ( collect_nat @ Q_3 ) ) )
% 0.55/0.78 => ( finite_finite_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [X_1: nat] : ( (&) @ ( P_13 @ X_1 ) @ ( Q_3 @ X_1 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_118_finite__Collect__conjI,axiom,
% 0.55/0.78 ! [Q_3: int > $o,P_13: int > $o] :
% 0.55/0.78 ( ( ( finite_finite_int @ ( collect_int @ P_13 ) )
% 0.55/0.78 | ( finite_finite_int @ ( collect_int @ Q_3 ) ) )
% 0.55/0.78 => ( finite_finite_int
% 0.55/0.78 @ ( collect_int
% 0.55/0.78 @ ^ [X_1: int] : ( (&) @ ( P_13 @ X_1 ) @ ( Q_3 @ X_1 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_119_Suc__diff__le,axiom,
% 0.55/0.78 ! [N: nat,M: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ N @ M )
% 0.55/0.78 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.55/0.78 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_120_finite__Collect__le__nat,axiom,
% 0.55/0.78 ! [K: nat] :
% 0.55/0.78 ( finite_finite_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [N_1: nat] : ( ord_less_eq_nat @ N_1 @ K ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_121_card__Collect__le__nat,axiom,
% 0.55/0.78 ! [N: nat] :
% 0.55/0.78 ( ( finite_card_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [I: nat] : ( ord_less_eq_nat @ I @ N ) ) )
% 0.55/0.78 = ( suc @ N ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_122_Suc__inject,axiom,
% 0.55/0.78 ! [X: nat,Y: nat] :
% 0.55/0.78 ( ( ( suc @ X )
% 0.55/0.78 = ( suc @ Y ) )
% 0.55/0.78 => ( X = Y ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_123_nat_Oinject,axiom,
% 0.55/0.78 ! [Nat_4: nat,Nat_1: nat] :
% 0.55/0.78 ( ( ( suc @ Nat_4 )
% 0.55/0.78 = ( suc @ Nat_1 ) )
% 0.55/0.78 <=> ( Nat_4 = Nat_1 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_124_Suc__n__not__n,axiom,
% 0.55/0.78 ! [N: nat] :
% 0.55/0.78 ( ( suc @ N )
% 0.55/0.78 != N ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_125_n__not__Suc__n,axiom,
% 0.55/0.78 ! [N: nat] :
% 0.55/0.78 ( N
% 0.55/0.78 != ( suc @ N ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_126_le__antisym,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.78 => ( ( ord_less_eq_nat @ N @ M )
% 0.55/0.78 => ( M = N ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_127_le__trans,axiom,
% 0.55/0.78 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.78 => ( ( ord_less_eq_nat @ J @ K )
% 0.55/0.78 => ( ord_less_eq_nat @ I_1 @ K ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_128_eq__imp__le,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ( M = N )
% 0.55/0.78 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_129_nat__le__linear,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.78 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_130_le__refl,axiom,
% 0.55/0.78 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_131_diff__commute,axiom,
% 0.55/0.78 ! [I_1: nat,J: nat,K: nat] :
% 0.55/0.78 ( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J ) @ K )
% 0.55/0.78 = ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ K ) @ J ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_132_finite__Collect__disjI,axiom,
% 0.55/0.78 ! [P_12: x_a > $o,Q_2: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a
% 0.55/0.78 @ ( collect_a
% 0.55/0.78 @ ^ [X_1: x_a] : ( (|) @ ( P_12 @ X_1 ) @ ( Q_2 @ X_1 ) ) ) )
% 0.55/0.78 <=> ( ( finite_finite_a @ ( collect_a @ P_12 ) )
% 0.55/0.78 & ( finite_finite_a @ ( collect_a @ Q_2 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_133_finite__Collect__disjI,axiom,
% 0.55/0.78 ! [P_12: ( int > $o ) > $o,Q_2: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o
% 0.55/0.78 @ ( collect_int_o
% 0.55/0.78 @ ^ [X_1: int > $o] : ( (|) @ ( P_12 @ X_1 ) @ ( Q_2 @ X_1 ) ) ) )
% 0.55/0.78 <=> ( ( finite_finite_int_o @ ( collect_int_o @ P_12 ) )
% 0.55/0.78 & ( finite_finite_int_o @ ( collect_int_o @ Q_2 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_134_finite__Collect__disjI,axiom,
% 0.55/0.78 ! [P_12: ( nat > $o ) > $o,Q_2: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o
% 0.55/0.78 @ ( collect_nat_o
% 0.55/0.78 @ ^ [X_1: nat > $o] : ( (|) @ ( P_12 @ X_1 ) @ ( Q_2 @ X_1 ) ) ) )
% 0.55/0.78 <=> ( ( finite_finite_nat_o @ ( collect_nat_o @ P_12 ) )
% 0.55/0.78 & ( finite_finite_nat_o @ ( collect_nat_o @ Q_2 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_135_finite__Collect__disjI,axiom,
% 0.55/0.78 ! [P_12: ( pname > $o ) > $o,Q_2: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o
% 0.55/0.78 @ ( collect_pname_o
% 0.55/0.78 @ ^ [X_1: pname > $o] : ( (|) @ ( P_12 @ X_1 ) @ ( Q_2 @ X_1 ) ) ) )
% 0.55/0.78 <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_12 ) )
% 0.55/0.78 & ( finite297249702name_o @ ( collect_pname_o @ Q_2 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_136_finite__Collect__disjI,axiom,
% 0.55/0.78 ! [P_12: ( x_a > $o ) > $o,Q_2: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o
% 0.55/0.78 @ ( collect_a_o
% 0.55/0.78 @ ^ [X_1: x_a > $o] : ( (|) @ ( P_12 @ X_1 ) @ ( Q_2 @ X_1 ) ) ) )
% 0.55/0.78 <=> ( ( finite_finite_a_o @ ( collect_a_o @ P_12 ) )
% 0.55/0.78 & ( finite_finite_a_o @ ( collect_a_o @ Q_2 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_137_finite__Collect__disjI,axiom,
% 0.55/0.78 ! [P_12: pname > $o,Q_2: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname
% 0.55/0.78 @ ( collect_pname
% 0.55/0.78 @ ^ [X_1: pname] : ( (|) @ ( P_12 @ X_1 ) @ ( Q_2 @ X_1 ) ) ) )
% 0.55/0.78 <=> ( ( finite_finite_pname @ ( collect_pname @ P_12 ) )
% 0.55/0.78 & ( finite_finite_pname @ ( collect_pname @ Q_2 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_138_finite__Collect__disjI,axiom,
% 0.55/0.78 ! [P_12: nat > $o,Q_2: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [X_1: nat] : ( (|) @ ( P_12 @ X_1 ) @ ( Q_2 @ X_1 ) ) ) )
% 0.55/0.78 <=> ( ( finite_finite_nat @ ( collect_nat @ P_12 ) )
% 0.55/0.78 & ( finite_finite_nat @ ( collect_nat @ Q_2 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_139_finite__Collect__disjI,axiom,
% 0.55/0.78 ! [P_12: int > $o,Q_2: int > $o] :
% 0.55/0.78 ( ( finite_finite_int
% 0.55/0.78 @ ( collect_int
% 0.55/0.78 @ ^ [X_1: int] : ( (|) @ ( P_12 @ X_1 ) @ ( Q_2 @ X_1 ) ) ) )
% 0.55/0.78 <=> ( ( finite_finite_int @ ( collect_int @ P_12 ) )
% 0.55/0.78 & ( finite_finite_int @ ( collect_int @ Q_2 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_140_finite__insert,axiom,
% 0.55/0.78 ! [A_152: int > $o,A_151: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ ( insert_int_o @ A_152 @ A_151 ) )
% 0.55/0.78 <=> ( finite_finite_int_o @ A_151 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_141_finite__insert,axiom,
% 0.55/0.78 ! [A_152: nat > $o,A_151: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ ( insert_nat_o @ A_152 @ A_151 ) )
% 0.55/0.78 <=> ( finite_finite_nat_o @ A_151 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_142_finite__insert,axiom,
% 0.55/0.78 ! [A_152: pname > $o,A_151: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ ( insert_pname_o @ A_152 @ A_151 ) )
% 0.55/0.78 <=> ( finite297249702name_o @ A_151 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_143_finite__insert,axiom,
% 0.55/0.78 ! [A_152: x_a > $o,A_151: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ ( insert_a_o @ A_152 @ A_151 ) )
% 0.55/0.78 <=> ( finite_finite_a_o @ A_151 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_144_finite__insert,axiom,
% 0.55/0.78 ! [A_152: pname,A_151: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ ( insert_pname @ A_152 @ A_151 ) )
% 0.55/0.78 <=> ( finite_finite_pname @ A_151 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_145_finite__insert,axiom,
% 0.55/0.78 ! [A_152: nat,A_151: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ ( insert_nat @ A_152 @ A_151 ) )
% 0.55/0.78 <=> ( finite_finite_nat @ A_151 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_146_finite__insert,axiom,
% 0.55/0.78 ! [A_152: int,A_151: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ ( insert_int @ A_152 @ A_151 ) )
% 0.55/0.78 <=> ( finite_finite_int @ A_151 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_147_finite__insert,axiom,
% 0.55/0.78 ! [A_152: x_a,A_151: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ ( insert_a @ A_152 @ A_151 ) )
% 0.55/0.78 <=> ( finite_finite_a @ A_151 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_148_finite__subset,axiom,
% 0.55/0.78 ! [A_150: ( int > $o ) > $o,B_87: ( int > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o_o @ A_150 @ B_87 )
% 0.55/0.78 => ( ( finite_finite_int_o @ B_87 )
% 0.55/0.78 => ( finite_finite_int_o @ A_150 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_149_finite__subset,axiom,
% 0.55/0.78 ! [A_150: ( nat > $o ) > $o,B_87: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o_o @ A_150 @ B_87 )
% 0.55/0.78 => ( ( finite_finite_nat_o @ B_87 )
% 0.55/0.78 => ( finite_finite_nat_o @ A_150 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_150_finite__subset,axiom,
% 0.55/0.78 ! [A_150: ( pname > $o ) > $o,B_87: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( ord_le1205211808me_o_o @ A_150 @ B_87 )
% 0.55/0.78 => ( ( finite297249702name_o @ B_87 )
% 0.55/0.78 => ( finite297249702name_o @ A_150 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_151_finite__subset,axiom,
% 0.55/0.78 ! [A_150: ( x_a > $o ) > $o,B_87: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o_o @ A_150 @ B_87 )
% 0.55/0.78 => ( ( finite_finite_a_o @ B_87 )
% 0.55/0.78 => ( finite_finite_a_o @ A_150 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_152_finite__subset,axiom,
% 0.55/0.78 ! [A_150: x_a > $o,B_87: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ A_150 @ B_87 )
% 0.55/0.78 => ( ( finite_finite_a @ B_87 )
% 0.55/0.78 => ( finite_finite_a @ A_150 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_153_finite__subset,axiom,
% 0.55/0.78 ! [A_150: pname > $o,B_87: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ A_150 @ B_87 )
% 0.55/0.78 => ( ( finite_finite_pname @ B_87 )
% 0.55/0.78 => ( finite_finite_pname @ A_150 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_154_finite__subset,axiom,
% 0.55/0.78 ! [A_150: nat > $o,B_87: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ A_150 @ B_87 )
% 0.55/0.78 => ( ( finite_finite_nat @ B_87 )
% 0.55/0.78 => ( finite_finite_nat @ A_150 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_155_finite__subset,axiom,
% 0.55/0.78 ! [A_150: int > $o,B_87: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ A_150 @ B_87 )
% 0.55/0.78 => ( ( finite_finite_int @ B_87 )
% 0.55/0.78 => ( finite_finite_int @ A_150 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_156_rev__finite__subset,axiom,
% 0.55/0.78 ! [A_149: ( int > $o ) > $o,B_86: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ B_86 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ A_149 @ B_86 )
% 0.55/0.78 => ( finite_finite_int_o @ A_149 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_157_rev__finite__subset,axiom,
% 0.55/0.78 ! [A_149: ( nat > $o ) > $o,B_86: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ B_86 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ A_149 @ B_86 )
% 0.55/0.78 => ( finite_finite_nat_o @ A_149 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_158_rev__finite__subset,axiom,
% 0.55/0.78 ! [A_149: ( pname > $o ) > $o,B_86: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ B_86 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ A_149 @ B_86 )
% 0.55/0.78 => ( finite297249702name_o @ A_149 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_159_rev__finite__subset,axiom,
% 0.55/0.78 ! [A_149: ( x_a > $o ) > $o,B_86: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ B_86 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ A_149 @ B_86 )
% 0.55/0.78 => ( finite_finite_a_o @ A_149 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_160_rev__finite__subset,axiom,
% 0.55/0.78 ! [A_149: x_a > $o,B_86: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_86 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ A_149 @ B_86 )
% 0.55/0.78 => ( finite_finite_a @ A_149 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_161_rev__finite__subset,axiom,
% 0.55/0.78 ! [A_149: pname > $o,B_86: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_86 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ A_149 @ B_86 )
% 0.55/0.78 => ( finite_finite_pname @ A_149 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_162_rev__finite__subset,axiom,
% 0.55/0.78 ! [A_149: nat > $o,B_86: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_86 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ A_149 @ B_86 )
% 0.55/0.78 => ( finite_finite_nat @ A_149 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_163_rev__finite__subset,axiom,
% 0.55/0.78 ! [A_149: int > $o,B_86: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_86 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ A_149 @ B_86 )
% 0.55/0.78 => ( finite_finite_int @ A_149 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_164_Suc__leD,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.55/0.78 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_165_le__SucE,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.55/0.78 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.55/0.78 => ( M
% 0.55/0.78 = ( suc @ N ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_166_le__SucI,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.78 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_167_Suc__le__mono,axiom,
% 0.55/0.78 ! [N: nat,M: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.55/0.78 <=> ( ord_less_eq_nat @ N @ M ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_168_le__Suc__eq,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.55/0.78 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.78 | ( M
% 0.55/0.78 = ( suc @ N ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_169_not__less__eq__eq,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ~ ( ord_less_eq_nat @ M @ N )
% 0.55/0.78 <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_170_Suc__n__not__le__n,axiom,
% 0.55/0.78 ! [N: nat] :
% 0.55/0.78 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_171_Suc__diff__diff,axiom,
% 0.55/0.78 ! [M: nat,N: nat,K: nat] :
% 0.55/0.78 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.55/0.78 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_172_diff__Suc__Suc,axiom,
% 0.55/0.78 ! [M: nat,N: nat] :
% 0.55/0.78 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.55/0.78 = ( minus_minus_nat @ M @ N ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_173_le__diff__iff,axiom,
% 0.55/0.78 ! [N: nat,K: nat,M: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ K @ M )
% 0.55/0.78 => ( ( ord_less_eq_nat @ K @ N )
% 0.55/0.78 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.55/0.78 <=> ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_174_Nat_Odiff__diff__eq,axiom,
% 0.55/0.78 ! [N: nat,K: nat,M: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ K @ M )
% 0.55/0.78 => ( ( ord_less_eq_nat @ K @ N )
% 0.55/0.78 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.55/0.78 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_175_eq__diff__iff,axiom,
% 0.55/0.78 ! [N: nat,K: nat,M: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ K @ M )
% 0.55/0.78 => ( ( ord_less_eq_nat @ K @ N )
% 0.55/0.78 => ( ( ( minus_minus_nat @ M @ K )
% 0.55/0.78 = ( minus_minus_nat @ N @ K ) )
% 0.55/0.78 <=> ( M = N ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_176_diff__diff__cancel,axiom,
% 0.55/0.78 ! [I_1: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ I_1 @ N )
% 0.55/0.78 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I_1 ) )
% 0.55/0.78 = I_1 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_177_diff__le__mono,axiom,
% 0.55/0.78 ! [L: nat,M: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.78 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_178_diff__le__mono2,axiom,
% 0.55/0.78 ! [L: nat,M: nat,N: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.78 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_179_diff__le__self,axiom,
% 0.55/0.78 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_180_finite__surj,axiom,
% 0.55/0.78 ! [B_85: x_a > $o,F_40: x_a > x_a,A_148: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_85 @ ( image_a_a @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_181_finite__surj,axiom,
% 0.55/0.78 ! [B_85: x_a > $o,F_40: ( int > $o ) > x_a,A_148: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_85 @ ( image_int_o_a @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_182_finite__surj,axiom,
% 0.55/0.78 ! [B_85: x_a > $o,F_40: ( nat > $o ) > x_a,A_148: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_85 @ ( image_nat_o_a @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_183_finite__surj,axiom,
% 0.55/0.78 ! [B_85: x_a > $o,F_40: ( pname > $o ) > x_a,A_148: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_85 @ ( image_pname_o_a @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_184_finite__surj,axiom,
% 0.55/0.78 ! [B_85: x_a > $o,F_40: ( x_a > $o ) > x_a,A_148: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_85 @ ( image_a_o_a @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_185_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( int > $o ) > $o,F_40: pname > int > $o,A_148: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ B_85 @ ( image_pname_int_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_186_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( nat > $o ) > $o,F_40: pname > nat > $o,A_148: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ B_85 @ ( image_pname_nat_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_nat_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_187_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( pname > $o ) > $o,F_40: pname > pname > $o,A_148: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_148 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ B_85 @ ( image_pname_pname_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite297249702name_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_188_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( x_a > $o ) > $o,F_40: pname > x_a > $o,A_148: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ B_85 @ ( image_pname_a_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_189_finite__surj,axiom,
% 0.55/0.78 ! [B_85: pname > $o,F_40: pname > pname,A_148: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_85 @ ( image_pname_pname @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_pname @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_190_finite__surj,axiom,
% 0.55/0.78 ! [B_85: x_a > $o,F_40: nat > x_a,A_148: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_85 @ ( image_nat_a @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_191_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( int > $o ) > $o,F_40: nat > int > $o,A_148: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ B_85 @ ( image_nat_int_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_192_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( nat > $o ) > $o,F_40: nat > nat > $o,A_148: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ B_85 @ ( image_nat_nat_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_nat_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_193_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( pname > $o ) > $o,F_40: nat > pname > $o,A_148: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_148 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ B_85 @ ( image_nat_pname_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite297249702name_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_194_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( x_a > $o ) > $o,F_40: nat > x_a > $o,A_148: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ B_85 @ ( image_nat_a_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_195_finite__surj,axiom,
% 0.55/0.78 ! [B_85: pname > $o,F_40: nat > pname,A_148: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_85 @ ( image_nat_pname @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_pname @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_196_finite__surj,axiom,
% 0.55/0.78 ! [B_85: x_a > $o,F_40: int > x_a,A_148: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_85 @ ( image_int_a @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_197_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( int > $o ) > $o,F_40: int > int > $o,A_148: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ B_85 @ ( image_int_int_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_198_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( nat > $o ) > $o,F_40: int > nat > $o,A_148: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ B_85 @ ( image_int_nat_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_nat_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_199_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( pname > $o ) > $o,F_40: int > pname > $o,A_148: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_148 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ B_85 @ ( image_int_pname_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite297249702name_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_200_finite__surj,axiom,
% 0.55/0.78 ! [B_85: ( x_a > $o ) > $o,F_40: int > x_a > $o,A_148: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ B_85 @ ( image_int_a_o @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a_o @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_201_finite__surj,axiom,
% 0.55/0.78 ! [B_85: pname > $o,F_40: int > pname,A_148: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_85 @ ( image_int_pname @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_pname @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_202_finite__surj,axiom,
% 0.55/0.78 ! [B_85: pname > $o,F_40: x_a > pname,A_148: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_85 @ ( image_a_pname @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_pname @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_203_finite__surj,axiom,
% 0.55/0.78 ! [B_85: pname > $o,F_40: ( int > $o ) > pname,A_148: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_85 @ ( image_int_o_pname @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_pname @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_204_finite__surj,axiom,
% 0.55/0.78 ! [B_85: pname > $o,F_40: ( nat > $o ) > pname,A_148: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_85 @ ( image_nat_o_pname @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_pname @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_205_finite__surj,axiom,
% 0.55/0.78 ! [B_85: pname > $o,F_40: ( pname > $o ) > pname,A_148: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_85 @ ( image_pname_o_pname @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_pname @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_206_finite__surj,axiom,
% 0.55/0.78 ! [B_85: pname > $o,F_40: ( x_a > $o ) > pname,A_148: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_85 @ ( image_a_o_pname @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_pname @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_207_finite__surj,axiom,
% 0.55/0.78 ! [B_85: nat > $o,F_40: x_a > nat,A_148: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_85 @ ( image_a_nat @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_nat @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_208_finite__surj,axiom,
% 0.55/0.78 ! [B_85: nat > $o,F_40: ( int > $o ) > nat,A_148: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_85 @ ( image_int_o_nat @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_nat @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_209_finite__surj,axiom,
% 0.55/0.78 ! [B_85: nat > $o,F_40: ( nat > $o ) > nat,A_148: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_85 @ ( image_nat_o_nat @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_nat @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_210_finite__surj,axiom,
% 0.55/0.78 ! [B_85: nat > $o,F_40: ( pname > $o ) > nat,A_148: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_85 @ ( image_pname_o_nat @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_nat @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_211_finite__surj,axiom,
% 0.55/0.78 ! [B_85: nat > $o,F_40: ( x_a > $o ) > nat,A_148: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_85 @ ( image_a_o_nat @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_nat @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_212_finite__surj,axiom,
% 0.55/0.78 ! [B_85: int > $o,F_40: x_a > int,A_148: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_85 @ ( image_a_int @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_213_finite__surj,axiom,
% 0.55/0.78 ! [B_85: int > $o,F_40: ( int > $o ) > int,A_148: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_85 @ ( image_int_o_int @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_214_finite__surj,axiom,
% 0.55/0.78 ! [B_85: int > $o,F_40: ( nat > $o ) > int,A_148: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_85 @ ( image_nat_o_int @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_215_finite__surj,axiom,
% 0.55/0.78 ! [B_85: int > $o,F_40: ( pname > $o ) > int,A_148: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_85 @ ( image_pname_o_int @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_216_finite__surj,axiom,
% 0.55/0.78 ! [B_85: int > $o,F_40: ( x_a > $o ) > int,A_148: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_85 @ ( image_a_o_int @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_217_finite__surj,axiom,
% 0.55/0.78 ! [B_85: x_a > $o,F_40: pname > x_a,A_148: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_85 @ ( image_pname_a @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_a @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_218_finite__surj,axiom,
% 0.55/0.78 ! [B_85: int > $o,F_40: nat > int,A_148: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ A_148 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_85 @ ( image_nat_int @ F_40 @ A_148 ) )
% 0.55/0.78 => ( finite_finite_int @ B_85 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_219_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( int > $o ) > x_a,A_147: ( int > $o ) > $o,B_84: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_84 @ ( image_int_o_a @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( int > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_o_a @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_220_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( nat > $o ) > x_a,A_147: ( nat > $o ) > $o,B_84: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_84 @ ( image_nat_o_a @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_o_a @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_221_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( pname > $o ) > x_a,A_147: ( pname > $o ) > $o,B_84: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_84 @ ( image_pname_o_a @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( ord_le1205211808me_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite297249702name_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_o_a @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_222_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( x_a > $o ) > x_a,A_147: ( x_a > $o ) > $o,B_84: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_84 @ ( image_a_o_a @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_o_a @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_223_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: x_a > x_a,A_147: x_a > $o,B_84: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_84 @ ( image_a_a @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_a @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_224_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: x_a > int > $o,A_147: x_a > $o,B_84: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ B_84 @ ( image_a_int_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_int_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_225_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: x_a > nat > $o,A_147: x_a > $o,B_84: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ B_84 @ ( image_a_nat_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_nat_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_226_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: x_a > pname > $o,A_147: x_a > $o,B_84: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ B_84 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ B_84 @ ( image_a_pname_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_pname_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_227_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: x_a > x_a > $o,A_147: x_a > $o,B_84: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ B_84 @ ( image_a_a_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_a_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_228_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: x_a > pname,A_147: x_a > $o,B_84: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_84 @ ( image_a_pname @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_pname @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_229_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( int > $o ) > pname,A_147: ( int > $o ) > $o,B_84: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_84 @ ( image_int_o_pname @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( int > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_o_pname @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_230_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( nat > $o ) > pname,A_147: ( nat > $o ) > $o,B_84: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_84 @ ( image_nat_o_pname @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_o_pname @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_231_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( pname > $o ) > pname,A_147: ( pname > $o ) > $o,B_84: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_84 @ ( image_pname_o_pname @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( ord_le1205211808me_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite297249702name_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_o_pname @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_232_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( x_a > $o ) > pname,A_147: ( x_a > $o ) > $o,B_84: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_84 @ ( image_a_o_pname @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_o_pname @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_233_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: x_a > nat,A_147: x_a > $o,B_84: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_84 @ ( image_a_nat @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_nat @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_234_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( int > $o ) > nat,A_147: ( int > $o ) > $o,B_84: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_84 @ ( image_int_o_nat @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( int > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_o_nat @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_235_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( nat > $o ) > nat,A_147: ( nat > $o ) > $o,B_84: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_84 @ ( image_nat_o_nat @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_o_nat @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_236_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( pname > $o ) > nat,A_147: ( pname > $o ) > $o,B_84: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_84 @ ( image_pname_o_nat @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( ord_le1205211808me_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite297249702name_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_o_nat @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_237_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( x_a > $o ) > nat,A_147: ( x_a > $o ) > $o,B_84: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_84 @ ( image_a_o_nat @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_o_nat @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_238_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: pname > nat,A_147: pname > $o,B_84: nat > $o] :
% 0.55/0.78 ( ( finite_finite_nat @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_84 @ ( image_pname_nat @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_pname @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_nat @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_239_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: x_a > int,A_147: x_a > $o,B_84: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_84 @ ( image_a_int @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_int @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_240_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( int > $o ) > int,A_147: ( int > $o ) > $o,B_84: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_84 @ ( image_int_o_int @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( int > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_o_int @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_241_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( nat > $o ) > int,A_147: ( nat > $o ) > $o,B_84: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_84 @ ( image_nat_o_int @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_o_int @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_242_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( pname > $o ) > int,A_147: ( pname > $o ) > $o,B_84: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_84 @ ( image_pname_o_int @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( ord_le1205211808me_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite297249702name_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_o_int @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_243_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: ( x_a > $o ) > int,A_147: ( x_a > $o ) > $o,B_84: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_84 @ ( image_a_o_int @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_a_o @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_a_o_int @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_244_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: pname > int,A_147: pname > $o,B_84: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_84 @ ( image_pname_int @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_pname @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_int @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_245_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: pname > int > $o,A_147: pname > $o,B_84: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ B_84 @ ( image_pname_int_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_pname @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_int_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_246_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: pname > nat > $o,A_147: pname > $o,B_84: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ B_84 @ ( image_pname_nat_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_pname @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_nat_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_247_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: pname > pname > $o,A_147: pname > $o,B_84: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ B_84 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ B_84 @ ( image_pname_pname_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_pname @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_pname_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_248_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: pname > x_a > $o,A_147: pname > $o,B_84: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ B_84 @ ( image_pname_a_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_pname @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_a_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_249_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: pname > pname,A_147: pname > $o,B_84: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_84 @ ( image_pname_pname @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_pname @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_pname @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_250_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: nat > x_a,A_147: nat > $o,B_84: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_84 @ ( image_nat_a @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_a @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_251_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: nat > int > $o,A_147: nat > $o,B_84: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ B_84 @ ( image_nat_int_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_int_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_252_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: nat > nat > $o,A_147: nat > $o,B_84: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ B_84 @ ( image_nat_nat_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_nat_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_253_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: nat > pname > $o,A_147: nat > $o,B_84: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ B_84 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ B_84 @ ( image_nat_pname_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_pname_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_254_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: nat > x_a > $o,A_147: nat > $o,B_84: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ B_84 @ ( image_nat_a_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_a_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_255_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: nat > pname,A_147: nat > $o,B_84: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_84 @ ( image_nat_pname @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_pname @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_256_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: int > x_a,A_147: int > $o,B_84: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_84 @ ( image_int_a @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_a @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_257_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: int > int > $o,A_147: int > $o,B_84: ( int > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_int_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o_o @ B_84 @ ( image_int_int_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_int_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_258_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: int > nat > $o,A_147: int > $o,B_84: ( nat > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_nat_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o_o @ B_84 @ ( image_int_nat_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_nat_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_259_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: int > pname > $o,A_147: int > $o,B_84: ( pname > $o ) > $o] :
% 0.55/0.78 ( ( finite297249702name_o @ B_84 )
% 0.55/0.78 => ( ( ord_le1205211808me_o_o @ B_84 @ ( image_int_pname_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_pname_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_260_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: int > x_a > $o,A_147: int > $o,B_84: ( x_a > $o ) > $o] :
% 0.55/0.78 ( ( finite_finite_a_o @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o_o @ B_84 @ ( image_int_a_o @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_a_o @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_261_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: int > pname,A_147: int > $o,B_84: pname > $o] :
% 0.55/0.78 ( ( finite_finite_pname @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_pname_o @ B_84 @ ( image_int_pname @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_int @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_int_pname @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_262_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: pname > x_a,A_147: pname > $o,B_84: x_a > $o] :
% 0.55/0.78 ( ( finite_finite_a @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_84 @ ( image_pname_a @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_pname @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_pname_a @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_263_finite__subset__image,axiom,
% 0.55/0.78 ! [F_39: nat > int,A_147: nat > $o,B_84: int > $o] :
% 0.55/0.78 ( ( finite_finite_int @ B_84 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_84 @ ( image_nat_int @ F_39 @ A_147 ) )
% 0.55/0.78 => ? [C_34: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ C_34 @ A_147 )
% 0.55/0.78 & ( finite_finite_nat @ C_34 )
% 0.55/0.78 & ( B_84
% 0.55/0.78 = ( image_nat_int @ F_39 @ C_34 ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_264_lift__Suc__mono__le,axiom,
% 0.55/0.78 ! [N_4: nat,N_3: nat,F_38: nat > pname > $o] :
% 0.55/0.78 ( ! [N_1: nat] : ( ord_less_eq_pname_o @ ( F_38 @ N_1 ) @ ( F_38 @ ( suc @ N_1 ) ) )
% 0.55/0.78 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.55/0.78 => ( ord_less_eq_pname_o @ ( F_38 @ N_4 ) @ ( F_38 @ N_3 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_265_lift__Suc__mono__le,axiom,
% 0.55/0.78 ! [N_4: nat,N_3: nat,F_38: nat > $o] :
% 0.55/0.78 ( ! [N_1: nat] : ( ord_less_eq_o @ ( F_38 @ N_1 ) @ ( F_38 @ ( suc @ N_1 ) ) )
% 0.55/0.78 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.55/0.78 => ( ord_less_eq_o @ ( F_38 @ N_4 ) @ ( F_38 @ N_3 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_266_lift__Suc__mono__le,axiom,
% 0.55/0.78 ! [N_4: nat,N_3: nat,F_38: nat > x_a > $o] :
% 0.55/0.78 ( ! [N_1: nat] : ( ord_less_eq_a_o @ ( F_38 @ N_1 ) @ ( F_38 @ ( suc @ N_1 ) ) )
% 0.55/0.78 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.55/0.78 => ( ord_less_eq_a_o @ ( F_38 @ N_4 ) @ ( F_38 @ N_3 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_267_lift__Suc__mono__le,axiom,
% 0.55/0.78 ! [N_4: nat,N_3: nat,F_38: nat > nat] :
% 0.55/0.78 ( ! [N_1: nat] : ( ord_less_eq_nat @ ( F_38 @ N_1 ) @ ( F_38 @ ( suc @ N_1 ) ) )
% 0.55/0.78 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.55/0.78 => ( ord_less_eq_nat @ ( F_38 @ N_4 ) @ ( F_38 @ N_3 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_268_lift__Suc__mono__le,axiom,
% 0.55/0.78 ! [N_4: nat,N_3: nat,F_38: nat > int] :
% 0.55/0.78 ( ! [N_1: nat] : ( ord_less_eq_int @ ( F_38 @ N_1 ) @ ( F_38 @ ( suc @ N_1 ) ) )
% 0.55/0.78 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.55/0.78 => ( ord_less_eq_int @ ( F_38 @ N_4 ) @ ( F_38 @ N_3 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_269_lift__Suc__mono__le,axiom,
% 0.55/0.78 ! [N_4: nat,N_3: nat,F_38: nat > nat > $o] :
% 0.55/0.78 ( ! [N_1: nat] : ( ord_less_eq_nat_o @ ( F_38 @ N_1 ) @ ( F_38 @ ( suc @ N_1 ) ) )
% 0.55/0.78 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.55/0.78 => ( ord_less_eq_nat_o @ ( F_38 @ N_4 ) @ ( F_38 @ N_3 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_270_lift__Suc__mono__le,axiom,
% 0.55/0.78 ! [N_4: nat,N_3: nat,F_38: nat > int > $o] :
% 0.55/0.78 ( ! [N_1: nat] : ( ord_less_eq_int_o @ ( F_38 @ N_1 ) @ ( F_38 @ ( suc @ N_1 ) ) )
% 0.55/0.78 => ( ( ord_less_eq_nat @ N_4 @ N_3 )
% 0.55/0.78 => ( ord_less_eq_int_o @ ( F_38 @ N_4 ) @ ( F_38 @ N_3 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_271_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: nat > int > $o,A_146: nat > $o] :
% 0.55/0.78 ( ~ ( finite_finite_nat @ A_146 )
% 0.55/0.78 => ( ( finite_finite_int_o @ ( image_nat_int_o @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: nat] :
% 0.55/0.78 ( ( member_nat @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [A_37: nat] :
% 0.55/0.78 ( (&) @ ( member_nat @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_272_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: nat > nat > $o,A_146: nat > $o] :
% 0.55/0.78 ( ~ ( finite_finite_nat @ A_146 )
% 0.55/0.78 => ( ( finite_finite_nat_o @ ( image_nat_nat_o @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: nat] :
% 0.55/0.78 ( ( member_nat @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [A_37: nat] :
% 0.55/0.78 ( (&) @ ( member_nat @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_273_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: nat > pname > $o,A_146: nat > $o] :
% 0.55/0.78 ( ~ ( finite_finite_nat @ A_146 )
% 0.55/0.78 => ( ( finite297249702name_o @ ( image_nat_pname_o @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: nat] :
% 0.55/0.78 ( ( member_nat @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [A_37: nat] :
% 0.55/0.78 ( (&) @ ( member_nat @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_274_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: nat > x_a > $o,A_146: nat > $o] :
% 0.55/0.78 ( ~ ( finite_finite_nat @ A_146 )
% 0.55/0.78 => ( ( finite_finite_a_o @ ( image_nat_a_o @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: nat] :
% 0.55/0.78 ( ( member_nat @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [A_37: nat] :
% 0.55/0.78 ( (&) @ ( member_nat @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_275_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: int > x_a,A_146: int > $o] :
% 0.55/0.78 ( ~ ( finite_finite_int @ A_146 )
% 0.55/0.78 => ( ( finite_finite_a @ ( image_int_a @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: int] :
% 0.55/0.78 ( ( member_int @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_int
% 0.55/0.78 @ ( collect_int
% 0.55/0.78 @ ^ [A_37: int] :
% 0.55/0.78 ( (&) @ ( member_int @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_276_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: int > int > $o,A_146: int > $o] :
% 0.55/0.78 ( ~ ( finite_finite_int @ A_146 )
% 0.55/0.78 => ( ( finite_finite_int_o @ ( image_int_int_o @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: int] :
% 0.55/0.78 ( ( member_int @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_int
% 0.55/0.78 @ ( collect_int
% 0.55/0.78 @ ^ [A_37: int] :
% 0.55/0.78 ( (&) @ ( member_int @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_277_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: int > nat > $o,A_146: int > $o] :
% 0.55/0.78 ( ~ ( finite_finite_int @ A_146 )
% 0.55/0.78 => ( ( finite_finite_nat_o @ ( image_int_nat_o @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: int] :
% 0.55/0.78 ( ( member_int @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_int
% 0.55/0.78 @ ( collect_int
% 0.55/0.78 @ ^ [A_37: int] :
% 0.55/0.78 ( (&) @ ( member_int @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_278_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: int > pname > $o,A_146: int > $o] :
% 0.55/0.78 ( ~ ( finite_finite_int @ A_146 )
% 0.55/0.78 => ( ( finite297249702name_o @ ( image_int_pname_o @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: int] :
% 0.55/0.78 ( ( member_int @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_int
% 0.55/0.78 @ ( collect_int
% 0.55/0.78 @ ^ [A_37: int] :
% 0.55/0.78 ( (&) @ ( member_int @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_279_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: int > x_a > $o,A_146: int > $o] :
% 0.55/0.78 ( ~ ( finite_finite_int @ A_146 )
% 0.55/0.78 => ( ( finite_finite_a_o @ ( image_int_a_o @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: int] :
% 0.55/0.78 ( ( member_int @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_int
% 0.55/0.78 @ ( collect_int
% 0.55/0.78 @ ^ [A_37: int] :
% 0.55/0.78 ( (&) @ ( member_int @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_280_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: pname > x_a,A_146: pname > $o] :
% 0.55/0.78 ( ~ ( finite_finite_pname @ A_146 )
% 0.55/0.78 => ( ( finite_finite_a @ ( image_pname_a @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: pname] :
% 0.55/0.78 ( ( member_pname @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_pname
% 0.55/0.78 @ ( collect_pname
% 0.55/0.78 @ ^ [A_37: pname] :
% 0.55/0.78 ( (&) @ ( member_pname @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_281_pigeonhole__infinite,axiom,
% 0.55/0.78 ! [F_37: nat > int,A_146: nat > $o] :
% 0.55/0.78 ( ~ ( finite_finite_nat @ A_146 )
% 0.55/0.78 => ( ( finite_finite_int @ ( image_nat_int @ F_37 @ A_146 ) )
% 0.55/0.78 => ? [X_1: nat] :
% 0.55/0.78 ( ( member_nat @ X_1 @ A_146 )
% 0.55/0.78 & ~ ( finite_finite_nat
% 0.55/0.78 @ ( collect_nat
% 0.55/0.78 @ ^ [A_37: nat] :
% 0.55/0.78 ( (&) @ ( member_nat @ A_37 @ A_146 )
% 0.55/0.78 @ ( ( F_37 @ A_37 )
% 0.55/0.78 = ( F_37 @ X_1 ) ) ) ) ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_282_image__eqI,axiom,
% 0.55/0.78 ! [A_145: nat > $o,B_83: int,F_36: nat > int,X_50: nat] :
% 0.55/0.78 ( ( B_83
% 0.55/0.78 = ( F_36 @ X_50 ) )
% 0.55/0.78 => ( ( member_nat @ X_50 @ A_145 )
% 0.55/0.78 => ( member_int @ B_83 @ ( image_nat_int @ F_36 @ A_145 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_283_image__eqI,axiom,
% 0.55/0.78 ! [A_145: pname > $o,B_83: x_a,F_36: pname > x_a,X_50: pname] :
% 0.55/0.78 ( ( B_83
% 0.55/0.78 = ( F_36 @ X_50 ) )
% 0.55/0.78 => ( ( member_pname @ X_50 @ A_145 )
% 0.55/0.78 => ( member_a @ B_83 @ ( image_pname_a @ F_36 @ A_145 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_284_equalityI,axiom,
% 0.55/0.78 ! [A_144: int > $o,B_82: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ A_144 @ B_82 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_82 @ A_144 )
% 0.55/0.78 => ( A_144 = B_82 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_285_equalityI,axiom,
% 0.55/0.78 ! [A_144: nat > $o,B_82: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ A_144 @ B_82 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_82 @ A_144 )
% 0.55/0.78 => ( A_144 = B_82 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_286_equalityI,axiom,
% 0.55/0.78 ! [A_144: x_a > $o,B_82: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ A_144 @ B_82 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ B_82 @ A_144 )
% 0.55/0.78 => ( A_144 = B_82 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_287_subsetD,axiom,
% 0.55/0.78 ! [C_33: int,A_143: int > $o,B_81: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ A_143 @ B_81 )
% 0.55/0.78 => ( ( member_int @ C_33 @ A_143 )
% 0.55/0.78 => ( member_int @ C_33 @ B_81 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_288_subsetD,axiom,
% 0.55/0.78 ! [C_33: nat,A_143: nat > $o,B_81: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ A_143 @ B_81 )
% 0.55/0.78 => ( ( member_nat @ C_33 @ A_143 )
% 0.55/0.78 => ( member_nat @ C_33 @ B_81 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_289_subsetD,axiom,
% 0.55/0.78 ! [C_33: x_a,A_143: x_a > $o,B_81: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ A_143 @ B_81 )
% 0.55/0.78 => ( ( member_a @ C_33 @ A_143 )
% 0.55/0.78 => ( member_a @ C_33 @ B_81 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_290_subsetD,axiom,
% 0.55/0.78 ! [C_33: pname,A_143: pname > $o,B_81: pname > $o] :
% 0.55/0.78 ( ( ord_less_eq_pname_o @ A_143 @ B_81 )
% 0.55/0.78 => ( ( member_pname @ C_33 @ A_143 )
% 0.55/0.78 => ( member_pname @ C_33 @ B_81 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_291_insertCI,axiom,
% 0.55/0.78 ! [B_80: x_a,A_142: x_a,B_79: x_a > $o] :
% 0.55/0.78 ( ( ~ ( member_a @ A_142 @ B_79 )
% 0.55/0.78 => ( A_142 = B_80 ) )
% 0.55/0.78 => ( member_a @ A_142 @ ( insert_a @ B_80 @ B_79 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_292_insertCI,axiom,
% 0.55/0.78 ! [B_80: int,A_142: int,B_79: int > $o] :
% 0.55/0.78 ( ( ~ ( member_int @ A_142 @ B_79 )
% 0.55/0.78 => ( A_142 = B_80 ) )
% 0.55/0.78 => ( member_int @ A_142 @ ( insert_int @ B_80 @ B_79 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_293_insertCI,axiom,
% 0.55/0.78 ! [B_80: nat,A_142: nat,B_79: nat > $o] :
% 0.55/0.78 ( ( ~ ( member_nat @ A_142 @ B_79 )
% 0.55/0.78 => ( A_142 = B_80 ) )
% 0.55/0.78 => ( member_nat @ A_142 @ ( insert_nat @ B_80 @ B_79 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_294_insertCI,axiom,
% 0.55/0.78 ! [B_80: pname,A_142: pname,B_79: pname > $o] :
% 0.55/0.78 ( ( ~ ( member_pname @ A_142 @ B_79 )
% 0.55/0.78 => ( A_142 = B_80 ) )
% 0.55/0.78 => ( member_pname @ A_142 @ ( insert_pname @ B_80 @ B_79 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_295_insertE,axiom,
% 0.55/0.78 ! [A_141: x_a,B_78: x_a,A_140: x_a > $o] :
% 0.55/0.78 ( ( member_a @ A_141 @ ( insert_a @ B_78 @ A_140 ) )
% 0.55/0.78 => ( ( A_141 != B_78 )
% 0.55/0.78 => ( member_a @ A_141 @ A_140 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_296_insertE,axiom,
% 0.55/0.78 ! [A_141: int,B_78: int,A_140: int > $o] :
% 0.55/0.78 ( ( member_int @ A_141 @ ( insert_int @ B_78 @ A_140 ) )
% 0.55/0.78 => ( ( A_141 != B_78 )
% 0.55/0.78 => ( member_int @ A_141 @ A_140 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_297_insertE,axiom,
% 0.55/0.78 ! [A_141: nat,B_78: nat,A_140: nat > $o] :
% 0.55/0.78 ( ( member_nat @ A_141 @ ( insert_nat @ B_78 @ A_140 ) )
% 0.55/0.78 => ( ( A_141 != B_78 )
% 0.55/0.78 => ( member_nat @ A_141 @ A_140 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_298_insertE,axiom,
% 0.55/0.78 ! [A_141: pname,B_78: pname,A_140: pname > $o] :
% 0.55/0.78 ( ( member_pname @ A_141 @ ( insert_pname @ B_78 @ A_140 ) )
% 0.55/0.78 => ( ( A_141 != B_78 )
% 0.55/0.78 => ( member_pname @ A_141 @ A_140 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_299_zero__induct__lemma,axiom,
% 0.55/0.78 ! [I_1: nat,P: nat > $o,K: nat] :
% 0.55/0.78 ( ( P @ K )
% 0.55/0.78 => ( ! [N_1: nat] :
% 0.55/0.78 ( ( P @ ( suc @ N_1 ) )
% 0.55/0.78 => ( P @ N_1 ) )
% 0.55/0.78 => ( P @ ( minus_minus_nat @ K @ I_1 ) ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_300_Suc__le__D,axiom,
% 0.55/0.78 ! [N: nat,M_3: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ ( suc @ N ) @ M_3 )
% 0.55/0.78 => ? [M_1: nat] :
% 0.55/0.78 ( M_3
% 0.55/0.78 = ( suc @ M_1 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_301_order__refl,axiom,
% 0.55/0.78 ! [X_49: int > $o] : ( ord_less_eq_int_o @ X_49 @ X_49 ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_302_order__refl,axiom,
% 0.55/0.78 ! [X_49: nat > $o] : ( ord_less_eq_nat_o @ X_49 @ X_49 ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_303_order__refl,axiom,
% 0.55/0.78 ! [X_49: int] : ( ord_less_eq_int @ X_49 @ X_49 ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_304_order__refl,axiom,
% 0.55/0.78 ! [X_49: nat] : ( ord_less_eq_nat @ X_49 @ X_49 ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_305_order__refl,axiom,
% 0.55/0.78 ! [X_49: x_a > $o] : ( ord_less_eq_a_o @ X_49 @ X_49 ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_306_linorder__linear,axiom,
% 0.55/0.78 ! [X_48: int,Y_12: int] :
% 0.55/0.78 ( ( ord_less_eq_int @ X_48 @ Y_12 )
% 0.55/0.78 | ( ord_less_eq_int @ Y_12 @ X_48 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_307_linorder__linear,axiom,
% 0.55/0.78 ! [X_48: nat,Y_12: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ X_48 @ Y_12 )
% 0.55/0.78 | ( ord_less_eq_nat @ Y_12 @ X_48 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_308_order__eq__iff,axiom,
% 0.55/0.78 ! [X_47: int > $o,Y_11: int > $o] :
% 0.55/0.78 ( ( X_47 = Y_11 )
% 0.55/0.78 <=> ( ( ord_less_eq_int_o @ X_47 @ Y_11 )
% 0.55/0.78 & ( ord_less_eq_int_o @ Y_11 @ X_47 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_309_order__eq__iff,axiom,
% 0.55/0.78 ! [X_47: nat > $o,Y_11: nat > $o] :
% 0.55/0.78 ( ( X_47 = Y_11 )
% 0.55/0.78 <=> ( ( ord_less_eq_nat_o @ X_47 @ Y_11 )
% 0.55/0.78 & ( ord_less_eq_nat_o @ Y_11 @ X_47 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_310_order__eq__iff,axiom,
% 0.55/0.78 ! [X_47: int,Y_11: int] :
% 0.55/0.78 ( ( X_47 = Y_11 )
% 0.55/0.78 <=> ( ( ord_less_eq_int @ X_47 @ Y_11 )
% 0.55/0.78 & ( ord_less_eq_int @ Y_11 @ X_47 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_311_order__eq__iff,axiom,
% 0.55/0.78 ! [X_47: nat,Y_11: nat] :
% 0.55/0.78 ( ( X_47 = Y_11 )
% 0.55/0.78 <=> ( ( ord_less_eq_nat @ X_47 @ Y_11 )
% 0.55/0.78 & ( ord_less_eq_nat @ Y_11 @ X_47 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_312_order__eq__iff,axiom,
% 0.55/0.78 ! [X_47: x_a > $o,Y_11: x_a > $o] :
% 0.55/0.78 ( ( X_47 = Y_11 )
% 0.55/0.78 <=> ( ( ord_less_eq_a_o @ X_47 @ Y_11 )
% 0.55/0.78 & ( ord_less_eq_a_o @ Y_11 @ X_47 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_313_order__eq__refl,axiom,
% 0.55/0.78 ! [X_46: int > $o,Y_10: int > $o] :
% 0.55/0.78 ( ( X_46 = Y_10 )
% 0.55/0.78 => ( ord_less_eq_int_o @ X_46 @ Y_10 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_314_order__eq__refl,axiom,
% 0.55/0.78 ! [X_46: nat > $o,Y_10: nat > $o] :
% 0.55/0.78 ( ( X_46 = Y_10 )
% 0.55/0.78 => ( ord_less_eq_nat_o @ X_46 @ Y_10 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_315_order__eq__refl,axiom,
% 0.55/0.78 ! [X_46: int,Y_10: int] :
% 0.55/0.78 ( ( X_46 = Y_10 )
% 0.55/0.78 => ( ord_less_eq_int @ X_46 @ Y_10 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_316_order__eq__refl,axiom,
% 0.55/0.78 ! [X_46: nat,Y_10: nat] :
% 0.55/0.78 ( ( X_46 = Y_10 )
% 0.55/0.78 => ( ord_less_eq_nat @ X_46 @ Y_10 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_317_order__eq__refl,axiom,
% 0.55/0.78 ! [X_46: x_a > $o,Y_10: x_a > $o] :
% 0.55/0.78 ( ( X_46 = Y_10 )
% 0.55/0.78 => ( ord_less_eq_a_o @ X_46 @ Y_10 ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_318_order__antisym__conv,axiom,
% 0.55/0.78 ! [Y_9: int > $o,X_45: int > $o] :
% 0.55/0.78 ( ( ord_less_eq_int_o @ Y_9 @ X_45 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ X_45 @ Y_9 )
% 0.55/0.78 <=> ( X_45 = Y_9 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_319_order__antisym__conv,axiom,
% 0.55/0.78 ! [Y_9: nat > $o,X_45: nat > $o] :
% 0.55/0.78 ( ( ord_less_eq_nat_o @ Y_9 @ X_45 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ X_45 @ Y_9 )
% 0.55/0.78 <=> ( X_45 = Y_9 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_320_order__antisym__conv,axiom,
% 0.55/0.78 ! [Y_9: int,X_45: int] :
% 0.55/0.78 ( ( ord_less_eq_int @ Y_9 @ X_45 )
% 0.55/0.78 => ( ( ord_less_eq_int @ X_45 @ Y_9 )
% 0.55/0.78 <=> ( X_45 = Y_9 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_321_order__antisym__conv,axiom,
% 0.55/0.78 ! [Y_9: nat,X_45: nat] :
% 0.55/0.78 ( ( ord_less_eq_nat @ Y_9 @ X_45 )
% 0.55/0.78 => ( ( ord_less_eq_nat @ X_45 @ Y_9 )
% 0.55/0.78 <=> ( X_45 = Y_9 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_322_order__antisym__conv,axiom,
% 0.55/0.78 ! [Y_9: x_a > $o,X_45: x_a > $o] :
% 0.55/0.78 ( ( ord_less_eq_a_o @ Y_9 @ X_45 )
% 0.55/0.78 => ( ( ord_less_eq_a_o @ X_45 @ Y_9 )
% 0.55/0.78 <=> ( X_45 = Y_9 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_323_ord__eq__le__trans,axiom,
% 0.55/0.78 ! [C_32: int > $o,A_139: int > $o,B_77: int > $o] :
% 0.55/0.78 ( ( A_139 = B_77 )
% 0.55/0.78 => ( ( ord_less_eq_int_o @ B_77 @ C_32 )
% 0.55/0.78 => ( ord_less_eq_int_o @ A_139 @ C_32 ) ) ) ).
% 0.55/0.78
% 0.55/0.78 thf(fact_324_ord__eq__le__trans,axiom,
% 0.55/0.78 ! [C_32: nat > $o,A_139: nat > $o,B_77: nat > $o] :
% 0.55/0.78 ( ( A_139 = B_77 )
% 0.55/0.78 => ( ( ord_less_eq_nat_o @ B_77 @ C_32 )
% 0.55/0.78 => ( ord_less_eq_nat_o @ A_139 @ C_32 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_325_ord__eq__le__trans,axiom,
% 0.55/0.79 ! [C_32: int,A_139: int,B_77: int] :
% 0.55/0.79 ( ( A_139 = B_77 )
% 0.55/0.79 => ( ( ord_less_eq_int @ B_77 @ C_32 )
% 0.55/0.79 => ( ord_less_eq_int @ A_139 @ C_32 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_326_ord__eq__le__trans,axiom,
% 0.55/0.79 ! [C_32: nat,A_139: nat,B_77: nat] :
% 0.55/0.79 ( ( A_139 = B_77 )
% 0.55/0.79 => ( ( ord_less_eq_nat @ B_77 @ C_32 )
% 0.55/0.79 => ( ord_less_eq_nat @ A_139 @ C_32 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_327_ord__eq__le__trans,axiom,
% 0.55/0.79 ! [C_32: x_a > $o,A_139: x_a > $o,B_77: x_a > $o] :
% 0.55/0.79 ( ( A_139 = B_77 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ B_77 @ C_32 )
% 0.55/0.79 => ( ord_less_eq_a_o @ A_139 @ C_32 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_328_xt1_I3_J,axiom,
% 0.55/0.79 ! [C_31: int > $o,A_138: int > $o,B_76: int > $o] :
% 0.55/0.79 ( ( A_138 = B_76 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ C_31 @ B_76 )
% 0.55/0.79 => ( ord_less_eq_int_o @ C_31 @ A_138 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_329_xt1_I3_J,axiom,
% 0.55/0.79 ! [C_31: nat > $o,A_138: nat > $o,B_76: nat > $o] :
% 0.55/0.79 ( ( A_138 = B_76 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ C_31 @ B_76 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ C_31 @ A_138 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_330_xt1_I3_J,axiom,
% 0.55/0.79 ! [C_31: int,A_138: int,B_76: int] :
% 0.55/0.79 ( ( A_138 = B_76 )
% 0.55/0.79 => ( ( ord_less_eq_int @ C_31 @ B_76 )
% 0.55/0.79 => ( ord_less_eq_int @ C_31 @ A_138 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_331_xt1_I3_J,axiom,
% 0.55/0.79 ! [C_31: nat,A_138: nat,B_76: nat] :
% 0.55/0.79 ( ( A_138 = B_76 )
% 0.55/0.79 => ( ( ord_less_eq_nat @ C_31 @ B_76 )
% 0.55/0.79 => ( ord_less_eq_nat @ C_31 @ A_138 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_332_xt1_I3_J,axiom,
% 0.55/0.79 ! [C_31: x_a > $o,A_138: x_a > $o,B_76: x_a > $o] :
% 0.55/0.79 ( ( A_138 = B_76 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ C_31 @ B_76 )
% 0.55/0.79 => ( ord_less_eq_a_o @ C_31 @ A_138 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_333_ord__le__eq__trans,axiom,
% 0.55/0.79 ! [C_30: int > $o,A_137: int > $o,B_75: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_137 @ B_75 )
% 0.55/0.79 => ( ( B_75 = C_30 )
% 0.55/0.79 => ( ord_less_eq_int_o @ A_137 @ C_30 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_334_ord__le__eq__trans,axiom,
% 0.55/0.79 ! [C_30: nat > $o,A_137: nat > $o,B_75: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_137 @ B_75 )
% 0.55/0.79 => ( ( B_75 = C_30 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ A_137 @ C_30 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_335_ord__le__eq__trans,axiom,
% 0.55/0.79 ! [C_30: int,A_137: int,B_75: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ A_137 @ B_75 )
% 0.55/0.79 => ( ( B_75 = C_30 )
% 0.55/0.79 => ( ord_less_eq_int @ A_137 @ C_30 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_336_ord__le__eq__trans,axiom,
% 0.55/0.79 ! [C_30: nat,A_137: nat,B_75: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ A_137 @ B_75 )
% 0.55/0.79 => ( ( B_75 = C_30 )
% 0.55/0.79 => ( ord_less_eq_nat @ A_137 @ C_30 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_337_ord__le__eq__trans,axiom,
% 0.55/0.79 ! [C_30: x_a > $o,A_137: x_a > $o,B_75: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_137 @ B_75 )
% 0.55/0.79 => ( ( B_75 = C_30 )
% 0.55/0.79 => ( ord_less_eq_a_o @ A_137 @ C_30 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_338_xt1_I4_J,axiom,
% 0.55/0.79 ! [C_29: int > $o,B_74: int > $o,A_136: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ B_74 @ A_136 )
% 0.55/0.79 => ( ( B_74 = C_29 )
% 0.55/0.79 => ( ord_less_eq_int_o @ C_29 @ A_136 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_339_xt1_I4_J,axiom,
% 0.55/0.79 ! [C_29: nat > $o,B_74: nat > $o,A_136: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ B_74 @ A_136 )
% 0.55/0.79 => ( ( B_74 = C_29 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ C_29 @ A_136 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_340_xt1_I4_J,axiom,
% 0.55/0.79 ! [C_29: int,B_74: int,A_136: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ B_74 @ A_136 )
% 0.55/0.79 => ( ( B_74 = C_29 )
% 0.55/0.79 => ( ord_less_eq_int @ C_29 @ A_136 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_341_xt1_I4_J,axiom,
% 0.55/0.79 ! [C_29: nat,B_74: nat,A_136: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ B_74 @ A_136 )
% 0.55/0.79 => ( ( B_74 = C_29 )
% 0.55/0.79 => ( ord_less_eq_nat @ C_29 @ A_136 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_342_xt1_I4_J,axiom,
% 0.55/0.79 ! [C_29: x_a > $o,B_74: x_a > $o,A_136: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ B_74 @ A_136 )
% 0.55/0.79 => ( ( B_74 = C_29 )
% 0.55/0.79 => ( ord_less_eq_a_o @ C_29 @ A_136 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_343_order__antisym,axiom,
% 0.55/0.79 ! [X_44: int > $o,Y_8: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ X_44 @ Y_8 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ Y_8 @ X_44 )
% 0.55/0.79 => ( X_44 = Y_8 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_344_order__antisym,axiom,
% 0.55/0.79 ! [X_44: nat > $o,Y_8: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ X_44 @ Y_8 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ Y_8 @ X_44 )
% 0.55/0.79 => ( X_44 = Y_8 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_345_order__antisym,axiom,
% 0.55/0.79 ! [X_44: int,Y_8: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ X_44 @ Y_8 )
% 0.55/0.79 => ( ( ord_less_eq_int @ Y_8 @ X_44 )
% 0.55/0.79 => ( X_44 = Y_8 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_346_order__antisym,axiom,
% 0.55/0.79 ! [X_44: nat,Y_8: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ X_44 @ Y_8 )
% 0.55/0.79 => ( ( ord_less_eq_nat @ Y_8 @ X_44 )
% 0.55/0.79 => ( X_44 = Y_8 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_347_order__antisym,axiom,
% 0.55/0.79 ! [X_44: x_a > $o,Y_8: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ X_44 @ Y_8 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ Y_8 @ X_44 )
% 0.55/0.79 => ( X_44 = Y_8 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_348_order__trans,axiom,
% 0.55/0.79 ! [Z_6: int > $o,X_43: int > $o,Y_7: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ X_43 @ Y_7 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ Y_7 @ Z_6 )
% 0.55/0.79 => ( ord_less_eq_int_o @ X_43 @ Z_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_349_order__trans,axiom,
% 0.55/0.79 ! [Z_6: nat > $o,X_43: nat > $o,Y_7: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ X_43 @ Y_7 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ Y_7 @ Z_6 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ X_43 @ Z_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_350_order__trans,axiom,
% 0.55/0.79 ! [Z_6: int,X_43: int,Y_7: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ X_43 @ Y_7 )
% 0.55/0.79 => ( ( ord_less_eq_int @ Y_7 @ Z_6 )
% 0.55/0.79 => ( ord_less_eq_int @ X_43 @ Z_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_351_order__trans,axiom,
% 0.55/0.79 ! [Z_6: nat,X_43: nat,Y_7: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ X_43 @ Y_7 )
% 0.55/0.79 => ( ( ord_less_eq_nat @ Y_7 @ Z_6 )
% 0.55/0.79 => ( ord_less_eq_nat @ X_43 @ Z_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_352_order__trans,axiom,
% 0.55/0.79 ! [Z_6: x_a > $o,X_43: x_a > $o,Y_7: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ X_43 @ Y_7 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ Y_7 @ Z_6 )
% 0.55/0.79 => ( ord_less_eq_a_o @ X_43 @ Z_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_353_xt1_I5_J,axiom,
% 0.55/0.79 ! [Y_6: int > $o,X_42: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ Y_6 @ X_42 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ X_42 @ Y_6 )
% 0.55/0.79 => ( X_42 = Y_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_354_xt1_I5_J,axiom,
% 0.55/0.79 ! [Y_6: nat > $o,X_42: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ Y_6 @ X_42 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ X_42 @ Y_6 )
% 0.55/0.79 => ( X_42 = Y_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_355_xt1_I5_J,axiom,
% 0.55/0.79 ! [Y_6: int,X_42: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ Y_6 @ X_42 )
% 0.55/0.79 => ( ( ord_less_eq_int @ X_42 @ Y_6 )
% 0.55/0.79 => ( X_42 = Y_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_356_xt1_I5_J,axiom,
% 0.55/0.79 ! [Y_6: nat,X_42: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ Y_6 @ X_42 )
% 0.55/0.79 => ( ( ord_less_eq_nat @ X_42 @ Y_6 )
% 0.55/0.79 => ( X_42 = Y_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_357_xt1_I5_J,axiom,
% 0.55/0.79 ! [Y_6: x_a > $o,X_42: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ Y_6 @ X_42 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ X_42 @ Y_6 )
% 0.55/0.79 => ( X_42 = Y_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_358_xt1_I6_J,axiom,
% 0.55/0.79 ! [Z_5: int > $o,Y_5: int > $o,X_41: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ Y_5 @ X_41 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ Z_5 @ Y_5 )
% 0.55/0.79 => ( ord_less_eq_int_o @ Z_5 @ X_41 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_359_xt1_I6_J,axiom,
% 0.55/0.79 ! [Z_5: nat > $o,Y_5: nat > $o,X_41: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ Y_5 @ X_41 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ Z_5 @ Y_5 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ Z_5 @ X_41 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_360_xt1_I6_J,axiom,
% 0.55/0.79 ! [Z_5: int,Y_5: int,X_41: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ Y_5 @ X_41 )
% 0.55/0.79 => ( ( ord_less_eq_int @ Z_5 @ Y_5 )
% 0.55/0.79 => ( ord_less_eq_int @ Z_5 @ X_41 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_361_xt1_I6_J,axiom,
% 0.55/0.79 ! [Z_5: nat,Y_5: nat,X_41: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ Y_5 @ X_41 )
% 0.55/0.79 => ( ( ord_less_eq_nat @ Z_5 @ Y_5 )
% 0.55/0.79 => ( ord_less_eq_nat @ Z_5 @ X_41 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_362_xt1_I6_J,axiom,
% 0.55/0.79 ! [Z_5: x_a > $o,Y_5: x_a > $o,X_41: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ Y_5 @ X_41 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ Z_5 @ Y_5 )
% 0.55/0.79 => ( ord_less_eq_a_o @ Z_5 @ X_41 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_363_linorder__le__cases,axiom,
% 0.55/0.79 ! [X_40: int,Y_4: int] :
% 0.55/0.79 ( ~ ( ord_less_eq_int @ X_40 @ Y_4 )
% 0.55/0.79 => ( ord_less_eq_int @ Y_4 @ X_40 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_364_linorder__le__cases,axiom,
% 0.55/0.79 ! [X_40: nat,Y_4: nat] :
% 0.55/0.79 ( ~ ( ord_less_eq_nat @ X_40 @ Y_4 )
% 0.55/0.79 => ( ord_less_eq_nat @ Y_4 @ X_40 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_365_insertI1,axiom,
% 0.55/0.79 ! [A_135: x_a,B_73: x_a > $o] : ( member_a @ A_135 @ ( insert_a @ A_135 @ B_73 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_366_insertI1,axiom,
% 0.55/0.79 ! [A_135: int,B_73: int > $o] : ( member_int @ A_135 @ ( insert_int @ A_135 @ B_73 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_367_insertI1,axiom,
% 0.55/0.79 ! [A_135: nat,B_73: nat > $o] : ( member_nat @ A_135 @ ( insert_nat @ A_135 @ B_73 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_368_insertI1,axiom,
% 0.55/0.79 ! [A_135: pname,B_73: pname > $o] : ( member_pname @ A_135 @ ( insert_pname @ A_135 @ B_73 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_369_insert__compr,axiom,
% 0.55/0.79 ! [A_134: x_a,B_72: x_a > $o] :
% 0.55/0.79 ( ( insert_a @ A_134 @ B_72 )
% 0.55/0.79 = ( collect_a
% 0.55/0.79 @ ^ [X_1: x_a] : ( (|) @ ( X_1 = A_134 ) @ ( member_a @ X_1 @ B_72 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_370_insert__compr,axiom,
% 0.55/0.79 ! [A_134: int,B_72: int > $o] :
% 0.55/0.79 ( ( insert_int @ A_134 @ B_72 )
% 0.55/0.79 = ( collect_int
% 0.55/0.79 @ ^ [X_1: int] : ( (|) @ ( X_1 = A_134 ) @ ( member_int @ X_1 @ B_72 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_371_insert__compr,axiom,
% 0.55/0.79 ! [A_134: nat,B_72: nat > $o] :
% 0.55/0.79 ( ( insert_nat @ A_134 @ B_72 )
% 0.55/0.79 = ( collect_nat
% 0.55/0.79 @ ^ [X_1: nat] : ( (|) @ ( X_1 = A_134 ) @ ( member_nat @ X_1 @ B_72 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_372_insert__compr,axiom,
% 0.55/0.79 ! [A_134: pname,B_72: pname > $o] :
% 0.55/0.79 ( ( insert_pname @ A_134 @ B_72 )
% 0.55/0.79 = ( collect_pname
% 0.55/0.79 @ ^ [X_1: pname] : ( (|) @ ( X_1 = A_134 ) @ ( member_pname @ X_1 @ B_72 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_373_insert__Collect,axiom,
% 0.55/0.79 ! [A_133: x_a,P_11: x_a > $o] :
% 0.55/0.79 ( ( insert_a @ A_133 @ ( collect_a @ P_11 ) )
% 0.55/0.79 = ( collect_a
% 0.55/0.79 @ ^ [U_1: x_a] : ( (=>) @ ( (~) @ ( U_1 = A_133 ) ) @ ( P_11 @ U_1 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_374_insert__Collect,axiom,
% 0.55/0.79 ! [A_133: int,P_11: int > $o] :
% 0.55/0.79 ( ( insert_int @ A_133 @ ( collect_int @ P_11 ) )
% 0.55/0.79 = ( collect_int
% 0.55/0.79 @ ^ [U_1: int] : ( (=>) @ ( (~) @ ( U_1 = A_133 ) ) @ ( P_11 @ U_1 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_375_insert__Collect,axiom,
% 0.55/0.79 ! [A_133: nat,P_11: nat > $o] :
% 0.55/0.79 ( ( insert_nat @ A_133 @ ( collect_nat @ P_11 ) )
% 0.55/0.79 = ( collect_nat
% 0.55/0.79 @ ^ [U_1: nat] : ( (=>) @ ( (~) @ ( U_1 = A_133 ) ) @ ( P_11 @ U_1 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_376_mem__def,axiom,
% 0.55/0.79 ! [X_39: int,A_132: int > $o] :
% 0.55/0.79 ( ( member_int @ X_39 @ A_132 )
% 0.55/0.79 <=> ( A_132 @ X_39 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_377_mem__def,axiom,
% 0.55/0.79 ! [X_39: nat,A_132: nat > $o] :
% 0.55/0.79 ( ( member_nat @ X_39 @ A_132 )
% 0.55/0.79 <=> ( A_132 @ X_39 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_378_mem__def,axiom,
% 0.55/0.79 ! [X_39: x_a,A_132: x_a > $o] :
% 0.55/0.79 ( ( member_a @ X_39 @ A_132 )
% 0.55/0.79 <=> ( A_132 @ X_39 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_379_mem__def,axiom,
% 0.55/0.79 ! [X_39: pname,A_132: pname > $o] :
% 0.55/0.79 ( ( member_pname @ X_39 @ A_132 )
% 0.55/0.79 <=> ( A_132 @ X_39 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_380_Collect__def,axiom,
% 0.55/0.79 ! [P_10: int > $o] :
% 0.55/0.79 ( ( collect_int @ P_10 )
% 0.55/0.79 = P_10 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_381_Collect__def,axiom,
% 0.55/0.79 ! [P_10: nat > $o] :
% 0.55/0.79 ( ( collect_nat @ P_10 )
% 0.55/0.79 = P_10 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_382_insert__absorb2,axiom,
% 0.55/0.79 ! [X_38: x_a,A_131: x_a > $o] :
% 0.55/0.79 ( ( insert_a @ X_38 @ ( insert_a @ X_38 @ A_131 ) )
% 0.55/0.79 = ( insert_a @ X_38 @ A_131 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_383_insert__commute,axiom,
% 0.55/0.79 ! [X_37: x_a,Y_3: x_a,A_130: x_a > $o] :
% 0.55/0.79 ( ( insert_a @ X_37 @ ( insert_a @ Y_3 @ A_130 ) )
% 0.55/0.79 = ( insert_a @ Y_3 @ ( insert_a @ X_37 @ A_130 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_384_insert__iff,axiom,
% 0.55/0.79 ! [A_129: x_a,B_71: x_a,A_128: x_a > $o] :
% 0.55/0.79 ( ( member_a @ A_129 @ ( insert_a @ B_71 @ A_128 ) )
% 0.55/0.79 <=> ( ( A_129 = B_71 )
% 0.55/0.79 | ( member_a @ A_129 @ A_128 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_385_insert__iff,axiom,
% 0.55/0.79 ! [A_129: int,B_71: int,A_128: int > $o] :
% 0.55/0.79 ( ( member_int @ A_129 @ ( insert_int @ B_71 @ A_128 ) )
% 0.55/0.79 <=> ( ( A_129 = B_71 )
% 0.55/0.79 | ( member_int @ A_129 @ A_128 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_386_insert__iff,axiom,
% 0.55/0.79 ! [A_129: nat,B_71: nat,A_128: nat > $o] :
% 0.55/0.79 ( ( member_nat @ A_129 @ ( insert_nat @ B_71 @ A_128 ) )
% 0.55/0.79 <=> ( ( A_129 = B_71 )
% 0.55/0.79 | ( member_nat @ A_129 @ A_128 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_387_insert__iff,axiom,
% 0.55/0.79 ! [A_129: pname,B_71: pname,A_128: pname > $o] :
% 0.55/0.79 ( ( member_pname @ A_129 @ ( insert_pname @ B_71 @ A_128 ) )
% 0.55/0.79 <=> ( ( A_129 = B_71 )
% 0.55/0.79 | ( member_pname @ A_129 @ A_128 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_388_insert__code,axiom,
% 0.55/0.79 ! [Y_2: x_a,A_127: x_a > $o,X_36: x_a] :
% 0.55/0.79 ( ( insert_a @ Y_2 @ A_127 @ X_36 )
% 0.55/0.79 <=> ( ( Y_2 = X_36 )
% 0.55/0.79 | ( A_127 @ X_36 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_389_insert__ident,axiom,
% 0.55/0.79 ! [B_70: x_a > $o,X_35: x_a,A_126: x_a > $o] :
% 0.55/0.79 ( ~ ( member_a @ X_35 @ A_126 )
% 0.55/0.79 => ( ~ ( member_a @ X_35 @ B_70 )
% 0.55/0.79 => ( ( ( insert_a @ X_35 @ A_126 )
% 0.55/0.79 = ( insert_a @ X_35 @ B_70 ) )
% 0.55/0.79 <=> ( A_126 = B_70 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_390_insert__ident,axiom,
% 0.55/0.79 ! [B_70: int > $o,X_35: int,A_126: int > $o] :
% 0.55/0.79 ( ~ ( member_int @ X_35 @ A_126 )
% 0.55/0.79 => ( ~ ( member_int @ X_35 @ B_70 )
% 0.55/0.79 => ( ( ( insert_int @ X_35 @ A_126 )
% 0.55/0.79 = ( insert_int @ X_35 @ B_70 ) )
% 0.55/0.79 <=> ( A_126 = B_70 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_391_insert__ident,axiom,
% 0.55/0.79 ! [B_70: nat > $o,X_35: nat,A_126: nat > $o] :
% 0.55/0.79 ( ~ ( member_nat @ X_35 @ A_126 )
% 0.55/0.79 => ( ~ ( member_nat @ X_35 @ B_70 )
% 0.55/0.79 => ( ( ( insert_nat @ X_35 @ A_126 )
% 0.55/0.79 = ( insert_nat @ X_35 @ B_70 ) )
% 0.55/0.79 <=> ( A_126 = B_70 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_392_insert__ident,axiom,
% 0.55/0.79 ! [B_70: pname > $o,X_35: pname,A_126: pname > $o] :
% 0.55/0.79 ( ~ ( member_pname @ X_35 @ A_126 )
% 0.55/0.79 => ( ~ ( member_pname @ X_35 @ B_70 )
% 0.55/0.79 => ( ( ( insert_pname @ X_35 @ A_126 )
% 0.55/0.79 = ( insert_pname @ X_35 @ B_70 ) )
% 0.55/0.79 <=> ( A_126 = B_70 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_393_insertI2,axiom,
% 0.55/0.79 ! [B_69: x_a,A_125: x_a,B_68: x_a > $o] :
% 0.55/0.79 ( ( member_a @ A_125 @ B_68 )
% 0.55/0.79 => ( member_a @ A_125 @ ( insert_a @ B_69 @ B_68 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_394_insertI2,axiom,
% 0.55/0.79 ! [B_69: int,A_125: int,B_68: int > $o] :
% 0.55/0.79 ( ( member_int @ A_125 @ B_68 )
% 0.55/0.79 => ( member_int @ A_125 @ ( insert_int @ B_69 @ B_68 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_395_insertI2,axiom,
% 0.55/0.79 ! [B_69: nat,A_125: nat,B_68: nat > $o] :
% 0.55/0.79 ( ( member_nat @ A_125 @ B_68 )
% 0.55/0.79 => ( member_nat @ A_125 @ ( insert_nat @ B_69 @ B_68 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_396_insertI2,axiom,
% 0.55/0.79 ! [B_69: pname,A_125: pname,B_68: pname > $o] :
% 0.55/0.79 ( ( member_pname @ A_125 @ B_68 )
% 0.55/0.79 => ( member_pname @ A_125 @ ( insert_pname @ B_69 @ B_68 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_397_insert__absorb,axiom,
% 0.55/0.79 ! [A_124: x_a,A_123: x_a > $o] :
% 0.55/0.79 ( ( member_a @ A_124 @ A_123 )
% 0.55/0.79 => ( ( insert_a @ A_124 @ A_123 )
% 0.55/0.79 = A_123 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_398_insert__absorb,axiom,
% 0.55/0.79 ! [A_124: int,A_123: int > $o] :
% 0.55/0.79 ( ( member_int @ A_124 @ A_123 )
% 0.55/0.79 => ( ( insert_int @ A_124 @ A_123 )
% 0.55/0.79 = A_123 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_399_insert__absorb,axiom,
% 0.55/0.79 ! [A_124: nat,A_123: nat > $o] :
% 0.55/0.79 ( ( member_nat @ A_124 @ A_123 )
% 0.55/0.79 => ( ( insert_nat @ A_124 @ A_123 )
% 0.55/0.79 = A_123 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_400_insert__absorb,axiom,
% 0.55/0.79 ! [A_124: pname,A_123: pname > $o] :
% 0.55/0.79 ( ( member_pname @ A_124 @ A_123 )
% 0.55/0.79 => ( ( insert_pname @ A_124 @ A_123 )
% 0.55/0.79 = A_123 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_401_subset__refl,axiom,
% 0.55/0.79 ! [A_122: int > $o] : ( ord_less_eq_int_o @ A_122 @ A_122 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_402_subset__refl,axiom,
% 0.55/0.79 ! [A_122: nat > $o] : ( ord_less_eq_nat_o @ A_122 @ A_122 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_403_subset__refl,axiom,
% 0.55/0.79 ! [A_122: x_a > $o] : ( ord_less_eq_a_o @ A_122 @ A_122 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_404_set__eq__subset,axiom,
% 0.55/0.79 ! [A_121: int > $o,B_67: int > $o] :
% 0.55/0.79 ( ( A_121 = B_67 )
% 0.55/0.79 <=> ( ( ord_less_eq_int_o @ A_121 @ B_67 )
% 0.55/0.79 & ( ord_less_eq_int_o @ B_67 @ A_121 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_405_set__eq__subset,axiom,
% 0.55/0.79 ! [A_121: nat > $o,B_67: nat > $o] :
% 0.55/0.79 ( ( A_121 = B_67 )
% 0.55/0.79 <=> ( ( ord_less_eq_nat_o @ A_121 @ B_67 )
% 0.55/0.79 & ( ord_less_eq_nat_o @ B_67 @ A_121 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_406_set__eq__subset,axiom,
% 0.55/0.79 ! [A_121: x_a > $o,B_67: x_a > $o] :
% 0.55/0.79 ( ( A_121 = B_67 )
% 0.55/0.79 <=> ( ( ord_less_eq_a_o @ A_121 @ B_67 )
% 0.55/0.79 & ( ord_less_eq_a_o @ B_67 @ A_121 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_407_equalityD1,axiom,
% 0.55/0.79 ! [A_120: int > $o,B_66: int > $o] :
% 0.55/0.79 ( ( A_120 = B_66 )
% 0.55/0.79 => ( ord_less_eq_int_o @ A_120 @ B_66 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_408_equalityD1,axiom,
% 0.55/0.79 ! [A_120: nat > $o,B_66: nat > $o] :
% 0.55/0.79 ( ( A_120 = B_66 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ A_120 @ B_66 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_409_equalityD1,axiom,
% 0.55/0.79 ! [A_120: x_a > $o,B_66: x_a > $o] :
% 0.55/0.79 ( ( A_120 = B_66 )
% 0.55/0.79 => ( ord_less_eq_a_o @ A_120 @ B_66 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_410_equalityD2,axiom,
% 0.55/0.79 ! [A_119: int > $o,B_65: int > $o] :
% 0.55/0.79 ( ( A_119 = B_65 )
% 0.55/0.79 => ( ord_less_eq_int_o @ B_65 @ A_119 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_411_equalityD2,axiom,
% 0.55/0.79 ! [A_119: nat > $o,B_65: nat > $o] :
% 0.55/0.79 ( ( A_119 = B_65 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ B_65 @ A_119 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_412_equalityD2,axiom,
% 0.55/0.79 ! [A_119: x_a > $o,B_65: x_a > $o] :
% 0.55/0.79 ( ( A_119 = B_65 )
% 0.55/0.79 => ( ord_less_eq_a_o @ B_65 @ A_119 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_413_in__mono,axiom,
% 0.55/0.79 ! [X_34: int,A_118: int > $o,B_64: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_118 @ B_64 )
% 0.55/0.79 => ( ( member_int @ X_34 @ A_118 )
% 0.55/0.79 => ( member_int @ X_34 @ B_64 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_414_in__mono,axiom,
% 0.55/0.79 ! [X_34: nat,A_118: nat > $o,B_64: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_118 @ B_64 )
% 0.55/0.79 => ( ( member_nat @ X_34 @ A_118 )
% 0.55/0.79 => ( member_nat @ X_34 @ B_64 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_415_in__mono,axiom,
% 0.55/0.79 ! [X_34: x_a,A_118: x_a > $o,B_64: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_118 @ B_64 )
% 0.55/0.79 => ( ( member_a @ X_34 @ A_118 )
% 0.55/0.79 => ( member_a @ X_34 @ B_64 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_416_in__mono,axiom,
% 0.55/0.79 ! [X_34: pname,A_118: pname > $o,B_64: pname > $o] :
% 0.55/0.79 ( ( ord_less_eq_pname_o @ A_118 @ B_64 )
% 0.55/0.79 => ( ( member_pname @ X_34 @ A_118 )
% 0.55/0.79 => ( member_pname @ X_34 @ B_64 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_417_set__rev__mp,axiom,
% 0.55/0.79 ! [B_63: int > $o,X_33: int,A_117: int > $o] :
% 0.55/0.79 ( ( member_int @ X_33 @ A_117 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ A_117 @ B_63 )
% 0.55/0.79 => ( member_int @ X_33 @ B_63 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_418_set__rev__mp,axiom,
% 0.55/0.79 ! [B_63: nat > $o,X_33: nat,A_117: nat > $o] :
% 0.55/0.79 ( ( member_nat @ X_33 @ A_117 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ A_117 @ B_63 )
% 0.55/0.79 => ( member_nat @ X_33 @ B_63 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_419_set__rev__mp,axiom,
% 0.55/0.79 ! [B_63: x_a > $o,X_33: x_a,A_117: x_a > $o] :
% 0.55/0.79 ( ( member_a @ X_33 @ A_117 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ A_117 @ B_63 )
% 0.55/0.79 => ( member_a @ X_33 @ B_63 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_420_set__rev__mp,axiom,
% 0.55/0.79 ! [B_63: pname > $o,X_33: pname,A_117: pname > $o] :
% 0.55/0.79 ( ( member_pname @ X_33 @ A_117 )
% 0.55/0.79 => ( ( ord_less_eq_pname_o @ A_117 @ B_63 )
% 0.55/0.79 => ( member_pname @ X_33 @ B_63 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_421_set__mp,axiom,
% 0.55/0.79 ! [X_32: int,A_116: int > $o,B_62: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_116 @ B_62 )
% 0.55/0.79 => ( ( member_int @ X_32 @ A_116 )
% 0.55/0.79 => ( member_int @ X_32 @ B_62 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_422_set__mp,axiom,
% 0.55/0.79 ! [X_32: nat,A_116: nat > $o,B_62: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_116 @ B_62 )
% 0.55/0.79 => ( ( member_nat @ X_32 @ A_116 )
% 0.55/0.79 => ( member_nat @ X_32 @ B_62 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_423_set__mp,axiom,
% 0.55/0.79 ! [X_32: x_a,A_116: x_a > $o,B_62: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_116 @ B_62 )
% 0.55/0.79 => ( ( member_a @ X_32 @ A_116 )
% 0.55/0.79 => ( member_a @ X_32 @ B_62 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_424_set__mp,axiom,
% 0.55/0.79 ! [X_32: pname,A_116: pname > $o,B_62: pname > $o] :
% 0.55/0.79 ( ( ord_less_eq_pname_o @ A_116 @ B_62 )
% 0.55/0.79 => ( ( member_pname @ X_32 @ A_116 )
% 0.55/0.79 => ( member_pname @ X_32 @ B_62 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_425_subset__trans,axiom,
% 0.55/0.79 ! [C_28: int > $o,A_115: int > $o,B_61: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_115 @ B_61 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ B_61 @ C_28 )
% 0.55/0.79 => ( ord_less_eq_int_o @ A_115 @ C_28 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_426_subset__trans,axiom,
% 0.55/0.79 ! [C_28: nat > $o,A_115: nat > $o,B_61: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_115 @ B_61 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ B_61 @ C_28 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ A_115 @ C_28 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_427_subset__trans,axiom,
% 0.55/0.79 ! [C_28: x_a > $o,A_115: x_a > $o,B_61: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_115 @ B_61 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ B_61 @ C_28 )
% 0.55/0.79 => ( ord_less_eq_a_o @ A_115 @ C_28 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_428_equalityE,axiom,
% 0.55/0.79 ! [A_114: int > $o,B_60: int > $o] :
% 0.55/0.79 ( ( A_114 = B_60 )
% 0.55/0.79 => ~ ( ( ord_less_eq_int_o @ A_114 @ B_60 )
% 0.55/0.79 => ~ ( ord_less_eq_int_o @ B_60 @ A_114 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_429_equalityE,axiom,
% 0.55/0.79 ! [A_114: nat > $o,B_60: nat > $o] :
% 0.55/0.79 ( ( A_114 = B_60 )
% 0.55/0.79 => ~ ( ( ord_less_eq_nat_o @ A_114 @ B_60 )
% 0.55/0.79 => ~ ( ord_less_eq_nat_o @ B_60 @ A_114 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_430_equalityE,axiom,
% 0.55/0.79 ! [A_114: x_a > $o,B_60: x_a > $o] :
% 0.55/0.79 ( ( A_114 = B_60 )
% 0.55/0.79 => ~ ( ( ord_less_eq_a_o @ A_114 @ B_60 )
% 0.55/0.79 => ~ ( ord_less_eq_a_o @ B_60 @ A_114 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_431_image__iff,axiom,
% 0.55/0.79 ! [Z_4: int,F_35: nat > int,A_113: nat > $o] :
% 0.55/0.79 ( ( member_int @ Z_4 @ ( image_nat_int @ F_35 @ A_113 ) )
% 0.55/0.79 <=> ? [X_1: nat] :
% 0.55/0.79 ( ( member_nat @ X_1 @ A_113 )
% 0.55/0.79 & ( Z_4
% 0.55/0.79 = ( F_35 @ X_1 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_432_image__iff,axiom,
% 0.55/0.79 ! [Z_4: x_a,F_35: pname > x_a,A_113: pname > $o] :
% 0.55/0.79 ( ( member_a @ Z_4 @ ( image_pname_a @ F_35 @ A_113 ) )
% 0.55/0.79 <=> ? [X_1: pname] :
% 0.55/0.79 ( ( member_pname @ X_1 @ A_113 )
% 0.55/0.79 & ( Z_4
% 0.55/0.79 = ( F_35 @ X_1 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_433_imageI,axiom,
% 0.55/0.79 ! [F_34: nat > int,X_31: nat,A_112: nat > $o] :
% 0.55/0.79 ( ( member_nat @ X_31 @ A_112 )
% 0.55/0.79 => ( member_int @ ( F_34 @ X_31 ) @ ( image_nat_int @ F_34 @ A_112 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_434_imageI,axiom,
% 0.55/0.79 ! [F_34: pname > x_a,X_31: pname,A_112: pname > $o] :
% 0.55/0.79 ( ( member_pname @ X_31 @ A_112 )
% 0.55/0.79 => ( member_a @ ( F_34 @ X_31 ) @ ( image_pname_a @ F_34 @ A_112 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_435_rev__image__eqI,axiom,
% 0.55/0.79 ! [B_59: int,F_33: nat > int,X_30: nat,A_111: nat > $o] :
% 0.55/0.79 ( ( member_nat @ X_30 @ A_111 )
% 0.55/0.79 => ( ( B_59
% 0.55/0.79 = ( F_33 @ X_30 ) )
% 0.55/0.79 => ( member_int @ B_59 @ ( image_nat_int @ F_33 @ A_111 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_436_rev__image__eqI,axiom,
% 0.55/0.79 ! [B_59: x_a,F_33: pname > x_a,X_30: pname,A_111: pname > $o] :
% 0.55/0.79 ( ( member_pname @ X_30 @ A_111 )
% 0.55/0.79 => ( ( B_59
% 0.55/0.79 = ( F_33 @ X_30 ) )
% 0.55/0.79 => ( member_a @ B_59 @ ( image_pname_a @ F_33 @ A_111 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_437_insert__compr__raw,axiom,
% 0.55/0.79 ! [X_1: x_a,Xa: x_a > $o] :
% 0.55/0.79 ( ( insert_a @ X_1 @ Xa )
% 0.55/0.79 = ( collect_a
% 0.55/0.79 @ ^ [Y_1: x_a] : ( (|) @ ( Y_1 = X_1 ) @ ( member_a @ Y_1 @ Xa ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_438_insert__compr__raw,axiom,
% 0.55/0.79 ! [X_1: int,Xa: int > $o] :
% 0.55/0.79 ( ( insert_int @ X_1 @ Xa )
% 0.55/0.79 = ( collect_int
% 0.55/0.79 @ ^ [Y_1: int] : ( (|) @ ( Y_1 = X_1 ) @ ( member_int @ Y_1 @ Xa ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_439_insert__compr__raw,axiom,
% 0.55/0.79 ! [X_1: nat,Xa: nat > $o] :
% 0.55/0.79 ( ( insert_nat @ X_1 @ Xa )
% 0.55/0.79 = ( collect_nat
% 0.55/0.79 @ ^ [Y_1: nat] : ( (|) @ ( Y_1 = X_1 ) @ ( member_nat @ Y_1 @ Xa ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_440_insert__compr__raw,axiom,
% 0.55/0.79 ! [X_1: pname,Xa: pname > $o] :
% 0.55/0.79 ( ( insert_pname @ X_1 @ Xa )
% 0.55/0.79 = ( collect_pname
% 0.55/0.79 @ ^ [Y_1: pname] : ( (|) @ ( Y_1 = X_1 ) @ ( member_pname @ Y_1 @ Xa ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_441_le__fun__def,axiom,
% 0.55/0.79 ! [F_32: int > $o,G_4: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ F_32 @ G_4 )
% 0.55/0.79 <=> ! [X_1: int] : ( ord_less_eq_o @ ( F_32 @ X_1 ) @ ( G_4 @ X_1 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_442_le__fun__def,axiom,
% 0.55/0.79 ! [F_32: nat > $o,G_4: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ F_32 @ G_4 )
% 0.55/0.79 <=> ! [X_1: nat] : ( ord_less_eq_o @ ( F_32 @ X_1 ) @ ( G_4 @ X_1 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_443_le__fun__def,axiom,
% 0.55/0.79 ! [F_32: x_a > $o,G_4: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ F_32 @ G_4 )
% 0.55/0.79 <=> ! [X_1: x_a] : ( ord_less_eq_o @ ( F_32 @ X_1 ) @ ( G_4 @ X_1 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_444_le__funD,axiom,
% 0.55/0.79 ! [X_29: int,F_31: int > $o,G_3: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ F_31 @ G_3 )
% 0.55/0.79 => ( ord_less_eq_o @ ( F_31 @ X_29 ) @ ( G_3 @ X_29 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_445_le__funD,axiom,
% 0.55/0.79 ! [X_29: nat,F_31: nat > $o,G_3: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ F_31 @ G_3 )
% 0.55/0.79 => ( ord_less_eq_o @ ( F_31 @ X_29 ) @ ( G_3 @ X_29 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_446_le__funD,axiom,
% 0.55/0.79 ! [X_29: x_a,F_31: x_a > $o,G_3: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ F_31 @ G_3 )
% 0.55/0.79 => ( ord_less_eq_o @ ( F_31 @ X_29 ) @ ( G_3 @ X_29 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_447_le__funE,axiom,
% 0.55/0.79 ! [X_28: int,F_30: int > $o,G_2: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ F_30 @ G_2 )
% 0.55/0.79 => ( ord_less_eq_o @ ( F_30 @ X_28 ) @ ( G_2 @ X_28 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_448_le__funE,axiom,
% 0.55/0.79 ! [X_28: nat,F_30: nat > $o,G_2: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ F_30 @ G_2 )
% 0.55/0.79 => ( ord_less_eq_o @ ( F_30 @ X_28 ) @ ( G_2 @ X_28 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_449_le__funE,axiom,
% 0.55/0.79 ! [X_28: x_a,F_30: x_a > $o,G_2: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ F_30 @ G_2 )
% 0.55/0.79 => ( ord_less_eq_o @ ( F_30 @ X_28 ) @ ( G_2 @ X_28 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_450_subset__insertI,axiom,
% 0.55/0.79 ! [B_58: x_a > $o,A_110: x_a] : ( ord_less_eq_a_o @ B_58 @ ( insert_a @ A_110 @ B_58 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_451_subset__insertI,axiom,
% 0.55/0.79 ! [B_58: int > $o,A_110: int] : ( ord_less_eq_int_o @ B_58 @ ( insert_int @ A_110 @ B_58 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_452_subset__insertI,axiom,
% 0.55/0.79 ! [B_58: nat > $o,A_110: nat] : ( ord_less_eq_nat_o @ B_58 @ ( insert_nat @ A_110 @ B_58 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_453_insert__subset,axiom,
% 0.55/0.79 ! [X_27: x_a,A_109: x_a > $o,B_57: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ ( insert_a @ X_27 @ A_109 ) @ B_57 )
% 0.55/0.79 <=> ( ( member_a @ X_27 @ B_57 )
% 0.55/0.79 & ( ord_less_eq_a_o @ A_109 @ B_57 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_454_insert__subset,axiom,
% 0.55/0.79 ! [X_27: int,A_109: int > $o,B_57: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ ( insert_int @ X_27 @ A_109 ) @ B_57 )
% 0.55/0.79 <=> ( ( member_int @ X_27 @ B_57 )
% 0.55/0.79 & ( ord_less_eq_int_o @ A_109 @ B_57 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_455_insert__subset,axiom,
% 0.55/0.79 ! [X_27: nat,A_109: nat > $o,B_57: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ ( insert_nat @ X_27 @ A_109 ) @ B_57 )
% 0.55/0.79 <=> ( ( member_nat @ X_27 @ B_57 )
% 0.55/0.79 & ( ord_less_eq_nat_o @ A_109 @ B_57 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_456_insert__subset,axiom,
% 0.55/0.79 ! [X_27: pname,A_109: pname > $o,B_57: pname > $o] :
% 0.55/0.79 ( ( ord_less_eq_pname_o @ ( insert_pname @ X_27 @ A_109 ) @ B_57 )
% 0.55/0.79 <=> ( ( member_pname @ X_27 @ B_57 )
% 0.55/0.79 & ( ord_less_eq_pname_o @ A_109 @ B_57 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_457_subset__insert,axiom,
% 0.55/0.79 ! [B_56: x_a > $o,X_26: x_a,A_108: x_a > $o] :
% 0.55/0.79 ( ~ ( member_a @ X_26 @ A_108 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ A_108 @ ( insert_a @ X_26 @ B_56 ) )
% 0.55/0.79 <=> ( ord_less_eq_a_o @ A_108 @ B_56 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_458_subset__insert,axiom,
% 0.55/0.79 ! [B_56: int > $o,X_26: int,A_108: int > $o] :
% 0.55/0.79 ( ~ ( member_int @ X_26 @ A_108 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ A_108 @ ( insert_int @ X_26 @ B_56 ) )
% 0.55/0.79 <=> ( ord_less_eq_int_o @ A_108 @ B_56 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_459_subset__insert,axiom,
% 0.55/0.79 ! [B_56: nat > $o,X_26: nat,A_108: nat > $o] :
% 0.55/0.79 ( ~ ( member_nat @ X_26 @ A_108 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ A_108 @ ( insert_nat @ X_26 @ B_56 ) )
% 0.55/0.79 <=> ( ord_less_eq_nat_o @ A_108 @ B_56 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_460_subset__insert,axiom,
% 0.55/0.79 ! [B_56: pname > $o,X_26: pname,A_108: pname > $o] :
% 0.55/0.79 ( ~ ( member_pname @ X_26 @ A_108 )
% 0.55/0.79 => ( ( ord_less_eq_pname_o @ A_108 @ ( insert_pname @ X_26 @ B_56 ) )
% 0.55/0.79 <=> ( ord_less_eq_pname_o @ A_108 @ B_56 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_461_subset__insertI2,axiom,
% 0.55/0.79 ! [B_55: x_a,A_107: x_a > $o,B_54: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_107 @ B_54 )
% 0.55/0.79 => ( ord_less_eq_a_o @ A_107 @ ( insert_a @ B_55 @ B_54 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_462_subset__insertI2,axiom,
% 0.55/0.79 ! [B_55: int,A_107: int > $o,B_54: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_107 @ B_54 )
% 0.55/0.79 => ( ord_less_eq_int_o @ A_107 @ ( insert_int @ B_55 @ B_54 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_463_subset__insertI2,axiom,
% 0.55/0.79 ! [B_55: nat,A_107: nat > $o,B_54: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_107 @ B_54 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ A_107 @ ( insert_nat @ B_55 @ B_54 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_464_insert__mono,axiom,
% 0.55/0.79 ! [A_106: x_a,C_27: x_a > $o,D_7: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ C_27 @ D_7 )
% 0.55/0.79 => ( ord_less_eq_a_o @ ( insert_a @ A_106 @ C_27 ) @ ( insert_a @ A_106 @ D_7 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_465_insert__mono,axiom,
% 0.55/0.79 ! [A_106: int,C_27: int > $o,D_7: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ C_27 @ D_7 )
% 0.55/0.79 => ( ord_less_eq_int_o @ ( insert_int @ A_106 @ C_27 ) @ ( insert_int @ A_106 @ D_7 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_466_insert__mono,axiom,
% 0.55/0.79 ! [A_106: nat,C_27: nat > $o,D_7: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ C_27 @ D_7 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ ( insert_nat @ A_106 @ C_27 ) @ ( insert_nat @ A_106 @ D_7 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_467_image__insert,axiom,
% 0.55/0.79 ! [F_29: nat > int,A_105: nat,B_53: nat > $o] :
% 0.55/0.79 ( ( image_nat_int @ F_29 @ ( insert_nat @ A_105 @ B_53 ) )
% 0.55/0.79 = ( insert_int @ ( F_29 @ A_105 ) @ ( image_nat_int @ F_29 @ B_53 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_468_image__insert,axiom,
% 0.55/0.79 ! [F_29: pname > x_a,A_105: pname,B_53: pname > $o] :
% 0.55/0.79 ( ( image_pname_a @ F_29 @ ( insert_pname @ A_105 @ B_53 ) )
% 0.55/0.79 = ( insert_a @ ( F_29 @ A_105 ) @ ( image_pname_a @ F_29 @ B_53 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_469_insert__image,axiom,
% 0.55/0.79 ! [F_28: nat > int,X_25: nat,A_104: nat > $o] :
% 0.55/0.79 ( ( member_nat @ X_25 @ A_104 )
% 0.55/0.79 => ( ( insert_int @ ( F_28 @ X_25 ) @ ( image_nat_int @ F_28 @ A_104 ) )
% 0.55/0.79 = ( image_nat_int @ F_28 @ A_104 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_470_insert__image,axiom,
% 0.55/0.79 ! [F_28: pname > x_a,X_25: pname,A_104: pname > $o] :
% 0.55/0.79 ( ( member_pname @ X_25 @ A_104 )
% 0.55/0.79 => ( ( insert_a @ ( F_28 @ X_25 ) @ ( image_pname_a @ F_28 @ A_104 ) )
% 0.55/0.79 = ( image_pname_a @ F_28 @ A_104 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_471_subset__image__iff,axiom,
% 0.55/0.79 ! [B_52: int > $o,F_27: nat > int,A_103: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ B_52 @ ( image_nat_int @ F_27 @ A_103 ) )
% 0.55/0.79 <=> ? [AA: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ AA @ A_103 )
% 0.55/0.79 & ( B_52
% 0.55/0.79 = ( image_nat_int @ F_27 @ AA ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_472_subset__image__iff,axiom,
% 0.55/0.79 ! [B_52: x_a > $o,F_27: pname > x_a,A_103: pname > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ B_52 @ ( image_pname_a @ F_27 @ A_103 ) )
% 0.55/0.79 <=> ? [AA: pname > $o] :
% 0.55/0.79 ( ( ord_less_eq_pname_o @ AA @ A_103 )
% 0.55/0.79 & ( B_52
% 0.55/0.79 = ( image_pname_a @ F_27 @ AA ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_473_image__mono,axiom,
% 0.55/0.79 ! [F_26: nat > int,A_102: nat > $o,B_51: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_102 @ B_51 )
% 0.55/0.79 => ( ord_less_eq_int_o @ ( image_nat_int @ F_26 @ A_102 ) @ ( image_nat_int @ F_26 @ B_51 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_474_image__mono,axiom,
% 0.55/0.79 ! [F_26: pname > x_a,A_102: pname > $o,B_51: pname > $o] :
% 0.55/0.79 ( ( ord_less_eq_pname_o @ A_102 @ B_51 )
% 0.55/0.79 => ( ord_less_eq_a_o @ ( image_pname_a @ F_26 @ A_102 ) @ ( image_pname_a @ F_26 @ B_51 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_475_imageE,axiom,
% 0.55/0.79 ! [B_50: int,F_25: nat > int,A_101: nat > $o] :
% 0.55/0.79 ( ( member_int @ B_50 @ ( image_nat_int @ F_25 @ A_101 ) )
% 0.55/0.79 => ~ ! [X_1: nat] :
% 0.55/0.79 ( ( B_50
% 0.55/0.79 = ( F_25 @ X_1 ) )
% 0.55/0.79 => ~ ( member_nat @ X_1 @ A_101 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_476_imageE,axiom,
% 0.55/0.79 ! [B_50: x_a,F_25: pname > x_a,A_101: pname > $o] :
% 0.55/0.79 ( ( member_a @ B_50 @ ( image_pname_a @ F_25 @ A_101 ) )
% 0.55/0.79 => ~ ! [X_1: pname] :
% 0.55/0.79 ( ( B_50
% 0.55/0.79 = ( F_25 @ X_1 ) )
% 0.55/0.79 => ~ ( member_pname @ X_1 @ A_101 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_477_subsetI,axiom,
% 0.55/0.79 ! [B_49: int > $o,A_100: int > $o] :
% 0.55/0.79 ( ! [X_1: int] :
% 0.55/0.79 ( ( member_int @ X_1 @ A_100 )
% 0.55/0.79 => ( member_int @ X_1 @ B_49 ) )
% 0.55/0.79 => ( ord_less_eq_int_o @ A_100 @ B_49 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_478_subsetI,axiom,
% 0.55/0.79 ! [B_49: nat > $o,A_100: nat > $o] :
% 0.55/0.79 ( ! [X_1: nat] :
% 0.55/0.79 ( ( member_nat @ X_1 @ A_100 )
% 0.55/0.79 => ( member_nat @ X_1 @ B_49 ) )
% 0.55/0.79 => ( ord_less_eq_nat_o @ A_100 @ B_49 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_479_subsetI,axiom,
% 0.55/0.79 ! [B_49: x_a > $o,A_100: x_a > $o] :
% 0.55/0.79 ( ! [X_1: x_a] :
% 0.55/0.79 ( ( member_a @ X_1 @ A_100 )
% 0.55/0.79 => ( member_a @ X_1 @ B_49 ) )
% 0.55/0.79 => ( ord_less_eq_a_o @ A_100 @ B_49 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_480_subsetI,axiom,
% 0.55/0.79 ! [B_49: pname > $o,A_100: pname > $o] :
% 0.55/0.79 ( ! [X_1: pname] :
% 0.55/0.79 ( ( member_pname @ X_1 @ A_100 )
% 0.55/0.79 => ( member_pname @ X_1 @ B_49 ) )
% 0.55/0.79 => ( ord_less_eq_pname_o @ A_100 @ B_49 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_481_image__subsetI,axiom,
% 0.55/0.79 ! [F_24: nat > int,B_48: int > $o,A_99: nat > $o] :
% 0.55/0.79 ( ! [X_1: nat] :
% 0.55/0.79 ( ( member_nat @ X_1 @ A_99 )
% 0.55/0.79 => ( member_int @ ( F_24 @ X_1 ) @ B_48 ) )
% 0.55/0.79 => ( ord_less_eq_int_o @ ( image_nat_int @ F_24 @ A_99 ) @ B_48 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_482_image__subsetI,axiom,
% 0.55/0.79 ! [F_24: pname > x_a,B_48: x_a > $o,A_99: pname > $o] :
% 0.55/0.79 ( ! [X_1: pname] :
% 0.55/0.79 ( ( member_pname @ X_1 @ A_99 )
% 0.55/0.79 => ( member_a @ ( F_24 @ X_1 ) @ B_48 ) )
% 0.55/0.79 => ( ord_less_eq_a_o @ ( image_pname_a @ F_24 @ A_99 ) @ B_48 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_483_le__funI,axiom,
% 0.55/0.79 ! [F_23: int > $o,G_1: int > $o] :
% 0.55/0.79 ( ! [X_1: int] : ( ord_less_eq_o @ ( F_23 @ X_1 ) @ ( G_1 @ X_1 ) )
% 0.55/0.79 => ( ord_less_eq_int_o @ F_23 @ G_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_484_le__funI,axiom,
% 0.55/0.79 ! [F_23: nat > $o,G_1: nat > $o] :
% 0.55/0.79 ( ! [X_1: nat] : ( ord_less_eq_o @ ( F_23 @ X_1 ) @ ( G_1 @ X_1 ) )
% 0.55/0.79 => ( ord_less_eq_nat_o @ F_23 @ G_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_485_le__funI,axiom,
% 0.55/0.79 ! [F_23: x_a > $o,G_1: x_a > $o] :
% 0.55/0.79 ( ! [X_1: x_a] : ( ord_less_eq_o @ ( F_23 @ X_1 ) @ ( G_1 @ X_1 ) )
% 0.55/0.79 => ( ord_less_eq_a_o @ F_23 @ G_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_486_finite__nat__set__iff__bounded__le,axiom,
% 0.55/0.79 ! [N_2: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ N_2 )
% 0.55/0.79 <=> ? [M_1: nat] :
% 0.55/0.79 ! [X_1: nat] :
% 0.55/0.79 ( ( member_nat @ X_1 @ N_2 )
% 0.55/0.79 => ( ord_less_eq_nat @ X_1 @ M_1 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_487_assms_I3_J,axiom,
% 0.55/0.79 ! [G: x_a > $o,C: com] :
% 0.55/0.79 ( ( wt @ C )
% 0.55/0.79 => ( ! [X_1: pname] :
% 0.55/0.79 ( ( member_pname @ X_1 @ u )
% 0.55/0.79 => ( p @ G @ ( insert_a @ ( mgt_call @ X_1 ) @ bot_bot_a_o ) ) )
% 0.55/0.79 => ( p @ G @ ( insert_a @ ( mgt @ C ) @ bot_bot_a_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_488_diff__eq__diff__less__eq,axiom,
% 0.55/0.79 ! [A_98: int,B_47: int,C_26: int,D_6: int] :
% 0.55/0.79 ( ( ( minus_minus_int @ A_98 @ B_47 )
% 0.55/0.79 = ( minus_minus_int @ C_26 @ D_6 ) )
% 0.55/0.79 => ( ( ord_less_eq_int @ A_98 @ B_47 )
% 0.55/0.79 <=> ( ord_less_eq_int @ C_26 @ D_6 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_489_less__eq__nat_Osimps_I2_J,axiom,
% 0.55/0.79 ! [M: nat,N: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.55/0.79 <=> ( nat_case_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_490_emptyE,axiom,
% 0.55/0.79 ! [A_97: int] :
% 0.55/0.79 ~ ( member_int @ A_97 @ bot_bot_int_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_491_emptyE,axiom,
% 0.55/0.79 ! [A_97: nat] :
% 0.55/0.79 ~ ( member_nat @ A_97 @ bot_bot_nat_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_492_emptyE,axiom,
% 0.55/0.79 ! [A_97: x_a] :
% 0.55/0.79 ~ ( member_a @ A_97 @ bot_bot_a_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_493_emptyE,axiom,
% 0.55/0.79 ! [A_97: pname] :
% 0.55/0.79 ~ ( member_pname @ A_97 @ bot_bot_pname_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_494_finite__Diff,axiom,
% 0.55/0.79 ! [B_46: int > $o,A_96: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_96 )
% 0.55/0.79 => ( finite_finite_int @ ( minus_minus_int_o @ A_96 @ B_46 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_495_finite__Diff,axiom,
% 0.55/0.79 ! [B_46: nat > $o,A_96: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_96 )
% 0.55/0.79 => ( finite_finite_nat @ ( minus_minus_nat_o @ A_96 @ B_46 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_496_finite__Diff,axiom,
% 0.55/0.79 ! [B_46: pname > $o,A_96: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_96 )
% 0.55/0.79 => ( finite_finite_pname @ ( minus_minus_pname_o @ A_96 @ B_46 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_497_finite_OemptyI,axiom,
% 0.55/0.79 finite_finite_int @ bot_bot_int_o ).
% 0.55/0.79
% 0.55/0.79 thf(fact_498_finite_OemptyI,axiom,
% 0.55/0.79 finite_finite_nat @ bot_bot_nat_o ).
% 0.55/0.79
% 0.55/0.79 thf(fact_499_finite_OemptyI,axiom,
% 0.55/0.79 finite_finite_pname @ bot_bot_pname_o ).
% 0.55/0.79
% 0.55/0.79 thf(fact_500_finite_OemptyI,axiom,
% 0.55/0.79 finite_finite_a @ bot_bot_a_o ).
% 0.55/0.79
% 0.55/0.79 thf(fact_501_empty__subsetI,axiom,
% 0.55/0.79 ! [A_95: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A_95 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_502_empty__subsetI,axiom,
% 0.55/0.79 ! [A_95: int > $o] : ( ord_less_eq_int_o @ bot_bot_int_o @ A_95 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_503_empty__subsetI,axiom,
% 0.55/0.79 ! [A_95: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A_95 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_504_equals0D,axiom,
% 0.55/0.79 ! [A_94: int,A_93: int > $o] :
% 0.55/0.79 ( ( A_93 = bot_bot_int_o )
% 0.55/0.79 => ~ ( member_int @ A_94 @ A_93 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_505_equals0D,axiom,
% 0.55/0.79 ! [A_94: nat,A_93: nat > $o] :
% 0.55/0.79 ( ( A_93 = bot_bot_nat_o )
% 0.55/0.79 => ~ ( member_nat @ A_94 @ A_93 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_506_equals0D,axiom,
% 0.55/0.79 ! [A_94: x_a,A_93: x_a > $o] :
% 0.55/0.79 ( ( A_93 = bot_bot_a_o )
% 0.55/0.79 => ~ ( member_a @ A_94 @ A_93 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_507_equals0D,axiom,
% 0.55/0.79 ! [A_94: pname,A_93: pname > $o] :
% 0.55/0.79 ( ( A_93 = bot_bot_pname_o )
% 0.55/0.79 => ~ ( member_pname @ A_94 @ A_93 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_508_Collect__empty__eq,axiom,
% 0.55/0.79 ! [P_9: int > $o] :
% 0.55/0.79 ( ( ( collect_int @ P_9 )
% 0.55/0.79 = bot_bot_int_o )
% 0.55/0.79 <=> ! [X_1: int] :
% 0.55/0.79 ~ ( P_9 @ X_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_509_Collect__empty__eq,axiom,
% 0.55/0.79 ! [P_9: nat > $o] :
% 0.55/0.79 ( ( ( collect_nat @ P_9 )
% 0.55/0.79 = bot_bot_nat_o )
% 0.55/0.79 <=> ! [X_1: nat] :
% 0.55/0.79 ~ ( P_9 @ X_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_510_Collect__empty__eq,axiom,
% 0.55/0.79 ! [P_9: x_a > $o] :
% 0.55/0.79 ( ( ( collect_a @ P_9 )
% 0.55/0.79 = bot_bot_a_o )
% 0.55/0.79 <=> ! [X_1: x_a] :
% 0.55/0.79 ~ ( P_9 @ X_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_511_Diff__cancel,axiom,
% 0.55/0.79 ! [A_92: nat > $o] :
% 0.55/0.79 ( ( minus_minus_nat_o @ A_92 @ A_92 )
% 0.55/0.79 = bot_bot_nat_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_512_Diff__cancel,axiom,
% 0.55/0.79 ! [A_92: int > $o] :
% 0.55/0.79 ( ( minus_minus_int_o @ A_92 @ A_92 )
% 0.55/0.79 = bot_bot_int_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_513_Diff__cancel,axiom,
% 0.55/0.79 ! [A_92: x_a > $o] :
% 0.55/0.79 ( ( minus_minus_a_o @ A_92 @ A_92 )
% 0.55/0.79 = bot_bot_a_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_514_Diff__empty,axiom,
% 0.55/0.79 ! [A_91: nat > $o] :
% 0.55/0.79 ( ( minus_minus_nat_o @ A_91 @ bot_bot_nat_o )
% 0.55/0.79 = A_91 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_515_Diff__empty,axiom,
% 0.55/0.79 ! [A_91: int > $o] :
% 0.55/0.79 ( ( minus_minus_int_o @ A_91 @ bot_bot_int_o )
% 0.55/0.79 = A_91 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_516_Diff__empty,axiom,
% 0.55/0.79 ! [A_91: x_a > $o] :
% 0.55/0.79 ( ( minus_minus_a_o @ A_91 @ bot_bot_a_o )
% 0.55/0.79 = A_91 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_517_empty__iff,axiom,
% 0.55/0.79 ! [C_25: int] :
% 0.55/0.79 ~ ( member_int @ C_25 @ bot_bot_int_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_518_empty__iff,axiom,
% 0.55/0.79 ! [C_25: nat] :
% 0.55/0.79 ~ ( member_nat @ C_25 @ bot_bot_nat_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_519_empty__iff,axiom,
% 0.55/0.79 ! [C_25: x_a] :
% 0.55/0.79 ~ ( member_a @ C_25 @ bot_bot_a_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_520_empty__iff,axiom,
% 0.55/0.79 ! [C_25: pname] :
% 0.55/0.79 ~ ( member_pname @ C_25 @ bot_bot_pname_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_521_empty__Collect__eq,axiom,
% 0.55/0.79 ! [P_8: int > $o] :
% 0.55/0.79 ( ( bot_bot_int_o
% 0.55/0.79 = ( collect_int @ P_8 ) )
% 0.55/0.79 <=> ! [X_1: int] :
% 0.55/0.79 ~ ( P_8 @ X_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_522_empty__Collect__eq,axiom,
% 0.55/0.79 ! [P_8: nat > $o] :
% 0.55/0.79 ( ( bot_bot_nat_o
% 0.55/0.79 = ( collect_nat @ P_8 ) )
% 0.55/0.79 <=> ! [X_1: nat] :
% 0.55/0.79 ~ ( P_8 @ X_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_523_empty__Collect__eq,axiom,
% 0.55/0.79 ! [P_8: x_a > $o] :
% 0.55/0.79 ( ( bot_bot_a_o
% 0.55/0.79 = ( collect_a @ P_8 ) )
% 0.55/0.79 <=> ! [X_1: x_a] :
% 0.55/0.79 ~ ( P_8 @ X_1 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_524_empty__Diff,axiom,
% 0.55/0.79 ! [A_90: nat > $o] :
% 0.55/0.79 ( ( minus_minus_nat_o @ bot_bot_nat_o @ A_90 )
% 0.55/0.79 = bot_bot_nat_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_525_empty__Diff,axiom,
% 0.55/0.79 ! [A_90: int > $o] :
% 0.55/0.79 ( ( minus_minus_int_o @ bot_bot_int_o @ A_90 )
% 0.55/0.79 = bot_bot_int_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_526_empty__Diff,axiom,
% 0.55/0.79 ! [A_90: x_a > $o] :
% 0.55/0.79 ( ( minus_minus_a_o @ bot_bot_a_o @ A_90 )
% 0.55/0.79 = bot_bot_a_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_527_ex__in__conv,axiom,
% 0.55/0.79 ! [A_89: int > $o] :
% 0.55/0.79 ( ? [X_1: int] : ( member_int @ X_1 @ A_89 )
% 0.55/0.79 <=> ( A_89 != bot_bot_int_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_528_ex__in__conv,axiom,
% 0.55/0.79 ! [A_89: nat > $o] :
% 0.55/0.79 ( ? [X_1: nat] : ( member_nat @ X_1 @ A_89 )
% 0.55/0.79 <=> ( A_89 != bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_529_ex__in__conv,axiom,
% 0.55/0.79 ! [A_89: x_a > $o] :
% 0.55/0.79 ( ? [X_1: x_a] : ( member_a @ X_1 @ A_89 )
% 0.55/0.79 <=> ( A_89 != bot_bot_a_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_530_ex__in__conv,axiom,
% 0.55/0.79 ! [A_89: pname > $o] :
% 0.55/0.79 ( ? [X_1: pname] : ( member_pname @ X_1 @ A_89 )
% 0.55/0.79 <=> ( A_89 != bot_bot_pname_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_531_all__not__in__conv,axiom,
% 0.55/0.79 ! [A_88: int > $o] :
% 0.55/0.79 ( ! [X_1: int] :
% 0.55/0.79 ~ ( member_int @ X_1 @ A_88 )
% 0.55/0.79 <=> ( A_88 = bot_bot_int_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_532_all__not__in__conv,axiom,
% 0.55/0.79 ! [A_88: nat > $o] :
% 0.55/0.79 ( ! [X_1: nat] :
% 0.55/0.79 ~ ( member_nat @ X_1 @ A_88 )
% 0.55/0.79 <=> ( A_88 = bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_533_all__not__in__conv,axiom,
% 0.55/0.79 ! [A_88: x_a > $o] :
% 0.55/0.79 ( ! [X_1: x_a] :
% 0.55/0.79 ~ ( member_a @ X_1 @ A_88 )
% 0.55/0.79 <=> ( A_88 = bot_bot_a_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_534_all__not__in__conv,axiom,
% 0.55/0.79 ! [A_88: pname > $o] :
% 0.55/0.79 ( ! [X_1: pname] :
% 0.55/0.79 ~ ( member_pname @ X_1 @ A_88 )
% 0.55/0.79 <=> ( A_88 = bot_bot_pname_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_535_bot__apply,axiom,
% 0.55/0.79 ! [X_24: nat] :
% 0.55/0.79 ( ( bot_bot_nat_o @ X_24 )
% 0.55/0.79 <=> bot_bot_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_536_bot__apply,axiom,
% 0.55/0.79 ! [X_24: int] :
% 0.55/0.79 ( ( bot_bot_int_o @ X_24 )
% 0.55/0.79 <=> bot_bot_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_537_bot__apply,axiom,
% 0.55/0.79 ! [X_24: x_a] :
% 0.55/0.79 ( ( bot_bot_a_o @ X_24 )
% 0.55/0.79 <=> bot_bot_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_538_empty__def,axiom,
% 0.55/0.79 ( bot_bot_int_o
% 0.55/0.79 = ( collect_int
% 0.55/0.79 @ ^ [X_1: int] : $false ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_539_empty__def,axiom,
% 0.55/0.79 ( bot_bot_nat_o
% 0.55/0.79 = ( collect_nat
% 0.55/0.79 @ ^ [X_1: nat] : $false ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_540_empty__def,axiom,
% 0.55/0.79 ( bot_bot_a_o
% 0.55/0.79 = ( collect_a
% 0.55/0.79 @ ^ [X_1: x_a] : $false ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_541_bot__fun__def,axiom,
% 0.55/0.79 ! [X_1: nat] :
% 0.55/0.79 ( ( bot_bot_nat_o @ X_1 )
% 0.55/0.79 <=> bot_bot_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_542_bot__fun__def,axiom,
% 0.55/0.79 ! [X_1: int] :
% 0.55/0.79 ( ( bot_bot_int_o @ X_1 )
% 0.55/0.79 <=> bot_bot_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_543_bot__fun__def,axiom,
% 0.55/0.79 ! [X_1: x_a] :
% 0.55/0.79 ( ( bot_bot_a_o @ X_1 )
% 0.55/0.79 <=> bot_bot_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_544_insert__Diff,axiom,
% 0.55/0.79 ! [A_87: x_a,A_86: x_a > $o] :
% 0.55/0.79 ( ( member_a @ A_87 @ A_86 )
% 0.55/0.79 => ( ( insert_a @ A_87 @ ( minus_minus_a_o @ A_86 @ ( insert_a @ A_87 @ bot_bot_a_o ) ) )
% 0.55/0.79 = A_86 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_545_insert__Diff,axiom,
% 0.55/0.79 ! [A_87: int,A_86: int > $o] :
% 0.55/0.79 ( ( member_int @ A_87 @ A_86 )
% 0.55/0.79 => ( ( insert_int @ A_87 @ ( minus_minus_int_o @ A_86 @ ( insert_int @ A_87 @ bot_bot_int_o ) ) )
% 0.55/0.79 = A_86 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_546_insert__Diff,axiom,
% 0.55/0.79 ! [A_87: nat,A_86: nat > $o] :
% 0.55/0.79 ( ( member_nat @ A_87 @ A_86 )
% 0.55/0.79 => ( ( insert_nat @ A_87 @ ( minus_minus_nat_o @ A_86 @ ( insert_nat @ A_87 @ bot_bot_nat_o ) ) )
% 0.55/0.79 = A_86 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_547_insert__Diff,axiom,
% 0.55/0.79 ! [A_87: pname,A_86: pname > $o] :
% 0.55/0.79 ( ( member_pname @ A_87 @ A_86 )
% 0.55/0.79 => ( ( insert_pname @ A_87 @ ( minus_minus_pname_o @ A_86 @ ( insert_pname @ A_87 @ bot_bot_pname_o ) ) )
% 0.55/0.79 = A_86 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_548_Diff__insert__absorb,axiom,
% 0.55/0.79 ! [X_23: x_a,A_85: x_a > $o] :
% 0.55/0.79 ( ~ ( member_a @ X_23 @ A_85 )
% 0.55/0.79 => ( ( minus_minus_a_o @ ( insert_a @ X_23 @ A_85 ) @ ( insert_a @ X_23 @ bot_bot_a_o ) )
% 0.55/0.79 = A_85 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_549_Diff__insert__absorb,axiom,
% 0.55/0.79 ! [X_23: int,A_85: int > $o] :
% 0.55/0.79 ( ~ ( member_int @ X_23 @ A_85 )
% 0.55/0.79 => ( ( minus_minus_int_o @ ( insert_int @ X_23 @ A_85 ) @ ( insert_int @ X_23 @ bot_bot_int_o ) )
% 0.55/0.79 = A_85 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_550_Diff__insert__absorb,axiom,
% 0.55/0.79 ! [X_23: nat,A_85: nat > $o] :
% 0.55/0.79 ( ~ ( member_nat @ X_23 @ A_85 )
% 0.55/0.79 => ( ( minus_minus_nat_o @ ( insert_nat @ X_23 @ A_85 ) @ ( insert_nat @ X_23 @ bot_bot_nat_o ) )
% 0.55/0.79 = A_85 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_551_Diff__insert__absorb,axiom,
% 0.55/0.79 ! [X_23: pname,A_85: pname > $o] :
% 0.55/0.79 ( ~ ( member_pname @ X_23 @ A_85 )
% 0.55/0.79 => ( ( minus_minus_pname_o @ ( insert_pname @ X_23 @ A_85 ) @ ( insert_pname @ X_23 @ bot_bot_pname_o ) )
% 0.55/0.79 = A_85 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_552_insert__Diff__single,axiom,
% 0.55/0.79 ! [A_84: x_a,A_83: x_a > $o] :
% 0.55/0.79 ( ( insert_a @ A_84 @ ( minus_minus_a_o @ A_83 @ ( insert_a @ A_84 @ bot_bot_a_o ) ) )
% 0.55/0.79 = ( insert_a @ A_84 @ A_83 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_553_insert__Diff__single,axiom,
% 0.55/0.79 ! [A_84: nat,A_83: nat > $o] :
% 0.55/0.79 ( ( insert_nat @ A_84 @ ( minus_minus_nat_o @ A_83 @ ( insert_nat @ A_84 @ bot_bot_nat_o ) ) )
% 0.55/0.79 = ( insert_nat @ A_84 @ A_83 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_554_insert__Diff__single,axiom,
% 0.55/0.79 ! [A_84: int,A_83: int > $o] :
% 0.55/0.79 ( ( insert_int @ A_84 @ ( minus_minus_int_o @ A_83 @ ( insert_int @ A_84 @ bot_bot_int_o ) ) )
% 0.55/0.79 = ( insert_int @ A_84 @ A_83 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_555_Diff__insert2,axiom,
% 0.55/0.79 ! [A_82: x_a > $o,A_81: x_a,B_45: x_a > $o] :
% 0.55/0.79 ( ( minus_minus_a_o @ A_82 @ ( insert_a @ A_81 @ B_45 ) )
% 0.55/0.79 = ( minus_minus_a_o @ ( minus_minus_a_o @ A_82 @ ( insert_a @ A_81 @ bot_bot_a_o ) ) @ B_45 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_556_Diff__insert2,axiom,
% 0.55/0.79 ! [A_82: nat > $o,A_81: nat,B_45: nat > $o] :
% 0.55/0.79 ( ( minus_minus_nat_o @ A_82 @ ( insert_nat @ A_81 @ B_45 ) )
% 0.55/0.79 = ( minus_minus_nat_o @ ( minus_minus_nat_o @ A_82 @ ( insert_nat @ A_81 @ bot_bot_nat_o ) ) @ B_45 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_557_Diff__insert2,axiom,
% 0.55/0.79 ! [A_82: int > $o,A_81: int,B_45: int > $o] :
% 0.55/0.79 ( ( minus_minus_int_o @ A_82 @ ( insert_int @ A_81 @ B_45 ) )
% 0.55/0.79 = ( minus_minus_int_o @ ( minus_minus_int_o @ A_82 @ ( insert_int @ A_81 @ bot_bot_int_o ) ) @ B_45 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_558_Diff__insert,axiom,
% 0.55/0.79 ! [A_80: x_a > $o,A_79: x_a,B_44: x_a > $o] :
% 0.55/0.79 ( ( minus_minus_a_o @ A_80 @ ( insert_a @ A_79 @ B_44 ) )
% 0.55/0.79 = ( minus_minus_a_o @ ( minus_minus_a_o @ A_80 @ B_44 ) @ ( insert_a @ A_79 @ bot_bot_a_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_559_Diff__insert,axiom,
% 0.55/0.79 ! [A_80: nat > $o,A_79: nat,B_44: nat > $o] :
% 0.55/0.79 ( ( minus_minus_nat_o @ A_80 @ ( insert_nat @ A_79 @ B_44 ) )
% 0.55/0.79 = ( minus_minus_nat_o @ ( minus_minus_nat_o @ A_80 @ B_44 ) @ ( insert_nat @ A_79 @ bot_bot_nat_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_560_Diff__insert,axiom,
% 0.55/0.79 ! [A_80: int > $o,A_79: int,B_44: int > $o] :
% 0.55/0.79 ( ( minus_minus_int_o @ A_80 @ ( insert_int @ A_79 @ B_44 ) )
% 0.55/0.79 = ( minus_minus_int_o @ ( minus_minus_int_o @ A_80 @ B_44 ) @ ( insert_int @ A_79 @ bot_bot_int_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_561_diff__single__insert,axiom,
% 0.55/0.79 ! [A_78: x_a > $o,X_22: x_a,B_43: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ ( minus_minus_a_o @ A_78 @ ( insert_a @ X_22 @ bot_bot_a_o ) ) @ B_43 )
% 0.55/0.79 => ( ( member_a @ X_22 @ A_78 )
% 0.55/0.79 => ( ord_less_eq_a_o @ A_78 @ ( insert_a @ X_22 @ B_43 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_562_diff__single__insert,axiom,
% 0.55/0.79 ! [A_78: int > $o,X_22: int,B_43: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ ( minus_minus_int_o @ A_78 @ ( insert_int @ X_22 @ bot_bot_int_o ) ) @ B_43 )
% 0.55/0.79 => ( ( member_int @ X_22 @ A_78 )
% 0.55/0.79 => ( ord_less_eq_int_o @ A_78 @ ( insert_int @ X_22 @ B_43 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_563_diff__single__insert,axiom,
% 0.55/0.79 ! [A_78: nat > $o,X_22: nat,B_43: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ ( minus_minus_nat_o @ A_78 @ ( insert_nat @ X_22 @ bot_bot_nat_o ) ) @ B_43 )
% 0.55/0.79 => ( ( member_nat @ X_22 @ A_78 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ A_78 @ ( insert_nat @ X_22 @ B_43 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_564_diff__single__insert,axiom,
% 0.55/0.79 ! [A_78: pname > $o,X_22: pname,B_43: pname > $o] :
% 0.55/0.79 ( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_78 @ ( insert_pname @ X_22 @ bot_bot_pname_o ) ) @ B_43 )
% 0.55/0.79 => ( ( member_pname @ X_22 @ A_78 )
% 0.55/0.79 => ( ord_less_eq_pname_o @ A_78 @ ( insert_pname @ X_22 @ B_43 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_565_subset__insert__iff,axiom,
% 0.55/0.79 ! [A_77: x_a > $o,X_21: x_a,B_42: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_77 @ ( insert_a @ X_21 @ B_42 ) )
% 0.55/0.79 <=> ( ( ( member_a @ X_21 @ A_77 )
% 0.55/0.79 => ( ord_less_eq_a_o @ ( minus_minus_a_o @ A_77 @ ( insert_a @ X_21 @ bot_bot_a_o ) ) @ B_42 ) )
% 0.55/0.79 & ( ~ ( member_a @ X_21 @ A_77 )
% 0.55/0.79 => ( ord_less_eq_a_o @ A_77 @ B_42 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_566_subset__insert__iff,axiom,
% 0.55/0.79 ! [A_77: int > $o,X_21: int,B_42: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_77 @ ( insert_int @ X_21 @ B_42 ) )
% 0.55/0.79 <=> ( ( ( member_int @ X_21 @ A_77 )
% 0.55/0.79 => ( ord_less_eq_int_o @ ( minus_minus_int_o @ A_77 @ ( insert_int @ X_21 @ bot_bot_int_o ) ) @ B_42 ) )
% 0.55/0.79 & ( ~ ( member_int @ X_21 @ A_77 )
% 0.55/0.79 => ( ord_less_eq_int_o @ A_77 @ B_42 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_567_subset__insert__iff,axiom,
% 0.55/0.79 ! [A_77: nat > $o,X_21: nat,B_42: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_77 @ ( insert_nat @ X_21 @ B_42 ) )
% 0.55/0.79 <=> ( ( ( member_nat @ X_21 @ A_77 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ ( minus_minus_nat_o @ A_77 @ ( insert_nat @ X_21 @ bot_bot_nat_o ) ) @ B_42 ) )
% 0.55/0.79 & ( ~ ( member_nat @ X_21 @ A_77 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ A_77 @ B_42 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_568_subset__insert__iff,axiom,
% 0.55/0.79 ! [A_77: pname > $o,X_21: pname,B_42: pname > $o] :
% 0.55/0.79 ( ( ord_less_eq_pname_o @ A_77 @ ( insert_pname @ X_21 @ B_42 ) )
% 0.55/0.79 <=> ( ( ( member_pname @ X_21 @ A_77 )
% 0.55/0.79 => ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_77 @ ( insert_pname @ X_21 @ bot_bot_pname_o ) ) @ B_42 ) )
% 0.55/0.79 & ( ~ ( member_pname @ X_21 @ A_77 )
% 0.55/0.79 => ( ord_less_eq_pname_o @ A_77 @ B_42 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_569_finite__Diff2,axiom,
% 0.55/0.79 ! [A_76: int > $o,B_41: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ B_41 )
% 0.55/0.79 => ( ( finite_finite_int @ ( minus_minus_int_o @ A_76 @ B_41 ) )
% 0.55/0.79 <=> ( finite_finite_int @ A_76 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_570_finite__Diff2,axiom,
% 0.55/0.79 ! [A_76: nat > $o,B_41: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ B_41 )
% 0.55/0.79 => ( ( finite_finite_nat @ ( minus_minus_nat_o @ A_76 @ B_41 ) )
% 0.55/0.79 <=> ( finite_finite_nat @ A_76 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_571_finite__Diff2,axiom,
% 0.55/0.79 ! [A_76: pname > $o,B_41: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ B_41 )
% 0.55/0.79 => ( ( finite_finite_pname @ ( minus_minus_pname_o @ A_76 @ B_41 ) )
% 0.55/0.79 <=> ( finite_finite_pname @ A_76 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_572_insert__Diff1,axiom,
% 0.55/0.79 ! [A_75: x_a > $o,X_20: x_a,B_40: x_a > $o] :
% 0.55/0.79 ( ( member_a @ X_20 @ B_40 )
% 0.55/0.79 => ( ( minus_minus_a_o @ ( insert_a @ X_20 @ A_75 ) @ B_40 )
% 0.55/0.79 = ( minus_minus_a_o @ A_75 @ B_40 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_573_insert__Diff1,axiom,
% 0.55/0.79 ! [A_75: int > $o,X_20: int,B_40: int > $o] :
% 0.55/0.79 ( ( member_int @ X_20 @ B_40 )
% 0.55/0.79 => ( ( minus_minus_int_o @ ( insert_int @ X_20 @ A_75 ) @ B_40 )
% 0.55/0.79 = ( minus_minus_int_o @ A_75 @ B_40 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_574_insert__Diff1,axiom,
% 0.55/0.79 ! [A_75: nat > $o,X_20: nat,B_40: nat > $o] :
% 0.55/0.79 ( ( member_nat @ X_20 @ B_40 )
% 0.55/0.79 => ( ( minus_minus_nat_o @ ( insert_nat @ X_20 @ A_75 ) @ B_40 )
% 0.55/0.79 = ( minus_minus_nat_o @ A_75 @ B_40 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_575_insert__Diff1,axiom,
% 0.55/0.79 ! [A_75: pname > $o,X_20: pname,B_40: pname > $o] :
% 0.55/0.79 ( ( member_pname @ X_20 @ B_40 )
% 0.55/0.79 => ( ( minus_minus_pname_o @ ( insert_pname @ X_20 @ A_75 ) @ B_40 )
% 0.55/0.79 = ( minus_minus_pname_o @ A_75 @ B_40 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_576_insert__Diff__if,axiom,
% 0.55/0.79 ! [A_74: x_a > $o,X_19: x_a,B_39: x_a > $o] :
% 0.55/0.79 ( ( ( member_a @ X_19 @ B_39 )
% 0.55/0.79 => ( ( minus_minus_a_o @ ( insert_a @ X_19 @ A_74 ) @ B_39 )
% 0.55/0.79 = ( minus_minus_a_o @ A_74 @ B_39 ) ) )
% 0.55/0.79 & ( ~ ( member_a @ X_19 @ B_39 )
% 0.55/0.79 => ( ( minus_minus_a_o @ ( insert_a @ X_19 @ A_74 ) @ B_39 )
% 0.55/0.79 = ( insert_a @ X_19 @ ( minus_minus_a_o @ A_74 @ B_39 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_577_insert__Diff__if,axiom,
% 0.55/0.79 ! [A_74: int > $o,X_19: int,B_39: int > $o] :
% 0.55/0.79 ( ( ( member_int @ X_19 @ B_39 )
% 0.55/0.79 => ( ( minus_minus_int_o @ ( insert_int @ X_19 @ A_74 ) @ B_39 )
% 0.55/0.79 = ( minus_minus_int_o @ A_74 @ B_39 ) ) )
% 0.55/0.79 & ( ~ ( member_int @ X_19 @ B_39 )
% 0.55/0.79 => ( ( minus_minus_int_o @ ( insert_int @ X_19 @ A_74 ) @ B_39 )
% 0.55/0.79 = ( insert_int @ X_19 @ ( minus_minus_int_o @ A_74 @ B_39 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_578_insert__Diff__if,axiom,
% 0.55/0.79 ! [A_74: nat > $o,X_19: nat,B_39: nat > $o] :
% 0.55/0.79 ( ( ( member_nat @ X_19 @ B_39 )
% 0.55/0.79 => ( ( minus_minus_nat_o @ ( insert_nat @ X_19 @ A_74 ) @ B_39 )
% 0.55/0.79 = ( minus_minus_nat_o @ A_74 @ B_39 ) ) )
% 0.55/0.79 & ( ~ ( member_nat @ X_19 @ B_39 )
% 0.55/0.79 => ( ( minus_minus_nat_o @ ( insert_nat @ X_19 @ A_74 ) @ B_39 )
% 0.55/0.79 = ( insert_nat @ X_19 @ ( minus_minus_nat_o @ A_74 @ B_39 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_579_insert__Diff__if,axiom,
% 0.55/0.79 ! [A_74: pname > $o,X_19: pname,B_39: pname > $o] :
% 0.55/0.79 ( ( ( member_pname @ X_19 @ B_39 )
% 0.55/0.79 => ( ( minus_minus_pname_o @ ( insert_pname @ X_19 @ A_74 ) @ B_39 )
% 0.55/0.79 = ( minus_minus_pname_o @ A_74 @ B_39 ) ) )
% 0.55/0.79 & ( ~ ( member_pname @ X_19 @ B_39 )
% 0.55/0.79 => ( ( minus_minus_pname_o @ ( insert_pname @ X_19 @ A_74 ) @ B_39 )
% 0.55/0.79 = ( insert_pname @ X_19 @ ( minus_minus_pname_o @ A_74 @ B_39 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_580_double__diff,axiom,
% 0.55/0.79 ! [C_24: int > $o,A_73: int > $o,B_38: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_73 @ B_38 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ B_38 @ C_24 )
% 0.55/0.79 => ( ( minus_minus_int_o @ B_38 @ ( minus_minus_int_o @ C_24 @ A_73 ) )
% 0.55/0.79 = A_73 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_581_double__diff,axiom,
% 0.55/0.79 ! [C_24: nat > $o,A_73: nat > $o,B_38: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_73 @ B_38 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ B_38 @ C_24 )
% 0.55/0.79 => ( ( minus_minus_nat_o @ B_38 @ ( minus_minus_nat_o @ C_24 @ A_73 ) )
% 0.55/0.79 = A_73 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_582_double__diff,axiom,
% 0.55/0.79 ! [C_24: x_a > $o,A_73: x_a > $o,B_38: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_73 @ B_38 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ B_38 @ C_24 )
% 0.55/0.79 => ( ( minus_minus_a_o @ B_38 @ ( minus_minus_a_o @ C_24 @ A_73 ) )
% 0.55/0.79 = A_73 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_583_Diff__mono,axiom,
% 0.55/0.79 ! [D_5: int > $o,B_37: int > $o,A_72: int > $o,C_23: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_72 @ C_23 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ D_5 @ B_37 )
% 0.55/0.79 => ( ord_less_eq_int_o @ ( minus_minus_int_o @ A_72 @ B_37 ) @ ( minus_minus_int_o @ C_23 @ D_5 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_584_Diff__mono,axiom,
% 0.55/0.79 ! [D_5: nat > $o,B_37: nat > $o,A_72: nat > $o,C_23: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_72 @ C_23 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ D_5 @ B_37 )
% 0.55/0.79 => ( ord_less_eq_nat_o @ ( minus_minus_nat_o @ A_72 @ B_37 ) @ ( minus_minus_nat_o @ C_23 @ D_5 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_585_Diff__mono,axiom,
% 0.55/0.79 ! [D_5: x_a > $o,B_37: x_a > $o,A_72: x_a > $o,C_23: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_72 @ C_23 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ D_5 @ B_37 )
% 0.55/0.79 => ( ord_less_eq_a_o @ ( minus_minus_a_o @ A_72 @ B_37 ) @ ( minus_minus_a_o @ C_23 @ D_5 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_586_Diff__subset,axiom,
% 0.55/0.79 ! [A_71: int > $o,B_36: int > $o] : ( ord_less_eq_int_o @ ( minus_minus_int_o @ A_71 @ B_36 ) @ A_71 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_587_Diff__subset,axiom,
% 0.55/0.79 ! [A_71: nat > $o,B_36: nat > $o] : ( ord_less_eq_nat_o @ ( minus_minus_nat_o @ A_71 @ B_36 ) @ A_71 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_588_Diff__subset,axiom,
% 0.55/0.79 ! [A_71: x_a > $o,B_36: x_a > $o] : ( ord_less_eq_a_o @ ( minus_minus_a_o @ A_71 @ B_36 ) @ A_71 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_589_singleton__inject,axiom,
% 0.55/0.79 ! [A_70: x_a,B_35: x_a] :
% 0.55/0.79 ( ( ( insert_a @ A_70 @ bot_bot_a_o )
% 0.55/0.79 = ( insert_a @ B_35 @ bot_bot_a_o ) )
% 0.55/0.79 => ( A_70 = B_35 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_590_singleton__inject,axiom,
% 0.55/0.79 ! [A_70: nat,B_35: nat] :
% 0.55/0.79 ( ( ( insert_nat @ A_70 @ bot_bot_nat_o )
% 0.55/0.79 = ( insert_nat @ B_35 @ bot_bot_nat_o ) )
% 0.55/0.79 => ( A_70 = B_35 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_591_singleton__inject,axiom,
% 0.55/0.79 ! [A_70: int,B_35: int] :
% 0.55/0.79 ( ( ( insert_int @ A_70 @ bot_bot_int_o )
% 0.55/0.79 = ( insert_int @ B_35 @ bot_bot_int_o ) )
% 0.55/0.79 => ( A_70 = B_35 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_592_singletonE,axiom,
% 0.55/0.79 ! [B_34: x_a,A_69: x_a] :
% 0.55/0.79 ( ( member_a @ B_34 @ ( insert_a @ A_69 @ bot_bot_a_o ) )
% 0.55/0.79 => ( B_34 = A_69 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_593_singletonE,axiom,
% 0.55/0.79 ! [B_34: int,A_69: int] :
% 0.55/0.79 ( ( member_int @ B_34 @ ( insert_int @ A_69 @ bot_bot_int_o ) )
% 0.55/0.79 => ( B_34 = A_69 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_594_singletonE,axiom,
% 0.55/0.79 ! [B_34: nat,A_69: nat] :
% 0.55/0.79 ( ( member_nat @ B_34 @ ( insert_nat @ A_69 @ bot_bot_nat_o ) )
% 0.55/0.79 => ( B_34 = A_69 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_595_singletonE,axiom,
% 0.55/0.79 ! [B_34: pname,A_69: pname] :
% 0.55/0.79 ( ( member_pname @ B_34 @ ( insert_pname @ A_69 @ bot_bot_pname_o ) )
% 0.55/0.79 => ( B_34 = A_69 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_596_doubleton__eq__iff,axiom,
% 0.55/0.79 ! [A_68: x_a,B_33: x_a,C_22: x_a,D_4: x_a] :
% 0.55/0.79 ( ( ( insert_a @ A_68 @ ( insert_a @ B_33 @ bot_bot_a_o ) )
% 0.55/0.79 = ( insert_a @ C_22 @ ( insert_a @ D_4 @ bot_bot_a_o ) ) )
% 0.55/0.79 <=> ( ( ( A_68 = C_22 )
% 0.55/0.79 & ( B_33 = D_4 ) )
% 0.55/0.79 | ( ( A_68 = D_4 )
% 0.55/0.79 & ( B_33 = C_22 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_597_doubleton__eq__iff,axiom,
% 0.55/0.79 ! [A_68: nat,B_33: nat,C_22: nat,D_4: nat] :
% 0.55/0.79 ( ( ( insert_nat @ A_68 @ ( insert_nat @ B_33 @ bot_bot_nat_o ) )
% 0.55/0.79 = ( insert_nat @ C_22 @ ( insert_nat @ D_4 @ bot_bot_nat_o ) ) )
% 0.55/0.79 <=> ( ( ( A_68 = C_22 )
% 0.55/0.79 & ( B_33 = D_4 ) )
% 0.55/0.79 | ( ( A_68 = D_4 )
% 0.55/0.79 & ( B_33 = C_22 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_598_doubleton__eq__iff,axiom,
% 0.55/0.79 ! [A_68: int,B_33: int,C_22: int,D_4: int] :
% 0.55/0.79 ( ( ( insert_int @ A_68 @ ( insert_int @ B_33 @ bot_bot_int_o ) )
% 0.55/0.79 = ( insert_int @ C_22 @ ( insert_int @ D_4 @ bot_bot_int_o ) ) )
% 0.55/0.79 <=> ( ( ( A_68 = C_22 )
% 0.55/0.79 & ( B_33 = D_4 ) )
% 0.55/0.79 | ( ( A_68 = D_4 )
% 0.55/0.79 & ( B_33 = C_22 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_599_singleton__iff,axiom,
% 0.55/0.79 ! [B_32: x_a,A_67: x_a] :
% 0.55/0.79 ( ( member_a @ B_32 @ ( insert_a @ A_67 @ bot_bot_a_o ) )
% 0.55/0.79 <=> ( B_32 = A_67 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_600_singleton__iff,axiom,
% 0.55/0.79 ! [B_32: int,A_67: int] :
% 0.55/0.79 ( ( member_int @ B_32 @ ( insert_int @ A_67 @ bot_bot_int_o ) )
% 0.55/0.79 <=> ( B_32 = A_67 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_601_singleton__iff,axiom,
% 0.55/0.79 ! [B_32: nat,A_67: nat] :
% 0.55/0.79 ( ( member_nat @ B_32 @ ( insert_nat @ A_67 @ bot_bot_nat_o ) )
% 0.55/0.79 <=> ( B_32 = A_67 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_602_singleton__iff,axiom,
% 0.55/0.79 ! [B_32: pname,A_67: pname] :
% 0.55/0.79 ( ( member_pname @ B_32 @ ( insert_pname @ A_67 @ bot_bot_pname_o ) )
% 0.55/0.79 <=> ( B_32 = A_67 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_603_insert__not__empty,axiom,
% 0.55/0.79 ! [A_66: x_a,A_65: x_a > $o] :
% 0.55/0.79 ( ( insert_a @ A_66 @ A_65 )
% 0.55/0.79 != bot_bot_a_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_604_insert__not__empty,axiom,
% 0.55/0.79 ! [A_66: nat,A_65: nat > $o] :
% 0.55/0.79 ( ( insert_nat @ A_66 @ A_65 )
% 0.55/0.79 != bot_bot_nat_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_605_insert__not__empty,axiom,
% 0.55/0.79 ! [A_66: int,A_65: int > $o] :
% 0.55/0.79 ( ( insert_int @ A_66 @ A_65 )
% 0.55/0.79 != bot_bot_int_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_606_empty__not__insert,axiom,
% 0.55/0.79 ! [A_64: x_a,A_63: x_a > $o] :
% 0.55/0.79 ( bot_bot_a_o
% 0.55/0.79 != ( insert_a @ A_64 @ A_63 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_607_empty__not__insert,axiom,
% 0.55/0.79 ! [A_64: nat,A_63: nat > $o] :
% 0.55/0.79 ( bot_bot_nat_o
% 0.55/0.79 != ( insert_nat @ A_64 @ A_63 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_608_empty__not__insert,axiom,
% 0.55/0.79 ! [A_64: int,A_63: int > $o] :
% 0.55/0.79 ( bot_bot_int_o
% 0.55/0.79 != ( insert_int @ A_64 @ A_63 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_609_subset__empty,axiom,
% 0.55/0.79 ! [A_62: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_62 @ bot_bot_nat_o )
% 0.55/0.79 <=> ( A_62 = bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_610_subset__empty,axiom,
% 0.55/0.79 ! [A_62: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_62 @ bot_bot_int_o )
% 0.55/0.79 <=> ( A_62 = bot_bot_int_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_611_subset__empty,axiom,
% 0.55/0.79 ! [A_62: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_62 @ bot_bot_a_o )
% 0.55/0.79 <=> ( A_62 = bot_bot_a_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_612_image__is__empty,axiom,
% 0.55/0.79 ! [F_22: nat > int,A_61: nat > $o] :
% 0.55/0.79 ( ( ( image_nat_int @ F_22 @ A_61 )
% 0.55/0.79 = bot_bot_int_o )
% 0.55/0.79 <=> ( A_61 = bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_613_image__is__empty,axiom,
% 0.55/0.79 ! [F_22: pname > x_a,A_61: pname > $o] :
% 0.55/0.79 ( ( ( image_pname_a @ F_22 @ A_61 )
% 0.55/0.79 = bot_bot_a_o )
% 0.55/0.79 <=> ( A_61 = bot_bot_pname_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_614_image__empty,axiom,
% 0.55/0.79 ! [F_21: nat > int] :
% 0.55/0.79 ( ( image_nat_int @ F_21 @ bot_bot_nat_o )
% 0.55/0.79 = bot_bot_int_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_615_image__empty,axiom,
% 0.55/0.79 ! [F_21: pname > x_a] :
% 0.55/0.79 ( ( image_pname_a @ F_21 @ bot_bot_pname_o )
% 0.55/0.79 = bot_bot_a_o ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_616_empty__is__image,axiom,
% 0.55/0.79 ! [F_20: nat > int,A_60: nat > $o] :
% 0.55/0.79 ( ( bot_bot_int_o
% 0.55/0.79 = ( image_nat_int @ F_20 @ A_60 ) )
% 0.55/0.79 <=> ( A_60 = bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_617_empty__is__image,axiom,
% 0.55/0.79 ! [F_20: pname > x_a,A_60: pname > $o] :
% 0.55/0.79 ( ( bot_bot_a_o
% 0.55/0.79 = ( image_pname_a @ F_20 @ A_60 ) )
% 0.55/0.79 <=> ( A_60 = bot_bot_pname_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_618_le__bot,axiom,
% 0.55/0.79 ! [A_59: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_59 @ bot_bot_nat_o )
% 0.55/0.79 => ( A_59 = bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_619_le__bot,axiom,
% 0.55/0.79 ! [A_59: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_59 @ bot_bot_int_o )
% 0.55/0.79 => ( A_59 = bot_bot_int_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_620_le__bot,axiom,
% 0.55/0.79 ! [A_59: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ A_59 @ bot_bot_nat )
% 0.55/0.79 => ( A_59 = bot_bot_nat ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_621_le__bot,axiom,
% 0.55/0.79 ! [A_59: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_59 @ bot_bot_a_o )
% 0.55/0.79 => ( A_59 = bot_bot_a_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_622_bot__unique,axiom,
% 0.55/0.79 ! [A_58: nat > $o] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_58 @ bot_bot_nat_o )
% 0.55/0.79 <=> ( A_58 = bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_623_bot__unique,axiom,
% 0.55/0.79 ! [A_58: int > $o] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_58 @ bot_bot_int_o )
% 0.55/0.79 <=> ( A_58 = bot_bot_int_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_624_bot__unique,axiom,
% 0.55/0.79 ! [A_58: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ A_58 @ bot_bot_nat )
% 0.55/0.79 <=> ( A_58 = bot_bot_nat ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_625_bot__unique,axiom,
% 0.55/0.79 ! [A_58: x_a > $o] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_58 @ bot_bot_a_o )
% 0.55/0.79 <=> ( A_58 = bot_bot_a_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_626_bot__least,axiom,
% 0.55/0.79 ! [A_57: nat > $o] : ( ord_less_eq_nat_o @ bot_bot_nat_o @ A_57 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_627_bot__least,axiom,
% 0.55/0.79 ! [A_57: int > $o] : ( ord_less_eq_int_o @ bot_bot_int_o @ A_57 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_628_bot__least,axiom,
% 0.55/0.79 ! [A_57: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A_57 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_629_bot__least,axiom,
% 0.55/0.79 ! [A_57: x_a > $o] : ( ord_less_eq_a_o @ bot_bot_a_o @ A_57 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_630_Collect__conv__if,axiom,
% 0.55/0.79 ! [P_7: x_a > $o,A_56: x_a] :
% 0.55/0.79 ( ( ( P_7 @ A_56 )
% 0.55/0.79 => ( ( collect_a
% 0.55/0.79 @ ^ [X_1: x_a] : ( (&) @ ( X_1 = A_56 ) @ ( P_7 @ X_1 ) ) )
% 0.55/0.79 = ( insert_a @ A_56 @ bot_bot_a_o ) ) )
% 0.55/0.79 & ( ~ ( P_7 @ A_56 )
% 0.55/0.79 => ( ( collect_a
% 0.55/0.79 @ ^ [X_1: x_a] : ( (&) @ ( X_1 = A_56 ) @ ( P_7 @ X_1 ) ) )
% 0.55/0.79 = bot_bot_a_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_631_Collect__conv__if,axiom,
% 0.55/0.79 ! [P_7: int > $o,A_56: int] :
% 0.55/0.79 ( ( ( P_7 @ A_56 )
% 0.55/0.79 => ( ( collect_int
% 0.55/0.79 @ ^ [X_1: int] : ( (&) @ ( X_1 = A_56 ) @ ( P_7 @ X_1 ) ) )
% 0.55/0.79 = ( insert_int @ A_56 @ bot_bot_int_o ) ) )
% 0.55/0.79 & ( ~ ( P_7 @ A_56 )
% 0.55/0.79 => ( ( collect_int
% 0.55/0.79 @ ^ [X_1: int] : ( (&) @ ( X_1 = A_56 ) @ ( P_7 @ X_1 ) ) )
% 0.55/0.79 = bot_bot_int_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_632_Collect__conv__if,axiom,
% 0.55/0.79 ! [P_7: nat > $o,A_56: nat] :
% 0.55/0.79 ( ( ( P_7 @ A_56 )
% 0.55/0.79 => ( ( collect_nat
% 0.55/0.79 @ ^ [X_1: nat] : ( (&) @ ( X_1 = A_56 ) @ ( P_7 @ X_1 ) ) )
% 0.55/0.79 = ( insert_nat @ A_56 @ bot_bot_nat_o ) ) )
% 0.55/0.79 & ( ~ ( P_7 @ A_56 )
% 0.55/0.79 => ( ( collect_nat
% 0.55/0.79 @ ^ [X_1: nat] : ( (&) @ ( X_1 = A_56 ) @ ( P_7 @ X_1 ) ) )
% 0.55/0.79 = bot_bot_nat_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_633_Collect__conv__if2,axiom,
% 0.55/0.79 ! [P_6: x_a > $o,A_55: x_a] :
% 0.55/0.79 ( ( ( P_6 @ A_55 )
% 0.55/0.79 => ( ( collect_a
% 0.55/0.79 @ ^ [X_1: x_a] : ( (&) @ ( A_55 = X_1 ) @ ( P_6 @ X_1 ) ) )
% 0.55/0.79 = ( insert_a @ A_55 @ bot_bot_a_o ) ) )
% 0.55/0.79 & ( ~ ( P_6 @ A_55 )
% 0.55/0.79 => ( ( collect_a
% 0.55/0.79 @ ^ [X_1: x_a] : ( (&) @ ( A_55 = X_1 ) @ ( P_6 @ X_1 ) ) )
% 0.55/0.79 = bot_bot_a_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_634_Collect__conv__if2,axiom,
% 0.55/0.79 ! [P_6: int > $o,A_55: int] :
% 0.55/0.79 ( ( ( P_6 @ A_55 )
% 0.55/0.79 => ( ( collect_int
% 0.55/0.79 @ ^ [X_1: int] : ( (&) @ ( A_55 = X_1 ) @ ( P_6 @ X_1 ) ) )
% 0.55/0.79 = ( insert_int @ A_55 @ bot_bot_int_o ) ) )
% 0.55/0.79 & ( ~ ( P_6 @ A_55 )
% 0.55/0.79 => ( ( collect_int
% 0.55/0.79 @ ^ [X_1: int] : ( (&) @ ( A_55 = X_1 ) @ ( P_6 @ X_1 ) ) )
% 0.55/0.79 = bot_bot_int_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_635_Collect__conv__if2,axiom,
% 0.55/0.79 ! [P_6: nat > $o,A_55: nat] :
% 0.55/0.79 ( ( ( P_6 @ A_55 )
% 0.55/0.79 => ( ( collect_nat
% 0.55/0.79 @ ^ [X_1: nat] : ( (&) @ ( A_55 = X_1 ) @ ( P_6 @ X_1 ) ) )
% 0.55/0.79 = ( insert_nat @ A_55 @ bot_bot_nat_o ) ) )
% 0.55/0.79 & ( ~ ( P_6 @ A_55 )
% 0.55/0.79 => ( ( collect_nat
% 0.55/0.79 @ ^ [X_1: nat] : ( (&) @ ( A_55 = X_1 ) @ ( P_6 @ X_1 ) ) )
% 0.55/0.79 = bot_bot_nat_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_636_singleton__conv,axiom,
% 0.55/0.79 ! [A_54: x_a] :
% 0.55/0.79 ( ( collect_a
% 0.55/0.79 @ ^ [X_1: x_a] : ( X_1 = A_54 ) )
% 0.55/0.79 = ( insert_a @ A_54 @ bot_bot_a_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_637_singleton__conv,axiom,
% 0.55/0.79 ! [A_54: int] :
% 0.55/0.79 ( ( collect_int
% 0.55/0.79 @ ^ [X_1: int] : ( X_1 = A_54 ) )
% 0.55/0.79 = ( insert_int @ A_54 @ bot_bot_int_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_638_singleton__conv,axiom,
% 0.55/0.79 ! [A_54: nat] :
% 0.55/0.79 ( ( collect_nat
% 0.55/0.79 @ ^ [X_1: nat] : ( X_1 = A_54 ) )
% 0.55/0.79 = ( insert_nat @ A_54 @ bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_639_singleton__conv2,axiom,
% 0.55/0.79 ! [A_53: x_a] :
% 0.55/0.79 ( ( collect_a @ ( fequal_a @ A_53 ) )
% 0.55/0.79 = ( insert_a @ A_53 @ bot_bot_a_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_640_singleton__conv2,axiom,
% 0.55/0.79 ! [A_53: int] :
% 0.55/0.79 ( ( collect_int @ ( fequal_int @ A_53 ) )
% 0.55/0.79 = ( insert_int @ A_53 @ bot_bot_int_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_641_singleton__conv2,axiom,
% 0.55/0.79 ! [A_53: nat] :
% 0.55/0.79 ( ( collect_nat @ ( fequal_nat @ A_53 ) )
% 0.55/0.79 = ( insert_nat @ A_53 @ bot_bot_nat_o ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_642_card__Suc__Diff1,axiom,
% 0.55/0.79 ! [X_18: x_a,A_52: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_52 )
% 0.55/0.79 => ( ( member_a @ X_18 @ A_52 )
% 0.55/0.79 => ( ( suc @ ( finite_card_a @ ( minus_minus_a_o @ A_52 @ ( insert_a @ X_18 @ bot_bot_a_o ) ) ) )
% 0.55/0.79 = ( finite_card_a @ A_52 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_643_card__Suc__Diff1,axiom,
% 0.55/0.79 ! [X_18: int,A_52: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_52 )
% 0.55/0.79 => ( ( member_int @ X_18 @ A_52 )
% 0.55/0.79 => ( ( suc @ ( finite_card_int @ ( minus_minus_int_o @ A_52 @ ( insert_int @ X_18 @ bot_bot_int_o ) ) ) )
% 0.55/0.79 = ( finite_card_int @ A_52 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_644_card__Suc__Diff1,axiom,
% 0.55/0.79 ! [X_18: nat,A_52: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_52 )
% 0.55/0.79 => ( ( member_nat @ X_18 @ A_52 )
% 0.55/0.79 => ( ( suc @ ( finite_card_nat @ ( minus_minus_nat_o @ A_52 @ ( insert_nat @ X_18 @ bot_bot_nat_o ) ) ) )
% 0.55/0.79 = ( finite_card_nat @ A_52 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_645_card__Suc__Diff1,axiom,
% 0.55/0.79 ! [X_18: pname,A_52: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_52 )
% 0.55/0.79 => ( ( member_pname @ X_18 @ A_52 )
% 0.55/0.79 => ( ( suc @ ( finite_card_pname @ ( minus_minus_pname_o @ A_52 @ ( insert_pname @ X_18 @ bot_bot_pname_o ) ) ) )
% 0.55/0.79 = ( finite_card_pname @ A_52 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_646_card__insert,axiom,
% 0.55/0.79 ! [X_17: x_a,A_51: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_51 )
% 0.55/0.79 => ( ( finite_card_a @ ( insert_a @ X_17 @ A_51 ) )
% 0.55/0.79 = ( suc @ ( finite_card_a @ ( minus_minus_a_o @ A_51 @ ( insert_a @ X_17 @ bot_bot_a_o ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_647_card__insert,axiom,
% 0.55/0.79 ! [X_17: int,A_51: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_51 )
% 0.55/0.79 => ( ( finite_card_int @ ( insert_int @ X_17 @ A_51 ) )
% 0.55/0.79 = ( suc @ ( finite_card_int @ ( minus_minus_int_o @ A_51 @ ( insert_int @ X_17 @ bot_bot_int_o ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_648_card__insert,axiom,
% 0.55/0.79 ! [X_17: nat,A_51: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_51 )
% 0.55/0.79 => ( ( finite_card_nat @ ( insert_nat @ X_17 @ A_51 ) )
% 0.55/0.79 = ( suc @ ( finite_card_nat @ ( minus_minus_nat_o @ A_51 @ ( insert_nat @ X_17 @ bot_bot_nat_o ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_649_card__insert,axiom,
% 0.55/0.79 ! [X_17: pname,A_51: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_51 )
% 0.55/0.79 => ( ( finite_card_pname @ ( insert_pname @ X_17 @ A_51 ) )
% 0.55/0.79 = ( suc @ ( finite_card_pname @ ( minus_minus_pname_o @ A_51 @ ( insert_pname @ X_17 @ bot_bot_pname_o ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_650_card__Diff1__le,axiom,
% 0.55/0.79 ! [X_16: x_a,A_50: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_50 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( finite_card_a @ ( minus_minus_a_o @ A_50 @ ( insert_a @ X_16 @ bot_bot_a_o ) ) ) @ ( finite_card_a @ A_50 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_651_card__Diff1__le,axiom,
% 0.55/0.79 ! [X_16: int,A_50: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_50 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_int_o @ A_50 @ ( insert_int @ X_16 @ bot_bot_int_o ) ) ) @ ( finite_card_int @ A_50 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_652_card__Diff1__le,axiom,
% 0.55/0.79 ! [X_16: nat,A_50: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_50 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_nat_o @ A_50 @ ( insert_nat @ X_16 @ bot_bot_nat_o ) ) ) @ ( finite_card_nat @ A_50 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_653_card__Diff1__le,axiom,
% 0.55/0.79 ! [X_16: pname,A_50: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_50 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ A_50 @ ( insert_pname @ X_16 @ bot_bot_pname_o ) ) ) @ ( finite_card_pname @ A_50 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_654_finite__Diff__insert,axiom,
% 0.55/0.79 ! [A_49: x_a > $o,A_48: x_a,B_31: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ ( minus_minus_a_o @ A_49 @ ( insert_a @ A_48 @ B_31 ) ) )
% 0.55/0.79 <=> ( finite_finite_a @ ( minus_minus_a_o @ A_49 @ B_31 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_655_finite__Diff__insert,axiom,
% 0.55/0.79 ! [A_49: int > $o,A_48: int,B_31: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ ( minus_minus_int_o @ A_49 @ ( insert_int @ A_48 @ B_31 ) ) )
% 0.55/0.79 <=> ( finite_finite_int @ ( minus_minus_int_o @ A_49 @ B_31 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_656_finite__Diff__insert,axiom,
% 0.55/0.79 ! [A_49: nat > $o,A_48: nat,B_31: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ ( minus_minus_nat_o @ A_49 @ ( insert_nat @ A_48 @ B_31 ) ) )
% 0.55/0.79 <=> ( finite_finite_nat @ ( minus_minus_nat_o @ A_49 @ B_31 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_657_finite__Diff__insert,axiom,
% 0.55/0.79 ! [A_49: pname > $o,A_48: pname,B_31: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ ( minus_minus_pname_o @ A_49 @ ( insert_pname @ A_48 @ B_31 ) ) )
% 0.55/0.79 <=> ( finite_finite_pname @ ( minus_minus_pname_o @ A_49 @ B_31 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_658_image__diff__subset,axiom,
% 0.55/0.79 ! [F_19: nat > int,A_47: nat > $o,B_30: nat > $o] : ( ord_less_eq_int_o @ ( minus_minus_int_o @ ( image_nat_int @ F_19 @ A_47 ) @ ( image_nat_int @ F_19 @ B_30 ) ) @ ( image_nat_int @ F_19 @ ( minus_minus_nat_o @ A_47 @ B_30 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_659_image__diff__subset,axiom,
% 0.55/0.79 ! [F_19: pname > x_a,A_47: pname > $o,B_30: pname > $o] : ( ord_less_eq_a_o @ ( minus_minus_a_o @ ( image_pname_a @ F_19 @ A_47 ) @ ( image_pname_a @ F_19 @ B_30 ) ) @ ( image_pname_a @ F_19 @ ( minus_minus_pname_o @ A_47 @ B_30 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_660_subset__singletonD,axiom,
% 0.55/0.79 ! [A_46: x_a > $o,X_15: x_a] :
% 0.55/0.79 ( ( ord_less_eq_a_o @ A_46 @ ( insert_a @ X_15 @ bot_bot_a_o ) )
% 0.55/0.79 => ( ( A_46 = bot_bot_a_o )
% 0.55/0.79 | ( A_46
% 0.55/0.79 = ( insert_a @ X_15 @ bot_bot_a_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_661_subset__singletonD,axiom,
% 0.55/0.79 ! [A_46: nat > $o,X_15: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat_o @ A_46 @ ( insert_nat @ X_15 @ bot_bot_nat_o ) )
% 0.55/0.79 => ( ( A_46 = bot_bot_nat_o )
% 0.55/0.79 | ( A_46
% 0.55/0.79 = ( insert_nat @ X_15 @ bot_bot_nat_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_662_subset__singletonD,axiom,
% 0.55/0.79 ! [A_46: int > $o,X_15: int] :
% 0.55/0.79 ( ( ord_less_eq_int_o @ A_46 @ ( insert_int @ X_15 @ bot_bot_int_o ) )
% 0.55/0.79 => ( ( A_46 = bot_bot_int_o )
% 0.55/0.79 | ( A_46
% 0.55/0.79 = ( insert_int @ X_15 @ bot_bot_int_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_663_nat__case__Suc,axiom,
% 0.55/0.79 ! [F1: nat,F2: nat > nat,Nat_3: nat] :
% 0.55/0.79 ( ( nat_case_nat @ F1 @ F2 @ ( suc @ Nat_3 ) )
% 0.55/0.79 = ( F2 @ Nat_3 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_664_nat__case__Suc,axiom,
% 0.55/0.79 ! [F1: $o,F2: nat > $o,Nat_3: nat] :
% 0.55/0.79 ( ( nat_case_o @ F1 @ F2 @ ( suc @ Nat_3 ) )
% 0.55/0.79 <=> ( F2 @ Nat_3 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_665_image__constant,axiom,
% 0.55/0.79 ! [C_21: int,X_14: nat,A_45: nat > $o] :
% 0.55/0.79 ( ( member_nat @ X_14 @ A_45 )
% 0.55/0.79 => ( ( image_nat_int
% 0.55/0.79 @ ^ [X_1: nat] : C_21
% 0.55/0.79 @ A_45 )
% 0.55/0.79 = ( insert_int @ C_21 @ bot_bot_int_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_666_image__constant,axiom,
% 0.55/0.79 ! [C_21: x_a,X_14: pname,A_45: pname > $o] :
% 0.55/0.79 ( ( member_pname @ X_14 @ A_45 )
% 0.55/0.79 => ( ( image_pname_a
% 0.55/0.79 @ ^ [X_1: pname] : C_21
% 0.55/0.79 @ A_45 )
% 0.55/0.79 = ( insert_a @ C_21 @ bot_bot_a_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_667_image__constant__conv,axiom,
% 0.55/0.79 ! [C_20: int,A_44: nat > $o] :
% 0.55/0.79 ( ( ( A_44 = bot_bot_nat_o )
% 0.55/0.79 => ( ( image_nat_int
% 0.55/0.79 @ ^ [X_1: nat] : C_20
% 0.55/0.79 @ A_44 )
% 0.55/0.79 = bot_bot_int_o ) )
% 0.55/0.79 & ( ( A_44 != bot_bot_nat_o )
% 0.55/0.79 => ( ( image_nat_int
% 0.55/0.79 @ ^ [X_1: nat] : C_20
% 0.55/0.79 @ A_44 )
% 0.55/0.79 = ( insert_int @ C_20 @ bot_bot_int_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_668_image__constant__conv,axiom,
% 0.55/0.79 ! [C_20: x_a,A_44: pname > $o] :
% 0.55/0.79 ( ( ( A_44 = bot_bot_pname_o )
% 0.55/0.79 => ( ( image_pname_a
% 0.55/0.79 @ ^ [X_1: pname] : C_20
% 0.55/0.79 @ A_44 )
% 0.55/0.79 = bot_bot_a_o ) )
% 0.55/0.79 & ( ( A_44 != bot_bot_pname_o )
% 0.55/0.79 => ( ( image_pname_a
% 0.55/0.79 @ ^ [X_1: pname] : C_20
% 0.55/0.79 @ A_44 )
% 0.55/0.79 = ( insert_a @ C_20 @ bot_bot_a_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_669_diff__eq__diff__eq,axiom,
% 0.55/0.79 ! [A_43: int,B_29: int,C_19: int,D_3: int] :
% 0.55/0.79 ( ( ( minus_minus_int @ A_43 @ B_29 )
% 0.55/0.79 = ( minus_minus_int @ C_19 @ D_3 ) )
% 0.55/0.79 => ( ( A_43 = B_29 )
% 0.55/0.79 <=> ( C_19 = D_3 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_670_card__Diff__subset,axiom,
% 0.55/0.79 ! [A_42: int > $o,B_28: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ B_28 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ B_28 @ A_42 )
% 0.55/0.79 => ( ( finite_card_int @ ( minus_minus_int_o @ A_42 @ B_28 ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_int @ A_42 ) @ ( finite_card_int @ B_28 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_671_card__Diff__subset,axiom,
% 0.55/0.79 ! [A_42: nat > $o,B_28: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ B_28 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ B_28 @ A_42 )
% 0.55/0.79 => ( ( finite_card_nat @ ( minus_minus_nat_o @ A_42 @ B_28 ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_nat @ A_42 ) @ ( finite_card_nat @ B_28 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_672_card__Diff__subset,axiom,
% 0.55/0.79 ! [A_42: x_a > $o,B_28: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ B_28 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ B_28 @ A_42 )
% 0.55/0.79 => ( ( finite_card_a @ ( minus_minus_a_o @ A_42 @ B_28 ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_a @ A_42 ) @ ( finite_card_a @ B_28 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_673_card__Diff__subset,axiom,
% 0.55/0.79 ! [A_42: pname > $o,B_28: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ B_28 )
% 0.55/0.79 => ( ( ord_less_eq_pname_o @ B_28 @ A_42 )
% 0.55/0.79 => ( ( finite_card_pname @ ( minus_minus_pname_o @ A_42 @ B_28 ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_pname @ A_42 ) @ ( finite_card_pname @ B_28 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_674_diff__card__le__card__Diff,axiom,
% 0.55/0.79 ! [A_41: int > $o,B_27: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ B_27 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_int @ A_41 ) @ ( finite_card_int @ B_27 ) ) @ ( finite_card_int @ ( minus_minus_int_o @ A_41 @ B_27 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_675_diff__card__le__card__Diff,axiom,
% 0.55/0.79 ! [A_41: nat > $o,B_27: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ B_27 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_nat @ A_41 ) @ ( finite_card_nat @ B_27 ) ) @ ( finite_card_nat @ ( minus_minus_nat_o @ A_41 @ B_27 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_676_diff__card__le__card__Diff,axiom,
% 0.55/0.79 ! [A_41: x_a > $o,B_27: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ B_27 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_a @ A_41 ) @ ( finite_card_a @ B_27 ) ) @ ( finite_card_a @ ( minus_minus_a_o @ A_41 @ B_27 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_677_diff__card__le__card__Diff,axiom,
% 0.55/0.79 ! [A_41: pname > $o,B_27: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ B_27 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_pname @ A_41 ) @ ( finite_card_pname @ B_27 ) ) @ ( finite_card_pname @ ( minus_minus_pname_o @ A_41 @ B_27 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_678_finite__subset__induct,axiom,
% 0.55/0.79 ! [P_5: ( x_a > $o ) > $o,A_40: x_a > $o,F_18: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ F_18 )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ F_18 @ A_40 )
% 0.55/0.79 => ( ( P_5 @ bot_bot_a_o )
% 0.55/0.79 => ( ! [A_37: x_a,F_2: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ F_2 )
% 0.55/0.79 => ( ( member_a @ A_37 @ A_40 )
% 0.55/0.79 => ( ~ ( member_a @ A_37 @ F_2 )
% 0.55/0.79 => ( ( P_5 @ F_2 )
% 0.55/0.79 => ( P_5 @ ( insert_a @ A_37 @ F_2 ) ) ) ) ) )
% 0.55/0.79 => ( P_5 @ F_18 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_679_finite__subset__induct,axiom,
% 0.55/0.79 ! [P_5: ( int > $o ) > $o,A_40: int > $o,F_18: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ F_18 )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ F_18 @ A_40 )
% 0.55/0.79 => ( ( P_5 @ bot_bot_int_o )
% 0.55/0.79 => ( ! [A_37: int,F_2: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ F_2 )
% 0.55/0.79 => ( ( member_int @ A_37 @ A_40 )
% 0.55/0.79 => ( ~ ( member_int @ A_37 @ F_2 )
% 0.55/0.79 => ( ( P_5 @ F_2 )
% 0.55/0.79 => ( P_5 @ ( insert_int @ A_37 @ F_2 ) ) ) ) ) )
% 0.55/0.79 => ( P_5 @ F_18 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_680_finite__subset__induct,axiom,
% 0.55/0.79 ! [P_5: ( nat > $o ) > $o,A_40: nat > $o,F_18: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ F_18 )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ F_18 @ A_40 )
% 0.55/0.79 => ( ( P_5 @ bot_bot_nat_o )
% 0.55/0.79 => ( ! [A_37: nat,F_2: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ F_2 )
% 0.55/0.79 => ( ( member_nat @ A_37 @ A_40 )
% 0.55/0.79 => ( ~ ( member_nat @ A_37 @ F_2 )
% 0.55/0.79 => ( ( P_5 @ F_2 )
% 0.55/0.79 => ( P_5 @ ( insert_nat @ A_37 @ F_2 ) ) ) ) ) )
% 0.55/0.79 => ( P_5 @ F_18 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_681_finite__subset__induct,axiom,
% 0.55/0.79 ! [P_5: ( pname > $o ) > $o,A_40: pname > $o,F_18: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ F_18 )
% 0.55/0.79 => ( ( ord_less_eq_pname_o @ F_18 @ A_40 )
% 0.55/0.79 => ( ( P_5 @ bot_bot_pname_o )
% 0.55/0.79 => ( ! [A_37: pname,F_2: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ F_2 )
% 0.55/0.79 => ( ( member_pname @ A_37 @ A_40 )
% 0.55/0.79 => ( ~ ( member_pname @ A_37 @ F_2 )
% 0.55/0.79 => ( ( P_5 @ F_2 )
% 0.55/0.79 => ( P_5 @ ( insert_pname @ A_37 @ F_2 ) ) ) ) ) )
% 0.55/0.79 => ( P_5 @ F_18 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_682_assms_I2_J,axiom,
% 0.55/0.79 ! [Pn: pname,G: x_a > $o] :
% 0.55/0.79 ( ( p @ ( insert_a @ ( mgt_call @ Pn ) @ G ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ Pn ) ) ) @ bot_bot_a_o ) )
% 0.55/0.79 => ( p @ G @ ( insert_a @ ( mgt_call @ Pn ) @ bot_bot_a_o ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_683_finite__empty__induct,axiom,
% 0.55/0.79 ! [P_4: ( x_a > $o ) > $o,A_39: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_39 )
% 0.55/0.79 => ( ( P_4 @ A_39 )
% 0.55/0.79 => ( ! [A_37: x_a,A_38: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_38 )
% 0.55/0.79 => ( ( member_a @ A_37 @ A_38 )
% 0.55/0.79 => ( ( P_4 @ A_38 )
% 0.55/0.79 => ( P_4 @ ( minus_minus_a_o @ A_38 @ ( insert_a @ A_37 @ bot_bot_a_o ) ) ) ) ) )
% 0.55/0.79 => ( P_4 @ bot_bot_a_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_684_finite__empty__induct,axiom,
% 0.55/0.79 ! [P_4: ( int > $o ) > $o,A_39: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_39 )
% 0.55/0.79 => ( ( P_4 @ A_39 )
% 0.55/0.79 => ( ! [A_37: int,A_38: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_38 )
% 0.55/0.79 => ( ( member_int @ A_37 @ A_38 )
% 0.55/0.79 => ( ( P_4 @ A_38 )
% 0.55/0.79 => ( P_4 @ ( minus_minus_int_o @ A_38 @ ( insert_int @ A_37 @ bot_bot_int_o ) ) ) ) ) )
% 0.55/0.79 => ( P_4 @ bot_bot_int_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_685_finite__empty__induct,axiom,
% 0.55/0.79 ! [P_4: ( nat > $o ) > $o,A_39: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_39 )
% 0.55/0.79 => ( ( P_4 @ A_39 )
% 0.55/0.79 => ( ! [A_37: nat,A_38: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_38 )
% 0.55/0.79 => ( ( member_nat @ A_37 @ A_38 )
% 0.55/0.79 => ( ( P_4 @ A_38 )
% 0.55/0.79 => ( P_4 @ ( minus_minus_nat_o @ A_38 @ ( insert_nat @ A_37 @ bot_bot_nat_o ) ) ) ) ) )
% 0.55/0.79 => ( P_4 @ bot_bot_nat_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_686_finite__empty__induct,axiom,
% 0.55/0.79 ! [P_4: ( pname > $o ) > $o,A_39: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_39 )
% 0.55/0.79 => ( ( P_4 @ A_39 )
% 0.55/0.79 => ( ! [A_37: pname,A_38: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_38 )
% 0.55/0.79 => ( ( member_pname @ A_37 @ A_38 )
% 0.55/0.79 => ( ( P_4 @ A_38 )
% 0.55/0.79 => ( P_4 @ ( minus_minus_pname_o @ A_38 @ ( insert_pname @ A_37 @ bot_bot_pname_o ) ) ) ) ) )
% 0.55/0.79 => ( P_4 @ bot_bot_pname_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_687_finite__induct,axiom,
% 0.55/0.79 ! [P_3: ( x_a > $o ) > $o,F_17: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ F_17 )
% 0.55/0.79 => ( ( P_3 @ bot_bot_a_o )
% 0.55/0.79 => ( ! [X_1: x_a,F_2: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ F_2 )
% 0.55/0.79 => ( ~ ( member_a @ X_1 @ F_2 )
% 0.55/0.79 => ( ( P_3 @ F_2 )
% 0.55/0.79 => ( P_3 @ ( insert_a @ X_1 @ F_2 ) ) ) ) )
% 0.55/0.79 => ( P_3 @ F_17 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_688_finite__induct,axiom,
% 0.55/0.79 ! [P_3: ( int > $o ) > $o,F_17: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ F_17 )
% 0.55/0.79 => ( ( P_3 @ bot_bot_int_o )
% 0.55/0.79 => ( ! [X_1: int,F_2: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ F_2 )
% 0.55/0.79 => ( ~ ( member_int @ X_1 @ F_2 )
% 0.55/0.79 => ( ( P_3 @ F_2 )
% 0.55/0.79 => ( P_3 @ ( insert_int @ X_1 @ F_2 ) ) ) ) )
% 0.55/0.79 => ( P_3 @ F_17 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_689_finite__induct,axiom,
% 0.55/0.79 ! [P_3: ( nat > $o ) > $o,F_17: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ F_17 )
% 0.55/0.79 => ( ( P_3 @ bot_bot_nat_o )
% 0.55/0.79 => ( ! [X_1: nat,F_2: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ F_2 )
% 0.55/0.79 => ( ~ ( member_nat @ X_1 @ F_2 )
% 0.55/0.79 => ( ( P_3 @ F_2 )
% 0.55/0.79 => ( P_3 @ ( insert_nat @ X_1 @ F_2 ) ) ) ) )
% 0.55/0.79 => ( P_3 @ F_17 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_690_finite__induct,axiom,
% 0.55/0.79 ! [P_3: ( pname > $o ) > $o,F_17: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ F_17 )
% 0.55/0.79 => ( ( P_3 @ bot_bot_pname_o )
% 0.55/0.79 => ( ! [X_1: pname,F_2: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ F_2 )
% 0.55/0.79 => ( ~ ( member_pname @ X_1 @ F_2 )
% 0.55/0.79 => ( ( P_3 @ F_2 )
% 0.55/0.79 => ( P_3 @ ( insert_pname @ X_1 @ F_2 ) ) ) ) )
% 0.55/0.79 => ( P_3 @ F_17 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_691_finite_Osimps,axiom,
% 0.55/0.79 ! [A_36: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_36 )
% 0.55/0.79 <=> ( ( A_36 = bot_bot_a_o )
% 0.55/0.79 | ? [A_38: x_a > $o,A_37: x_a] :
% 0.55/0.79 ( ( A_36
% 0.55/0.79 = ( insert_a @ A_37 @ A_38 ) )
% 0.55/0.79 & ( finite_finite_a @ A_38 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_692_finite_Osimps,axiom,
% 0.55/0.79 ! [A_36: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_36 )
% 0.55/0.79 <=> ( ( A_36 = bot_bot_int_o )
% 0.55/0.79 | ? [A_38: int > $o,A_37: int] :
% 0.55/0.79 ( ( A_36
% 0.55/0.79 = ( insert_int @ A_37 @ A_38 ) )
% 0.55/0.79 & ( finite_finite_int @ A_38 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_693_finite_Osimps,axiom,
% 0.55/0.79 ! [A_36: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_36 )
% 0.55/0.79 <=> ( ( A_36 = bot_bot_nat_o )
% 0.55/0.79 | ? [A_38: nat > $o,A_37: nat] :
% 0.55/0.79 ( ( A_36
% 0.55/0.79 = ( insert_nat @ A_37 @ A_38 ) )
% 0.55/0.79 & ( finite_finite_nat @ A_38 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_694_finite_Osimps,axiom,
% 0.55/0.79 ! [A_36: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_36 )
% 0.55/0.79 <=> ( ( A_36 = bot_bot_pname_o )
% 0.55/0.79 | ? [A_38: pname > $o,A_37: pname] :
% 0.55/0.79 ( ( A_36
% 0.55/0.79 = ( insert_pname @ A_37 @ A_38 ) )
% 0.55/0.79 & ( finite_finite_pname @ A_38 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_695_finite__less__ub,axiom,
% 0.55/0.79 ! [U: nat,F: nat > nat] :
% 0.55/0.79 ( ! [N_1: nat] : ( ord_less_eq_nat @ N_1 @ ( F @ N_1 ) )
% 0.55/0.79 => ( finite_finite_nat
% 0.55/0.79 @ ( collect_nat
% 0.55/0.79 @ ^ [N_1: nat] : ( ord_less_eq_nat @ ( F @ N_1 ) @ U ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_696_the__elem__eq,axiom,
% 0.55/0.79 ! [X_13: x_a] :
% 0.55/0.79 ( ( the_elem_a @ ( insert_a @ X_13 @ bot_bot_a_o ) )
% 0.55/0.79 = X_13 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_697_the__elem__eq,axiom,
% 0.55/0.79 ! [X_13: nat] :
% 0.55/0.79 ( ( the_elem_nat @ ( insert_nat @ X_13 @ bot_bot_nat_o ) )
% 0.55/0.79 = X_13 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_698_the__elem__eq,axiom,
% 0.55/0.79 ! [X_13: int] :
% 0.55/0.79 ( ( the_elem_int @ ( insert_int @ X_13 @ bot_bot_int_o ) )
% 0.55/0.79 = X_13 ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_699_nonempty__iff,axiom,
% 0.55/0.79 ! [A_35: x_a > $o] :
% 0.55/0.79 ( ( A_35 != bot_bot_a_o )
% 0.55/0.79 <=> ? [X_1: x_a,B_26: x_a > $o] :
% 0.55/0.79 ( ( A_35
% 0.55/0.79 = ( insert_a @ X_1 @ B_26 ) )
% 0.55/0.79 & ~ ( member_a @ X_1 @ B_26 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_700_nonempty__iff,axiom,
% 0.55/0.79 ! [A_35: int > $o] :
% 0.55/0.79 ( ( A_35 != bot_bot_int_o )
% 0.55/0.79 <=> ? [X_1: int,B_26: int > $o] :
% 0.55/0.79 ( ( A_35
% 0.55/0.79 = ( insert_int @ X_1 @ B_26 ) )
% 0.55/0.79 & ~ ( member_int @ X_1 @ B_26 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_701_nonempty__iff,axiom,
% 0.55/0.79 ! [A_35: nat > $o] :
% 0.55/0.79 ( ( A_35 != bot_bot_nat_o )
% 0.55/0.79 <=> ? [X_1: nat,B_26: nat > $o] :
% 0.55/0.79 ( ( A_35
% 0.55/0.79 = ( insert_nat @ X_1 @ B_26 ) )
% 0.55/0.79 & ~ ( member_nat @ X_1 @ B_26 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_702_nonempty__iff,axiom,
% 0.55/0.79 ! [A_35: pname > $o] :
% 0.55/0.79 ( ( A_35 != bot_bot_pname_o )
% 0.55/0.79 <=> ? [X_1: pname,B_26: pname > $o] :
% 0.55/0.79 ( ( A_35
% 0.55/0.79 = ( insert_pname @ X_1 @ B_26 ) )
% 0.55/0.79 & ~ ( member_pname @ X_1 @ B_26 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_703_assms_I4_J,axiom,
% 0.55/0.79 ! [Pn: pname] :
% 0.55/0.79 ( ( member_pname @ Pn @ u )
% 0.55/0.79 => ( wt @ ( the_com @ ( body @ Pn ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_704_DiffE,axiom,
% 0.55/0.79 ! [C_18: int,A_34: int > $o,B_25: int > $o] :
% 0.55/0.79 ( ( member_int @ C_18 @ ( minus_minus_int_o @ A_34 @ B_25 ) )
% 0.55/0.79 => ~ ( ( member_int @ C_18 @ A_34 )
% 0.55/0.79 => ( member_int @ C_18 @ B_25 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_705_DiffE,axiom,
% 0.55/0.79 ! [C_18: nat,A_34: nat > $o,B_25: nat > $o] :
% 0.55/0.79 ( ( member_nat @ C_18 @ ( minus_minus_nat_o @ A_34 @ B_25 ) )
% 0.55/0.79 => ~ ( ( member_nat @ C_18 @ A_34 )
% 0.55/0.79 => ( member_nat @ C_18 @ B_25 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_706_DiffE,axiom,
% 0.55/0.79 ! [C_18: x_a,A_34: x_a > $o,B_25: x_a > $o] :
% 0.55/0.79 ( ( member_a @ C_18 @ ( minus_minus_a_o @ A_34 @ B_25 ) )
% 0.55/0.79 => ~ ( ( member_a @ C_18 @ A_34 )
% 0.55/0.79 => ( member_a @ C_18 @ B_25 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_707_DiffE,axiom,
% 0.55/0.79 ! [C_18: pname,A_34: pname > $o,B_25: pname > $o] :
% 0.55/0.79 ( ( member_pname @ C_18 @ ( minus_minus_pname_o @ A_34 @ B_25 ) )
% 0.55/0.79 => ~ ( ( member_pname @ C_18 @ A_34 )
% 0.55/0.79 => ( member_pname @ C_18 @ B_25 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_708_DiffI,axiom,
% 0.55/0.79 ! [B_24: int > $o,C_17: int,A_33: int > $o] :
% 0.55/0.79 ( ( member_int @ C_17 @ A_33 )
% 0.55/0.79 => ( ~ ( member_int @ C_17 @ B_24 )
% 0.55/0.79 => ( member_int @ C_17 @ ( minus_minus_int_o @ A_33 @ B_24 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_709_DiffI,axiom,
% 0.55/0.79 ! [B_24: nat > $o,C_17: nat,A_33: nat > $o] :
% 0.55/0.79 ( ( member_nat @ C_17 @ A_33 )
% 0.55/0.79 => ( ~ ( member_nat @ C_17 @ B_24 )
% 0.55/0.79 => ( member_nat @ C_17 @ ( minus_minus_nat_o @ A_33 @ B_24 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_710_DiffI,axiom,
% 0.55/0.79 ! [B_24: x_a > $o,C_17: x_a,A_33: x_a > $o] :
% 0.55/0.79 ( ( member_a @ C_17 @ A_33 )
% 0.55/0.79 => ( ~ ( member_a @ C_17 @ B_24 )
% 0.55/0.79 => ( member_a @ C_17 @ ( minus_minus_a_o @ A_33 @ B_24 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_711_DiffI,axiom,
% 0.55/0.79 ! [B_24: pname > $o,C_17: pname,A_33: pname > $o] :
% 0.55/0.79 ( ( member_pname @ C_17 @ A_33 )
% 0.55/0.79 => ( ~ ( member_pname @ C_17 @ B_24 )
% 0.55/0.79 => ( member_pname @ C_17 @ ( minus_minus_pname_o @ A_33 @ B_24 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_712_DiffD2,axiom,
% 0.55/0.79 ! [C_16: int,A_32: int > $o,B_23: int > $o] :
% 0.55/0.79 ( ( member_int @ C_16 @ ( minus_minus_int_o @ A_32 @ B_23 ) )
% 0.55/0.79 => ~ ( member_int @ C_16 @ B_23 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_713_DiffD2,axiom,
% 0.55/0.79 ! [C_16: nat,A_32: nat > $o,B_23: nat > $o] :
% 0.55/0.79 ( ( member_nat @ C_16 @ ( minus_minus_nat_o @ A_32 @ B_23 ) )
% 0.55/0.79 => ~ ( member_nat @ C_16 @ B_23 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_714_DiffD2,axiom,
% 0.55/0.79 ! [C_16: x_a,A_32: x_a > $o,B_23: x_a > $o] :
% 0.55/0.79 ( ( member_a @ C_16 @ ( minus_minus_a_o @ A_32 @ B_23 ) )
% 0.55/0.79 => ~ ( member_a @ C_16 @ B_23 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_715_DiffD2,axiom,
% 0.55/0.79 ! [C_16: pname,A_32: pname > $o,B_23: pname > $o] :
% 0.55/0.79 ( ( member_pname @ C_16 @ ( minus_minus_pname_o @ A_32 @ B_23 ) )
% 0.55/0.79 => ~ ( member_pname @ C_16 @ B_23 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_716_DiffD1,axiom,
% 0.55/0.79 ! [C_15: int,A_31: int > $o,B_22: int > $o] :
% 0.55/0.79 ( ( member_int @ C_15 @ ( minus_minus_int_o @ A_31 @ B_22 ) )
% 0.55/0.79 => ( member_int @ C_15 @ A_31 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_717_DiffD1,axiom,
% 0.55/0.79 ! [C_15: nat,A_31: nat > $o,B_22: nat > $o] :
% 0.55/0.79 ( ( member_nat @ C_15 @ ( minus_minus_nat_o @ A_31 @ B_22 ) )
% 0.55/0.79 => ( member_nat @ C_15 @ A_31 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_718_DiffD1,axiom,
% 0.55/0.79 ! [C_15: x_a,A_31: x_a > $o,B_22: x_a > $o] :
% 0.55/0.79 ( ( member_a @ C_15 @ ( minus_minus_a_o @ A_31 @ B_22 ) )
% 0.55/0.79 => ( member_a @ C_15 @ A_31 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_719_DiffD1,axiom,
% 0.55/0.79 ! [C_15: pname,A_31: pname > $o,B_22: pname > $o] :
% 0.55/0.79 ( ( member_pname @ C_15 @ ( minus_minus_pname_o @ A_31 @ B_22 ) )
% 0.55/0.79 => ( member_pname @ C_15 @ A_31 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_720_Diff__iff,axiom,
% 0.55/0.79 ! [C_14: int,A_30: int > $o,B_21: int > $o] :
% 0.55/0.79 ( ( member_int @ C_14 @ ( minus_minus_int_o @ A_30 @ B_21 ) )
% 0.55/0.79 <=> ( ( member_int @ C_14 @ A_30 )
% 0.55/0.79 & ~ ( member_int @ C_14 @ B_21 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_721_Diff__iff,axiom,
% 0.55/0.79 ! [C_14: nat,A_30: nat > $o,B_21: nat > $o] :
% 0.55/0.79 ( ( member_nat @ C_14 @ ( minus_minus_nat_o @ A_30 @ B_21 ) )
% 0.55/0.79 <=> ( ( member_nat @ C_14 @ A_30 )
% 0.55/0.79 & ~ ( member_nat @ C_14 @ B_21 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_722_Diff__iff,axiom,
% 0.55/0.79 ! [C_14: x_a,A_30: x_a > $o,B_21: x_a > $o] :
% 0.55/0.79 ( ( member_a @ C_14 @ ( minus_minus_a_o @ A_30 @ B_21 ) )
% 0.55/0.79 <=> ( ( member_a @ C_14 @ A_30 )
% 0.55/0.79 & ~ ( member_a @ C_14 @ B_21 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_723_Diff__iff,axiom,
% 0.55/0.79 ! [C_14: pname,A_30: pname > $o,B_21: pname > $o] :
% 0.55/0.79 ( ( member_pname @ C_14 @ ( minus_minus_pname_o @ A_30 @ B_21 ) )
% 0.55/0.79 <=> ( ( member_pname @ C_14 @ A_30 )
% 0.55/0.79 & ~ ( member_pname @ C_14 @ B_21 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_724_set__diff__eq,axiom,
% 0.55/0.79 ! [A_29: int > $o,B_20: int > $o] :
% 0.55/0.79 ( ( minus_minus_int_o @ A_29 @ B_20 )
% 0.55/0.79 = ( collect_int
% 0.55/0.79 @ ^ [X_1: int] : ( (&) @ ( member_int @ X_1 @ A_29 ) @ ( (~) @ ( member_int @ X_1 @ B_20 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_725_set__diff__eq,axiom,
% 0.55/0.79 ! [A_29: nat > $o,B_20: nat > $o] :
% 0.55/0.79 ( ( minus_minus_nat_o @ A_29 @ B_20 )
% 0.55/0.79 = ( collect_nat
% 0.55/0.79 @ ^ [X_1: nat] : ( (&) @ ( member_nat @ X_1 @ A_29 ) @ ( (~) @ ( member_nat @ X_1 @ B_20 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_726_set__diff__eq,axiom,
% 0.55/0.79 ! [A_29: x_a > $o,B_20: x_a > $o] :
% 0.55/0.79 ( ( minus_minus_a_o @ A_29 @ B_20 )
% 0.55/0.79 = ( collect_a
% 0.55/0.79 @ ^ [X_1: x_a] : ( (&) @ ( member_a @ X_1 @ A_29 ) @ ( (~) @ ( member_a @ X_1 @ B_20 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_727_set__diff__eq,axiom,
% 0.55/0.79 ! [A_29: pname > $o,B_20: pname > $o] :
% 0.55/0.79 ( ( minus_minus_pname_o @ A_29 @ B_20 )
% 0.55/0.79 = ( collect_pname
% 0.55/0.79 @ ^ [X_1: pname] : ( (&) @ ( member_pname @ X_1 @ A_29 ) @ ( (~) @ ( member_pname @ X_1 @ B_20 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_728_folding__one_Oinsert__remove,axiom,
% 0.55/0.79 ! [X_12: x_a,A_28: x_a > $o,F_16: x_a > x_a > x_a,F_15: ( x_a > $o ) > x_a] :
% 0.55/0.79 ( ( finite_folding_one_a @ F_16 @ F_15 )
% 0.55/0.79 => ( ( finite_finite_a @ A_28 )
% 0.55/0.79 => ( ( ( ( minus_minus_a_o @ A_28 @ ( insert_a @ X_12 @ bot_bot_a_o ) )
% 0.55/0.79 = bot_bot_a_o )
% 0.55/0.79 => ( ( F_15 @ ( insert_a @ X_12 @ A_28 ) )
% 0.55/0.79 = X_12 ) )
% 0.55/0.79 & ( ( ( minus_minus_a_o @ A_28 @ ( insert_a @ X_12 @ bot_bot_a_o ) )
% 0.55/0.79 != bot_bot_a_o )
% 0.55/0.79 => ( ( F_15 @ ( insert_a @ X_12 @ A_28 ) )
% 0.55/0.79 = ( F_16 @ X_12 @ ( F_15 @ ( minus_minus_a_o @ A_28 @ ( insert_a @ X_12 @ bot_bot_a_o ) ) ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_729_folding__one_Oinsert__remove,axiom,
% 0.55/0.79 ! [X_12: int,A_28: int > $o,F_16: int > int > int,F_15: ( int > $o ) > int] :
% 0.55/0.79 ( ( finite1626084323ne_int @ F_16 @ F_15 )
% 0.55/0.79 => ( ( finite_finite_int @ A_28 )
% 0.55/0.79 => ( ( ( ( minus_minus_int_o @ A_28 @ ( insert_int @ X_12 @ bot_bot_int_o ) )
% 0.55/0.79 = bot_bot_int_o )
% 0.55/0.79 => ( ( F_15 @ ( insert_int @ X_12 @ A_28 ) )
% 0.55/0.79 = X_12 ) )
% 0.55/0.79 & ( ( ( minus_minus_int_o @ A_28 @ ( insert_int @ X_12 @ bot_bot_int_o ) )
% 0.55/0.79 != bot_bot_int_o )
% 0.55/0.79 => ( ( F_15 @ ( insert_int @ X_12 @ A_28 ) )
% 0.55/0.79 = ( F_16 @ X_12 @ ( F_15 @ ( minus_minus_int_o @ A_28 @ ( insert_int @ X_12 @ bot_bot_int_o ) ) ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_730_folding__one_Oinsert__remove,axiom,
% 0.55/0.79 ! [X_12: nat,A_28: nat > $o,F_16: nat > nat > nat,F_15: ( nat > $o ) > nat] :
% 0.55/0.79 ( ( finite988810631ne_nat @ F_16 @ F_15 )
% 0.55/0.79 => ( ( finite_finite_nat @ A_28 )
% 0.55/0.79 => ( ( ( ( minus_minus_nat_o @ A_28 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) )
% 0.55/0.79 = bot_bot_nat_o )
% 0.55/0.79 => ( ( F_15 @ ( insert_nat @ X_12 @ A_28 ) )
% 0.55/0.79 = X_12 ) )
% 0.55/0.79 & ( ( ( minus_minus_nat_o @ A_28 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) )
% 0.55/0.79 != bot_bot_nat_o )
% 0.55/0.79 => ( ( F_15 @ ( insert_nat @ X_12 @ A_28 ) )
% 0.55/0.79 = ( F_16 @ X_12 @ ( F_15 @ ( minus_minus_nat_o @ A_28 @ ( insert_nat @ X_12 @ bot_bot_nat_o ) ) ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_731_folding__one_Oinsert__remove,axiom,
% 0.55/0.79 ! [X_12: pname,A_28: pname > $o,F_16: pname > pname > pname,F_15: ( pname > $o ) > pname] :
% 0.55/0.79 ( ( finite1282449217_pname @ F_16 @ F_15 )
% 0.55/0.79 => ( ( finite_finite_pname @ A_28 )
% 0.55/0.79 => ( ( ( ( minus_minus_pname_o @ A_28 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 0.55/0.79 = bot_bot_pname_o )
% 0.55/0.79 => ( ( F_15 @ ( insert_pname @ X_12 @ A_28 ) )
% 0.55/0.79 = X_12 ) )
% 0.55/0.79 & ( ( ( minus_minus_pname_o @ A_28 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) )
% 0.55/0.79 != bot_bot_pname_o )
% 0.55/0.79 => ( ( F_15 @ ( insert_pname @ X_12 @ A_28 ) )
% 0.55/0.79 = ( F_16 @ X_12 @ ( F_15 @ ( minus_minus_pname_o @ A_28 @ ( insert_pname @ X_12 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_732_folding__one_Oremove,axiom,
% 0.55/0.79 ! [X_11: x_a,A_27: x_a > $o,F_14: x_a > x_a > x_a,F_13: ( x_a > $o ) > x_a] :
% 0.55/0.79 ( ( finite_folding_one_a @ F_14 @ F_13 )
% 0.55/0.79 => ( ( finite_finite_a @ A_27 )
% 0.55/0.79 => ( ( member_a @ X_11 @ A_27 )
% 0.55/0.79 => ( ( ( ( minus_minus_a_o @ A_27 @ ( insert_a @ X_11 @ bot_bot_a_o ) )
% 0.55/0.79 = bot_bot_a_o )
% 0.55/0.79 => ( ( F_13 @ A_27 )
% 0.55/0.79 = X_11 ) )
% 0.55/0.79 & ( ( ( minus_minus_a_o @ A_27 @ ( insert_a @ X_11 @ bot_bot_a_o ) )
% 0.55/0.79 != bot_bot_a_o )
% 0.55/0.79 => ( ( F_13 @ A_27 )
% 0.55/0.79 = ( F_14 @ X_11 @ ( F_13 @ ( minus_minus_a_o @ A_27 @ ( insert_a @ X_11 @ bot_bot_a_o ) ) ) ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_733_folding__one_Oremove,axiom,
% 0.55/0.79 ! [X_11: int,A_27: int > $o,F_14: int > int > int,F_13: ( int > $o ) > int] :
% 0.55/0.79 ( ( finite1626084323ne_int @ F_14 @ F_13 )
% 0.55/0.79 => ( ( finite_finite_int @ A_27 )
% 0.55/0.79 => ( ( member_int @ X_11 @ A_27 )
% 0.55/0.79 => ( ( ( ( minus_minus_int_o @ A_27 @ ( insert_int @ X_11 @ bot_bot_int_o ) )
% 0.55/0.79 = bot_bot_int_o )
% 0.55/0.79 => ( ( F_13 @ A_27 )
% 0.55/0.79 = X_11 ) )
% 0.55/0.79 & ( ( ( minus_minus_int_o @ A_27 @ ( insert_int @ X_11 @ bot_bot_int_o ) )
% 0.55/0.79 != bot_bot_int_o )
% 0.55/0.79 => ( ( F_13 @ A_27 )
% 0.55/0.79 = ( F_14 @ X_11 @ ( F_13 @ ( minus_minus_int_o @ A_27 @ ( insert_int @ X_11 @ bot_bot_int_o ) ) ) ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_734_folding__one_Oremove,axiom,
% 0.55/0.79 ! [X_11: nat,A_27: nat > $o,F_14: nat > nat > nat,F_13: ( nat > $o ) > nat] :
% 0.55/0.79 ( ( finite988810631ne_nat @ F_14 @ F_13 )
% 0.55/0.79 => ( ( finite_finite_nat @ A_27 )
% 0.55/0.79 => ( ( member_nat @ X_11 @ A_27 )
% 0.55/0.79 => ( ( ( ( minus_minus_nat_o @ A_27 @ ( insert_nat @ X_11 @ bot_bot_nat_o ) )
% 0.55/0.79 = bot_bot_nat_o )
% 0.55/0.79 => ( ( F_13 @ A_27 )
% 0.55/0.79 = X_11 ) )
% 0.55/0.79 & ( ( ( minus_minus_nat_o @ A_27 @ ( insert_nat @ X_11 @ bot_bot_nat_o ) )
% 0.55/0.79 != bot_bot_nat_o )
% 0.55/0.79 => ( ( F_13 @ A_27 )
% 0.55/0.79 = ( F_14 @ X_11 @ ( F_13 @ ( minus_minus_nat_o @ A_27 @ ( insert_nat @ X_11 @ bot_bot_nat_o ) ) ) ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_735_folding__one_Oremove,axiom,
% 0.55/0.79 ! [X_11: pname,A_27: pname > $o,F_14: pname > pname > pname,F_13: ( pname > $o ) > pname] :
% 0.55/0.79 ( ( finite1282449217_pname @ F_14 @ F_13 )
% 0.55/0.79 => ( ( finite_finite_pname @ A_27 )
% 0.55/0.79 => ( ( member_pname @ X_11 @ A_27 )
% 0.55/0.79 => ( ( ( ( minus_minus_pname_o @ A_27 @ ( insert_pname @ X_11 @ bot_bot_pname_o ) )
% 0.55/0.79 = bot_bot_pname_o )
% 0.55/0.79 => ( ( F_13 @ A_27 )
% 0.55/0.79 = X_11 ) )
% 0.55/0.79 & ( ( ( minus_minus_pname_o @ A_27 @ ( insert_pname @ X_11 @ bot_bot_pname_o ) )
% 0.55/0.79 != bot_bot_pname_o )
% 0.55/0.79 => ( ( F_13 @ A_27 )
% 0.55/0.79 = ( F_14 @ X_11 @ ( F_13 @ ( minus_minus_pname_o @ A_27 @ ( insert_pname @ X_11 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_736_card__Diff__singleton__if,axiom,
% 0.55/0.79 ! [X_10: x_a,A_26: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_26 )
% 0.55/0.79 => ( ( ( member_a @ X_10 @ A_26 )
% 0.55/0.79 => ( ( finite_card_a @ ( minus_minus_a_o @ A_26 @ ( insert_a @ X_10 @ bot_bot_a_o ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_a @ A_26 ) @ one_one_nat ) ) )
% 0.55/0.79 & ( ~ ( member_a @ X_10 @ A_26 )
% 0.55/0.79 => ( ( finite_card_a @ ( minus_minus_a_o @ A_26 @ ( insert_a @ X_10 @ bot_bot_a_o ) ) )
% 0.55/0.79 = ( finite_card_a @ A_26 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_737_card__Diff__singleton__if,axiom,
% 0.55/0.79 ! [X_10: int,A_26: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_26 )
% 0.55/0.79 => ( ( ( member_int @ X_10 @ A_26 )
% 0.55/0.79 => ( ( finite_card_int @ ( minus_minus_int_o @ A_26 @ ( insert_int @ X_10 @ bot_bot_int_o ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_int @ A_26 ) @ one_one_nat ) ) )
% 0.55/0.79 & ( ~ ( member_int @ X_10 @ A_26 )
% 0.55/0.79 => ( ( finite_card_int @ ( minus_minus_int_o @ A_26 @ ( insert_int @ X_10 @ bot_bot_int_o ) ) )
% 0.55/0.79 = ( finite_card_int @ A_26 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_738_card__Diff__singleton__if,axiom,
% 0.55/0.79 ! [X_10: nat,A_26: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_26 )
% 0.55/0.79 => ( ( ( member_nat @ X_10 @ A_26 )
% 0.55/0.79 => ( ( finite_card_nat @ ( minus_minus_nat_o @ A_26 @ ( insert_nat @ X_10 @ bot_bot_nat_o ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_nat @ A_26 ) @ one_one_nat ) ) )
% 0.55/0.79 & ( ~ ( member_nat @ X_10 @ A_26 )
% 0.55/0.79 => ( ( finite_card_nat @ ( minus_minus_nat_o @ A_26 @ ( insert_nat @ X_10 @ bot_bot_nat_o ) ) )
% 0.55/0.79 = ( finite_card_nat @ A_26 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_739_card__Diff__singleton__if,axiom,
% 0.55/0.79 ! [X_10: pname,A_26: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_26 )
% 0.55/0.79 => ( ( ( member_pname @ X_10 @ A_26 )
% 0.55/0.79 => ( ( finite_card_pname @ ( minus_minus_pname_o @ A_26 @ ( insert_pname @ X_10 @ bot_bot_pname_o ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_pname @ A_26 ) @ one_one_nat ) ) )
% 0.55/0.79 & ( ~ ( member_pname @ X_10 @ A_26 )
% 0.55/0.79 => ( ( finite_card_pname @ ( minus_minus_pname_o @ A_26 @ ( insert_pname @ X_10 @ bot_bot_pname_o ) ) )
% 0.55/0.79 = ( finite_card_pname @ A_26 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_740_card__Diff__singleton,axiom,
% 0.55/0.79 ! [X_9: x_a,A_25: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_25 )
% 0.55/0.79 => ( ( member_a @ X_9 @ A_25 )
% 0.55/0.79 => ( ( finite_card_a @ ( minus_minus_a_o @ A_25 @ ( insert_a @ X_9 @ bot_bot_a_o ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_a @ A_25 ) @ one_one_nat ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_741_card__Diff__singleton,axiom,
% 0.55/0.79 ! [X_9: int,A_25: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_25 )
% 0.55/0.79 => ( ( member_int @ X_9 @ A_25 )
% 0.55/0.79 => ( ( finite_card_int @ ( minus_minus_int_o @ A_25 @ ( insert_int @ X_9 @ bot_bot_int_o ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_int @ A_25 ) @ one_one_nat ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_742_card__Diff__singleton,axiom,
% 0.55/0.79 ! [X_9: nat,A_25: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_25 )
% 0.55/0.79 => ( ( member_nat @ X_9 @ A_25 )
% 0.55/0.79 => ( ( finite_card_nat @ ( minus_minus_nat_o @ A_25 @ ( insert_nat @ X_9 @ bot_bot_nat_o ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_nat @ A_25 ) @ one_one_nat ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_743_card__Diff__singleton,axiom,
% 0.55/0.79 ! [X_9: pname,A_25: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_25 )
% 0.55/0.79 => ( ( member_pname @ X_9 @ A_25 )
% 0.55/0.79 => ( ( finite_card_pname @ ( minus_minus_pname_o @ A_25 @ ( insert_pname @ X_9 @ bot_bot_pname_o ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_pname @ A_25 ) @ one_one_nat ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_744_one__reorient,axiom,
% 0.55/0.79 ! [X_8: int] :
% 0.55/0.79 ( ( one_one_int = X_8 )
% 0.55/0.79 <=> ( X_8 = one_one_int ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_745_one__reorient,axiom,
% 0.55/0.79 ! [X_8: nat] :
% 0.55/0.79 ( ( one_one_nat = X_8 )
% 0.55/0.79 <=> ( X_8 = one_one_nat ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_746_diff__Suc__1,axiom,
% 0.55/0.79 ! [N: nat] :
% 0.55/0.79 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.55/0.79 = N ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_747_diff__Suc__eq__diff__pred,axiom,
% 0.55/0.79 ! [M: nat,N: nat] :
% 0.55/0.79 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.55/0.79 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_748_folding__one_Osingleton,axiom,
% 0.55/0.79 ! [X_7: x_a,F_12: x_a > x_a > x_a,F_11: ( x_a > $o ) > x_a] :
% 0.55/0.79 ( ( finite_folding_one_a @ F_12 @ F_11 )
% 0.55/0.79 => ( ( F_11 @ ( insert_a @ X_7 @ bot_bot_a_o ) )
% 0.55/0.79 = X_7 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_749_folding__one_Osingleton,axiom,
% 0.55/0.79 ! [X_7: nat,F_12: nat > nat > nat,F_11: ( nat > $o ) > nat] :
% 0.55/0.79 ( ( finite988810631ne_nat @ F_12 @ F_11 )
% 0.55/0.79 => ( ( F_11 @ ( insert_nat @ X_7 @ bot_bot_nat_o ) )
% 0.55/0.79 = X_7 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_750_folding__one_Osingleton,axiom,
% 0.55/0.79 ! [X_7: int,F_12: int > int > int,F_11: ( int > $o ) > int] :
% 0.55/0.79 ( ( finite1626084323ne_int @ F_12 @ F_11 )
% 0.55/0.79 => ( ( F_11 @ ( insert_int @ X_7 @ bot_bot_int_o ) )
% 0.55/0.79 = X_7 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_751_card__Diff__insert,axiom,
% 0.55/0.79 ! [B_19: x_a > $o,A_24: x_a,A_23: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_23 )
% 0.55/0.79 => ( ( member_a @ A_24 @ A_23 )
% 0.55/0.79 => ( ~ ( member_a @ A_24 @ B_19 )
% 0.55/0.79 => ( ( finite_card_a @ ( minus_minus_a_o @ A_23 @ ( insert_a @ A_24 @ B_19 ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_a @ ( minus_minus_a_o @ A_23 @ B_19 ) ) @ one_one_nat ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_752_card__Diff__insert,axiom,
% 0.55/0.79 ! [B_19: int > $o,A_24: int,A_23: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_23 )
% 0.55/0.79 => ( ( member_int @ A_24 @ A_23 )
% 0.55/0.79 => ( ~ ( member_int @ A_24 @ B_19 )
% 0.55/0.79 => ( ( finite_card_int @ ( minus_minus_int_o @ A_23 @ ( insert_int @ A_24 @ B_19 ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_int_o @ A_23 @ B_19 ) ) @ one_one_nat ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_753_card__Diff__insert,axiom,
% 0.55/0.79 ! [B_19: nat > $o,A_24: nat,A_23: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_23 )
% 0.55/0.79 => ( ( member_nat @ A_24 @ A_23 )
% 0.55/0.79 => ( ~ ( member_nat @ A_24 @ B_19 )
% 0.55/0.79 => ( ( finite_card_nat @ ( minus_minus_nat_o @ A_23 @ ( insert_nat @ A_24 @ B_19 ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_nat_o @ A_23 @ B_19 ) ) @ one_one_nat ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_754_card__Diff__insert,axiom,
% 0.55/0.79 ! [B_19: pname > $o,A_24: pname,A_23: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_23 )
% 0.55/0.79 => ( ( member_pname @ A_24 @ A_23 )
% 0.55/0.79 => ( ~ ( member_pname @ A_24 @ B_19 )
% 0.55/0.79 => ( ( finite_card_pname @ ( minus_minus_pname_o @ A_23 @ ( insert_pname @ A_24 @ B_19 ) ) )
% 0.55/0.79 = ( minus_minus_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ A_23 @ B_19 ) ) @ one_one_nat ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_755_folding__one_Oinsert,axiom,
% 0.55/0.79 ! [X_6: x_a,A_22: x_a > $o,F_10: x_a > x_a > x_a,F_9: ( x_a > $o ) > x_a] :
% 0.55/0.79 ( ( finite_folding_one_a @ F_10 @ F_9 )
% 0.55/0.79 => ( ( finite_finite_a @ A_22 )
% 0.55/0.79 => ( ~ ( member_a @ X_6 @ A_22 )
% 0.55/0.79 => ( ( A_22 != bot_bot_a_o )
% 0.55/0.79 => ( ( F_9 @ ( insert_a @ X_6 @ A_22 ) )
% 0.55/0.79 = ( F_10 @ X_6 @ ( F_9 @ A_22 ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_756_folding__one_Oinsert,axiom,
% 0.55/0.79 ! [X_6: int,A_22: int > $o,F_10: int > int > int,F_9: ( int > $o ) > int] :
% 0.55/0.79 ( ( finite1626084323ne_int @ F_10 @ F_9 )
% 0.55/0.79 => ( ( finite_finite_int @ A_22 )
% 0.55/0.79 => ( ~ ( member_int @ X_6 @ A_22 )
% 0.55/0.79 => ( ( A_22 != bot_bot_int_o )
% 0.55/0.79 => ( ( F_9 @ ( insert_int @ X_6 @ A_22 ) )
% 0.55/0.79 = ( F_10 @ X_6 @ ( F_9 @ A_22 ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_757_folding__one_Oinsert,axiom,
% 0.55/0.79 ! [X_6: nat,A_22: nat > $o,F_10: nat > nat > nat,F_9: ( nat > $o ) > nat] :
% 0.55/0.79 ( ( finite988810631ne_nat @ F_10 @ F_9 )
% 0.55/0.79 => ( ( finite_finite_nat @ A_22 )
% 0.55/0.79 => ( ~ ( member_nat @ X_6 @ A_22 )
% 0.55/0.79 => ( ( A_22 != bot_bot_nat_o )
% 0.55/0.79 => ( ( F_9 @ ( insert_nat @ X_6 @ A_22 ) )
% 0.55/0.79 = ( F_10 @ X_6 @ ( F_9 @ A_22 ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_758_folding__one_Oinsert,axiom,
% 0.55/0.79 ! [X_6: pname,A_22: pname > $o,F_10: pname > pname > pname,F_9: ( pname > $o ) > pname] :
% 0.55/0.79 ( ( finite1282449217_pname @ F_10 @ F_9 )
% 0.55/0.79 => ( ( finite_finite_pname @ A_22 )
% 0.55/0.79 => ( ~ ( member_pname @ X_6 @ A_22 )
% 0.55/0.79 => ( ( A_22 != bot_bot_pname_o )
% 0.55/0.79 => ( ( F_9 @ ( insert_pname @ X_6 @ A_22 ) )
% 0.55/0.79 = ( F_10 @ X_6 @ ( F_9 @ A_22 ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_759_folding__one_Oclosed,axiom,
% 0.55/0.79 ! [A_21: x_a > $o,F_8: x_a > x_a > x_a,F_7: ( x_a > $o ) > x_a] :
% 0.55/0.79 ( ( finite_folding_one_a @ F_8 @ F_7 )
% 0.55/0.79 => ( ( finite_finite_a @ A_21 )
% 0.55/0.79 => ( ( A_21 != bot_bot_a_o )
% 0.55/0.79 => ( ! [X_1: x_a,Y_1: x_a] : ( member_a @ ( F_8 @ X_1 @ Y_1 ) @ ( insert_a @ X_1 @ ( insert_a @ Y_1 @ bot_bot_a_o ) ) )
% 0.55/0.79 => ( member_a @ ( F_7 @ A_21 ) @ A_21 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_760_folding__one_Oclosed,axiom,
% 0.55/0.79 ! [A_21: int > $o,F_8: int > int > int,F_7: ( int > $o ) > int] :
% 0.55/0.79 ( ( finite1626084323ne_int @ F_8 @ F_7 )
% 0.55/0.79 => ( ( finite_finite_int @ A_21 )
% 0.55/0.79 => ( ( A_21 != bot_bot_int_o )
% 0.55/0.79 => ( ! [X_1: int,Y_1: int] : ( member_int @ ( F_8 @ X_1 @ Y_1 ) @ ( insert_int @ X_1 @ ( insert_int @ Y_1 @ bot_bot_int_o ) ) )
% 0.55/0.79 => ( member_int @ ( F_7 @ A_21 ) @ A_21 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_761_folding__one_Oclosed,axiom,
% 0.55/0.79 ! [A_21: nat > $o,F_8: nat > nat > nat,F_7: ( nat > $o ) > nat] :
% 0.55/0.79 ( ( finite988810631ne_nat @ F_8 @ F_7 )
% 0.55/0.79 => ( ( finite_finite_nat @ A_21 )
% 0.55/0.79 => ( ( A_21 != bot_bot_nat_o )
% 0.55/0.79 => ( ! [X_1: nat,Y_1: nat] : ( member_nat @ ( F_8 @ X_1 @ Y_1 ) @ ( insert_nat @ X_1 @ ( insert_nat @ Y_1 @ bot_bot_nat_o ) ) )
% 0.55/0.79 => ( member_nat @ ( F_7 @ A_21 ) @ A_21 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_762_folding__one_Oclosed,axiom,
% 0.55/0.79 ! [A_21: pname > $o,F_8: pname > pname > pname,F_7: ( pname > $o ) > pname] :
% 0.55/0.79 ( ( finite1282449217_pname @ F_8 @ F_7 )
% 0.55/0.79 => ( ( finite_finite_pname @ A_21 )
% 0.55/0.79 => ( ( A_21 != bot_bot_pname_o )
% 0.55/0.79 => ( ! [X_1: pname,Y_1: pname] : ( member_pname @ ( F_8 @ X_1 @ Y_1 ) @ ( insert_pname @ X_1 @ ( insert_pname @ Y_1 @ bot_bot_pname_o ) ) )
% 0.55/0.79 => ( member_pname @ ( F_7 @ A_21 ) @ A_21 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_763_card_Oremove,axiom,
% 0.55/0.79 ! [X_5: x_a,A_20: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_20 )
% 0.55/0.79 => ( ( member_a @ X_5 @ A_20 )
% 0.55/0.79 => ( ( finite_card_a @ A_20 )
% 0.55/0.79 = ( plus_plus_nat @ one_one_nat @ ( finite_card_a @ ( minus_minus_a_o @ A_20 @ ( insert_a @ X_5 @ bot_bot_a_o ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_764_card_Oremove,axiom,
% 0.55/0.79 ! [X_5: int,A_20: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_20 )
% 0.55/0.79 => ( ( member_int @ X_5 @ A_20 )
% 0.55/0.79 => ( ( finite_card_int @ A_20 )
% 0.55/0.79 = ( plus_plus_nat @ one_one_nat @ ( finite_card_int @ ( minus_minus_int_o @ A_20 @ ( insert_int @ X_5 @ bot_bot_int_o ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_765_card_Oremove,axiom,
% 0.55/0.79 ! [X_5: nat,A_20: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_20 )
% 0.55/0.79 => ( ( member_nat @ X_5 @ A_20 )
% 0.55/0.79 => ( ( finite_card_nat @ A_20 )
% 0.55/0.79 = ( plus_plus_nat @ one_one_nat @ ( finite_card_nat @ ( minus_minus_nat_o @ A_20 @ ( insert_nat @ X_5 @ bot_bot_nat_o ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_766_card_Oremove,axiom,
% 0.55/0.79 ! [X_5: pname,A_20: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_20 )
% 0.55/0.79 => ( ( member_pname @ X_5 @ A_20 )
% 0.55/0.79 => ( ( finite_card_pname @ A_20 )
% 0.55/0.79 = ( plus_plus_nat @ one_one_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ A_20 @ ( insert_pname @ X_5 @ bot_bot_pname_o ) ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_767_card_Oinsert__remove,axiom,
% 0.55/0.79 ! [X_4: x_a,A_19: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ A_19 )
% 0.55/0.79 => ( ( finite_card_a @ ( insert_a @ X_4 @ A_19 ) )
% 0.55/0.79 = ( plus_plus_nat @ one_one_nat @ ( finite_card_a @ ( minus_minus_a_o @ A_19 @ ( insert_a @ X_4 @ bot_bot_a_o ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_768_card_Oinsert__remove,axiom,
% 0.55/0.79 ! [X_4: int,A_19: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ A_19 )
% 0.55/0.79 => ( ( finite_card_int @ ( insert_int @ X_4 @ A_19 ) )
% 0.55/0.79 = ( plus_plus_nat @ one_one_nat @ ( finite_card_int @ ( minus_minus_int_o @ A_19 @ ( insert_int @ X_4 @ bot_bot_int_o ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_769_card_Oinsert__remove,axiom,
% 0.55/0.79 ! [X_4: nat,A_19: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ A_19 )
% 0.55/0.79 => ( ( finite_card_nat @ ( insert_nat @ X_4 @ A_19 ) )
% 0.55/0.79 = ( plus_plus_nat @ one_one_nat @ ( finite_card_nat @ ( minus_minus_nat_o @ A_19 @ ( insert_nat @ X_4 @ bot_bot_nat_o ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_770_card_Oinsert__remove,axiom,
% 0.55/0.79 ! [X_4: pname,A_19: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ A_19 )
% 0.55/0.79 => ( ( finite_card_pname @ ( insert_pname @ X_4 @ A_19 ) )
% 0.55/0.79 = ( plus_plus_nat @ one_one_nat @ ( finite_card_pname @ ( minus_minus_pname_o @ A_19 @ ( insert_pname @ X_4 @ bot_bot_pname_o ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_771_folding__one__idem_Osubset__idem,axiom,
% 0.55/0.79 ! [B_18: int > $o,A_18: int > $o,F_6: int > int > int,F_5: ( int > $o ) > int] :
% 0.55/0.79 ( ( finite1432773856em_int @ F_6 @ F_5 )
% 0.55/0.79 => ( ( finite_finite_int @ A_18 )
% 0.55/0.79 => ( ( B_18 != bot_bot_int_o )
% 0.55/0.79 => ( ( ord_less_eq_int_o @ B_18 @ A_18 )
% 0.55/0.79 => ( ( F_6 @ ( F_5 @ B_18 ) @ ( F_5 @ A_18 ) )
% 0.55/0.79 = ( F_5 @ A_18 ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_772_folding__one__idem_Osubset__idem,axiom,
% 0.55/0.79 ! [B_18: nat > $o,A_18: nat > $o,F_6: nat > nat > nat,F_5: ( nat > $o ) > nat] :
% 0.55/0.79 ( ( finite795500164em_nat @ F_6 @ F_5 )
% 0.55/0.79 => ( ( finite_finite_nat @ A_18 )
% 0.55/0.79 => ( ( B_18 != bot_bot_nat_o )
% 0.55/0.79 => ( ( ord_less_eq_nat_o @ B_18 @ A_18 )
% 0.55/0.79 => ( ( F_6 @ ( F_5 @ B_18 ) @ ( F_5 @ A_18 ) )
% 0.55/0.79 = ( F_5 @ A_18 ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_773_folding__one__idem_Osubset__idem,axiom,
% 0.55/0.79 ! [B_18: pname > $o,A_18: pname > $o,F_6: pname > pname > pname,F_5: ( pname > $o ) > pname] :
% 0.55/0.79 ( ( finite89670078_pname @ F_6 @ F_5 )
% 0.55/0.79 => ( ( finite_finite_pname @ A_18 )
% 0.55/0.79 => ( ( B_18 != bot_bot_pname_o )
% 0.55/0.79 => ( ( ord_less_eq_pname_o @ B_18 @ A_18 )
% 0.55/0.79 => ( ( F_6 @ ( F_5 @ B_18 ) @ ( F_5 @ A_18 ) )
% 0.55/0.79 = ( F_5 @ A_18 ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_774_folding__one__idem_Osubset__idem,axiom,
% 0.55/0.79 ! [B_18: x_a > $o,A_18: x_a > $o,F_6: x_a > x_a > x_a,F_5: ( x_a > $o ) > x_a] :
% 0.55/0.79 ( ( finite1819937229idem_a @ F_6 @ F_5 )
% 0.55/0.79 => ( ( finite_finite_a @ A_18 )
% 0.55/0.79 => ( ( B_18 != bot_bot_a_o )
% 0.55/0.79 => ( ( ord_less_eq_a_o @ B_18 @ A_18 )
% 0.55/0.79 => ( ( F_6 @ ( F_5 @ B_18 ) @ ( F_5 @ A_18 ) )
% 0.55/0.79 = ( F_5 @ A_18 ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_775_folding__one__idem_Oinsert__idem,axiom,
% 0.55/0.79 ! [X_3: x_a,A_17: x_a > $o,F_4: x_a > x_a > x_a,F_3: ( x_a > $o ) > x_a] :
% 0.55/0.79 ( ( finite1819937229idem_a @ F_4 @ F_3 )
% 0.55/0.79 => ( ( finite_finite_a @ A_17 )
% 0.55/0.79 => ( ( A_17 != bot_bot_a_o )
% 0.55/0.79 => ( ( F_3 @ ( insert_a @ X_3 @ A_17 ) )
% 0.55/0.79 = ( F_4 @ X_3 @ ( F_3 @ A_17 ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_776_folding__one__idem_Oinsert__idem,axiom,
% 0.55/0.79 ! [X_3: int,A_17: int > $o,F_4: int > int > int,F_3: ( int > $o ) > int] :
% 0.55/0.79 ( ( finite1432773856em_int @ F_4 @ F_3 )
% 0.55/0.79 => ( ( finite_finite_int @ A_17 )
% 0.55/0.79 => ( ( A_17 != bot_bot_int_o )
% 0.55/0.79 => ( ( F_3 @ ( insert_int @ X_3 @ A_17 ) )
% 0.55/0.79 = ( F_4 @ X_3 @ ( F_3 @ A_17 ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_777_folding__one__idem_Oinsert__idem,axiom,
% 0.55/0.79 ! [X_3: nat,A_17: nat > $o,F_4: nat > nat > nat,F_3: ( nat > $o ) > nat] :
% 0.55/0.79 ( ( finite795500164em_nat @ F_4 @ F_3 )
% 0.55/0.79 => ( ( finite_finite_nat @ A_17 )
% 0.55/0.79 => ( ( A_17 != bot_bot_nat_o )
% 0.55/0.79 => ( ( F_3 @ ( insert_nat @ X_3 @ A_17 ) )
% 0.55/0.79 = ( F_4 @ X_3 @ ( F_3 @ A_17 ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_778_folding__one__idem_Oinsert__idem,axiom,
% 0.55/0.79 ! [X_3: pname,A_17: pname > $o,F_4: pname > pname > pname,F_3: ( pname > $o ) > pname] :
% 0.55/0.79 ( ( finite89670078_pname @ F_4 @ F_3 )
% 0.55/0.79 => ( ( finite_finite_pname @ A_17 )
% 0.55/0.79 => ( ( A_17 != bot_bot_pname_o )
% 0.55/0.79 => ( ( F_3 @ ( insert_pname @ X_3 @ A_17 ) )
% 0.55/0.79 = ( F_4 @ X_3 @ ( F_3 @ A_17 ) ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_779_finite__ne__induct,axiom,
% 0.55/0.79 ! [P_2: ( x_a > $o ) > $o,F_1: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ F_1 )
% 0.55/0.79 => ( ( F_1 != bot_bot_a_o )
% 0.55/0.79 => ( ! [X_1: x_a] : ( P_2 @ ( insert_a @ X_1 @ bot_bot_a_o ) )
% 0.55/0.79 => ( ! [X_1: x_a,F_2: x_a > $o] :
% 0.55/0.79 ( ( finite_finite_a @ F_2 )
% 0.55/0.79 => ( ( F_2 != bot_bot_a_o )
% 0.55/0.79 => ( ~ ( member_a @ X_1 @ F_2 )
% 0.55/0.79 => ( ( P_2 @ F_2 )
% 0.55/0.79 => ( P_2 @ ( insert_a @ X_1 @ F_2 ) ) ) ) ) )
% 0.55/0.79 => ( P_2 @ F_1 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_780_finite__ne__induct,axiom,
% 0.55/0.79 ! [P_2: ( int > $o ) > $o,F_1: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ F_1 )
% 0.55/0.79 => ( ( F_1 != bot_bot_int_o )
% 0.55/0.79 => ( ! [X_1: int] : ( P_2 @ ( insert_int @ X_1 @ bot_bot_int_o ) )
% 0.55/0.79 => ( ! [X_1: int,F_2: int > $o] :
% 0.55/0.79 ( ( finite_finite_int @ F_2 )
% 0.55/0.79 => ( ( F_2 != bot_bot_int_o )
% 0.55/0.79 => ( ~ ( member_int @ X_1 @ F_2 )
% 0.55/0.79 => ( ( P_2 @ F_2 )
% 0.55/0.79 => ( P_2 @ ( insert_int @ X_1 @ F_2 ) ) ) ) ) )
% 0.55/0.79 => ( P_2 @ F_1 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_781_finite__ne__induct,axiom,
% 0.55/0.79 ! [P_2: ( nat > $o ) > $o,F_1: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ F_1 )
% 0.55/0.79 => ( ( F_1 != bot_bot_nat_o )
% 0.55/0.79 => ( ! [X_1: nat] : ( P_2 @ ( insert_nat @ X_1 @ bot_bot_nat_o ) )
% 0.55/0.79 => ( ! [X_1: nat,F_2: nat > $o] :
% 0.55/0.79 ( ( finite_finite_nat @ F_2 )
% 0.55/0.79 => ( ( F_2 != bot_bot_nat_o )
% 0.55/0.79 => ( ~ ( member_nat @ X_1 @ F_2 )
% 0.55/0.79 => ( ( P_2 @ F_2 )
% 0.55/0.79 => ( P_2 @ ( insert_nat @ X_1 @ F_2 ) ) ) ) ) )
% 0.55/0.79 => ( P_2 @ F_1 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_782_finite__ne__induct,axiom,
% 0.55/0.79 ! [P_2: ( pname > $o ) > $o,F_1: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ F_1 )
% 0.55/0.79 => ( ( F_1 != bot_bot_pname_o )
% 0.55/0.79 => ( ! [X_1: pname] : ( P_2 @ ( insert_pname @ X_1 @ bot_bot_pname_o ) )
% 0.55/0.79 => ( ! [X_1: pname,F_2: pname > $o] :
% 0.55/0.79 ( ( finite_finite_pname @ F_2 )
% 0.55/0.79 => ( ( F_2 != bot_bot_pname_o )
% 0.55/0.79 => ( ~ ( member_pname @ X_1 @ F_2 )
% 0.55/0.79 => ( ( P_2 @ F_2 )
% 0.55/0.79 => ( P_2 @ ( insert_pname @ X_1 @ F_2 ) ) ) ) ) )
% 0.55/0.79 => ( P_2 @ F_1 ) ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_783_the__elem__def,axiom,
% 0.55/0.79 ! [X_2: x_a > $o] :
% 0.55/0.79 ( ( the_elem_a @ X_2 )
% 0.55/0.79 = ( the_a
% 0.55/0.79 @ ^ [X_1: x_a] :
% 0.55/0.79 ( X_2
% 0.55/0.79 = ( insert_a @ X_1 @ bot_bot_a_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_784_the__elem__def,axiom,
% 0.55/0.79 ! [X_2: nat > $o] :
% 0.55/0.79 ( ( the_elem_nat @ X_2 )
% 0.55/0.79 = ( the_nat
% 0.55/0.79 @ ^ [X_1: nat] :
% 0.55/0.79 ( X_2
% 0.55/0.79 = ( insert_nat @ X_1 @ bot_bot_nat_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_785_the__elem__def,axiom,
% 0.55/0.79 ! [X_2: int > $o] :
% 0.55/0.79 ( ( the_elem_int @ X_2 )
% 0.55/0.79 = ( the_int
% 0.55/0.79 @ ^ [X_1: int] :
% 0.55/0.79 ( X_2
% 0.55/0.79 = ( insert_int @ X_1 @ bot_bot_int_o ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_786_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.55/0.79 ! [A_16: int,B_17: int,C_13: int] :
% 0.55/0.79 ( ( plus_plus_int @ ( plus_plus_int @ A_16 @ B_17 ) @ C_13 )
% 0.55/0.79 = ( plus_plus_int @ A_16 @ ( plus_plus_int @ B_17 @ C_13 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_787_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.55/0.79 ! [A_16: nat,B_17: nat,C_13: nat] :
% 0.55/0.79 ( ( plus_plus_nat @ ( plus_plus_nat @ A_16 @ B_17 ) @ C_13 )
% 0.55/0.79 = ( plus_plus_nat @ A_16 @ ( plus_plus_nat @ B_17 @ C_13 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_788_add__left__cancel,axiom,
% 0.55/0.79 ! [A_15: int,B_16: int,C_12: int] :
% 0.55/0.79 ( ( ( plus_plus_int @ A_15 @ B_16 )
% 0.55/0.79 = ( plus_plus_int @ A_15 @ C_12 ) )
% 0.55/0.79 <=> ( B_16 = C_12 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_789_add__left__cancel,axiom,
% 0.55/0.79 ! [A_15: nat,B_16: nat,C_12: nat] :
% 0.55/0.79 ( ( ( plus_plus_nat @ A_15 @ B_16 )
% 0.55/0.79 = ( plus_plus_nat @ A_15 @ C_12 ) )
% 0.55/0.79 <=> ( B_16 = C_12 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_790_add__right__cancel,axiom,
% 0.55/0.79 ! [B_15: int,A_14: int,C_11: int] :
% 0.55/0.79 ( ( ( plus_plus_int @ B_15 @ A_14 )
% 0.55/0.79 = ( plus_plus_int @ C_11 @ A_14 ) )
% 0.55/0.79 <=> ( B_15 = C_11 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_791_add__right__cancel,axiom,
% 0.55/0.79 ! [B_15: nat,A_14: nat,C_11: nat] :
% 0.55/0.79 ( ( ( plus_plus_nat @ B_15 @ A_14 )
% 0.55/0.79 = ( plus_plus_nat @ C_11 @ A_14 ) )
% 0.55/0.79 <=> ( B_15 = C_11 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_792_add__left__imp__eq,axiom,
% 0.55/0.79 ! [A_13: int,B_14: int,C_10: int] :
% 0.55/0.79 ( ( ( plus_plus_int @ A_13 @ B_14 )
% 0.55/0.79 = ( plus_plus_int @ A_13 @ C_10 ) )
% 0.55/0.79 => ( B_14 = C_10 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_793_add__left__imp__eq,axiom,
% 0.55/0.79 ! [A_13: nat,B_14: nat,C_10: nat] :
% 0.55/0.79 ( ( ( plus_plus_nat @ A_13 @ B_14 )
% 0.55/0.79 = ( plus_plus_nat @ A_13 @ C_10 ) )
% 0.55/0.79 => ( B_14 = C_10 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_794_add__imp__eq,axiom,
% 0.55/0.79 ! [A_12: int,B_13: int,C_9: int] :
% 0.55/0.79 ( ( ( plus_plus_int @ A_12 @ B_13 )
% 0.55/0.79 = ( plus_plus_int @ A_12 @ C_9 ) )
% 0.55/0.79 => ( B_13 = C_9 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_795_add__imp__eq,axiom,
% 0.55/0.79 ! [A_12: nat,B_13: nat,C_9: nat] :
% 0.55/0.79 ( ( ( plus_plus_nat @ A_12 @ B_13 )
% 0.55/0.79 = ( plus_plus_nat @ A_12 @ C_9 ) )
% 0.55/0.79 => ( B_13 = C_9 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_796_add__right__imp__eq,axiom,
% 0.55/0.79 ! [B_12: int,A_11: int,C_8: int] :
% 0.55/0.79 ( ( ( plus_plus_int @ B_12 @ A_11 )
% 0.55/0.79 = ( plus_plus_int @ C_8 @ A_11 ) )
% 0.55/0.79 => ( B_12 = C_8 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_797_add__right__imp__eq,axiom,
% 0.55/0.79 ! [B_12: nat,A_11: nat,C_8: nat] :
% 0.55/0.79 ( ( ( plus_plus_nat @ B_12 @ A_11 )
% 0.55/0.79 = ( plus_plus_nat @ C_8 @ A_11 ) )
% 0.55/0.79 => ( B_12 = C_8 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_798_nat__add__commute,axiom,
% 0.55/0.79 ! [M: nat,N: nat] :
% 0.55/0.79 ( ( plus_plus_nat @ M @ N )
% 0.55/0.79 = ( plus_plus_nat @ N @ M ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_799_nat__add__left__commute,axiom,
% 0.55/0.79 ! [X: nat,Y: nat,Z: nat] :
% 0.55/0.79 ( ( plus_plus_nat @ X @ ( plus_plus_nat @ Y @ Z ) )
% 0.55/0.79 = ( plus_plus_nat @ Y @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_800_nat__add__assoc,axiom,
% 0.55/0.79 ! [M: nat,N: nat,K: nat] :
% 0.55/0.79 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.55/0.79 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N @ K ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_801_nat__add__left__cancel,axiom,
% 0.55/0.79 ! [K: nat,M: nat,N: nat] :
% 0.55/0.79 ( ( ( plus_plus_nat @ K @ M )
% 0.55/0.79 = ( plus_plus_nat @ K @ N ) )
% 0.55/0.79 <=> ( M = N ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_802_nat__add__right__cancel,axiom,
% 0.55/0.79 ! [M: nat,K: nat,N: nat] :
% 0.55/0.79 ( ( ( plus_plus_nat @ M @ K )
% 0.55/0.79 = ( plus_plus_nat @ N @ K ) )
% 0.55/0.79 <=> ( M = N ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_803_add__le__cancel__right,axiom,
% 0.55/0.79 ! [A_10: int,C_7: int,B_11: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ ( plus_plus_int @ A_10 @ C_7 ) @ ( plus_plus_int @ B_11 @ C_7 ) )
% 0.55/0.79 <=> ( ord_less_eq_int @ A_10 @ B_11 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_804_add__le__cancel__right,axiom,
% 0.55/0.79 ! [A_10: nat,C_7: nat,B_11: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A_10 @ C_7 ) @ ( plus_plus_nat @ B_11 @ C_7 ) )
% 0.55/0.79 <=> ( ord_less_eq_nat @ A_10 @ B_11 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_805_add__le__cancel__left,axiom,
% 0.55/0.79 ! [C_6: int,A_9: int,B_10: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ ( plus_plus_int @ C_6 @ A_9 ) @ ( plus_plus_int @ C_6 @ B_10 ) )
% 0.55/0.79 <=> ( ord_less_eq_int @ A_9 @ B_10 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_806_add__le__cancel__left,axiom,
% 0.55/0.79 ! [C_6: nat,A_9: nat,B_10: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C_6 @ A_9 ) @ ( plus_plus_nat @ C_6 @ B_10 ) )
% 0.55/0.79 <=> ( ord_less_eq_nat @ A_9 @ B_10 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_807_add__right__mono,axiom,
% 0.55/0.79 ! [C_5: int,A_8: int,B_9: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ A_8 @ B_9 )
% 0.55/0.79 => ( ord_less_eq_int @ ( plus_plus_int @ A_8 @ C_5 ) @ ( plus_plus_int @ B_9 @ C_5 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_808_add__right__mono,axiom,
% 0.55/0.79 ! [C_5: nat,A_8: nat,B_9: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ A_8 @ B_9 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( plus_plus_nat @ A_8 @ C_5 ) @ ( plus_plus_nat @ B_9 @ C_5 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_809_add__left__mono,axiom,
% 0.55/0.79 ! [C_4: int,A_7: int,B_8: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ A_7 @ B_8 )
% 0.55/0.79 => ( ord_less_eq_int @ ( plus_plus_int @ C_4 @ A_7 ) @ ( plus_plus_int @ C_4 @ B_8 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_810_add__left__mono,axiom,
% 0.55/0.79 ! [C_4: nat,A_7: nat,B_8: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ A_7 @ B_8 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( plus_plus_nat @ C_4 @ A_7 ) @ ( plus_plus_nat @ C_4 @ B_8 ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_811_add__mono,axiom,
% 0.55/0.79 ! [C_3: int,D_2: int,A_6: int,B_7: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ A_6 @ B_7 )
% 0.55/0.79 => ( ( ord_less_eq_int @ C_3 @ D_2 )
% 0.55/0.79 => ( ord_less_eq_int @ ( plus_plus_int @ A_6 @ C_3 ) @ ( plus_plus_int @ B_7 @ D_2 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_812_add__mono,axiom,
% 0.55/0.79 ! [C_3: nat,D_2: nat,A_6: nat,B_7: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ A_6 @ B_7 )
% 0.55/0.79 => ( ( ord_less_eq_nat @ C_3 @ D_2 )
% 0.55/0.79 => ( ord_less_eq_nat @ ( plus_plus_nat @ A_6 @ C_3 ) @ ( plus_plus_nat @ B_7 @ D_2 ) ) ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_813_add__le__imp__le__right,axiom,
% 0.55/0.79 ! [A_5: int,C_2: int,B_6: int] :
% 0.55/0.79 ( ( ord_less_eq_int @ ( plus_plus_int @ A_5 @ C_2 ) @ ( plus_plus_int @ B_6 @ C_2 ) )
% 0.55/0.79 => ( ord_less_eq_int @ A_5 @ B_6 ) ) ).
% 0.55/0.79
% 0.55/0.79 thf(fact_814_add__le__imp__le__right,axiom,
% 0.55/0.79 ! [A_5: nat,C_2: nat,B_6: nat] :
% 0.55/0.79 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A_5 @ C_2 ) @ ( plus_plus_nat @ B_6 @ C_2 ) )
% 0.55/0.80 => ( ord_less_eq_nat @ A_5 @ B_6 ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_815_add__le__imp__le__left,axiom,
% 0.55/0.80 ! [C_1: int,A_4: int,B_5: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( plus_plus_int @ C_1 @ A_4 ) @ ( plus_plus_int @ C_1 @ B_5 ) )
% 0.55/0.80 => ( ord_less_eq_int @ A_4 @ B_5 ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_816_add__le__imp__le__left,axiom,
% 0.55/0.80 ! [C_1: nat,A_4: nat,B_5: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C_1 @ A_4 ) @ ( plus_plus_nat @ C_1 @ B_5 ) )
% 0.55/0.80 => ( ord_less_eq_nat @ A_4 @ B_5 ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_817_diff__add__cancel,axiom,
% 0.55/0.80 ! [A_3: int,B_4: int] :
% 0.55/0.80 ( ( plus_plus_int @ ( minus_minus_int @ A_3 @ B_4 ) @ B_4 )
% 0.55/0.80 = A_3 ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_818_add__diff__cancel,axiom,
% 0.55/0.80 ! [A_2: int,B_3: int] :
% 0.55/0.80 ( ( minus_minus_int @ ( plus_plus_int @ A_2 @ B_3 ) @ B_3 )
% 0.55/0.80 = A_2 ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_819_add__Suc__right,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.55/0.80 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_820_add__Suc,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.55/0.80 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_821_add__Suc__shift,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.55/0.80 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_822_le__add2,axiom,
% 0.55/0.80 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_823_le__add1,axiom,
% 0.55/0.80 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_824_le__iff__add,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.80 <=> ? [K_1: nat] :
% 0.55/0.80 ( N
% 0.55/0.80 = ( plus_plus_nat @ M @ K_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_825_nat__add__left__cancel__le,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_826_trans__le__add1,axiom,
% 0.55/0.80 ! [M: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_827_trans__le__add2,axiom,
% 0.55/0.80 ! [M: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_828_add__le__mono1,axiom,
% 0.55/0.80 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_829_add__le__mono,axiom,
% 0.55/0.80 ! [K: nat,L: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_eq_nat @ K @ L )
% 0.55/0.80 => ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_830_add__leD2,axiom,
% 0.55/0.80 ! [M: nat,K: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.55/0.80 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_831_add__leD1,axiom,
% 0.55/0.80 ! [M: nat,K: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.55/0.80 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_832_add__leE,axiom,
% 0.55/0.80 ! [M: nat,K: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.55/0.80 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.80 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_833_diff__add__inverse2,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.55/0.80 = M ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_834_diff__add__inverse,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.55/0.80 = M ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_835_diff__diff__left,axiom,
% 0.55/0.80 ! [I_1: nat,J: nat,K: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J ) @ K )
% 0.55/0.80 = ( minus_minus_nat @ I_1 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_836_diff__cancel,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.55/0.80 = ( minus_minus_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_837_diff__cancel2,axiom,
% 0.55/0.80 ! [M: nat,K: nat,N: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.55/0.80 = ( minus_minus_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_838_diff__diff__right,axiom,
% 0.55/0.80 ! [I_1: nat,K: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ J )
% 0.55/0.80 => ( ( minus_minus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
% 0.55/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_839_le__diff__conv,axiom,
% 0.55/0.80 ! [J: nat,K: nat,I_1: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I_1 )
% 0.55/0.80 <=> ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I_1 @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_840_le__add__diff,axiom,
% 0.55/0.80 ! [M: nat,K: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ N )
% 0.55/0.80 => ( ord_less_eq_nat @ M @ ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_841_le__add__diff__inverse,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ N @ M )
% 0.55/0.80 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.55/0.80 = M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_842_add__diff__assoc,axiom,
% 0.55/0.80 ! [I_1: nat,K: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ J )
% 0.55/0.80 => ( ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
% 0.55/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J ) @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_843_le__diff__conv2,axiom,
% 0.55/0.80 ! [I_1: nat,K: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ J )
% 0.55/0.80 => ( ( ord_less_eq_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_844_le__add__diff__inverse2,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ N @ M )
% 0.55/0.80 => ( ( plus_plus_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.55/0.80 = M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_845_le__imp__diff__is__add,axiom,
% 0.55/0.80 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ( minus_minus_nat @ J @ I_1 )
% 0.55/0.80 = K )
% 0.55/0.80 <=> ( J
% 0.55/0.80 = ( plus_plus_nat @ K @ I_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_846_diff__add__assoc,axiom,
% 0.55/0.80 ! [I_1: nat,K: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ J )
% 0.55/0.80 => ( ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J ) @ K )
% 0.55/0.80 = ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_847_add__diff__assoc2,axiom,
% 0.55/0.80 ! [I_1: nat,K: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ J )
% 0.55/0.80 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I_1 )
% 0.55/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I_1 ) @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_848_diff__add__assoc2,axiom,
% 0.55/0.80 ! [I_1: nat,K: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ J )
% 0.55/0.80 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I_1 ) @ K )
% 0.55/0.80 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_849_Suc__eq__plus1__left,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( suc @ N )
% 0.55/0.80 = ( plus_plus_nat @ one_one_nat @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_850_Suc__eq__plus1,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( suc @ N )
% 0.55/0.80 = ( plus_plus_nat @ N @ one_one_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_851_diff__Suc__diff__eq1,axiom,
% 0.55/0.80 ! [M: nat,K: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ J )
% 0.55/0.80 => ( ( minus_minus_nat @ M @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 0.55/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( suc @ J ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_852_diff__Suc__diff__eq2,axiom,
% 0.55/0.80 ! [M: nat,K: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ J )
% 0.55/0.80 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ M )
% 0.55/0.80 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ M ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_853_termination__basic__simps_I4_J,axiom,
% 0.55/0.80 ! [Y: nat,X: nat,Z: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ X @ Z )
% 0.55/0.80 => ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_854_termination__basic__simps_I3_J,axiom,
% 0.55/0.80 ! [Z: nat,X: nat,Y: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ X @ Y )
% 0.55/0.80 => ( ord_less_eq_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_855_lessI,axiom,
% 0.55/0.80 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_856_Suc__mono,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_857_finite__Collect__less__nat,axiom,
% 0.55/0.80 ! [K: nat] :
% 0.55/0.80 ( finite_finite_nat
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [N_1: nat] : ( ord_less_nat @ N_1 @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_858_less__not__refl,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ~ ( ord_less_nat @ N @ N ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_859_nat__neq__iff,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( M != N )
% 0.55/0.80 <=> ( ( ord_less_nat @ M @ N )
% 0.55/0.80 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_860_linorder__neqE__nat,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( X != Y )
% 0.55/0.80 => ( ~ ( ord_less_nat @ X @ Y )
% 0.55/0.80 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_861_less__irrefl__nat,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ~ ( ord_less_nat @ N @ N ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_862_less__not__refl2,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( ord_less_nat @ N @ M )
% 0.55/0.80 => ( M != N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_863_less__not__refl3,axiom,
% 0.55/0.80 ! [S: nat,T: nat] :
% 0.55/0.80 ( ( ord_less_nat @ S @ T )
% 0.55/0.80 => ( S != T ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_864_nat__less__cases,axiom,
% 0.55/0.80 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.55/0.80 ( ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( P @ N @ M ) )
% 0.55/0.80 => ( ( ( M = N )
% 0.55/0.80 => ( P @ N @ M ) )
% 0.55/0.80 => ( ( ( ord_less_nat @ N @ M )
% 0.55/0.80 => ( P @ N @ M ) )
% 0.55/0.80 => ( P @ N @ M ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_865_not__less__eq,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ~ ( ord_less_nat @ M @ N )
% 0.55/0.80 <=> ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_866_less__Suc__eq,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.55/0.80 <=> ( ( ord_less_nat @ M @ N )
% 0.55/0.80 | ( M = N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_867_Suc__less__eq,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.55/0.80 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_868_not__less__less__Suc__eq,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ~ ( ord_less_nat @ N @ M )
% 0.55/0.80 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.55/0.80 <=> ( N = M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_869_less__antisym,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ~ ( ord_less_nat @ N @ M )
% 0.55/0.80 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.55/0.80 => ( M = N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_870_less__SucI,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_871_Suc__lessI,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( ( ( suc @ M )
% 0.55/0.80 != N )
% 0.55/0.80 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_872_less__trans__Suc,axiom,
% 0.55/0.80 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_nat @ J @ K )
% 0.55/0.80 => ( ord_less_nat @ ( suc @ I_1 ) @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_873_less__SucE,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.55/0.80 => ( ~ ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( M = N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_874_Suc__lessD,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.55/0.80 => ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_875_Suc__less__SucD,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.55/0.80 => ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_876_not__add__less1,axiom,
% 0.55/0.80 ! [I_1: nat,J: nat] :
% 0.55/0.80 ~ ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J ) @ I_1 ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_877_not__add__less2,axiom,
% 0.55/0.80 ! [J: nat,I_1: nat] :
% 0.55/0.80 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I_1 ) @ I_1 ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_878_nat__add__left__cancel__less,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.55/0.80 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_879_trans__less__add1,axiom,
% 0.55/0.80 ! [M: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_nat @ I_1 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_880_trans__less__add2,axiom,
% 0.55/0.80 ! [M: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_nat @ I_1 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_881_add__less__mono1,axiom,
% 0.55/0.80 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_882_add__less__mono,axiom,
% 0.55/0.80 ! [K: nat,L: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_nat @ K @ L )
% 0.55/0.80 => ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_883_less__add__eq__less,axiom,
% 0.55/0.80 ! [M: nat,N: nat,K: nat,L: nat] :
% 0.55/0.80 ( ( ord_less_nat @ K @ L )
% 0.55/0.80 => ( ( ( plus_plus_nat @ M @ L )
% 0.55/0.80 = ( plus_plus_nat @ K @ N ) )
% 0.55/0.80 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_884_add__lessD1,axiom,
% 0.55/0.80 ! [I_1: nat,J: nat,K: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J ) @ K )
% 0.55/0.80 => ( ord_less_nat @ I_1 @ K ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_885_termination__basic__simps_I1_J,axiom,
% 0.55/0.80 ! [Z: nat,X: nat,Y: nat] :
% 0.55/0.80 ( ( ord_less_nat @ X @ Y )
% 0.55/0.80 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_886_termination__basic__simps_I2_J,axiom,
% 0.55/0.80 ! [Y: nat,X: nat,Z: nat] :
% 0.55/0.80 ( ( ord_less_nat @ X @ Z )
% 0.55/0.80 => ( ord_less_nat @ X @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_887_nat__less__le,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.80 & ( M != N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_888_le__eq__less__or__eq,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.80 <=> ( ( ord_less_nat @ M @ N )
% 0.55/0.80 | ( M = N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_889_less__imp__le__nat,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_890_le__neq__implies__less,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.80 => ( ( M != N )
% 0.55/0.80 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_891_less__or__eq__imp__le,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( ord_less_nat @ M @ N )
% 0.55/0.80 | ( M = N ) )
% 0.55/0.80 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_892_termination__basic__simps_I5_J,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( ord_less_nat @ X @ Y )
% 0.55/0.80 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_893_less__imp__diff__less,axiom,
% 0.55/0.80 ! [N: nat,J: nat,K: nat] :
% 0.55/0.80 ( ( ord_less_nat @ J @ K )
% 0.55/0.80 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_894_diff__less__mono2,axiom,
% 0.55/0.80 ! [L: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( ( ord_less_nat @ M @ L )
% 0.55/0.80 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_895_finite__nat__set__iff__bounded,axiom,
% 0.55/0.80 ! [N_2: nat > $o] :
% 0.55/0.80 ( ( finite_finite_nat @ N_2 )
% 0.55/0.80 <=> ? [M_1: nat] :
% 0.55/0.80 ! [X_1: nat] :
% 0.55/0.80 ( ( member_nat @ X_1 @ N_2 )
% 0.55/0.80 => ( ord_less_nat @ X_1 @ M_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_896_card__Collect__less__nat,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( finite_card_nat
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [I: nat] : ( ord_less_nat @ I @ N ) ) )
% 0.55/0.80 = N ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_897_finite__M__bounded__by__nat,axiom,
% 0.55/0.80 ! [P: nat > $o,I_1: nat] :
% 0.55/0.80 ( finite_finite_nat
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [K_1: nat] : ( (&) @ ( P @ K_1 ) @ ( ord_less_nat @ K_1 @ I_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_898_less__add__Suc1,axiom,
% 0.55/0.80 ! [I_1: nat,M: nat] : ( ord_less_nat @ I_1 @ ( suc @ ( plus_plus_nat @ I_1 @ M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_899_less__add__Suc2,axiom,
% 0.55/0.80 ! [I_1: nat,M: nat] : ( ord_less_nat @ I_1 @ ( suc @ ( plus_plus_nat @ M @ I_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_900_less__iff__Suc__add,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 <=> ? [K_1: nat] :
% 0.55/0.80 ( N
% 0.55/0.80 = ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_901_less__eq__Suc__le,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( ord_less_nat @ N @ M )
% 0.55/0.80 <=> ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_902_less__Suc__eq__le,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_903_Suc__le__eq,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.55/0.80 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_904_le__imp__less__Suc,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.80 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_905_Suc__leI,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_906_le__less__Suc__eq,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.80 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.55/0.80 <=> ( N = M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_907_Suc__le__lessD,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.55/0.80 => ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_908_diff__less__Suc,axiom,
% 0.55/0.80 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_909_less__diff__conv,axiom,
% 0.55/0.80 ! [I_1: nat,J: nat,K: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
% 0.55/0.80 <=> ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_910_add__diff__inverse,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ~ ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.55/0.80 = M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_911_diff__less__mono,axiom,
% 0.55/0.80 ! [C: nat,A_1: nat,B_2: nat] :
% 0.55/0.80 ( ( ord_less_nat @ A_1 @ B_2 )
% 0.55/0.80 => ( ( ord_less_eq_nat @ C @ A_1 )
% 0.55/0.80 => ( ord_less_nat @ ( minus_minus_nat @ A_1 @ C ) @ ( minus_minus_nat @ B_2 @ C ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_912_less__diff__iff,axiom,
% 0.55/0.80 ! [N: nat,K: nat,M: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K @ M )
% 0.55/0.80 => ( ( ord_less_eq_nat @ K @ N )
% 0.55/0.80 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.55/0.80 <=> ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_913_less__eq__Suc__le__raw,axiom,
% 0.55/0.80 ! [X_1: nat] :
% 0.55/0.80 ( ( ord_less_nat @ X_1 )
% 0.55/0.80 = ( ord_less_eq_nat @ ( suc @ X_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_914_mono__nat__linear__lb,axiom,
% 0.55/0.80 ! [M: nat,K: nat,F: nat > nat] :
% 0.55/0.80 ( ! [M_1: nat,N_1: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M_1 @ N_1 )
% 0.55/0.80 => ( ord_less_nat @ ( F @ M_1 ) @ ( F @ N_1 ) ) )
% 0.55/0.80 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_915_inc__induct,axiom,
% 0.55/0.80 ! [P: nat > $o,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ( P @ J )
% 0.55/0.80 => ( ! [I: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I @ J )
% 0.55/0.80 => ( ( P @ ( suc @ I ) )
% 0.55/0.80 => ( P @ I ) ) )
% 0.55/0.80 => ( P @ I_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_916_less__imp__Suc__add,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ? [K_1: nat] :
% 0.55/0.80 ( N
% 0.55/0.80 = ( suc @ ( plus_plus_nat @ M @ K_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_917_bounded__nat__set__is__finite,axiom,
% 0.55/0.80 ! [N: nat,N_2: nat > $o] :
% 0.55/0.80 ( ! [X_1: nat] :
% 0.55/0.80 ( ( member_nat @ X_1 @ N_2 )
% 0.55/0.80 => ( ord_less_nat @ X_1 @ N ) )
% 0.55/0.80 => ( finite_finite_nat @ N_2 ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_918_less__mono__imp__le__mono,axiom,
% 0.55/0.80 ! [I_1: nat,J: nat,F: nat > nat] :
% 0.55/0.80 ( ! [I: nat,J_1: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I @ J_1 )
% 0.55/0.80 => ( ord_less_nat @ ( F @ I ) @ ( F @ J_1 ) ) )
% 0.55/0.80 => ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_eq_nat @ ( F @ I_1 ) @ ( F @ J ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_919_lessE,axiom,
% 0.55/0.80 ! [I_1: nat,K: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ K )
% 0.55/0.80 => ( ( K
% 0.55/0.80 != ( suc @ I_1 ) )
% 0.55/0.80 => ~ ! [J_1: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.55/0.80 => ( K
% 0.55/0.80 != ( suc @ J_1 ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_920_Suc__lessE,axiom,
% 0.55/0.80 ! [I_1: nat,K: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( suc @ I_1 ) @ K )
% 0.55/0.80 => ~ ! [J_1: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.55/0.80 => ( K
% 0.55/0.80 != ( suc @ J_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_921_less__zeroE,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_922_le0,axiom,
% 0.55/0.80 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_923_zero__less__Suc,axiom,
% 0.55/0.80 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_924_le__0__eq,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.55/0.80 <=> ( N = zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_925_less__eq__nat_Osimps_I1_J,axiom,
% 0.55/0.80 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_926_diffs0__imp__equal,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( minus_minus_nat @ M @ N )
% 0.55/0.80 = zero_zero_nat )
% 0.55/0.80 => ( ( ( minus_minus_nat @ N @ M )
% 0.55/0.80 = zero_zero_nat )
% 0.55/0.80 => ( M = N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_927_diff__self__eq__0,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ M @ M )
% 0.55/0.80 = zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_928_minus__nat_Odiff__0,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.55/0.80 = M ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_929_diff__0__eq__0,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.55/0.80 = zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_930_bot__nat__def,axiom,
% 0.55/0.80 bot_bot_nat = zero_zero_nat ).
% 0.55/0.80
% 0.55/0.80 thf(fact_931_add__eq__self__zero,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( plus_plus_nat @ M @ N )
% 0.55/0.80 = M )
% 0.55/0.80 => ( N = zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_932_add__is__0,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( plus_plus_nat @ M @ N )
% 0.55/0.80 = zero_zero_nat )
% 0.55/0.80 <=> ( ( M = zero_zero_nat )
% 0.55/0.80 & ( N = zero_zero_nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_933_Nat_Oadd__0__right,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.55/0.80 = M ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_934_plus__nat_Oadd__0,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.55/0.80 = N ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_935_gr0I,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( N != zero_zero_nat )
% 0.55/0.80 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_936_gr__implies__not0,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( N != zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_937_less__nat__zero__code,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_938_neq0__conv,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( N != zero_zero_nat )
% 0.55/0.80 <=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_939_not__less0,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_940_Suc__neq__Zero,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( ( suc @ M )
% 0.55/0.80 != zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_941_Zero__neq__Suc,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( zero_zero_nat
% 0.55/0.80 != ( suc @ M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_942_nat_Osimps_I3_J,axiom,
% 0.55/0.80 ! [Nat_2: nat] :
% 0.55/0.80 ( ( suc @ Nat_2 )
% 0.55/0.80 != zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_943_Suc__not__Zero,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( ( suc @ M )
% 0.55/0.80 != zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_944_nat_Osimps_I2_J,axiom,
% 0.55/0.80 ! [Nat_1: nat] :
% 0.55/0.80 ( zero_zero_nat
% 0.55/0.80 != ( suc @ Nat_1 ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_945_Zero__not__Suc,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( zero_zero_nat
% 0.55/0.80 != ( suc @ M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_946_gr0__conv__Suc,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.55/0.80 <=> ? [M_1: nat] :
% 0.55/0.80 ( N
% 0.55/0.80 = ( suc @ M_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_947_less__Suc0,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.55/0.80 <=> ( N = zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_948_less__Suc__eq__0__disj,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.55/0.80 <=> ( ( M = zero_zero_nat )
% 0.55/0.80 | ? [J_1: nat] :
% 0.55/0.80 ( ( M
% 0.55/0.80 = ( suc @ J_1 ) )
% 0.55/0.80 & ( ord_less_nat @ J_1 @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_949_one__is__add,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( suc @ zero_zero_nat )
% 0.55/0.80 = ( plus_plus_nat @ M @ N ) )
% 0.55/0.80 <=> ( ( ( M
% 0.55/0.80 = ( suc @ zero_zero_nat ) )
% 0.55/0.80 & ( N = zero_zero_nat ) )
% 0.55/0.80 | ( ( M = zero_zero_nat )
% 0.55/0.80 & ( N
% 0.55/0.80 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_950_add__is__1,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( plus_plus_nat @ M @ N )
% 0.55/0.80 = ( suc @ zero_zero_nat ) )
% 0.55/0.80 <=> ( ( ( M
% 0.55/0.80 = ( suc @ zero_zero_nat ) )
% 0.55/0.80 & ( N = zero_zero_nat ) )
% 0.55/0.80 | ( ( M = zero_zero_nat )
% 0.55/0.80 & ( N
% 0.55/0.80 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_951_add__gr__0,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.55/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.55/0.80 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_952_zero__less__diff,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.55/0.80 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_953_diff__less,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.55/0.80 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.55/0.80 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_954_diff__add__0,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.55/0.80 = zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_955_diff__is__0__eq,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( minus_minus_nat @ M @ N )
% 0.55/0.80 = zero_zero_nat )
% 0.55/0.80 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_956_diff__is__0__eq_H,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ M @ N )
% 0.55/0.80 => ( ( minus_minus_nat @ M @ N )
% 0.55/0.80 = zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_957_One__nat__def,axiom,
% 0.55/0.80 ( one_one_nat
% 0.55/0.80 = ( suc @ zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_958_diff__Suc,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.55/0.80 = ( nat_case_nat @ zero_zero_nat
% 0.55/0.80 @ ^ [K_1: nat] : K_1
% 0.55/0.80 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_959_Suc__pred,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.55/0.80 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.55/0.80 = N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_960_diff__Suc__less,axiom,
% 0.55/0.80 ! [I_1: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.55/0.80 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I_1 ) ) @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_961_nat__diff__split,axiom,
% 0.55/0.80 ! [P: nat > $o,A_1: nat,B_2: nat] :
% 0.55/0.80 ( ( P @ ( minus_minus_nat @ A_1 @ B_2 ) )
% 0.55/0.80 <=> ( ( ( ord_less_nat @ A_1 @ B_2 )
% 0.55/0.80 => ( P @ zero_zero_nat ) )
% 0.55/0.80 & ! [D_1: nat] :
% 0.55/0.80 ( ( A_1
% 0.55/0.80 = ( plus_plus_nat @ B_2 @ D_1 ) )
% 0.55/0.80 => ( P @ D_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_962_nat__diff__split__asm,axiom,
% 0.55/0.80 ! [P: nat > $o,A_1: nat,B_2: nat] :
% 0.55/0.80 ( ( P @ ( minus_minus_nat @ A_1 @ B_2 ) )
% 0.55/0.80 <=> ~ ( ( ( ord_less_nat @ A_1 @ B_2 )
% 0.55/0.80 & ~ ( P @ zero_zero_nat ) )
% 0.55/0.80 | ? [D_1: nat] :
% 0.55/0.80 ( ( A_1
% 0.55/0.80 = ( plus_plus_nat @ B_2 @ D_1 ) )
% 0.55/0.80 & ~ ( P @ D_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_963_card__less__Suc,axiom,
% 0.55/0.80 ! [I_1: nat,M_2: nat > $o] :
% 0.55/0.80 ( ( member_nat @ zero_zero_nat @ M_2 )
% 0.55/0.80 => ( ( suc
% 0.55/0.80 @ ( finite_card_nat
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [K_1: nat] : ( (&) @ ( member_nat @ ( suc @ K_1 ) @ M_2 ) @ ( ord_less_nat @ K_1 @ I_1 ) ) ) ) )
% 0.55/0.80 = ( finite_card_nat
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [K_1: nat] : ( (&) @ ( member_nat @ K_1 @ M_2 ) @ ( ord_less_nat @ K_1 @ ( suc @ I_1 ) ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_964_card__less,axiom,
% 0.55/0.80 ! [I_1: nat,M_2: nat > $o] :
% 0.55/0.80 ( ( member_nat @ zero_zero_nat @ M_2 )
% 0.55/0.80 => ( ( finite_card_nat
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [K_1: nat] : ( (&) @ ( member_nat @ K_1 @ M_2 ) @ ( ord_less_nat @ K_1 @ ( suc @ I_1 ) ) ) ) )
% 0.55/0.80 != zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_965_card__less__Suc2,axiom,
% 0.55/0.80 ! [I_1: nat,M_2: nat > $o] :
% 0.55/0.80 ( ~ ( member_nat @ zero_zero_nat @ M_2 )
% 0.55/0.80 => ( ( finite_card_nat
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [K_1: nat] : ( (&) @ ( member_nat @ ( suc @ K_1 ) @ M_2 ) @ ( ord_less_nat @ K_1 @ I_1 ) ) ) )
% 0.55/0.80 = ( finite_card_nat
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [K_1: nat] : ( (&) @ ( member_nat @ K_1 @ M_2 ) @ ( ord_less_nat @ K_1 @ ( suc @ I_1 ) ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_966_Suc__diff__1,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.55/0.80 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.55/0.80 = N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_967_Suc__pred_H,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.55/0.80 => ( N
% 0.55/0.80 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_968_add__eq__if,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( ( M = zero_zero_nat )
% 0.55/0.80 => ( ( plus_plus_nat @ M @ N )
% 0.55/0.80 = N ) )
% 0.55/0.80 & ( ( M != zero_zero_nat )
% 0.55/0.80 => ( ( plus_plus_nat @ M @ N )
% 0.55/0.80 = ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_969_ex__least__nat__less,axiom,
% 0.55/0.80 ! [N: nat,P: nat > $o] :
% 0.55/0.80 ( ~ ( P @ zero_zero_nat )
% 0.55/0.80 => ( ( P @ N )
% 0.55/0.80 => ? [K_1: nat] :
% 0.55/0.80 ( ( ord_less_nat @ K_1 @ N )
% 0.55/0.80 & ! [I: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I @ K_1 )
% 0.55/0.80 => ~ ( P @ I ) )
% 0.55/0.80 & ( P @ ( plus_plus_nat @ K_1 @ one_one_nat ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_970_ex__least__nat__le,axiom,
% 0.55/0.80 ! [N: nat,P: nat > $o] :
% 0.55/0.80 ( ~ ( P @ zero_zero_nat )
% 0.55/0.80 => ( ( P @ N )
% 0.55/0.80 => ? [K_1: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ K_1 @ N )
% 0.55/0.80 & ! [I: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I @ K_1 )
% 0.55/0.80 => ~ ( P @ I ) )
% 0.55/0.80 & ( P @ K_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_971_less__imp__add__positive,axiom,
% 0.55/0.80 ! [I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J )
% 0.55/0.80 => ? [K_1: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.55/0.80 & ( ( plus_plus_nat @ I_1 @ K_1 )
% 0.55/0.80 = J ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_972_gr0__implies__Suc,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.55/0.80 => ? [M_1: nat] :
% 0.55/0.80 ( N
% 0.55/0.80 = ( suc @ M_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_973_nat_Oexhaust,axiom,
% 0.55/0.80 ! [Y: nat] :
% 0.55/0.80 ( ( Y != zero_zero_nat )
% 0.55/0.80 => ~ ! [Nat: nat] :
% 0.55/0.80 ( Y
% 0.55/0.80 != ( suc @ Nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_974_zero__induct,axiom,
% 0.55/0.80 ! [P: nat > $o,K: nat] :
% 0.55/0.80 ( ( P @ K )
% 0.55/0.80 => ( ! [N_1: nat] :
% 0.55/0.80 ( ( P @ ( suc @ N_1 ) )
% 0.55/0.80 => ( P @ N_1 ) )
% 0.55/0.80 => ( P @ zero_zero_nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_975_not0__implies__Suc,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( N != zero_zero_nat )
% 0.55/0.80 => ? [M_1: nat] :
% 0.55/0.80 ( N
% 0.55/0.80 = ( suc @ M_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_976_nat__induct,axiom,
% 0.55/0.80 ! [N: nat,P: nat > $o] :
% 0.55/0.80 ( ( P @ zero_zero_nat )
% 0.55/0.80 => ( ! [N_1: nat] :
% 0.55/0.80 ( ( P @ N_1 )
% 0.55/0.80 => ( P @ ( suc @ N_1 ) ) )
% 0.55/0.80 => ( P @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_977_expand__Suc,axiom,
% 0.55/0.80 ! [V: int] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V ) )
% 0.55/0.80 => ( ( number_number_of_nat @ V )
% 0.55/0.80 = ( suc @ ( minus_minus_nat @ ( number_number_of_nat @ V ) @ one_one_nat ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_978_mult__0,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.55/0.80 = zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_979_mult__0__right,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.55/0.80 = zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_980_mult__is__0,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( times_times_nat @ M @ N )
% 0.55/0.80 = zero_zero_nat )
% 0.55/0.80 <=> ( ( M = zero_zero_nat )
% 0.55/0.80 | ( N = zero_zero_nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_981_mult__cancel1,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ( times_times_nat @ K @ M )
% 0.55/0.80 = ( times_times_nat @ K @ N ) )
% 0.55/0.80 <=> ( ( M = N )
% 0.55/0.80 | ( K = zero_zero_nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_982_mult__cancel2,axiom,
% 0.55/0.80 ! [M: nat,K: nat,N: nat] :
% 0.55/0.80 ( ( ( times_times_nat @ M @ K )
% 0.55/0.80 = ( times_times_nat @ N @ K ) )
% 0.55/0.80 <=> ( ( M = N )
% 0.55/0.80 | ( K = zero_zero_nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_983_Suc__mult__cancel1,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 0.55/0.80 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.55/0.80 <=> ( M = N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_984_add__mult__distrib,axiom,
% 0.55/0.80 ! [M: nat,N: nat,K: nat] :
% 0.55/0.80 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.55/0.80 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_985_add__mult__distrib2,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.55/0.80 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_986_mult__le__mono,axiom,
% 0.55/0.80 ! [K: nat,L: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_eq_nat @ K @ L )
% 0.55/0.80 => ( ord_less_eq_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_987_mult__le__mono2,axiom,
% 0.55/0.80 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I_1 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_988_mult__le__mono1,axiom,
% 0.55/0.80 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ord_less_eq_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_989_le__cube,axiom,
% 0.55/0.80 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_990_le__square,axiom,
% 0.55/0.80 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_991_diff__mult__distrib,axiom,
% 0.55/0.80 ! [M: nat,N: nat,K: nat] :
% 0.55/0.80 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.55/0.80 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_992_diff__mult__distrib2,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.55/0.80 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_993_nat__mult__eq__1__iff,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( times_times_nat @ M @ N )
% 0.55/0.80 = one_one_nat )
% 0.55/0.80 <=> ( ( M = one_one_nat )
% 0.55/0.80 & ( N = one_one_nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_994_nat__mult__1__right,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( times_times_nat @ N @ one_one_nat )
% 0.55/0.80 = N ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_995_nat__1__eq__mult__iff,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( one_one_nat
% 0.55/0.80 = ( times_times_nat @ M @ N ) )
% 0.55/0.80 <=> ( ( M = one_one_nat )
% 0.55/0.80 & ( N = one_one_nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_996_nat__mult__1,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( times_times_nat @ one_one_nat @ N )
% 0.55/0.80 = N ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_997_mult__eq__1__iff,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( times_times_nat @ M @ N )
% 0.55/0.80 = ( suc @ zero_zero_nat ) )
% 0.55/0.80 <=> ( ( M
% 0.55/0.80 = ( suc @ zero_zero_nat ) )
% 0.55/0.80 & ( N
% 0.55/0.80 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_998_mult__less__mono2,axiom,
% 0.55/0.80 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 => ( ord_less_nat @ ( times_times_nat @ K @ I_1 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_999_mult__less__mono1,axiom,
% 0.55/0.80 ! [K: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 => ( ord_less_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1000_mult__less__cancel2,axiom,
% 0.55/0.80 ! [M: nat,K: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.55/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1001_mult__less__cancel1,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.55/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1002_nat__0__less__mult__iff,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.55/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.55/0.80 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1003_Suc__mult__less__cancel1,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.55/0.80 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1004_mult__Suc__right,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( times_times_nat @ M @ ( suc @ N ) )
% 0.55/0.80 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1005_mult__Suc,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( times_times_nat @ ( suc @ M ) @ N )
% 0.55/0.80 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1006_Suc__mult__le__cancel1,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1007_mult__eq__self__implies__10,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( M
% 0.55/0.80 = ( times_times_nat @ M @ N ) )
% 0.55/0.80 => ( ( N = one_one_nat )
% 0.55/0.80 | ( M = zero_zero_nat ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1008_n__less__m__mult__n,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.55/0.80 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.55/0.80 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1009_n__less__n__mult__m,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.55/0.80 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.55/0.80 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1010_one__less__mult,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.55/0.80 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.55/0.80 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1011_one__le__mult__iff,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 0.55/0.80 <=> ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.55/0.80 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1012_mult__le__cancel1,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.55/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1013_mult__le__cancel2,axiom,
% 0.55/0.80 ! [M: nat,K: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.55/0.80 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1014_mult__eq__if,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( ( M = zero_zero_nat )
% 0.55/0.80 => ( ( times_times_nat @ M @ N )
% 0.55/0.80 = zero_zero_nat ) )
% 0.55/0.80 & ( ( M != zero_zero_nat )
% 0.55/0.80 => ( ( times_times_nat @ M @ N )
% 0.55/0.80 = ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1015_nat__less__add__iff2,axiom,
% 0.55/0.80 ! [U: nat,M: nat,N: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.55/0.80 <=> ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1016_nat__mult__commute,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( times_times_nat @ M @ N )
% 0.55/0.80 = ( times_times_nat @ N @ M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1017_nat__mult__assoc,axiom,
% 0.55/0.80 ! [M: nat,N: nat,K: nat] :
% 0.55/0.80 ( ( times_times_nat @ ( times_times_nat @ M @ N ) @ K )
% 0.55/0.80 = ( times_times_nat @ M @ ( times_times_nat @ N @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1018_less__number__of__int__code,axiom,
% 0.55/0.80 ! [K: int,L: int] :
% 0.55/0.80 ( ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
% 0.55/0.80 <=> ( ord_less_int @ K @ L ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1019_zmult__1,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( times_times_int @ one_one_int @ Z )
% 0.55/0.80 = Z ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1020_zmult__1__right,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( times_times_int @ Z @ one_one_int )
% 0.55/0.80 = Z ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1021_zmult__commute,axiom,
% 0.55/0.80 ! [Z: int,W: int] :
% 0.55/0.80 ( ( times_times_int @ Z @ W )
% 0.55/0.80 = ( times_times_int @ W @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1022_times__numeral__code_I5_J,axiom,
% 0.55/0.80 ! [V: int,W: int] :
% 0.55/0.80 ( ( times_times_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) )
% 0.55/0.80 = ( number_number_of_int @ ( times_times_int @ V @ W ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1023_zmult__assoc,axiom,
% 0.55/0.80 ! [Z1: int,Z2: int,Z3: int] :
% 0.55/0.80 ( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
% 0.55/0.80 = ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1024_less__eq__number__of__int__code,axiom,
% 0.55/0.80 ! [K: int,L: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
% 0.55/0.80 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1025_zdiff__zmult__distrib,axiom,
% 0.55/0.80 ! [Z1: int,Z2: int,W: int] :
% 0.55/0.80 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z2 ) @ W )
% 0.55/0.80 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1026_zdiff__zmult__distrib2,axiom,
% 0.55/0.80 ! [W: int,Z1: int,Z2: int] :
% 0.55/0.80 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z2 ) )
% 0.55/0.80 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1027_zadd__zmult__distrib2,axiom,
% 0.55/0.80 ! [W: int,Z1: int,Z2: int] :
% 0.55/0.80 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
% 0.55/0.80 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1028_plus__numeral__code_I9_J,axiom,
% 0.55/0.80 ! [V: int,W: int] :
% 0.55/0.80 ( ( plus_plus_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) )
% 0.55/0.80 = ( number_number_of_int @ ( plus_plus_int @ V @ W ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1029_zadd__zmult__distrib,axiom,
% 0.55/0.80 ! [Z1: int,Z2: int,W: int] :
% 0.55/0.80 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
% 0.55/0.80 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1030_zmult__zless__mono2,axiom,
% 0.55/0.80 ! [K: int,I_1: int,J: int] :
% 0.55/0.80 ( ( ord_less_int @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_int @ zero_zero_int @ K )
% 0.55/0.80 => ( ord_less_int @ ( times_times_int @ K @ I_1 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1031_pos__zmult__eq__1__iff,axiom,
% 0.55/0.80 ! [N: int,M: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ M )
% 0.55/0.80 => ( ( ( times_times_int @ M @ N )
% 0.55/0.80 = one_one_int )
% 0.55/0.80 <=> ( ( M = one_one_int )
% 0.55/0.80 & ( N = one_one_int ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1032_odd__nonzero,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 0.55/0.80 != zero_zero_int ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1033_zadd__0__right,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( plus_plus_int @ Z @ zero_zero_int )
% 0.55/0.80 = Z ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1034_zadd__0,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( plus_plus_int @ zero_zero_int @ Z )
% 0.55/0.80 = Z ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1035_int__0__less__1,axiom,
% 0.55/0.80 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1036_int__one__le__iff__zero__less,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.55/0.80 <=> ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1037_less__bin__lemma,axiom,
% 0.55/0.80 ! [K: int,L: int] :
% 0.55/0.80 ( ( ord_less_int @ K @ L )
% 0.55/0.80 <=> ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1038_le__imp__0__less,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.55/0.80 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1039_odd__less__0,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.55/0.80 <=> ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1040_zadd__left__mono,axiom,
% 0.55/0.80 ! [K: int,I_1: int,J: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ I_1 @ J )
% 0.55/0.80 => ( ord_less_eq_int @ ( plus_plus_int @ K @ I_1 ) @ ( plus_plus_int @ K @ J ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1041_zadd__assoc,axiom,
% 0.55/0.80 ! [Z1: int,Z2: int,Z3: int] :
% 0.55/0.80 ( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
% 0.55/0.80 = ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1042_zadd__left__commute,axiom,
% 0.55/0.80 ! [X: int,Y: int,Z: int] :
% 0.55/0.80 ( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
% 0.55/0.80 = ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1043_zadd__commute,axiom,
% 0.55/0.80 ! [Z: int,W: int] :
% 0.55/0.80 ( ( plus_plus_int @ Z @ W )
% 0.55/0.80 = ( plus_plus_int @ W @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1044_zle__refl,axiom,
% 0.55/0.80 ! [W: int] : ( ord_less_eq_int @ W @ W ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1045_zle__linear,axiom,
% 0.55/0.80 ! [Z: int,W: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ Z @ W )
% 0.55/0.80 | ( ord_less_eq_int @ W @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1046_zle__trans,axiom,
% 0.55/0.80 ! [K: int,I_1: int,J: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_eq_int @ J @ K )
% 0.55/0.80 => ( ord_less_eq_int @ I_1 @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1047_zle__antisym,axiom,
% 0.55/0.80 ! [Z: int,W: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ Z @ W )
% 0.55/0.80 => ( ( ord_less_eq_int @ W @ Z )
% 0.55/0.80 => ( Z = W ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1048_zle__diff1__eq,axiom,
% 0.55/0.80 ! [W: int,Z: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.55/0.80 <=> ( ord_less_int @ W @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1049_zless__linear,axiom,
% 0.55/0.80 ! [X: int,Y: int] :
% 0.55/0.80 ( ( ord_less_int @ X @ Y )
% 0.55/0.80 | ( X = Y )
% 0.55/0.80 | ( ord_less_int @ Y @ X ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1050_zless__le,axiom,
% 0.55/0.80 ! [Z: int,W: int] :
% 0.55/0.80 ( ( ord_less_int @ Z @ W )
% 0.55/0.80 <=> ( ( ord_less_eq_int @ Z @ W )
% 0.55/0.80 & ( Z != W ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1051_zadd__strict__right__mono,axiom,
% 0.55/0.80 ! [K: int,I_1: int,J: int] :
% 0.55/0.80 ( ( ord_less_int @ I_1 @ J )
% 0.55/0.80 => ( ord_less_int @ ( plus_plus_int @ I_1 @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1052_zadd__zless__mono,axiom,
% 0.55/0.80 ! [Z_3: int,Z: int,W_1: int,W: int] :
% 0.55/0.80 ( ( ord_less_int @ W_1 @ W )
% 0.55/0.80 => ( ( ord_less_eq_int @ Z_3 @ Z )
% 0.55/0.80 => ( ord_less_int @ ( plus_plus_int @ W_1 @ Z_3 ) @ ( plus_plus_int @ W @ Z ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1053_zle__add1__eq__le,axiom,
% 0.55/0.80 ! [W: int,Z: int] :
% 0.55/0.80 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.55/0.80 <=> ( ord_less_eq_int @ W @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1054_add1__zle__eq,axiom,
% 0.55/0.80 ! [W: int,Z: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.55/0.80 <=> ( ord_less_int @ W @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1055_zless__imp__add1__zle,axiom,
% 0.55/0.80 ! [W: int,Z: int] :
% 0.55/0.80 ( ( ord_less_int @ W @ Z )
% 0.55/0.80 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1056_zless__add1__eq,axiom,
% 0.55/0.80 ! [W: int,Z: int] :
% 0.55/0.80 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.55/0.80 <=> ( ( ord_less_int @ W @ Z )
% 0.55/0.80 | ( W = Z ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1057_nat__mult__eq__cancel__disj,axiom,
% 0.55/0.80 ! [K: nat,M: nat,N: nat] :
% 0.55/0.80 ( ( ( times_times_nat @ K @ M )
% 0.55/0.80 = ( times_times_nat @ K @ N ) )
% 0.55/0.80 <=> ( ( K = zero_zero_nat )
% 0.55/0.80 | ( M = N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1058_left__add__mult__distrib,axiom,
% 0.55/0.80 ! [I_1: nat,U: nat,J: nat,K: nat] :
% 0.55/0.80 ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.55/0.80 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I_1 @ J ) @ U ) @ K ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1059_nat__mult__eq__cancel1,axiom,
% 0.55/0.80 ! [M: nat,N: nat,K: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 => ( ( ( times_times_nat @ K @ M )
% 0.55/0.80 = ( times_times_nat @ K @ N ) )
% 0.55/0.80 <=> ( M = N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1060_nat__mult__less__cancel1,axiom,
% 0.55/0.80 ! [M: nat,N: nat,K: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.55/0.80 <=> ( ord_less_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1061_nat__mult__le__cancel1,axiom,
% 0.55/0.80 ! [M: nat,N: nat,K: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1062_nat__le__add__iff1,axiom,
% 0.55/0.80 ! [U: nat,M: nat,N: nat,J: nat,I_1: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ J @ I_1 )
% 0.55/0.80 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1063_nat__diff__add__eq1,axiom,
% 0.55/0.80 ! [U: nat,M: nat,N: nat,J: nat,I_1: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ J @ I_1 )
% 0.55/0.80 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.55/0.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1064_nat__eq__add__iff1,axiom,
% 0.55/0.80 ! [U: nat,M: nat,N: nat,J: nat,I_1: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ J @ I_1 )
% 0.55/0.80 => ( ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M )
% 0.55/0.80 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.55/0.80 <=> ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J ) @ U ) @ M )
% 0.55/0.80 = N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1065_nat__le__add__iff2,axiom,
% 0.55/0.80 ! [U: nat,M: nat,N: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1066_nat__diff__add__eq2,axiom,
% 0.55/0.80 ! [U: nat,M: nat,N: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.55/0.80 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1067_nat__eq__add__iff2,axiom,
% 0.55/0.80 ! [U: nat,M: nat,N: nat,I_1: nat,J: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.55/0.80 => ( ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M )
% 0.55/0.80 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.55/0.80 <=> ( M
% 0.55/0.80 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1068_nat__less__add__iff1,axiom,
% 0.55/0.80 ! [U: nat,M: nat,N: nat,J: nat,I_1: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ J @ I_1 )
% 0.55/0.80 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.55/0.80 <=> ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1069_zdiv__mono2__neg__lemma,axiom,
% 0.55/0.80 ! [B_2: int,Q_1: int,R_1: int,B_1: int,Q: int,R: int] :
% 0.55/0.80 ( ( ( plus_plus_int @ ( times_times_int @ B_2 @ Q_1 ) @ R_1 )
% 0.55/0.80 = ( plus_plus_int @ ( times_times_int @ B_1 @ Q ) @ R ) )
% 0.55/0.80 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_1 @ Q ) @ R ) @ zero_zero_int )
% 0.55/0.80 => ( ( ord_less_int @ R_1 @ B_2 )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.55/0.80 => ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.55/0.80 => ( ( ord_less_eq_int @ B_1 @ B_2 )
% 0.55/0.80 => ( ord_less_eq_int @ Q @ Q_1 ) ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1070_unique__quotient__lemma__neg,axiom,
% 0.55/0.80 ! [B_2: int,Q: int,R: int,Q_1: int,R_1: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B_2 @ Q ) @ R ) @ ( plus_plus_int @ ( times_times_int @ B_2 @ Q_1 ) @ R_1 ) )
% 0.55/0.80 => ( ( ord_less_eq_int @ R_1 @ zero_zero_int )
% 0.55/0.80 => ( ( ord_less_int @ B_2 @ R_1 )
% 0.55/0.80 => ( ( ord_less_int @ B_2 @ R )
% 0.55/0.80 => ( ord_less_eq_int @ Q_1 @ Q ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1071_number__of__is__id,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( number_number_of_int @ K )
% 0.55/0.80 = K ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1072_int__0__neq__1,axiom,
% 0.55/0.80 zero_zero_int != one_one_int ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1073_self__quotient__aux1,axiom,
% 0.55/0.80 ! [R_1: int,Q_1: int,A_1: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ A_1 )
% 0.55/0.80 => ( ( A_1
% 0.55/0.80 = ( plus_plus_int @ R_1 @ ( times_times_int @ A_1 @ Q_1 ) ) )
% 0.55/0.80 => ( ( ord_less_int @ R_1 @ A_1 )
% 0.55/0.80 => ( ord_less_eq_int @ one_one_int @ Q_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1074_self__quotient__aux2,axiom,
% 0.55/0.80 ! [R_1: int,Q_1: int,A_1: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ A_1 )
% 0.55/0.80 => ( ( A_1
% 0.55/0.80 = ( plus_plus_int @ R_1 @ ( times_times_int @ A_1 @ Q_1 ) ) )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
% 0.55/0.80 => ( ord_less_eq_int @ Q_1 @ one_one_int ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1075_q__pos__lemma,axiom,
% 0.55/0.80 ! [B_1: int,Q: int,R: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_1 @ Q ) @ R ) )
% 0.55/0.80 => ( ( ord_less_int @ R @ B_1 )
% 0.55/0.80 => ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.55/0.80 => ( ord_less_eq_int @ zero_zero_int @ Q ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1076_q__neg__lemma,axiom,
% 0.55/0.80 ! [B_1: int,Q: int,R: int] :
% 0.55/0.80 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_1 @ Q ) @ R ) @ zero_zero_int )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.55/0.80 => ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.55/0.80 => ( ord_less_eq_int @ Q @ zero_zero_int ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1077_unique__quotient__lemma,axiom,
% 0.55/0.80 ! [B_2: int,Q: int,R: int,Q_1: int,R_1: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B_2 @ Q ) @ R ) @ ( plus_plus_int @ ( times_times_int @ B_2 @ Q_1 ) @ R_1 ) )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.55/0.80 => ( ( ord_less_int @ R @ B_2 )
% 0.55/0.80 => ( ( ord_less_int @ R_1 @ B_2 )
% 0.55/0.80 => ( ord_less_eq_int @ Q @ Q_1 ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1078_zdiv__mono2__lemma,axiom,
% 0.55/0.80 ! [B_2: int,Q_1: int,R_1: int,B_1: int,Q: int,R: int] :
% 0.55/0.80 ( ( ( plus_plus_int @ ( times_times_int @ B_2 @ Q_1 ) @ R_1 )
% 0.55/0.80 = ( plus_plus_int @ ( times_times_int @ B_1 @ Q ) @ R ) )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_1 @ Q ) @ R ) )
% 0.55/0.80 => ( ( ord_less_int @ R @ B_1 )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
% 0.55/0.80 => ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.55/0.80 => ( ( ord_less_eq_int @ B_1 @ B_2 )
% 0.55/0.80 => ( ord_less_eq_int @ Q_1 @ Q ) ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1079_int__less__induct,axiom,
% 0.55/0.80 ! [P: int > $o,I_1: int,K: int] :
% 0.55/0.80 ( ( ord_less_int @ I_1 @ K )
% 0.55/0.80 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 0.55/0.80 => ( ! [I: int] :
% 0.55/0.80 ( ( ord_less_int @ I @ K )
% 0.55/0.80 => ( ( P @ I )
% 0.55/0.80 => ( P @ ( minus_minus_int @ I @ one_one_int ) ) ) )
% 0.55/0.80 => ( P @ I_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1080_int__le__induct,axiom,
% 0.55/0.80 ! [P: int > $o,I_1: int,K: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ I_1 @ K )
% 0.55/0.80 => ( ( P @ K )
% 0.55/0.80 => ( ! [I: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ I @ K )
% 0.55/0.80 => ( ( P @ I )
% 0.55/0.80 => ( P @ ( minus_minus_int @ I @ one_one_int ) ) ) )
% 0.55/0.80 => ( P @ I_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1081_int__gr__induct,axiom,
% 0.55/0.80 ! [P: int > $o,K: int,I_1: int] :
% 0.55/0.80 ( ( ord_less_int @ K @ I_1 )
% 0.55/0.80 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.55/0.80 => ( ! [I: int] :
% 0.55/0.80 ( ( ord_less_int @ K @ I )
% 0.55/0.80 => ( ( P @ I )
% 0.55/0.80 => ( P @ ( plus_plus_int @ I @ one_one_int ) ) ) )
% 0.55/0.80 => ( P @ I_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1082_int__ge__induct,axiom,
% 0.55/0.80 ! [P: int > $o,K: int,I_1: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ K @ I_1 )
% 0.55/0.80 => ( ( P @ K )
% 0.55/0.80 => ( ! [I: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ K @ I )
% 0.55/0.80 => ( ( P @ I )
% 0.55/0.80 => ( P @ ( plus_plus_int @ I @ one_one_int ) ) ) )
% 0.55/0.80 => ( P @ I_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1083_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 0.55/0.80 ! [Y: int,X: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.55/0.80 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ X @ Y ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1084_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 0.55/0.80 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1085_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 0.55/0.80 ! [Y: int,X: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.55/0.80 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ X @ Y ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1086_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 0.55/0.80 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1087_transfer__nat__int__set__cong,axiom,
% 0.55/0.80 ! [P_1: int > $o,P: int > $o] :
% 0.55/0.80 ( ! [X_1: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.55/0.80 => ( ( P @ X_1 )
% 0.55/0.80 <=> ( P_1 @ X_1 ) ) )
% 0.55/0.80 => ( ( collect_int
% 0.55/0.80 @ ^ [X_1: int] : ( (&) @ ( ord_less_eq_int @ zero_zero_int @ X_1 ) @ ( P @ X_1 ) ) )
% 0.55/0.80 = ( collect_int
% 0.55/0.80 @ ^ [X_1: int] : ( (&) @ ( ord_less_eq_int @ zero_zero_int @ X_1 ) @ ( P_1 @ X_1 ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1088_decr__mult__lemma,axiom,
% 0.55/0.80 ! [K: int,P: int > $o,D: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ D )
% 0.55/0.80 => ( ! [X_1: int] :
% 0.55/0.80 ( ( P @ X_1 )
% 0.55/0.80 => ( P @ ( minus_minus_int @ X_1 @ D ) ) )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.55/0.80 => ! [X_1: int] :
% 0.55/0.80 ( ( P @ X_1 )
% 0.55/0.80 => ( P @ ( minus_minus_int @ X_1 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1089_conj__le__cong,axiom,
% 0.55/0.80 ! [P_1: $o,P: $o,X: int] :
% 0.55/0.80 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 => ( P
% 0.55/0.80 <=> P_1 ) )
% 0.55/0.80 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 & P )
% 0.55/0.80 <=> ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 & P_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1090_imp__le__cong,axiom,
% 0.55/0.80 ! [P_1: $o,P: $o,X: int] :
% 0.55/0.80 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 => ( P
% 0.55/0.80 <=> P_1 ) )
% 0.55/0.80 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 => P )
% 0.55/0.80 <=> ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 => P_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1091_incr__mult__lemma,axiom,
% 0.55/0.80 ! [K: int,P: int > $o,D: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ D )
% 0.55/0.80 => ( ! [X_1: int] :
% 0.55/0.80 ( ( P @ X_1 )
% 0.55/0.80 => ( P @ ( plus_plus_int @ X_1 @ D ) ) )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.55/0.80 => ! [X_1: int] :
% 0.55/0.80 ( ( P @ X_1 )
% 0.55/0.80 => ( P @ ( plus_plus_int @ X_1 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1092_int__induct,axiom,
% 0.55/0.80 ! [I_1: int,P: int > $o,K: int] :
% 0.55/0.80 ( ( P @ K )
% 0.55/0.80 => ( ! [I: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ K @ I )
% 0.55/0.80 => ( ( P @ I )
% 0.55/0.80 => ( P @ ( plus_plus_int @ I @ one_one_int ) ) ) )
% 0.55/0.80 => ( ! [I: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ I @ K )
% 0.55/0.80 => ( ( P @ I )
% 0.55/0.80 => ( P @ ( minus_minus_int @ I @ one_one_int ) ) ) )
% 0.55/0.80 => ( P @ I_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1093_minusinfinity,axiom,
% 0.55/0.80 ! [P: int > $o,P1: int > $o,D: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ D )
% 0.55/0.80 => ( ! [X_1: int,K_1: int] :
% 0.55/0.80 ( ( P1 @ X_1 )
% 0.55/0.80 <=> ( P1 @ ( minus_minus_int @ X_1 @ ( times_times_int @ K_1 @ D ) ) ) )
% 0.55/0.80 => ( ? [Z_2: int] :
% 0.55/0.80 ! [X_1: int] :
% 0.55/0.80 ( ( ord_less_int @ X_1 @ Z_2 )
% 0.55/0.80 => ( ( P @ X_1 )
% 0.55/0.80 <=> ( P1 @ X_1 ) ) )
% 0.55/0.80 => ( ( ex @ P1 )
% 0.55/0.80 => ( ex @ P ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1094_plusinfinity,axiom,
% 0.55/0.80 ! [P: int > $o,P_1: int > $o,D: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ D )
% 0.55/0.80 => ( ! [X_1: int,K_1: int] :
% 0.55/0.80 ( ( P_1 @ X_1 )
% 0.55/0.80 <=> ( P_1 @ ( minus_minus_int @ X_1 @ ( times_times_int @ K_1 @ D ) ) ) )
% 0.55/0.80 => ( ? [Z_2: int] :
% 0.55/0.80 ! [X_1: int] :
% 0.55/0.80 ( ( ord_less_int @ Z_2 @ X_1 )
% 0.55/0.80 => ( ( P @ X_1 )
% 0.55/0.80 <=> ( P_1 @ X_1 ) ) )
% 0.55/0.80 => ( ( ex @ P_1 )
% 0.55/0.80 => ( ex @ P ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1095_tsub__def,axiom,
% 0.55/0.80 ! [Y: int,X: int] :
% 0.55/0.80 ( ( ( ord_less_eq_int @ Y @ X )
% 0.55/0.80 => ( ( nat_tsub @ X @ Y )
% 0.55/0.80 = ( minus_minus_int @ X @ Y ) ) )
% 0.55/0.80 & ( ~ ( ord_less_eq_int @ Y @ X )
% 0.55/0.80 => ( ( nat_tsub @ X @ Y )
% 0.55/0.80 = zero_zero_int ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1096_zero__zle__int,axiom,
% 0.55/0.80 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1621563631at_int @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1097_int__less__0__conv,axiom,
% 0.55/0.80 ! [K: nat] :
% 0.55/0.80 ~ ( ord_less_int @ ( semiri1621563631at_int @ K ) @ zero_zero_int ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1098_int__1,axiom,
% 0.55/0.80 ( ( semiri1621563631at_int @ one_one_nat )
% 0.55/0.80 = one_one_int ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1099_int__0,axiom,
% 0.55/0.80 ( ( semiri1621563631at_int @ zero_zero_nat )
% 0.55/0.80 = zero_zero_int ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1100_int__eq__0__conv,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ( semiri1621563631at_int @ N )
% 0.55/0.80 = zero_zero_int )
% 0.55/0.80 <=> ( N = zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1101_zless__int,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.55/0.80 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1102_zle__int,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1103_zadd__int,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.55/0.80 = ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1104_zadd__int__left,axiom,
% 0.55/0.80 ! [M: nat,N: nat,Z: int] :
% 0.55/0.80 ( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( plus_plus_int @ ( semiri1621563631at_int @ N ) @ Z ) )
% 0.55/0.80 = ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1105_zle__iff__zadd,axiom,
% 0.55/0.80 ! [W: int,Z: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ W @ Z )
% 0.55/0.80 <=> ? [N_1: nat] :
% 0.55/0.80 ( Z
% 0.55/0.80 = ( plus_plus_int @ W @ ( semiri1621563631at_int @ N_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1106_zmult__int,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( times_times_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.55/0.80 = ( semiri1621563631at_int @ ( times_times_nat @ M @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1107_int__mult,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( semiri1621563631at_int @ ( times_times_nat @ M @ N ) )
% 0.55/0.80 = ( times_times_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1108_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( times_times_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.55/0.80 = ( semiri1621563631at_int @ ( times_times_nat @ X @ Y ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1109_transfer__int__nat__relations_I2_J,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( ord_less_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.55/0.80 <=> ( ord_less_nat @ X @ Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1110_transfer__int__nat__relations_I3_J,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.55/0.80 <=> ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1111_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( nat_tsub @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.55/0.80 = ( semiri1621563631at_int @ ( minus_minus_nat @ X @ Y ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1112_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( plus_plus_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.55/0.80 = ( semiri1621563631at_int @ ( plus_plus_nat @ X @ Y ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 0.55/0.80 ! [A: nat > $o] :
% 0.55/0.80 ( ( finite_card_nat @ A )
% 0.55/0.80 = ( finite_card_int @ ( image_nat_int @ semiri1621563631at_int @ A ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1114_transfer__nat__int__set__relations_I1_J,axiom,
% 0.55/0.80 ! [A: nat > $o] :
% 0.55/0.80 ( ( finite_finite_nat @ A )
% 0.55/0.80 <=> ( finite_finite_int @ ( image_nat_int @ semiri1621563631at_int @ A ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1115_transfer__int__nat__numerals_I2_J,axiom,
% 0.55/0.80 ( one_one_int
% 0.55/0.80 = ( semiri1621563631at_int @ one_one_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1116_transfer__int__nat__numerals_I1_J,axiom,
% 0.55/0.80 ( zero_zero_int
% 0.55/0.80 = ( semiri1621563631at_int @ zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1117_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 0.55/0.80 ! [P: int > $o] :
% 0.55/0.80 ( ( collect_int
% 0.55/0.80 @ ^ [X_1: int] : ( (&) @ ( ord_less_eq_int @ zero_zero_int @ X_1 ) @ ( P @ X_1 ) ) )
% 0.55/0.80 = ( image_nat_int @ semiri1621563631at_int
% 0.55/0.80 @ ( collect_nat
% 0.55/0.80 @ ^ [X_1: nat] : ( P @ ( semiri1621563631at_int @ X_1 ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1118_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 0.55/0.80 ! [Z: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1621563631at_int @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1119_transfer__int__nat__quantifiers_I2_J,axiom,
% 0.55/0.80 ! [P: int > $o] :
% 0.55/0.80 ( ? [X_1: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.55/0.80 & ( P @ X_1 ) )
% 0.55/0.80 <=> ? [X_1: nat] : ( P @ ( semiri1621563631at_int @ X_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1120_transfer__int__nat__quantifiers_I1_J,axiom,
% 0.55/0.80 ! [P: int > $o] :
% 0.55/0.80 ( ! [X_1: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.55/0.80 => ( P @ X_1 ) )
% 0.55/0.80 <=> ! [X_1: nat] : ( P @ ( semiri1621563631at_int @ X_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1121_int__le__0__conv,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( semiri1621563631at_int @ N ) @ zero_zero_int )
% 0.55/0.80 <=> ( N = zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1122_int__Suc0__eq__1,axiom,
% 0.55/0.80 ( ( semiri1621563631at_int @ ( suc @ zero_zero_nat ) )
% 0.55/0.80 = one_one_int ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1123_zless__iff__Suc__zadd,axiom,
% 0.55/0.80 ! [W: int,Z: int] :
% 0.55/0.80 ( ( ord_less_int @ W @ Z )
% 0.55/0.80 <=> ? [N_1: nat] :
% 0.55/0.80 ( Z
% 0.55/0.80 = ( plus_plus_int @ W @ ( semiri1621563631at_int @ ( suc @ N_1 ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1124_int__Suc,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( ( semiri1621563631at_int @ ( suc @ M ) )
% 0.55/0.80 = ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ M ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1125_zdiff__int,axiom,
% 0.55/0.80 ! [N: nat,M: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ N @ M )
% 0.55/0.80 => ( ( minus_minus_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.55/0.80 = ( semiri1621563631at_int @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1126_zero__less__int__conv,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ ( semiri1621563631at_int @ N ) )
% 0.55/0.80 <=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1127_zmult__zless__mono2__lemma,axiom,
% 0.55/0.80 ! [K: nat,I_1: int,J: int] :
% 0.55/0.80 ( ( ord_less_int @ I_1 @ J )
% 0.55/0.80 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.55/0.80 => ( ord_less_int @ ( times_times_int @ ( semiri1621563631at_int @ K ) @ I_1 ) @ ( times_times_int @ ( semiri1621563631at_int @ K ) @ J ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1128_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 0.55/0.80 ! [Y: int,X: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.55/0.80 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.55/0.80 => ( ord_less_eq_int @ zero_zero_int @ ( nat_tsub @ X @ Y ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1129_zdiff__int__split,axiom,
% 0.55/0.80 ! [P: int > $o,X: nat,Y: nat] :
% 0.55/0.80 ( ( P @ ( semiri1621563631at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 0.55/0.80 <=> ( ( ( ord_less_eq_nat @ Y @ X )
% 0.55/0.80 => ( P @ ( minus_minus_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) ) ) )
% 0.55/0.80 & ( ( ord_less_nat @ X @ Y )
% 0.55/0.80 => ( P @ zero_zero_int ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1130_tsub__eq,axiom,
% 0.55/0.80 ! [Y: int,X: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ Y @ X )
% 0.55/0.80 => ( ( nat_tsub @ X @ Y )
% 0.55/0.80 = ( minus_minus_int @ X @ Y ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1131_zero__less__imp__eq__int,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ K )
% 0.55/0.80 => ? [N_1: nat] :
% 0.55/0.80 ( ( ord_less_nat @ zero_zero_nat @ N_1 )
% 0.55/0.80 & ( K
% 0.55/0.80 = ( semiri1621563631at_int @ N_1 ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1132_int__int__eq,axiom,
% 0.55/0.80 ! [M: nat,N: nat] :
% 0.55/0.80 ( ( ( semiri1621563631at_int @ M )
% 0.55/0.80 = ( semiri1621563631at_int @ N ) )
% 0.55/0.80 <=> ( M = N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1133_transfer__nat__int__set__relations_I4_J,axiom,
% 0.55/0.80 ! [A: nat > $o,B: nat > $o] :
% 0.55/0.80 ( ( ord_less_nat_o @ A @ B )
% 0.55/0.80 <=> ( ord_less_int_o @ ( image_nat_int @ semiri1621563631at_int @ A ) @ ( image_nat_int @ semiri1621563631at_int @ B ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1134_transfer__nat__int__set__relations_I5_J,axiom,
% 0.55/0.80 ! [A: nat > $o,B: nat > $o] :
% 0.55/0.80 ( ( ord_less_eq_nat_o @ A @ B )
% 0.55/0.80 <=> ( ord_less_eq_int_o @ ( image_nat_int @ semiri1621563631at_int @ A ) @ ( image_nat_int @ semiri1621563631at_int @ B ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 0.55/0.80 ( bot_bot_int_o
% 0.55/0.80 = ( image_nat_int @ semiri1621563631at_int @ bot_bot_nat_o ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1136_transfer__nat__int__set__relations_I3_J,axiom,
% 0.55/0.80 ! [A: nat > $o,B: nat > $o] :
% 0.55/0.80 ( ( A = B )
% 0.55/0.80 <=> ( ( image_nat_int @ semiri1621563631at_int @ A )
% 0.55/0.80 = ( image_nat_int @ semiri1621563631at_int @ B ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1137_transfer__nat__int__set__relations_I2_J,axiom,
% 0.55/0.80 ! [X: nat,A: nat > $o] :
% 0.55/0.80 ( ( member_nat @ X @ A )
% 0.55/0.80 <=> ( member_int @ ( semiri1621563631at_int @ X ) @ ( image_nat_int @ semiri1621563631at_int @ A ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1138_int__if__cong,axiom,
% 0.55/0.80 ! [X: nat,Y: nat,P: $o] :
% 0.55/0.80 ( ( P
% 0.55/0.80 => ( ( semiri1621563631at_int @ X )
% 0.55/0.80 = ( semiri1621563631at_int @ ( if_nat @ P @ X @ Y ) ) ) )
% 0.55/0.80 & ( ~ P
% 0.55/0.80 => ( ( semiri1621563631at_int @ Y )
% 0.55/0.80 = ( semiri1621563631at_int @ ( if_nat @ P @ X @ Y ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1139_transfer__int__nat__relations_I1_J,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( ( semiri1621563631at_int @ X )
% 0.55/0.80 = ( semiri1621563631at_int @ Y ) )
% 0.55/0.80 <=> ( X = Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1140_nonneg__int__cases,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.55/0.80 => ~ ! [N_1: nat] :
% 0.55/0.80 ( K
% 0.55/0.80 != ( semiri1621563631at_int @ N_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1141_nonneg__eq__int,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.55/0.80 => ~ ! [M_1: nat] :
% 0.55/0.80 ( Z
% 0.55/0.80 != ( semiri1621563631at_int @ M_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1142_zero__le__imp__eq__int,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.55/0.80 => ? [N_1: nat] :
% 0.55/0.80 ( K
% 0.55/0.80 = ( semiri1621563631at_int @ N_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1143_int__diff__cases,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ~ ! [M_1: nat,N_1: nat] :
% 0.55/0.80 ( Z
% 0.55/0.80 != ( minus_minus_int @ ( semiri1621563631at_int @ M_1 ) @ ( semiri1621563631at_int @ N_1 ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1144_decr__lemma,axiom,
% 0.55/0.80 ! [X: int,Z: int,D: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ D )
% 0.55/0.80 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1145_zabs__less__one__iff,axiom,
% 0.55/0.80 ! [Z: int] :
% 0.55/0.80 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 0.55/0.80 <=> ( Z = zero_zero_int ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1146_neg__def,axiom,
% 0.55/0.80 ! [Z_1: int] :
% 0.55/0.80 ( ( nat_neg @ Z_1 )
% 0.55/0.80 <=> ( ord_less_int @ Z_1 @ zero_zero_int ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1147_not__neg__eq__ge__0,axiom,
% 0.55/0.80 ! [X: int] :
% 0.55/0.80 ( ~ ( nat_neg @ X )
% 0.55/0.80 <=> ( ord_less_eq_int @ zero_zero_int @ X ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1148_not__neg__1,axiom,
% 0.55/0.80 ~ ( nat_neg @ one_one_int ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1149_not__neg__0,axiom,
% 0.55/0.80 ~ ( nat_neg @ zero_zero_int ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1150_abs__zmult__eq__1,axiom,
% 0.55/0.80 ! [M: int,N: int] :
% 0.55/0.80 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 0.55/0.80 = one_one_int )
% 0.55/0.80 => ( ( abs_abs_int @ M )
% 0.55/0.80 = one_one_int ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1151_not__neg__int,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ~ ( nat_neg @ ( semiri1621563631at_int @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1152_abs__int__eq,axiom,
% 0.55/0.80 ! [M: nat] :
% 0.55/0.80 ( ( abs_abs_int @ ( semiri1621563631at_int @ M ) )
% 0.55/0.80 = ( semiri1621563631at_int @ M ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1153_neg__imp__number__of__eq__0,axiom,
% 0.55/0.80 ! [V: int] :
% 0.55/0.80 ( ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( number_number_of_nat @ V )
% 0.55/0.80 = zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1154_eq__nat__number__of,axiom,
% 0.55/0.80 ! [V: int,V_1: int] :
% 0.55/0.80 ( ( ( number_number_of_nat @ V )
% 0.55/0.80 = ( number_number_of_nat @ V_1 ) )
% 0.55/0.80 <=> ( ( ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ord_less_eq_int @ ( number_number_of_int @ V_1 ) @ zero_zero_int ) )
% 0.55/0.80 & ( ~ ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( ( nat_neg @ ( number_number_of_int @ V_1 ) )
% 0.55/0.80 => ( ( number_number_of_int @ V )
% 0.55/0.80 = zero_zero_int ) )
% 0.55/0.80 & ( ~ ( nat_neg @ ( number_number_of_int @ V_1 ) )
% 0.55/0.80 => ( V = V_1 ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1155_nat__number__of__add__left,axiom,
% 0.55/0.80 ! [V_1: int,K: nat,V: int] :
% 0.55/0.80 ( ( ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( plus_plus_nat @ ( number_number_of_nat @ V ) @ ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ K ) )
% 0.55/0.80 = ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ K ) ) )
% 0.55/0.80 & ( ~ ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( ( nat_neg @ ( number_number_of_int @ V_1 ) )
% 0.55/0.80 => ( ( plus_plus_nat @ ( number_number_of_nat @ V ) @ ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ K ) )
% 0.55/0.80 = ( plus_plus_nat @ ( number_number_of_nat @ V ) @ K ) ) )
% 0.55/0.80 & ( ~ ( nat_neg @ ( number_number_of_int @ V_1 ) )
% 0.55/0.80 => ( ( plus_plus_nat @ ( number_number_of_nat @ V ) @ ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ K ) )
% 0.55/0.80 = ( plus_plus_nat @ ( number_number_of_nat @ ( plus_plus_int @ V @ V_1 ) ) @ K ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1156_int__nat__number__of,axiom,
% 0.55/0.80 ! [V: int] :
% 0.55/0.80 ( ( ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( semiri1621563631at_int @ ( number_number_of_nat @ V ) )
% 0.55/0.80 = zero_zero_int ) )
% 0.55/0.80 & ( ~ ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( semiri1621563631at_int @ ( number_number_of_nat @ V ) )
% 0.55/0.80 = ( number_number_of_int @ V ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1157_incr__lemma,axiom,
% 0.55/0.80 ! [Z: int,X: int,D: int] :
% 0.55/0.80 ( ( ord_less_int @ zero_zero_int @ D )
% 0.55/0.80 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1158_int__val__lemma,axiom,
% 0.55/0.80 ! [K: int,F: nat > int,N: nat] :
% 0.55/0.80 ( ! [I: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I @ N )
% 0.55/0.80 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I @ one_one_nat ) ) @ ( F @ I ) ) ) @ one_one_int ) )
% 0.55/0.80 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.55/0.80 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.55/0.80 => ? [I: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I @ N )
% 0.55/0.80 & ( ( F @ I )
% 0.55/0.80 = K ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1159_nat0__intermed__int__val,axiom,
% 0.55/0.80 ! [K: int,F: nat > int,N: nat] :
% 0.55/0.80 ( ! [I: nat] :
% 0.55/0.80 ( ( ord_less_nat @ I @ N )
% 0.55/0.80 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I @ one_one_nat ) ) @ ( F @ I ) ) ) @ one_one_int ) )
% 0.55/0.80 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.55/0.80 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.55/0.80 => ? [I: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ I @ N )
% 0.55/0.80 & ( ( F @ I )
% 0.55/0.80 = K ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1160_nat__intermed__int__val,axiom,
% 0.55/0.80 ! [K: int,F: nat > int,N: nat,M: nat] :
% 0.55/0.80 ( ! [I: nat] :
% 0.55/0.80 ( ( ( ord_less_eq_nat @ M @ I )
% 0.55/0.80 & ( ord_less_nat @ I @ N ) )
% 0.55/0.80 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I @ one_one_nat ) ) @ ( F @ I ) ) ) @ one_one_int ) )
% 0.55/0.80 => ( ( ord_less_nat @ M @ N )
% 0.55/0.80 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 0.55/0.80 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.55/0.80 => ? [I: nat] :
% 0.55/0.80 ( ( ord_less_eq_nat @ M @ I )
% 0.55/0.80 & ( ord_less_eq_nat @ I @ N )
% 0.55/0.80 & ( ( F @ I )
% 0.55/0.80 = K ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1161_Suc__nat__number__of__add,axiom,
% 0.55/0.80 ! [N: nat,V: int] :
% 0.55/0.80 ( ( ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( suc @ ( plus_plus_nat @ ( number_number_of_nat @ V ) @ N ) )
% 0.55/0.80 = ( plus_plus_nat @ one_one_nat @ N ) ) )
% 0.55/0.80 & ( ~ ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( suc @ ( plus_plus_nat @ ( number_number_of_nat @ V ) @ N ) )
% 0.55/0.80 = ( plus_plus_nat @ ( number_number_of_nat @ ( succ @ V ) ) @ N ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1162_succ__def,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( succ @ K )
% 0.55/0.80 = ( plus_plus_int @ K @ one_one_int ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1163_Suc__nat__number__of,axiom,
% 0.55/0.80 ! [V: int] :
% 0.55/0.80 ( ( ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( suc @ ( number_number_of_nat @ V ) )
% 0.55/0.80 = one_one_nat ) )
% 0.55/0.80 & ( ~ ( nat_neg @ ( number_number_of_int @ V ) )
% 0.55/0.80 => ( ( suc @ ( number_number_of_nat @ V ) )
% 0.55/0.80 = ( number_number_of_nat @ ( succ @ V ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1164_nat__number__of__Bit1,axiom,
% 0.55/0.80 ! [W: int] :
% 0.55/0.80 ( ( ( nat_neg @ ( number_number_of_int @ W ) )
% 0.55/0.80 => ( ( number_number_of_nat @ ( bit1 @ W ) )
% 0.55/0.80 = zero_zero_nat ) )
% 0.55/0.80 & ( ~ ( nat_neg @ ( number_number_of_int @ W ) )
% 0.55/0.80 => ( ( number_number_of_nat @ ( bit1 @ W ) )
% 0.55/0.80 = ( suc @ ( plus_plus_nat @ ( number_number_of_nat @ W ) @ ( number_number_of_nat @ W ) ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1165_nat__1__add__number__of,axiom,
% 0.55/0.80 ! [V: int] :
% 0.55/0.80 ( ( ( ord_less_int @ V @ pls )
% 0.55/0.80 => ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ V ) )
% 0.55/0.80 = one_one_nat ) )
% 0.55/0.80 & ( ~ ( ord_less_int @ V @ pls )
% 0.55/0.80 => ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ V ) )
% 0.55/0.80 = ( number_number_of_nat @ ( succ @ V ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1166_succ__Pls,axiom,
% 0.55/0.80 ( ( succ @ pls )
% 0.55/0.80 = ( bit1 @ pls ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1167_neg__number__of__Bit1,axiom,
% 0.55/0.80 ! [W: int] :
% 0.55/0.80 ( ( nat_neg @ ( number_number_of_int @ ( bit1 @ W ) ) )
% 0.55/0.80 <=> ( nat_neg @ ( number_number_of_int @ W ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1168_not__neg__number__of__Pls,axiom,
% 0.55/0.80 ~ ( nat_neg @ ( number_number_of_int @ pls ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1169_transfer__int__nat__numerals_I4_J,axiom,
% 0.55/0.80 ( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
% 0.55/0.80 = ( semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1170_numeral__1__eq__Suc__0,axiom,
% 0.55/0.80 ( ( number_number_of_nat @ ( bit1 @ pls ) )
% 0.55/0.80 = ( suc @ zero_zero_nat ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1171_numeral__3__eq__3,axiom,
% 0.55/0.80 ( ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) )
% 0.55/0.80 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1172_Suc3__eq__add__3,axiom,
% 0.55/0.80 ! [N: nat] :
% 0.55/0.80 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 0.55/0.80 = ( plus_plus_nat @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) @ N ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1173_Numeral1__eq1__nat,axiom,
% 0.55/0.80 ( one_one_nat
% 0.55/0.80 = ( number_number_of_nat @ ( bit1 @ pls ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1174_nat__numeral__1__eq__1,axiom,
% 0.55/0.80 ( ( number_number_of_nat @ ( bit1 @ pls ) )
% 0.55/0.80 = one_one_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1175_one__is__num__one,axiom,
% 0.55/0.80 ( one_one_int
% 0.55/0.80 = ( number_number_of_int @ ( bit1 @ pls ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1176_zero__is__num__zero,axiom,
% 0.55/0.80 ( zero_zero_int
% 0.55/0.80 = ( number_number_of_int @ pls ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1177_Bit1__def,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( bit1 @ K )
% 0.55/0.80 = ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1178_nat__number__of__Pls,axiom,
% 0.55/0.80 ( ( number_number_of_nat @ pls )
% 0.55/0.80 = zero_zero_nat ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1179_semiring__norm_I113_J,axiom,
% 0.55/0.80 ( zero_zero_nat
% 0.55/0.80 = ( number_number_of_nat @ pls ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1180_Pls__def,axiom,
% 0.55/0.80 pls = zero_zero_int ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1181_rel__simps_I51_J,axiom,
% 0.55/0.80 ! [K: int,L: int] :
% 0.55/0.80 ( ( ( bit1 @ K )
% 0.55/0.80 = ( bit1 @ L ) )
% 0.55/0.80 <=> ( K = L ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1182_rel__simps_I46_J,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( bit1 @ K )
% 0.55/0.80 != pls ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1183_rel__simps_I39_J,axiom,
% 0.55/0.80 ! [L: int] :
% 0.55/0.80 ( pls
% 0.55/0.80 != ( bit1 @ L ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1184_diff__bin__simps_I1_J,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( minus_minus_int @ K @ pls )
% 0.55/0.80 = K ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1185_add__Pls,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( plus_plus_int @ pls @ K )
% 0.55/0.80 = K ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1186_add__Pls__right,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( plus_plus_int @ K @ pls )
% 0.55/0.80 = K ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1187_mult__Pls,axiom,
% 0.55/0.80 ! [W: int] :
% 0.55/0.80 ( ( times_times_int @ pls @ W )
% 0.55/0.80 = pls ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1188_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 0.55/0.80 ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1189_rel__simps_I19_J,axiom,
% 0.55/0.80 ord_less_eq_int @ pls @ pls ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1190_rel__simps_I22_J,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
% 0.55/0.80 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1191_rel__simps_I34_J,axiom,
% 0.55/0.80 ! [K: int,L: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.55/0.80 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1192_less__eq__int__code_I16_J,axiom,
% 0.55/0.80 ! [K1: int,K2: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
% 0.55/0.80 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1193_rel__simps_I2_J,axiom,
% 0.55/0.80 ~ ( ord_less_int @ pls @ pls ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1194_rel__simps_I12_J,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( ord_less_int @ ( bit1 @ K ) @ pls )
% 0.55/0.80 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1195_rel__simps_I17_J,axiom,
% 0.55/0.80 ! [K: int,L: int] :
% 0.55/0.80 ( ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.55/0.80 <=> ( ord_less_int @ K @ L ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1196_less__int__code_I16_J,axiom,
% 0.55/0.80 ! [K1: int,K2: int] :
% 0.55/0.80 ( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
% 0.55/0.80 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1197_rel__simps_I29_J,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
% 0.55/0.80 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(fact_1198_rel__simps_I5_J,axiom,
% 0.55/0.80 ! [K: int] :
% 0.55/0.80 ( ( ord_less_int @ pls @ ( bit1 @ K ) )
% 0.55/0.80 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.55/0.80
% 0.55/0.80 %----Helper facts (9)
% 0.55/0.80 thf(help_fequal_1_1_fequal_000t__a_T,axiom,
% 0.55/0.80 ! [X: x_a,Y: x_a] :
% 0.55/0.80 ( ~ ( fequal_a @ X @ Y )
% 0.55/0.80 | ( X = Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(help_fequal_2_1_fequal_000t__a_T,axiom,
% 0.55/0.80 ! [X: x_a,Y: x_a] :
% 0.55/0.80 ( ( X != Y )
% 0.55/0.80 | ( fequal_a @ X @ Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(help_If_1_1_If_000tc__Nat__Onat_T,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( if_nat @ $true @ X @ Y )
% 0.55/0.80 = X ) ).
% 0.55/0.80
% 0.55/0.80 thf(help_If_2_1_If_000tc__Nat__Onat_T,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( if_nat @ $false @ X @ Y )
% 0.55/0.80 = Y ) ).
% 0.55/0.80
% 0.55/0.80 thf(help_If_3_1_If_000tc__Nat__Onat_T,axiom,
% 0.55/0.80 ! [P: $o] :
% 0.55/0.80 ( ( P = $true )
% 0.55/0.80 | ( P = $false ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(help_fequal_1_1_fequal_000tc__Int__Oint_T,axiom,
% 0.55/0.80 ! [X: int,Y: int] :
% 0.55/0.80 ( ~ ( fequal_int @ X @ Y )
% 0.55/0.80 | ( X = Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(help_fequal_2_1_fequal_000tc__Int__Oint_T,axiom,
% 0.55/0.80 ! [X: int,Y: int] :
% 0.55/0.80 ( ( X != Y )
% 0.55/0.80 | ( fequal_int @ X @ Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(help_fequal_1_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ~ ( fequal_nat @ X @ Y )
% 0.55/0.80 | ( X = Y ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(help_fequal_2_1_fequal_000tc__Nat__Onat_T,axiom,
% 0.55/0.80 ! [X: nat,Y: nat] :
% 0.55/0.80 ( ( X != Y )
% 0.55/0.80 | ( fequal_nat @ X @ Y ) ) ).
% 0.55/0.80
% 0.55/0.80 %----Conjectures (7)
% 0.55/0.80 thf(conj_0,hypothesis,
% 0.55/0.80 finite_finite_pname @ u ).
% 0.55/0.80
% 0.55/0.80 thf(conj_1,hypothesis,
% 0.55/0.80 ord_less_eq_a_o @ g @ ( image_pname_a @ mgt_call @ u ) ).
% 0.55/0.80
% 0.55/0.80 thf(conj_2,hypothesis,
% 0.55/0.80 ord_less_eq_nat @ ( suc @ na ) @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(conj_3,hypothesis,
% 0.55/0.80 ( ( finite_card_a @ g )
% 0.55/0.80 = ( minus_minus_nat @ ( finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) @ ( suc @ na ) ) ) ).
% 0.55/0.80
% 0.55/0.80 thf(conj_4,hypothesis,
% 0.62/1.00 member_pname @ pn @ u ).
% 0.62/1.00
% 0.62/1.00 thf(conj_5,hypothesis,
% 0.62/1.00 ~ ( member_a @ ( mgt_call @ pn ) @ g ) ).
% 0.62/1.00
% 0.62/1.00 thf(conj_6,conjecture,
% 0.62/1.00 ord_less_eq_a_o @ ( insert_a @ ( mgt_call @ pn ) @ g ) @ ( image_pname_a @ mgt_call @ u ) ).
% 0.62/1.00
% 0.62/1.00 %------------------------------------------------------------------------------
% 0.62/1.00 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Z5YMGcFuii/cvc5---1.0.5_18286.p...
% 0.62/1.00 (declare-sort $$unsorted 0)
% 0.62/1.00 (declare-sort tptp.x_a 0)
% 0.62/1.00 (declare-sort tptp.com 0)
% 0.62/1.00 (declare-sort tptp.pname 0)
% 0.62/1.00 (declare-sort tptp.int 0)
% 0.62/1.00 (declare-sort tptp.nat 0)
% 0.62/1.00 (declare-sort tptp.option_com 0)
% 0.62/1.00 (declare-fun tptp.body (tptp.pname) tptp.option_com)
% 0.62/1.00 (declare-fun tptp.ex ((-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_card_a_o ((-> (-> tptp.x_a Bool) Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.finite_card_pname_o ((-> (-> tptp.pname Bool) Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.finite_card_int_o ((-> (-> tptp.int Bool) Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.finite_card_nat_o ((-> (-> tptp.nat Bool) Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.finite_card_a ((-> tptp.x_a Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.finite_card_pname ((-> tptp.pname Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.finite_card_int ((-> tptp.int Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.finite_card_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.finite_finite_a_o_o ((-> (-> (-> tptp.x_a Bool) Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite1066544169me_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite229719499nt_o_o ((-> (-> (-> tptp.int Bool) Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite1676163439at_o_o ((-> (-> (-> tptp.nat Bool) Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_finite_a_o ((-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite297249702name_o ((-> (-> tptp.pname Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_finite_int_o ((-> (-> tptp.int Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_finite_nat_o ((-> (-> tptp.nat Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_finite_a ((-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_finite_pname ((-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_finite_int ((-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_finite_nat ((-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.finite_folding_one_a ((-> tptp.x_a tptp.x_a tptp.x_a) (-> (-> tptp.x_a Bool) tptp.x_a)) Bool)
% 0.62/1.00 (declare-fun tptp.finite1282449217_pname ((-> tptp.pname tptp.pname tptp.pname) (-> (-> tptp.pname Bool) tptp.pname)) Bool)
% 0.62/1.00 (declare-fun tptp.finite1626084323ne_int ((-> tptp.int tptp.int tptp.int) (-> (-> tptp.int Bool) tptp.int)) Bool)
% 0.62/1.00 (declare-fun tptp.finite988810631ne_nat ((-> tptp.nat tptp.nat tptp.nat) (-> (-> tptp.nat Bool) tptp.nat)) Bool)
% 0.62/1.00 (declare-fun tptp.finite1819937229idem_a ((-> tptp.x_a tptp.x_a tptp.x_a) (-> (-> tptp.x_a Bool) tptp.x_a)) Bool)
% 0.62/1.00 (declare-fun tptp.finite89670078_pname ((-> tptp.pname tptp.pname tptp.pname) (-> (-> tptp.pname Bool) tptp.pname)) Bool)
% 0.62/1.00 (declare-fun tptp.finite1432773856em_int ((-> tptp.int tptp.int tptp.int) (-> (-> tptp.int Bool) tptp.int)) Bool)
% 0.62/1.00 (declare-fun tptp.finite795500164em_nat ((-> tptp.nat tptp.nat tptp.nat) (-> (-> tptp.nat Bool) tptp.nat)) Bool)
% 0.62/1.00 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 0.62/1.00 (declare-fun tptp.minus_minus_a_o ((-> tptp.x_a Bool) (-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.minus_minus_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 0.62/1.00 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.62/1.00 (declare-fun tptp.one_one_int () tptp.int)
% 0.62/1.00 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.62/1.00 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 0.62/1.00 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.62/1.00 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 0.62/1.00 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 0.62/1.00 (declare-fun tptp.zero_zero_int () tptp.int)
% 0.62/1.00 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.62/1.00 (declare-fun tptp.the_a ((-> tptp.x_a Bool)) tptp.x_a)
% 0.62/1.00 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 0.62/1.00 (declare-fun tptp.the_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 0.62/1.00 (declare-fun tptp.bit1 (tptp.int) tptp.int)
% 0.62/1.00 (declare-fun tptp.pls () tptp.int)
% 0.62/1.00 (declare-fun tptp.number_number_of_int (tptp.int) tptp.int)
% 0.62/1.00 (declare-fun tptp.number_number_of_nat (tptp.int) tptp.nat)
% 0.62/1.00 (declare-fun tptp.succ (tptp.int) tptp.int)
% 0.62/1.00 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.62/1.00 (declare-fun tptp.nat_case_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.nat_case_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 0.62/1.00 (declare-fun tptp.semiri1621563631at_int (tptp.nat) tptp.int)
% 0.62/1.00 (declare-fun tptp.nat_neg (tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.nat_tsub (tptp.int tptp.int) tptp.int)
% 0.62/1.00 (declare-fun tptp.the_com (tptp.option_com) tptp.com)
% 0.62/1.00 (declare-fun tptp.bot_bot_a_o (tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.bot_bot_pname_o (tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.bot_bot_o () Bool)
% 0.62/1.00 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 0.62/1.00 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_a_o_o ((-> (-> tptp.x_a Bool) Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_le1205211808me_o_o ((-> (-> tptp.pname Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_int_o_o ((-> (-> tptp.int Bool) Bool) (-> (-> tptp.int Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_nat_o_o ((-> (-> tptp.nat Bool) Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_a_o ((-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_pname_o ((-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.collect_a_o_o ((-> (-> (-> tptp.x_a Bool) Bool) Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.collect_pname_o_o ((-> (-> (-> tptp.pname Bool) Bool) Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.collect_int_o_o ((-> (-> (-> tptp.int Bool) Bool) Bool) (-> (-> tptp.int Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.collect_nat_o_o ((-> (-> (-> tptp.nat Bool) Bool) Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.collect_a_o ((-> (-> tptp.x_a Bool) Bool) (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.collect_pname_o ((-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.collect_int_o ((-> (-> tptp.int Bool) Bool) (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.collect_nat_o ((-> (-> tptp.nat Bool) Bool) (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.collect_a ((-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.collect_pname ((-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.collect_int ((-> tptp.int Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.collect_nat ((-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_o_a ((-> (-> tptp.x_a Bool) tptp.x_a) (-> (-> tptp.x_a Bool) Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_o_pname ((-> (-> tptp.x_a Bool) tptp.pname) (-> (-> tptp.x_a Bool) Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_o_int ((-> (-> tptp.x_a Bool) tptp.int) (-> (-> tptp.x_a Bool) Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_o_nat ((-> (-> tptp.x_a Bool) tptp.nat) (-> (-> tptp.x_a Bool) Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_o_a ((-> (-> tptp.pname Bool) tptp.x_a) (-> (-> tptp.pname Bool) Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_o_pname ((-> (-> tptp.pname Bool) tptp.pname) (-> (-> tptp.pname Bool) Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_o_int ((-> (-> tptp.pname Bool) tptp.int) (-> (-> tptp.pname Bool) Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_o_nat ((-> (-> tptp.pname Bool) tptp.nat) (-> (-> tptp.pname Bool) Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_o_a ((-> (-> tptp.int Bool) tptp.x_a) (-> (-> tptp.int Bool) Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_o_pname ((-> (-> tptp.int Bool) tptp.pname) (-> (-> tptp.int Bool) Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_o_int ((-> (-> tptp.int Bool) tptp.int) (-> (-> tptp.int Bool) Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_o_nat ((-> (-> tptp.int Bool) tptp.nat) (-> (-> tptp.int Bool) Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_o_a ((-> (-> tptp.nat Bool) tptp.x_a) (-> (-> tptp.nat Bool) Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_o_pname ((-> (-> tptp.nat Bool) tptp.pname) (-> (-> tptp.nat Bool) Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_o_int ((-> (-> tptp.nat Bool) tptp.int) (-> (-> tptp.nat Bool) Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_o_nat ((-> (-> tptp.nat Bool) tptp.nat) (-> (-> tptp.nat Bool) Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_a_o ((-> tptp.x_a tptp.x_a Bool) (-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_pname_o ((-> tptp.x_a tptp.pname Bool) (-> tptp.x_a Bool) (-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_int_o ((-> tptp.x_a tptp.int Bool) (-> tptp.x_a Bool) (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_nat_o ((-> tptp.x_a tptp.nat Bool) (-> tptp.x_a Bool) (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_a ((-> tptp.x_a tptp.x_a) (-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_pname ((-> tptp.x_a tptp.pname) (-> tptp.x_a Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_int ((-> tptp.x_a tptp.int) (-> tptp.x_a Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.image_a_nat ((-> tptp.x_a tptp.nat) (-> tptp.x_a Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_a_o ((-> tptp.pname tptp.x_a Bool) (-> tptp.pname Bool) (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_pname_o ((-> tptp.pname tptp.pname Bool) (-> tptp.pname Bool) (-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_int_o ((-> tptp.pname tptp.int Bool) (-> tptp.pname Bool) (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_nat_o ((-> tptp.pname tptp.nat Bool) (-> tptp.pname Bool) (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_a ((-> tptp.pname tptp.x_a) (-> tptp.pname Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_pname ((-> tptp.pname tptp.pname) (-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_int ((-> tptp.pname tptp.int) (-> tptp.pname Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.image_pname_nat ((-> tptp.pname tptp.nat) (-> tptp.pname Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_a_o ((-> tptp.int tptp.x_a Bool) (-> tptp.int Bool) (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_pname_o ((-> tptp.int tptp.pname Bool) (-> tptp.int Bool) (-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_nat_o ((-> tptp.int tptp.nat Bool) (-> tptp.int Bool) (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_a ((-> tptp.int tptp.x_a) (-> tptp.int Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.image_int_pname ((-> tptp.int tptp.pname) (-> tptp.int Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_a_o ((-> tptp.nat tptp.x_a Bool) (-> tptp.nat Bool) (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_pname_o ((-> tptp.nat tptp.pname Bool) (-> tptp.nat Bool) (-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_int_o ((-> tptp.nat tptp.int Bool) (-> tptp.nat Bool) (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_a ((-> tptp.nat tptp.x_a) (-> tptp.nat Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_pname ((-> tptp.nat tptp.pname) (-> tptp.nat Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) (-> tptp.nat Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.insert_a_o ((-> tptp.x_a Bool) (-> (-> tptp.x_a Bool) Bool) (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.insert_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool) (-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.insert_int_o ((-> tptp.int Bool) (-> (-> tptp.int Bool) Bool) (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.insert_nat_o ((-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool) (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.insert_a (tptp.x_a (-> tptp.x_a Bool) tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.insert_pname (tptp.pname (-> tptp.pname Bool) tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.insert_int (tptp.int (-> tptp.int Bool) tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.insert_nat (tptp.nat (-> tptp.nat Bool) tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.the_elem_a ((-> tptp.x_a Bool)) tptp.x_a)
% 0.62/1.00 (declare-fun tptp.the_elem_int ((-> tptp.int Bool)) tptp.int)
% 0.62/1.00 (declare-fun tptp.the_elem_nat ((-> tptp.nat Bool)) tptp.nat)
% 0.62/1.00 (declare-fun tptp.fequal_a (tptp.x_a tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.fequal_int (tptp.int tptp.int) Bool)
% 0.62/1.00 (declare-fun tptp.fequal_nat (tptp.nat tptp.nat) Bool)
% 0.62/1.00 (declare-fun tptp.member_a_o ((-> tptp.x_a Bool) (-> (-> tptp.x_a Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.member_pname_o ((-> tptp.pname Bool) (-> (-> tptp.pname Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.member_int_o ((-> tptp.int Bool) (-> (-> tptp.int Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.member_nat_o ((-> tptp.nat Bool) (-> (-> tptp.nat Bool) Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.member_a (tptp.x_a (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.member_pname (tptp.pname (-> tptp.pname Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.member_int (tptp.int (-> tptp.int Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.member_nat (tptp.nat (-> tptp.nat Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.g (tptp.x_a) Bool)
% 0.62/1.00 (declare-fun tptp.p ((-> tptp.x_a Bool) (-> tptp.x_a Bool)) Bool)
% 0.62/1.00 (declare-fun tptp.u (tptp.pname) Bool)
% 0.62/1.00 (declare-fun tptp.mgt (tptp.com) tptp.x_a)
% 0.62/1.00 (declare-fun tptp.mgt_call (tptp.pname) tptp.x_a)
% 0.62/1.00 (declare-fun tptp.na () tptp.nat)
% 0.62/1.00 (declare-fun tptp.pn () tptp.pname)
% 0.62/1.00 (declare-fun tptp.wt (tptp.com) Bool)
% 0.62/1.00 (assert (forall ((Ts (-> tptp.x_a Bool)) (G (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Ts) G) (@ (@ tptp.p G) Ts))))
% 0.62/1.00 (assert (forall ((A_161 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_161) (@ tptp.finite229719499nt_o_o (@ tptp.collect_int_o_o (lambda ((B_26 (-> (-> tptp.int Bool) Bool))) (@ (@ tptp.ord_less_eq_int_o_o B_26) A_161)))))))
% 0.62/1.00 (assert (forall ((A_161 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_161) (@ tptp.finite1676163439at_o_o (@ tptp.collect_nat_o_o (lambda ((B_26 (-> (-> tptp.nat Bool) Bool))) (@ (@ tptp.ord_less_eq_nat_o_o B_26) A_161)))))))
% 0.62/1.00 (assert (forall ((A_161 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_161) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((B_26 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o B_26) A_161)))))))
% 0.62/1.00 (assert (forall ((A_161 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_161) (@ tptp.finite_finite_a_o_o (@ tptp.collect_a_o_o (lambda ((B_26 (-> (-> tptp.x_a Bool) Bool))) (@ (@ tptp.ord_less_eq_a_o_o B_26) A_161)))))))
% 0.62/1.00 (assert (forall ((A_161 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_161) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((B_26 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o B_26) A_161)))))))
% 0.62/1.00 (assert (forall ((A_161 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_161) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((B_26 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o B_26) A_161)))))))
% 0.62/1.00 (assert (forall ((A_161 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_161) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((B_26 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o B_26) A_161)))))))
% 0.62/1.00 (assert (forall ((A_161 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_161) (@ tptp.finite_finite_int_o (@ tptp.collect_int_o (lambda ((B_26 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o B_26) A_161)))))))
% 0.62/1.00 (assert (forall ((H (-> tptp.pname tptp.int Bool)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite_finite_int_o (@ (@ tptp.image_pname_int_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.pname tptp.nat Bool)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_pname_nat_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.pname tptp.pname Bool)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.pname tptp.x_a Bool)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite_finite_a_o (@ (@ tptp.image_pname_a_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.nat tptp.x_a)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_a (@ (@ tptp.image_nat_a H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.nat tptp.int Bool)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_int_o (@ (@ tptp.image_nat_int_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.nat tptp.nat Bool)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.nat tptp.pname Bool)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.nat tptp.x_a Bool)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.int tptp.x_a)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite_finite_a (@ (@ tptp.image_int_a H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.int tptp.int Bool)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite_finite_int_o (@ (@ tptp.image_int_int_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.int tptp.nat Bool)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_int_nat_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.int tptp.pname Bool)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite297249702name_o (@ (@ tptp.image_int_pname_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.int tptp.x_a Bool)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite_finite_a_o (@ (@ tptp.image_int_a_o H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.x_a tptp.pname)) (F_42 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_pname H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.int Bool) tptp.pname)) (F_42 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_int_o_pname H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.nat Bool) tptp.pname)) (F_42 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_pname H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.pname)) (F_42 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.x_a Bool) tptp.pname)) (F_42 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_pname H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.x_a tptp.nat)) (F_42 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_nat H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.int Bool) tptp.nat)) (F_42 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_int_o_nat H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.nat Bool) tptp.nat)) (F_42 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_nat H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.nat)) (F_42 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_nat H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.x_a Bool) tptp.nat)) (F_42 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_nat H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.x_a tptp.int)) (F_42 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_a_int H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.int Bool) tptp.int)) (F_42 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_int_o_int H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.nat Bool) tptp.int)) (F_42 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_nat_o_int H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.pname Bool) tptp.int)) (F_42 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_pname_o_int H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> (-> tptp.x_a Bool) tptp.int)) (F_42 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_a_o_int H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.pname tptp.x_a)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a H) F_42)))))
% 0.62/1.00 (assert (forall ((H (-> tptp.nat tptp.int)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int H) F_42)))))
% 0.62/1.00 (assert (forall ((A_160 (-> tptp.int Bool)) (A_159 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_159) (@ tptp.finite_finite_int_o (@ (@ tptp.insert_int_o A_160) A_159)))))
% 0.62/1.00 (assert (forall ((A_160 (-> tptp.nat Bool)) (A_159 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_159) (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_160) A_159)))))
% 0.62/1.00 (assert (forall ((A_160 (-> tptp.pname Bool)) (A_159 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_159) (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_160) A_159)))))
% 0.62/1.00 (assert (forall ((A_160 (-> tptp.x_a Bool)) (A_159 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_159) (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_160) A_159)))))
% 0.62/1.00 (assert (forall ((A_160 tptp.pname) (A_159 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_159) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_160) A_159)))))
% 0.62/1.00 (assert (forall ((A_160 tptp.nat) (A_159 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_159) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_160) A_159)))))
% 0.62/1.00 (assert (forall ((A_160 tptp.int) (A_159 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_159) (@ tptp.finite_finite_int (@ (@ tptp.insert_int A_160) A_159)))))
% 0.62/1.00 (assert (forall ((A_160 tptp.x_a) (A_159 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_159) (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_160) A_159)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.pname tptp.pname)) (A_158 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_pname_pname F_41) A_158))) (@ tptp.finite_card_pname A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.x_a tptp.x_a)) (A_158 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_a F_41) A_158))) (@ tptp.finite_card_a A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.int Bool) tptp.x_a)) (A_158 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_int_o_a F_41) A_158))) (@ tptp.finite_card_int_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.nat Bool) tptp.x_a)) (A_158 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_o_a F_41) A_158))) (@ tptp.finite_card_nat_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.pname Bool) tptp.x_a)) (A_158 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_o_a F_41) A_158))) (@ tptp.finite_card_pname_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_158 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_o_a F_41) A_158))) (@ tptp.finite_card_a_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.pname tptp.nat)) (A_158 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_nat F_41) A_158))) (@ tptp.finite_card_pname A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.x_a tptp.nat)) (A_158 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_nat F_41) A_158))) (@ tptp.finite_card_a A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.int Bool) tptp.nat)) (A_158 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_int_o_nat F_41) A_158))) (@ tptp.finite_card_int_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.nat Bool) tptp.nat)) (A_158 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_nat_o_nat F_41) A_158))) (@ tptp.finite_card_nat_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.pname Bool) tptp.nat)) (A_158 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_o_nat F_41) A_158))) (@ tptp.finite_card_pname_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.x_a Bool) tptp.nat)) (A_158 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_o_nat F_41) A_158))) (@ tptp.finite_card_a_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.pname tptp.int)) (A_158 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_pname_int F_41) A_158))) (@ tptp.finite_card_pname A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.x_a tptp.int)) (A_158 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_a_int F_41) A_158))) (@ tptp.finite_card_a A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.int Bool) tptp.int)) (A_158 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_int_o_int F_41) A_158))) (@ tptp.finite_card_int_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.nat Bool) tptp.int)) (A_158 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_nat_o_int F_41) A_158))) (@ tptp.finite_card_nat_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.pname Bool) tptp.int)) (A_158 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_pname_o_int F_41) A_158))) (@ tptp.finite_card_pname_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> (-> tptp.x_a Bool) tptp.int)) (A_158 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_a_o_int F_41) A_158))) (@ tptp.finite_card_a_o A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.x_a tptp.pname)) (A_158 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_a_pname F_41) A_158))) (@ tptp.finite_card_a A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.nat tptp.pname)) (A_158 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_nat_pname F_41) A_158))) (@ tptp.finite_card_nat A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.int tptp.pname)) (A_158 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_int_pname F_41) A_158))) (@ tptp.finite_card_int A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.pname tptp.x_a)) (A_158 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_a F_41) A_158))) (@ tptp.finite_card_pname A_158)))))
% 0.62/1.00 (assert (forall ((F_41 (-> tptp.nat tptp.int)) (A_158 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_nat_int F_41) A_158))) (@ tptp.finite_card_nat A_158)))))
% 0.62/1.00 (assert (forall ((A_157 (-> (-> tptp.int Bool) Bool)) (B_89 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_89) (=> (@ (@ tptp.ord_less_eq_int_o_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int_o A_157)) (@ tptp.finite_card_int_o B_89))))))
% 0.62/1.00 (assert (forall ((A_157 (-> (-> tptp.nat Bool) Bool)) (B_89 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_89) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_157)) (@ tptp.finite_card_nat_o B_89))))))
% 0.62/1.00 (assert (forall ((A_157 (-> (-> tptp.pname Bool) Bool)) (B_89 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_89) (=> (@ (@ tptp.ord_le1205211808me_o_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_157)) (@ tptp.finite_card_pname_o B_89))))))
% 0.62/1.00 (assert (forall ((A_157 (-> (-> tptp.x_a Bool) Bool)) (B_89 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_89) (=> (@ (@ tptp.ord_less_eq_a_o_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_157)) (@ tptp.finite_card_a_o B_89))))))
% 0.62/1.00 (assert (forall ((A_157 (-> tptp.pname Bool)) (B_89 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_89) (=> (@ (@ tptp.ord_less_eq_pname_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_157)) (@ tptp.finite_card_pname B_89))))))
% 0.62/1.00 (assert (forall ((A_157 (-> tptp.x_a Bool)) (B_89 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_89) (=> (@ (@ tptp.ord_less_eq_a_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_157)) (@ tptp.finite_card_a B_89))))))
% 0.62/1.00 (assert (forall ((A_157 (-> tptp.nat Bool)) (B_89 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_89) (=> (@ (@ tptp.ord_less_eq_nat_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_157)) (@ tptp.finite_card_nat B_89))))))
% 0.62/1.00 (assert (forall ((A_157 (-> tptp.int Bool)) (B_89 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_89) (=> (@ (@ tptp.ord_less_eq_int_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A_157)) (@ tptp.finite_card_int B_89))))))
% 0.62/1.00 (assert (forall ((A_156 (-> (-> tptp.int Bool) Bool)) (B_88 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_88) (=> (@ (@ tptp.ord_less_eq_int_o_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int_o B_88)) (@ tptp.finite_card_int_o A_156)) (= A_156 B_88))))))
% 0.62/1.00 (assert (forall ((A_156 (-> (-> tptp.nat Bool) Bool)) (B_88 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_88) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o B_88)) (@ tptp.finite_card_nat_o A_156)) (= A_156 B_88))))))
% 0.62/1.00 (assert (forall ((A_156 (-> (-> tptp.pname Bool) Bool)) (B_88 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_88) (=> (@ (@ tptp.ord_le1205211808me_o_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o B_88)) (@ tptp.finite_card_pname_o A_156)) (= A_156 B_88))))))
% 0.62/1.00 (assert (forall ((A_156 (-> (-> tptp.x_a Bool) Bool)) (B_88 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_88) (=> (@ (@ tptp.ord_less_eq_a_o_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o B_88)) (@ tptp.finite_card_a_o A_156)) (= A_156 B_88))))))
% 0.62/1.00 (assert (forall ((A_156 (-> tptp.pname Bool)) (B_88 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_88) (=> (@ (@ tptp.ord_less_eq_pname_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname B_88)) (@ tptp.finite_card_pname A_156)) (= A_156 B_88))))))
% 0.62/1.00 (assert (forall ((A_156 (-> tptp.x_a Bool)) (B_88 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_88) (=> (@ (@ tptp.ord_less_eq_a_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a B_88)) (@ tptp.finite_card_a A_156)) (= A_156 B_88))))))
% 0.62/1.00 (assert (forall ((A_156 (-> tptp.nat Bool)) (B_88 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_88) (=> (@ (@ tptp.ord_less_eq_nat_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B_88)) (@ tptp.finite_card_nat A_156)) (= A_156 B_88))))))
% 0.62/1.00 (assert (forall ((A_156 (-> tptp.int Bool)) (B_88 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_88) (=> (@ (@ tptp.ord_less_eq_int_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int B_88)) (@ tptp.finite_card_int A_156)) (= A_156 B_88))))))
% 0.62/1.00 (assert (forall ((X_53 (-> tptp.int Bool)) (A_155 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int_o A_155)) (@ tptp.finite_card_int_o (@ (@ tptp.insert_int_o X_53) A_155))))))
% 0.62/1.00 (assert (forall ((X_53 (-> tptp.nat Bool)) (A_155 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_155)) (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_53) A_155))))))
% 0.62/1.00 (assert (forall ((X_53 (-> tptp.pname Bool)) (A_155 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_155)) (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_53) A_155))))))
% 0.62/1.00 (assert (forall ((X_53 (-> tptp.x_a Bool)) (A_155 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_155)) (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_53) A_155))))))
% 0.62/1.00 (assert (forall ((X_53 tptp.pname) (A_155 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_155)) (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_53) A_155))))))
% 0.62/1.00 (assert (forall ((X_53 tptp.nat) (A_155 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_155)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_53) A_155))))))
% 0.62/1.00 (assert (forall ((X_53 tptp.int) (A_155 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A_155)) (@ tptp.finite_card_int (@ (@ tptp.insert_int X_53) A_155))))))
% 0.62/1.00 (assert (forall ((X_53 tptp.x_a) (A_155 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_155)) (@ tptp.finite_card_a (@ (@ tptp.insert_a X_53) A_155))))))
% 0.62/1.00 (assert (forall ((X_52 (-> tptp.int Bool)) (A_154 (-> (-> tptp.int Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_int_o A_154))) (let ((_let_2 (@ tptp.finite_card_int_o (@ (@ tptp.insert_int_o X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_int_o X_52) A_154))) (=> (@ tptp.finite_finite_int_o A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.62/1.00 (assert (forall ((X_52 (-> tptp.nat Bool)) (A_154 (-> (-> tptp.nat Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_nat_o A_154))) (let ((_let_2 (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_nat_o X_52) A_154))) (=> (@ tptp.finite_finite_nat_o A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.62/1.00 (assert (forall ((X_52 (-> tptp.pname Bool)) (A_154 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_pname_o A_154))) (let ((_let_2 (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_pname_o X_52) A_154))) (=> (@ tptp.finite297249702name_o A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.62/1.00 (assert (forall ((X_52 (-> tptp.x_a Bool)) (A_154 (-> (-> tptp.x_a Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_a_o A_154))) (let ((_let_2 (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_a_o X_52) A_154))) (=> (@ tptp.finite_finite_a_o A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.62/1.00 (assert (forall ((X_52 tptp.pname) (A_154 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.finite_card_pname A_154))) (let ((_let_2 (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_pname X_52) A_154))) (=> (@ tptp.finite_finite_pname A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.62/1.00 (assert (forall ((X_52 tptp.nat) (A_154 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_card_nat A_154))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_nat X_52) A_154))) (=> (@ tptp.finite_finite_nat A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.62/1.00 (assert (forall ((X_52 tptp.int) (A_154 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_card_int A_154))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.insert_int X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_int X_52) A_154))) (=> (@ tptp.finite_finite_int A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.62/1.00 (assert (forall ((X_52 tptp.x_a) (A_154 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.finite_card_a A_154))) (let ((_let_2 (@ tptp.finite_card_a (@ (@ tptp.insert_a X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_a X_52) A_154))) (=> (@ tptp.finite_finite_a A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))))
% 0.62/1.00 (assert (forall ((X_51 (-> tptp.int Bool)) (A_153 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_153) (=> (not (@ (@ tptp.member_int_o X_51) A_153)) (= (@ tptp.finite_card_int_o (@ (@ tptp.insert_int_o X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_int_o A_153)))))))
% 0.62/1.00 (assert (forall ((X_51 (-> tptp.nat Bool)) (A_153 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_153) (=> (not (@ (@ tptp.member_nat_o X_51) A_153)) (= (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_nat_o A_153)))))))
% 0.62/1.00 (assert (forall ((X_51 (-> tptp.pname Bool)) (A_153 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_153) (=> (not (@ (@ tptp.member_pname_o X_51) A_153)) (= (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_pname_o A_153)))))))
% 0.62/1.00 (assert (forall ((X_51 (-> tptp.x_a Bool)) (A_153 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_153) (=> (not (@ (@ tptp.member_a_o X_51) A_153)) (= (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_a_o A_153)))))))
% 0.62/1.00 (assert (forall ((X_51 tptp.pname) (A_153 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_153) (=> (not (@ (@ tptp.member_pname X_51) A_153)) (= (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_pname A_153)))))))
% 0.62/1.00 (assert (forall ((X_51 tptp.nat) (A_153 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_153) (=> (not (@ (@ tptp.member_nat X_51) A_153)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_nat A_153)))))))
% 0.62/1.00 (assert (forall ((X_51 tptp.int) (A_153 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_153) (=> (not (@ (@ tptp.member_int X_51) A_153)) (= (@ tptp.finite_card_int (@ (@ tptp.insert_int X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_int A_153)))))))
% 0.62/1.00 (assert (forall ((X_51 tptp.x_a) (A_153 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_153) (=> (not (@ (@ tptp.member_a X_51) A_153)) (= (@ tptp.finite_card_a (@ (@ tptp.insert_a X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_a A_153)))))))
% 0.62/1.00 (assert (forall ((Q_3 (-> tptp.x_a Bool)) (P_13 (-> tptp.x_a Bool))) (=> (or (@ tptp.finite_finite_a (@ tptp.collect_a P_13)) (@ tptp.finite_finite_a (@ tptp.collect_a Q_3))) (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (@ P_13 X_1) (@ Q_3 X_1))))))))
% 0.62/1.00 (assert (forall ((Q_3 (-> (-> tptp.int Bool) Bool)) (P_13 (-> (-> tptp.int Bool) Bool))) (=> (or (@ tptp.finite_finite_int_o (@ tptp.collect_int_o P_13)) (@ tptp.finite_finite_int_o (@ tptp.collect_int_o Q_3))) (@ tptp.finite_finite_int_o (@ tptp.collect_int_o (lambda ((X_1 (-> tptp.int Bool))) (and (@ P_13 X_1) (@ Q_3 X_1))))))))
% 0.62/1.00 (assert (forall ((Q_3 (-> (-> tptp.nat Bool) Bool)) (P_13 (-> (-> tptp.nat Bool) Bool))) (=> (or (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_13)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q_3))) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (@ P_13 X_1) (@ Q_3 X_1))))))))
% 0.62/1.00 (assert (forall ((Q_3 (-> (-> tptp.pname Bool) Bool)) (P_13 (-> (-> tptp.pname Bool) Bool))) (=> (or (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_13)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_3))) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (@ P_13 X_1) (@ Q_3 X_1))))))))
% 0.62/1.00 (assert (forall ((Q_3 (-> (-> tptp.x_a Bool) Bool)) (P_13 (-> (-> tptp.x_a Bool) Bool))) (=> (or (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_13)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q_3))) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (@ P_13 X_1) (@ Q_3 X_1))))))))
% 0.62/1.00 (assert (forall ((Q_3 (-> tptp.pname Bool)) (P_13 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_13)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_3))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (@ P_13 X_1) (@ Q_3 X_1))))))))
% 0.62/1.00 (assert (forall ((Q_3 (-> tptp.nat Bool)) (P_13 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P_13)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (@ P_13 X_1) (@ Q_3 X_1))))))))
% 0.62/1.00 (assert (forall ((Q_3 (-> tptp.int Bool)) (P_13 (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P_13)) (@ tptp.finite_finite_int (@ tptp.collect_int Q_3))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (@ P_13 X_1) (@ Q_3 X_1))))))))
% 0.62/1.00 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 0.62/1.00 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) K))))))
% 0.62/1.00 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_eq_nat I) N)))) (@ tptp.suc N))))
% 0.62/1.00 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 0.62/1.00 (assert (forall ((Nat_4 tptp.nat) (Nat_1 tptp.nat)) (= (= (@ tptp.suc Nat_4) (@ tptp.suc Nat_1)) (= Nat_4 Nat_1))))
% 0.62/1.00 (assert (forall ((N tptp.nat)) (not (= (@ tptp.suc N) N))))
% 0.62/1.00 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.62/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.62/1.00 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.62/1.00 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 0.62/1.00 (assert (forall ((P_12 (-> tptp.x_a Bool)) (Q_2 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_a (@ tptp.collect_a P_12)) (@ tptp.finite_finite_a (@ tptp.collect_a Q_2))))))
% 0.62/1.00 (assert (forall ((P_12 (-> (-> tptp.int Bool) Bool)) (Q_2 (-> (-> tptp.int Bool) Bool))) (= (@ tptp.finite_finite_int_o (@ tptp.collect_int_o (lambda ((X_1 (-> tptp.int Bool))) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_int_o (@ tptp.collect_int_o P_12)) (@ tptp.finite_finite_int_o (@ tptp.collect_int_o Q_2))))))
% 0.62/1.00 (assert (forall ((P_12 (-> (-> tptp.nat Bool) Bool)) (Q_2 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_12)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q_2))))))
% 0.62/1.00 (assert (forall ((P_12 (-> (-> tptp.pname Bool) Bool)) (Q_2 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_12)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_2))))))
% 0.62/1.00 (assert (forall ((P_12 (-> (-> tptp.x_a Bool) Bool)) (Q_2 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_12)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q_2))))))
% 0.62/1.00 (assert (forall ((P_12 (-> tptp.pname Bool)) (Q_2 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_12)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_2))))))
% 0.62/1.00 (assert (forall ((P_12 (-> tptp.nat Bool)) (Q_2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P_12)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_2))))))
% 0.62/1.00 (assert (forall ((P_12 (-> tptp.int Bool)) (Q_2 (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X_1 tptp.int)) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P_12)) (@ tptp.finite_finite_int (@ tptp.collect_int Q_2))))))
% 0.62/1.00 (assert (forall ((A_152 (-> tptp.int Bool)) (A_151 (-> (-> tptp.int Bool) Bool))) (= (@ tptp.finite_finite_int_o (@ (@ tptp.insert_int_o A_152) A_151)) (@ tptp.finite_finite_int_o A_151))))
% 0.62/1.00 (assert (forall ((A_152 (-> tptp.nat Bool)) (A_151 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_152) A_151)) (@ tptp.finite_finite_nat_o A_151))))
% 0.62/1.00 (assert (forall ((A_152 (-> tptp.pname Bool)) (A_151 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_152) A_151)) (@ tptp.finite297249702name_o A_151))))
% 0.62/1.00 (assert (forall ((A_152 (-> tptp.x_a Bool)) (A_151 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_152) A_151)) (@ tptp.finite_finite_a_o A_151))))
% 0.62/1.00 (assert (forall ((A_152 tptp.pname) (A_151 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_152) A_151)) (@ tptp.finite_finite_pname A_151))))
% 0.62/1.00 (assert (forall ((A_152 tptp.nat) (A_151 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_152) A_151)) (@ tptp.finite_finite_nat A_151))))
% 0.62/1.00 (assert (forall ((A_152 tptp.int) (A_151 (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ (@ tptp.insert_int A_152) A_151)) (@ tptp.finite_finite_int A_151))))
% 0.62/1.00 (assert (forall ((A_152 tptp.x_a) (A_151 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_152) A_151)) (@ tptp.finite_finite_a A_151))))
% 0.62/1.00 (assert (forall ((A_150 (-> (-> tptp.int Bool) Bool)) (B_87 (-> (-> tptp.int Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_int_o_o A_150) B_87) (=> (@ tptp.finite_finite_int_o B_87) (@ tptp.finite_finite_int_o A_150)))))
% 0.62/1.00 (assert (forall ((A_150 (-> (-> tptp.nat Bool) Bool)) (B_87 (-> (-> tptp.nat Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_150) B_87) (=> (@ tptp.finite_finite_nat_o B_87) (@ tptp.finite_finite_nat_o A_150)))))
% 0.62/1.00 (assert (forall ((A_150 (-> (-> tptp.pname Bool) Bool)) (B_87 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_150) B_87) (=> (@ tptp.finite297249702name_o B_87) (@ tptp.finite297249702name_o A_150)))))
% 0.62/1.00 (assert (forall ((A_150 (-> (-> tptp.x_a Bool) Bool)) (B_87 (-> (-> tptp.x_a Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_a_o_o A_150) B_87) (=> (@ tptp.finite_finite_a_o B_87) (@ tptp.finite_finite_a_o A_150)))))
% 0.62/1.00 (assert (forall ((A_150 (-> tptp.x_a Bool)) (B_87 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_150) B_87) (=> (@ tptp.finite_finite_a B_87) (@ tptp.finite_finite_a A_150)))))
% 0.62/1.00 (assert (forall ((A_150 (-> tptp.pname Bool)) (B_87 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_150) B_87) (=> (@ tptp.finite_finite_pname B_87) (@ tptp.finite_finite_pname A_150)))))
% 0.62/1.00 (assert (forall ((A_150 (-> tptp.nat Bool)) (B_87 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_150) B_87) (=> (@ tptp.finite_finite_nat B_87) (@ tptp.finite_finite_nat A_150)))))
% 0.62/1.00 (assert (forall ((A_150 (-> tptp.int Bool)) (B_87 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_150) B_87) (=> (@ tptp.finite_finite_int B_87) (@ tptp.finite_finite_int A_150)))))
% 0.62/1.00 (assert (forall ((A_149 (-> (-> tptp.int Bool) Bool)) (B_86 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_86) (=> (@ (@ tptp.ord_less_eq_int_o_o A_149) B_86) (@ tptp.finite_finite_int_o A_149)))))
% 0.62/1.00 (assert (forall ((A_149 (-> (-> tptp.nat Bool) Bool)) (B_86 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_86) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_149) B_86) (@ tptp.finite_finite_nat_o A_149)))))
% 0.62/1.00 (assert (forall ((A_149 (-> (-> tptp.pname Bool) Bool)) (B_86 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_86) (=> (@ (@ tptp.ord_le1205211808me_o_o A_149) B_86) (@ tptp.finite297249702name_o A_149)))))
% 0.62/1.00 (assert (forall ((A_149 (-> (-> tptp.x_a Bool) Bool)) (B_86 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_86) (=> (@ (@ tptp.ord_less_eq_a_o_o A_149) B_86) (@ tptp.finite_finite_a_o A_149)))))
% 0.62/1.00 (assert (forall ((A_149 (-> tptp.x_a Bool)) (B_86 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_86) (=> (@ (@ tptp.ord_less_eq_a_o A_149) B_86) (@ tptp.finite_finite_a A_149)))))
% 0.62/1.00 (assert (forall ((A_149 (-> tptp.pname Bool)) (B_86 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_86) (=> (@ (@ tptp.ord_less_eq_pname_o A_149) B_86) (@ tptp.finite_finite_pname A_149)))))
% 0.62/1.00 (assert (forall ((A_149 (-> tptp.nat Bool)) (B_86 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_86) (=> (@ (@ tptp.ord_less_eq_nat_o A_149) B_86) (@ tptp.finite_finite_nat A_149)))))
% 0.62/1.00 (assert (forall ((A_149 (-> tptp.int Bool)) (B_86 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_86) (=> (@ (@ tptp.ord_less_eq_int_o A_149) B_86) (@ tptp.finite_finite_int A_149)))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.62/1.00 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 0.62/1.00 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 0.62/1.00 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 0.62/1.00 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 0.62/1.00 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 0.62/1.00 (assert (forall ((I_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I_1) N) (= (@ _let_1 (@ _let_1 I_1)) I_1)))))
% 0.62/1.00 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 0.62/1.00 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> tptp.x_a tptp.x_a)) (A_148 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_a_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> (-> tptp.int Bool) tptp.x_a)) (A_148 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_int_o_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> (-> tptp.nat Bool) tptp.x_a)) (A_148 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_nat_o_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> (-> tptp.pname Bool) tptp.x_a)) (A_148 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_pname_o_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_148 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_a_o_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.int Bool) Bool)) (F_40 (-> tptp.pname tptp.int Bool)) (A_148 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_148) (=> (@ (@ tptp.ord_less_eq_int_o_o B_85) (@ (@ tptp.image_pname_int_o F_40) A_148)) (@ tptp.finite_finite_int_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.nat Bool) Bool)) (F_40 (-> tptp.pname tptp.nat Bool)) (A_148 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_148) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_85) (@ (@ tptp.image_pname_nat_o F_40) A_148)) (@ tptp.finite_finite_nat_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.pname Bool) Bool)) (F_40 (-> tptp.pname tptp.pname Bool)) (A_148 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_148) (=> (@ (@ tptp.ord_le1205211808me_o_o B_85) (@ (@ tptp.image_pname_pname_o F_40) A_148)) (@ tptp.finite297249702name_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.x_a Bool) Bool)) (F_40 (-> tptp.pname tptp.x_a Bool)) (A_148 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_148) (=> (@ (@ tptp.ord_less_eq_a_o_o B_85) (@ (@ tptp.image_pname_a_o F_40) A_148)) (@ tptp.finite_finite_a_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> tptp.pname tptp.pname)) (A_148 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_pname_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> tptp.nat tptp.x_a)) (A_148 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_nat_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.int Bool) Bool)) (F_40 (-> tptp.nat tptp.int Bool)) (A_148 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_148) (=> (@ (@ tptp.ord_less_eq_int_o_o B_85) (@ (@ tptp.image_nat_int_o F_40) A_148)) (@ tptp.finite_finite_int_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.nat Bool) Bool)) (F_40 (-> tptp.nat tptp.nat Bool)) (A_148 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_148) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_85) (@ (@ tptp.image_nat_nat_o F_40) A_148)) (@ tptp.finite_finite_nat_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.pname Bool) Bool)) (F_40 (-> tptp.nat tptp.pname Bool)) (A_148 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_148) (=> (@ (@ tptp.ord_le1205211808me_o_o B_85) (@ (@ tptp.image_nat_pname_o F_40) A_148)) (@ tptp.finite297249702name_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.x_a Bool) Bool)) (F_40 (-> tptp.nat tptp.x_a Bool)) (A_148 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_148) (=> (@ (@ tptp.ord_less_eq_a_o_o B_85) (@ (@ tptp.image_nat_a_o F_40) A_148)) (@ tptp.finite_finite_a_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> tptp.nat tptp.pname)) (A_148 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_nat_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> tptp.int tptp.x_a)) (A_148 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_int_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.int Bool) Bool)) (F_40 (-> tptp.int tptp.int Bool)) (A_148 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_148) (=> (@ (@ tptp.ord_less_eq_int_o_o B_85) (@ (@ tptp.image_int_int_o F_40) A_148)) (@ tptp.finite_finite_int_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.nat Bool) Bool)) (F_40 (-> tptp.int tptp.nat Bool)) (A_148 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_148) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_85) (@ (@ tptp.image_int_nat_o F_40) A_148)) (@ tptp.finite_finite_nat_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.pname Bool) Bool)) (F_40 (-> tptp.int tptp.pname Bool)) (A_148 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_148) (=> (@ (@ tptp.ord_le1205211808me_o_o B_85) (@ (@ tptp.image_int_pname_o F_40) A_148)) (@ tptp.finite297249702name_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> (-> tptp.x_a Bool) Bool)) (F_40 (-> tptp.int tptp.x_a Bool)) (A_148 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_148) (=> (@ (@ tptp.ord_less_eq_a_o_o B_85) (@ (@ tptp.image_int_a_o F_40) A_148)) (@ tptp.finite_finite_a_o B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> tptp.int tptp.pname)) (A_148 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_int_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> tptp.x_a tptp.pname)) (A_148 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_a_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> (-> tptp.int Bool) tptp.pname)) (A_148 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_int_o_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> (-> tptp.nat Bool) tptp.pname)) (A_148 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_nat_o_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> (-> tptp.pname Bool) tptp.pname)) (A_148 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_pname_o_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> (-> tptp.x_a Bool) tptp.pname)) (A_148 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_a_o_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.nat Bool)) (F_40 (-> tptp.x_a tptp.nat)) (A_148 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_148) (=> (@ (@ tptp.ord_less_eq_nat_o B_85) (@ (@ tptp.image_a_nat F_40) A_148)) (@ tptp.finite_finite_nat B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.nat Bool)) (F_40 (-> (-> tptp.int Bool) tptp.nat)) (A_148 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_148) (=> (@ (@ tptp.ord_less_eq_nat_o B_85) (@ (@ tptp.image_int_o_nat F_40) A_148)) (@ tptp.finite_finite_nat B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.nat Bool)) (F_40 (-> (-> tptp.nat Bool) tptp.nat)) (A_148 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_148) (=> (@ (@ tptp.ord_less_eq_nat_o B_85) (@ (@ tptp.image_nat_o_nat F_40) A_148)) (@ tptp.finite_finite_nat B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.nat Bool)) (F_40 (-> (-> tptp.pname Bool) tptp.nat)) (A_148 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_148) (=> (@ (@ tptp.ord_less_eq_nat_o B_85) (@ (@ tptp.image_pname_o_nat F_40) A_148)) (@ tptp.finite_finite_nat B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.nat Bool)) (F_40 (-> (-> tptp.x_a Bool) tptp.nat)) (A_148 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_148) (=> (@ (@ tptp.ord_less_eq_nat_o B_85) (@ (@ tptp.image_a_o_nat F_40) A_148)) (@ tptp.finite_finite_nat B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.int Bool)) (F_40 (-> tptp.x_a tptp.int)) (A_148 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_148) (=> (@ (@ tptp.ord_less_eq_int_o B_85) (@ (@ tptp.image_a_int F_40) A_148)) (@ tptp.finite_finite_int B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.int Bool)) (F_40 (-> (-> tptp.int Bool) tptp.int)) (A_148 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_148) (=> (@ (@ tptp.ord_less_eq_int_o B_85) (@ (@ tptp.image_int_o_int F_40) A_148)) (@ tptp.finite_finite_int B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.int Bool)) (F_40 (-> (-> tptp.nat Bool) tptp.int)) (A_148 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_148) (=> (@ (@ tptp.ord_less_eq_int_o B_85) (@ (@ tptp.image_nat_o_int F_40) A_148)) (@ tptp.finite_finite_int B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.int Bool)) (F_40 (-> (-> tptp.pname Bool) tptp.int)) (A_148 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_148) (=> (@ (@ tptp.ord_less_eq_int_o B_85) (@ (@ tptp.image_pname_o_int F_40) A_148)) (@ tptp.finite_finite_int B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.int Bool)) (F_40 (-> (-> tptp.x_a Bool) tptp.int)) (A_148 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_148) (=> (@ (@ tptp.ord_less_eq_int_o B_85) (@ (@ tptp.image_a_o_int F_40) A_148)) (@ tptp.finite_finite_int B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> tptp.pname tptp.x_a)) (A_148 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_pname_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))))
% 0.62/1.00 (assert (forall ((B_85 (-> tptp.int Bool)) (F_40 (-> tptp.nat tptp.int)) (A_148 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_148) (=> (@ (@ tptp.ord_less_eq_int_o B_85) (@ (@ tptp.image_nat_int F_40) A_148)) (@ tptp.finite_finite_int B_85)))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.int Bool) tptp.x_a)) (A_147 (-> (-> tptp.int Bool) Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_int_o_a F_39) A_147)) (exists ((C_34 (-> (-> tptp.int Bool) Bool))) (and (@ (@ tptp.ord_less_eq_int_o_o C_34) A_147) (@ tptp.finite_finite_int_o C_34) (= B_84 (@ (@ tptp.image_int_o_a F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.nat Bool) tptp.x_a)) (A_147 (-> (-> tptp.nat Bool) Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_nat_o_a F_39) A_147)) (exists ((C_34 (-> (-> tptp.nat Bool) Bool))) (and (@ (@ tptp.ord_less_eq_nat_o_o C_34) A_147) (@ tptp.finite_finite_nat_o C_34) (= B_84 (@ (@ tptp.image_nat_o_a F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.pname Bool) tptp.x_a)) (A_147 (-> (-> tptp.pname Bool) Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_pname_o_a F_39) A_147)) (exists ((C_34 (-> (-> tptp.pname Bool) Bool))) (and (@ (@ tptp.ord_le1205211808me_o_o C_34) A_147) (@ tptp.finite297249702name_o C_34) (= B_84 (@ (@ tptp.image_pname_o_a F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_147 (-> (-> tptp.x_a Bool) Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_a_o_a F_39) A_147)) (exists ((C_34 (-> (-> tptp.x_a Bool) Bool))) (and (@ (@ tptp.ord_less_eq_a_o_o C_34) A_147) (@ tptp.finite_finite_a_o C_34) (= B_84 (@ (@ tptp.image_a_o_a F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.x_a tptp.x_a)) (A_147 (-> tptp.x_a Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_a_a F_39) A_147)) (exists ((C_34 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_34) A_147) (@ tptp.finite_finite_a C_34) (= B_84 (@ (@ tptp.image_a_a F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.x_a tptp.int Bool)) (A_147 (-> tptp.x_a Bool)) (B_84 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_84) (=> (@ (@ tptp.ord_less_eq_int_o_o B_84) (@ (@ tptp.image_a_int_o F_39) A_147)) (exists ((C_34 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_34) A_147) (@ tptp.finite_finite_a C_34) (= B_84 (@ (@ tptp.image_a_int_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.x_a tptp.nat Bool)) (A_147 (-> tptp.x_a Bool)) (B_84 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_84) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_84) (@ (@ tptp.image_a_nat_o F_39) A_147)) (exists ((C_34 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_34) A_147) (@ tptp.finite_finite_a C_34) (= B_84 (@ (@ tptp.image_a_nat_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.x_a tptp.pname Bool)) (A_147 (-> tptp.x_a Bool)) (B_84 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_84) (=> (@ (@ tptp.ord_le1205211808me_o_o B_84) (@ (@ tptp.image_a_pname_o F_39) A_147)) (exists ((C_34 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_34) A_147) (@ tptp.finite_finite_a C_34) (= B_84 (@ (@ tptp.image_a_pname_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.x_a tptp.x_a Bool)) (A_147 (-> tptp.x_a Bool)) (B_84 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_84) (=> (@ (@ tptp.ord_less_eq_a_o_o B_84) (@ (@ tptp.image_a_a_o F_39) A_147)) (exists ((C_34 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_34) A_147) (@ tptp.finite_finite_a C_34) (= B_84 (@ (@ tptp.image_a_a_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.x_a tptp.pname)) (A_147 (-> tptp.x_a Bool)) (B_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_84) (=> (@ (@ tptp.ord_less_eq_pname_o B_84) (@ (@ tptp.image_a_pname F_39) A_147)) (exists ((C_34 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_34) A_147) (@ tptp.finite_finite_a C_34) (= B_84 (@ (@ tptp.image_a_pname F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.int Bool) tptp.pname)) (A_147 (-> (-> tptp.int Bool) Bool)) (B_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_84) (=> (@ (@ tptp.ord_less_eq_pname_o B_84) (@ (@ tptp.image_int_o_pname F_39) A_147)) (exists ((C_34 (-> (-> tptp.int Bool) Bool))) (and (@ (@ tptp.ord_less_eq_int_o_o C_34) A_147) (@ tptp.finite_finite_int_o C_34) (= B_84 (@ (@ tptp.image_int_o_pname F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.nat Bool) tptp.pname)) (A_147 (-> (-> tptp.nat Bool) Bool)) (B_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_84) (=> (@ (@ tptp.ord_less_eq_pname_o B_84) (@ (@ tptp.image_nat_o_pname F_39) A_147)) (exists ((C_34 (-> (-> tptp.nat Bool) Bool))) (and (@ (@ tptp.ord_less_eq_nat_o_o C_34) A_147) (@ tptp.finite_finite_nat_o C_34) (= B_84 (@ (@ tptp.image_nat_o_pname F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.pname Bool) tptp.pname)) (A_147 (-> (-> tptp.pname Bool) Bool)) (B_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_84) (=> (@ (@ tptp.ord_less_eq_pname_o B_84) (@ (@ tptp.image_pname_o_pname F_39) A_147)) (exists ((C_34 (-> (-> tptp.pname Bool) Bool))) (and (@ (@ tptp.ord_le1205211808me_o_o C_34) A_147) (@ tptp.finite297249702name_o C_34) (= B_84 (@ (@ tptp.image_pname_o_pname F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.x_a Bool) tptp.pname)) (A_147 (-> (-> tptp.x_a Bool) Bool)) (B_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_84) (=> (@ (@ tptp.ord_less_eq_pname_o B_84) (@ (@ tptp.image_a_o_pname F_39) A_147)) (exists ((C_34 (-> (-> tptp.x_a Bool) Bool))) (and (@ (@ tptp.ord_less_eq_a_o_o C_34) A_147) (@ tptp.finite_finite_a_o C_34) (= B_84 (@ (@ tptp.image_a_o_pname F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.x_a tptp.nat)) (A_147 (-> tptp.x_a Bool)) (B_84 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_84) (=> (@ (@ tptp.ord_less_eq_nat_o B_84) (@ (@ tptp.image_a_nat F_39) A_147)) (exists ((C_34 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_34) A_147) (@ tptp.finite_finite_a C_34) (= B_84 (@ (@ tptp.image_a_nat F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.int Bool) tptp.nat)) (A_147 (-> (-> tptp.int Bool) Bool)) (B_84 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_84) (=> (@ (@ tptp.ord_less_eq_nat_o B_84) (@ (@ tptp.image_int_o_nat F_39) A_147)) (exists ((C_34 (-> (-> tptp.int Bool) Bool))) (and (@ (@ tptp.ord_less_eq_int_o_o C_34) A_147) (@ tptp.finite_finite_int_o C_34) (= B_84 (@ (@ tptp.image_int_o_nat F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.nat Bool) tptp.nat)) (A_147 (-> (-> tptp.nat Bool) Bool)) (B_84 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_84) (=> (@ (@ tptp.ord_less_eq_nat_o B_84) (@ (@ tptp.image_nat_o_nat F_39) A_147)) (exists ((C_34 (-> (-> tptp.nat Bool) Bool))) (and (@ (@ tptp.ord_less_eq_nat_o_o C_34) A_147) (@ tptp.finite_finite_nat_o C_34) (= B_84 (@ (@ tptp.image_nat_o_nat F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.pname Bool) tptp.nat)) (A_147 (-> (-> tptp.pname Bool) Bool)) (B_84 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_84) (=> (@ (@ tptp.ord_less_eq_nat_o B_84) (@ (@ tptp.image_pname_o_nat F_39) A_147)) (exists ((C_34 (-> (-> tptp.pname Bool) Bool))) (and (@ (@ tptp.ord_le1205211808me_o_o C_34) A_147) (@ tptp.finite297249702name_o C_34) (= B_84 (@ (@ tptp.image_pname_o_nat F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.x_a Bool) tptp.nat)) (A_147 (-> (-> tptp.x_a Bool) Bool)) (B_84 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_84) (=> (@ (@ tptp.ord_less_eq_nat_o B_84) (@ (@ tptp.image_a_o_nat F_39) A_147)) (exists ((C_34 (-> (-> tptp.x_a Bool) Bool))) (and (@ (@ tptp.ord_less_eq_a_o_o C_34) A_147) (@ tptp.finite_finite_a_o C_34) (= B_84 (@ (@ tptp.image_a_o_nat F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.pname tptp.nat)) (A_147 (-> tptp.pname Bool)) (B_84 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_84) (=> (@ (@ tptp.ord_less_eq_nat_o B_84) (@ (@ tptp.image_pname_nat F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_nat F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.x_a tptp.int)) (A_147 (-> tptp.x_a Bool)) (B_84 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_84) (=> (@ (@ tptp.ord_less_eq_int_o B_84) (@ (@ tptp.image_a_int F_39) A_147)) (exists ((C_34 (-> tptp.x_a Bool))) (and (@ (@ tptp.ord_less_eq_a_o C_34) A_147) (@ tptp.finite_finite_a C_34) (= B_84 (@ (@ tptp.image_a_int F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.int Bool) tptp.int)) (A_147 (-> (-> tptp.int Bool) Bool)) (B_84 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_84) (=> (@ (@ tptp.ord_less_eq_int_o B_84) (@ (@ tptp.image_int_o_int F_39) A_147)) (exists ((C_34 (-> (-> tptp.int Bool) Bool))) (and (@ (@ tptp.ord_less_eq_int_o_o C_34) A_147) (@ tptp.finite_finite_int_o C_34) (= B_84 (@ (@ tptp.image_int_o_int F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.nat Bool) tptp.int)) (A_147 (-> (-> tptp.nat Bool) Bool)) (B_84 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_84) (=> (@ (@ tptp.ord_less_eq_int_o B_84) (@ (@ tptp.image_nat_o_int F_39) A_147)) (exists ((C_34 (-> (-> tptp.nat Bool) Bool))) (and (@ (@ tptp.ord_less_eq_nat_o_o C_34) A_147) (@ tptp.finite_finite_nat_o C_34) (= B_84 (@ (@ tptp.image_nat_o_int F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.pname Bool) tptp.int)) (A_147 (-> (-> tptp.pname Bool) Bool)) (B_84 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_84) (=> (@ (@ tptp.ord_less_eq_int_o B_84) (@ (@ tptp.image_pname_o_int F_39) A_147)) (exists ((C_34 (-> (-> tptp.pname Bool) Bool))) (and (@ (@ tptp.ord_le1205211808me_o_o C_34) A_147) (@ tptp.finite297249702name_o C_34) (= B_84 (@ (@ tptp.image_pname_o_int F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> (-> tptp.x_a Bool) tptp.int)) (A_147 (-> (-> tptp.x_a Bool) Bool)) (B_84 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_84) (=> (@ (@ tptp.ord_less_eq_int_o B_84) (@ (@ tptp.image_a_o_int F_39) A_147)) (exists ((C_34 (-> (-> tptp.x_a Bool) Bool))) (and (@ (@ tptp.ord_less_eq_a_o_o C_34) A_147) (@ tptp.finite_finite_a_o C_34) (= B_84 (@ (@ tptp.image_a_o_int F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.pname tptp.int)) (A_147 (-> tptp.pname Bool)) (B_84 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_84) (=> (@ (@ tptp.ord_less_eq_int_o B_84) (@ (@ tptp.image_pname_int F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_int F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.pname tptp.int Bool)) (A_147 (-> tptp.pname Bool)) (B_84 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_84) (=> (@ (@ tptp.ord_less_eq_int_o_o B_84) (@ (@ tptp.image_pname_int_o F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_int_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.pname tptp.nat Bool)) (A_147 (-> tptp.pname Bool)) (B_84 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_84) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_84) (@ (@ tptp.image_pname_nat_o F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_nat_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.pname tptp.pname Bool)) (A_147 (-> tptp.pname Bool)) (B_84 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_84) (=> (@ (@ tptp.ord_le1205211808me_o_o B_84) (@ (@ tptp.image_pname_pname_o F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_pname_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.pname tptp.x_a Bool)) (A_147 (-> tptp.pname Bool)) (B_84 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_84) (=> (@ (@ tptp.ord_less_eq_a_o_o B_84) (@ (@ tptp.image_pname_a_o F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_a_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.pname tptp.pname)) (A_147 (-> tptp.pname Bool)) (B_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_84) (=> (@ (@ tptp.ord_less_eq_pname_o B_84) (@ (@ tptp.image_pname_pname F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_pname F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.nat tptp.x_a)) (A_147 (-> tptp.nat Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_nat_a F_39) A_147)) (exists ((C_34 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_34) A_147) (@ tptp.finite_finite_nat C_34) (= B_84 (@ (@ tptp.image_nat_a F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.nat tptp.int Bool)) (A_147 (-> tptp.nat Bool)) (B_84 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_84) (=> (@ (@ tptp.ord_less_eq_int_o_o B_84) (@ (@ tptp.image_nat_int_o F_39) A_147)) (exists ((C_34 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_34) A_147) (@ tptp.finite_finite_nat C_34) (= B_84 (@ (@ tptp.image_nat_int_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.nat tptp.nat Bool)) (A_147 (-> tptp.nat Bool)) (B_84 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_84) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_84) (@ (@ tptp.image_nat_nat_o F_39) A_147)) (exists ((C_34 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_34) A_147) (@ tptp.finite_finite_nat C_34) (= B_84 (@ (@ tptp.image_nat_nat_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.nat tptp.pname Bool)) (A_147 (-> tptp.nat Bool)) (B_84 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_84) (=> (@ (@ tptp.ord_le1205211808me_o_o B_84) (@ (@ tptp.image_nat_pname_o F_39) A_147)) (exists ((C_34 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_34) A_147) (@ tptp.finite_finite_nat C_34) (= B_84 (@ (@ tptp.image_nat_pname_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.nat tptp.x_a Bool)) (A_147 (-> tptp.nat Bool)) (B_84 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_84) (=> (@ (@ tptp.ord_less_eq_a_o_o B_84) (@ (@ tptp.image_nat_a_o F_39) A_147)) (exists ((C_34 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_34) A_147) (@ tptp.finite_finite_nat C_34) (= B_84 (@ (@ tptp.image_nat_a_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.nat tptp.pname)) (A_147 (-> tptp.nat Bool)) (B_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_84) (=> (@ (@ tptp.ord_less_eq_pname_o B_84) (@ (@ tptp.image_nat_pname F_39) A_147)) (exists ((C_34 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_34) A_147) (@ tptp.finite_finite_nat C_34) (= B_84 (@ (@ tptp.image_nat_pname F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.int tptp.x_a)) (A_147 (-> tptp.int Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_int_a F_39) A_147)) (exists ((C_34 (-> tptp.int Bool))) (and (@ (@ tptp.ord_less_eq_int_o C_34) A_147) (@ tptp.finite_finite_int C_34) (= B_84 (@ (@ tptp.image_int_a F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.int tptp.int Bool)) (A_147 (-> tptp.int Bool)) (B_84 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_84) (=> (@ (@ tptp.ord_less_eq_int_o_o B_84) (@ (@ tptp.image_int_int_o F_39) A_147)) (exists ((C_34 (-> tptp.int Bool))) (and (@ (@ tptp.ord_less_eq_int_o C_34) A_147) (@ tptp.finite_finite_int C_34) (= B_84 (@ (@ tptp.image_int_int_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.int tptp.nat Bool)) (A_147 (-> tptp.int Bool)) (B_84 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_84) (=> (@ (@ tptp.ord_less_eq_nat_o_o B_84) (@ (@ tptp.image_int_nat_o F_39) A_147)) (exists ((C_34 (-> tptp.int Bool))) (and (@ (@ tptp.ord_less_eq_int_o C_34) A_147) (@ tptp.finite_finite_int C_34) (= B_84 (@ (@ tptp.image_int_nat_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.int tptp.pname Bool)) (A_147 (-> tptp.int Bool)) (B_84 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_84) (=> (@ (@ tptp.ord_le1205211808me_o_o B_84) (@ (@ tptp.image_int_pname_o F_39) A_147)) (exists ((C_34 (-> tptp.int Bool))) (and (@ (@ tptp.ord_less_eq_int_o C_34) A_147) (@ tptp.finite_finite_int C_34) (= B_84 (@ (@ tptp.image_int_pname_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.int tptp.x_a Bool)) (A_147 (-> tptp.int Bool)) (B_84 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_84) (=> (@ (@ tptp.ord_less_eq_a_o_o B_84) (@ (@ tptp.image_int_a_o F_39) A_147)) (exists ((C_34 (-> tptp.int Bool))) (and (@ (@ tptp.ord_less_eq_int_o C_34) A_147) (@ tptp.finite_finite_int C_34) (= B_84 (@ (@ tptp.image_int_a_o F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.int tptp.pname)) (A_147 (-> tptp.int Bool)) (B_84 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_84) (=> (@ (@ tptp.ord_less_eq_pname_o B_84) (@ (@ tptp.image_int_pname F_39) A_147)) (exists ((C_34 (-> tptp.int Bool))) (and (@ (@ tptp.ord_less_eq_int_o C_34) A_147) (@ tptp.finite_finite_int C_34) (= B_84 (@ (@ tptp.image_int_pname F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.pname tptp.x_a)) (A_147 (-> tptp.pname Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_pname_a F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_a F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((F_39 (-> tptp.nat tptp.int)) (A_147 (-> tptp.nat Bool)) (B_84 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_84) (=> (@ (@ tptp.ord_less_eq_int_o B_84) (@ (@ tptp.image_nat_int F_39) A_147)) (exists ((C_34 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_34) A_147) (@ tptp.finite_finite_nat C_34) (= B_84 (@ (@ tptp.image_nat_int F_39) C_34))))))))
% 0.62/1.00 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.pname Bool))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_pname_o (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_pname_o (@ F_38 N_4)) (@ F_38 N_3))))))
% 0.62/1.00 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat Bool))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_o (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_o (@ F_38 N_4)) (@ F_38 N_3))))))
% 0.62/1.00 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.x_a Bool))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_a_o (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_a_o (@ F_38 N_4)) (@ F_38 N_3))))))
% 0.62/1.00 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.nat))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat (@ F_38 N_4)) (@ F_38 N_3))))))
% 0.62/1.00 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.int))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_int (@ F_38 N_4)) (@ F_38 N_3))))))
% 0.62/1.00 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.nat Bool))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat_o (@ F_38 N_4)) (@ F_38 N_3))))))
% 0.62/1.00 (assert (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.int Bool))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_int_o (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_int_o (@ F_38 N_4)) (@ F_38 N_3))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.nat tptp.int Bool)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite_finite_int_o (@ (@ tptp.image_nat_int_o F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.nat tptp.nat Bool)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.nat tptp.pname Bool)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.nat tptp.x_a Bool)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.int tptp.x_a)) (A_146 (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A_146)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_int_a F_37) A_146)) (exists ((X_1 tptp.int)) (and (@ (@ tptp.member_int X_1) A_146) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A_37 tptp.int)) (and (@ (@ tptp.member_int A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.int tptp.int Bool)) (A_146 (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A_146)) (=> (@ tptp.finite_finite_int_o (@ (@ tptp.image_int_int_o F_37) A_146)) (exists ((X_1 tptp.int)) (and (@ (@ tptp.member_int X_1) A_146) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A_37 tptp.int)) (and (@ (@ tptp.member_int A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.int tptp.nat Bool)) (A_146 (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A_146)) (=> (@ tptp.finite_finite_nat_o (@ (@ tptp.image_int_nat_o F_37) A_146)) (exists ((X_1 tptp.int)) (and (@ (@ tptp.member_int X_1) A_146) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A_37 tptp.int)) (and (@ (@ tptp.member_int A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.int tptp.pname Bool)) (A_146 (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A_146)) (=> (@ tptp.finite297249702name_o (@ (@ tptp.image_int_pname_o F_37) A_146)) (exists ((X_1 tptp.int)) (and (@ (@ tptp.member_int X_1) A_146) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A_37 tptp.int)) (and (@ (@ tptp.member_int A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.int tptp.x_a Bool)) (A_146 (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A_146)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_int_a_o F_37) A_146)) (exists ((X_1 tptp.int)) (and (@ (@ tptp.member_int X_1) A_146) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A_37 tptp.int)) (and (@ (@ tptp.member_int A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.pname tptp.x_a)) (A_146 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_146)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a F_37) A_146)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_146) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_37 tptp.pname)) (and (@ (@ tptp.member_pname A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((F_37 (-> tptp.nat tptp.int)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))))
% 0.62/1.00 (assert (forall ((A_145 (-> tptp.nat Bool)) (B_83 tptp.int) (F_36 (-> tptp.nat tptp.int)) (X_50 tptp.nat)) (=> (= B_83 (@ F_36 X_50)) (=> (@ (@ tptp.member_nat X_50) A_145) (@ (@ tptp.member_int B_83) (@ (@ tptp.image_nat_int F_36) A_145))))))
% 0.62/1.00 (assert (forall ((A_145 (-> tptp.pname Bool)) (B_83 tptp.x_a) (F_36 (-> tptp.pname tptp.x_a)) (X_50 tptp.pname)) (=> (= B_83 (@ F_36 X_50)) (=> (@ (@ tptp.member_pname X_50) A_145) (@ (@ tptp.member_a B_83) (@ (@ tptp.image_pname_a F_36) A_145))))))
% 0.62/1.00 (assert (forall ((A_144 (-> tptp.int Bool)) (B_82 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_144) B_82) (=> (@ (@ tptp.ord_less_eq_int_o B_82) A_144) (= A_144 B_82)))))
% 0.62/1.00 (assert (forall ((A_144 (-> tptp.nat Bool)) (B_82 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_144) B_82) (=> (@ (@ tptp.ord_less_eq_nat_o B_82) A_144) (= A_144 B_82)))))
% 0.62/1.00 (assert (forall ((A_144 (-> tptp.x_a Bool)) (B_82 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_144) B_82) (=> (@ (@ tptp.ord_less_eq_a_o B_82) A_144) (= A_144 B_82)))))
% 0.62/1.00 (assert (forall ((C_33 tptp.int) (A_143 (-> tptp.int Bool)) (B_81 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_33))) (=> (@ (@ tptp.ord_less_eq_int_o A_143) B_81) (=> (@ _let_1 A_143) (@ _let_1 B_81))))))
% 0.62/1.00 (assert (forall ((C_33 tptp.nat) (A_143 (-> tptp.nat Bool)) (B_81 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_33))) (=> (@ (@ tptp.ord_less_eq_nat_o A_143) B_81) (=> (@ _let_1 A_143) (@ _let_1 B_81))))))
% 0.62/1.00 (assert (forall ((C_33 tptp.x_a) (A_143 (-> tptp.x_a Bool)) (B_81 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_33))) (=> (@ (@ tptp.ord_less_eq_a_o A_143) B_81) (=> (@ _let_1 A_143) (@ _let_1 B_81))))))
% 0.62/1.00 (assert (forall ((C_33 tptp.pname) (A_143 (-> tptp.pname Bool)) (B_81 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_33))) (=> (@ (@ tptp.ord_less_eq_pname_o A_143) B_81) (=> (@ _let_1 A_143) (@ _let_1 B_81))))))
% 0.62/1.00 (assert (forall ((B_80 tptp.x_a) (A_142 tptp.x_a) (B_79 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_142))) (=> (=> (not (@ _let_1 B_79)) (= A_142 B_80)) (@ _let_1 (@ (@ tptp.insert_a B_80) B_79))))))
% 0.62/1.00 (assert (forall ((B_80 tptp.int) (A_142 tptp.int) (B_79 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_142))) (=> (=> (not (@ _let_1 B_79)) (= A_142 B_80)) (@ _let_1 (@ (@ tptp.insert_int B_80) B_79))))))
% 0.62/1.00 (assert (forall ((B_80 tptp.nat) (A_142 tptp.nat) (B_79 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_142))) (=> (=> (not (@ _let_1 B_79)) (= A_142 B_80)) (@ _let_1 (@ (@ tptp.insert_nat B_80) B_79))))))
% 0.62/1.00 (assert (forall ((B_80 tptp.pname) (A_142 tptp.pname) (B_79 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_142))) (=> (=> (not (@ _let_1 B_79)) (= A_142 B_80)) (@ _let_1 (@ (@ tptp.insert_pname B_80) B_79))))))
% 0.62/1.00 (assert (forall ((A_141 tptp.x_a) (B_78 tptp.x_a) (A_140 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_141))) (=> (@ _let_1 (@ (@ tptp.insert_a B_78) A_140)) (=> (not (= A_141 B_78)) (@ _let_1 A_140))))))
% 0.62/1.00 (assert (forall ((A_141 tptp.int) (B_78 tptp.int) (A_140 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_141))) (=> (@ _let_1 (@ (@ tptp.insert_int B_78) A_140)) (=> (not (= A_141 B_78)) (@ _let_1 A_140))))))
% 0.62/1.00 (assert (forall ((A_141 tptp.nat) (B_78 tptp.nat) (A_140 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_141))) (=> (@ _let_1 (@ (@ tptp.insert_nat B_78) A_140)) (=> (not (= A_141 B_78)) (@ _let_1 A_140))))))
% 0.62/1.00 (assert (forall ((A_141 tptp.pname) (B_78 tptp.pname) (A_140 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_141))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_78) A_140)) (=> (not (= A_141 B_78)) (@ _let_1 A_140))))))
% 0.62/1.00 (assert (forall ((I_1 tptp.nat) (P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N_1 tptp.nat)) (=> (@ P (@ tptp.suc N_1)) (@ P N_1))) (@ P (@ (@ tptp.minus_minus_nat K) I_1))))))
% 0.62/1.00 (assert (forall ((N tptp.nat) (M_3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M_3) (exists ((M_1 tptp.nat)) (= M_3 (@ tptp.suc M_1))))))
% 0.62/1.00 (assert (forall ((X_49 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o X_49) X_49)))
% 0.62/1.00 (assert (forall ((X_49 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o X_49) X_49)))
% 0.62/1.00 (assert (forall ((X_49 tptp.int)) (@ (@ tptp.ord_less_eq_int X_49) X_49)))
% 0.62/1.00 (assert (forall ((X_49 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X_49) X_49)))
% 0.62/1.00 (assert (forall ((X_49 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o X_49) X_49)))
% 0.62/1.00 (assert (forall ((X_48 tptp.int) (Y_12 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X_48) Y_12) (@ (@ tptp.ord_less_eq_int Y_12) X_48))))
% 0.62/1.00 (assert (forall ((X_48 tptp.nat) (Y_12 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X_48) Y_12) (@ (@ tptp.ord_less_eq_nat Y_12) X_48))))
% 0.62/1.00 (assert (forall ((X_47 (-> tptp.int Bool)) (Y_11 (-> tptp.int Bool))) (= (= X_47 Y_11) (and (@ (@ tptp.ord_less_eq_int_o X_47) Y_11) (@ (@ tptp.ord_less_eq_int_o Y_11) X_47)))))
% 0.62/1.00 (assert (forall ((X_47 (-> tptp.nat Bool)) (Y_11 (-> tptp.nat Bool))) (= (= X_47 Y_11) (and (@ (@ tptp.ord_less_eq_nat_o X_47) Y_11) (@ (@ tptp.ord_less_eq_nat_o Y_11) X_47)))))
% 0.62/1.00 (assert (forall ((X_47 tptp.int) (Y_11 tptp.int)) (= (= X_47 Y_11) (and (@ (@ tptp.ord_less_eq_int X_47) Y_11) (@ (@ tptp.ord_less_eq_int Y_11) X_47)))))
% 0.62/1.00 (assert (forall ((X_47 tptp.nat) (Y_11 tptp.nat)) (= (= X_47 Y_11) (and (@ (@ tptp.ord_less_eq_nat X_47) Y_11) (@ (@ tptp.ord_less_eq_nat Y_11) X_47)))))
% 0.62/1.00 (assert (forall ((X_47 (-> tptp.x_a Bool)) (Y_11 (-> tptp.x_a Bool))) (= (= X_47 Y_11) (and (@ (@ tptp.ord_less_eq_a_o X_47) Y_11) (@ (@ tptp.ord_less_eq_a_o Y_11) X_47)))))
% 0.62/1.00 (assert (forall ((X_46 (-> tptp.int Bool)) (Y_10 (-> tptp.int Bool))) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_int_o X_46) Y_10))))
% 0.62/1.00 (assert (forall ((X_46 (-> tptp.nat Bool)) (Y_10 (-> tptp.nat Bool))) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_nat_o X_46) Y_10))))
% 0.62/1.00 (assert (forall ((X_46 tptp.int) (Y_10 tptp.int)) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_int X_46) Y_10))))
% 0.62/1.00 (assert (forall ((X_46 tptp.nat) (Y_10 tptp.nat)) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_nat X_46) Y_10))))
% 0.62/1.00 (assert (forall ((X_46 (-> tptp.x_a Bool)) (Y_10 (-> tptp.x_a Bool))) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_a_o X_46) Y_10))))
% 0.62/1.00 (assert (forall ((Y_9 (-> tptp.int Bool)) (X_45 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o Y_9) X_45) (= (@ (@ tptp.ord_less_eq_int_o X_45) Y_9) (= X_45 Y_9)))))
% 0.62/1.00 (assert (forall ((Y_9 (-> tptp.nat Bool)) (X_45 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o Y_9) X_45) (= (@ (@ tptp.ord_less_eq_nat_o X_45) Y_9) (= X_45 Y_9)))))
% 0.62/1.00 (assert (forall ((Y_9 tptp.int) (X_45 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y_9) X_45) (= (@ (@ tptp.ord_less_eq_int X_45) Y_9) (= X_45 Y_9)))))
% 0.62/1.00 (assert (forall ((Y_9 tptp.nat) (X_45 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y_9) X_45) (= (@ (@ tptp.ord_less_eq_nat X_45) Y_9) (= X_45 Y_9)))))
% 0.62/1.00 (assert (forall ((Y_9 (-> tptp.x_a Bool)) (X_45 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Y_9) X_45) (= (@ (@ tptp.ord_less_eq_a_o X_45) Y_9) (= X_45 Y_9)))))
% 0.62/1.00 (assert (forall ((C_32 (-> tptp.int Bool)) (A_139 (-> tptp.int Bool)) (B_77 (-> tptp.int Bool))) (=> (= A_139 B_77) (=> (@ (@ tptp.ord_less_eq_int_o B_77) C_32) (@ (@ tptp.ord_less_eq_int_o A_139) C_32)))))
% 0.62/1.00 (assert (forall ((C_32 (-> tptp.nat Bool)) (A_139 (-> tptp.nat Bool)) (B_77 (-> tptp.nat Bool))) (=> (= A_139 B_77) (=> (@ (@ tptp.ord_less_eq_nat_o B_77) C_32) (@ (@ tptp.ord_less_eq_nat_o A_139) C_32)))))
% 0.62/1.00 (assert (forall ((C_32 tptp.int) (A_139 tptp.int) (B_77 tptp.int)) (=> (= A_139 B_77) (=> (@ (@ tptp.ord_less_eq_int B_77) C_32) (@ (@ tptp.ord_less_eq_int A_139) C_32)))))
% 0.62/1.00 (assert (forall ((C_32 tptp.nat) (A_139 tptp.nat) (B_77 tptp.nat)) (=> (= A_139 B_77) (=> (@ (@ tptp.ord_less_eq_nat B_77) C_32) (@ (@ tptp.ord_less_eq_nat A_139) C_32)))))
% 0.62/1.00 (assert (forall ((C_32 (-> tptp.x_a Bool)) (A_139 (-> tptp.x_a Bool)) (B_77 (-> tptp.x_a Bool))) (=> (= A_139 B_77) (=> (@ (@ tptp.ord_less_eq_a_o B_77) C_32) (@ (@ tptp.ord_less_eq_a_o A_139) C_32)))))
% 0.62/1.00 (assert (forall ((C_31 (-> tptp.int Bool)) (A_138 (-> tptp.int Bool)) (B_76 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o C_31))) (=> (= A_138 B_76) (=> (@ _let_1 B_76) (@ _let_1 A_138))))))
% 0.62/1.00 (assert (forall ((C_31 (-> tptp.nat Bool)) (A_138 (-> tptp.nat Bool)) (B_76 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o C_31))) (=> (= A_138 B_76) (=> (@ _let_1 B_76) (@ _let_1 A_138))))))
% 0.62/1.00 (assert (forall ((C_31 tptp.int) (A_138 tptp.int) (B_76 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C_31))) (=> (= A_138 B_76) (=> (@ _let_1 B_76) (@ _let_1 A_138))))))
% 0.62/1.00 (assert (forall ((C_31 tptp.nat) (A_138 tptp.nat) (B_76 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C_31))) (=> (= A_138 B_76) (=> (@ _let_1 B_76) (@ _let_1 A_138))))))
% 0.62/1.00 (assert (forall ((C_31 (-> tptp.x_a Bool)) (A_138 (-> tptp.x_a Bool)) (B_76 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o C_31))) (=> (= A_138 B_76) (=> (@ _let_1 B_76) (@ _let_1 A_138))))))
% 0.62/1.00 (assert (forall ((C_30 (-> tptp.int Bool)) (A_137 (-> tptp.int Bool)) (B_75 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o A_137))) (=> (@ _let_1 B_75) (=> (= B_75 C_30) (@ _let_1 C_30))))))
% 0.62/1.00 (assert (forall ((C_30 (-> tptp.nat Bool)) (A_137 (-> tptp.nat Bool)) (B_75 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_137))) (=> (@ _let_1 B_75) (=> (= B_75 C_30) (@ _let_1 C_30))))))
% 0.62/1.00 (assert (forall ((C_30 tptp.int) (A_137 tptp.int) (B_75 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A_137))) (=> (@ _let_1 B_75) (=> (= B_75 C_30) (@ _let_1 C_30))))))
% 0.62/1.00 (assert (forall ((C_30 tptp.nat) (A_137 tptp.nat) (B_75 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A_137))) (=> (@ _let_1 B_75) (=> (= B_75 C_30) (@ _let_1 C_30))))))
% 0.62/1.00 (assert (forall ((C_30 (-> tptp.x_a Bool)) (A_137 (-> tptp.x_a Bool)) (B_75 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_137))) (=> (@ _let_1 B_75) (=> (= B_75 C_30) (@ _let_1 C_30))))))
% 0.62/1.00 (assert (forall ((C_29 (-> tptp.int Bool)) (B_74 (-> tptp.int Bool)) (A_136 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o B_74) A_136) (=> (= B_74 C_29) (@ (@ tptp.ord_less_eq_int_o C_29) A_136)))))
% 0.62/1.00 (assert (forall ((C_29 (-> tptp.nat Bool)) (B_74 (-> tptp.nat Bool)) (A_136 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o B_74) A_136) (=> (= B_74 C_29) (@ (@ tptp.ord_less_eq_nat_o C_29) A_136)))))
% 0.62/1.00 (assert (forall ((C_29 tptp.int) (B_74 tptp.int) (A_136 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B_74) A_136) (=> (= B_74 C_29) (@ (@ tptp.ord_less_eq_int C_29) A_136)))))
% 0.62/1.00 (assert (forall ((C_29 tptp.nat) (B_74 tptp.nat) (A_136 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B_74) A_136) (=> (= B_74 C_29) (@ (@ tptp.ord_less_eq_nat C_29) A_136)))))
% 0.62/1.00 (assert (forall ((C_29 (-> tptp.x_a Bool)) (B_74 (-> tptp.x_a Bool)) (A_136 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o B_74) A_136) (=> (= B_74 C_29) (@ (@ tptp.ord_less_eq_a_o C_29) A_136)))))
% 0.62/1.00 (assert (forall ((X_44 (-> tptp.int Bool)) (Y_8 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o X_44) Y_8) (=> (@ (@ tptp.ord_less_eq_int_o Y_8) X_44) (= X_44 Y_8)))))
% 0.62/1.00 (assert (forall ((X_44 (-> tptp.nat Bool)) (Y_8 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o X_44) Y_8) (=> (@ (@ tptp.ord_less_eq_nat_o Y_8) X_44) (= X_44 Y_8)))))
% 0.62/1.00 (assert (forall ((X_44 tptp.int) (Y_8 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X_44) Y_8) (=> (@ (@ tptp.ord_less_eq_int Y_8) X_44) (= X_44 Y_8)))))
% 0.62/1.00 (assert (forall ((X_44 tptp.nat) (Y_8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X_44) Y_8) (=> (@ (@ tptp.ord_less_eq_nat Y_8) X_44) (= X_44 Y_8)))))
% 0.62/1.00 (assert (forall ((X_44 (-> tptp.x_a Bool)) (Y_8 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o X_44) Y_8) (=> (@ (@ tptp.ord_less_eq_a_o Y_8) X_44) (= X_44 Y_8)))))
% 0.62/1.00 (assert (forall ((Z_6 (-> tptp.int Bool)) (X_43 (-> tptp.int Bool)) (Y_7 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o X_43))) (=> (@ _let_1 Y_7) (=> (@ (@ tptp.ord_less_eq_int_o Y_7) Z_6) (@ _let_1 Z_6))))))
% 0.62/1.00 (assert (forall ((Z_6 (-> tptp.nat Bool)) (X_43 (-> tptp.nat Bool)) (Y_7 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o X_43))) (=> (@ _let_1 Y_7) (=> (@ (@ tptp.ord_less_eq_nat_o Y_7) Z_6) (@ _let_1 Z_6))))))
% 0.62/1.00 (assert (forall ((Z_6 tptp.int) (X_43 tptp.int) (Y_7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X_43))) (=> (@ _let_1 Y_7) (=> (@ (@ tptp.ord_less_eq_int Y_7) Z_6) (@ _let_1 Z_6))))))
% 0.62/1.00 (assert (forall ((Z_6 tptp.nat) (X_43 tptp.nat) (Y_7 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X_43))) (=> (@ _let_1 Y_7) (=> (@ (@ tptp.ord_less_eq_nat Y_7) Z_6) (@ _let_1 Z_6))))))
% 0.62/1.00 (assert (forall ((Z_6 (-> tptp.x_a Bool)) (X_43 (-> tptp.x_a Bool)) (Y_7 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o X_43))) (=> (@ _let_1 Y_7) (=> (@ (@ tptp.ord_less_eq_a_o Y_7) Z_6) (@ _let_1 Z_6))))))
% 0.62/1.00 (assert (forall ((Y_6 (-> tptp.int Bool)) (X_42 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o Y_6) X_42) (=> (@ (@ tptp.ord_less_eq_int_o X_42) Y_6) (= X_42 Y_6)))))
% 0.62/1.00 (assert (forall ((Y_6 (-> tptp.nat Bool)) (X_42 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o Y_6) X_42) (=> (@ (@ tptp.ord_less_eq_nat_o X_42) Y_6) (= X_42 Y_6)))))
% 0.62/1.00 (assert (forall ((Y_6 tptp.int) (X_42 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y_6) X_42) (=> (@ (@ tptp.ord_less_eq_int X_42) Y_6) (= X_42 Y_6)))))
% 0.62/1.00 (assert (forall ((Y_6 tptp.nat) (X_42 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y_6) X_42) (=> (@ (@ tptp.ord_less_eq_nat X_42) Y_6) (= X_42 Y_6)))))
% 0.62/1.00 (assert (forall ((Y_6 (-> tptp.x_a Bool)) (X_42 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o Y_6) X_42) (=> (@ (@ tptp.ord_less_eq_a_o X_42) Y_6) (= X_42 Y_6)))))
% 0.62/1.00 (assert (forall ((Z_5 (-> tptp.int Bool)) (Y_5 (-> tptp.int Bool)) (X_41 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o Z_5))) (=> (@ (@ tptp.ord_less_eq_int_o Y_5) X_41) (=> (@ _let_1 Y_5) (@ _let_1 X_41))))))
% 0.62/1.00 (assert (forall ((Z_5 (-> tptp.nat Bool)) (Y_5 (-> tptp.nat Bool)) (X_41 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o Z_5))) (=> (@ (@ tptp.ord_less_eq_nat_o Y_5) X_41) (=> (@ _let_1 Y_5) (@ _let_1 X_41))))))
% 0.62/1.00 (assert (forall ((Z_5 tptp.int) (Y_5 tptp.int) (X_41 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z_5))) (=> (@ (@ tptp.ord_less_eq_int Y_5) X_41) (=> (@ _let_1 Y_5) (@ _let_1 X_41))))))
% 0.62/1.00 (assert (forall ((Z_5 tptp.nat) (Y_5 tptp.nat) (X_41 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z_5))) (=> (@ (@ tptp.ord_less_eq_nat Y_5) X_41) (=> (@ _let_1 Y_5) (@ _let_1 X_41))))))
% 0.62/1.00 (assert (forall ((Z_5 (-> tptp.x_a Bool)) (Y_5 (-> tptp.x_a Bool)) (X_41 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o Z_5))) (=> (@ (@ tptp.ord_less_eq_a_o Y_5) X_41) (=> (@ _let_1 Y_5) (@ _let_1 X_41))))))
% 0.62/1.00 (assert (forall ((X_40 tptp.int) (Y_4 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X_40) Y_4)) (@ (@ tptp.ord_less_eq_int Y_4) X_40))))
% 0.62/1.00 (assert (forall ((X_40 tptp.nat) (Y_4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X_40) Y_4)) (@ (@ tptp.ord_less_eq_nat Y_4) X_40))))
% 0.62/1.00 (assert (forall ((A_135 tptp.x_a) (B_73 (-> tptp.x_a Bool))) (@ (@ tptp.member_a A_135) (@ (@ tptp.insert_a A_135) B_73))))
% 0.62/1.00 (assert (forall ((A_135 tptp.int) (B_73 (-> tptp.int Bool))) (@ (@ tptp.member_int A_135) (@ (@ tptp.insert_int A_135) B_73))))
% 0.62/1.00 (assert (forall ((A_135 tptp.nat) (B_73 (-> tptp.nat Bool))) (@ (@ tptp.member_nat A_135) (@ (@ tptp.insert_nat A_135) B_73))))
% 0.62/1.00 (assert (forall ((A_135 tptp.pname) (B_73 (-> tptp.pname Bool))) (@ (@ tptp.member_pname A_135) (@ (@ tptp.insert_pname A_135) B_73))))
% 0.62/1.00 (assert (forall ((A_134 tptp.x_a) (B_72 (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a A_134) B_72) (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (or (= X_1 A_134) (@ (@ tptp.member_a X_1) B_72)))))))
% 0.62/1.00 (assert (forall ((A_134 tptp.int) (B_72 (-> tptp.int Bool))) (= (@ (@ tptp.insert_int A_134) B_72) (@ tptp.collect_int (lambda ((X_1 tptp.int)) (or (= X_1 A_134) (@ (@ tptp.member_int X_1) B_72)))))))
% 0.62/1.00 (assert (forall ((A_134 tptp.nat) (B_72 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_134) B_72) (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (or (= X_1 A_134) (@ (@ tptp.member_nat X_1) B_72)))))))
% 0.62/1.00 (assert (forall ((A_134 tptp.pname) (B_72 (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname A_134) B_72) (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (= X_1 A_134) (@ (@ tptp.member_pname X_1) B_72)))))))
% 0.62/1.00 (assert (forall ((A_133 tptp.x_a) (P_11 (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a A_133) (@ tptp.collect_a P_11)) (@ tptp.collect_a (lambda ((U_1 tptp.x_a)) (=> (not (= U_1 A_133)) (@ P_11 U_1)))))))
% 0.62/1.00 (assert (forall ((A_133 tptp.int) (P_11 (-> tptp.int Bool))) (= (@ (@ tptp.insert_int A_133) (@ tptp.collect_int P_11)) (@ tptp.collect_int (lambda ((U_1 tptp.int)) (=> (not (= U_1 A_133)) (@ P_11 U_1)))))))
% 0.62/1.00 (assert (forall ((A_133 tptp.nat) (P_11 (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat A_133) (@ tptp.collect_nat P_11)) (@ tptp.collect_nat (lambda ((U_1 tptp.nat)) (=> (not (= U_1 A_133)) (@ P_11 U_1)))))))
% 0.62/1.00 (assert (forall ((X_39 tptp.int) (A_132 (-> tptp.int Bool))) (= (@ (@ tptp.member_int X_39) A_132) (@ A_132 X_39))))
% 0.62/1.00 (assert (forall ((X_39 tptp.nat) (A_132 (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X_39) A_132) (@ A_132 X_39))))
% 0.62/1.00 (assert (forall ((X_39 tptp.x_a) (A_132 (-> tptp.x_a Bool))) (= (@ (@ tptp.member_a X_39) A_132) (@ A_132 X_39))))
% 0.62/1.00 (assert (forall ((X_39 tptp.pname) (A_132 (-> tptp.pname Bool))) (= (@ (@ tptp.member_pname X_39) A_132) (@ A_132 X_39))))
% 0.62/1.00 (assert (forall ((P_10 (-> tptp.int Bool))) (= (@ tptp.collect_int P_10) P_10)))
% 0.62/1.00 (assert (forall ((P_10 (-> tptp.nat Bool))) (= (@ tptp.collect_nat P_10) P_10)))
% 0.62/1.00 (assert (forall ((X_38 tptp.x_a) (A_131 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_38))) (let ((_let_2 (@ _let_1 A_131))) (= (@ _let_1 _let_2) _let_2)))))
% 0.62/1.00 (assert (forall ((X_37 tptp.x_a) (Y_3 tptp.x_a) (A_130 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_37))) (let ((_let_2 (@ tptp.insert_a Y_3))) (= (@ _let_1 (@ _let_2 A_130)) (@ _let_2 (@ _let_1 A_130)))))))
% 0.62/1.00 (assert (forall ((A_129 tptp.x_a) (B_71 tptp.x_a) (A_128 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_129))) (= (@ _let_1 (@ (@ tptp.insert_a B_71) A_128)) (or (= A_129 B_71) (@ _let_1 A_128))))))
% 0.62/1.00 (assert (forall ((A_129 tptp.int) (B_71 tptp.int) (A_128 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_129))) (= (@ _let_1 (@ (@ tptp.insert_int B_71) A_128)) (or (= A_129 B_71) (@ _let_1 A_128))))))
% 0.62/1.00 (assert (forall ((A_129 tptp.nat) (B_71 tptp.nat) (A_128 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_129))) (= (@ _let_1 (@ (@ tptp.insert_nat B_71) A_128)) (or (= A_129 B_71) (@ _let_1 A_128))))))
% 0.62/1.00 (assert (forall ((A_129 tptp.pname) (B_71 tptp.pname) (A_128 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_129))) (= (@ _let_1 (@ (@ tptp.insert_pname B_71) A_128)) (or (= A_129 B_71) (@ _let_1 A_128))))))
% 0.62/1.00 (assert (forall ((Y_2 tptp.x_a) (A_127 (-> tptp.x_a Bool)) (X_36 tptp.x_a)) (= (@ (@ (@ tptp.insert_a Y_2) A_127) X_36) (or (= Y_2 X_36) (@ A_127 X_36)))))
% 0.62/1.00 (assert (forall ((B_70 (-> tptp.x_a Bool)) (X_35 tptp.x_a) (A_126 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_35))) (let ((_let_2 (@ tptp.member_a X_35))) (=> (not (@ _let_2 A_126)) (=> (not (@ _let_2 B_70)) (= (= (@ _let_1 A_126) (@ _let_1 B_70)) (= A_126 B_70))))))))
% 0.62/1.00 (assert (forall ((B_70 (-> tptp.int Bool)) (X_35 tptp.int) (A_126 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_35))) (let ((_let_2 (@ tptp.member_int X_35))) (=> (not (@ _let_2 A_126)) (=> (not (@ _let_2 B_70)) (= (= (@ _let_1 A_126) (@ _let_1 B_70)) (= A_126 B_70))))))))
% 0.62/1.00 (assert (forall ((B_70 (-> tptp.nat Bool)) (X_35 tptp.nat) (A_126 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_35))) (let ((_let_2 (@ tptp.member_nat X_35))) (=> (not (@ _let_2 A_126)) (=> (not (@ _let_2 B_70)) (= (= (@ _let_1 A_126) (@ _let_1 B_70)) (= A_126 B_70))))))))
% 0.62/1.00 (assert (forall ((B_70 (-> tptp.pname Bool)) (X_35 tptp.pname) (A_126 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_35))) (let ((_let_2 (@ tptp.member_pname X_35))) (=> (not (@ _let_2 A_126)) (=> (not (@ _let_2 B_70)) (= (= (@ _let_1 A_126) (@ _let_1 B_70)) (= A_126 B_70))))))))
% 0.62/1.00 (assert (forall ((B_69 tptp.x_a) (A_125 tptp.x_a) (B_68 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_125))) (=> (@ _let_1 B_68) (@ _let_1 (@ (@ tptp.insert_a B_69) B_68))))))
% 0.62/1.00 (assert (forall ((B_69 tptp.int) (A_125 tptp.int) (B_68 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_125))) (=> (@ _let_1 B_68) (@ _let_1 (@ (@ tptp.insert_int B_69) B_68))))))
% 0.62/1.00 (assert (forall ((B_69 tptp.nat) (A_125 tptp.nat) (B_68 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_125))) (=> (@ _let_1 B_68) (@ _let_1 (@ (@ tptp.insert_nat B_69) B_68))))))
% 0.62/1.00 (assert (forall ((B_69 tptp.pname) (A_125 tptp.pname) (B_68 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_125))) (=> (@ _let_1 B_68) (@ _let_1 (@ (@ tptp.insert_pname B_69) B_68))))))
% 0.62/1.00 (assert (forall ((A_124 tptp.x_a) (A_123 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a A_124) A_123) (= (@ (@ tptp.insert_a A_124) A_123) A_123))))
% 0.62/1.00 (assert (forall ((A_124 tptp.int) (A_123 (-> tptp.int Bool))) (=> (@ (@ tptp.member_int A_124) A_123) (= (@ (@ tptp.insert_int A_124) A_123) A_123))))
% 0.62/1.00 (assert (forall ((A_124 tptp.nat) (A_123 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat A_124) A_123) (= (@ (@ tptp.insert_nat A_124) A_123) A_123))))
% 0.62/1.00 (assert (forall ((A_124 tptp.pname) (A_123 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_124) A_123) (= (@ (@ tptp.insert_pname A_124) A_123) A_123))))
% 0.62/1.00 (assert (forall ((A_122 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o A_122) A_122)))
% 0.62/1.00 (assert (forall ((A_122 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o A_122) A_122)))
% 0.62/1.00 (assert (forall ((A_122 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o A_122) A_122)))
% 0.62/1.00 (assert (forall ((A_121 (-> tptp.int Bool)) (B_67 (-> tptp.int Bool))) (= (= A_121 B_67) (and (@ (@ tptp.ord_less_eq_int_o A_121) B_67) (@ (@ tptp.ord_less_eq_int_o B_67) A_121)))))
% 0.62/1.00 (assert (forall ((A_121 (-> tptp.nat Bool)) (B_67 (-> tptp.nat Bool))) (= (= A_121 B_67) (and (@ (@ tptp.ord_less_eq_nat_o A_121) B_67) (@ (@ tptp.ord_less_eq_nat_o B_67) A_121)))))
% 0.62/1.00 (assert (forall ((A_121 (-> tptp.x_a Bool)) (B_67 (-> tptp.x_a Bool))) (= (= A_121 B_67) (and (@ (@ tptp.ord_less_eq_a_o A_121) B_67) (@ (@ tptp.ord_less_eq_a_o B_67) A_121)))))
% 0.62/1.00 (assert (forall ((A_120 (-> tptp.int Bool)) (B_66 (-> tptp.int Bool))) (=> (= A_120 B_66) (@ (@ tptp.ord_less_eq_int_o A_120) B_66))))
% 0.62/1.00 (assert (forall ((A_120 (-> tptp.nat Bool)) (B_66 (-> tptp.nat Bool))) (=> (= A_120 B_66) (@ (@ tptp.ord_less_eq_nat_o A_120) B_66))))
% 0.62/1.00 (assert (forall ((A_120 (-> tptp.x_a Bool)) (B_66 (-> tptp.x_a Bool))) (=> (= A_120 B_66) (@ (@ tptp.ord_less_eq_a_o A_120) B_66))))
% 0.62/1.00 (assert (forall ((A_119 (-> tptp.int Bool)) (B_65 (-> tptp.int Bool))) (=> (= A_119 B_65) (@ (@ tptp.ord_less_eq_int_o B_65) A_119))))
% 0.62/1.00 (assert (forall ((A_119 (-> tptp.nat Bool)) (B_65 (-> tptp.nat Bool))) (=> (= A_119 B_65) (@ (@ tptp.ord_less_eq_nat_o B_65) A_119))))
% 0.62/1.00 (assert (forall ((A_119 (-> tptp.x_a Bool)) (B_65 (-> tptp.x_a Bool))) (=> (= A_119 B_65) (@ (@ tptp.ord_less_eq_a_o B_65) A_119))))
% 0.62/1.00 (assert (forall ((X_34 tptp.int) (A_118 (-> tptp.int Bool)) (B_64 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int X_34))) (=> (@ (@ tptp.ord_less_eq_int_o A_118) B_64) (=> (@ _let_1 A_118) (@ _let_1 B_64))))))
% 0.62/1.00 (assert (forall ((X_34 tptp.nat) (A_118 (-> tptp.nat Bool)) (B_64 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_34))) (=> (@ (@ tptp.ord_less_eq_nat_o A_118) B_64) (=> (@ _let_1 A_118) (@ _let_1 B_64))))))
% 0.62/1.00 (assert (forall ((X_34 tptp.x_a) (A_118 (-> tptp.x_a Bool)) (B_64 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_34))) (=> (@ (@ tptp.ord_less_eq_a_o A_118) B_64) (=> (@ _let_1 A_118) (@ _let_1 B_64))))))
% 0.62/1.00 (assert (forall ((X_34 tptp.pname) (A_118 (-> tptp.pname Bool)) (B_64 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_34))) (=> (@ (@ tptp.ord_less_eq_pname_o A_118) B_64) (=> (@ _let_1 A_118) (@ _let_1 B_64))))))
% 0.62/1.00 (assert (forall ((B_63 (-> tptp.int Bool)) (X_33 tptp.int) (A_117 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int X_33))) (=> (@ _let_1 A_117) (=> (@ (@ tptp.ord_less_eq_int_o A_117) B_63) (@ _let_1 B_63))))))
% 0.62/1.00 (assert (forall ((B_63 (-> tptp.nat Bool)) (X_33 tptp.nat) (A_117 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_33))) (=> (@ _let_1 A_117) (=> (@ (@ tptp.ord_less_eq_nat_o A_117) B_63) (@ _let_1 B_63))))))
% 0.62/1.00 (assert (forall ((B_63 (-> tptp.x_a Bool)) (X_33 tptp.x_a) (A_117 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_33))) (=> (@ _let_1 A_117) (=> (@ (@ tptp.ord_less_eq_a_o A_117) B_63) (@ _let_1 B_63))))))
% 0.62/1.00 (assert (forall ((B_63 (-> tptp.pname Bool)) (X_33 tptp.pname) (A_117 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_33))) (=> (@ _let_1 A_117) (=> (@ (@ tptp.ord_less_eq_pname_o A_117) B_63) (@ _let_1 B_63))))))
% 0.62/1.00 (assert (forall ((X_32 tptp.int) (A_116 (-> tptp.int Bool)) (B_62 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int X_32))) (=> (@ (@ tptp.ord_less_eq_int_o A_116) B_62) (=> (@ _let_1 A_116) (@ _let_1 B_62))))))
% 0.62/1.00 (assert (forall ((X_32 tptp.nat) (A_116 (-> tptp.nat Bool)) (B_62 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_32))) (=> (@ (@ tptp.ord_less_eq_nat_o A_116) B_62) (=> (@ _let_1 A_116) (@ _let_1 B_62))))))
% 0.62/1.00 (assert (forall ((X_32 tptp.x_a) (A_116 (-> tptp.x_a Bool)) (B_62 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_32))) (=> (@ (@ tptp.ord_less_eq_a_o A_116) B_62) (=> (@ _let_1 A_116) (@ _let_1 B_62))))))
% 0.62/1.00 (assert (forall ((X_32 tptp.pname) (A_116 (-> tptp.pname Bool)) (B_62 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_32))) (=> (@ (@ tptp.ord_less_eq_pname_o A_116) B_62) (=> (@ _let_1 A_116) (@ _let_1 B_62))))))
% 0.62/1.00 (assert (forall ((C_28 (-> tptp.int Bool)) (A_115 (-> tptp.int Bool)) (B_61 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o A_115))) (=> (@ _let_1 B_61) (=> (@ (@ tptp.ord_less_eq_int_o B_61) C_28) (@ _let_1 C_28))))))
% 0.62/1.00 (assert (forall ((C_28 (-> tptp.nat Bool)) (A_115 (-> tptp.nat Bool)) (B_61 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_115))) (=> (@ _let_1 B_61) (=> (@ (@ tptp.ord_less_eq_nat_o B_61) C_28) (@ _let_1 C_28))))))
% 0.62/1.00 (assert (forall ((C_28 (-> tptp.x_a Bool)) (A_115 (-> tptp.x_a Bool)) (B_61 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_115))) (=> (@ _let_1 B_61) (=> (@ (@ tptp.ord_less_eq_a_o B_61) C_28) (@ _let_1 C_28))))))
% 0.62/1.00 (assert (forall ((A_114 (-> tptp.int Bool)) (B_60 (-> tptp.int Bool))) (=> (= A_114 B_60) (not (=> (@ (@ tptp.ord_less_eq_int_o A_114) B_60) (not (@ (@ tptp.ord_less_eq_int_o B_60) A_114)))))))
% 0.62/1.00 (assert (forall ((A_114 (-> tptp.nat Bool)) (B_60 (-> tptp.nat Bool))) (=> (= A_114 B_60) (not (=> (@ (@ tptp.ord_less_eq_nat_o A_114) B_60) (not (@ (@ tptp.ord_less_eq_nat_o B_60) A_114)))))))
% 0.62/1.00 (assert (forall ((A_114 (-> tptp.x_a Bool)) (B_60 (-> tptp.x_a Bool))) (=> (= A_114 B_60) (not (=> (@ (@ tptp.ord_less_eq_a_o A_114) B_60) (not (@ (@ tptp.ord_less_eq_a_o B_60) A_114)))))))
% 0.62/1.00 (assert (forall ((Z_4 tptp.int) (F_35 (-> tptp.nat tptp.int)) (A_113 (-> tptp.nat Bool))) (= (@ (@ tptp.member_int Z_4) (@ (@ tptp.image_nat_int F_35) A_113)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_113) (= Z_4 (@ F_35 X_1)))))))
% 0.62/1.00 (assert (forall ((Z_4 tptp.x_a) (F_35 (-> tptp.pname tptp.x_a)) (A_113 (-> tptp.pname Bool))) (= (@ (@ tptp.member_a Z_4) (@ (@ tptp.image_pname_a F_35) A_113)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_113) (= Z_4 (@ F_35 X_1)))))))
% 0.62/1.00 (assert (forall ((F_34 (-> tptp.nat tptp.int)) (X_31 tptp.nat) (A_112 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_31) A_112) (@ (@ tptp.member_int (@ F_34 X_31)) (@ (@ tptp.image_nat_int F_34) A_112)))))
% 0.62/1.00 (assert (forall ((F_34 (-> tptp.pname tptp.x_a)) (X_31 tptp.pname) (A_112 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_31) A_112) (@ (@ tptp.member_a (@ F_34 X_31)) (@ (@ tptp.image_pname_a F_34) A_112)))))
% 0.62/1.00 (assert (forall ((B_59 tptp.int) (F_33 (-> tptp.nat tptp.int)) (X_30 tptp.nat) (A_111 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_30) A_111) (=> (= B_59 (@ F_33 X_30)) (@ (@ tptp.member_int B_59) (@ (@ tptp.image_nat_int F_33) A_111))))))
% 0.62/1.00 (assert (forall ((B_59 tptp.x_a) (F_33 (-> tptp.pname tptp.x_a)) (X_30 tptp.pname) (A_111 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_30) A_111) (=> (= B_59 (@ F_33 X_30)) (@ (@ tptp.member_a B_59) (@ (@ tptp.image_pname_a F_33) A_111))))))
% 0.62/1.00 (assert (forall ((X_1 tptp.x_a) (Xa (-> tptp.x_a Bool))) (= (@ (@ tptp.insert_a X_1) Xa) (@ tptp.collect_a (lambda ((Y_1 tptp.x_a)) (or (= Y_1 X_1) (@ (@ tptp.member_a Y_1) Xa)))))))
% 0.62/1.00 (assert (forall ((X_1 tptp.int) (Xa (-> tptp.int Bool))) (= (@ (@ tptp.insert_int X_1) Xa) (@ tptp.collect_int (lambda ((Y_1 tptp.int)) (or (= Y_1 X_1) (@ (@ tptp.member_int Y_1) Xa)))))))
% 0.62/1.00 (assert (forall ((X_1 tptp.nat) (Xa (-> tptp.nat Bool))) (= (@ (@ tptp.insert_nat X_1) Xa) (@ tptp.collect_nat (lambda ((Y_1 tptp.nat)) (or (= Y_1 X_1) (@ (@ tptp.member_nat Y_1) Xa)))))))
% 0.62/1.00 (assert (forall ((X_1 tptp.pname) (Xa (-> tptp.pname Bool))) (= (@ (@ tptp.insert_pname X_1) Xa) (@ tptp.collect_pname (lambda ((Y_1 tptp.pname)) (or (= Y_1 X_1) (@ (@ tptp.member_pname Y_1) Xa)))))))
% 0.62/1.00 (assert (forall ((F_32 (-> tptp.int Bool)) (G_4 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_int_o F_32) G_4) (forall ((X_1 tptp.int)) (@ (@ tptp.ord_less_eq_o (@ F_32 X_1)) (@ G_4 X_1))))))
% 0.62/1.00 (assert (forall ((F_32 (-> tptp.nat Bool)) (G_4 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o F_32) G_4) (forall ((X_1 tptp.nat)) (@ (@ tptp.ord_less_eq_o (@ F_32 X_1)) (@ G_4 X_1))))))
% 0.62/1.00 (assert (forall ((F_32 (-> tptp.x_a Bool)) (G_4 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o F_32) G_4) (forall ((X_1 tptp.x_a)) (@ (@ tptp.ord_less_eq_o (@ F_32 X_1)) (@ G_4 X_1))))))
% 0.62/1.00 (assert (forall ((X_29 tptp.int) (F_31 (-> tptp.int Bool)) (G_3 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o F_31) G_3) (@ (@ tptp.ord_less_eq_o (@ F_31 X_29)) (@ G_3 X_29)))))
% 0.62/1.00 (assert (forall ((X_29 tptp.nat) (F_31 (-> tptp.nat Bool)) (G_3 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o F_31) G_3) (@ (@ tptp.ord_less_eq_o (@ F_31 X_29)) (@ G_3 X_29)))))
% 0.62/1.00 (assert (forall ((X_29 tptp.x_a) (F_31 (-> tptp.x_a Bool)) (G_3 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o F_31) G_3) (@ (@ tptp.ord_less_eq_o (@ F_31 X_29)) (@ G_3 X_29)))))
% 0.62/1.00 (assert (forall ((X_28 tptp.int) (F_30 (-> tptp.int Bool)) (G_2 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o F_30) G_2) (@ (@ tptp.ord_less_eq_o (@ F_30 X_28)) (@ G_2 X_28)))))
% 0.62/1.00 (assert (forall ((X_28 tptp.nat) (F_30 (-> tptp.nat Bool)) (G_2 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o F_30) G_2) (@ (@ tptp.ord_less_eq_o (@ F_30 X_28)) (@ G_2 X_28)))))
% 0.62/1.00 (assert (forall ((X_28 tptp.x_a) (F_30 (-> tptp.x_a Bool)) (G_2 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o F_30) G_2) (@ (@ tptp.ord_less_eq_o (@ F_30 X_28)) (@ G_2 X_28)))))
% 0.62/1.00 (assert (forall ((B_58 (-> tptp.x_a Bool)) (A_110 tptp.x_a)) (@ (@ tptp.ord_less_eq_a_o B_58) (@ (@ tptp.insert_a A_110) B_58))))
% 0.62/1.00 (assert (forall ((B_58 (-> tptp.int Bool)) (A_110 tptp.int)) (@ (@ tptp.ord_less_eq_int_o B_58) (@ (@ tptp.insert_int A_110) B_58))))
% 0.62/1.00 (assert (forall ((B_58 (-> tptp.nat Bool)) (A_110 tptp.nat)) (@ (@ tptp.ord_less_eq_nat_o B_58) (@ (@ tptp.insert_nat A_110) B_58))))
% 0.62/1.00 (assert (forall ((X_27 tptp.x_a) (A_109 (-> tptp.x_a Bool)) (B_57 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a X_27) A_109)) B_57) (and (@ (@ tptp.member_a X_27) B_57) (@ (@ tptp.ord_less_eq_a_o A_109) B_57)))))
% 0.62/1.00 (assert (forall ((X_27 tptp.int) (A_109 (-> tptp.int Bool)) (B_57 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.insert_int X_27) A_109)) B_57) (and (@ (@ tptp.member_int X_27) B_57) (@ (@ tptp.ord_less_eq_int_o A_109) B_57)))))
% 0.62/1.00 (assert (forall ((X_27 tptp.nat) (A_109 (-> tptp.nat Bool)) (B_57 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.insert_nat X_27) A_109)) B_57) (and (@ (@ tptp.member_nat X_27) B_57) (@ (@ tptp.ord_less_eq_nat_o A_109) B_57)))))
% 0.62/1.00 (assert (forall ((X_27 tptp.pname) (A_109 (-> tptp.pname Bool)) (B_57 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.insert_pname X_27) A_109)) B_57) (and (@ (@ tptp.member_pname X_27) B_57) (@ (@ tptp.ord_less_eq_pname_o A_109) B_57)))))
% 0.62/1.00 (assert (forall ((B_56 (-> tptp.x_a Bool)) (X_26 tptp.x_a) (A_108 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_108))) (=> (not (@ (@ tptp.member_a X_26) A_108)) (= (@ _let_1 (@ (@ tptp.insert_a X_26) B_56)) (@ _let_1 B_56))))))
% 0.62/1.00 (assert (forall ((B_56 (-> tptp.int Bool)) (X_26 tptp.int) (A_108 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o A_108))) (=> (not (@ (@ tptp.member_int X_26) A_108)) (= (@ _let_1 (@ (@ tptp.insert_int X_26) B_56)) (@ _let_1 B_56))))))
% 0.62/1.00 (assert (forall ((B_56 (-> tptp.nat Bool)) (X_26 tptp.nat) (A_108 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_108))) (=> (not (@ (@ tptp.member_nat X_26) A_108)) (= (@ _let_1 (@ (@ tptp.insert_nat X_26) B_56)) (@ _let_1 B_56))))))
% 0.62/1.00 (assert (forall ((B_56 (-> tptp.pname Bool)) (X_26 tptp.pname) (A_108 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_108))) (=> (not (@ (@ tptp.member_pname X_26) A_108)) (= (@ _let_1 (@ (@ tptp.insert_pname X_26) B_56)) (@ _let_1 B_56))))))
% 0.62/1.00 (assert (forall ((B_55 tptp.x_a) (A_107 (-> tptp.x_a Bool)) (B_54 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_107))) (=> (@ _let_1 B_54) (@ _let_1 (@ (@ tptp.insert_a B_55) B_54))))))
% 0.62/1.00 (assert (forall ((B_55 tptp.int) (A_107 (-> tptp.int Bool)) (B_54 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o A_107))) (=> (@ _let_1 B_54) (@ _let_1 (@ (@ tptp.insert_int B_55) B_54))))))
% 0.62/1.00 (assert (forall ((B_55 tptp.nat) (A_107 (-> tptp.nat Bool)) (B_54 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_107))) (=> (@ _let_1 B_54) (@ _let_1 (@ (@ tptp.insert_nat B_55) B_54))))))
% 0.62/1.00 (assert (forall ((A_106 tptp.x_a) (C_27 (-> tptp.x_a Bool)) (D_7 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_106))) (=> (@ (@ tptp.ord_less_eq_a_o C_27) D_7) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 C_27)) (@ _let_1 D_7))))))
% 0.62/1.00 (assert (forall ((A_106 tptp.int) (C_27 (-> tptp.int Bool)) (D_7 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_106))) (=> (@ (@ tptp.ord_less_eq_int_o C_27) D_7) (@ (@ tptp.ord_less_eq_int_o (@ _let_1 C_27)) (@ _let_1 D_7))))))
% 0.62/1.00 (assert (forall ((A_106 tptp.nat) (C_27 (-> tptp.nat Bool)) (D_7 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_106))) (=> (@ (@ tptp.ord_less_eq_nat_o C_27) D_7) (@ (@ tptp.ord_less_eq_nat_o (@ _let_1 C_27)) (@ _let_1 D_7))))))
% 0.62/1.00 (assert (forall ((F_29 (-> tptp.nat tptp.int)) (A_105 tptp.nat) (B_53 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int F_29))) (= (@ _let_1 (@ (@ tptp.insert_nat A_105) B_53)) (@ (@ tptp.insert_int (@ F_29 A_105)) (@ _let_1 B_53))))))
% 0.62/1.00 (assert (forall ((F_29 (-> tptp.pname tptp.x_a)) (A_105 tptp.pname) (B_53 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_29))) (= (@ _let_1 (@ (@ tptp.insert_pname A_105) B_53)) (@ (@ tptp.insert_a (@ F_29 A_105)) (@ _let_1 B_53))))))
% 0.62/1.00 (assert (forall ((F_28 (-> tptp.nat tptp.int)) (X_25 tptp.nat) (A_104 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.image_nat_int F_28) A_104))) (=> (@ (@ tptp.member_nat X_25) A_104) (= (@ (@ tptp.insert_int (@ F_28 X_25)) _let_1) _let_1)))))
% 0.62/1.00 (assert (forall ((F_28 (-> tptp.pname tptp.x_a)) (X_25 tptp.pname) (A_104 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_a F_28) A_104))) (=> (@ (@ tptp.member_pname X_25) A_104) (= (@ (@ tptp.insert_a (@ F_28 X_25)) _let_1) _let_1)))))
% 0.62/1.00 (assert (forall ((B_52 (-> tptp.int Bool)) (F_27 (-> tptp.nat tptp.int)) (A_103 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_int_o B_52) (@ (@ tptp.image_nat_int F_27) A_103)) (exists ((AA (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o AA) A_103) (= B_52 (@ (@ tptp.image_nat_int F_27) AA)))))))
% 0.62/1.00 (assert (forall ((B_52 (-> tptp.x_a Bool)) (F_27 (-> tptp.pname tptp.x_a)) (A_103 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_a_o B_52) (@ (@ tptp.image_pname_a F_27) A_103)) (exists ((AA (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o AA) A_103) (= B_52 (@ (@ tptp.image_pname_a F_27) AA)))))))
% 0.62/1.00 (assert (forall ((F_26 (-> tptp.nat tptp.int)) (A_102 (-> tptp.nat Bool)) (B_51 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int F_26))) (=> (@ (@ tptp.ord_less_eq_nat_o A_102) B_51) (@ (@ tptp.ord_less_eq_int_o (@ _let_1 A_102)) (@ _let_1 B_51))))))
% 0.62/1.00 (assert (forall ((F_26 (-> tptp.pname tptp.x_a)) (A_102 (-> tptp.pname Bool)) (B_51 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_26))) (=> (@ (@ tptp.ord_less_eq_pname_o A_102) B_51) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 A_102)) (@ _let_1 B_51))))))
% 0.62/1.00 (assert (forall ((B_50 tptp.int) (F_25 (-> tptp.nat tptp.int)) (A_101 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_int B_50) (@ (@ tptp.image_nat_int F_25) A_101)) (not (forall ((X_1 tptp.nat)) (=> (= B_50 (@ F_25 X_1)) (not (@ (@ tptp.member_nat X_1) A_101))))))))
% 0.62/1.00 (assert (forall ((B_50 tptp.x_a) (F_25 (-> tptp.pname tptp.x_a)) (A_101 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_a B_50) (@ (@ tptp.image_pname_a F_25) A_101)) (not (forall ((X_1 tptp.pname)) (=> (= B_50 (@ F_25 X_1)) (not (@ (@ tptp.member_pname X_1) A_101))))))))
% 0.62/1.00 (assert (forall ((B_49 (-> tptp.int Bool)) (A_100 (-> tptp.int Bool))) (=> (forall ((X_1 tptp.int)) (let ((_let_1 (@ tptp.member_int X_1))) (=> (@ _let_1 A_100) (@ _let_1 B_49)))) (@ (@ tptp.ord_less_eq_int_o A_100) B_49))))
% 0.62/1.00 (assert (forall ((B_49 (-> tptp.nat Bool)) (A_100 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X_1))) (=> (@ _let_1 A_100) (@ _let_1 B_49)))) (@ (@ tptp.ord_less_eq_nat_o A_100) B_49))))
% 0.62/1.00 (assert (forall ((B_49 (-> tptp.x_a Bool)) (A_100 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (let ((_let_1 (@ tptp.member_a X_1))) (=> (@ _let_1 A_100) (@ _let_1 B_49)))) (@ (@ tptp.ord_less_eq_a_o A_100) B_49))))
% 0.62/1.00 (assert (forall ((B_49 (-> tptp.pname Bool)) (A_100 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (let ((_let_1 (@ tptp.member_pname X_1))) (=> (@ _let_1 A_100) (@ _let_1 B_49)))) (@ (@ tptp.ord_less_eq_pname_o A_100) B_49))))
% 0.62/1.00 (assert (forall ((F_24 (-> tptp.nat tptp.int)) (B_48 (-> tptp.int Bool)) (A_99 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) A_99) (@ (@ tptp.member_int (@ F_24 X_1)) B_48))) (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.image_nat_int F_24) A_99)) B_48))))
% 0.62/1.00 (assert (forall ((F_24 (-> tptp.pname tptp.x_a)) (B_48 (-> tptp.x_a Bool)) (A_99 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) A_99) (@ (@ tptp.member_a (@ F_24 X_1)) B_48))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.image_pname_a F_24) A_99)) B_48))))
% 0.62/1.00 (assert (forall ((F_23 (-> tptp.int Bool)) (G_1 (-> tptp.int Bool))) (=> (forall ((X_1 tptp.int)) (@ (@ tptp.ord_less_eq_o (@ F_23 X_1)) (@ G_1 X_1))) (@ (@ tptp.ord_less_eq_int_o F_23) G_1))))
% 0.62/1.00 (assert (forall ((F_23 (-> tptp.nat Bool)) (G_1 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (@ (@ tptp.ord_less_eq_o (@ F_23 X_1)) (@ G_1 X_1))) (@ (@ tptp.ord_less_eq_nat_o F_23) G_1))))
% 0.62/1.00 (assert (forall ((F_23 (-> tptp.x_a Bool)) (G_1 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (@ (@ tptp.ord_less_eq_o (@ F_23 X_1)) (@ G_1 X_1))) (@ (@ tptp.ord_less_eq_a_o F_23) G_1))))
% 0.62/1.00 (assert (forall ((N_2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_2) (exists ((M_1 tptp.nat)) (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_2) (@ (@ tptp.ord_less_eq_nat X_1) M_1)))))))
% 0.62/1.00 (assert (forall ((G (-> tptp.x_a Bool)) (C tptp.com)) (=> (@ tptp.wt C) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) tptp.u) (@ (@ tptp.p G) (@ (@ tptp.insert_a (@ tptp.mgt_call X_1)) tptp.bot_bot_a_o)))) (@ (@ tptp.p G) (@ (@ tptp.insert_a (@ tptp.mgt C)) tptp.bot_bot_a_o))))))
% 0.62/1.00 (assert (forall ((A_98 tptp.int) (B_47 tptp.int) (C_26 tptp.int) (D_6 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_98) B_47) (@ (@ tptp.minus_minus_int C_26) D_6)) (= (@ (@ tptp.ord_less_eq_int A_98) B_47) (@ (@ tptp.ord_less_eq_int C_26) D_6)))))
% 0.62/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.nat_case_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 0.62/1.00 (assert (forall ((A_97 tptp.int)) (not (@ (@ tptp.member_int A_97) tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((A_97 tptp.nat)) (not (@ (@ tptp.member_nat A_97) tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((A_97 tptp.x_a)) (not (@ (@ tptp.member_a A_97) tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((A_97 tptp.pname)) (not (@ (@ tptp.member_pname A_97) tptp.bot_bot_pname_o))))
% 0.62/1.00 (assert (forall ((B_46 (-> tptp.int Bool)) (A_96 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_96) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_int_o A_96) B_46)))))
% 0.62/1.00 (assert (forall ((B_46 (-> tptp.nat Bool)) (A_96 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_96) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_nat_o A_96) B_46)))))
% 0.62/1.00 (assert (forall ((B_46 (-> tptp.pname Bool)) (A_96 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_96) (@ tptp.finite_finite_pname (@ (@ tptp.minus_minus_pname_o A_96) B_46)))))
% 0.62/1.00 (assert (@ tptp.finite_finite_int tptp.bot_bot_int_o))
% 0.62/1.00 (assert (@ tptp.finite_finite_nat tptp.bot_bot_nat_o))
% 0.62/1.00 (assert (@ tptp.finite_finite_pname tptp.bot_bot_pname_o))
% 0.62/1.00 (assert (@ tptp.finite_finite_a tptp.bot_bot_a_o))
% 0.62/1.00 (assert (forall ((A_95 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o tptp.bot_bot_nat_o) A_95)))
% 0.62/1.00 (assert (forall ((A_95 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o tptp.bot_bot_int_o) A_95)))
% 0.62/1.00 (assert (forall ((A_95 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o tptp.bot_bot_a_o) A_95)))
% 0.62/1.00 (assert (forall ((A_94 tptp.int) (A_93 (-> tptp.int Bool))) (=> (= A_93 tptp.bot_bot_int_o) (not (@ (@ tptp.member_int A_94) A_93)))))
% 0.62/1.00 (assert (forall ((A_94 tptp.nat) (A_93 (-> tptp.nat Bool))) (=> (= A_93 tptp.bot_bot_nat_o) (not (@ (@ tptp.member_nat A_94) A_93)))))
% 0.62/1.00 (assert (forall ((A_94 tptp.x_a) (A_93 (-> tptp.x_a Bool))) (=> (= A_93 tptp.bot_bot_a_o) (not (@ (@ tptp.member_a A_94) A_93)))))
% 0.62/1.00 (assert (forall ((A_94 tptp.pname) (A_93 (-> tptp.pname Bool))) (=> (= A_93 tptp.bot_bot_pname_o) (not (@ (@ tptp.member_pname A_94) A_93)))))
% 0.62/1.00 (assert (forall ((P_9 (-> tptp.int Bool))) (= (= (@ tptp.collect_int P_9) tptp.bot_bot_int_o) (forall ((X_1 tptp.int)) (not (@ P_9 X_1))))))
% 0.62/1.00 (assert (forall ((P_9 (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P_9) tptp.bot_bot_nat_o) (forall ((X_1 tptp.nat)) (not (@ P_9 X_1))))))
% 0.62/1.00 (assert (forall ((P_9 (-> tptp.x_a Bool))) (= (= (@ tptp.collect_a P_9) tptp.bot_bot_a_o) (forall ((X_1 tptp.x_a)) (not (@ P_9 X_1))))))
% 0.62/1.00 (assert (forall ((A_92 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_92) A_92) tptp.bot_bot_nat_o)))
% 0.62/1.00 (assert (forall ((A_92 (-> tptp.int Bool))) (= (@ (@ tptp.minus_minus_int_o A_92) A_92) tptp.bot_bot_int_o)))
% 0.62/1.00 (assert (forall ((A_92 (-> tptp.x_a Bool))) (= (@ (@ tptp.minus_minus_a_o A_92) A_92) tptp.bot_bot_a_o)))
% 0.62/1.00 (assert (forall ((A_91 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_91) tptp.bot_bot_nat_o) A_91)))
% 0.62/1.00 (assert (forall ((A_91 (-> tptp.int Bool))) (= (@ (@ tptp.minus_minus_int_o A_91) tptp.bot_bot_int_o) A_91)))
% 0.62/1.00 (assert (forall ((A_91 (-> tptp.x_a Bool))) (= (@ (@ tptp.minus_minus_a_o A_91) tptp.bot_bot_a_o) A_91)))
% 0.62/1.00 (assert (forall ((C_25 tptp.int)) (not (@ (@ tptp.member_int C_25) tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((C_25 tptp.nat)) (not (@ (@ tptp.member_nat C_25) tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((C_25 tptp.x_a)) (not (@ (@ tptp.member_a C_25) tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((C_25 tptp.pname)) (not (@ (@ tptp.member_pname C_25) tptp.bot_bot_pname_o))))
% 0.62/1.00 (assert (forall ((P_8 (-> tptp.int Bool))) (= (= tptp.bot_bot_int_o (@ tptp.collect_int P_8)) (forall ((X_1 tptp.int)) (not (@ P_8 X_1))))))
% 0.62/1.00 (assert (forall ((P_8 (-> tptp.nat Bool))) (= (= tptp.bot_bot_nat_o (@ tptp.collect_nat P_8)) (forall ((X_1 tptp.nat)) (not (@ P_8 X_1))))))
% 0.62/1.00 (assert (forall ((P_8 (-> tptp.x_a Bool))) (= (= tptp.bot_bot_a_o (@ tptp.collect_a P_8)) (forall ((X_1 tptp.x_a)) (not (@ P_8 X_1))))))
% 0.62/1.00 (assert (forall ((A_90 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o tptp.bot_bot_nat_o) A_90) tptp.bot_bot_nat_o)))
% 0.62/1.00 (assert (forall ((A_90 (-> tptp.int Bool))) (= (@ (@ tptp.minus_minus_int_o tptp.bot_bot_int_o) A_90) tptp.bot_bot_int_o)))
% 0.62/1.00 (assert (forall ((A_90 (-> tptp.x_a Bool))) (= (@ (@ tptp.minus_minus_a_o tptp.bot_bot_a_o) A_90) tptp.bot_bot_a_o)))
% 0.62/1.00 (assert (forall ((A_89 (-> tptp.int Bool))) (= (exists ((X_1 tptp.int)) (@ (@ tptp.member_int X_1) A_89)) (not (= A_89 tptp.bot_bot_int_o)))))
% 0.62/1.00 (assert (forall ((A_89 (-> tptp.nat Bool))) (= (exists ((X_1 tptp.nat)) (@ (@ tptp.member_nat X_1) A_89)) (not (= A_89 tptp.bot_bot_nat_o)))))
% 0.62/1.00 (assert (forall ((A_89 (-> tptp.x_a Bool))) (= (exists ((X_1 tptp.x_a)) (@ (@ tptp.member_a X_1) A_89)) (not (= A_89 tptp.bot_bot_a_o)))))
% 0.62/1.00 (assert (forall ((A_89 (-> tptp.pname Bool))) (= (exists ((X_1 tptp.pname)) (@ (@ tptp.member_pname X_1) A_89)) (not (= A_89 tptp.bot_bot_pname_o)))))
% 0.62/1.00 (assert (forall ((A_88 (-> tptp.int Bool))) (= (forall ((X_1 tptp.int)) (not (@ (@ tptp.member_int X_1) A_88))) (= A_88 tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((A_88 (-> tptp.nat Bool))) (= (forall ((X_1 tptp.nat)) (not (@ (@ tptp.member_nat X_1) A_88))) (= A_88 tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((A_88 (-> tptp.x_a Bool))) (= (forall ((X_1 tptp.x_a)) (not (@ (@ tptp.member_a X_1) A_88))) (= A_88 tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((A_88 (-> tptp.pname Bool))) (= (forall ((X_1 tptp.pname)) (not (@ (@ tptp.member_pname X_1) A_88))) (= A_88 tptp.bot_bot_pname_o))))
% 0.62/1.00 (assert (forall ((X_24 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_24) tptp.bot_bot_o)))
% 0.62/1.00 (assert (forall ((X_24 tptp.int)) (= (@ tptp.bot_bot_int_o X_24) tptp.bot_bot_o)))
% 0.62/1.00 (assert (forall ((X_24 tptp.x_a)) (= (@ tptp.bot_bot_a_o X_24) tptp.bot_bot_o)))
% 0.62/1.00 (assert (= tptp.bot_bot_int_o (@ tptp.collect_int (lambda ((X_1 tptp.int)) false))))
% 0.62/1.00 (assert (= tptp.bot_bot_nat_o (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) false))))
% 0.62/1.00 (assert (= tptp.bot_bot_a_o (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) false))))
% 0.62/1.00 (assert (forall ((X_1 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_1) tptp.bot_bot_o)))
% 0.62/1.00 (assert (forall ((X_1 tptp.int)) (= (@ tptp.bot_bot_int_o X_1) tptp.bot_bot_o)))
% 0.62/1.00 (assert (forall ((X_1 tptp.x_a)) (= (@ tptp.bot_bot_a_o X_1) tptp.bot_bot_o)))
% 0.62/1.00 (assert (forall ((A_87 tptp.x_a) (A_86 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_87))) (=> (@ (@ tptp.member_a A_87) A_86) (= (@ _let_1 (@ (@ tptp.minus_minus_a_o A_86) (@ _let_1 tptp.bot_bot_a_o))) A_86)))))
% 0.62/1.00 (assert (forall ((A_87 tptp.int) (A_86 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_87))) (=> (@ (@ tptp.member_int A_87) A_86) (= (@ _let_1 (@ (@ tptp.minus_minus_int_o A_86) (@ _let_1 tptp.bot_bot_int_o))) A_86)))))
% 0.62/1.00 (assert (forall ((A_87 tptp.nat) (A_86 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_87))) (=> (@ (@ tptp.member_nat A_87) A_86) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_86) (@ _let_1 tptp.bot_bot_nat_o))) A_86)))))
% 0.62/1.00 (assert (forall ((A_87 tptp.pname) (A_86 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_87))) (=> (@ (@ tptp.member_pname A_87) A_86) (= (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_86) (@ _let_1 tptp.bot_bot_pname_o))) A_86)))))
% 0.62/1.00 (assert (forall ((X_23 tptp.x_a) (A_85 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_23))) (=> (not (@ (@ tptp.member_a X_23) A_85)) (= (@ (@ tptp.minus_minus_a_o (@ _let_1 A_85)) (@ _let_1 tptp.bot_bot_a_o)) A_85)))))
% 0.62/1.00 (assert (forall ((X_23 tptp.int) (A_85 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_23))) (=> (not (@ (@ tptp.member_int X_23) A_85)) (= (@ (@ tptp.minus_minus_int_o (@ _let_1 A_85)) (@ _let_1 tptp.bot_bot_int_o)) A_85)))))
% 0.62/1.00 (assert (forall ((X_23 tptp.nat) (A_85 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_23))) (=> (not (@ (@ tptp.member_nat X_23) A_85)) (= (@ (@ tptp.minus_minus_nat_o (@ _let_1 A_85)) (@ _let_1 tptp.bot_bot_nat_o)) A_85)))))
% 0.62/1.00 (assert (forall ((X_23 tptp.pname) (A_85 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_23))) (=> (not (@ (@ tptp.member_pname X_23) A_85)) (= (@ (@ tptp.minus_minus_pname_o (@ _let_1 A_85)) (@ _let_1 tptp.bot_bot_pname_o)) A_85)))))
% 0.62/1.00 (assert (forall ((A_84 tptp.x_a) (A_83 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_84))) (= (@ _let_1 (@ (@ tptp.minus_minus_a_o A_83) (@ _let_1 tptp.bot_bot_a_o))) (@ _let_1 A_83)))))
% 0.62/1.00 (assert (forall ((A_84 tptp.nat) (A_83 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_84))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_83) (@ _let_1 tptp.bot_bot_nat_o))) (@ _let_1 A_83)))))
% 0.62/1.00 (assert (forall ((A_84 tptp.int) (A_83 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_84))) (= (@ _let_1 (@ (@ tptp.minus_minus_int_o A_83) (@ _let_1 tptp.bot_bot_int_o))) (@ _let_1 A_83)))))
% 0.62/1.00 (assert (forall ((A_82 (-> tptp.x_a Bool)) (A_81 tptp.x_a) (B_45 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_81))) (let ((_let_2 (@ tptp.minus_minus_a_o A_82))) (= (@ _let_2 (@ _let_1 B_45)) (@ (@ tptp.minus_minus_a_o (@ _let_2 (@ _let_1 tptp.bot_bot_a_o))) B_45))))))
% 0.62/1.00 (assert (forall ((A_82 (-> tptp.nat Bool)) (A_81 tptp.nat) (B_45 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_81))) (let ((_let_2 (@ tptp.minus_minus_nat_o A_82))) (= (@ _let_2 (@ _let_1 B_45)) (@ (@ tptp.minus_minus_nat_o (@ _let_2 (@ _let_1 tptp.bot_bot_nat_o))) B_45))))))
% 0.62/1.00 (assert (forall ((A_82 (-> tptp.int Bool)) (A_81 tptp.int) (B_45 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_81))) (let ((_let_2 (@ tptp.minus_minus_int_o A_82))) (= (@ _let_2 (@ _let_1 B_45)) (@ (@ tptp.minus_minus_int_o (@ _let_2 (@ _let_1 tptp.bot_bot_int_o))) B_45))))))
% 0.62/1.00 (assert (forall ((A_80 (-> tptp.x_a Bool)) (A_79 tptp.x_a) (B_44 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_79))) (let ((_let_2 (@ tptp.minus_minus_a_o A_80))) (= (@ _let_2 (@ _let_1 B_44)) (@ (@ tptp.minus_minus_a_o (@ _let_2 B_44)) (@ _let_1 tptp.bot_bot_a_o)))))))
% 0.62/1.00 (assert (forall ((A_80 (-> tptp.nat Bool)) (A_79 tptp.nat) (B_44 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_79))) (let ((_let_2 (@ tptp.minus_minus_nat_o A_80))) (= (@ _let_2 (@ _let_1 B_44)) (@ (@ tptp.minus_minus_nat_o (@ _let_2 B_44)) (@ _let_1 tptp.bot_bot_nat_o)))))))
% 0.62/1.00 (assert (forall ((A_80 (-> tptp.int Bool)) (A_79 tptp.int) (B_44 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_79))) (let ((_let_2 (@ tptp.minus_minus_int_o A_80))) (= (@ _let_2 (@ _let_1 B_44)) (@ (@ tptp.minus_minus_int_o (@ _let_2 B_44)) (@ _let_1 tptp.bot_bot_int_o)))))))
% 0.62/1.00 (assert (forall ((A_78 (-> tptp.x_a Bool)) (X_22 tptp.x_a) (B_43 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_22))) (=> (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.minus_minus_a_o A_78) (@ _let_1 tptp.bot_bot_a_o))) B_43) (=> (@ (@ tptp.member_a X_22) A_78) (@ (@ tptp.ord_less_eq_a_o A_78) (@ _let_1 B_43)))))))
% 0.62/1.00 (assert (forall ((A_78 (-> tptp.int Bool)) (X_22 tptp.int) (B_43 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_22))) (=> (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.minus_minus_int_o A_78) (@ _let_1 tptp.bot_bot_int_o))) B_43) (=> (@ (@ tptp.member_int X_22) A_78) (@ (@ tptp.ord_less_eq_int_o A_78) (@ _let_1 B_43)))))))
% 0.62/1.00 (assert (forall ((A_78 (-> tptp.nat Bool)) (X_22 tptp.nat) (B_43 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_22))) (=> (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.minus_minus_nat_o A_78) (@ _let_1 tptp.bot_bot_nat_o))) B_43) (=> (@ (@ tptp.member_nat X_22) A_78) (@ (@ tptp.ord_less_eq_nat_o A_78) (@ _let_1 B_43)))))))
% 0.62/1.00 (assert (forall ((A_78 (-> tptp.pname Bool)) (X_22 tptp.pname) (B_43 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_22))) (=> (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.minus_minus_pname_o A_78) (@ _let_1 tptp.bot_bot_pname_o))) B_43) (=> (@ (@ tptp.member_pname X_22) A_78) (@ (@ tptp.ord_less_eq_pname_o A_78) (@ _let_1 B_43)))))))
% 0.62/1.00 (assert (forall ((A_77 (-> tptp.x_a Bool)) (X_21 tptp.x_a) (B_42 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_77))) (let ((_let_2 (@ (@ tptp.member_a X_21) A_77))) (let ((_let_3 (@ tptp.insert_a X_21))) (= (@ _let_1 (@ _let_3 B_42)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.minus_minus_a_o A_77) (@ _let_3 tptp.bot_bot_a_o))) B_42)) (=> (not _let_2) (@ _let_1 B_42)))))))))
% 0.62/1.00 (assert (forall ((A_77 (-> tptp.int Bool)) (X_21 tptp.int) (B_42 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o A_77))) (let ((_let_2 (@ (@ tptp.member_int X_21) A_77))) (let ((_let_3 (@ tptp.insert_int X_21))) (= (@ _let_1 (@ _let_3 B_42)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.minus_minus_int_o A_77) (@ _let_3 tptp.bot_bot_int_o))) B_42)) (=> (not _let_2) (@ _let_1 B_42)))))))))
% 0.62/1.00 (assert (forall ((A_77 (-> tptp.nat Bool)) (X_21 tptp.nat) (B_42 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_77))) (let ((_let_2 (@ (@ tptp.member_nat X_21) A_77))) (let ((_let_3 (@ tptp.insert_nat X_21))) (= (@ _let_1 (@ _let_3 B_42)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.minus_minus_nat_o A_77) (@ _let_3 tptp.bot_bot_nat_o))) B_42)) (=> (not _let_2) (@ _let_1 B_42)))))))))
% 0.62/1.00 (assert (forall ((A_77 (-> tptp.pname Bool)) (X_21 tptp.pname) (B_42 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_77))) (let ((_let_2 (@ (@ tptp.member_pname X_21) A_77))) (let ((_let_3 (@ tptp.insert_pname X_21))) (= (@ _let_1 (@ _let_3 B_42)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.minus_minus_pname_o A_77) (@ _let_3 tptp.bot_bot_pname_o))) B_42)) (=> (not _let_2) (@ _let_1 B_42)))))))))
% 0.62/1.00 (assert (forall ((A_76 (-> tptp.int Bool)) (B_41 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_41) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_int_o A_76) B_41)) (@ tptp.finite_finite_int A_76)))))
% 0.62/1.00 (assert (forall ((A_76 (-> tptp.nat Bool)) (B_41 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_41) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_nat_o A_76) B_41)) (@ tptp.finite_finite_nat A_76)))))
% 0.62/1.00 (assert (forall ((A_76 (-> tptp.pname Bool)) (B_41 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_41) (= (@ tptp.finite_finite_pname (@ (@ tptp.minus_minus_pname_o A_76) B_41)) (@ tptp.finite_finite_pname A_76)))))
% 0.62/1.00 (assert (forall ((A_75 (-> tptp.x_a Bool)) (X_20 tptp.x_a) (B_40 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a X_20) B_40) (= (@ (@ tptp.minus_minus_a_o (@ (@ tptp.insert_a X_20) A_75)) B_40) (@ (@ tptp.minus_minus_a_o A_75) B_40)))))
% 0.62/1.00 (assert (forall ((A_75 (-> tptp.int Bool)) (X_20 tptp.int) (B_40 (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X_20) B_40) (= (@ (@ tptp.minus_minus_int_o (@ (@ tptp.insert_int X_20) A_75)) B_40) (@ (@ tptp.minus_minus_int_o A_75) B_40)))))
% 0.62/1.00 (assert (forall ((A_75 (-> tptp.nat Bool)) (X_20 tptp.nat) (B_40 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_20) B_40) (= (@ (@ tptp.minus_minus_nat_o (@ (@ tptp.insert_nat X_20) A_75)) B_40) (@ (@ tptp.minus_minus_nat_o A_75) B_40)))))
% 0.62/1.00 (assert (forall ((A_75 (-> tptp.pname Bool)) (X_20 tptp.pname) (B_40 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_20) B_40) (= (@ (@ tptp.minus_minus_pname_o (@ (@ tptp.insert_pname X_20) A_75)) B_40) (@ (@ tptp.minus_minus_pname_o A_75) B_40)))))
% 0.62/1.00 (assert (forall ((A_74 (-> tptp.x_a Bool)) (X_19 tptp.x_a) (B_39 (-> tptp.x_a Bool))) (let ((_let_1 (@ (@ tptp.minus_minus_a_o A_74) B_39))) (let ((_let_2 (@ tptp.insert_a X_19))) (let ((_let_3 (@ (@ tptp.minus_minus_a_o (@ _let_2 A_74)) B_39))) (let ((_let_4 (@ (@ tptp.member_a X_19) B_39))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 0.62/1.00 (assert (forall ((A_74 (-> tptp.int Bool)) (X_19 tptp.int) (B_39 (-> tptp.int Bool))) (let ((_let_1 (@ (@ tptp.minus_minus_int_o A_74) B_39))) (let ((_let_2 (@ tptp.insert_int X_19))) (let ((_let_3 (@ (@ tptp.minus_minus_int_o (@ _let_2 A_74)) B_39))) (let ((_let_4 (@ (@ tptp.member_int X_19) B_39))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 0.62/1.00 (assert (forall ((A_74 (-> tptp.nat Bool)) (X_19 tptp.nat) (B_39 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.minus_minus_nat_o A_74) B_39))) (let ((_let_2 (@ tptp.insert_nat X_19))) (let ((_let_3 (@ (@ tptp.minus_minus_nat_o (@ _let_2 A_74)) B_39))) (let ((_let_4 (@ (@ tptp.member_nat X_19) B_39))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 0.62/1.00 (assert (forall ((A_74 (-> tptp.pname Bool)) (X_19 tptp.pname) (B_39 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.minus_minus_pname_o A_74) B_39))) (let ((_let_2 (@ tptp.insert_pname X_19))) (let ((_let_3 (@ (@ tptp.minus_minus_pname_o (@ _let_2 A_74)) B_39))) (let ((_let_4 (@ (@ tptp.member_pname X_19) B_39))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 0.62/1.00 (assert (forall ((C_24 (-> tptp.int Bool)) (A_73 (-> tptp.int Bool)) (B_38 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_73) B_38) (=> (@ (@ tptp.ord_less_eq_int_o B_38) C_24) (= (@ (@ tptp.minus_minus_int_o B_38) (@ (@ tptp.minus_minus_int_o C_24) A_73)) A_73)))))
% 0.62/1.00 (assert (forall ((C_24 (-> tptp.nat Bool)) (A_73 (-> tptp.nat Bool)) (B_38 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_73) B_38) (=> (@ (@ tptp.ord_less_eq_nat_o B_38) C_24) (= (@ (@ tptp.minus_minus_nat_o B_38) (@ (@ tptp.minus_minus_nat_o C_24) A_73)) A_73)))))
% 0.62/1.00 (assert (forall ((C_24 (-> tptp.x_a Bool)) (A_73 (-> tptp.x_a Bool)) (B_38 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_73) B_38) (=> (@ (@ tptp.ord_less_eq_a_o B_38) C_24) (= (@ (@ tptp.minus_minus_a_o B_38) (@ (@ tptp.minus_minus_a_o C_24) A_73)) A_73)))))
% 0.62/1.00 (assert (forall ((D_5 (-> tptp.int Bool)) (B_37 (-> tptp.int Bool)) (A_72 (-> tptp.int Bool)) (C_23 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_72) C_23) (=> (@ (@ tptp.ord_less_eq_int_o D_5) B_37) (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.minus_minus_int_o A_72) B_37)) (@ (@ tptp.minus_minus_int_o C_23) D_5))))))
% 0.62/1.00 (assert (forall ((D_5 (-> tptp.nat Bool)) (B_37 (-> tptp.nat Bool)) (A_72 (-> tptp.nat Bool)) (C_23 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_72) C_23) (=> (@ (@ tptp.ord_less_eq_nat_o D_5) B_37) (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.minus_minus_nat_o A_72) B_37)) (@ (@ tptp.minus_minus_nat_o C_23) D_5))))))
% 0.62/1.00 (assert (forall ((D_5 (-> tptp.x_a Bool)) (B_37 (-> tptp.x_a Bool)) (A_72 (-> tptp.x_a Bool)) (C_23 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_72) C_23) (=> (@ (@ tptp.ord_less_eq_a_o D_5) B_37) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.minus_minus_a_o A_72) B_37)) (@ (@ tptp.minus_minus_a_o C_23) D_5))))))
% 0.62/1.00 (assert (forall ((A_71 (-> tptp.int Bool)) (B_36 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.minus_minus_int_o A_71) B_36)) A_71)))
% 0.62/1.00 (assert (forall ((A_71 (-> tptp.nat Bool)) (B_36 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.minus_minus_nat_o A_71) B_36)) A_71)))
% 0.62/1.00 (assert (forall ((A_71 (-> tptp.x_a Bool)) (B_36 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.minus_minus_a_o A_71) B_36)) A_71)))
% 0.62/1.00 (assert (forall ((A_70 tptp.x_a) (B_35 tptp.x_a)) (=> (= (@ (@ tptp.insert_a A_70) tptp.bot_bot_a_o) (@ (@ tptp.insert_a B_35) tptp.bot_bot_a_o)) (= A_70 B_35))))
% 0.62/1.00 (assert (forall ((A_70 tptp.nat) (B_35 tptp.nat)) (=> (= (@ (@ tptp.insert_nat A_70) tptp.bot_bot_nat_o) (@ (@ tptp.insert_nat B_35) tptp.bot_bot_nat_o)) (= A_70 B_35))))
% 0.62/1.00 (assert (forall ((A_70 tptp.int) (B_35 tptp.int)) (=> (= (@ (@ tptp.insert_int A_70) tptp.bot_bot_int_o) (@ (@ tptp.insert_int B_35) tptp.bot_bot_int_o)) (= A_70 B_35))))
% 0.62/1.00 (assert (forall ((B_34 tptp.x_a) (A_69 tptp.x_a)) (=> (@ (@ tptp.member_a B_34) (@ (@ tptp.insert_a A_69) tptp.bot_bot_a_o)) (= B_34 A_69))))
% 0.62/1.00 (assert (forall ((B_34 tptp.int) (A_69 tptp.int)) (=> (@ (@ tptp.member_int B_34) (@ (@ tptp.insert_int A_69) tptp.bot_bot_int_o)) (= B_34 A_69))))
% 0.62/1.00 (assert (forall ((B_34 tptp.nat) (A_69 tptp.nat)) (=> (@ (@ tptp.member_nat B_34) (@ (@ tptp.insert_nat A_69) tptp.bot_bot_nat_o)) (= B_34 A_69))))
% 0.62/1.00 (assert (forall ((B_34 tptp.pname) (A_69 tptp.pname)) (=> (@ (@ tptp.member_pname B_34) (@ (@ tptp.insert_pname A_69) tptp.bot_bot_pname_o)) (= B_34 A_69))))
% 0.62/1.00 (assert (forall ((A_68 tptp.x_a) (B_33 tptp.x_a) (C_22 tptp.x_a) (D_4 tptp.x_a)) (= (= (@ (@ tptp.insert_a A_68) (@ (@ tptp.insert_a B_33) tptp.bot_bot_a_o)) (@ (@ tptp.insert_a C_22) (@ (@ tptp.insert_a D_4) tptp.bot_bot_a_o))) (or (and (= A_68 C_22) (= B_33 D_4)) (and (= A_68 D_4) (= B_33 C_22))))))
% 0.62/1.00 (assert (forall ((A_68 tptp.nat) (B_33 tptp.nat) (C_22 tptp.nat) (D_4 tptp.nat)) (= (= (@ (@ tptp.insert_nat A_68) (@ (@ tptp.insert_nat B_33) tptp.bot_bot_nat_o)) (@ (@ tptp.insert_nat C_22) (@ (@ tptp.insert_nat D_4) tptp.bot_bot_nat_o))) (or (and (= A_68 C_22) (= B_33 D_4)) (and (= A_68 D_4) (= B_33 C_22))))))
% 0.62/1.00 (assert (forall ((A_68 tptp.int) (B_33 tptp.int) (C_22 tptp.int) (D_4 tptp.int)) (= (= (@ (@ tptp.insert_int A_68) (@ (@ tptp.insert_int B_33) tptp.bot_bot_int_o)) (@ (@ tptp.insert_int C_22) (@ (@ tptp.insert_int D_4) tptp.bot_bot_int_o))) (or (and (= A_68 C_22) (= B_33 D_4)) (and (= A_68 D_4) (= B_33 C_22))))))
% 0.62/1.00 (assert (forall ((B_32 tptp.x_a) (A_67 tptp.x_a)) (= (@ (@ tptp.member_a B_32) (@ (@ tptp.insert_a A_67) tptp.bot_bot_a_o)) (= B_32 A_67))))
% 0.62/1.00 (assert (forall ((B_32 tptp.int) (A_67 tptp.int)) (= (@ (@ tptp.member_int B_32) (@ (@ tptp.insert_int A_67) tptp.bot_bot_int_o)) (= B_32 A_67))))
% 0.62/1.00 (assert (forall ((B_32 tptp.nat) (A_67 tptp.nat)) (= (@ (@ tptp.member_nat B_32) (@ (@ tptp.insert_nat A_67) tptp.bot_bot_nat_o)) (= B_32 A_67))))
% 0.62/1.00 (assert (forall ((B_32 tptp.pname) (A_67 tptp.pname)) (= (@ (@ tptp.member_pname B_32) (@ (@ tptp.insert_pname A_67) tptp.bot_bot_pname_o)) (= B_32 A_67))))
% 0.62/1.00 (assert (forall ((A_66 tptp.x_a) (A_65 (-> tptp.x_a Bool))) (not (= (@ (@ tptp.insert_a A_66) A_65) tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((A_66 tptp.nat) (A_65 (-> tptp.nat Bool))) (not (= (@ (@ tptp.insert_nat A_66) A_65) tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((A_66 tptp.int) (A_65 (-> tptp.int Bool))) (not (= (@ (@ tptp.insert_int A_66) A_65) tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((A_64 tptp.x_a) (A_63 (-> tptp.x_a Bool))) (not (= tptp.bot_bot_a_o (@ (@ tptp.insert_a A_64) A_63)))))
% 0.62/1.00 (assert (forall ((A_64 tptp.nat) (A_63 (-> tptp.nat Bool))) (not (= tptp.bot_bot_nat_o (@ (@ tptp.insert_nat A_64) A_63)))))
% 0.62/1.00 (assert (forall ((A_64 tptp.int) (A_63 (-> tptp.int Bool))) (not (= tptp.bot_bot_int_o (@ (@ tptp.insert_int A_64) A_63)))))
% 0.62/1.00 (assert (forall ((A_62 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o A_62) tptp.bot_bot_nat_o) (= A_62 tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((A_62 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_int_o A_62) tptp.bot_bot_int_o) (= A_62 tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((A_62 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o A_62) tptp.bot_bot_a_o) (= A_62 tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((F_22 (-> tptp.nat tptp.int)) (A_61 (-> tptp.nat Bool))) (= (= (@ (@ tptp.image_nat_int F_22) A_61) tptp.bot_bot_int_o) (= A_61 tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((F_22 (-> tptp.pname tptp.x_a)) (A_61 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_pname_a F_22) A_61) tptp.bot_bot_a_o) (= A_61 tptp.bot_bot_pname_o))))
% 0.62/1.00 (assert (forall ((F_21 (-> tptp.nat tptp.int))) (= (@ (@ tptp.image_nat_int F_21) tptp.bot_bot_nat_o) tptp.bot_bot_int_o)))
% 0.62/1.00 (assert (forall ((F_21 (-> tptp.pname tptp.x_a))) (= (@ (@ tptp.image_pname_a F_21) tptp.bot_bot_pname_o) tptp.bot_bot_a_o)))
% 0.62/1.00 (assert (forall ((F_20 (-> tptp.nat tptp.int)) (A_60 (-> tptp.nat Bool))) (= (= tptp.bot_bot_int_o (@ (@ tptp.image_nat_int F_20) A_60)) (= A_60 tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((F_20 (-> tptp.pname tptp.x_a)) (A_60 (-> tptp.pname Bool))) (= (= tptp.bot_bot_a_o (@ (@ tptp.image_pname_a F_20) A_60)) (= A_60 tptp.bot_bot_pname_o))))
% 0.62/1.00 (assert (forall ((A_59 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_59) tptp.bot_bot_nat_o) (= A_59 tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((A_59 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_59) tptp.bot_bot_int_o) (= A_59 tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((A_59 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_59) tptp.bot_bot_nat) (= A_59 tptp.bot_bot_nat))))
% 0.62/1.00 (assert (forall ((A_59 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_59) tptp.bot_bot_a_o) (= A_59 tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((A_58 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o A_58) tptp.bot_bot_nat_o) (= A_58 tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((A_58 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_int_o A_58) tptp.bot_bot_int_o) (= A_58 tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((A_58 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A_58) tptp.bot_bot_nat) (= A_58 tptp.bot_bot_nat))))
% 0.62/1.00 (assert (forall ((A_58 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o A_58) tptp.bot_bot_a_o) (= A_58 tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((A_57 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o tptp.bot_bot_nat_o) A_57)))
% 0.62/1.00 (assert (forall ((A_57 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o tptp.bot_bot_int_o) A_57)))
% 0.62/1.00 (assert (forall ((A_57 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A_57)))
% 0.62/1.00 (assert (forall ((A_57 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o tptp.bot_bot_a_o) A_57)))
% 0.62/1.00 (assert (forall ((P_7 (-> tptp.x_a Bool)) (A_56 tptp.x_a)) (let ((_let_1 (@ P_7 A_56))) (and (=> _let_1 (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= X_1 A_56) (@ P_7 X_1)))) (@ (@ tptp.insert_a A_56) tptp.bot_bot_a_o))) (=> (not _let_1) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= X_1 A_56) (@ P_7 X_1)))) tptp.bot_bot_a_o))))))
% 0.62/1.00 (assert (forall ((P_7 (-> tptp.int Bool)) (A_56 tptp.int)) (let ((_let_1 (@ P_7 A_56))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (= X_1 A_56) (@ P_7 X_1)))) (@ (@ tptp.insert_int A_56) tptp.bot_bot_int_o))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (= X_1 A_56) (@ P_7 X_1)))) tptp.bot_bot_int_o))))))
% 0.62/1.00 (assert (forall ((P_7 (-> tptp.nat Bool)) (A_56 tptp.nat)) (let ((_let_1 (@ P_7 A_56))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= X_1 A_56) (@ P_7 X_1)))) (@ (@ tptp.insert_nat A_56) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= X_1 A_56) (@ P_7 X_1)))) tptp.bot_bot_nat_o))))))
% 0.62/1.00 (assert (forall ((P_6 (-> tptp.x_a Bool)) (A_55 tptp.x_a)) (let ((_let_1 (@ P_6 A_55))) (and (=> _let_1 (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= A_55 X_1) (@ P_6 X_1)))) (@ (@ tptp.insert_a A_55) tptp.bot_bot_a_o))) (=> (not _let_1) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= A_55 X_1) (@ P_6 X_1)))) tptp.bot_bot_a_o))))))
% 0.62/1.00 (assert (forall ((P_6 (-> tptp.int Bool)) (A_55 tptp.int)) (let ((_let_1 (@ P_6 A_55))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (= A_55 X_1) (@ P_6 X_1)))) (@ (@ tptp.insert_int A_55) tptp.bot_bot_int_o))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (= A_55 X_1) (@ P_6 X_1)))) tptp.bot_bot_int_o))))))
% 0.62/1.00 (assert (forall ((P_6 (-> tptp.nat Bool)) (A_55 tptp.nat)) (let ((_let_1 (@ P_6 A_55))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= A_55 X_1) (@ P_6 X_1)))) (@ (@ tptp.insert_nat A_55) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= A_55 X_1) (@ P_6 X_1)))) tptp.bot_bot_nat_o))))))
% 0.62/1.00 (assert (forall ((A_54 tptp.x_a)) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (= X_1 A_54))) (@ (@ tptp.insert_a A_54) tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((A_54 tptp.int)) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (= X_1 A_54))) (@ (@ tptp.insert_int A_54) tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((A_54 tptp.nat)) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (= X_1 A_54))) (@ (@ tptp.insert_nat A_54) tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((A_53 tptp.x_a)) (= (@ tptp.collect_a (@ tptp.fequal_a A_53)) (@ (@ tptp.insert_a A_53) tptp.bot_bot_a_o))))
% 0.62/1.00 (assert (forall ((A_53 tptp.int)) (= (@ tptp.collect_int (@ tptp.fequal_int A_53)) (@ (@ tptp.insert_int A_53) tptp.bot_bot_int_o))))
% 0.62/1.00 (assert (forall ((A_53 tptp.nat)) (= (@ tptp.collect_nat (@ tptp.fequal_nat A_53)) (@ (@ tptp.insert_nat A_53) tptp.bot_bot_nat_o))))
% 0.62/1.00 (assert (forall ((X_18 tptp.x_a) (A_52 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_52) (=> (@ (@ tptp.member_a X_18) A_52) (= (@ tptp.suc (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_52) (@ (@ tptp.insert_a X_18) tptp.bot_bot_a_o)))) (@ tptp.finite_card_a A_52))))))
% 0.62/1.00 (assert (forall ((X_18 tptp.int) (A_52 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_52) (=> (@ (@ tptp.member_int X_18) A_52) (= (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_52) (@ (@ tptp.insert_int X_18) tptp.bot_bot_int_o)))) (@ tptp.finite_card_int A_52))))))
% 0.62/1.00 (assert (forall ((X_18 tptp.nat) (A_52 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_52) (=> (@ (@ tptp.member_nat X_18) A_52) (= (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_52) (@ (@ tptp.insert_nat X_18) tptp.bot_bot_nat_o)))) (@ tptp.finite_card_nat A_52))))))
% 0.62/1.00 (assert (forall ((X_18 tptp.pname) (A_52 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_52) (=> (@ (@ tptp.member_pname X_18) A_52) (= (@ tptp.suc (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_52) (@ (@ tptp.insert_pname X_18) tptp.bot_bot_pname_o)))) (@ tptp.finite_card_pname A_52))))))
% 0.62/1.00 (assert (forall ((X_17 tptp.x_a) (A_51 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_17))) (=> (@ tptp.finite_finite_a A_51) (= (@ tptp.finite_card_a (@ _let_1 A_51)) (@ tptp.suc (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_51) (@ _let_1 tptp.bot_bot_a_o)))))))))
% 0.62/1.00 (assert (forall ((X_17 tptp.int) (A_51 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_17))) (=> (@ tptp.finite_finite_int A_51) (= (@ tptp.finite_card_int (@ _let_1 A_51)) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_51) (@ _let_1 tptp.bot_bot_int_o)))))))))
% 0.62/1.00 (assert (forall ((X_17 tptp.nat) (A_51 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_17))) (=> (@ tptp.finite_finite_nat A_51) (= (@ tptp.finite_card_nat (@ _let_1 A_51)) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_51) (@ _let_1 tptp.bot_bot_nat_o)))))))))
% 0.62/1.00 (assert (forall ((X_17 tptp.pname) (A_51 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_17))) (=> (@ tptp.finite_finite_pname A_51) (= (@ tptp.finite_card_pname (@ _let_1 A_51)) (@ tptp.suc (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_51) (@ _let_1 tptp.bot_bot_pname_o)))))))))
% 0.62/1.00 (assert (forall ((X_16 tptp.x_a) (A_50 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_50) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_50) (@ (@ tptp.insert_a X_16) tptp.bot_bot_a_o)))) (@ tptp.finite_card_a A_50)))))
% 0.62/1.00 (assert (forall ((X_16 tptp.int) (A_50 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_50) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_50) (@ (@ tptp.insert_int X_16) tptp.bot_bot_int_o)))) (@ tptp.finite_card_int A_50)))))
% 0.62/1.00 (assert (forall ((X_16 tptp.nat) (A_50 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_50) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_50) (@ (@ tptp.insert_nat X_16) tptp.bot_bot_nat_o)))) (@ tptp.finite_card_nat A_50)))))
% 0.62/1.00 (assert (forall ((X_16 tptp.pname) (A_50 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_50) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_50) (@ (@ tptp.insert_pname X_16) tptp.bot_bot_pname_o)))) (@ tptp.finite_card_pname A_50)))))
% 0.62/1.00 (assert (forall ((A_49 (-> tptp.x_a Bool)) (A_48 tptp.x_a) (B_31 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.minus_minus_a_o A_49))) (= (@ tptp.finite_finite_a (@ _let_1 (@ (@ tptp.insert_a A_48) B_31))) (@ tptp.finite_finite_a (@ _let_1 B_31))))))
% 0.62/1.00 (assert (forall ((A_49 (-> tptp.int Bool)) (A_48 tptp.int) (B_31 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.minus_minus_int_o A_49))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A_48) B_31))) (@ tptp.finite_finite_int (@ _let_1 B_31))))))
% 0.62/1.00 (assert (forall ((A_49 (-> tptp.nat Bool)) (A_48 tptp.nat) (B_31 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.minus_minus_nat_o A_49))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A_48) B_31))) (@ tptp.finite_finite_nat (@ _let_1 B_31))))))
% 0.62/1.00 (assert (forall ((A_49 (-> tptp.pname Bool)) (A_48 tptp.pname) (B_31 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.minus_minus_pname_o A_49))) (= (@ tptp.finite_finite_pname (@ _let_1 (@ (@ tptp.insert_pname A_48) B_31))) (@ tptp.finite_finite_pname (@ _let_1 B_31))))))
% 0.62/1.00 (assert (forall ((F_19 (-> tptp.nat tptp.int)) (A_47 (-> tptp.nat Bool)) (B_30 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int F_19))) (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.minus_minus_int_o (@ _let_1 A_47)) (@ _let_1 B_30))) (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_47) B_30))))))
% 0.62/1.00 (assert (forall ((F_19 (-> tptp.pname tptp.x_a)) (A_47 (-> tptp.pname Bool)) (B_30 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_19))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.minus_minus_a_o (@ _let_1 A_47)) (@ _let_1 B_30))) (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_47) B_30))))))
% 0.62/1.00 (assert (forall ((A_46 (-> tptp.x_a Bool)) (X_15 tptp.x_a)) (let ((_let_1 (@ (@ tptp.insert_a X_15) tptp.bot_bot_a_o))) (=> (@ (@ tptp.ord_less_eq_a_o A_46) _let_1) (or (= A_46 tptp.bot_bot_a_o) (= A_46 _let_1))))))
% 0.62/1.00 (assert (forall ((A_46 (-> tptp.nat Bool)) (X_15 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X_15) tptp.bot_bot_nat_o))) (=> (@ (@ tptp.ord_less_eq_nat_o A_46) _let_1) (or (= A_46 tptp.bot_bot_nat_o) (= A_46 _let_1))))))
% 0.62/1.00 (assert (forall ((A_46 (-> tptp.int Bool)) (X_15 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X_15) tptp.bot_bot_int_o))) (=> (@ (@ tptp.ord_less_eq_int_o A_46) _let_1) (or (= A_46 tptp.bot_bot_int_o) (= A_46 _let_1))))))
% 0.62/1.00 (assert (forall ((F1 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Nat_3 tptp.nat)) (= (@ (@ (@ tptp.nat_case_nat F1) F2) (@ tptp.suc Nat_3)) (@ F2 Nat_3))))
% 0.62/1.00 (assert (forall ((F1 Bool) (F2 (-> tptp.nat Bool)) (Nat_3 tptp.nat)) (= (@ (@ (@ tptp.nat_case_o F1) F2) (@ tptp.suc Nat_3)) (@ F2 Nat_3))))
% 0.62/1.00 (assert (forall ((C_21 tptp.int) (X_14 tptp.nat) (A_45 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_14) A_45) (= (@ (@ tptp.image_nat_int (lambda ((X_1 tptp.nat)) C_21)) A_45) (@ (@ tptp.insert_int C_21) tptp.bot_bot_int_o)))))
% 0.62/1.00 (assert (forall ((C_21 tptp.x_a) (X_14 tptp.pname) (A_45 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_14) A_45) (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_21)) A_45) (@ (@ tptp.insert_a C_21) tptp.bot_bot_a_o)))))
% 0.62/1.00 (assert (forall ((C_20 tptp.int) (A_44 (-> tptp.nat Bool))) (let ((_let_1 (= A_44 tptp.bot_bot_nat_o))) (and (=> _let_1 (= (@ (@ tptp.image_nat_int (lambda ((X_1 tptp.nat)) C_20)) A_44) tptp.bot_bot_int_o)) (=> (not _let_1) (= (@ (@ tptp.image_nat_int (lambda ((X_1 tptp.nat)) C_20)) A_44) (@ (@ tptp.insert_int C_20) tptp.bot_bot_int_o)))))))
% 0.62/1.00 (assert (forall ((C_20 tptp.x_a) (A_44 (-> tptp.pname Bool))) (let ((_let_1 (= A_44 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_20)) A_44) tptp.bot_bot_a_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_20)) A_44) (@ (@ tptp.insert_a C_20) tptp.bot_bot_a_o)))))))
% 0.62/1.00 (assert (forall ((A_43 tptp.int) (B_29 tptp.int) (C_19 tptp.int) (D_3 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_43) B_29) (@ (@ tptp.minus_minus_int C_19) D_3)) (= (= A_43 B_29) (= C_19 D_3)))))
% 0.62/1.00 (assert (forall ((A_42 (-> tptp.int Bool)) (B_28 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_28) (=> (@ (@ tptp.ord_less_eq_int_o B_28) A_42) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_42) B_28)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A_42)) (@ tptp.finite_card_int B_28)))))))
% 0.62/1.00 (assert (forall ((A_42 (-> tptp.nat Bool)) (B_28 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_28) (=> (@ (@ tptp.ord_less_eq_nat_o B_28) A_42) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_42) B_28)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A_42)) (@ tptp.finite_card_nat B_28)))))))
% 0.62/1.00 (assert (forall ((A_42 (-> tptp.x_a Bool)) (B_28 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_28) (=> (@ (@ tptp.ord_less_eq_a_o B_28) A_42) (= (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_42) B_28)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a A_42)) (@ tptp.finite_card_a B_28)))))))
% 0.62/1.00 (assert (forall ((A_42 (-> tptp.pname Bool)) (B_28 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_28) (=> (@ (@ tptp.ord_less_eq_pname_o B_28) A_42) (= (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_42) B_28)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_pname A_42)) (@ tptp.finite_card_pname B_28)))))))
% 0.62/1.00 (assert (forall ((A_41 (-> tptp.int Bool)) (B_27 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_27) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A_41)) (@ tptp.finite_card_int B_27))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_41) B_27))))))
% 0.62/1.00 (assert (forall ((A_41 (-> tptp.nat Bool)) (B_27 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_27) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A_41)) (@ tptp.finite_card_nat B_27))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_41) B_27))))))
% 0.62/1.00 (assert (forall ((A_41 (-> tptp.x_a Bool)) (B_27 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_27) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a A_41)) (@ tptp.finite_card_a B_27))) (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_41) B_27))))))
% 0.62/1.00 (assert (forall ((A_41 (-> tptp.pname Bool)) (B_27 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_27) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_pname A_41)) (@ tptp.finite_card_pname B_27))) (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_41) B_27))))))
% 0.62/1.00 (assert (forall ((P_5 (-> (-> tptp.x_a Bool) Bool)) (A_40 (-> tptp.x_a Bool)) (F_18 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_18) (=> (@ (@ tptp.ord_less_eq_a_o F_18) A_40) (=> (@ P_5 tptp.bot_bot_a_o) (=> (forall ((A_37 tptp.x_a) (F_2 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_37))) (=> (@ tptp.finite_finite_a F_2) (=> (@ _let_1 A_40) (=> (not (@ _let_1 F_2)) (=> (@ P_5 F_2) (@ P_5 (@ (@ tptp.insert_a A_37) F_2)))))))) (@ P_5 F_18)))))))
% 0.62/1.00 (assert (forall ((P_5 (-> (-> tptp.int Bool) Bool)) (A_40 (-> tptp.int Bool)) (F_18 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_18) (=> (@ (@ tptp.ord_less_eq_int_o F_18) A_40) (=> (@ P_5 tptp.bot_bot_int_o) (=> (forall ((A_37 tptp.int) (F_2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_37))) (=> (@ tptp.finite_finite_int F_2) (=> (@ _let_1 A_40) (=> (not (@ _let_1 F_2)) (=> (@ P_5 F_2) (@ P_5 (@ (@ tptp.insert_int A_37) F_2)))))))) (@ P_5 F_18)))))))
% 0.62/1.00 (assert (forall ((P_5 (-> (-> tptp.nat Bool) Bool)) (A_40 (-> tptp.nat Bool)) (F_18 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_18) (=> (@ (@ tptp.ord_less_eq_nat_o F_18) A_40) (=> (@ P_5 tptp.bot_bot_nat_o) (=> (forall ((A_37 tptp.nat) (F_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_37))) (=> (@ tptp.finite_finite_nat F_2) (=> (@ _let_1 A_40) (=> (not (@ _let_1 F_2)) (=> (@ P_5 F_2) (@ P_5 (@ (@ tptp.insert_nat A_37) F_2)))))))) (@ P_5 F_18)))))))
% 0.62/1.00 (assert (forall ((P_5 (-> (-> tptp.pname Bool) Bool)) (A_40 (-> tptp.pname Bool)) (F_18 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_18) (=> (@ (@ tptp.ord_less_eq_pname_o F_18) A_40) (=> (@ P_5 tptp.bot_bot_pname_o) (=> (forall ((A_37 tptp.pname) (F_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_37))) (=> (@ tptp.finite_finite_pname F_2) (=> (@ _let_1 A_40) (=> (not (@ _let_1 F_2)) (=> (@ P_5 F_2) (@ P_5 (@ (@ tptp.insert_pname A_37) F_2)))))))) (@ P_5 F_18)))))))
% 0.62/1.00 (assert (forall ((Pn tptp.pname) (G (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a (@ tptp.mgt_call Pn)))) (=> (@ (@ tptp.p (@ _let_1 G)) (@ (@ tptp.insert_a (@ tptp.mgt (@ tptp.the_com (@ tptp.body Pn)))) tptp.bot_bot_a_o)) (@ (@ tptp.p G) (@ _let_1 tptp.bot_bot_a_o))))))
% 0.62/1.00 (assert (forall ((P_4 (-> (-> tptp.x_a Bool) Bool)) (A_39 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_39) (=> (@ P_4 A_39) (=> (forall ((A_37 tptp.x_a) (A_38 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_38) (=> (@ (@ tptp.member_a A_37) A_38) (=> (@ P_4 A_38) (@ P_4 (@ (@ tptp.minus_minus_a_o A_38) (@ (@ tptp.insert_a A_37) tptp.bot_bot_a_o))))))) (@ P_4 tptp.bot_bot_a_o))))))
% 0.62/1.00 (assert (forall ((P_4 (-> (-> tptp.int Bool) Bool)) (A_39 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_39) (=> (@ P_4 A_39) (=> (forall ((A_37 tptp.int) (A_38 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_38) (=> (@ (@ tptp.member_int A_37) A_38) (=> (@ P_4 A_38) (@ P_4 (@ (@ tptp.minus_minus_int_o A_38) (@ (@ tptp.insert_int A_37) tptp.bot_bot_int_o))))))) (@ P_4 tptp.bot_bot_int_o))))))
% 0.62/1.00 (assert (forall ((P_4 (-> (-> tptp.nat Bool) Bool)) (A_39 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_39) (=> (@ P_4 A_39) (=> (forall ((A_37 tptp.nat) (A_38 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_38) (=> (@ (@ tptp.member_nat A_37) A_38) (=> (@ P_4 A_38) (@ P_4 (@ (@ tptp.minus_minus_nat_o A_38) (@ (@ tptp.insert_nat A_37) tptp.bot_bot_nat_o))))))) (@ P_4 tptp.bot_bot_nat_o))))))
% 0.62/1.00 (assert (forall ((P_4 (-> (-> tptp.pname Bool) Bool)) (A_39 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_39) (=> (@ P_4 A_39) (=> (forall ((A_37 tptp.pname) (A_38 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_38) (=> (@ (@ tptp.member_pname A_37) A_38) (=> (@ P_4 A_38) (@ P_4 (@ (@ tptp.minus_minus_pname_o A_38) (@ (@ tptp.insert_pname A_37) tptp.bot_bot_pname_o))))))) (@ P_4 tptp.bot_bot_pname_o))))))
% 0.62/1.00 (assert (forall ((P_3 (-> (-> tptp.x_a Bool) Bool)) (F_17 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_17) (=> (@ P_3 tptp.bot_bot_a_o) (=> (forall ((X_1 tptp.x_a) (F_2 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_2) (=> (not (@ (@ tptp.member_a X_1) F_2)) (=> (@ P_3 F_2) (@ P_3 (@ (@ tptp.insert_a X_1) F_2)))))) (@ P_3 F_17))))))
% 0.62/1.00 (assert (forall ((P_3 (-> (-> tptp.int Bool) Bool)) (F_17 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_17) (=> (@ P_3 tptp.bot_bot_int_o) (=> (forall ((X_1 tptp.int) (F_2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_2) (=> (not (@ (@ tptp.member_int X_1) F_2)) (=> (@ P_3 F_2) (@ P_3 (@ (@ tptp.insert_int X_1) F_2)))))) (@ P_3 F_17))))))
% 0.62/1.00 (assert (forall ((P_3 (-> (-> tptp.nat Bool) Bool)) (F_17 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_17) (=> (@ P_3 tptp.bot_bot_nat_o) (=> (forall ((X_1 tptp.nat) (F_2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_2) (=> (not (@ (@ tptp.member_nat X_1) F_2)) (=> (@ P_3 F_2) (@ P_3 (@ (@ tptp.insert_nat X_1) F_2)))))) (@ P_3 F_17))))))
% 0.62/1.00 (assert (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (=> (@ P_3 tptp.bot_bot_pname_o) (=> (forall ((X_1 tptp.pname) (F_2 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_2) (=> (not (@ (@ tptp.member_pname X_1) F_2)) (=> (@ P_3 F_2) (@ P_3 (@ (@ tptp.insert_pname X_1) F_2)))))) (@ P_3 F_17))))))
% 0.62/1.00 (assert (forall ((A_36 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a A_36) (or (= A_36 tptp.bot_bot_a_o) (exists ((A_38 (-> tptp.x_a Bool)) (A_37 tptp.x_a)) (and (= A_36 (@ (@ tptp.insert_a A_37) A_38)) (@ tptp.finite_finite_a A_38)))))))
% 0.62/1.00 (assert (forall ((A_36 (-> tptp.int Bool))) (= (@ tptp.finite_finite_int A_36) (or (= A_36 tptp.bot_bot_int_o) (exists ((A_38 (-> tptp.int Bool)) (A_37 tptp.int)) (and (= A_36 (@ (@ tptp.insert_int A_37) A_38)) (@ tptp.finite_finite_int A_38)))))))
% 0.62/1.00 (assert (forall ((A_36 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat A_36) (or (= A_36 tptp.bot_bot_nat_o) (exists ((A_38 (-> tptp.nat Bool)) (A_37 tptp.nat)) (and (= A_36 (@ (@ tptp.insert_nat A_37) A_38)) (@ tptp.finite_finite_nat A_38)))))))
% 0.62/1.00 (assert (forall ((A_36 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname A_36) (or (= A_36 tptp.bot_bot_pname_o) (exists ((A_38 (-> tptp.pname Bool)) (A_37 tptp.pname)) (and (= A_36 (@ (@ tptp.insert_pname A_37) A_38)) (@ tptp.finite_finite_pname A_38)))))))
% 0.62/1.00 (assert (forall ((U tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) (@ F N_1))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N_1)) U)))))))
% 0.62/1.00 (assert (forall ((X_13 tptp.x_a)) (= (@ tptp.the_elem_a (@ (@ tptp.insert_a X_13) tptp.bot_bot_a_o)) X_13)))
% 0.62/1.00 (assert (forall ((X_13 tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat X_13) tptp.bot_bot_nat_o)) X_13)))
% 0.62/1.00 (assert (forall ((X_13 tptp.int)) (= (@ tptp.the_elem_int (@ (@ tptp.insert_int X_13) tptp.bot_bot_int_o)) X_13)))
% 0.62/1.00 (assert (forall ((A_35 (-> tptp.x_a Bool))) (= (not (= A_35 tptp.bot_bot_a_o)) (exists ((X_1 tptp.x_a) (B_26 (-> tptp.x_a Bool))) (and (= A_35 (@ (@ tptp.insert_a X_1) B_26)) (not (@ (@ tptp.member_a X_1) B_26)))))))
% 0.62/1.00 (assert (forall ((A_35 (-> tptp.int Bool))) (= (not (= A_35 tptp.bot_bot_int_o)) (exists ((X_1 tptp.int) (B_26 (-> tptp.int Bool))) (and (= A_35 (@ (@ tptp.insert_int X_1) B_26)) (not (@ (@ tptp.member_int X_1) B_26)))))))
% 0.62/1.00 (assert (forall ((A_35 (-> tptp.nat Bool))) (= (not (= A_35 tptp.bot_bot_nat_o)) (exists ((X_1 tptp.nat) (B_26 (-> tptp.nat Bool))) (and (= A_35 (@ (@ tptp.insert_nat X_1) B_26)) (not (@ (@ tptp.member_nat X_1) B_26)))))))
% 0.62/1.00 (assert (forall ((A_35 (-> tptp.pname Bool))) (= (not (= A_35 tptp.bot_bot_pname_o)) (exists ((X_1 tptp.pname) (B_26 (-> tptp.pname Bool))) (and (= A_35 (@ (@ tptp.insert_pname X_1) B_26)) (not (@ (@ tptp.member_pname X_1) B_26)))))))
% 0.62/1.00 (assert (forall ((Pn tptp.pname)) (=> (@ (@ tptp.member_pname Pn) tptp.u) (@ tptp.wt (@ tptp.the_com (@ tptp.body Pn))))))
% 0.62/1.00 (assert (forall ((C_18 tptp.int) (A_34 (-> tptp.int Bool)) (B_25 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_18))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int_o A_34) B_25)) (not (=> (@ _let_1 A_34) (@ _let_1 B_25)))))))
% 0.62/1.00 (assert (forall ((C_18 tptp.nat) (A_34 (-> tptp.nat Bool)) (B_25 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_18))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_34) B_25)) (not (=> (@ _let_1 A_34) (@ _let_1 B_25)))))))
% 0.62/1.00 (assert (forall ((C_18 tptp.x_a) (A_34 (-> tptp.x_a Bool)) (B_25 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_18))) (=> (@ _let_1 (@ (@ tptp.minus_minus_a_o A_34) B_25)) (not (=> (@ _let_1 A_34) (@ _let_1 B_25)))))))
% 0.62/1.00 (assert (forall ((C_18 tptp.pname) (A_34 (-> tptp.pname Bool)) (B_25 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_18))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_34) B_25)) (not (=> (@ _let_1 A_34) (@ _let_1 B_25)))))))
% 0.62/1.00 (assert (forall ((B_24 (-> tptp.int Bool)) (C_17 tptp.int) (A_33 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_17))) (=> (@ _let_1 A_33) (=> (not (@ _let_1 B_24)) (@ _let_1 (@ (@ tptp.minus_minus_int_o A_33) B_24)))))))
% 0.62/1.00 (assert (forall ((B_24 (-> tptp.nat Bool)) (C_17 tptp.nat) (A_33 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_17))) (=> (@ _let_1 A_33) (=> (not (@ _let_1 B_24)) (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_33) B_24)))))))
% 0.62/1.00 (assert (forall ((B_24 (-> tptp.x_a Bool)) (C_17 tptp.x_a) (A_33 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_17))) (=> (@ _let_1 A_33) (=> (not (@ _let_1 B_24)) (@ _let_1 (@ (@ tptp.minus_minus_a_o A_33) B_24)))))))
% 0.62/1.00 (assert (forall ((B_24 (-> tptp.pname Bool)) (C_17 tptp.pname) (A_33 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_17))) (=> (@ _let_1 A_33) (=> (not (@ _let_1 B_24)) (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_33) B_24)))))))
% 0.62/1.00 (assert (forall ((C_16 tptp.int) (A_32 (-> tptp.int Bool)) (B_23 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_16))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int_o A_32) B_23)) (not (@ _let_1 B_23))))))
% 0.62/1.00 (assert (forall ((C_16 tptp.nat) (A_32 (-> tptp.nat Bool)) (B_23 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_16))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_32) B_23)) (not (@ _let_1 B_23))))))
% 0.62/1.00 (assert (forall ((C_16 tptp.x_a) (A_32 (-> tptp.x_a Bool)) (B_23 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_16))) (=> (@ _let_1 (@ (@ tptp.minus_minus_a_o A_32) B_23)) (not (@ _let_1 B_23))))))
% 0.62/1.00 (assert (forall ((C_16 tptp.pname) (A_32 (-> tptp.pname Bool)) (B_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_16))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_32) B_23)) (not (@ _let_1 B_23))))))
% 0.62/1.00 (assert (forall ((C_15 tptp.int) (A_31 (-> tptp.int Bool)) (B_22 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_15))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int_o A_31) B_22)) (@ _let_1 A_31)))))
% 0.62/1.00 (assert (forall ((C_15 tptp.nat) (A_31 (-> tptp.nat Bool)) (B_22 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_15))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_31) B_22)) (@ _let_1 A_31)))))
% 0.62/1.00 (assert (forall ((C_15 tptp.x_a) (A_31 (-> tptp.x_a Bool)) (B_22 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_15))) (=> (@ _let_1 (@ (@ tptp.minus_minus_a_o A_31) B_22)) (@ _let_1 A_31)))))
% 0.62/1.00 (assert (forall ((C_15 tptp.pname) (A_31 (-> tptp.pname Bool)) (B_22 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_15))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_31) B_22)) (@ _let_1 A_31)))))
% 0.62/1.00 (assert (forall ((C_14 tptp.int) (A_30 (-> tptp.int Bool)) (B_21 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_14))) (= (@ _let_1 (@ (@ tptp.minus_minus_int_o A_30) B_21)) (and (@ _let_1 A_30) (not (@ _let_1 B_21)))))))
% 0.62/1.00 (assert (forall ((C_14 tptp.nat) (A_30 (-> tptp.nat Bool)) (B_21 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_14))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_30) B_21)) (and (@ _let_1 A_30) (not (@ _let_1 B_21)))))))
% 0.62/1.00 (assert (forall ((C_14 tptp.x_a) (A_30 (-> tptp.x_a Bool)) (B_21 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_14))) (= (@ _let_1 (@ (@ tptp.minus_minus_a_o A_30) B_21)) (and (@ _let_1 A_30) (not (@ _let_1 B_21)))))))
% 0.62/1.00 (assert (forall ((C_14 tptp.pname) (A_30 (-> tptp.pname Bool)) (B_21 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_14))) (= (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_30) B_21)) (and (@ _let_1 A_30) (not (@ _let_1 B_21)))))))
% 0.62/1.00 (assert (forall ((A_29 (-> tptp.int Bool)) (B_20 (-> tptp.int Bool))) (= (@ (@ tptp.minus_minus_int_o A_29) B_20) (@ tptp.collect_int (lambda ((X_1 tptp.int)) (let ((_let_1 (@ tptp.member_int X_1))) (and (@ _let_1 A_29) (not (@ _let_1 B_20)))))))))
% 0.62/1.01 (assert (forall ((A_29 (-> tptp.nat Bool)) (B_20 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_29) B_20) (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X_1))) (and (@ _let_1 A_29) (not (@ _let_1 B_20)))))))))
% 0.62/1.01 (assert (forall ((A_29 (-> tptp.x_a Bool)) (B_20 (-> tptp.x_a Bool))) (= (@ (@ tptp.minus_minus_a_o A_29) B_20) (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (let ((_let_1 (@ tptp.member_a X_1))) (and (@ _let_1 A_29) (not (@ _let_1 B_20)))))))))
% 0.62/1.01 (assert (forall ((A_29 (-> tptp.pname Bool)) (B_20 (-> tptp.pname Bool))) (= (@ (@ tptp.minus_minus_pname_o A_29) B_20) (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (let ((_let_1 (@ tptp.member_pname X_1))) (and (@ _let_1 A_29) (not (@ _let_1 B_20)))))))))
% 0.62/1.01 (assert (forall ((X_12 tptp.x_a) (A_28 (-> tptp.x_a Bool)) (F_16 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_15 (-> (-> tptp.x_a Bool) tptp.x_a))) (let ((_let_1 (@ tptp.insert_a X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_a_o A_28) (@ _let_1 tptp.bot_bot_a_o)))) (let ((_let_3 (@ F_15 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_a_o))) (=> (@ (@ tptp.finite_folding_one_a F_16) F_15) (=> (@ tptp.finite_finite_a A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_16 X_12) (@ F_15 _let_2)))))))))))))
% 0.62/1.01 (assert (forall ((X_12 tptp.int) (A_28 (-> tptp.int Bool)) (F_16 (-> tptp.int tptp.int tptp.int)) (F_15 (-> (-> tptp.int Bool) tptp.int))) (let ((_let_1 (@ tptp.insert_int X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_int_o A_28) (@ _let_1 tptp.bot_bot_int_o)))) (let ((_let_3 (@ F_15 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_int_o))) (=> (@ (@ tptp.finite1626084323ne_int F_16) F_15) (=> (@ tptp.finite_finite_int A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_16 X_12) (@ F_15 _let_2)))))))))))))
% 0.62/1.01 (assert (forall ((X_12 tptp.nat) (A_28 (-> tptp.nat Bool)) (F_16 (-> tptp.nat tptp.nat tptp.nat)) (F_15 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ tptp.insert_nat X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_nat_o A_28) (@ _let_1 tptp.bot_bot_nat_o)))) (let ((_let_3 (@ F_15 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_nat_o))) (=> (@ (@ tptp.finite988810631ne_nat F_16) F_15) (=> (@ tptp.finite_finite_nat A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_16 X_12) (@ F_15 _let_2)))))))))))))
% 0.62/1.01 (assert (forall ((X_12 tptp.pname) (A_28 (-> tptp.pname Bool)) (F_16 (-> tptp.pname tptp.pname tptp.pname)) (F_15 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ tptp.insert_pname X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_pname_o A_28) (@ _let_1 tptp.bot_bot_pname_o)))) (let ((_let_3 (@ F_15 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_pname_o))) (=> (@ (@ tptp.finite1282449217_pname F_16) F_15) (=> (@ tptp.finite_finite_pname A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_16 X_12) (@ F_15 _let_2)))))))))))))
% 0.62/1.01 (assert (forall ((X_11 tptp.x_a) (A_27 (-> tptp.x_a Bool)) (F_14 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_13 (-> (-> tptp.x_a Bool) tptp.x_a))) (let ((_let_1 (@ (@ tptp.minus_minus_a_o A_27) (@ (@ tptp.insert_a X_11) tptp.bot_bot_a_o)))) (let ((_let_2 (@ F_13 A_27))) (let ((_let_3 (= _let_1 tptp.bot_bot_a_o))) (=> (@ (@ tptp.finite_folding_one_a F_14) F_13) (=> (@ tptp.finite_finite_a A_27) (=> (@ (@ tptp.member_a X_11) A_27) (and (=> _let_3 (= _let_2 X_11)) (=> (not _let_3) (= _let_2 (@ (@ F_14 X_11) (@ F_13 _let_1)))))))))))))
% 0.62/1.01 (assert (forall ((X_11 tptp.int) (A_27 (-> tptp.int Bool)) (F_14 (-> tptp.int tptp.int tptp.int)) (F_13 (-> (-> tptp.int Bool) tptp.int))) (let ((_let_1 (@ (@ tptp.minus_minus_int_o A_27) (@ (@ tptp.insert_int X_11) tptp.bot_bot_int_o)))) (let ((_let_2 (@ F_13 A_27))) (let ((_let_3 (= _let_1 tptp.bot_bot_int_o))) (=> (@ (@ tptp.finite1626084323ne_int F_14) F_13) (=> (@ tptp.finite_finite_int A_27) (=> (@ (@ tptp.member_int X_11) A_27) (and (=> _let_3 (= _let_2 X_11)) (=> (not _let_3) (= _let_2 (@ (@ F_14 X_11) (@ F_13 _let_1)))))))))))))
% 0.62/1.01 (assert (forall ((X_11 tptp.nat) (A_27 (-> tptp.nat Bool)) (F_14 (-> tptp.nat tptp.nat tptp.nat)) (F_13 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ (@ tptp.minus_minus_nat_o A_27) (@ (@ tptp.insert_nat X_11) tptp.bot_bot_nat_o)))) (let ((_let_2 (@ F_13 A_27))) (let ((_let_3 (= _let_1 tptp.bot_bot_nat_o))) (=> (@ (@ tptp.finite988810631ne_nat F_14) F_13) (=> (@ tptp.finite_finite_nat A_27) (=> (@ (@ tptp.member_nat X_11) A_27) (and (=> _let_3 (= _let_2 X_11)) (=> (not _let_3) (= _let_2 (@ (@ F_14 X_11) (@ F_13 _let_1)))))))))))))
% 0.62/1.01 (assert (forall ((X_11 tptp.pname) (A_27 (-> tptp.pname Bool)) (F_14 (-> tptp.pname tptp.pname tptp.pname)) (F_13 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ (@ tptp.minus_minus_pname_o A_27) (@ (@ tptp.insert_pname X_11) tptp.bot_bot_pname_o)))) (let ((_let_2 (@ F_13 A_27))) (let ((_let_3 (= _let_1 tptp.bot_bot_pname_o))) (=> (@ (@ tptp.finite1282449217_pname F_14) F_13) (=> (@ tptp.finite_finite_pname A_27) (=> (@ (@ tptp.member_pname X_11) A_27) (and (=> _let_3 (= _let_2 X_11)) (=> (not _let_3) (= _let_2 (@ (@ F_14 X_11) (@ F_13 _let_1)))))))))))))
% 0.62/1.01 (assert (forall ((X_10 tptp.x_a) (A_26 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.finite_card_a A_26))) (let ((_let_2 (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_26) (@ (@ tptp.insert_a X_10) tptp.bot_bot_a_o))))) (let ((_let_3 (@ (@ tptp.member_a X_10) A_26))) (=> (@ tptp.finite_finite_a A_26) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))))
% 0.62/1.01 (assert (forall ((X_10 tptp.int) (A_26 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_card_int A_26))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_26) (@ (@ tptp.insert_int X_10) tptp.bot_bot_int_o))))) (let ((_let_3 (@ (@ tptp.member_int X_10) A_26))) (=> (@ tptp.finite_finite_int A_26) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))))
% 0.62/1.01 (assert (forall ((X_10 tptp.nat) (A_26 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_card_nat A_26))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_26) (@ (@ tptp.insert_nat X_10) tptp.bot_bot_nat_o))))) (let ((_let_3 (@ (@ tptp.member_nat X_10) A_26))) (=> (@ tptp.finite_finite_nat A_26) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))))
% 0.62/1.01 (assert (forall ((X_10 tptp.pname) (A_26 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.finite_card_pname A_26))) (let ((_let_2 (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_26) (@ (@ tptp.insert_pname X_10) tptp.bot_bot_pname_o))))) (let ((_let_3 (@ (@ tptp.member_pname X_10) A_26))) (=> (@ tptp.finite_finite_pname A_26) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))))
% 0.62/1.01 (assert (forall ((X_9 tptp.x_a) (A_25 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_25) (=> (@ (@ tptp.member_a X_9) A_25) (= (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_25) (@ (@ tptp.insert_a X_9) tptp.bot_bot_a_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a A_25)) tptp.one_one_nat))))))
% 0.62/1.01 (assert (forall ((X_9 tptp.int) (A_25 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_25) (=> (@ (@ tptp.member_int X_9) A_25) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_25) (@ (@ tptp.insert_int X_9) tptp.bot_bot_int_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A_25)) tptp.one_one_nat))))))
% 0.62/1.01 (assert (forall ((X_9 tptp.nat) (A_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_25) (=> (@ (@ tptp.member_nat X_9) A_25) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_25) (@ (@ tptp.insert_nat X_9) tptp.bot_bot_nat_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A_25)) tptp.one_one_nat))))))
% 0.62/1.01 (assert (forall ((X_9 tptp.pname) (A_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_25) (=> (@ (@ tptp.member_pname X_9) A_25) (= (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_25) (@ (@ tptp.insert_pname X_9) tptp.bot_bot_pname_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_pname A_25)) tptp.one_one_nat))))))
% 0.62/1.01 (assert (forall ((X_8 tptp.int)) (= (= tptp.one_one_int X_8) (= X_8 tptp.one_one_int))))
% 0.62/1.01 (assert (forall ((X_8 tptp.nat)) (= (= tptp.one_one_nat X_8) (= X_8 tptp.one_one_nat))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 0.62/1.01 (assert (forall ((X_7 tptp.x_a) (F_12 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_11 (-> (-> tptp.x_a Bool) tptp.x_a))) (=> (@ (@ tptp.finite_folding_one_a F_12) F_11) (= (@ F_11 (@ (@ tptp.insert_a X_7) tptp.bot_bot_a_o)) X_7))))
% 0.62/1.01 (assert (forall ((X_7 tptp.nat) (F_12 (-> tptp.nat tptp.nat tptp.nat)) (F_11 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_12) F_11) (= (@ F_11 (@ (@ tptp.insert_nat X_7) tptp.bot_bot_nat_o)) X_7))))
% 0.62/1.01 (assert (forall ((X_7 tptp.int) (F_12 (-> tptp.int tptp.int tptp.int)) (F_11 (-> (-> tptp.int Bool) tptp.int))) (=> (@ (@ tptp.finite1626084323ne_int F_12) F_11) (= (@ F_11 (@ (@ tptp.insert_int X_7) tptp.bot_bot_int_o)) X_7))))
% 0.62/1.01 (assert (forall ((B_19 (-> tptp.x_a Bool)) (A_24 tptp.x_a) (A_23 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.minus_minus_a_o A_23))) (let ((_let_2 (@ tptp.member_a A_24))) (=> (@ tptp.finite_finite_a A_23) (=> (@ _let_2 A_23) (=> (not (@ _let_2 B_19)) (= (@ tptp.finite_card_a (@ _let_1 (@ (@ tptp.insert_a A_24) B_19))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a (@ _let_1 B_19))) tptp.one_one_nat)))))))))
% 0.62/1.01 (assert (forall ((B_19 (-> tptp.int Bool)) (A_24 tptp.int) (A_23 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.minus_minus_int_o A_23))) (let ((_let_2 (@ tptp.member_int A_24))) (=> (@ tptp.finite_finite_int A_23) (=> (@ _let_2 A_23) (=> (not (@ _let_2 B_19)) (= (@ tptp.finite_card_int (@ _let_1 (@ (@ tptp.insert_int A_24) B_19))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int (@ _let_1 B_19))) tptp.one_one_nat)))))))))
% 0.62/1.01 (assert (forall ((B_19 (-> tptp.nat Bool)) (A_24 tptp.nat) (A_23 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.minus_minus_nat_o A_23))) (let ((_let_2 (@ tptp.member_nat A_24))) (=> (@ tptp.finite_finite_nat A_23) (=> (@ _let_2 A_23) (=> (not (@ _let_2 B_19)) (= (@ tptp.finite_card_nat (@ _let_1 (@ (@ tptp.insert_nat A_24) B_19))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat (@ _let_1 B_19))) tptp.one_one_nat)))))))))
% 0.62/1.01 (assert (forall ((B_19 (-> tptp.pname Bool)) (A_24 tptp.pname) (A_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.minus_minus_pname_o A_23))) (let ((_let_2 (@ tptp.member_pname A_24))) (=> (@ tptp.finite_finite_pname A_23) (=> (@ _let_2 A_23) (=> (not (@ _let_2 B_19)) (= (@ tptp.finite_card_pname (@ _let_1 (@ (@ tptp.insert_pname A_24) B_19))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_pname (@ _let_1 B_19))) tptp.one_one_nat)))))))))
% 0.62/1.01 (assert (forall ((X_6 tptp.x_a) (A_22 (-> tptp.x_a Bool)) (F_10 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_9 (-> (-> tptp.x_a Bool) tptp.x_a))) (=> (@ (@ tptp.finite_folding_one_a F_10) F_9) (=> (@ tptp.finite_finite_a A_22) (=> (not (@ (@ tptp.member_a X_6) A_22)) (=> (not (= A_22 tptp.bot_bot_a_o)) (= (@ F_9 (@ (@ tptp.insert_a X_6) A_22)) (@ (@ F_10 X_6) (@ F_9 A_22)))))))))
% 0.62/1.01 (assert (forall ((X_6 tptp.int) (A_22 (-> tptp.int Bool)) (F_10 (-> tptp.int tptp.int tptp.int)) (F_9 (-> (-> tptp.int Bool) tptp.int))) (=> (@ (@ tptp.finite1626084323ne_int F_10) F_9) (=> (@ tptp.finite_finite_int A_22) (=> (not (@ (@ tptp.member_int X_6) A_22)) (=> (not (= A_22 tptp.bot_bot_int_o)) (= (@ F_9 (@ (@ tptp.insert_int X_6) A_22)) (@ (@ F_10 X_6) (@ F_9 A_22)))))))))
% 0.62/1.01 (assert (forall ((X_6 tptp.nat) (A_22 (-> tptp.nat Bool)) (F_10 (-> tptp.nat tptp.nat tptp.nat)) (F_9 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_10) F_9) (=> (@ tptp.finite_finite_nat A_22) (=> (not (@ (@ tptp.member_nat X_6) A_22)) (=> (not (= A_22 tptp.bot_bot_nat_o)) (= (@ F_9 (@ (@ tptp.insert_nat X_6) A_22)) (@ (@ F_10 X_6) (@ F_9 A_22)))))))))
% 0.62/1.01 (assert (forall ((X_6 tptp.pname) (A_22 (-> tptp.pname Bool)) (F_10 (-> tptp.pname tptp.pname tptp.pname)) (F_9 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_10) F_9) (=> (@ tptp.finite_finite_pname A_22) (=> (not (@ (@ tptp.member_pname X_6) A_22)) (=> (not (= A_22 tptp.bot_bot_pname_o)) (= (@ F_9 (@ (@ tptp.insert_pname X_6) A_22)) (@ (@ F_10 X_6) (@ F_9 A_22)))))))))
% 0.62/1.01 (assert (forall ((A_21 (-> tptp.x_a Bool)) (F_8 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_7 (-> (-> tptp.x_a Bool) tptp.x_a))) (=> (@ (@ tptp.finite_folding_one_a F_8) F_7) (=> (@ tptp.finite_finite_a A_21) (=> (not (= A_21 tptp.bot_bot_a_o)) (=> (forall ((X_1 tptp.x_a) (Y_1 tptp.x_a)) (@ (@ tptp.member_a (@ (@ F_8 X_1) Y_1)) (@ (@ tptp.insert_a X_1) (@ (@ tptp.insert_a Y_1) tptp.bot_bot_a_o)))) (@ (@ tptp.member_a (@ F_7 A_21)) A_21)))))))
% 0.62/1.01 (assert (forall ((A_21 (-> tptp.int Bool)) (F_8 (-> tptp.int tptp.int tptp.int)) (F_7 (-> (-> tptp.int Bool) tptp.int))) (=> (@ (@ tptp.finite1626084323ne_int F_8) F_7) (=> (@ tptp.finite_finite_int A_21) (=> (not (= A_21 tptp.bot_bot_int_o)) (=> (forall ((X_1 tptp.int) (Y_1 tptp.int)) (@ (@ tptp.member_int (@ (@ F_8 X_1) Y_1)) (@ (@ tptp.insert_int X_1) (@ (@ tptp.insert_int Y_1) tptp.bot_bot_int_o)))) (@ (@ tptp.member_int (@ F_7 A_21)) A_21)))))))
% 0.62/1.01 (assert (forall ((A_21 (-> tptp.nat Bool)) (F_8 (-> tptp.nat tptp.nat tptp.nat)) (F_7 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_8) F_7) (=> (@ tptp.finite_finite_nat A_21) (=> (not (= A_21 tptp.bot_bot_nat_o)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (@ (@ tptp.member_nat (@ (@ F_8 X_1) Y_1)) (@ (@ tptp.insert_nat X_1) (@ (@ tptp.insert_nat Y_1) tptp.bot_bot_nat_o)))) (@ (@ tptp.member_nat (@ F_7 A_21)) A_21)))))))
% 0.62/1.01 (assert (forall ((A_21 (-> tptp.pname Bool)) (F_8 (-> tptp.pname tptp.pname tptp.pname)) (F_7 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_8) F_7) (=> (@ tptp.finite_finite_pname A_21) (=> (not (= A_21 tptp.bot_bot_pname_o)) (=> (forall ((X_1 tptp.pname) (Y_1 tptp.pname)) (@ (@ tptp.member_pname (@ (@ F_8 X_1) Y_1)) (@ (@ tptp.insert_pname X_1) (@ (@ tptp.insert_pname Y_1) tptp.bot_bot_pname_o)))) (@ (@ tptp.member_pname (@ F_7 A_21)) A_21)))))))
% 0.62/1.01 (assert (forall ((X_5 tptp.x_a) (A_20 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_20) (=> (@ (@ tptp.member_a X_5) A_20) (= (@ tptp.finite_card_a A_20) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_20) (@ (@ tptp.insert_a X_5) tptp.bot_bot_a_o)))))))))
% 0.62/1.01 (assert (forall ((X_5 tptp.int) (A_20 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_20) (=> (@ (@ tptp.member_int X_5) A_20) (= (@ tptp.finite_card_int A_20) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_20) (@ (@ tptp.insert_int X_5) tptp.bot_bot_int_o)))))))))
% 0.62/1.01 (assert (forall ((X_5 tptp.nat) (A_20 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_20) (=> (@ (@ tptp.member_nat X_5) A_20) (= (@ tptp.finite_card_nat A_20) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_20) (@ (@ tptp.insert_nat X_5) tptp.bot_bot_nat_o)))))))))
% 0.62/1.01 (assert (forall ((X_5 tptp.pname) (A_20 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_20) (=> (@ (@ tptp.member_pname X_5) A_20) (= (@ tptp.finite_card_pname A_20) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_20) (@ (@ tptp.insert_pname X_5) tptp.bot_bot_pname_o)))))))))
% 0.62/1.01 (assert (forall ((X_4 tptp.x_a) (A_19 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_4))) (=> (@ tptp.finite_finite_a A_19) (= (@ tptp.finite_card_a (@ _let_1 A_19)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_19) (@ _let_1 tptp.bot_bot_a_o)))))))))
% 0.62/1.01 (assert (forall ((X_4 tptp.int) (A_19 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_4))) (=> (@ tptp.finite_finite_int A_19) (= (@ tptp.finite_card_int (@ _let_1 A_19)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_19) (@ _let_1 tptp.bot_bot_int_o)))))))))
% 0.62/1.01 (assert (forall ((X_4 tptp.nat) (A_19 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_4))) (=> (@ tptp.finite_finite_nat A_19) (= (@ tptp.finite_card_nat (@ _let_1 A_19)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_19) (@ _let_1 tptp.bot_bot_nat_o)))))))))
% 0.62/1.01 (assert (forall ((X_4 tptp.pname) (A_19 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_4))) (=> (@ tptp.finite_finite_pname A_19) (= (@ tptp.finite_card_pname (@ _let_1 A_19)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_19) (@ _let_1 tptp.bot_bot_pname_o)))))))))
% 0.62/1.01 (assert (forall ((B_18 (-> tptp.int Bool)) (A_18 (-> tptp.int Bool)) (F_6 (-> tptp.int tptp.int tptp.int)) (F_5 (-> (-> tptp.int Bool) tptp.int))) (let ((_let_1 (@ F_5 A_18))) (=> (@ (@ tptp.finite1432773856em_int F_6) F_5) (=> (@ tptp.finite_finite_int A_18) (=> (not (= B_18 tptp.bot_bot_int_o)) (=> (@ (@ tptp.ord_less_eq_int_o B_18) A_18) (= (@ (@ F_6 (@ F_5 B_18)) _let_1) _let_1))))))))
% 0.62/1.01 (assert (forall ((B_18 (-> tptp.nat Bool)) (A_18 (-> tptp.nat Bool)) (F_6 (-> tptp.nat tptp.nat tptp.nat)) (F_5 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ F_5 A_18))) (=> (@ (@ tptp.finite795500164em_nat F_6) F_5) (=> (@ tptp.finite_finite_nat A_18) (=> (not (= B_18 tptp.bot_bot_nat_o)) (=> (@ (@ tptp.ord_less_eq_nat_o B_18) A_18) (= (@ (@ F_6 (@ F_5 B_18)) _let_1) _let_1))))))))
% 0.62/1.01 (assert (forall ((B_18 (-> tptp.pname Bool)) (A_18 (-> tptp.pname Bool)) (F_6 (-> tptp.pname tptp.pname tptp.pname)) (F_5 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ F_5 A_18))) (=> (@ (@ tptp.finite89670078_pname F_6) F_5) (=> (@ tptp.finite_finite_pname A_18) (=> (not (= B_18 tptp.bot_bot_pname_o)) (=> (@ (@ tptp.ord_less_eq_pname_o B_18) A_18) (= (@ (@ F_6 (@ F_5 B_18)) _let_1) _let_1))))))))
% 0.62/1.01 (assert (forall ((B_18 (-> tptp.x_a Bool)) (A_18 (-> tptp.x_a Bool)) (F_6 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_5 (-> (-> tptp.x_a Bool) tptp.x_a))) (let ((_let_1 (@ F_5 A_18))) (=> (@ (@ tptp.finite1819937229idem_a F_6) F_5) (=> (@ tptp.finite_finite_a A_18) (=> (not (= B_18 tptp.bot_bot_a_o)) (=> (@ (@ tptp.ord_less_eq_a_o B_18) A_18) (= (@ (@ F_6 (@ F_5 B_18)) _let_1) _let_1))))))))
% 0.62/1.01 (assert (forall ((X_3 tptp.x_a) (A_17 (-> tptp.x_a Bool)) (F_4 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_3 (-> (-> tptp.x_a Bool) tptp.x_a))) (=> (@ (@ tptp.finite1819937229idem_a F_4) F_3) (=> (@ tptp.finite_finite_a A_17) (=> (not (= A_17 tptp.bot_bot_a_o)) (= (@ F_3 (@ (@ tptp.insert_a X_3) A_17)) (@ (@ F_4 X_3) (@ F_3 A_17))))))))
% 0.62/1.01 (assert (forall ((X_3 tptp.int) (A_17 (-> tptp.int Bool)) (F_4 (-> tptp.int tptp.int tptp.int)) (F_3 (-> (-> tptp.int Bool) tptp.int))) (=> (@ (@ tptp.finite1432773856em_int F_4) F_3) (=> (@ tptp.finite_finite_int A_17) (=> (not (= A_17 tptp.bot_bot_int_o)) (= (@ F_3 (@ (@ tptp.insert_int X_3) A_17)) (@ (@ F_4 X_3) (@ F_3 A_17))))))))
% 0.62/1.01 (assert (forall ((X_3 tptp.nat) (A_17 (-> tptp.nat Bool)) (F_4 (-> tptp.nat tptp.nat tptp.nat)) (F_3 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite795500164em_nat F_4) F_3) (=> (@ tptp.finite_finite_nat A_17) (=> (not (= A_17 tptp.bot_bot_nat_o)) (= (@ F_3 (@ (@ tptp.insert_nat X_3) A_17)) (@ (@ F_4 X_3) (@ F_3 A_17))))))))
% 0.62/1.01 (assert (forall ((X_3 tptp.pname) (A_17 (-> tptp.pname Bool)) (F_4 (-> tptp.pname tptp.pname tptp.pname)) (F_3 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_4) F_3) (=> (@ tptp.finite_finite_pname A_17) (=> (not (= A_17 tptp.bot_bot_pname_o)) (= (@ F_3 (@ (@ tptp.insert_pname X_3) A_17)) (@ (@ F_4 X_3) (@ F_3 A_17))))))))
% 0.62/1.01 (assert (forall ((P_2 (-> (-> tptp.x_a Bool) Bool)) (F_1 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_1) (=> (not (= F_1 tptp.bot_bot_a_o)) (=> (forall ((X_1 tptp.x_a)) (@ P_2 (@ (@ tptp.insert_a X_1) tptp.bot_bot_a_o))) (=> (forall ((X_1 tptp.x_a) (F_2 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_2) (=> (not (= F_2 tptp.bot_bot_a_o)) (=> (not (@ (@ tptp.member_a X_1) F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_a X_1) F_2))))))) (@ P_2 F_1)))))))
% 0.62/1.01 (assert (forall ((P_2 (-> (-> tptp.int Bool) Bool)) (F_1 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_1) (=> (not (= F_1 tptp.bot_bot_int_o)) (=> (forall ((X_1 tptp.int)) (@ P_2 (@ (@ tptp.insert_int X_1) tptp.bot_bot_int_o))) (=> (forall ((X_1 tptp.int) (F_2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_2) (=> (not (= F_2 tptp.bot_bot_int_o)) (=> (not (@ (@ tptp.member_int X_1) F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_int X_1) F_2))))))) (@ P_2 F_1)))))))
% 0.62/1.01 (assert (forall ((P_2 (-> (-> tptp.nat Bool) Bool)) (F_1 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_1) (=> (not (= F_1 tptp.bot_bot_nat_o)) (=> (forall ((X_1 tptp.nat)) (@ P_2 (@ (@ tptp.insert_nat X_1) tptp.bot_bot_nat_o))) (=> (forall ((X_1 tptp.nat) (F_2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_2) (=> (not (= F_2 tptp.bot_bot_nat_o)) (=> (not (@ (@ tptp.member_nat X_1) F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_nat X_1) F_2))))))) (@ P_2 F_1)))))))
% 0.62/1.01 (assert (forall ((P_2 (-> (-> tptp.pname Bool) Bool)) (F_1 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_1) (=> (not (= F_1 tptp.bot_bot_pname_o)) (=> (forall ((X_1 tptp.pname)) (@ P_2 (@ (@ tptp.insert_pname X_1) tptp.bot_bot_pname_o))) (=> (forall ((X_1 tptp.pname) (F_2 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_2) (=> (not (= F_2 tptp.bot_bot_pname_o)) (=> (not (@ (@ tptp.member_pname X_1) F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_pname X_1) F_2))))))) (@ P_2 F_1)))))))
% 0.62/1.01 (assert (forall ((X_2 (-> tptp.x_a Bool))) (= (@ tptp.the_elem_a X_2) (@ tptp.the_a (lambda ((X_1 tptp.x_a)) (= X_2 (@ (@ tptp.insert_a X_1) tptp.bot_bot_a_o)))))))
% 0.62/1.01 (assert (forall ((X_2 (-> tptp.nat Bool))) (= (@ tptp.the_elem_nat X_2) (@ tptp.the_nat (lambda ((X_1 tptp.nat)) (= X_2 (@ (@ tptp.insert_nat X_1) tptp.bot_bot_nat_o)))))))
% 0.62/1.01 (assert (forall ((X_2 (-> tptp.int Bool))) (= (@ tptp.the_elem_int X_2) (@ tptp.the_int (lambda ((X_1 tptp.int)) (= X_2 (@ (@ tptp.insert_int X_1) tptp.bot_bot_int_o)))))))
% 0.62/1.01 (assert (forall ((A_16 tptp.int) (B_17 tptp.int) (C_13 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_16))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_17)) C_13) (@ _let_1 (@ (@ tptp.plus_plus_int B_17) C_13))))))
% 0.62/1.01 (assert (forall ((A_16 tptp.nat) (B_17 tptp.nat) (C_13 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_16))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_17)) C_13) (@ _let_1 (@ (@ tptp.plus_plus_nat B_17) C_13))))))
% 0.62/1.01 (assert (forall ((A_15 tptp.int) (B_16 tptp.int) (C_12 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_15))) (= (= (@ _let_1 B_16) (@ _let_1 C_12)) (= B_16 C_12)))))
% 0.62/1.01 (assert (forall ((A_15 tptp.nat) (B_16 tptp.nat) (C_12 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_15))) (= (= (@ _let_1 B_16) (@ _let_1 C_12)) (= B_16 C_12)))))
% 0.62/1.01 (assert (forall ((B_15 tptp.int) (A_14 tptp.int) (C_11 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B_15) A_14) (@ (@ tptp.plus_plus_int C_11) A_14)) (= B_15 C_11))))
% 0.62/1.01 (assert (forall ((B_15 tptp.nat) (A_14 tptp.nat) (C_11 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B_15) A_14) (@ (@ tptp.plus_plus_nat C_11) A_14)) (= B_15 C_11))))
% 0.62/1.01 (assert (forall ((A_13 tptp.int) (B_14 tptp.int) (C_10 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_13))) (=> (= (@ _let_1 B_14) (@ _let_1 C_10)) (= B_14 C_10)))))
% 0.62/1.01 (assert (forall ((A_13 tptp.nat) (B_14 tptp.nat) (C_10 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_13))) (=> (= (@ _let_1 B_14) (@ _let_1 C_10)) (= B_14 C_10)))))
% 0.62/1.01 (assert (forall ((A_12 tptp.int) (B_13 tptp.int) (C_9 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_12))) (=> (= (@ _let_1 B_13) (@ _let_1 C_9)) (= B_13 C_9)))))
% 0.62/1.01 (assert (forall ((A_12 tptp.nat) (B_13 tptp.nat) (C_9 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_12))) (=> (= (@ _let_1 B_13) (@ _let_1 C_9)) (= B_13 C_9)))))
% 0.62/1.01 (assert (forall ((B_12 tptp.int) (A_11 tptp.int) (C_8 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B_12) A_11) (@ (@ tptp.plus_plus_int C_8) A_11)) (= B_12 C_8))))
% 0.62/1.01 (assert (forall ((B_12 tptp.nat) (A_11 tptp.nat) (C_8 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B_12) A_11) (@ (@ tptp.plus_plus_nat C_8) A_11)) (= B_12 C_8))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) K))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K) (@ (@ tptp.plus_plus_nat N) K)) (= M N))))
% 0.62/1.01 (assert (forall ((A_10 tptp.int) (C_7 tptp.int) (B_11 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_10) C_7)) (@ (@ tptp.plus_plus_int B_11) C_7)) (@ (@ tptp.ord_less_eq_int A_10) B_11))))
% 0.62/1.01 (assert (forall ((A_10 tptp.nat) (C_7 tptp.nat) (B_11 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_10) C_7)) (@ (@ tptp.plus_plus_nat B_11) C_7)) (@ (@ tptp.ord_less_eq_nat A_10) B_11))))
% 0.62/1.01 (assert (forall ((C_6 tptp.int) (A_9 tptp.int) (B_10 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_6))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A_9)) (@ _let_1 B_10)) (@ (@ tptp.ord_less_eq_int A_9) B_10)))))
% 0.62/1.01 (assert (forall ((C_6 tptp.nat) (A_9 tptp.nat) (B_10 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_6))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_9)) (@ _let_1 B_10)) (@ (@ tptp.ord_less_eq_nat A_9) B_10)))))
% 0.62/1.01 (assert (forall ((C_5 tptp.int) (A_8 tptp.int) (B_9 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_8) B_9) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_8) C_5)) (@ (@ tptp.plus_plus_int B_9) C_5)))))
% 0.62/1.01 (assert (forall ((C_5 tptp.nat) (A_8 tptp.nat) (B_9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_8) B_9) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_8) C_5)) (@ (@ tptp.plus_plus_nat B_9) C_5)))))
% 0.62/1.01 (assert (forall ((C_4 tptp.int) (A_7 tptp.int) (B_8 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_4))) (=> (@ (@ tptp.ord_less_eq_int A_7) B_8) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_7)) (@ _let_1 B_8))))))
% 0.62/1.01 (assert (forall ((C_4 tptp.nat) (A_7 tptp.nat) (B_8 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_4))) (=> (@ (@ tptp.ord_less_eq_nat A_7) B_8) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_7)) (@ _let_1 B_8))))))
% 0.62/1.01 (assert (forall ((C_3 tptp.int) (D_2 tptp.int) (A_6 tptp.int) (B_7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_6) B_7) (=> (@ (@ tptp.ord_less_eq_int C_3) D_2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_6) C_3)) (@ (@ tptp.plus_plus_int B_7) D_2))))))
% 0.62/1.01 (assert (forall ((C_3 tptp.nat) (D_2 tptp.nat) (A_6 tptp.nat) (B_7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_6) B_7) (=> (@ (@ tptp.ord_less_eq_nat C_3) D_2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_6) C_3)) (@ (@ tptp.plus_plus_nat B_7) D_2))))))
% 0.62/1.01 (assert (forall ((A_5 tptp.int) (C_2 tptp.int) (B_6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_5) C_2)) (@ (@ tptp.plus_plus_int B_6) C_2)) (@ (@ tptp.ord_less_eq_int A_5) B_6))))
% 0.62/1.01 (assert (forall ((A_5 tptp.nat) (C_2 tptp.nat) (B_6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_5) C_2)) (@ (@ tptp.plus_plus_nat B_6) C_2)) (@ (@ tptp.ord_less_eq_nat A_5) B_6))))
% 0.62/1.01 (assert (forall ((C_1 tptp.int) (A_4 tptp.int) (B_5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_1))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A_4)) (@ _let_1 B_5)) (@ (@ tptp.ord_less_eq_int A_4) B_5)))))
% 0.62/1.01 (assert (forall ((C_1 tptp.nat) (A_4 tptp.nat) (B_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_1))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_4)) (@ _let_1 B_5)) (@ (@ tptp.ord_less_eq_nat A_4) B_5)))))
% 0.62/1.01 (assert (forall ((A_3 tptp.int) (B_4 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_3) B_4)) B_4) A_3)))
% 0.62/1.01 (assert (forall ((A_2 tptp.int) (B_3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_2) B_3)) B_3) A_2)))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M) K_1))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I_1) K)) J)))))
% 0.62/1.01 (assert (forall ((J tptp.nat) (K tptp.nat) (I_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I_1) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I_1) K)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) K)))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) J)))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) N)) N) M))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (= (@ (@ tptp.minus_minus_nat J) I_1) K) (= J (@ (@ tptp.plus_plus_nat K) I_1))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I_1)) K)))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I_1)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I_1)))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ tptp.suc N) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) N))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ tptp.suc N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat M) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ tptp.suc J))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) M) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) M))))))
% 0.62/1.01 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.62/1.01 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 0.62/1.01 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_1 tptp.nat)) (@ (@ tptp.ord_less_nat N_1) K))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.62/1.01 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.62/1.01 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ P N) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N) _let_1) (=> (=> (= M N) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N) M) _let_1) _let_1))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I_1)) K)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J)) I_1))))
% 0.62/1.01 (assert (forall ((J tptp.nat) (I_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I_1)) I_1))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J)) K) (@ (@ tptp.ord_less_nat I_1) K))))
% 0.62/1.01 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.62/1.01 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (not (= M N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 0.62/1.01 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 0.62/1.01 (assert (forall ((N_2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_2) (exists ((M_1 tptp.nat)) (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_2) (@ (@ tptp.ord_less_nat X_1) M_1)))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_nat I) N)))) N)))
% 0.62/1.01 (assert (forall ((P (-> tptp.nat Bool)) (I_1 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ P K_1) (@ (@ tptp.ord_less_nat K_1) I_1)))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I_1) (@ tptp.suc (@ (@ tptp.plus_plus_nat I_1) M)))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I_1) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I_1)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_1)))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) J))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 0.62/1.01 (assert (forall ((C tptp.nat) (A_1 tptp.nat) (B_2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_1) B_2) (=> (@ (@ tptp.ord_less_eq_nat C) A_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A_1) C)) (@ (@ tptp.minus_minus_nat B_2) C))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 0.62/1.01 (assert (forall ((X_1 tptp.nat)) (= (@ tptp.ord_less_nat X_1) (@ tptp.ord_less_eq_nat (@ tptp.suc X_1)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_1) N_1) (@ (@ tptp.ord_less_nat (@ F M_1)) (@ F N_1)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.nat Bool)) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ P J) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ P (@ tptp.suc I)) (@ P I)))) (@ P I_1))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_1)))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (N_2 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_2) (@ (@ tptp.ord_less_nat X_1) N))) (@ tptp.finite_finite_nat N_2))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_1) (@ (@ tptp.ord_less_nat (@ F I)) (@ F J_1)))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ F I_1)) (@ F J))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) K) (=> (not (= K (@ tptp.suc I_1))) (not (forall ((J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (not (= K (@ tptp.suc J_1))))))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I_1)) K) (not (forall ((J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (not (= K (@ tptp.suc J_1)))))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.62/1.01 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.62/1.01 (assert (forall ((Nat_2 tptp.nat)) (not (= (@ tptp.suc Nat_2) tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((Nat_1 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat_1)))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M_1 tptp.nat)) (= N (@ tptp.suc M_1))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J_1 tptp.nat)) (and (= M (@ tptp.suc J_1)) (@ (@ tptp.ord_less_nat J_1) N)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 0.62/1.01 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.nat_case_nat tptp.zero_zero_nat) (lambda ((K_1 tptp.nat)) K_1)) (@ _let_1 N))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I_1))) N))))
% 0.62/1.01 (assert (forall ((P (-> tptp.nat Bool)) (A_1 tptp.nat) (B_2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A_1) B_2)) (and (=> (@ (@ tptp.ord_less_nat A_1) B_2) (@ P tptp.zero_zero_nat)) (forall ((D_1 tptp.nat)) (=> (= A_1 (@ (@ tptp.plus_plus_nat B_2) D_1)) (@ P D_1)))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.nat Bool)) (A_1 tptp.nat) (B_2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A_1) B_2)) (not (or (and (@ (@ tptp.ord_less_nat A_1) B_2) (not (@ P tptp.zero_zero_nat))) (exists ((D_1 tptp.nat)) (and (= A_1 (@ (@ tptp.plus_plus_nat B_2) D_1)) (not (@ P D_1)))))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (M_2 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M_2) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K_1)) M_2) (@ (@ tptp.ord_less_nat K_1) I_1)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat K_1) M_2) (@ (@ tptp.ord_less_nat K_1) (@ tptp.suc I_1))))))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (M_2 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M_2) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat K_1) M_2) (@ (@ tptp.ord_less_nat K_1) (@ tptp.suc I_1)))))) tptp.zero_zero_nat)))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (M_2 (-> tptp.nat Bool))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M_2)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K_1)) M_2) (@ (@ tptp.ord_less_nat K_1) I_1))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat K_1) M_2) (@ (@ tptp.ord_less_nat K_1) (@ tptp.suc I_1))))))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N)) (=> (not _let_2) (= _let_1 (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (@ P N) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat K_1) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K_1) (not (@ P I)))) (@ P (@ (@ tptp.plus_plus_nat K_1) tptp.one_one_nat))))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (@ P N) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K_1) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K_1) (not (@ P I)))) (@ P K_1)))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (= (@ (@ tptp.plus_plus_nat I_1) K_1) J))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M_1 tptp.nat)) (= N (@ tptp.suc M_1))))))
% 0.62/1.01 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat tptp.nat)) (not (= Y (@ tptp.suc Nat))))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N_1 tptp.nat)) (=> (@ P (@ tptp.suc N_1)) (@ P N_1))) (@ P tptp.zero_zero_nat)))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M_1 tptp.nat)) (= N (@ tptp.suc M_1))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N_1 tptp.nat)) (=> (@ P N_1) (@ P (@ tptp.suc N_1)))) (@ P N)))))
% 0.62/1.01 (assert (forall ((V tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 (@ tptp.suc (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat)))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) L))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I_1)) (@ _let_1 J))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) K)))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I_1)) (@ _let_1 J)))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) K))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M) N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))))
% 0.62/1.01 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat M) N) (@ (@ tptp.times_times_nat N) M))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ (@ tptp.times_times_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.times_times_nat N) K))))))
% 0.62/1.01 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_int K) L))))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) Z) Z)))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) tptp.one_one_int) Z)))
% 0.62/1.01 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))))
% 0.62/1.01 (assert (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V) W)))))
% 0.62/1.01 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z1))) (= (@ (@ tptp.times_times_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_int Z2) Z3))))))
% 0.62/1.01 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.62/1.01 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z2)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z2)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z2))))))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z2)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z2))))))
% 0.62/1.01 (assert (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V) W)))))
% 0.62/1.01 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z2)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))))
% 0.62/1.01 (assert (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I_1) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J)))))))
% 0.62/1.01 (assert (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int Z) tptp.zero_zero_int) Z)))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) Z) Z)))
% 0.62/1.01 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 0.62/1.01 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int K) L) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int K) L)) tptp.zero_zero_int))))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 0.62/1.01 (assert (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I_1) J) (@ (@ tptp.ord_less_eq_int (@ _let_1 I_1)) (@ _let_1 J))))))
% 0.62/1.01 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int Z1))) (= (@ (@ tptp.plus_plus_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.plus_plus_int Z2) Z3))))))
% 0.62/1.01 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.plus_plus_int Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.62/1.01 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int Z) W) (@ (@ tptp.plus_plus_int W) Z))))
% 0.62/1.01 (assert (forall ((W tptp.int)) (@ (@ tptp.ord_less_eq_int W) W)))
% 0.62/1.01 (assert (forall ((Z tptp.int) (W tptp.int)) (or (@ (@ tptp.ord_less_eq_int Z) W) (@ (@ tptp.ord_less_eq_int W) Z))))
% 0.62/1.01 (assert (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_int J) K) (@ _let_1 K))))))
% 0.62/1.01 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) W) (=> (@ (@ tptp.ord_less_eq_int W) Z) (= Z W)))))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 0.62/1.01 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 0.62/1.01 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.ord_less_int Z) W) (and (@ (@ tptp.ord_less_eq_int Z) W) (not (= Z W))))))
% 0.62/1.01 (assert (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) J) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I_1) K)) (@ (@ tptp.plus_plus_int J) K)))))
% 0.62/1.01 (assert (forall ((Z_3 tptp.int) (Z tptp.int) (W_1 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int W_1) W) (=> (@ (@ tptp.ord_less_eq_int Z_3) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int W_1) Z_3)) (@ (@ tptp.plus_plus_int W) Z))))))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I_1) J)) U)) K))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 0.62/1.01 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))))
% 0.62/1.01 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))))
% 0.62/1.01 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M) N)))))
% 0.62/1.01 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))))
% 0.62/1.01 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))))
% 0.62/1.01 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))))
% 0.62/1.01 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))))
% 0.62/1.01 (assert (forall ((B_2 tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (B_1 tptp.int) (Q tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q)) R))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_2) Q_1)) R_1) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R_1) B_2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (=> (@ (@ tptp.ord_less_eq_int B_1) B_2) (@ (@ tptp.ord_less_eq_int Q) Q_1))))))))))
% 0.62/1.01 (assert (forall ((B_2 tptp.int) (Q tptp.int) (R tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B_2))) (let ((_let_2 (@ tptp.times_times_int B_2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q)) R)) (@ (@ tptp.plus_plus_int (@ _let_2 Q_1)) R_1)) (=> (@ (@ tptp.ord_less_eq_int R_1) tptp.zero_zero_int) (=> (@ _let_1 R_1) (=> (@ _let_1 R) (@ (@ tptp.ord_less_eq_int Q_1) Q)))))))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ tptp.number_number_of_int K) K)))
% 0.62/1.01 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 0.62/1.01 (assert (forall ((R_1 tptp.int) (Q_1 tptp.int) (A_1 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_1) (=> (= A_1 (@ (@ tptp.plus_plus_int R_1) (@ (@ tptp.times_times_int A_1) Q_1))) (=> (@ (@ tptp.ord_less_int R_1) A_1) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Q_1))))))
% 0.62/1.01 (assert (forall ((R_1 tptp.int) (Q_1 tptp.int) (A_1 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_1) (=> (= A_1 (@ (@ tptp.plus_plus_int R_1) (@ (@ tptp.times_times_int A_1) Q_1))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_1) (@ (@ tptp.ord_less_eq_int Q_1) tptp.one_one_int))))))
% 0.62/1.01 (assert (forall ((B_1 tptp.int) (Q tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q)) R)) (=> (@ (@ tptp.ord_less_int R) B_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (@ _let_1 Q)))))))
% 0.62/1.01 (assert (forall ((B_1 tptp.int) (Q tptp.int) (R tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q)) R)) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (@ (@ tptp.ord_less_eq_int Q) tptp.zero_zero_int))))))
% 0.62/1.01 (assert (forall ((B_2 tptp.int) (Q tptp.int) (R tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B_2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q)) R)) (@ (@ tptp.plus_plus_int (@ _let_1 Q_1)) R_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B_2) (=> (@ (@ tptp.ord_less_int R_1) B_2) (@ (@ tptp.ord_less_eq_int Q) Q_1))))))))
% 0.62/1.01 (assert (forall ((B_2 tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (B_1 tptp.int) (Q tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q)) R))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_2) Q_1)) R_1) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R) B_1) (=> (@ _let_1 R_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (=> (@ (@ tptp.ord_less_eq_int B_1) B_2) (@ (@ tptp.ord_less_eq_int Q_1) Q)))))))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool)) (I_1 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P I) (@ P (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P I_1))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool)) (I_1 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I_1) K) (=> (@ P K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P I) (@ P (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P I_1))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I_1) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P I) (@ P (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P I_1))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I_1) (=> (@ P K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P I) (@ P (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P I_1))))))
% 0.62/1.01 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.times_times_int X) Y)))))))
% 0.62/1.01 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 0.62/1.01 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_int X) Y)))))))
% 0.62/1.01 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 0.62/1.01 (assert (forall ((P_1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (= (@ P X_1) (@ P_1 X_1)))) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1)))) (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P_1 X_1))))))))
% 0.62/1.01 (assert (forall ((K tptp.int) (P (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.minus_minus_int X_1) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.minus_minus_int X_1) (@ (@ tptp.times_times_int K) D))))))))))
% 0.62/1.01 (assert (forall ((P_1 Bool) (P Bool) (X tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (=> (=> _let_1 (= P P_1)) (= (and _let_1 P) (and _let_1 P_1))))))
% 0.62/1.01 (assert (forall ((P_1 Bool) (P Bool) (X tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (=> (=> _let_1 (= P P_1)) (= (=> _let_1 P) (=> _let_1 P_1))))))
% 0.62/1.01 (assert (forall ((K tptp.int) (P (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.plus_plus_int X_1) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.plus_plus_int X_1) (@ (@ tptp.times_times_int K) D))))))))))
% 0.62/1.01 (assert (forall ((I_1 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P I) (@ P (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P I) (@ P (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P I_1))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool)) (P1 (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int) (K_1 tptp.int)) (= (@ P1 X_1) (@ P1 (@ (@ tptp.minus_minus_int X_1) (@ (@ tptp.times_times_int K_1) D))))) (=> (exists ((Z_2 tptp.int)) (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_int X_1) Z_2) (= (@ P X_1) (@ P1 X_1))))) (=> (@ tptp.ex P1) (@ tptp.ex P)))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool)) (P_1 (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int) (K_1 tptp.int)) (= (@ P_1 X_1) (@ P_1 (@ (@ tptp.minus_minus_int X_1) (@ (@ tptp.times_times_int K_1) D))))) (=> (exists ((Z_2 tptp.int)) (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_int Z_2) X_1) (= (@ P X_1) (@ P_1 X_1))))) (=> (@ tptp.ex P_1) (@ tptp.ex P)))))))
% 0.62/1.01 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nat_tsub X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int Y) X))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_int X) Y))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N))))
% 0.62/1.01 (assert (forall ((K tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int K)) tptp.zero_zero_int))))
% 0.62/1.01 (assert (= (@ tptp.semiri1621563631at_int tptp.one_one_nat) tptp.one_one_int))
% 0.62/1.01 (assert (= (@ tptp.semiri1621563631at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1621563631at_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) Z) (exists ((N_1 tptp.nat)) (= Z (@ (@ tptp.plus_plus_int W) (@ tptp.semiri1621563631at_int N_1)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M) N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat X) Y)))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.ord_less_nat X) Y))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.nat_tsub (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat X) Y)))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat X) Y)))))
% 0.62/1.01 (assert (forall ((A (-> tptp.nat Bool))) (= (@ tptp.finite_card_nat A) (@ tptp.finite_card_int (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) A)))))
% 0.62/1.01 (assert (forall ((A (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat A) (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) A)))))
% 0.62/1.01 (assert (= tptp.one_one_int (@ tptp.semiri1621563631at_int tptp.one_one_nat)))
% 0.62/1.01 (assert (= tptp.zero_zero_int (@ tptp.semiri1621563631at_int tptp.zero_zero_nat)))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1)))) (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))))))
% 0.62/1.01 (assert (forall ((Z tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int Z))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool))) (= (exists ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1))) (exists ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool))) (= (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1))) (forall ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int N)) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 0.62/1.01 (assert (= (@ tptp.semiri1621563631at_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 0.62/1.01 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) Z) (exists ((N_1 tptp.nat)) (= Z (@ (@ tptp.plus_plus_int W) (@ tptp.semiri1621563631at_int (@ tptp.suc N_1))))))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int M)))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat M) N))))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.62/1.01 (assert (forall ((K tptp.nat) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1621563631at_int K)))) (=> (@ (@ tptp.ord_less_int I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J)))))))
% 0.62/1.01 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.nat_tsub X) Y)))))))
% 0.62/1.01 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 0.62/1.01 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.nat_tsub X) Y) (@ (@ tptp.minus_minus_int X) Y)))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1) (= K (@ tptp.semiri1621563631at_int N_1)))))))
% 0.62/1.01 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1621563631at_int M) (@ tptp.semiri1621563631at_int N)) (= M N))))
% 0.62/1.01 (assert (forall ((A (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int tptp.semiri1621563631at_int))) (= (@ (@ tptp.ord_less_nat_o A) B) (@ (@ tptp.ord_less_int_o (@ _let_1 A)) (@ _let_1 B))))))
% 0.62/1.01 (assert (forall ((A (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int tptp.semiri1621563631at_int))) (= (@ (@ tptp.ord_less_eq_nat_o A) B) (@ (@ tptp.ord_less_eq_int_o (@ _let_1 A)) (@ _let_1 B))))))
% 0.62/1.01 (assert (= tptp.bot_bot_int_o (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) tptp.bot_bot_nat_o)))
% 0.62/1.01 (assert (forall ((A (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int tptp.semiri1621563631at_int))) (= (= A B) (= (@ _let_1 A) (@ _let_1 B))))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (A (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_int (@ tptp.semiri1621563631at_int X)) (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) A)))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (let ((_let_1 (@ tptp.semiri1621563631at_int (@ (@ (@ tptp.if_nat P) X) Y)))) (and (=> P (= (@ tptp.semiri1621563631at_int X) _let_1)) (=> (not P) (= (@ tptp.semiri1621563631at_int Y) _let_1))))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.semiri1621563631at_int X) (@ tptp.semiri1621563631at_int Y)) (= X Y))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N_1 tptp.nat)) (not (= K (@ tptp.semiri1621563631at_int N_1))))))))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (not (forall ((M_1 tptp.nat)) (not (= Z (@ tptp.semiri1621563631at_int M_1))))))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N_1 tptp.nat)) (= K (@ tptp.semiri1621563631at_int N_1))))))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (not (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int M_1)) (@ tptp.semiri1621563631at_int N_1))))))))
% 0.62/1.01 (assert (forall ((X tptp.int) (Z tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 0.62/1.01 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 0.62/1.01 (assert (forall ((Z_1 tptp.int)) (= (@ tptp.nat_neg Z_1) (@ (@ tptp.ord_less_int Z_1) tptp.zero_zero_int))))
% 0.62/1.01 (assert (forall ((X tptp.int)) (= (not (@ tptp.nat_neg X)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))))
% 0.62/1.01 (assert (not (@ tptp.nat_neg tptp.one_one_int)))
% 0.62/1.01 (assert (not (@ tptp.nat_neg tptp.zero_zero_int)))
% 0.62/1.01 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (not (@ tptp.nat_neg (@ tptp.semiri1621563631at_int N)))))
% 0.62/1.01 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.semiri1621563631at_int M))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 0.62/1.01 (assert (forall ((V tptp.int)) (=> (@ tptp.nat_neg (@ tptp.number_number_of_int V)) (= (@ tptp.number_number_of_nat V) tptp.zero_zero_nat))))
% 0.62/1.01 (assert (forall ((V tptp.int) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_1))) (let ((_let_2 (@ tptp.nat_neg _let_1))) (let ((_let_3 (@ tptp.number_number_of_int V))) (let ((_let_4 (@ tptp.nat_neg _let_3))) (= (= (@ tptp.number_number_of_nat V) (@ tptp.number_number_of_nat V_1)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (=> (not _let_4) (and (=> _let_2 (= _let_3 tptp.zero_zero_int)) (=> (not _let_2) (= V V_1))))))))))))
% 0.62/1.01 (assert (forall ((V_1 tptp.int) (K tptp.nat) (V tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V_1)) K))) (let ((_let_2 (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V)))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.nat_neg (@ tptp.number_number_of_int V_1)))) (let ((_let_5 (@ tptp.nat_neg (@ tptp.number_number_of_int V)))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_2 K))) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V) V_1))) K)))))))))))))
% 0.62/1.01 (assert (forall ((V tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V))) (let ((_let_2 (@ tptp.semiri1621563631at_int (@ tptp.number_number_of_nat V)))) (let ((_let_3 (@ tptp.nat_neg _let_1))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 0.62/1.01 (assert (forall ((Z tptp.int) (X tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D))))))
% 0.62/1.01 (assert (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K))))))))
% 0.62/1.01 (assert (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K))))))))
% 0.62/1.01 (assert (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((I tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I) (@ (@ tptp.ord_less_nat I) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I) (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K)))))))))
% 0.62/1.01 (assert (forall ((N tptp.nat) (V tptp.int)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V)) N)))) (let ((_let_2 (@ tptp.nat_neg (@ tptp.number_number_of_int V)))) (and (=> _let_2 (= _let_1 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) N))) (=> (not _let_2) (= _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat (@ tptp.succ V))) N))))))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ tptp.succ K) (@ (@ tptp.plus_plus_int K) tptp.one_one_int))))
% 0.62/1.01 (assert (forall ((V tptp.int)) (let ((_let_1 (@ tptp.suc (@ tptp.number_number_of_nat V)))) (let ((_let_2 (@ tptp.nat_neg (@ tptp.number_number_of_int V)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ tptp.succ V)))))))))
% 0.62/1.01 (assert (forall ((W tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W))) (let ((_let_2 (@ tptp.number_number_of_nat (@ tptp.bit1 W)))) (let ((_let_3 (@ tptp.nat_neg (@ tptp.number_number_of_int W)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_1) _let_1))))))))))
% 0.62/1.01 (assert (forall ((V tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.number_number_of_nat V)))) (let ((_let_2 (@ (@ tptp.ord_less_int V) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ tptp.succ V)))))))))
% 0.62/1.01 (assert (= (@ tptp.succ tptp.pls) (@ tptp.bit1 tptp.pls)))
% 0.62/1.01 (assert (forall ((W tptp.int)) (= (@ tptp.nat_neg (@ tptp.number_number_of_int (@ tptp.bit1 W))) (@ tptp.nat_neg (@ tptp.number_number_of_int W)))))
% 0.62/1.01 (assert (not (@ tptp.nat_neg (@ tptp.number_number_of_int tptp.pls))))
% 0.62/1.01 (assert (let ((_let_1 (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (= (@ tptp.number_number_of_int _let_1) (@ tptp.semiri1621563631at_int (@ tptp.number_number_of_nat _let_1)))))
% 0.62/1.01 (assert (= (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls)) (@ tptp.suc tptp.zero_zero_nat)))
% 0.62/1.01 (assert (= (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls))) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 0.62/1.01 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) N))))
% 0.62/1.01 (assert (= tptp.one_one_nat (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls))))
% 0.62/1.01 (assert (= (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls)) tptp.one_one_nat))
% 0.62/1.01 (assert (= tptp.one_one_int (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))))
% 0.62/1.01 (assert (= tptp.zero_zero_int (@ tptp.number_number_of_int tptp.pls)))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ tptp.bit1 K) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) K)) K))))
% 0.62/1.01 (assert (= (@ tptp.number_number_of_nat tptp.pls) tptp.zero_zero_nat))
% 0.62/1.01 (assert (= tptp.zero_zero_nat (@ tptp.number_number_of_nat tptp.pls)))
% 0.62/1.01 (assert (= tptp.pls tptp.zero_zero_int))
% 0.62/1.01 (assert (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit1 K) (@ tptp.bit1 L)) (= K L))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (not (= (@ tptp.bit1 K) tptp.pls))))
% 0.62/1.01 (assert (forall ((L tptp.int)) (not (= tptp.pls (@ tptp.bit1 L)))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.pls) K)))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.pls) K) K)))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.pls) K)))
% 0.62/1.01 (assert (forall ((W tptp.int)) (= (@ (@ tptp.times_times_int tptp.pls) W) tptp.pls)))
% 0.62/1.01 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))))
% 0.62/1.01 (assert (@ (@ tptp.ord_less_eq_int tptp.pls) tptp.pls))
% 0.62/1.01 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))))
% 0.62/1.01 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.62/1.01 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.62/1.01 (assert (not (@ (@ tptp.ord_less_int tptp.pls) tptp.pls)))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.62/1.01 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.62/1.01 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.62/1.01 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int tptp.pls) (@ tptp.bit1 K)) (@ (@ tptp.ord_less_eq_int tptp.pls) K))))
% 0.62/1.01 (assert (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (@ (@ tptp.fequal_a X) Y)) (= X Y))))
% 0.62/1.01 (assert (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (= X Y)) (@ (@ tptp.fequal_a X) Y))))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 0.62/1.01 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 0.62/1.01 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 0.62/1.01 (assert (forall ((X tptp.int) (Y tptp.int)) (or (not (@ (@ tptp.fequal_int X) Y)) (= X Y))))
% 1.73/1.95 (assert (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (@ (@ tptp.fequal_int X) Y))))
% 1.73/1.95 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (not (@ (@ tptp.fequal_nat X) Y)) (= X Y))))
% 1.73/1.95 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (@ (@ tptp.fequal_nat X) Y))))
% 1.73/1.95 (assert (@ tptp.finite_finite_pname tptp.u))
% 1.73/1.95 (assert (@ (@ tptp.ord_less_eq_a_o tptp.g) (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u)))
% 1.73/1.95 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.na)) (@ tptp.finite_card_a (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u))))
% 1.73/1.95 (assert (= (@ tptp.finite_card_a tptp.g) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u))) (@ tptp.suc tptp.na))))
% 1.73/1.95 (assert (@ (@ tptp.member_pname tptp.pn) tptp.u))
% 1.73/1.95 (assert (not (@ (@ tptp.member_a (@ tptp.mgt_call tptp.pn)) tptp.g)))
% 1.73/1.95 (assert (not (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a (@ tptp.mgt_call tptp.pn)) tptp.g)) (@ (@ tptp.image_pname_a tptp.mgt_call) tptp.u))))
% 1.73/1.95 (set-info :filename cvc5---1.0.5_18286)
% 1.73/1.95 (check-sat-assuming ( true ))
% 1.73/1.95 ------- get file name : TPTP file name is SWW473^3
% 1.73/1.95 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18286.smt2...
% 1.73/1.95 --- Run --ho-elim --full-saturate-quant at 10...
% 1.73/1.95 % SZS status Theorem for SWW473^3
% 1.73/1.95 % SZS output start Proof for SWW473^3
% 1.73/1.95 (
% 1.73/1.95 (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 (@ tptp.bit1 tptp.pls))) (let ((_let_9 (@ tptp.bit1 _let_8))) (let ((_let_10 (@ tptp.number_number_of_int _let_9))) (let ((_let_11 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_12 (@ tptp.number_number_of_nat tptp.pls))) (let ((_let_13 (@ tptp.number_number_of_int tptp.pls))) (let ((_let_14 (@ tptp.number_number_of_nat _let_8))) (let ((_let_15 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_16 (@ tptp.number_number_of_nat _let_9))) (let ((_let_17 (@ tptp.semiri1621563631at_int tptp.zero_zero_nat))) (let ((_let_18 (@ tptp.semiri1621563631at_int tptp.one_one_nat))) (let ((_let_19 (forall ((X_27 tptp.x_a) (A_109 (-> tptp.x_a Bool)) (B_57 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.insert_a X_27) A_109)) B_57) (and (@ (@ tptp.member_a X_27) B_57) (@ (@ tptp.ord_less_eq_a_o A_109) B_57)))))) (let ((_let_20 (forall ((A_145 (-> tptp.pname Bool)) (B_83 tptp.x_a) (F_36 (-> tptp.pname tptp.x_a)) (X_50 tptp.pname)) (=> (= B_83 (@ F_36 X_50)) (=> (@ (@ tptp.member_pname X_50) A_145) (@ (@ tptp.member_a B_83) (@ (@ tptp.image_pname_a F_36) A_145))))))) (let ((_let_21 (forall ((BOUND_VARIABLE_40132 |u_(-> tptp.pname Bool)|) (BOUND_VARIABLE_40133 |u_(-> tptp.pname tptp.x_a)|) (X_50 tptp.pname)) (or (not (ho_150 (ho_149 k_148 X_50) BOUND_VARIABLE_40132)) (ho_155 (ho_154 k_153 (ho_168 BOUND_VARIABLE_40133 X_50)) (ho_432 (ho_431 k_430 BOUND_VARIABLE_40133) BOUND_VARIABLE_40132)))))) (let ((_let_22 (ho_432 (ho_431 k_430 k_525) k_526))) (let ((_let_23 (ho_168 k_525 tptp.pn))) (let ((_let_24 (ho_155 (ho_154 k_153 _let_23) _let_22))) (let ((_let_25 (ho_150 (ho_149 k_148 tptp.pn) k_526))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_20)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A_145 (-> tptp.pname Bool)) (F_36 (-> tptp.pname tptp.x_a)) (X_50 tptp.pname)) (or (not (@ (@ tptp.member_pname X_50) A_145)) (@ (@ tptp.member_a (@ F_36 X_50)) (@ (@ tptp.image_pname_a F_36) A_145)))) _let_21))))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (ho_155 (ho_280 k_281 k_589) _let_22))) (let ((_let_31 (and _let_24 _let_30))) (let ((_let_32 (not _let_24))) (let ((_let_33 (ho_155 (ho_280 k_281 (ho_140 (ho_142 k_141 _let_23) k_589)) _let_22))) (let ((_let_34 (= _let_33 _let_31))) (let ((_let_35 (not _let_31))) (let ((_let_36 (forall ((X_27 tptp.x_a) (BOUND_VARIABLE_41904 |u_(-> tptp.x_a Bool)|) (BOUND_VARIABLE_41903 |u_(-> tptp.x_a Bool)|)) (= (and (ho_155 (ho_154 k_153 X_27) BOUND_VARIABLE_41903) (ho_155 (ho_280 k_281 BOUND_VARIABLE_41904) BOUND_VARIABLE_41903)) (ho_155 (ho_280 k_281 (ho_140 (ho_142 k_141 X_27) BOUND_VARIABLE_41904)) BOUND_VARIABLE_41903))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_19)) (PREPROCESS :args ((= _let_19 _let_36)))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (k_526 k_525 tptp.pn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_21))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_24 _let_29))) (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_31)) :args ((or (not _let_30) _let_31 _let_32))) (EQ_RESOLVE (ASSUME :args (_let_7)) (PREPROCESS :args ((= _let_7 _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_34)) :args ((or _let_33 _let_35 (not _let_34)))) (EQ_RESOLVE (ASSUME :args (_let_3)) (PREPROCESS :args ((= _let_3 (not _let_33))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_23 k_589 _let_22 QUANTIFIERS_INST_E_MATCHING ((ho_155 (ho_280 k_281 (ho_140 (ho_142 k_141 X_27) BOUND_VARIABLE_41904)) BOUND_VARIABLE_41903)))) :args (_let_36)))) _let_37 :args (_let_34 false _let_36)) :args (_let_35 true _let_33 false _let_34)) :args (_let_32 false _let_30 true _let_31)) :args (_let_29 false _let_25 true _let_24)) _let_28 :args (false true _let_27 false _let_21)) :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_161 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_161) (@ tptp.finite229719499nt_o_o (@ tptp.collect_int_o_o (lambda ((B_26 (-> (-> tptp.int Bool) Bool))) (@ (@ tptp.ord_less_eq_int_o_o B_26) A_161)))))) (forall ((A_161 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_161) (@ tptp.finite1676163439at_o_o (@ tptp.collect_nat_o_o (lambda ((B_26 (-> (-> tptp.nat Bool) Bool))) (@ (@ tptp.ord_less_eq_nat_o_o B_26) A_161)))))) (forall ((A_161 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_161) (@ tptp.finite1066544169me_o_o (@ tptp.collect_pname_o_o (lambda ((B_26 (-> (-> tptp.pname Bool) Bool))) (@ (@ tptp.ord_le1205211808me_o_o B_26) A_161)))))) (forall ((A_161 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_161) (@ tptp.finite_finite_a_o_o (@ tptp.collect_a_o_o (lambda ((B_26 (-> (-> tptp.x_a Bool) Bool))) (@ (@ tptp.ord_less_eq_a_o_o B_26) A_161)))))) (forall ((A_161 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_161) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((B_26 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o B_26) A_161)))))) (forall ((A_161 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_161) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((B_26 (-> tptp.pname Bool))) (@ (@ tptp.ord_less_eq_pname_o B_26) A_161)))))) (forall ((A_161 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_161) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((B_26 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o B_26) A_161)))))) (forall ((A_161 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_161) (@ tptp.finite_finite_int_o (@ tptp.collect_int_o (lambda ((B_26 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o B_26) A_161)))))) (forall ((H (-> tptp.pname tptp.int Bool)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite_finite_int_o (@ (@ tptp.image_pname_int_o H) F_42)))) (forall ((H (-> tptp.pname tptp.nat Bool)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_pname_nat_o H) F_42)))) (forall ((H (-> tptp.pname tptp.pname Bool)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite297249702name_o (@ (@ tptp.image_pname_pname_o H) F_42)))) (forall ((H (-> tptp.pname tptp.x_a Bool)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite_finite_a_o (@ (@ tptp.image_pname_a_o H) F_42)))) (forall ((H (-> tptp.nat tptp.x_a)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_a (@ (@ tptp.image_nat_a H) F_42)))) (forall ((H (-> tptp.nat tptp.int Bool)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_int_o (@ (@ tptp.image_nat_int_o H) F_42)))) (forall ((H (-> tptp.nat tptp.nat Bool)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o H) F_42)))) (forall ((H (-> tptp.nat tptp.pname Bool)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o H) F_42)))) (forall ((H (-> tptp.nat tptp.x_a Bool)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o H) F_42)))) (forall ((H (-> tptp.int tptp.x_a)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite_finite_a (@ (@ tptp.image_int_a H) F_42)))) (forall ((H (-> tptp.int tptp.int Bool)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite_finite_int_o (@ (@ tptp.image_int_int_o H) F_42)))) (forall ((H (-> tptp.int tptp.nat Bool)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite_finite_nat_o (@ (@ tptp.image_int_nat_o H) F_42)))) (forall ((H (-> tptp.int tptp.pname Bool)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite297249702name_o (@ (@ tptp.image_int_pname_o H) F_42)))) (forall ((H (-> tptp.int tptp.x_a Bool)) (F_42 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_42) (@ tptp.finite_finite_a_o (@ (@ tptp.image_int_a_o H) F_42)))) (forall ((H (-> tptp.x_a tptp.pname)) (F_42 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_pname H) F_42)))) (forall ((H (-> (-> tptp.int Bool) tptp.pname)) (F_42 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_int_o_pname H) F_42)))) (forall ((H (-> (-> tptp.nat Bool) tptp.pname)) (F_42 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_nat_o_pname H) F_42)))) (forall ((H (-> (-> tptp.pname Bool) tptp.pname)) (F_42 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_pname_o_pname H) F_42)))) (forall ((H (-> (-> tptp.x_a Bool) tptp.pname)) (F_42 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_42) (@ tptp.finite_finite_pname (@ (@ tptp.image_a_o_pname H) F_42)))) (forall ((H (-> tptp.x_a tptp.nat)) (F_42 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_nat H) F_42)))) (forall ((H (-> (-> tptp.int Bool) tptp.nat)) (F_42 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_int_o_nat H) F_42)))) (forall ((H (-> (-> tptp.nat Bool) tptp.nat)) (F_42 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_o_nat H) F_42)))) (forall ((H (-> (-> tptp.pname Bool) tptp.nat)) (F_42 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_pname_o_nat H) F_42)))) (forall ((H (-> (-> tptp.x_a Bool) tptp.nat)) (F_42 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_42) (@ tptp.finite_finite_nat (@ (@ tptp.image_a_o_nat H) F_42)))) (forall ((H (-> tptp.x_a tptp.int)) (F_42 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_a_int H) F_42)))) (forall ((H (-> (-> tptp.int Bool) tptp.int)) (F_42 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_int_o_int H) F_42)))) (forall ((H (-> (-> tptp.nat Bool) tptp.int)) (F_42 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_nat_o_int H) F_42)))) (forall ((H (-> (-> tptp.pname Bool) tptp.int)) (F_42 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_pname_o_int H) F_42)))) (forall ((H (-> (-> tptp.x_a Bool) tptp.int)) (F_42 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_a_o_int H) F_42)))) (forall ((H (-> tptp.pname tptp.x_a)) (F_42 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_42) (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a H) F_42)))) (forall ((H (-> tptp.nat tptp.int)) (F_42 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_42) (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int H) F_42)))) (forall ((A_160 (-> tptp.int Bool)) (A_159 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_159) (@ tptp.finite_finite_int_o (@ (@ tptp.insert_int_o A_160) A_159)))) (forall ((A_160 (-> tptp.nat Bool)) (A_159 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_159) (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_160) A_159)))) (forall ((A_160 (-> tptp.pname Bool)) (A_159 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_159) (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_160) A_159)))) (forall ((A_160 (-> tptp.x_a Bool)) (A_159 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_159) (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_160) A_159)))) (forall ((A_160 tptp.pname) (A_159 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_159) (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_160) A_159)))) (forall ((A_160 tptp.nat) (A_159 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_159) (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_160) A_159)))) (forall ((A_160 tptp.int) (A_159 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_159) (@ tptp.finite_finite_int (@ (@ tptp.insert_int A_160) A_159)))) (forall ((A_160 tptp.x_a) (A_159 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_159) (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_160) A_159)))) (forall ((F_41 (-> tptp.pname tptp.pname)) (A_158 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_pname_pname F_41) A_158))) (@ tptp.finite_card_pname A_158)))) (forall ((F_41 (-> tptp.x_a tptp.x_a)) (A_158 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_a F_41) A_158))) (@ tptp.finite_card_a A_158)))) (forall ((F_41 (-> (-> tptp.int Bool) tptp.x_a)) (A_158 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_int_o_a F_41) A_158))) (@ tptp.finite_card_int_o A_158)))) (forall ((F_41 (-> (-> tptp.nat Bool) tptp.x_a)) (A_158 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_nat_o_a F_41) A_158))) (@ tptp.finite_card_nat_o A_158)))) (forall ((F_41 (-> (-> tptp.pname Bool) tptp.x_a)) (A_158 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_o_a F_41) A_158))) (@ tptp.finite_card_pname_o A_158)))) (forall ((F_41 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_158 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_a_o_a F_41) A_158))) (@ tptp.finite_card_a_o A_158)))) (forall ((F_41 (-> tptp.pname tptp.nat)) (A_158 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_nat F_41) A_158))) (@ tptp.finite_card_pname A_158)))) (forall ((F_41 (-> tptp.x_a tptp.nat)) (A_158 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_nat F_41) A_158))) (@ tptp.finite_card_a A_158)))) (forall ((F_41 (-> (-> tptp.int Bool) tptp.nat)) (A_158 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_int_o_nat F_41) A_158))) (@ tptp.finite_card_int_o A_158)))) (forall ((F_41 (-> (-> tptp.nat Bool) tptp.nat)) (A_158 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_nat_o_nat F_41) A_158))) (@ tptp.finite_card_nat_o A_158)))) (forall ((F_41 (-> (-> tptp.pname Bool) tptp.nat)) (A_158 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_pname_o_nat F_41) A_158))) (@ tptp.finite_card_pname_o A_158)))) (forall ((F_41 (-> (-> tptp.x_a Bool) tptp.nat)) (A_158 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_a_o_nat F_41) A_158))) (@ tptp.finite_card_a_o A_158)))) (forall ((F_41 (-> tptp.pname tptp.int)) (A_158 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_pname_int F_41) A_158))) (@ tptp.finite_card_pname A_158)))) (forall ((F_41 (-> tptp.x_a tptp.int)) (A_158 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_a_int F_41) A_158))) (@ tptp.finite_card_a A_158)))) (forall ((F_41 (-> (-> tptp.int Bool) tptp.int)) (A_158 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_int_o_int F_41) A_158))) (@ tptp.finite_card_int_o A_158)))) (forall ((F_41 (-> (-> tptp.nat Bool) tptp.int)) (A_158 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_nat_o_int F_41) A_158))) (@ tptp.finite_card_nat_o A_158)))) (forall ((F_41 (-> (-> tptp.pname Bool) tptp.int)) (A_158 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_pname_o_int F_41) A_158))) (@ tptp.finite_card_pname_o A_158)))) (forall ((F_41 (-> (-> tptp.x_a Bool) tptp.int)) (A_158 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_a_o_int F_41) A_158))) (@ tptp.finite_card_a_o A_158)))) (forall ((F_41 (-> tptp.x_a tptp.pname)) (A_158 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_a_pname F_41) A_158))) (@ tptp.finite_card_a A_158)))) (forall ((F_41 (-> tptp.nat tptp.pname)) (A_158 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_nat_pname F_41) A_158))) (@ tptp.finite_card_nat A_158)))) (forall ((F_41 (-> tptp.int tptp.pname)) (A_158 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.image_int_pname F_41) A_158))) (@ tptp.finite_card_int A_158)))) (forall ((F_41 (-> tptp.pname tptp.x_a)) (A_158 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.image_pname_a F_41) A_158))) (@ tptp.finite_card_pname A_158)))) (forall ((F_41 (-> tptp.nat tptp.int)) (A_158 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_158) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_nat_int F_41) A_158))) (@ tptp.finite_card_nat A_158)))) (forall ((A_157 (-> (-> tptp.int Bool) Bool)) (B_89 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_89) (=> (@ (@ tptp.ord_less_eq_int_o_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int_o A_157)) (@ tptp.finite_card_int_o B_89))))) (forall ((A_157 (-> (-> tptp.nat Bool) Bool)) (B_89 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_89) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_157)) (@ tptp.finite_card_nat_o B_89))))) (forall ((A_157 (-> (-> tptp.pname Bool) Bool)) (B_89 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_89) (=> (@ (@ tptp.ord_le1205211808me_o_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_157)) (@ tptp.finite_card_pname_o B_89))))) (forall ((A_157 (-> (-> tptp.x_a Bool) Bool)) (B_89 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_89) (=> (@ (@ tptp.ord_less_eq_a_o_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_157)) (@ tptp.finite_card_a_o B_89))))) (forall ((A_157 (-> tptp.pname Bool)) (B_89 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_89) (=> (@ (@ tptp.ord_less_eq_pname_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_157)) (@ tptp.finite_card_pname B_89))))) (forall ((A_157 (-> tptp.x_a Bool)) (B_89 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_89) (=> (@ (@ tptp.ord_less_eq_a_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_157)) (@ tptp.finite_card_a B_89))))) (forall ((A_157 (-> tptp.nat Bool)) (B_89 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_89) (=> (@ (@ tptp.ord_less_eq_nat_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_157)) (@ tptp.finite_card_nat B_89))))) (forall ((A_157 (-> tptp.int Bool)) (B_89 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_89) (=> (@ (@ tptp.ord_less_eq_int_o A_157) B_89) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A_157)) (@ tptp.finite_card_int B_89))))) (forall ((A_156 (-> (-> tptp.int Bool) Bool)) (B_88 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_88) (=> (@ (@ tptp.ord_less_eq_int_o_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int_o B_88)) (@ tptp.finite_card_int_o A_156)) (= A_156 B_88))))) (forall ((A_156 (-> (-> tptp.nat Bool) Bool)) (B_88 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_88) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o B_88)) (@ tptp.finite_card_nat_o A_156)) (= A_156 B_88))))) (forall ((A_156 (-> (-> tptp.pname Bool) Bool)) (B_88 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_88) (=> (@ (@ tptp.ord_le1205211808me_o_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o B_88)) (@ tptp.finite_card_pname_o A_156)) (= A_156 B_88))))) (forall ((A_156 (-> (-> tptp.x_a Bool) Bool)) (B_88 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_88) (=> (@ (@ tptp.ord_less_eq_a_o_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o B_88)) (@ tptp.finite_card_a_o A_156)) (= A_156 B_88))))) (forall ((A_156 (-> tptp.pname Bool)) (B_88 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_88) (=> (@ (@ tptp.ord_less_eq_pname_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname B_88)) (@ tptp.finite_card_pname A_156)) (= A_156 B_88))))) (forall ((A_156 (-> tptp.x_a Bool)) (B_88 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_88) (=> (@ (@ tptp.ord_less_eq_a_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a B_88)) (@ tptp.finite_card_a A_156)) (= A_156 B_88))))) (forall ((A_156 (-> tptp.nat Bool)) (B_88 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_88) (=> (@ (@ tptp.ord_less_eq_nat_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B_88)) (@ tptp.finite_card_nat A_156)) (= A_156 B_88))))) (forall ((A_156 (-> tptp.int Bool)) (B_88 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_88) (=> (@ (@ tptp.ord_less_eq_int_o A_156) B_88) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int B_88)) (@ tptp.finite_card_int A_156)) (= A_156 B_88))))) (forall ((X_53 (-> tptp.int Bool)) (A_155 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int_o A_155)) (@ tptp.finite_card_int_o (@ (@ tptp.insert_int_o X_53) A_155))))) (forall ((X_53 (-> tptp.nat Bool)) (A_155 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat_o A_155)) (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_53) A_155))))) (forall ((X_53 (-> tptp.pname Bool)) (A_155 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname_o A_155)) (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_53) A_155))))) (forall ((X_53 (-> tptp.x_a Bool)) (A_155 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a_o A_155)) (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_53) A_155))))) (forall ((X_53 tptp.pname) (A_155 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname A_155)) (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_53) A_155))))) (forall ((X_53 tptp.nat) (A_155 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A_155)) (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_53) A_155))))) (forall ((X_53 tptp.int) (A_155 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A_155)) (@ tptp.finite_card_int (@ (@ tptp.insert_int X_53) A_155))))) (forall ((X_53 tptp.x_a) (A_155 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_155) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a A_155)) (@ tptp.finite_card_a (@ (@ tptp.insert_a X_53) A_155))))) (forall ((X_52 (-> tptp.int Bool)) (A_154 (-> (-> tptp.int Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_int_o A_154))) (let ((_let_2 (@ tptp.finite_card_int_o (@ (@ tptp.insert_int_o X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_int_o X_52) A_154))) (=> (@ tptp.finite_finite_int_o A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_52 (-> tptp.nat Bool)) (A_154 (-> (-> tptp.nat Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_nat_o A_154))) (let ((_let_2 (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_nat_o X_52) A_154))) (=> (@ tptp.finite_finite_nat_o A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_52 (-> tptp.pname Bool)) (A_154 (-> (-> tptp.pname Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_pname_o A_154))) (let ((_let_2 (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_pname_o X_52) A_154))) (=> (@ tptp.finite297249702name_o A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_52 (-> tptp.x_a Bool)) (A_154 (-> (-> tptp.x_a Bool) Bool))) (let ((_let_1 (@ tptp.finite_card_a_o A_154))) (let ((_let_2 (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_a_o X_52) A_154))) (=> (@ tptp.finite_finite_a_o A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_52 tptp.pname) (A_154 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.finite_card_pname A_154))) (let ((_let_2 (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_pname X_52) A_154))) (=> (@ tptp.finite_finite_pname A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_52 tptp.nat) (A_154 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_card_nat A_154))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_nat X_52) A_154))) (=> (@ tptp.finite_finite_nat A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_52 tptp.int) (A_154 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_card_int A_154))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.insert_int X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_int X_52) A_154))) (=> (@ tptp.finite_finite_int A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_52 tptp.x_a) (A_154 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.finite_card_a A_154))) (let ((_let_2 (@ tptp.finite_card_a (@ (@ tptp.insert_a X_52) A_154)))) (let ((_let_3 (@ (@ tptp.member_a X_52) A_154))) (=> (@ tptp.finite_finite_a A_154) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.suc _let_1))))))))) (forall ((X_51 (-> tptp.int Bool)) (A_153 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_153) (=> (not (@ (@ tptp.member_int_o X_51) A_153)) (= (@ tptp.finite_card_int_o (@ (@ tptp.insert_int_o X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_int_o A_153)))))) (forall ((X_51 (-> tptp.nat Bool)) (A_153 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_153) (=> (not (@ (@ tptp.member_nat_o X_51) A_153)) (= (@ tptp.finite_card_nat_o (@ (@ tptp.insert_nat_o X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_nat_o A_153)))))) (forall ((X_51 (-> tptp.pname Bool)) (A_153 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_153) (=> (not (@ (@ tptp.member_pname_o X_51) A_153)) (= (@ tptp.finite_card_pname_o (@ (@ tptp.insert_pname_o X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_pname_o A_153)))))) (forall ((X_51 (-> tptp.x_a Bool)) (A_153 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_153) (=> (not (@ (@ tptp.member_a_o X_51) A_153)) (= (@ tptp.finite_card_a_o (@ (@ tptp.insert_a_o X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_a_o A_153)))))) (forall ((X_51 tptp.pname) (A_153 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_153) (=> (not (@ (@ tptp.member_pname X_51) A_153)) (= (@ tptp.finite_card_pname (@ (@ tptp.insert_pname X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_pname A_153)))))) (forall ((X_51 tptp.nat) (A_153 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_153) (=> (not (@ (@ tptp.member_nat X_51) A_153)) (= (@ tptp.finite_card_nat (@ (@ tptp.insert_nat X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_nat A_153)))))) (forall ((X_51 tptp.int) (A_153 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_153) (=> (not (@ (@ tptp.member_int X_51) A_153)) (= (@ tptp.finite_card_int (@ (@ tptp.insert_int X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_int A_153)))))) (forall ((X_51 tptp.x_a) (A_153 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_153) (=> (not (@ (@ tptp.member_a X_51) A_153)) (= (@ tptp.finite_card_a (@ (@ tptp.insert_a X_51) A_153)) (@ tptp.suc (@ tptp.finite_card_a A_153)))))) (forall ((Q_3 (-> tptp.x_a Bool)) (P_13 (-> tptp.x_a Bool))) (=> (or (@ tptp.finite_finite_a (@ tptp.collect_a P_13)) (@ tptp.finite_finite_a (@ tptp.collect_a Q_3))) (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (@ P_13 X_1) (@ Q_3 X_1))))))) (forall ((Q_3 (-> (-> tptp.int Bool) Bool)) (P_13 (-> (-> tptp.int Bool) Bool))) (=> (or (@ tptp.finite_finite_int_o (@ tptp.collect_int_o P_13)) (@ tptp.finite_finite_int_o (@ tptp.collect_int_o Q_3))) (@ tptp.finite_finite_int_o (@ tptp.collect_int_o (lambda ((X_1 (-> tptp.int Bool))) (and (@ P_13 X_1) (@ Q_3 X_1))))))) (forall ((Q_3 (-> (-> tptp.nat Bool) Bool)) (P_13 (-> (-> tptp.nat Bool) Bool))) (=> (or (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_13)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q_3))) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (and (@ P_13 X_1) (@ Q_3 X_1))))))) (forall ((Q_3 (-> (-> tptp.pname Bool) Bool)) (P_13 (-> (-> tptp.pname Bool) Bool))) (=> (or (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_13)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_3))) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (and (@ P_13 X_1) (@ Q_3 X_1))))))) (forall ((Q_3 (-> (-> tptp.x_a Bool) Bool)) (P_13 (-> (-> tptp.x_a Bool) Bool))) (=> (or (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_13)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q_3))) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (and (@ P_13 X_1) (@ Q_3 X_1))))))) (forall ((Q_3 (-> tptp.pname Bool)) (P_13 (-> tptp.pname Bool))) (=> (or (@ tptp.finite_finite_pname (@ tptp.collect_pname P_13)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_3))) (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (and (@ P_13 X_1) (@ Q_3 X_1))))))) (forall ((Q_3 (-> tptp.nat Bool)) (P_13 (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P_13)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (@ P_13 X_1) (@ Q_3 X_1))))))) (forall ((Q_3 (-> tptp.int Bool)) (P_13 (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P_13)) (@ tptp.finite_finite_int (@ tptp.collect_int Q_3))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (@ P_13 X_1) (@ Q_3 X_1))))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) K))))) (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_eq_nat I) N)))) (@ tptp.suc N))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))) (forall ((Nat_4 tptp.nat) (Nat_1 tptp.nat)) (= (= (@ tptp.suc Nat_4) (@ tptp.suc Nat_1)) (= Nat_4 Nat_1))) (forall ((N tptp.nat)) (not (= (@ tptp.suc N) N))) (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))) (forall ((P_12 (-> tptp.x_a Bool)) (Q_2 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_a (@ tptp.collect_a P_12)) (@ tptp.finite_finite_a (@ tptp.collect_a Q_2))))) (forall ((P_12 (-> (-> tptp.int Bool) Bool)) (Q_2 (-> (-> tptp.int Bool) Bool))) (= (@ tptp.finite_finite_int_o (@ tptp.collect_int_o (lambda ((X_1 (-> tptp.int Bool))) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_int_o (@ tptp.collect_int_o P_12)) (@ tptp.finite_finite_int_o (@ tptp.collect_int_o Q_2))))) (forall ((P_12 (-> (-> tptp.nat Bool) Bool)) (Q_2 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o (lambda ((X_1 (-> tptp.nat Bool))) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o P_12)) (@ tptp.finite_finite_nat_o (@ tptp.collect_nat_o Q_2))))) (forall ((P_12 (-> (-> tptp.pname Bool) Bool)) (Q_2 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ tptp.collect_pname_o (lambda ((X_1 (-> tptp.pname Bool))) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite297249702name_o (@ tptp.collect_pname_o P_12)) (@ tptp.finite297249702name_o (@ tptp.collect_pname_o Q_2))))) (forall ((P_12 (-> (-> tptp.x_a Bool) Bool)) (Q_2 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ tptp.collect_a_o (lambda ((X_1 (-> tptp.x_a Bool))) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_a_o (@ tptp.collect_a_o P_12)) (@ tptp.finite_finite_a_o (@ tptp.collect_a_o Q_2))))) (forall ((P_12 (-> tptp.pname Bool)) (Q_2 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_pname (@ tptp.collect_pname P_12)) (@ tptp.finite_finite_pname (@ tptp.collect_pname Q_2))))) (forall ((P_12 (-> tptp.nat Bool)) (Q_2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P_12)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q_2))))) (forall ((P_12 (-> tptp.int Bool)) (Q_2 (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X_1 tptp.int)) (or (@ P_12 X_1) (@ Q_2 X_1))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P_12)) (@ tptp.finite_finite_int (@ tptp.collect_int Q_2))))) (forall ((A_152 (-> tptp.int Bool)) (A_151 (-> (-> tptp.int Bool) Bool))) (= (@ tptp.finite_finite_int_o (@ (@ tptp.insert_int_o A_152) A_151)) (@ tptp.finite_finite_int_o A_151))) (forall ((A_152 (-> tptp.nat Bool)) (A_151 (-> (-> tptp.nat Bool) Bool))) (= (@ tptp.finite_finite_nat_o (@ (@ tptp.insert_nat_o A_152) A_151)) (@ tptp.finite_finite_nat_o A_151))) (forall ((A_152 (-> tptp.pname Bool)) (A_151 (-> (-> tptp.pname Bool) Bool))) (= (@ tptp.finite297249702name_o (@ (@ tptp.insert_pname_o A_152) A_151)) (@ tptp.finite297249702name_o A_151))) (forall ((A_152 (-> tptp.x_a Bool)) (A_151 (-> (-> tptp.x_a Bool) Bool))) (= (@ tptp.finite_finite_a_o (@ (@ tptp.insert_a_o A_152) A_151)) (@ tptp.finite_finite_a_o A_151))) (forall ((A_152 tptp.pname) (A_151 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname (@ (@ tptp.insert_pname A_152) A_151)) (@ tptp.finite_finite_pname A_151))) (forall ((A_152 tptp.nat) (A_151 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ (@ tptp.insert_nat A_152) A_151)) (@ tptp.finite_finite_nat A_151))) (forall ((A_152 tptp.int) (A_151 (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ (@ tptp.insert_int A_152) A_151)) (@ tptp.finite_finite_int A_151))) (forall ((A_152 tptp.x_a) (A_151 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a (@ (@ tptp.insert_a A_152) A_151)) (@ tptp.finite_finite_a A_151))) (forall ((A_150 (-> (-> tptp.int Bool) Bool)) (B_87 (-> (-> tptp.int Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_int_o_o A_150) B_87) (=> (@ tptp.finite_finite_int_o B_87) (@ tptp.finite_finite_int_o A_150)))) (forall ((A_150 (-> (-> tptp.nat Bool) Bool)) (B_87 (-> (-> tptp.nat Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_150) B_87) (=> (@ tptp.finite_finite_nat_o B_87) (@ tptp.finite_finite_nat_o A_150)))) (forall ((A_150 (-> (-> tptp.pname Bool) Bool)) (B_87 (-> (-> tptp.pname Bool) Bool))) (=> (@ (@ tptp.ord_le1205211808me_o_o A_150) B_87) (=> (@ tptp.finite297249702name_o B_87) (@ tptp.finite297249702name_o A_150)))) (forall ((A_150 (-> (-> tptp.x_a Bool) Bool)) (B_87 (-> (-> tptp.x_a Bool) Bool))) (=> (@ (@ tptp.ord_less_eq_a_o_o A_150) B_87) (=> (@ tptp.finite_finite_a_o B_87) (@ tptp.finite_finite_a_o A_150)))) (forall ((A_150 (-> tptp.x_a Bool)) (B_87 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_150) B_87) (=> (@ tptp.finite_finite_a B_87) (@ tptp.finite_finite_a A_150)))) (forall ((A_150 (-> tptp.pname Bool)) (B_87 (-> tptp.pname Bool))) (=> (@ (@ tptp.ord_less_eq_pname_o A_150) B_87) (=> (@ tptp.finite_finite_pname B_87) (@ tptp.finite_finite_pname A_150)))) (forall ((A_150 (-> tptp.nat Bool)) (B_87 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_150) B_87) (=> (@ tptp.finite_finite_nat B_87) (@ tptp.finite_finite_nat A_150)))) (forall ((A_150 (-> tptp.int Bool)) (B_87 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_150) B_87) (=> (@ tptp.finite_finite_int B_87) (@ tptp.finite_finite_int A_150)))) (forall ((A_149 (-> (-> tptp.int Bool) Bool)) (B_86 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o B_86) (=> (@ (@ tptp.ord_less_eq_int_o_o A_149) B_86) (@ tptp.finite_finite_int_o A_149)))) (forall ((A_149 (-> (-> tptp.nat Bool) Bool)) (B_86 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o B_86) (=> (@ (@ tptp.ord_less_eq_nat_o_o A_149) B_86) (@ tptp.finite_finite_nat_o A_149)))) (forall ((A_149 (-> (-> tptp.pname Bool) Bool)) (B_86 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o B_86) (=> (@ (@ tptp.ord_le1205211808me_o_o A_149) B_86) (@ tptp.finite297249702name_o A_149)))) (forall ((A_149 (-> (-> tptp.x_a Bool) Bool)) (B_86 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o B_86) (=> (@ (@ tptp.ord_less_eq_a_o_o A_149) B_86) (@ tptp.finite_finite_a_o A_149)))) (forall ((A_149 (-> tptp.x_a Bool)) (B_86 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_86) (=> (@ (@ tptp.ord_less_eq_a_o A_149) B_86) (@ tptp.finite_finite_a A_149)))) (forall ((A_149 (-> tptp.pname Bool)) (B_86 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_86) (=> (@ (@ tptp.ord_less_eq_pname_o A_149) B_86) (@ tptp.finite_finite_pname A_149)))) (forall ((A_149 (-> tptp.nat Bool)) (B_86 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_86) (=> (@ (@ tptp.ord_less_eq_nat_o A_149) B_86) (@ tptp.finite_finite_nat A_149)))) (forall ((A_149 (-> tptp.int Bool)) (B_86 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_86) (=> (@ (@ tptp.ord_less_eq_int_o A_149) B_86) (@ tptp.finite_finite_int A_149)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))) (forall ((I_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I_1) N) (= (@ _let_1 (@ _let_1 I_1)) I_1)))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)) (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> tptp.x_a tptp.x_a)) (A_148 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_a_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))) (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> (-> tptp.int Bool) tptp.x_a)) (A_148 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_int_o_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))) (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> (-> tptp.nat Bool) tptp.x_a)) (A_148 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_nat_o_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))) (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> (-> tptp.pname Bool) tptp.x_a)) (A_148 (-> (-> tptp.pname Bool) Bool))) (=> (@ tptp.finite297249702name_o A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_pname_o_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))) (forall ((B_85 (-> tptp.x_a Bool)) (F_40 (-> (-> tptp.x_a Bool) tptp.x_a)) (A_148 (-> (-> tptp.x_a Bool) Bool))) (=> (@ tptp.finite_finite_a_o A_148) (=> (@ (@ tptp.ord_less_eq_a_o B_85) (@ (@ tptp.image_a_o_a F_40) A_148)) (@ tptp.finite_finite_a B_85)))) (forall ((B_85 (-> (-> tptp.int Bool) Bool)) (F_40 (-> tptp.pname tptp.int Bool)) (A_148 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_148) (=> (@ (@ tptp.ord_less_eq_int_o_o B_85) (@ (@ 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B_85)))) (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> tptp.int tptp.pname)) (A_148 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_int_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))) (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> tptp.x_a tptp.pname)) (A_148 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_a_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))) (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> (-> tptp.int Bool) tptp.pname)) (A_148 (-> (-> tptp.int Bool) Bool))) (=> (@ tptp.finite_finite_int_o A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ tptp.image_int_o_pname F_40) A_148)) (@ tptp.finite_finite_pname B_85)))) (forall ((B_85 (-> tptp.pname Bool)) (F_40 (-> (-> tptp.nat Bool) tptp.pname)) (A_148 (-> (-> tptp.nat Bool) Bool))) (=> (@ tptp.finite_finite_nat_o A_148) (=> (@ (@ tptp.ord_less_eq_pname_o B_85) (@ (@ 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tptp.pname tptp.x_a)) (A_147 (-> tptp.pname Bool)) (B_84 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_84) (=> (@ (@ tptp.ord_less_eq_a_o B_84) (@ (@ tptp.image_pname_a F_39) A_147)) (exists ((C_34 (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o C_34) A_147) (@ tptp.finite_finite_pname C_34) (= B_84 (@ (@ tptp.image_pname_a F_39) C_34))))))) (forall ((F_39 (-> tptp.nat tptp.int)) (A_147 (-> tptp.nat Bool)) (B_84 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_84) (=> (@ (@ tptp.ord_less_eq_int_o B_84) (@ (@ tptp.image_nat_int F_39) A_147)) (exists ((C_34 (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o C_34) A_147) (@ tptp.finite_finite_nat C_34) (= B_84 (@ (@ tptp.image_nat_int F_39) C_34))))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.pname Bool))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_pname_o (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_pname_o (@ F_38 N_4)) (@ F_38 N_3))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat Bool))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_o (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_o (@ F_38 N_4)) (@ F_38 N_3))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.x_a Bool))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_a_o (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_a_o (@ F_38 N_4)) (@ F_38 N_3))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.nat))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ tptp.ord_less_eq_nat N_4) N_3) (@ (@ tptp.ord_less_eq_nat (@ F_38 N_4)) (@ F_38 N_3))))) (forall ((N_4 tptp.nat) (N_3 tptp.nat) (F_38 (-> tptp.nat tptp.int))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F_38 N_1)) (@ F_38 (@ tptp.suc N_1)))) (=> (@ (@ 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A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))) (forall ((F_37 (-> tptp.nat tptp.nat Bool)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite_finite_nat_o (@ (@ tptp.image_nat_nat_o F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))) (forall ((F_37 (-> tptp.nat tptp.pname Bool)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite297249702name_o (@ (@ tptp.image_nat_pname_o F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))) (forall ((F_37 (-> tptp.nat tptp.x_a Bool)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_nat_a_o F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))) (forall ((F_37 (-> tptp.int tptp.x_a)) (A_146 (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A_146)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_int_a F_37) A_146)) (exists ((X_1 tptp.int)) (and (@ (@ tptp.member_int X_1) A_146) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A_37 tptp.int)) (and (@ (@ tptp.member_int A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))) (forall ((F_37 (-> tptp.int tptp.int Bool)) (A_146 (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A_146)) (=> (@ tptp.finite_finite_int_o (@ (@ tptp.image_int_int_o F_37) A_146)) (exists ((X_1 tptp.int)) (and (@ (@ tptp.member_int X_1) A_146) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda 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(not (@ tptp.finite_finite_int A_146)) (=> (@ tptp.finite_finite_a_o (@ (@ tptp.image_int_a_o F_37) A_146)) (exists ((X_1 tptp.int)) (and (@ (@ tptp.member_int X_1) A_146) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A_37 tptp.int)) (and (@ (@ tptp.member_int A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))) (forall ((F_37 (-> tptp.pname tptp.x_a)) (A_146 (-> tptp.pname Bool))) (=> (not (@ tptp.finite_finite_pname A_146)) (=> (@ tptp.finite_finite_a (@ (@ tptp.image_pname_a F_37) A_146)) (exists ((X_1 tptp.pname)) (and (@ (@ tptp.member_pname X_1) A_146) (not (@ tptp.finite_finite_pname (@ tptp.collect_pname (lambda ((A_37 tptp.pname)) (and (@ (@ tptp.member_pname A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))) (forall ((F_37 (-> tptp.nat tptp.int)) (A_146 (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A_146)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int F_37) A_146)) (exists ((X_1 tptp.nat)) (and (@ (@ tptp.member_nat X_1) A_146) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A_37 tptp.nat)) (and (@ (@ tptp.member_nat A_37) A_146) (= (@ F_37 A_37) (@ F_37 X_1)))))))))))) (forall ((A_145 (-> tptp.nat Bool)) (B_83 tptp.int) (F_36 (-> tptp.nat tptp.int)) (X_50 tptp.nat)) (=> (= B_83 (@ F_36 X_50)) (=> (@ (@ tptp.member_nat X_50) A_145) (@ (@ tptp.member_int B_83) (@ (@ tptp.image_nat_int F_36) A_145))))) _let_20 (forall ((A_144 (-> tptp.int Bool)) (B_82 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_144) B_82) (=> (@ (@ tptp.ord_less_eq_int_o B_82) A_144) (= A_144 B_82)))) (forall ((A_144 (-> tptp.nat Bool)) (B_82 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_144) B_82) (=> (@ (@ tptp.ord_less_eq_nat_o B_82) A_144) (= A_144 B_82)))) (forall ((A_144 (-> tptp.x_a Bool)) (B_82 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_144) B_82) (=> (@ (@ tptp.ord_less_eq_a_o B_82) A_144) (= A_144 B_82)))) (forall ((C_33 tptp.int) (A_143 (-> tptp.int Bool)) (B_81 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_33))) (=> (@ (@ tptp.ord_less_eq_int_o A_143) B_81) (=> (@ _let_1 A_143) (@ _let_1 B_81))))) (forall ((C_33 tptp.nat) (A_143 (-> tptp.nat Bool)) (B_81 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_33))) (=> (@ (@ tptp.ord_less_eq_nat_o A_143) B_81) (=> (@ _let_1 A_143) (@ _let_1 B_81))))) (forall ((C_33 tptp.x_a) (A_143 (-> tptp.x_a Bool)) (B_81 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_33))) (=> (@ (@ tptp.ord_less_eq_a_o A_143) B_81) (=> (@ _let_1 A_143) (@ _let_1 B_81))))) (forall ((C_33 tptp.pname) (A_143 (-> tptp.pname Bool)) (B_81 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_33))) (=> (@ (@ tptp.ord_less_eq_pname_o A_143) B_81) (=> (@ _let_1 A_143) (@ _let_1 B_81))))) (forall ((B_80 tptp.x_a) (A_142 tptp.x_a) (B_79 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_142))) (=> (=> (not (@ _let_1 B_79)) (= A_142 B_80)) (@ _let_1 (@ (@ tptp.insert_a B_80) B_79))))) (forall ((B_80 tptp.int) (A_142 tptp.int) (B_79 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_142))) (=> (=> (not (@ _let_1 B_79)) (= A_142 B_80)) (@ _let_1 (@ (@ tptp.insert_int B_80) B_79))))) (forall ((B_80 tptp.nat) (A_142 tptp.nat) (B_79 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_142))) (=> (=> (not (@ _let_1 B_79)) (= A_142 B_80)) (@ _let_1 (@ (@ tptp.insert_nat B_80) B_79))))) (forall ((B_80 tptp.pname) (A_142 tptp.pname) (B_79 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_142))) (=> (=> (not (@ _let_1 B_79)) (= A_142 B_80)) (@ _let_1 (@ (@ tptp.insert_pname B_80) B_79))))) (forall ((A_141 tptp.x_a) (B_78 tptp.x_a) (A_140 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_141))) (=> (@ _let_1 (@ (@ tptp.insert_a B_78) A_140)) (=> (not (= A_141 B_78)) (@ _let_1 A_140))))) (forall ((A_141 tptp.int) (B_78 tptp.int) (A_140 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_141))) (=> (@ _let_1 (@ (@ tptp.insert_int B_78) A_140)) (=> (not (= A_141 B_78)) (@ _let_1 A_140))))) (forall ((A_141 tptp.nat) (B_78 tptp.nat) (A_140 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_141))) (=> (@ _let_1 (@ (@ tptp.insert_nat B_78) A_140)) (=> (not (= A_141 B_78)) (@ _let_1 A_140))))) (forall ((A_141 tptp.pname) (B_78 tptp.pname) (A_140 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_141))) (=> (@ _let_1 (@ (@ tptp.insert_pname B_78) A_140)) (=> (not (= A_141 B_78)) (@ _let_1 A_140))))) (forall ((I_1 tptp.nat) (P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N_1 tptp.nat)) (=> (@ P (@ tptp.suc N_1)) (@ P N_1))) (@ P (@ (@ tptp.minus_minus_nat K) I_1))))) (forall ((N tptp.nat) (M_3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M_3) (exists ((M_1 tptp.nat)) (= M_3 (@ tptp.suc M_1))))) (forall ((X_49 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o X_49) X_49)) (forall ((X_49 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o X_49) X_49)) (forall ((X_49 tptp.int)) (@ (@ tptp.ord_less_eq_int X_49) X_49)) (forall ((X_49 tptp.nat)) (@ (@ 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((X_47 (-> tptp.x_a Bool)) (Y_11 (-> tptp.x_a Bool))) (= (= X_47 Y_11) (and (@ (@ tptp.ord_less_eq_a_o X_47) Y_11) (@ (@ tptp.ord_less_eq_a_o Y_11) X_47)))) (forall ((X_46 (-> tptp.int Bool)) (Y_10 (-> tptp.int Bool))) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_int_o X_46) Y_10))) (forall ((X_46 (-> tptp.nat Bool)) (Y_10 (-> tptp.nat Bool))) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_nat_o X_46) Y_10))) (forall ((X_46 tptp.int) (Y_10 tptp.int)) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_int X_46) Y_10))) (forall ((X_46 tptp.nat) (Y_10 tptp.nat)) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_nat X_46) Y_10))) (forall ((X_46 (-> tptp.x_a Bool)) (Y_10 (-> tptp.x_a Bool))) (=> (= X_46 Y_10) (@ (@ tptp.ord_less_eq_a_o X_46) Y_10))) (forall ((Y_9 (-> tptp.int Bool)) (X_45 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o Y_9) X_45) (= (@ (@ tptp.ord_less_eq_int_o X_45) Y_9) (= X_45 Y_9)))) (forall ((Y_9 (-> tptp.nat Bool)) (X_45 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o Y_9) X_45) (= (@ 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(B_71 tptp.int) (A_128 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_129))) (= (@ _let_1 (@ (@ tptp.insert_int B_71) A_128)) (or (= A_129 B_71) (@ _let_1 A_128))))) (forall ((A_129 tptp.nat) (B_71 tptp.nat) (A_128 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_129))) (= (@ _let_1 (@ (@ tptp.insert_nat B_71) A_128)) (or (= A_129 B_71) (@ _let_1 A_128))))) (forall ((A_129 tptp.pname) (B_71 tptp.pname) (A_128 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_129))) (= (@ _let_1 (@ (@ tptp.insert_pname B_71) A_128)) (or (= A_129 B_71) (@ _let_1 A_128))))) (forall ((Y_2 tptp.x_a) (A_127 (-> tptp.x_a Bool)) (X_36 tptp.x_a)) (= (@ (@ (@ tptp.insert_a Y_2) A_127) X_36) (or (= Y_2 X_36) (@ A_127 X_36)))) (forall ((B_70 (-> tptp.x_a Bool)) (X_35 tptp.x_a) (A_126 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_35))) (let ((_let_2 (@ tptp.member_a X_35))) (=> (not (@ _let_2 A_126)) (=> (not (@ _let_2 B_70)) (= (= (@ _let_1 A_126) (@ _let_1 B_70)) (= A_126 B_70))))))) (forall ((B_70 (-> tptp.int Bool)) (X_35 tptp.int) (A_126 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_35))) (let ((_let_2 (@ tptp.member_int X_35))) (=> (not (@ _let_2 A_126)) (=> (not (@ _let_2 B_70)) (= (= (@ _let_1 A_126) (@ _let_1 B_70)) (= A_126 B_70))))))) (forall ((B_70 (-> tptp.nat Bool)) (X_35 tptp.nat) (A_126 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_35))) (let ((_let_2 (@ tptp.member_nat X_35))) (=> (not (@ _let_2 A_126)) (=> (not (@ _let_2 B_70)) (= (= (@ _let_1 A_126) (@ _let_1 B_70)) (= A_126 B_70))))))) (forall ((B_70 (-> tptp.pname Bool)) (X_35 tptp.pname) (A_126 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_35))) (let ((_let_2 (@ tptp.member_pname X_35))) (=> (not (@ _let_2 A_126)) (=> (not (@ _let_2 B_70)) (= (= (@ _let_1 A_126) (@ _let_1 B_70)) (= A_126 B_70))))))) (forall ((B_69 tptp.x_a) (A_125 tptp.x_a) (B_68 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_125))) (=> (@ _let_1 B_68) (@ _let_1 (@ (@ 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(forall ((A_124 tptp.pname) (A_123 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname A_124) A_123) (= (@ (@ tptp.insert_pname A_124) A_123) A_123))) (forall ((A_122 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o A_122) A_122)) (forall ((A_122 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o A_122) A_122)) (forall ((A_122 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o A_122) A_122)) (forall ((A_121 (-> tptp.int Bool)) (B_67 (-> tptp.int Bool))) (= (= A_121 B_67) (and (@ (@ tptp.ord_less_eq_int_o A_121) B_67) (@ (@ tptp.ord_less_eq_int_o B_67) A_121)))) (forall ((A_121 (-> tptp.nat Bool)) (B_67 (-> tptp.nat Bool))) (= (= A_121 B_67) (and (@ (@ tptp.ord_less_eq_nat_o A_121) B_67) (@ (@ tptp.ord_less_eq_nat_o B_67) A_121)))) (forall ((A_121 (-> tptp.x_a Bool)) (B_67 (-> tptp.x_a Bool))) (= (= A_121 B_67) (and (@ (@ tptp.ord_less_eq_a_o A_121) B_67) (@ (@ tptp.ord_less_eq_a_o B_67) A_121)))) (forall ((A_120 (-> tptp.int Bool)) (B_66 (-> tptp.int Bool))) (=> (= A_120 B_66) (@ (@ 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((_let_1 (@ tptp.member_a X_33))) (=> (@ _let_1 A_117) (=> (@ (@ tptp.ord_less_eq_a_o A_117) B_63) (@ _let_1 B_63))))) (forall ((B_63 (-> tptp.pname Bool)) (X_33 tptp.pname) (A_117 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname X_33))) (=> (@ _let_1 A_117) (=> (@ (@ tptp.ord_less_eq_pname_o A_117) B_63) (@ _let_1 B_63))))) (forall ((X_32 tptp.int) (A_116 (-> tptp.int Bool)) (B_62 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int X_32))) (=> (@ (@ tptp.ord_less_eq_int_o A_116) B_62) (=> (@ _let_1 A_116) (@ _let_1 B_62))))) (forall ((X_32 tptp.nat) (A_116 (-> tptp.nat Bool)) (B_62 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X_32))) (=> (@ (@ tptp.ord_less_eq_nat_o A_116) B_62) (=> (@ _let_1 A_116) (@ _let_1 B_62))))) (forall ((X_32 tptp.x_a) (A_116 (-> tptp.x_a Bool)) (B_62 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a X_32))) (=> (@ (@ tptp.ord_less_eq_a_o A_116) B_62) (=> (@ _let_1 A_116) (@ _let_1 B_62))))) (forall ((X_32 tptp.pname) (A_116 (-> 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tptp.pname) (A_109 (-> tptp.pname Bool)) (B_57 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.insert_pname X_27) A_109)) B_57) (and (@ (@ tptp.member_pname X_27) B_57) (@ (@ tptp.ord_less_eq_pname_o A_109) B_57)))) (forall ((B_56 (-> tptp.x_a Bool)) (X_26 tptp.x_a) (A_108 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_108))) (=> (not (@ (@ tptp.member_a X_26) A_108)) (= (@ _let_1 (@ (@ tptp.insert_a X_26) B_56)) (@ _let_1 B_56))))) (forall ((B_56 (-> tptp.int Bool)) (X_26 tptp.int) (A_108 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o A_108))) (=> (not (@ (@ tptp.member_int X_26) A_108)) (= (@ _let_1 (@ (@ tptp.insert_int X_26) B_56)) (@ _let_1 B_56))))) (forall ((B_56 (-> tptp.nat Bool)) (X_26 tptp.nat) (A_108 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_108))) (=> (not (@ (@ tptp.member_nat X_26) A_108)) (= (@ _let_1 (@ (@ tptp.insert_nat X_26) B_56)) (@ _let_1 B_56))))) (forall ((B_56 (-> tptp.pname Bool)) (X_26 tptp.pname) (A_108 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_108))) (=> (not (@ (@ tptp.member_pname X_26) A_108)) (= (@ _let_1 (@ (@ tptp.insert_pname X_26) B_56)) (@ _let_1 B_56))))) (forall ((B_55 tptp.x_a) (A_107 (-> tptp.x_a Bool)) (B_54 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_107))) (=> (@ _let_1 B_54) (@ _let_1 (@ (@ tptp.insert_a B_55) B_54))))) (forall ((B_55 tptp.int) (A_107 (-> tptp.int Bool)) (B_54 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o A_107))) (=> (@ _let_1 B_54) (@ _let_1 (@ (@ tptp.insert_int B_55) B_54))))) (forall ((B_55 tptp.nat) (A_107 (-> tptp.nat Bool)) (B_54 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_107))) (=> (@ _let_1 B_54) (@ _let_1 (@ (@ tptp.insert_nat B_55) B_54))))) (forall ((A_106 tptp.x_a) (C_27 (-> tptp.x_a Bool)) (D_7 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_106))) (=> (@ (@ tptp.ord_less_eq_a_o C_27) D_7) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 C_27)) (@ _let_1 D_7))))) (forall ((A_106 tptp.int) (C_27 (-> tptp.int Bool)) (D_7 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_106))) (=> (@ (@ tptp.ord_less_eq_int_o C_27) D_7) (@ (@ tptp.ord_less_eq_int_o (@ _let_1 C_27)) (@ _let_1 D_7))))) (forall ((A_106 tptp.nat) (C_27 (-> tptp.nat Bool)) (D_7 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_106))) (=> (@ (@ tptp.ord_less_eq_nat_o C_27) D_7) (@ (@ tptp.ord_less_eq_nat_o (@ _let_1 C_27)) (@ _let_1 D_7))))) (forall ((F_29 (-> tptp.nat tptp.int)) (A_105 tptp.nat) (B_53 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int F_29))) (= (@ _let_1 (@ (@ tptp.insert_nat A_105) B_53)) (@ (@ tptp.insert_int (@ F_29 A_105)) (@ _let_1 B_53))))) (forall ((F_29 (-> tptp.pname tptp.x_a)) (A_105 tptp.pname) (B_53 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_29))) (= (@ _let_1 (@ (@ tptp.insert_pname A_105) B_53)) (@ (@ tptp.insert_a (@ F_29 A_105)) (@ _let_1 B_53))))) (forall ((F_28 (-> tptp.nat tptp.int)) (X_25 tptp.nat) (A_104 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.image_nat_int F_28) A_104))) (=> (@ (@ tptp.member_nat X_25) A_104) (= (@ (@ tptp.insert_int (@ F_28 X_25)) _let_1) _let_1)))) (forall ((F_28 (-> tptp.pname tptp.x_a)) (X_25 tptp.pname) (A_104 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.image_pname_a F_28) A_104))) (=> (@ (@ tptp.member_pname X_25) A_104) (= (@ (@ tptp.insert_a (@ F_28 X_25)) _let_1) _let_1)))) (forall ((B_52 (-> tptp.int Bool)) (F_27 (-> tptp.nat tptp.int)) (A_103 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_int_o B_52) (@ (@ tptp.image_nat_int F_27) A_103)) (exists ((AA (-> tptp.nat Bool))) (and (@ (@ tptp.ord_less_eq_nat_o AA) A_103) (= B_52 (@ (@ tptp.image_nat_int F_27) AA)))))) (forall ((B_52 (-> tptp.x_a Bool)) (F_27 (-> tptp.pname tptp.x_a)) (A_103 (-> tptp.pname Bool))) (= (@ (@ tptp.ord_less_eq_a_o B_52) (@ (@ tptp.image_pname_a F_27) A_103)) (exists ((AA (-> tptp.pname Bool))) (and (@ (@ tptp.ord_less_eq_pname_o AA) A_103) (= B_52 (@ (@ tptp.image_pname_a F_27) AA)))))) (forall ((F_26 (-> tptp.nat tptp.int)) (A_102 (-> tptp.nat Bool)) (B_51 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int F_26))) (=> (@ (@ tptp.ord_less_eq_nat_o A_102) B_51) (@ (@ tptp.ord_less_eq_int_o (@ _let_1 A_102)) (@ _let_1 B_51))))) (forall ((F_26 (-> tptp.pname tptp.x_a)) (A_102 (-> tptp.pname Bool)) (B_51 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_26))) (=> (@ (@ tptp.ord_less_eq_pname_o A_102) B_51) (@ (@ tptp.ord_less_eq_a_o (@ _let_1 A_102)) (@ _let_1 B_51))))) (forall ((B_50 tptp.int) (F_25 (-> tptp.nat tptp.int)) (A_101 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_int B_50) (@ (@ tptp.image_nat_int F_25) A_101)) (not (forall ((X_1 tptp.nat)) (=> (= B_50 (@ F_25 X_1)) (not (@ (@ tptp.member_nat X_1) A_101))))))) (forall ((B_50 tptp.x_a) (F_25 (-> tptp.pname tptp.x_a)) (A_101 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_a B_50) (@ (@ tptp.image_pname_a F_25) A_101)) (not (forall ((X_1 tptp.pname)) (=> (= B_50 (@ F_25 X_1)) (not (@ (@ tptp.member_pname X_1) A_101))))))) (forall ((B_49 (-> tptp.int Bool)) (A_100 (-> tptp.int Bool))) (=> (forall ((X_1 tptp.int)) (let ((_let_1 (@ tptp.member_int X_1))) (=> (@ _let_1 A_100) (@ _let_1 B_49)))) (@ (@ tptp.ord_less_eq_int_o A_100) B_49))) (forall ((B_49 (-> tptp.nat Bool)) (A_100 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X_1))) (=> (@ _let_1 A_100) (@ _let_1 B_49)))) (@ (@ tptp.ord_less_eq_nat_o A_100) B_49))) (forall ((B_49 (-> tptp.x_a Bool)) (A_100 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (let ((_let_1 (@ tptp.member_a X_1))) (=> (@ _let_1 A_100) (@ _let_1 B_49)))) (@ (@ tptp.ord_less_eq_a_o A_100) B_49))) (forall ((B_49 (-> tptp.pname Bool)) (A_100 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (let ((_let_1 (@ tptp.member_pname X_1))) (=> (@ _let_1 A_100) (@ _let_1 B_49)))) (@ (@ tptp.ord_less_eq_pname_o A_100) B_49))) (forall ((F_24 (-> tptp.nat tptp.int)) (B_48 (-> tptp.int Bool)) (A_99 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) A_99) (@ (@ tptp.member_int (@ F_24 X_1)) B_48))) (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.image_nat_int F_24) A_99)) B_48))) (forall ((F_24 (-> tptp.pname tptp.x_a)) (B_48 (-> tptp.x_a Bool)) (A_99 (-> tptp.pname Bool))) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) A_99) (@ (@ tptp.member_a (@ F_24 X_1)) B_48))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.image_pname_a F_24) A_99)) B_48))) (forall ((F_23 (-> tptp.int Bool)) (G_1 (-> tptp.int Bool))) (=> (forall ((X_1 tptp.int)) (@ (@ tptp.ord_less_eq_o (@ F_23 X_1)) (@ G_1 X_1))) (@ (@ tptp.ord_less_eq_int_o F_23) G_1))) (forall ((F_23 (-> tptp.nat Bool)) (G_1 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (@ (@ tptp.ord_less_eq_o (@ F_23 X_1)) (@ G_1 X_1))) (@ (@ tptp.ord_less_eq_nat_o F_23) G_1))) (forall ((F_23 (-> tptp.x_a Bool)) (G_1 (-> tptp.x_a Bool))) (=> (forall ((X_1 tptp.x_a)) (@ (@ tptp.ord_less_eq_o (@ F_23 X_1)) (@ G_1 X_1))) (@ (@ tptp.ord_less_eq_a_o F_23) G_1))) (forall ((N_2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_2) (exists ((M_1 tptp.nat)) (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_2) (@ (@ tptp.ord_less_eq_nat X_1) M_1)))))) (forall ((G (-> tptp.x_a Bool)) (C tptp.com)) (=> (@ tptp.wt C) (=> (forall ((X_1 tptp.pname)) (=> (@ (@ tptp.member_pname X_1) tptp.u) (@ (@ tptp.p G) (@ (@ tptp.insert_a (@ tptp.mgt_call X_1)) tptp.bot_bot_a_o)))) (@ (@ tptp.p G) (@ (@ tptp.insert_a (@ tptp.mgt C)) tptp.bot_bot_a_o))))) (forall ((A_98 tptp.int) (B_47 tptp.int) (C_26 tptp.int) (D_6 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_98) B_47) (@ (@ tptp.minus_minus_int C_26) D_6)) (= (@ (@ tptp.ord_less_eq_int A_98) B_47) (@ (@ tptp.ord_less_eq_int C_26) D_6)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.nat_case_o false) (@ tptp.ord_less_eq_nat M)) N))) (forall ((A_97 tptp.int)) (not (@ (@ tptp.member_int A_97) tptp.bot_bot_int_o))) (forall ((A_97 tptp.nat)) (not (@ (@ tptp.member_nat A_97) tptp.bot_bot_nat_o))) (forall ((A_97 tptp.x_a)) (not (@ (@ tptp.member_a A_97) tptp.bot_bot_a_o))) (forall ((A_97 tptp.pname)) (not (@ (@ tptp.member_pname A_97) tptp.bot_bot_pname_o))) (forall ((B_46 (-> tptp.int Bool)) (A_96 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_96) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_int_o A_96) B_46)))) (forall ((B_46 (-> tptp.nat Bool)) (A_96 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_96) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_nat_o A_96) B_46)))) (forall ((B_46 (-> tptp.pname Bool)) (A_96 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_96) (@ tptp.finite_finite_pname (@ (@ tptp.minus_minus_pname_o A_96) B_46)))) (@ tptp.finite_finite_int tptp.bot_bot_int_o) (@ tptp.finite_finite_nat tptp.bot_bot_nat_o) (@ tptp.finite_finite_pname tptp.bot_bot_pname_o) (@ tptp.finite_finite_a tptp.bot_bot_a_o) (forall ((A_95 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o tptp.bot_bot_nat_o) A_95)) (forall ((A_95 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o tptp.bot_bot_int_o) A_95)) (forall ((A_95 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o tptp.bot_bot_a_o) A_95)) (forall ((A_94 tptp.int) (A_93 (-> tptp.int Bool))) (=> (= A_93 tptp.bot_bot_int_o) (not (@ (@ tptp.member_int A_94) A_93)))) (forall ((A_94 tptp.nat) (A_93 (-> tptp.nat Bool))) (=> (= A_93 tptp.bot_bot_nat_o) (not (@ (@ tptp.member_nat A_94) A_93)))) (forall ((A_94 tptp.x_a) (A_93 (-> tptp.x_a Bool))) (=> (= A_93 tptp.bot_bot_a_o) (not (@ (@ tptp.member_a A_94) A_93)))) (forall ((A_94 tptp.pname) (A_93 (-> tptp.pname Bool))) (=> (= A_93 tptp.bot_bot_pname_o) (not (@ (@ tptp.member_pname A_94) A_93)))) (forall ((P_9 (-> tptp.int Bool))) (= (= (@ tptp.collect_int P_9) tptp.bot_bot_int_o) (forall ((X_1 tptp.int)) (not (@ P_9 X_1))))) (forall ((P_9 (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P_9) tptp.bot_bot_nat_o) (forall ((X_1 tptp.nat)) (not (@ P_9 X_1))))) (forall ((P_9 (-> tptp.x_a Bool))) (= (= (@ tptp.collect_a P_9) tptp.bot_bot_a_o) (forall ((X_1 tptp.x_a)) (not (@ P_9 X_1))))) (forall ((A_92 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_92) A_92) tptp.bot_bot_nat_o)) (forall ((A_92 (-> tptp.int Bool))) (= (@ (@ tptp.minus_minus_int_o A_92) A_92) tptp.bot_bot_int_o)) (forall ((A_92 (-> tptp.x_a Bool))) (= (@ (@ tptp.minus_minus_a_o A_92) A_92) tptp.bot_bot_a_o)) (forall ((A_91 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_91) tptp.bot_bot_nat_o) A_91)) (forall ((A_91 (-> tptp.int Bool))) (= (@ (@ tptp.minus_minus_int_o A_91) tptp.bot_bot_int_o) A_91)) (forall ((A_91 (-> tptp.x_a Bool))) (= (@ (@ tptp.minus_minus_a_o A_91) tptp.bot_bot_a_o) A_91)) (forall ((C_25 tptp.int)) (not (@ (@ tptp.member_int C_25) tptp.bot_bot_int_o))) (forall ((C_25 tptp.nat)) (not (@ (@ tptp.member_nat C_25) tptp.bot_bot_nat_o))) (forall ((C_25 tptp.x_a)) (not (@ (@ tptp.member_a C_25) tptp.bot_bot_a_o))) (forall ((C_25 tptp.pname)) (not (@ (@ tptp.member_pname C_25) tptp.bot_bot_pname_o))) (forall ((P_8 (-> tptp.int Bool))) (= (= tptp.bot_bot_int_o (@ tptp.collect_int P_8)) (forall ((X_1 tptp.int)) (not (@ P_8 X_1))))) (forall ((P_8 (-> tptp.nat Bool))) (= (= tptp.bot_bot_nat_o (@ tptp.collect_nat P_8)) (forall ((X_1 tptp.nat)) (not (@ P_8 X_1))))) (forall ((P_8 (-> tptp.x_a Bool))) (= (= tptp.bot_bot_a_o (@ tptp.collect_a P_8)) (forall ((X_1 tptp.x_a)) (not (@ P_8 X_1))))) (forall ((A_90 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o tptp.bot_bot_nat_o) A_90) tptp.bot_bot_nat_o)) (forall ((A_90 (-> tptp.int Bool))) (= (@ (@ tptp.minus_minus_int_o tptp.bot_bot_int_o) A_90) tptp.bot_bot_int_o)) (forall ((A_90 (-> tptp.x_a Bool))) (= (@ (@ tptp.minus_minus_a_o tptp.bot_bot_a_o) A_90) tptp.bot_bot_a_o)) (forall ((A_89 (-> tptp.int Bool))) (= (exists ((X_1 tptp.int)) (@ (@ tptp.member_int X_1) A_89)) (not (= A_89 tptp.bot_bot_int_o)))) (forall ((A_89 (-> tptp.nat Bool))) (= (exists ((X_1 tptp.nat)) (@ (@ tptp.member_nat X_1) A_89)) (not (= A_89 tptp.bot_bot_nat_o)))) (forall ((A_89 (-> tptp.x_a Bool))) (= (exists ((X_1 tptp.x_a)) (@ (@ tptp.member_a X_1) A_89)) (not (= A_89 tptp.bot_bot_a_o)))) (forall ((A_89 (-> tptp.pname Bool))) (= (exists ((X_1 tptp.pname)) (@ (@ tptp.member_pname X_1) A_89)) (not (= A_89 tptp.bot_bot_pname_o)))) (forall ((A_88 (-> tptp.int Bool))) (= (forall ((X_1 tptp.int)) (not (@ (@ tptp.member_int X_1) A_88))) (= A_88 tptp.bot_bot_int_o))) (forall ((A_88 (-> tptp.nat Bool))) (= (forall ((X_1 tptp.nat)) (not (@ (@ tptp.member_nat X_1) A_88))) (= A_88 tptp.bot_bot_nat_o))) (forall ((A_88 (-> tptp.x_a Bool))) (= (forall ((X_1 tptp.x_a)) (not (@ (@ tptp.member_a X_1) A_88))) (= A_88 tptp.bot_bot_a_o))) (forall ((A_88 (-> tptp.pname Bool))) (= (forall ((X_1 tptp.pname)) (not (@ (@ tptp.member_pname X_1) A_88))) (= A_88 tptp.bot_bot_pname_o))) (forall ((X_24 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_24) tptp.bot_bot_o)) (forall ((X_24 tptp.int)) (= (@ tptp.bot_bot_int_o X_24) tptp.bot_bot_o)) (forall ((X_24 tptp.x_a)) (= (@ tptp.bot_bot_a_o X_24) tptp.bot_bot_o)) (= tptp.bot_bot_int_o (@ tptp.collect_int (lambda ((X_1 tptp.int)) false))) (= tptp.bot_bot_nat_o (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) false))) (= tptp.bot_bot_a_o (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) false))) (forall ((X_1 tptp.nat)) (= (@ tptp.bot_bot_nat_o X_1) tptp.bot_bot_o)) (forall ((X_1 tptp.int)) (= (@ tptp.bot_bot_int_o X_1) tptp.bot_bot_o)) (forall ((X_1 tptp.x_a)) (= (@ tptp.bot_bot_a_o X_1) tptp.bot_bot_o)) (forall ((A_87 tptp.x_a) (A_86 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_87))) (=> (@ (@ tptp.member_a A_87) A_86) (= (@ _let_1 (@ (@ tptp.minus_minus_a_o A_86) (@ _let_1 tptp.bot_bot_a_o))) A_86)))) (forall ((A_87 tptp.int) (A_86 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_87))) (=> (@ (@ tptp.member_int A_87) A_86) (= (@ _let_1 (@ (@ tptp.minus_minus_int_o A_86) (@ _let_1 tptp.bot_bot_int_o))) A_86)))) (forall ((A_87 tptp.nat) (A_86 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_87))) (=> (@ (@ tptp.member_nat A_87) A_86) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_86) (@ _let_1 tptp.bot_bot_nat_o))) A_86)))) (forall ((A_87 tptp.pname) (A_86 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname A_87))) (=> (@ (@ tptp.member_pname A_87) A_86) (= (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_86) (@ _let_1 tptp.bot_bot_pname_o))) A_86)))) (forall ((X_23 tptp.x_a) (A_85 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_23))) (=> (not (@ (@ tptp.member_a X_23) A_85)) (= (@ (@ tptp.minus_minus_a_o (@ _let_1 A_85)) (@ _let_1 tptp.bot_bot_a_o)) A_85)))) (forall ((X_23 tptp.int) (A_85 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_23))) (=> (not (@ (@ tptp.member_int X_23) A_85)) (= (@ (@ tptp.minus_minus_int_o (@ _let_1 A_85)) (@ _let_1 tptp.bot_bot_int_o)) A_85)))) (forall ((X_23 tptp.nat) (A_85 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_23))) (=> (not (@ (@ tptp.member_nat X_23) A_85)) (= (@ (@ tptp.minus_minus_nat_o (@ _let_1 A_85)) (@ _let_1 tptp.bot_bot_nat_o)) A_85)))) (forall ((X_23 tptp.pname) (A_85 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_23))) (=> (not (@ (@ tptp.member_pname X_23) A_85)) (= (@ (@ tptp.minus_minus_pname_o (@ _let_1 A_85)) (@ _let_1 tptp.bot_bot_pname_o)) A_85)))) (forall ((A_84 tptp.x_a) (A_83 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_84))) (= (@ _let_1 (@ (@ tptp.minus_minus_a_o A_83) (@ _let_1 tptp.bot_bot_a_o))) (@ _let_1 A_83)))) (forall ((A_84 tptp.nat) (A_83 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_84))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_83) (@ _let_1 tptp.bot_bot_nat_o))) (@ _let_1 A_83)))) (forall ((A_84 tptp.int) (A_83 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_84))) (= (@ _let_1 (@ (@ tptp.minus_minus_int_o A_83) (@ _let_1 tptp.bot_bot_int_o))) (@ _let_1 A_83)))) (forall ((A_82 (-> tptp.x_a Bool)) (A_81 tptp.x_a) (B_45 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_81))) (let ((_let_2 (@ tptp.minus_minus_a_o A_82))) (= (@ _let_2 (@ _let_1 B_45)) (@ (@ tptp.minus_minus_a_o (@ _let_2 (@ _let_1 tptp.bot_bot_a_o))) B_45))))) (forall ((A_82 (-> tptp.nat Bool)) (A_81 tptp.nat) (B_45 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_81))) (let ((_let_2 (@ tptp.minus_minus_nat_o A_82))) (= (@ _let_2 (@ _let_1 B_45)) (@ (@ tptp.minus_minus_nat_o (@ _let_2 (@ _let_1 tptp.bot_bot_nat_o))) B_45))))) (forall ((A_82 (-> tptp.int Bool)) (A_81 tptp.int) (B_45 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_81))) (let ((_let_2 (@ tptp.minus_minus_int_o A_82))) (= (@ _let_2 (@ _let_1 B_45)) (@ (@ tptp.minus_minus_int_o (@ _let_2 (@ _let_1 tptp.bot_bot_int_o))) B_45))))) (forall ((A_80 (-> tptp.x_a Bool)) (A_79 tptp.x_a) (B_44 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a A_79))) (let ((_let_2 (@ tptp.minus_minus_a_o A_80))) (= (@ _let_2 (@ _let_1 B_44)) (@ (@ tptp.minus_minus_a_o (@ _let_2 B_44)) (@ _let_1 tptp.bot_bot_a_o)))))) (forall ((A_80 (-> tptp.nat Bool)) (A_79 tptp.nat) (B_44 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat A_79))) (let ((_let_2 (@ tptp.minus_minus_nat_o A_80))) (= (@ _let_2 (@ _let_1 B_44)) (@ (@ tptp.minus_minus_nat_o (@ _let_2 B_44)) (@ _let_1 tptp.bot_bot_nat_o)))))) (forall ((A_80 (-> tptp.int Bool)) (A_79 tptp.int) (B_44 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int A_79))) (let ((_let_2 (@ tptp.minus_minus_int_o A_80))) (= (@ _let_2 (@ _let_1 B_44)) (@ (@ tptp.minus_minus_int_o (@ _let_2 B_44)) (@ _let_1 tptp.bot_bot_int_o)))))) (forall ((A_78 (-> tptp.x_a Bool)) (X_22 tptp.x_a) (B_43 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_22))) (=> (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.minus_minus_a_o A_78) (@ _let_1 tptp.bot_bot_a_o))) B_43) (=> (@ (@ tptp.member_a X_22) A_78) (@ (@ tptp.ord_less_eq_a_o A_78) (@ _let_1 B_43)))))) (forall ((A_78 (-> tptp.int Bool)) (X_22 tptp.int) (B_43 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_22))) (=> (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.minus_minus_int_o A_78) (@ _let_1 tptp.bot_bot_int_o))) B_43) (=> (@ (@ tptp.member_int X_22) A_78) (@ (@ tptp.ord_less_eq_int_o A_78) (@ _let_1 B_43)))))) (forall ((A_78 (-> tptp.nat Bool)) (X_22 tptp.nat) (B_43 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_22))) (=> (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.minus_minus_nat_o A_78) (@ _let_1 tptp.bot_bot_nat_o))) B_43) (=> (@ (@ tptp.member_nat X_22) A_78) (@ (@ tptp.ord_less_eq_nat_o A_78) (@ _let_1 B_43)))))) (forall ((A_78 (-> tptp.pname Bool)) (X_22 tptp.pname) (B_43 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_22))) (=> (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.minus_minus_pname_o A_78) (@ _let_1 tptp.bot_bot_pname_o))) B_43) (=> (@ (@ tptp.member_pname X_22) A_78) (@ (@ tptp.ord_less_eq_pname_o A_78) (@ _let_1 B_43)))))) (forall ((A_77 (-> tptp.x_a Bool)) (X_21 tptp.x_a) (B_42 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.ord_less_eq_a_o A_77))) (let ((_let_2 (@ (@ tptp.member_a X_21) A_77))) (let ((_let_3 (@ tptp.insert_a X_21))) (= (@ _let_1 (@ _let_3 B_42)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.minus_minus_a_o A_77) (@ _let_3 tptp.bot_bot_a_o))) B_42)) (=> (not _let_2) (@ _let_1 B_42)))))))) (forall ((A_77 (-> tptp.int Bool)) (X_21 tptp.int) (B_42 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_int_o A_77))) (let ((_let_2 (@ (@ tptp.member_int X_21) A_77))) (let ((_let_3 (@ tptp.insert_int X_21))) (= (@ _let_1 (@ _let_3 B_42)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.minus_minus_int_o A_77) (@ _let_3 tptp.bot_bot_int_o))) B_42)) (=> (not _let_2) (@ _let_1 B_42)))))))) (forall ((A_77 (-> tptp.nat Bool)) (X_21 tptp.nat) (B_42 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_nat_o A_77))) (let ((_let_2 (@ (@ tptp.member_nat X_21) A_77))) (let ((_let_3 (@ tptp.insert_nat X_21))) (= (@ _let_1 (@ _let_3 B_42)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_nat_o (@ (@ tptp.minus_minus_nat_o A_77) (@ _let_3 tptp.bot_bot_nat_o))) B_42)) (=> (not _let_2) (@ _let_1 B_42)))))))) (forall ((A_77 (-> tptp.pname Bool)) (X_21 tptp.pname) (B_42 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.ord_less_eq_pname_o A_77))) (let ((_let_2 (@ (@ tptp.member_pname X_21) A_77))) (let ((_let_3 (@ tptp.insert_pname X_21))) (= (@ _let_1 (@ _let_3 B_42)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_pname_o (@ (@ tptp.minus_minus_pname_o A_77) (@ _let_3 tptp.bot_bot_pname_o))) B_42)) (=> (not _let_2) (@ _let_1 B_42)))))))) (forall ((A_76 (-> tptp.int Bool)) (B_41 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_41) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_int_o A_76) B_41)) (@ tptp.finite_finite_int A_76)))) (forall ((A_76 (-> tptp.nat Bool)) (B_41 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_41) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_nat_o A_76) B_41)) (@ tptp.finite_finite_nat A_76)))) (forall ((A_76 (-> tptp.pname Bool)) (B_41 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_41) (= (@ tptp.finite_finite_pname (@ (@ tptp.minus_minus_pname_o A_76) B_41)) (@ tptp.finite_finite_pname A_76)))) (forall ((A_75 (-> tptp.x_a Bool)) (X_20 tptp.x_a) (B_40 (-> tptp.x_a Bool))) (=> (@ (@ tptp.member_a X_20) B_40) (= (@ (@ tptp.minus_minus_a_o (@ (@ tptp.insert_a X_20) A_75)) B_40) (@ (@ tptp.minus_minus_a_o A_75) B_40)))) (forall ((A_75 (-> tptp.int Bool)) (X_20 tptp.int) (B_40 (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X_20) B_40) (= (@ (@ tptp.minus_minus_int_o (@ (@ tptp.insert_int X_20) A_75)) B_40) (@ (@ tptp.minus_minus_int_o A_75) B_40)))) (forall ((A_75 (-> tptp.nat Bool)) (X_20 tptp.nat) (B_40 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_20) B_40) (= (@ (@ tptp.minus_minus_nat_o (@ (@ tptp.insert_nat X_20) A_75)) B_40) (@ (@ tptp.minus_minus_nat_o A_75) B_40)))) (forall ((A_75 (-> tptp.pname Bool)) (X_20 tptp.pname) (B_40 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_20) B_40) (= (@ (@ tptp.minus_minus_pname_o (@ (@ tptp.insert_pname X_20) A_75)) B_40) (@ (@ tptp.minus_minus_pname_o A_75) B_40)))) (forall ((A_74 (-> tptp.x_a Bool)) (X_19 tptp.x_a) (B_39 (-> tptp.x_a Bool))) (let ((_let_1 (@ (@ tptp.minus_minus_a_o A_74) B_39))) (let ((_let_2 (@ tptp.insert_a X_19))) (let ((_let_3 (@ (@ tptp.minus_minus_a_o (@ _let_2 A_74)) B_39))) (let ((_let_4 (@ (@ tptp.member_a X_19) B_39))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((A_74 (-> tptp.int Bool)) (X_19 tptp.int) (B_39 (-> tptp.int Bool))) (let ((_let_1 (@ (@ tptp.minus_minus_int_o A_74) B_39))) (let ((_let_2 (@ tptp.insert_int X_19))) (let ((_let_3 (@ (@ tptp.minus_minus_int_o (@ _let_2 A_74)) B_39))) (let ((_let_4 (@ (@ tptp.member_int X_19) B_39))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((A_74 (-> tptp.nat Bool)) (X_19 tptp.nat) (B_39 (-> tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.minus_minus_nat_o A_74) B_39))) (let ((_let_2 (@ tptp.insert_nat X_19))) (let ((_let_3 (@ (@ tptp.minus_minus_nat_o (@ _let_2 A_74)) B_39))) (let ((_let_4 (@ (@ tptp.member_nat X_19) B_39))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((A_74 (-> tptp.pname Bool)) (X_19 tptp.pname) (B_39 (-> tptp.pname Bool))) (let ((_let_1 (@ (@ tptp.minus_minus_pname_o A_74) B_39))) (let ((_let_2 (@ tptp.insert_pname X_19))) (let ((_let_3 (@ (@ tptp.minus_minus_pname_o (@ _let_2 A_74)) B_39))) (let ((_let_4 (@ (@ tptp.member_pname X_19) B_39))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))) (forall ((C_24 (-> tptp.int Bool)) (A_73 (-> tptp.int Bool)) (B_38 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_73) B_38) (=> (@ (@ tptp.ord_less_eq_int_o B_38) C_24) (= (@ (@ tptp.minus_minus_int_o B_38) (@ (@ tptp.minus_minus_int_o C_24) A_73)) A_73)))) (forall ((C_24 (-> tptp.nat Bool)) (A_73 (-> tptp.nat Bool)) (B_38 (-> tptp.nat 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(=> (= (@ (@ tptp.insert_nat A_70) tptp.bot_bot_nat_o) (@ (@ tptp.insert_nat B_35) tptp.bot_bot_nat_o)) (= A_70 B_35))) (forall ((A_70 tptp.int) (B_35 tptp.int)) (=> (= (@ (@ tptp.insert_int A_70) tptp.bot_bot_int_o) (@ (@ tptp.insert_int B_35) tptp.bot_bot_int_o)) (= A_70 B_35))) (forall ((B_34 tptp.x_a) (A_69 tptp.x_a)) (=> (@ (@ tptp.member_a B_34) (@ (@ tptp.insert_a A_69) tptp.bot_bot_a_o)) (= B_34 A_69))) (forall ((B_34 tptp.int) (A_69 tptp.int)) (=> (@ (@ tptp.member_int B_34) (@ (@ tptp.insert_int A_69) tptp.bot_bot_int_o)) (= B_34 A_69))) (forall ((B_34 tptp.nat) (A_69 tptp.nat)) (=> (@ (@ tptp.member_nat B_34) (@ (@ tptp.insert_nat A_69) tptp.bot_bot_nat_o)) (= B_34 A_69))) (forall ((B_34 tptp.pname) (A_69 tptp.pname)) (=> (@ (@ tptp.member_pname B_34) (@ (@ tptp.insert_pname A_69) tptp.bot_bot_pname_o)) (= B_34 A_69))) (forall ((A_68 tptp.x_a) (B_33 tptp.x_a) (C_22 tptp.x_a) (D_4 tptp.x_a)) (= (= (@ (@ tptp.insert_a A_68) (@ (@ tptp.insert_a B_33) tptp.bot_bot_a_o)) (@ (@ tptp.insert_a C_22) (@ (@ tptp.insert_a D_4) tptp.bot_bot_a_o))) (or (and (= A_68 C_22) (= B_33 D_4)) (and (= A_68 D_4) (= B_33 C_22))))) (forall ((A_68 tptp.nat) (B_33 tptp.nat) (C_22 tptp.nat) (D_4 tptp.nat)) (= (= (@ (@ tptp.insert_nat A_68) (@ (@ tptp.insert_nat B_33) tptp.bot_bot_nat_o)) (@ (@ tptp.insert_nat C_22) (@ (@ tptp.insert_nat D_4) tptp.bot_bot_nat_o))) (or (and (= A_68 C_22) (= B_33 D_4)) (and (= A_68 D_4) (= B_33 C_22))))) (forall ((A_68 tptp.int) (B_33 tptp.int) (C_22 tptp.int) (D_4 tptp.int)) (= (= (@ (@ tptp.insert_int A_68) (@ (@ tptp.insert_int B_33) tptp.bot_bot_int_o)) (@ (@ tptp.insert_int C_22) (@ (@ tptp.insert_int D_4) tptp.bot_bot_int_o))) (or (and (= A_68 C_22) (= B_33 D_4)) (and (= A_68 D_4) (= B_33 C_22))))) (forall ((B_32 tptp.x_a) (A_67 tptp.x_a)) (= (@ (@ tptp.member_a B_32) (@ (@ tptp.insert_a A_67) tptp.bot_bot_a_o)) (= B_32 A_67))) (forall ((B_32 tptp.int) (A_67 tptp.int)) (= (@ (@ tptp.member_int B_32) (@ (@ tptp.insert_int A_67) tptp.bot_bot_int_o)) (= B_32 A_67))) (forall ((B_32 tptp.nat) (A_67 tptp.nat)) (= (@ (@ tptp.member_nat B_32) (@ (@ tptp.insert_nat A_67) tptp.bot_bot_nat_o)) (= B_32 A_67))) (forall ((B_32 tptp.pname) (A_67 tptp.pname)) (= (@ (@ tptp.member_pname B_32) (@ (@ tptp.insert_pname A_67) tptp.bot_bot_pname_o)) (= B_32 A_67))) (forall ((A_66 tptp.x_a) (A_65 (-> tptp.x_a Bool))) (not (= (@ (@ tptp.insert_a A_66) A_65) tptp.bot_bot_a_o))) (forall ((A_66 tptp.nat) (A_65 (-> tptp.nat Bool))) (not (= (@ (@ tptp.insert_nat A_66) A_65) tptp.bot_bot_nat_o))) (forall ((A_66 tptp.int) (A_65 (-> tptp.int Bool))) (not (= (@ (@ tptp.insert_int A_66) A_65) tptp.bot_bot_int_o))) (forall ((A_64 tptp.x_a) (A_63 (-> tptp.x_a Bool))) (not (= tptp.bot_bot_a_o (@ (@ tptp.insert_a A_64) A_63)))) (forall ((A_64 tptp.nat) (A_63 (-> tptp.nat Bool))) (not (= tptp.bot_bot_nat_o (@ (@ tptp.insert_nat A_64) A_63)))) (forall ((A_64 tptp.int) (A_63 (-> tptp.int Bool))) (not (= tptp.bot_bot_int_o (@ (@ tptp.insert_int A_64) A_63)))) (forall ((A_62 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o A_62) tptp.bot_bot_nat_o) (= A_62 tptp.bot_bot_nat_o))) (forall ((A_62 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_int_o A_62) tptp.bot_bot_int_o) (= A_62 tptp.bot_bot_int_o))) (forall ((A_62 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o A_62) tptp.bot_bot_a_o) (= A_62 tptp.bot_bot_a_o))) (forall ((F_22 (-> tptp.nat tptp.int)) (A_61 (-> tptp.nat Bool))) (= (= (@ (@ tptp.image_nat_int F_22) A_61) tptp.bot_bot_int_o) (= A_61 tptp.bot_bot_nat_o))) (forall ((F_22 (-> tptp.pname tptp.x_a)) (A_61 (-> tptp.pname Bool))) (= (= (@ (@ tptp.image_pname_a F_22) A_61) tptp.bot_bot_a_o) (= A_61 tptp.bot_bot_pname_o))) (forall ((F_21 (-> tptp.nat tptp.int))) (= (@ (@ tptp.image_nat_int F_21) tptp.bot_bot_nat_o) tptp.bot_bot_int_o)) (forall ((F_21 (-> tptp.pname tptp.x_a))) (= (@ (@ tptp.image_pname_a F_21) tptp.bot_bot_pname_o) tptp.bot_bot_a_o)) (forall ((F_20 (-> tptp.nat tptp.int)) (A_60 (-> tptp.nat Bool))) (= (= tptp.bot_bot_int_o (@ (@ tptp.image_nat_int F_20) A_60)) (= A_60 tptp.bot_bot_nat_o))) (forall ((F_20 (-> tptp.pname tptp.x_a)) (A_60 (-> tptp.pname Bool))) (= (= tptp.bot_bot_a_o (@ (@ tptp.image_pname_a F_20) A_60)) (= A_60 tptp.bot_bot_pname_o))) (forall ((A_59 (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat_o A_59) tptp.bot_bot_nat_o) (= A_59 tptp.bot_bot_nat_o))) (forall ((A_59 (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int_o A_59) tptp.bot_bot_int_o) (= A_59 tptp.bot_bot_int_o))) (forall ((A_59 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_59) tptp.bot_bot_nat) (= A_59 tptp.bot_bot_nat))) (forall ((A_59 (-> tptp.x_a Bool))) (=> (@ (@ tptp.ord_less_eq_a_o A_59) tptp.bot_bot_a_o) (= A_59 tptp.bot_bot_a_o))) (forall ((A_58 (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_nat_o A_58) tptp.bot_bot_nat_o) (= A_58 tptp.bot_bot_nat_o))) (forall ((A_58 (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_int_o A_58) tptp.bot_bot_int_o) (= A_58 tptp.bot_bot_int_o))) (forall ((A_58 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A_58) tptp.bot_bot_nat) (= A_58 tptp.bot_bot_nat))) (forall ((A_58 (-> tptp.x_a Bool))) (= (@ (@ tptp.ord_less_eq_a_o A_58) tptp.bot_bot_a_o) (= A_58 tptp.bot_bot_a_o))) (forall ((A_57 (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_nat_o tptp.bot_bot_nat_o) A_57)) (forall ((A_57 (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_int_o tptp.bot_bot_int_o) A_57)) (forall ((A_57 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A_57)) (forall ((A_57 (-> tptp.x_a Bool))) (@ (@ tptp.ord_less_eq_a_o tptp.bot_bot_a_o) A_57)) (forall ((P_7 (-> tptp.x_a Bool)) (A_56 tptp.x_a)) (let ((_let_1 (@ P_7 A_56))) (and (=> _let_1 (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= X_1 A_56) (@ P_7 X_1)))) (@ (@ tptp.insert_a A_56) tptp.bot_bot_a_o))) (=> (not _let_1) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= X_1 A_56) (@ P_7 X_1)))) tptp.bot_bot_a_o))))) (forall ((P_7 (-> tptp.int Bool)) (A_56 tptp.int)) (let ((_let_1 (@ P_7 A_56))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (= X_1 A_56) (@ P_7 X_1)))) (@ (@ tptp.insert_int A_56) tptp.bot_bot_int_o))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (= X_1 A_56) (@ P_7 X_1)))) tptp.bot_bot_int_o))))) (forall ((P_7 (-> tptp.nat Bool)) (A_56 tptp.nat)) (let ((_let_1 (@ P_7 A_56))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= X_1 A_56) (@ P_7 X_1)))) (@ (@ tptp.insert_nat A_56) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= X_1 A_56) (@ P_7 X_1)))) tptp.bot_bot_nat_o))))) (forall ((P_6 (-> tptp.x_a Bool)) (A_55 tptp.x_a)) (let ((_let_1 (@ P_6 A_55))) (and (=> _let_1 (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= A_55 X_1) (@ P_6 X_1)))) (@ (@ tptp.insert_a A_55) tptp.bot_bot_a_o))) (=> (not _let_1) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (and (= A_55 X_1) (@ P_6 X_1)))) tptp.bot_bot_a_o))))) (forall ((P_6 (-> tptp.int Bool)) (A_55 tptp.int)) (let ((_let_1 (@ P_6 A_55))) (and (=> _let_1 (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (= A_55 X_1) (@ P_6 X_1)))) (@ (@ tptp.insert_int A_55) tptp.bot_bot_int_o))) (=> (not _let_1) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (= A_55 X_1) (@ P_6 X_1)))) tptp.bot_bot_int_o))))) (forall ((P_6 (-> tptp.nat Bool)) (A_55 tptp.nat)) (let ((_let_1 (@ P_6 A_55))) (and (=> _let_1 (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= A_55 X_1) (@ P_6 X_1)))) (@ (@ tptp.insert_nat A_55) tptp.bot_bot_nat_o))) (=> (not _let_1) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (and (= A_55 X_1) (@ P_6 X_1)))) tptp.bot_bot_nat_o))))) (forall ((A_54 tptp.x_a)) (= (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (= X_1 A_54))) (@ (@ tptp.insert_a A_54) tptp.bot_bot_a_o))) (forall ((A_54 tptp.int)) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (= X_1 A_54))) (@ (@ tptp.insert_int A_54) tptp.bot_bot_int_o))) (forall ((A_54 tptp.nat)) (= (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (= X_1 A_54))) (@ (@ tptp.insert_nat A_54) tptp.bot_bot_nat_o))) (forall ((A_53 tptp.x_a)) (= (@ tptp.collect_a (@ tptp.fequal_a A_53)) (@ (@ tptp.insert_a A_53) tptp.bot_bot_a_o))) (forall ((A_53 tptp.int)) (= (@ tptp.collect_int (@ tptp.fequal_int A_53)) (@ (@ tptp.insert_int A_53) tptp.bot_bot_int_o))) (forall ((A_53 tptp.nat)) (= (@ tptp.collect_nat (@ tptp.fequal_nat A_53)) (@ (@ tptp.insert_nat A_53) tptp.bot_bot_nat_o))) (forall ((X_18 tptp.x_a) (A_52 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_52) (=> (@ (@ tptp.member_a X_18) A_52) (= (@ tptp.suc (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_52) (@ (@ tptp.insert_a X_18) tptp.bot_bot_a_o)))) (@ tptp.finite_card_a A_52))))) (forall ((X_18 tptp.int) (A_52 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_52) (=> (@ (@ tptp.member_int X_18) A_52) (= (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_52) (@ (@ tptp.insert_int X_18) tptp.bot_bot_int_o)))) (@ tptp.finite_card_int A_52))))) (forall ((X_18 tptp.nat) (A_52 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_52) (=> (@ (@ tptp.member_nat X_18) A_52) (= (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_52) (@ (@ tptp.insert_nat X_18) tptp.bot_bot_nat_o)))) (@ tptp.finite_card_nat A_52))))) (forall ((X_18 tptp.pname) (A_52 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_52) (=> (@ (@ tptp.member_pname X_18) A_52) (= (@ tptp.suc (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_52) (@ (@ tptp.insert_pname X_18) tptp.bot_bot_pname_o)))) (@ tptp.finite_card_pname A_52))))) (forall ((X_17 tptp.x_a) (A_51 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_17))) (=> (@ tptp.finite_finite_a A_51) (= (@ tptp.finite_card_a (@ _let_1 A_51)) (@ tptp.suc (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_51) (@ _let_1 tptp.bot_bot_a_o)))))))) (forall ((X_17 tptp.int) (A_51 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_17))) (=> (@ tptp.finite_finite_int A_51) (= (@ tptp.finite_card_int (@ _let_1 A_51)) (@ tptp.suc (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_51) (@ _let_1 tptp.bot_bot_int_o)))))))) (forall ((X_17 tptp.nat) (A_51 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_17))) (=> (@ tptp.finite_finite_nat A_51) (= (@ tptp.finite_card_nat (@ _let_1 A_51)) (@ tptp.suc (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_51) (@ _let_1 tptp.bot_bot_nat_o)))))))) (forall ((X_17 tptp.pname) (A_51 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_17))) (=> (@ tptp.finite_finite_pname A_51) (= (@ tptp.finite_card_pname (@ _let_1 A_51)) (@ tptp.suc (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_51) (@ _let_1 tptp.bot_bot_pname_o)))))))) (forall ((X_16 tptp.x_a) (A_50 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_50) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_50) (@ (@ tptp.insert_a X_16) tptp.bot_bot_a_o)))) (@ tptp.finite_card_a A_50)))) (forall ((X_16 tptp.int) (A_50 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_50) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_50) (@ (@ tptp.insert_int X_16) tptp.bot_bot_int_o)))) (@ tptp.finite_card_int A_50)))) (forall ((X_16 tptp.nat) (A_50 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_50) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_50) (@ (@ tptp.insert_nat X_16) tptp.bot_bot_nat_o)))) (@ tptp.finite_card_nat A_50)))) (forall ((X_16 tptp.pname) (A_50 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_50) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_50) (@ (@ tptp.insert_pname X_16) tptp.bot_bot_pname_o)))) (@ tptp.finite_card_pname A_50)))) (forall ((A_49 (-> tptp.x_a Bool)) (A_48 tptp.x_a) (B_31 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.minus_minus_a_o A_49))) (= (@ tptp.finite_finite_a (@ _let_1 (@ (@ tptp.insert_a A_48) B_31))) (@ tptp.finite_finite_a (@ _let_1 B_31))))) (forall ((A_49 (-> tptp.int Bool)) (A_48 tptp.int) (B_31 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.minus_minus_int_o A_49))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A_48) B_31))) (@ tptp.finite_finite_int (@ _let_1 B_31))))) (forall ((A_49 (-> tptp.nat Bool)) (A_48 tptp.nat) (B_31 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.minus_minus_nat_o A_49))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A_48) B_31))) (@ tptp.finite_finite_nat (@ _let_1 B_31))))) (forall ((A_49 (-> tptp.pname Bool)) (A_48 tptp.pname) (B_31 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.minus_minus_pname_o A_49))) (= (@ tptp.finite_finite_pname (@ _let_1 (@ (@ tptp.insert_pname A_48) B_31))) (@ tptp.finite_finite_pname (@ _let_1 B_31))))) (forall ((F_19 (-> tptp.nat tptp.int)) (A_47 (-> tptp.nat Bool)) (B_30 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int F_19))) (@ (@ tptp.ord_less_eq_int_o (@ (@ tptp.minus_minus_int_o (@ _let_1 A_47)) (@ _let_1 B_30))) (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_47) B_30))))) (forall ((F_19 (-> tptp.pname tptp.x_a)) (A_47 (-> tptp.pname Bool)) (B_30 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.image_pname_a F_19))) (@ (@ tptp.ord_less_eq_a_o (@ (@ tptp.minus_minus_a_o (@ _let_1 A_47)) (@ _let_1 B_30))) (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_47) B_30))))) (forall ((A_46 (-> tptp.x_a Bool)) (X_15 tptp.x_a)) (let ((_let_1 (@ (@ tptp.insert_a X_15) tptp.bot_bot_a_o))) (=> (@ (@ tptp.ord_less_eq_a_o A_46) _let_1) (or (= A_46 tptp.bot_bot_a_o) (= A_46 _let_1))))) (forall ((A_46 (-> tptp.nat Bool)) (X_15 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X_15) tptp.bot_bot_nat_o))) (=> (@ (@ tptp.ord_less_eq_nat_o A_46) _let_1) (or (= A_46 tptp.bot_bot_nat_o) (= A_46 _let_1))))) (forall ((A_46 (-> tptp.int Bool)) (X_15 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X_15) tptp.bot_bot_int_o))) (=> (@ (@ tptp.ord_less_eq_int_o A_46) _let_1) (or (= A_46 tptp.bot_bot_int_o) (= A_46 _let_1))))) (forall ((F1 tptp.nat) (F2 (-> tptp.nat tptp.nat)) (Nat_3 tptp.nat)) (= (@ (@ (@ tptp.nat_case_nat F1) F2) (@ tptp.suc Nat_3)) (@ F2 Nat_3))) (forall ((F1 Bool) (F2 (-> tptp.nat Bool)) (Nat_3 tptp.nat)) (= (@ (@ (@ tptp.nat_case_o F1) F2) (@ tptp.suc Nat_3)) (@ F2 Nat_3))) (forall ((C_21 tptp.int) (X_14 tptp.nat) (A_45 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X_14) A_45) (= (@ (@ tptp.image_nat_int (lambda ((X_1 tptp.nat)) C_21)) A_45) (@ (@ tptp.insert_int C_21) tptp.bot_bot_int_o)))) (forall ((C_21 tptp.x_a) (X_14 tptp.pname) (A_45 (-> tptp.pname Bool))) (=> (@ (@ tptp.member_pname X_14) A_45) (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_21)) A_45) (@ (@ tptp.insert_a C_21) tptp.bot_bot_a_o)))) (forall ((C_20 tptp.int) (A_44 (-> tptp.nat Bool))) (let ((_let_1 (= A_44 tptp.bot_bot_nat_o))) (and (=> _let_1 (= (@ (@ tptp.image_nat_int (lambda ((X_1 tptp.nat)) C_20)) A_44) tptp.bot_bot_int_o)) (=> (not _let_1) (= (@ (@ tptp.image_nat_int (lambda ((X_1 tptp.nat)) C_20)) A_44) (@ (@ tptp.insert_int C_20) tptp.bot_bot_int_o)))))) (forall ((C_20 tptp.x_a) (A_44 (-> tptp.pname Bool))) (let ((_let_1 (= A_44 tptp.bot_bot_pname_o))) (and (=> _let_1 (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_20)) A_44) tptp.bot_bot_a_o)) (=> (not _let_1) (= (@ (@ tptp.image_pname_a (lambda ((X_1 tptp.pname)) C_20)) A_44) (@ (@ tptp.insert_a C_20) tptp.bot_bot_a_o)))))) (forall ((A_43 tptp.int) (B_29 tptp.int) (C_19 tptp.int) (D_3 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_43) B_29) (@ (@ tptp.minus_minus_int C_19) D_3)) (= (= A_43 B_29) (= C_19 D_3)))) (forall ((A_42 (-> tptp.int Bool)) (B_28 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_28) (=> (@ (@ tptp.ord_less_eq_int_o B_28) A_42) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_42) B_28)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A_42)) (@ tptp.finite_card_int B_28)))))) (forall ((A_42 (-> tptp.nat Bool)) (B_28 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_28) (=> (@ (@ tptp.ord_less_eq_nat_o B_28) A_42) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_42) B_28)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A_42)) (@ tptp.finite_card_nat B_28)))))) (forall ((A_42 (-> tptp.x_a Bool)) (B_28 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_28) (=> (@ (@ tptp.ord_less_eq_a_o B_28) A_42) (= (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_42) B_28)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a A_42)) (@ tptp.finite_card_a B_28)))))) (forall ((A_42 (-> tptp.pname Bool)) (B_28 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_28) (=> (@ (@ tptp.ord_less_eq_pname_o B_28) A_42) (= (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_42) B_28)) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_pname A_42)) (@ tptp.finite_card_pname B_28)))))) (forall ((A_41 (-> tptp.int Bool)) (B_27 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int B_27) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A_41)) (@ tptp.finite_card_int B_27))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_41) B_27))))) (forall ((A_41 (-> tptp.nat Bool)) (B_27 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B_27) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A_41)) (@ tptp.finite_card_nat B_27))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_41) B_27))))) (forall ((A_41 (-> tptp.x_a Bool)) (B_27 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a B_27) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a A_41)) (@ tptp.finite_card_a B_27))) (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_41) B_27))))) (forall ((A_41 (-> tptp.pname Bool)) (B_27 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname B_27) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_pname A_41)) (@ tptp.finite_card_pname B_27))) (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_41) B_27))))) (forall ((P_5 (-> (-> tptp.x_a Bool) Bool)) (A_40 (-> tptp.x_a Bool)) (F_18 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_18) (=> (@ (@ tptp.ord_less_eq_a_o F_18) A_40) (=> (@ P_5 tptp.bot_bot_a_o) (=> (forall ((A_37 tptp.x_a) (F_2 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a A_37))) (=> (@ tptp.finite_finite_a F_2) (=> (@ _let_1 A_40) (=> (not (@ _let_1 F_2)) (=> (@ P_5 F_2) (@ P_5 (@ (@ tptp.insert_a A_37) F_2)))))))) (@ P_5 F_18)))))) (forall ((P_5 (-> (-> tptp.int Bool) Bool)) (A_40 (-> tptp.int Bool)) (F_18 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_18) (=> (@ (@ tptp.ord_less_eq_int_o F_18) A_40) (=> (@ P_5 tptp.bot_bot_int_o) (=> (forall ((A_37 tptp.int) (F_2 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int A_37))) (=> (@ tptp.finite_finite_int F_2) (=> (@ _let_1 A_40) (=> (not (@ _let_1 F_2)) (=> (@ P_5 F_2) (@ P_5 (@ (@ tptp.insert_int A_37) F_2)))))))) (@ P_5 F_18)))))) (forall ((P_5 (-> (-> tptp.nat Bool) Bool)) (A_40 (-> tptp.nat Bool)) (F_18 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_18) (=> (@ (@ tptp.ord_less_eq_nat_o F_18) A_40) (=> (@ P_5 tptp.bot_bot_nat_o) (=> (forall ((A_37 tptp.nat) (F_2 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat A_37))) (=> (@ tptp.finite_finite_nat F_2) (=> (@ _let_1 A_40) (=> (not (@ _let_1 F_2)) (=> (@ P_5 F_2) (@ P_5 (@ (@ tptp.insert_nat A_37) F_2)))))))) (@ P_5 F_18)))))) (forall ((P_5 (-> (-> tptp.pname Bool) Bool)) (A_40 (-> tptp.pname Bool)) (F_18 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_18) (=> (@ (@ tptp.ord_less_eq_pname_o F_18) A_40) (=> (@ P_5 tptp.bot_bot_pname_o) (=> (forall ((A_37 tptp.pname) (F_2 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname A_37))) (=> (@ tptp.finite_finite_pname F_2) (=> (@ _let_1 A_40) (=> (not (@ _let_1 F_2)) (=> (@ P_5 F_2) (@ P_5 (@ (@ tptp.insert_pname A_37) F_2)))))))) (@ P_5 F_18)))))) (forall ((Pn tptp.pname) (G (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a (@ tptp.mgt_call Pn)))) (=> (@ (@ tptp.p (@ _let_1 G)) (@ (@ tptp.insert_a (@ tptp.mgt (@ tptp.the_com (@ tptp.body Pn)))) tptp.bot_bot_a_o)) (@ (@ tptp.p G) (@ _let_1 tptp.bot_bot_a_o))))) (forall ((P_4 (-> (-> tptp.x_a Bool) Bool)) (A_39 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_39) (=> (@ P_4 A_39) (=> (forall ((A_37 tptp.x_a) (A_38 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_38) (=> (@ (@ tptp.member_a A_37) A_38) (=> (@ P_4 A_38) (@ P_4 (@ (@ tptp.minus_minus_a_o A_38) (@ (@ tptp.insert_a A_37) tptp.bot_bot_a_o))))))) (@ P_4 tptp.bot_bot_a_o))))) (forall ((P_4 (-> (-> tptp.int Bool) Bool)) (A_39 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_39) (=> (@ P_4 A_39) (=> (forall ((A_37 tptp.int) (A_38 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_38) (=> (@ (@ tptp.member_int A_37) A_38) (=> (@ P_4 A_38) (@ P_4 (@ (@ tptp.minus_minus_int_o A_38) (@ (@ tptp.insert_int A_37) tptp.bot_bot_int_o))))))) (@ P_4 tptp.bot_bot_int_o))))) (forall ((P_4 (-> (-> tptp.nat Bool) Bool)) (A_39 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_39) (=> (@ P_4 A_39) (=> (forall ((A_37 tptp.nat) (A_38 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_38) (=> (@ (@ tptp.member_nat A_37) A_38) (=> (@ P_4 A_38) (@ P_4 (@ (@ tptp.minus_minus_nat_o A_38) (@ (@ tptp.insert_nat A_37) tptp.bot_bot_nat_o))))))) (@ P_4 tptp.bot_bot_nat_o))))) (forall ((P_4 (-> (-> tptp.pname Bool) Bool)) (A_39 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_39) (=> (@ P_4 A_39) (=> (forall ((A_37 tptp.pname) (A_38 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_38) (=> (@ (@ tptp.member_pname A_37) A_38) (=> (@ P_4 A_38) (@ P_4 (@ (@ tptp.minus_minus_pname_o A_38) (@ (@ tptp.insert_pname A_37) tptp.bot_bot_pname_o))))))) (@ P_4 tptp.bot_bot_pname_o))))) (forall ((P_3 (-> (-> tptp.x_a Bool) Bool)) (F_17 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_17) (=> (@ P_3 tptp.bot_bot_a_o) (=> (forall ((X_1 tptp.x_a) (F_2 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_2) (=> (not (@ (@ tptp.member_a X_1) F_2)) (=> (@ P_3 F_2) (@ P_3 (@ (@ tptp.insert_a X_1) F_2)))))) (@ P_3 F_17))))) (forall ((P_3 (-> (-> tptp.int Bool) Bool)) (F_17 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_17) (=> (@ P_3 tptp.bot_bot_int_o) (=> (forall ((X_1 tptp.int) (F_2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_2) (=> (not (@ (@ tptp.member_int X_1) F_2)) (=> (@ P_3 F_2) (@ P_3 (@ (@ tptp.insert_int X_1) F_2)))))) (@ P_3 F_17))))) (forall ((P_3 (-> (-> tptp.nat Bool) Bool)) (F_17 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_17) (=> (@ P_3 tptp.bot_bot_nat_o) (=> (forall ((X_1 tptp.nat) (F_2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_2) (=> (not (@ (@ tptp.member_nat X_1) F_2)) (=> (@ P_3 F_2) (@ P_3 (@ (@ tptp.insert_nat X_1) F_2)))))) (@ P_3 F_17))))) (forall ((P_3 (-> (-> tptp.pname Bool) Bool)) (F_17 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_17) (=> (@ P_3 tptp.bot_bot_pname_o) (=> (forall ((X_1 tptp.pname) (F_2 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_2) (=> (not (@ (@ tptp.member_pname X_1) F_2)) (=> (@ P_3 F_2) (@ P_3 (@ (@ tptp.insert_pname X_1) F_2)))))) (@ P_3 F_17))))) (forall ((A_36 (-> tptp.x_a Bool))) (= (@ tptp.finite_finite_a A_36) (or (= A_36 tptp.bot_bot_a_o) (exists ((A_38 (-> tptp.x_a Bool)) (A_37 tptp.x_a)) (and (= A_36 (@ (@ tptp.insert_a A_37) A_38)) (@ tptp.finite_finite_a A_38)))))) (forall ((A_36 (-> tptp.int Bool))) (= (@ tptp.finite_finite_int A_36) (or (= A_36 tptp.bot_bot_int_o) (exists ((A_38 (-> tptp.int Bool)) (A_37 tptp.int)) (and (= A_36 (@ (@ tptp.insert_int A_37) A_38)) (@ tptp.finite_finite_int A_38)))))) (forall ((A_36 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat A_36) (or (= A_36 tptp.bot_bot_nat_o) (exists ((A_38 (-> tptp.nat Bool)) (A_37 tptp.nat)) (and (= A_36 (@ (@ tptp.insert_nat A_37) A_38)) (@ tptp.finite_finite_nat A_38)))))) (forall ((A_36 (-> tptp.pname Bool))) (= (@ tptp.finite_finite_pname A_36) (or (= A_36 tptp.bot_bot_pname_o) (exists ((A_38 (-> tptp.pname Bool)) (A_37 tptp.pname)) (and (= A_36 (@ (@ tptp.insert_pname A_37) A_38)) (@ tptp.finite_finite_pname A_38)))))) (forall ((U tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N_1) (@ F N_1))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_1 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N_1)) U)))))) (forall ((X_13 tptp.x_a)) (= (@ tptp.the_elem_a (@ (@ tptp.insert_a X_13) tptp.bot_bot_a_o)) X_13)) (forall ((X_13 tptp.nat)) (= (@ tptp.the_elem_nat (@ (@ tptp.insert_nat X_13) tptp.bot_bot_nat_o)) X_13)) (forall ((X_13 tptp.int)) (= (@ tptp.the_elem_int (@ (@ tptp.insert_int X_13) tptp.bot_bot_int_o)) X_13)) (forall ((A_35 (-> tptp.x_a Bool))) (= (not (= A_35 tptp.bot_bot_a_o)) (exists ((X_1 tptp.x_a) (B_26 (-> tptp.x_a Bool))) (and (= A_35 (@ (@ tptp.insert_a X_1) B_26)) (not (@ (@ tptp.member_a X_1) B_26)))))) (forall ((A_35 (-> tptp.int Bool))) (= (not (= A_35 tptp.bot_bot_int_o)) (exists ((X_1 tptp.int) (B_26 (-> tptp.int Bool))) (and (= A_35 (@ (@ tptp.insert_int X_1) B_26)) (not (@ (@ tptp.member_int X_1) B_26)))))) (forall ((A_35 (-> tptp.nat Bool))) (= (not (= A_35 tptp.bot_bot_nat_o)) (exists ((X_1 tptp.nat) (B_26 (-> tptp.nat Bool))) (and (= A_35 (@ (@ tptp.insert_nat X_1) B_26)) (not (@ (@ tptp.member_nat X_1) B_26)))))) (forall ((A_35 (-> tptp.pname Bool))) (= (not (= A_35 tptp.bot_bot_pname_o)) (exists ((X_1 tptp.pname) (B_26 (-> tptp.pname Bool))) (and (= A_35 (@ (@ tptp.insert_pname X_1) B_26)) (not (@ (@ tptp.member_pname X_1) B_26)))))) (forall ((Pn tptp.pname)) (=> (@ (@ tptp.member_pname Pn) tptp.u) (@ tptp.wt (@ tptp.the_com (@ tptp.body Pn))))) (forall ((C_18 tptp.int) (A_34 (-> tptp.int Bool)) (B_25 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_18))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int_o A_34) B_25)) (not (=> (@ _let_1 A_34) (@ _let_1 B_25)))))) (forall ((C_18 tptp.nat) (A_34 (-> tptp.nat Bool)) (B_25 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_18))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_34) B_25)) (not (=> (@ _let_1 A_34) (@ _let_1 B_25)))))) (forall ((C_18 tptp.x_a) (A_34 (-> tptp.x_a Bool)) (B_25 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_18))) (=> (@ _let_1 (@ (@ tptp.minus_minus_a_o A_34) B_25)) (not (=> (@ _let_1 A_34) (@ _let_1 B_25)))))) (forall ((C_18 tptp.pname) (A_34 (-> tptp.pname Bool)) (B_25 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_18))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_34) B_25)) (not (=> (@ _let_1 A_34) (@ _let_1 B_25)))))) (forall ((B_24 (-> tptp.int Bool)) (C_17 tptp.int) (A_33 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_17))) (=> (@ _let_1 A_33) (=> (not (@ _let_1 B_24)) (@ _let_1 (@ (@ tptp.minus_minus_int_o A_33) B_24)))))) (forall ((B_24 (-> tptp.nat Bool)) (C_17 tptp.nat) (A_33 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_17))) (=> (@ _let_1 A_33) (=> (not (@ _let_1 B_24)) (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_33) B_24)))))) (forall ((B_24 (-> tptp.x_a Bool)) (C_17 tptp.x_a) (A_33 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_17))) (=> (@ _let_1 A_33) (=> (not (@ _let_1 B_24)) (@ _let_1 (@ (@ tptp.minus_minus_a_o A_33) B_24)))))) (forall ((B_24 (-> tptp.pname Bool)) (C_17 tptp.pname) (A_33 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_17))) (=> (@ _let_1 A_33) (=> (not (@ _let_1 B_24)) (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_33) B_24)))))) (forall ((C_16 tptp.int) (A_32 (-> tptp.int Bool)) (B_23 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_16))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int_o A_32) B_23)) (not (@ _let_1 B_23))))) (forall ((C_16 tptp.nat) (A_32 (-> tptp.nat Bool)) (B_23 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_16))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_32) B_23)) (not (@ _let_1 B_23))))) (forall ((C_16 tptp.x_a) (A_32 (-> tptp.x_a Bool)) (B_23 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_16))) (=> (@ _let_1 (@ (@ tptp.minus_minus_a_o A_32) B_23)) (not (@ _let_1 B_23))))) (forall ((C_16 tptp.pname) (A_32 (-> tptp.pname Bool)) (B_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_16))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_32) B_23)) (not (@ _let_1 B_23))))) (forall ((C_15 tptp.int) (A_31 (-> tptp.int Bool)) (B_22 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_15))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int_o A_31) B_22)) (@ _let_1 A_31)))) (forall ((C_15 tptp.nat) (A_31 (-> tptp.nat Bool)) (B_22 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_15))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_31) B_22)) (@ _let_1 A_31)))) (forall ((C_15 tptp.x_a) (A_31 (-> tptp.x_a Bool)) (B_22 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_15))) (=> (@ _let_1 (@ (@ tptp.minus_minus_a_o A_31) B_22)) (@ _let_1 A_31)))) (forall ((C_15 tptp.pname) (A_31 (-> tptp.pname Bool)) (B_22 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_15))) (=> (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_31) B_22)) (@ _let_1 A_31)))) (forall ((C_14 tptp.int) (A_30 (-> tptp.int Bool)) (B_21 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int C_14))) (= (@ _let_1 (@ (@ tptp.minus_minus_int_o A_30) B_21)) (and (@ _let_1 A_30) (not (@ _let_1 B_21)))))) (forall ((C_14 tptp.nat) (A_30 (-> tptp.nat Bool)) (B_21 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat C_14))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat_o A_30) B_21)) (and (@ _let_1 A_30) (not (@ _let_1 B_21)))))) (forall ((C_14 tptp.x_a) (A_30 (-> tptp.x_a Bool)) (B_21 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.member_a C_14))) (= (@ _let_1 (@ (@ tptp.minus_minus_a_o A_30) B_21)) (and (@ _let_1 A_30) (not (@ _let_1 B_21)))))) (forall ((C_14 tptp.pname) (A_30 (-> tptp.pname Bool)) (B_21 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.member_pname C_14))) (= (@ _let_1 (@ (@ tptp.minus_minus_pname_o A_30) B_21)) (and (@ _let_1 A_30) (not (@ _let_1 B_21)))))) (forall ((A_29 (-> tptp.int Bool)) (B_20 (-> tptp.int Bool))) (= (@ (@ tptp.minus_minus_int_o A_29) B_20) (@ tptp.collect_int (lambda ((X_1 tptp.int)) (let ((_let_1 (@ tptp.member_int X_1))) (and (@ _let_1 A_29) (not (@ _let_1 B_20)))))))) (forall ((A_29 (-> tptp.nat Bool)) (B_20 (-> tptp.nat Bool))) (= (@ (@ tptp.minus_minus_nat_o A_29) B_20) (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X_1))) (and (@ _let_1 A_29) (not (@ _let_1 B_20)))))))) (forall ((A_29 (-> tptp.x_a Bool)) (B_20 (-> tptp.x_a Bool))) (= (@ (@ tptp.minus_minus_a_o A_29) B_20) (@ tptp.collect_a (lambda ((X_1 tptp.x_a)) (let ((_let_1 (@ tptp.member_a X_1))) (and (@ _let_1 A_29) (not (@ _let_1 B_20)))))))) (forall ((A_29 (-> tptp.pname Bool)) (B_20 (-> tptp.pname Bool))) (= (@ (@ tptp.minus_minus_pname_o A_29) B_20) (@ tptp.collect_pname (lambda ((X_1 tptp.pname)) (let ((_let_1 (@ tptp.member_pname X_1))) (and (@ _let_1 A_29) (not (@ _let_1 B_20)))))))) (forall ((X_12 tptp.x_a) (A_28 (-> tptp.x_a Bool)) (F_16 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_15 (-> (-> tptp.x_a Bool) tptp.x_a))) (let ((_let_1 (@ tptp.insert_a X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_a_o A_28) (@ _let_1 tptp.bot_bot_a_o)))) (let ((_let_3 (@ F_15 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_a_o))) (=> (@ (@ tptp.finite_folding_one_a F_16) F_15) (=> (@ tptp.finite_finite_a A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_16 X_12) (@ F_15 _let_2)))))))))))) (forall ((X_12 tptp.int) (A_28 (-> tptp.int Bool)) (F_16 (-> tptp.int tptp.int tptp.int)) (F_15 (-> (-> tptp.int Bool) tptp.int))) (let ((_let_1 (@ tptp.insert_int X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_int_o A_28) (@ _let_1 tptp.bot_bot_int_o)))) (let ((_let_3 (@ F_15 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_int_o))) (=> (@ (@ tptp.finite1626084323ne_int F_16) F_15) (=> (@ tptp.finite_finite_int A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_16 X_12) (@ F_15 _let_2)))))))))))) (forall ((X_12 tptp.nat) (A_28 (-> tptp.nat Bool)) (F_16 (-> tptp.nat tptp.nat tptp.nat)) (F_15 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ tptp.insert_nat X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_nat_o A_28) (@ _let_1 tptp.bot_bot_nat_o)))) (let ((_let_3 (@ F_15 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_nat_o))) (=> (@ (@ tptp.finite988810631ne_nat F_16) F_15) (=> (@ tptp.finite_finite_nat A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_16 X_12) (@ F_15 _let_2)))))))))))) (forall ((X_12 tptp.pname) (A_28 (-> tptp.pname Bool)) (F_16 (-> tptp.pname tptp.pname tptp.pname)) (F_15 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ tptp.insert_pname X_12))) (let ((_let_2 (@ (@ tptp.minus_minus_pname_o A_28) (@ _let_1 tptp.bot_bot_pname_o)))) (let ((_let_3 (@ F_15 (@ _let_1 A_28)))) (let ((_let_4 (= _let_2 tptp.bot_bot_pname_o))) (=> (@ (@ tptp.finite1282449217_pname F_16) F_15) (=> (@ tptp.finite_finite_pname A_28) (and (=> _let_4 (= _let_3 X_12)) (=> (not _let_4) (= _let_3 (@ (@ F_16 X_12) (@ F_15 _let_2)))))))))))) (forall ((X_11 tptp.x_a) (A_27 (-> tptp.x_a Bool)) (F_14 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_13 (-> (-> tptp.x_a Bool) tptp.x_a))) (let ((_let_1 (@ (@ tptp.minus_minus_a_o A_27) (@ (@ tptp.insert_a X_11) tptp.bot_bot_a_o)))) (let ((_let_2 (@ F_13 A_27))) (let ((_let_3 (= _let_1 tptp.bot_bot_a_o))) (=> (@ (@ tptp.finite_folding_one_a F_14) F_13) (=> (@ tptp.finite_finite_a A_27) (=> (@ (@ tptp.member_a X_11) A_27) (and (=> _let_3 (= _let_2 X_11)) (=> (not _let_3) (= _let_2 (@ (@ F_14 X_11) (@ F_13 _let_1)))))))))))) (forall ((X_11 tptp.int) (A_27 (-> tptp.int Bool)) (F_14 (-> tptp.int tptp.int tptp.int)) (F_13 (-> (-> tptp.int Bool) tptp.int))) (let ((_let_1 (@ (@ tptp.minus_minus_int_o A_27) (@ (@ tptp.insert_int X_11) tptp.bot_bot_int_o)))) (let ((_let_2 (@ F_13 A_27))) (let ((_let_3 (= _let_1 tptp.bot_bot_int_o))) (=> (@ (@ tptp.finite1626084323ne_int F_14) F_13) (=> (@ tptp.finite_finite_int A_27) (=> (@ (@ tptp.member_int X_11) A_27) (and (=> _let_3 (= _let_2 X_11)) (=> (not _let_3) (= _let_2 (@ (@ F_14 X_11) (@ F_13 _let_1)))))))))))) (forall ((X_11 tptp.nat) (A_27 (-> tptp.nat Bool)) (F_14 (-> tptp.nat tptp.nat tptp.nat)) (F_13 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ (@ tptp.minus_minus_nat_o A_27) (@ (@ tptp.insert_nat X_11) tptp.bot_bot_nat_o)))) (let ((_let_2 (@ F_13 A_27))) (let ((_let_3 (= _let_1 tptp.bot_bot_nat_o))) (=> (@ (@ tptp.finite988810631ne_nat F_14) F_13) (=> (@ tptp.finite_finite_nat A_27) (=> (@ (@ tptp.member_nat X_11) A_27) (and (=> _let_3 (= _let_2 X_11)) (=> (not _let_3) (= _let_2 (@ (@ F_14 X_11) (@ F_13 _let_1)))))))))))) (forall ((X_11 tptp.pname) (A_27 (-> tptp.pname Bool)) (F_14 (-> tptp.pname tptp.pname tptp.pname)) (F_13 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ (@ tptp.minus_minus_pname_o A_27) (@ (@ tptp.insert_pname X_11) tptp.bot_bot_pname_o)))) (let ((_let_2 (@ F_13 A_27))) (let ((_let_3 (= _let_1 tptp.bot_bot_pname_o))) (=> (@ (@ tptp.finite1282449217_pname F_14) F_13) (=> (@ tptp.finite_finite_pname A_27) (=> (@ (@ tptp.member_pname X_11) A_27) (and (=> _let_3 (= _let_2 X_11)) (=> (not _let_3) (= _let_2 (@ (@ F_14 X_11) (@ F_13 _let_1)))))))))))) (forall ((X_10 tptp.x_a) (A_26 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.finite_card_a A_26))) (let ((_let_2 (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_26) (@ (@ tptp.insert_a X_10) tptp.bot_bot_a_o))))) (let ((_let_3 (@ (@ tptp.member_a X_10) A_26))) (=> (@ tptp.finite_finite_a A_26) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((X_10 tptp.int) (A_26 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_card_int A_26))) (let ((_let_2 (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_26) (@ (@ tptp.insert_int X_10) tptp.bot_bot_int_o))))) (let ((_let_3 (@ (@ tptp.member_int X_10) A_26))) (=> (@ tptp.finite_finite_int A_26) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((X_10 tptp.nat) (A_26 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_card_nat A_26))) (let ((_let_2 (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_26) (@ (@ tptp.insert_nat X_10) tptp.bot_bot_nat_o))))) (let ((_let_3 (@ (@ tptp.member_nat X_10) A_26))) (=> (@ tptp.finite_finite_nat A_26) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((X_10 tptp.pname) (A_26 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.finite_card_pname A_26))) (let ((_let_2 (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_26) (@ (@ tptp.insert_pname X_10) tptp.bot_bot_pname_o))))) (let ((_let_3 (@ (@ tptp.member_pname X_10) A_26))) (=> (@ tptp.finite_finite_pname A_26) (and (=> _let_3 (= _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat))) (=> (not _let_3) (= _let_2 _let_1)))))))) (forall ((X_9 tptp.x_a) (A_25 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_25) (=> (@ (@ tptp.member_a X_9) A_25) (= (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_25) (@ (@ tptp.insert_a X_9) tptp.bot_bot_a_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a A_25)) tptp.one_one_nat))))) (forall ((X_9 tptp.int) (A_25 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_25) (=> (@ (@ tptp.member_int X_9) A_25) (= (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_25) (@ (@ tptp.insert_int X_9) tptp.bot_bot_int_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int A_25)) tptp.one_one_nat))))) (forall ((X_9 tptp.nat) (A_25 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_25) (=> (@ (@ tptp.member_nat X_9) A_25) (= (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_25) (@ (@ tptp.insert_nat X_9) tptp.bot_bot_nat_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat A_25)) tptp.one_one_nat))))) (forall ((X_9 tptp.pname) (A_25 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_25) (=> (@ (@ tptp.member_pname X_9) A_25) (= (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_25) (@ (@ tptp.insert_pname X_9) tptp.bot_bot_pname_o))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_pname A_25)) tptp.one_one_nat))))) (forall ((X_8 tptp.int)) (= (= tptp.one_one_int X_8) (= X_8 tptp.one_one_int))) (forall ((X_8 tptp.nat)) (= (= tptp.one_one_nat X_8) (= X_8 tptp.one_one_nat))) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))) (forall ((X_7 tptp.x_a) (F_12 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_11 (-> (-> tptp.x_a Bool) tptp.x_a))) (=> (@ (@ tptp.finite_folding_one_a F_12) F_11) (= (@ F_11 (@ (@ tptp.insert_a X_7) tptp.bot_bot_a_o)) X_7))) (forall ((X_7 tptp.nat) (F_12 (-> tptp.nat tptp.nat tptp.nat)) (F_11 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_12) F_11) (= (@ F_11 (@ (@ tptp.insert_nat X_7) tptp.bot_bot_nat_o)) X_7))) (forall ((X_7 tptp.int) (F_12 (-> tptp.int tptp.int tptp.int)) (F_11 (-> (-> tptp.int Bool) tptp.int))) (=> (@ (@ tptp.finite1626084323ne_int F_12) F_11) (= (@ F_11 (@ (@ tptp.insert_int X_7) tptp.bot_bot_int_o)) X_7))) (forall ((B_19 (-> tptp.x_a Bool)) (A_24 tptp.x_a) (A_23 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.minus_minus_a_o A_23))) (let ((_let_2 (@ tptp.member_a A_24))) (=> (@ tptp.finite_finite_a A_23) (=> (@ _let_2 A_23) (=> (not (@ _let_2 B_19)) (= (@ tptp.finite_card_a (@ _let_1 (@ (@ tptp.insert_a A_24) B_19))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_a (@ _let_1 B_19))) tptp.one_one_nat)))))))) (forall ((B_19 (-> tptp.int Bool)) (A_24 tptp.int) (A_23 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.minus_minus_int_o A_23))) (let ((_let_2 (@ tptp.member_int A_24))) (=> (@ tptp.finite_finite_int A_23) (=> (@ _let_2 A_23) (=> (not (@ _let_2 B_19)) (= (@ tptp.finite_card_int (@ _let_1 (@ (@ tptp.insert_int A_24) B_19))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_int (@ _let_1 B_19))) tptp.one_one_nat)))))))) (forall ((B_19 (-> tptp.nat Bool)) (A_24 tptp.nat) (A_23 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.minus_minus_nat_o A_23))) (let ((_let_2 (@ tptp.member_nat A_24))) (=> (@ tptp.finite_finite_nat A_23) (=> (@ _let_2 A_23) (=> (not (@ _let_2 B_19)) (= (@ tptp.finite_card_nat (@ _let_1 (@ (@ tptp.insert_nat A_24) B_19))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_nat (@ _let_1 B_19))) tptp.one_one_nat)))))))) (forall ((B_19 (-> tptp.pname Bool)) (A_24 tptp.pname) (A_23 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.minus_minus_pname_o A_23))) (let ((_let_2 (@ tptp.member_pname A_24))) (=> (@ tptp.finite_finite_pname A_23) (=> (@ _let_2 A_23) (=> (not (@ _let_2 B_19)) (= (@ tptp.finite_card_pname (@ _let_1 (@ (@ tptp.insert_pname A_24) B_19))) (@ (@ tptp.minus_minus_nat (@ tptp.finite_card_pname (@ _let_1 B_19))) tptp.one_one_nat)))))))) (forall ((X_6 tptp.x_a) (A_22 (-> tptp.x_a Bool)) (F_10 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_9 (-> (-> tptp.x_a Bool) tptp.x_a))) (=> (@ (@ tptp.finite_folding_one_a F_10) F_9) (=> (@ tptp.finite_finite_a A_22) (=> (not (@ (@ tptp.member_a X_6) A_22)) (=> (not (= A_22 tptp.bot_bot_a_o)) (= (@ F_9 (@ (@ tptp.insert_a X_6) A_22)) (@ (@ F_10 X_6) (@ F_9 A_22)))))))) (forall ((X_6 tptp.int) (A_22 (-> tptp.int Bool)) (F_10 (-> tptp.int tptp.int tptp.int)) (F_9 (-> (-> tptp.int Bool) tptp.int))) (=> (@ (@ tptp.finite1626084323ne_int F_10) F_9) (=> (@ tptp.finite_finite_int A_22) (=> (not (@ (@ tptp.member_int X_6) A_22)) (=> (not (= A_22 tptp.bot_bot_int_o)) (= (@ F_9 (@ (@ tptp.insert_int X_6) A_22)) (@ (@ F_10 X_6) (@ F_9 A_22)))))))) (forall ((X_6 tptp.nat) (A_22 (-> tptp.nat Bool)) (F_10 (-> tptp.nat tptp.nat tptp.nat)) (F_9 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_10) F_9) (=> (@ tptp.finite_finite_nat A_22) (=> (not (@ (@ tptp.member_nat X_6) A_22)) (=> (not (= A_22 tptp.bot_bot_nat_o)) (= (@ F_9 (@ (@ tptp.insert_nat X_6) A_22)) (@ (@ F_10 X_6) (@ F_9 A_22)))))))) (forall ((X_6 tptp.pname) (A_22 (-> tptp.pname Bool)) (F_10 (-> tptp.pname tptp.pname tptp.pname)) (F_9 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_10) F_9) (=> (@ tptp.finite_finite_pname A_22) (=> (not (@ (@ tptp.member_pname X_6) A_22)) (=> (not (= A_22 tptp.bot_bot_pname_o)) (= (@ F_9 (@ (@ tptp.insert_pname X_6) A_22)) (@ (@ F_10 X_6) (@ F_9 A_22)))))))) (forall ((A_21 (-> tptp.x_a Bool)) (F_8 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_7 (-> (-> tptp.x_a Bool) tptp.x_a))) (=> (@ (@ tptp.finite_folding_one_a F_8) F_7) (=> (@ tptp.finite_finite_a A_21) (=> (not (= A_21 tptp.bot_bot_a_o)) (=> (forall ((X_1 tptp.x_a) (Y_1 tptp.x_a)) (@ (@ tptp.member_a (@ (@ F_8 X_1) Y_1)) (@ (@ tptp.insert_a X_1) (@ (@ tptp.insert_a Y_1) tptp.bot_bot_a_o)))) (@ (@ tptp.member_a (@ F_7 A_21)) A_21)))))) (forall ((A_21 (-> tptp.int Bool)) (F_8 (-> tptp.int tptp.int tptp.int)) (F_7 (-> (-> tptp.int Bool) tptp.int))) (=> (@ (@ tptp.finite1626084323ne_int F_8) F_7) (=> (@ tptp.finite_finite_int A_21) (=> (not (= A_21 tptp.bot_bot_int_o)) (=> (forall ((X_1 tptp.int) (Y_1 tptp.int)) (@ (@ tptp.member_int (@ (@ F_8 X_1) Y_1)) (@ (@ tptp.insert_int X_1) (@ (@ tptp.insert_int Y_1) tptp.bot_bot_int_o)))) (@ (@ tptp.member_int (@ F_7 A_21)) A_21)))))) (forall ((A_21 (-> tptp.nat Bool)) (F_8 (-> tptp.nat tptp.nat tptp.nat)) (F_7 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite988810631ne_nat F_8) F_7) (=> (@ tptp.finite_finite_nat A_21) (=> (not (= A_21 tptp.bot_bot_nat_o)) (=> (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (@ (@ tptp.member_nat (@ (@ F_8 X_1) Y_1)) (@ (@ tptp.insert_nat X_1) (@ (@ tptp.insert_nat Y_1) tptp.bot_bot_nat_o)))) (@ (@ tptp.member_nat (@ F_7 A_21)) A_21)))))) (forall ((A_21 (-> tptp.pname Bool)) (F_8 (-> tptp.pname tptp.pname tptp.pname)) (F_7 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite1282449217_pname F_8) F_7) (=> (@ tptp.finite_finite_pname A_21) (=> (not (= A_21 tptp.bot_bot_pname_o)) (=> (forall ((X_1 tptp.pname) (Y_1 tptp.pname)) (@ (@ tptp.member_pname (@ (@ F_8 X_1) Y_1)) (@ (@ tptp.insert_pname X_1) (@ (@ tptp.insert_pname Y_1) tptp.bot_bot_pname_o)))) (@ (@ tptp.member_pname (@ F_7 A_21)) A_21)))))) (forall ((X_5 tptp.x_a) (A_20 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a A_20) (=> (@ (@ tptp.member_a X_5) A_20) (= (@ tptp.finite_card_a A_20) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_20) (@ (@ tptp.insert_a X_5) tptp.bot_bot_a_o)))))))) (forall ((X_5 tptp.int) (A_20 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A_20) (=> (@ (@ tptp.member_int X_5) A_20) (= (@ tptp.finite_card_int A_20) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_20) (@ (@ tptp.insert_int X_5) tptp.bot_bot_int_o)))))))) (forall ((X_5 tptp.nat) (A_20 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A_20) (=> (@ (@ tptp.member_nat X_5) A_20) (= (@ tptp.finite_card_nat A_20) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_20) (@ (@ tptp.insert_nat X_5) tptp.bot_bot_nat_o)))))))) (forall ((X_5 tptp.pname) (A_20 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname A_20) (=> (@ (@ tptp.member_pname X_5) A_20) (= (@ tptp.finite_card_pname A_20) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_20) (@ (@ tptp.insert_pname X_5) tptp.bot_bot_pname_o)))))))) (forall ((X_4 tptp.x_a) (A_19 (-> tptp.x_a Bool))) (let ((_let_1 (@ tptp.insert_a X_4))) (=> (@ tptp.finite_finite_a A_19) (= (@ tptp.finite_card_a (@ _let_1 A_19)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_a (@ (@ tptp.minus_minus_a_o A_19) (@ _let_1 tptp.bot_bot_a_o)))))))) (forall ((X_4 tptp.int) (A_19 (-> tptp.int Bool))) (let ((_let_1 (@ tptp.insert_int X_4))) (=> (@ tptp.finite_finite_int A_19) (= (@ tptp.finite_card_int (@ _let_1 A_19)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_int_o A_19) (@ _let_1 tptp.bot_bot_int_o)))))))) (forall ((X_4 tptp.nat) (A_19 (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.insert_nat X_4))) (=> (@ tptp.finite_finite_nat A_19) (= (@ tptp.finite_card_nat (@ _let_1 A_19)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_nat_o A_19) (@ _let_1 tptp.bot_bot_nat_o)))))))) (forall ((X_4 tptp.pname) (A_19 (-> tptp.pname Bool))) (let ((_let_1 (@ tptp.insert_pname X_4))) (=> (@ tptp.finite_finite_pname A_19) (= (@ tptp.finite_card_pname (@ _let_1 A_19)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.finite_card_pname (@ (@ tptp.minus_minus_pname_o A_19) (@ _let_1 tptp.bot_bot_pname_o)))))))) (forall ((B_18 (-> tptp.int Bool)) (A_18 (-> tptp.int Bool)) (F_6 (-> tptp.int tptp.int tptp.int)) (F_5 (-> (-> tptp.int Bool) tptp.int))) (let ((_let_1 (@ F_5 A_18))) (=> (@ (@ tptp.finite1432773856em_int F_6) F_5) (=> (@ tptp.finite_finite_int A_18) (=> (not (= B_18 tptp.bot_bot_int_o)) (=> (@ (@ tptp.ord_less_eq_int_o B_18) A_18) (= (@ (@ F_6 (@ F_5 B_18)) _let_1) _let_1))))))) (forall ((B_18 (-> tptp.nat Bool)) (A_18 (-> tptp.nat Bool)) (F_6 (-> tptp.nat tptp.nat tptp.nat)) (F_5 (-> (-> tptp.nat Bool) tptp.nat))) (let ((_let_1 (@ F_5 A_18))) (=> (@ (@ tptp.finite795500164em_nat F_6) F_5) (=> (@ tptp.finite_finite_nat A_18) (=> (not (= B_18 tptp.bot_bot_nat_o)) (=> (@ (@ tptp.ord_less_eq_nat_o B_18) A_18) (= (@ (@ F_6 (@ F_5 B_18)) _let_1) _let_1))))))) (forall ((B_18 (-> tptp.pname Bool)) (A_18 (-> tptp.pname Bool)) (F_6 (-> tptp.pname tptp.pname tptp.pname)) (F_5 (-> (-> tptp.pname Bool) tptp.pname))) (let ((_let_1 (@ F_5 A_18))) (=> (@ (@ tptp.finite89670078_pname F_6) F_5) (=> (@ tptp.finite_finite_pname A_18) (=> (not (= B_18 tptp.bot_bot_pname_o)) (=> (@ (@ tptp.ord_less_eq_pname_o B_18) A_18) (= (@ (@ F_6 (@ F_5 B_18)) _let_1) _let_1))))))) (forall ((B_18 (-> tptp.x_a Bool)) (A_18 (-> tptp.x_a Bool)) (F_6 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_5 (-> (-> tptp.x_a Bool) tptp.x_a))) (let ((_let_1 (@ F_5 A_18))) (=> (@ (@ tptp.finite1819937229idem_a F_6) F_5) (=> (@ tptp.finite_finite_a A_18) (=> (not (= B_18 tptp.bot_bot_a_o)) (=> (@ (@ tptp.ord_less_eq_a_o B_18) A_18) (= (@ (@ F_6 (@ F_5 B_18)) _let_1) _let_1))))))) (forall ((X_3 tptp.x_a) (A_17 (-> tptp.x_a Bool)) (F_4 (-> tptp.x_a tptp.x_a tptp.x_a)) (F_3 (-> (-> tptp.x_a Bool) tptp.x_a))) (=> (@ (@ tptp.finite1819937229idem_a F_4) F_3) (=> (@ tptp.finite_finite_a A_17) (=> (not (= A_17 tptp.bot_bot_a_o)) (= (@ F_3 (@ (@ tptp.insert_a X_3) A_17)) (@ (@ F_4 X_3) (@ F_3 A_17))))))) (forall ((X_3 tptp.int) (A_17 (-> tptp.int Bool)) (F_4 (-> tptp.int tptp.int tptp.int)) (F_3 (-> (-> tptp.int Bool) tptp.int))) (=> (@ (@ tptp.finite1432773856em_int F_4) F_3) (=> (@ tptp.finite_finite_int A_17) (=> (not (= A_17 tptp.bot_bot_int_o)) (= (@ F_3 (@ (@ tptp.insert_int X_3) A_17)) (@ (@ F_4 X_3) (@ F_3 A_17))))))) (forall ((X_3 tptp.nat) (A_17 (-> tptp.nat Bool)) (F_4 (-> tptp.nat tptp.nat tptp.nat)) (F_3 (-> (-> tptp.nat Bool) tptp.nat))) (=> (@ (@ tptp.finite795500164em_nat F_4) F_3) (=> (@ tptp.finite_finite_nat A_17) (=> (not (= A_17 tptp.bot_bot_nat_o)) (= (@ F_3 (@ (@ tptp.insert_nat X_3) A_17)) (@ (@ F_4 X_3) (@ F_3 A_17))))))) (forall ((X_3 tptp.pname) (A_17 (-> tptp.pname Bool)) (F_4 (-> tptp.pname tptp.pname tptp.pname)) (F_3 (-> (-> tptp.pname Bool) tptp.pname))) (=> (@ (@ tptp.finite89670078_pname F_4) F_3) (=> (@ tptp.finite_finite_pname A_17) (=> (not (= A_17 tptp.bot_bot_pname_o)) (= (@ F_3 (@ (@ tptp.insert_pname X_3) A_17)) (@ (@ F_4 X_3) (@ F_3 A_17))))))) (forall ((P_2 (-> (-> tptp.x_a Bool) Bool)) (F_1 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_1) (=> (not (= F_1 tptp.bot_bot_a_o)) (=> (forall ((X_1 tptp.x_a)) (@ P_2 (@ (@ tptp.insert_a X_1) tptp.bot_bot_a_o))) (=> (forall ((X_1 tptp.x_a) (F_2 (-> tptp.x_a Bool))) (=> (@ tptp.finite_finite_a F_2) (=> (not (= F_2 tptp.bot_bot_a_o)) (=> (not (@ (@ tptp.member_a X_1) F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_a X_1) F_2))))))) (@ P_2 F_1)))))) (forall ((P_2 (-> (-> tptp.int Bool) Bool)) (F_1 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_1) (=> (not (= F_1 tptp.bot_bot_int_o)) (=> (forall ((X_1 tptp.int)) (@ P_2 (@ (@ tptp.insert_int X_1) tptp.bot_bot_int_o))) (=> (forall ((X_1 tptp.int) (F_2 (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int F_2) (=> (not (= F_2 tptp.bot_bot_int_o)) (=> (not (@ (@ tptp.member_int X_1) F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_int X_1) F_2))))))) (@ P_2 F_1)))))) (forall ((P_2 (-> (-> tptp.nat Bool) Bool)) (F_1 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_1) (=> (not (= F_1 tptp.bot_bot_nat_o)) (=> (forall ((X_1 tptp.nat)) (@ P_2 (@ (@ tptp.insert_nat X_1) tptp.bot_bot_nat_o))) (=> (forall ((X_1 tptp.nat) (F_2 (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat F_2) (=> (not (= F_2 tptp.bot_bot_nat_o)) (=> (not (@ (@ tptp.member_nat X_1) F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_nat X_1) F_2))))))) (@ P_2 F_1)))))) (forall ((P_2 (-> (-> tptp.pname Bool) Bool)) (F_1 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_1) (=> (not (= F_1 tptp.bot_bot_pname_o)) (=> (forall ((X_1 tptp.pname)) (@ P_2 (@ (@ tptp.insert_pname X_1) tptp.bot_bot_pname_o))) (=> (forall ((X_1 tptp.pname) (F_2 (-> tptp.pname Bool))) (=> (@ tptp.finite_finite_pname F_2) (=> (not (= F_2 tptp.bot_bot_pname_o)) (=> (not (@ (@ tptp.member_pname X_1) F_2)) (=> (@ P_2 F_2) (@ P_2 (@ (@ tptp.insert_pname X_1) F_2))))))) (@ P_2 F_1)))))) (forall ((X_2 (-> tptp.x_a Bool))) (= (@ tptp.the_elem_a X_2) (@ tptp.the_a (lambda ((X_1 tptp.x_a)) (= X_2 (@ (@ tptp.insert_a X_1) tptp.bot_bot_a_o)))))) (forall ((X_2 (-> tptp.nat Bool))) (= (@ tptp.the_elem_nat X_2) (@ tptp.the_nat (lambda ((X_1 tptp.nat)) (= X_2 (@ (@ tptp.insert_nat X_1) tptp.bot_bot_nat_o)))))) (forall ((X_2 (-> tptp.int Bool))) (= (@ tptp.the_elem_int X_2) (@ tptp.the_int (lambda ((X_1 tptp.int)) (= X_2 (@ (@ tptp.insert_int X_1) tptp.bot_bot_int_o)))))) (forall ((A_16 tptp.int) (B_17 tptp.int) (C_13 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_16))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_17)) C_13) (@ _let_1 (@ (@ tptp.plus_plus_int B_17) C_13))))) (forall ((A_16 tptp.nat) (B_17 tptp.nat) (C_13 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_16))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_17)) C_13) (@ _let_1 (@ (@ tptp.plus_plus_nat B_17) C_13))))) (forall ((A_15 tptp.int) (B_16 tptp.int) (C_12 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_15))) (= (= (@ _let_1 B_16) (@ _let_1 C_12)) (= B_16 C_12)))) (forall ((A_15 tptp.nat) (B_16 tptp.nat) (C_12 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_15))) (= (= (@ _let_1 B_16) (@ _let_1 C_12)) (= B_16 C_12)))) (forall ((B_15 tptp.int) (A_14 tptp.int) (C_11 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B_15) A_14) (@ (@ tptp.plus_plus_int C_11) A_14)) (= B_15 C_11))) (forall ((B_15 tptp.nat) (A_14 tptp.nat) (C_11 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B_15) A_14) (@ (@ tptp.plus_plus_nat C_11) A_14)) (= B_15 C_11))) (forall ((A_13 tptp.int) (B_14 tptp.int) (C_10 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_13))) (=> (= (@ _let_1 B_14) (@ _let_1 C_10)) (= B_14 C_10)))) (forall ((A_13 tptp.nat) (B_14 tptp.nat) (C_10 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_13))) (=> (= (@ _let_1 B_14) (@ _let_1 C_10)) (= B_14 C_10)))) (forall ((A_12 tptp.int) (B_13 tptp.int) (C_9 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_12))) (=> (= (@ _let_1 B_13) (@ _let_1 C_9)) (= B_13 C_9)))) (forall ((A_12 tptp.nat) (B_13 tptp.nat) (C_9 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_12))) (=> (= (@ _let_1 B_13) (@ _let_1 C_9)) (= B_13 C_9)))) (forall ((B_12 tptp.int) (A_11 tptp.int) (C_8 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B_12) A_11) (@ (@ tptp.plus_plus_int C_8) A_11)) (= B_12 C_8))) (forall ((B_12 tptp.nat) (A_11 tptp.nat) (C_8 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B_12) A_11) (@ (@ tptp.plus_plus_nat C_8) A_11)) (= B_12 C_8))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) K))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K) (@ (@ tptp.plus_plus_nat N) K)) (= M N))) (forall ((A_10 tptp.int) (C_7 tptp.int) (B_11 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_10) C_7)) (@ (@ tptp.plus_plus_int B_11) C_7)) (@ (@ tptp.ord_less_eq_int A_10) B_11))) (forall ((A_10 tptp.nat) (C_7 tptp.nat) (B_11 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_10) C_7)) (@ (@ tptp.plus_plus_nat B_11) C_7)) (@ (@ tptp.ord_less_eq_nat A_10) B_11))) (forall ((C_6 tptp.int) (A_9 tptp.int) (B_10 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_6))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A_9)) (@ _let_1 B_10)) (@ (@ tptp.ord_less_eq_int A_9) B_10)))) (forall ((C_6 tptp.nat) (A_9 tptp.nat) (B_10 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_6))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_9)) (@ _let_1 B_10)) (@ (@ tptp.ord_less_eq_nat A_9) B_10)))) (forall ((C_5 tptp.int) (A_8 tptp.int) (B_9 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_8) B_9) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_8) C_5)) (@ (@ tptp.plus_plus_int B_9) C_5)))) (forall ((C_5 tptp.nat) (A_8 tptp.nat) (B_9 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_8) B_9) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_8) C_5)) (@ (@ tptp.plus_plus_nat B_9) C_5)))) (forall ((C_4 tptp.int) (A_7 tptp.int) (B_8 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_4))) (=> (@ (@ tptp.ord_less_eq_int A_7) B_8) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_7)) (@ _let_1 B_8))))) (forall ((C_4 tptp.nat) (A_7 tptp.nat) (B_8 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_4))) (=> (@ (@ tptp.ord_less_eq_nat A_7) B_8) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_7)) (@ _let_1 B_8))))) (forall ((C_3 tptp.int) (D_2 tptp.int) (A_6 tptp.int) (B_7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_6) B_7) (=> (@ (@ tptp.ord_less_eq_int C_3) D_2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_6) C_3)) (@ (@ tptp.plus_plus_int B_7) D_2))))) (forall ((C_3 tptp.nat) (D_2 tptp.nat) (A_6 tptp.nat) (B_7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_6) B_7) (=> (@ (@ tptp.ord_less_eq_nat C_3) D_2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_6) C_3)) (@ (@ tptp.plus_plus_nat B_7) D_2))))) (forall ((A_5 tptp.int) (C_2 tptp.int) (B_6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_5) C_2)) (@ (@ tptp.plus_plus_int B_6) C_2)) (@ (@ tptp.ord_less_eq_int A_5) B_6))) (forall ((A_5 tptp.nat) (C_2 tptp.nat) (B_6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_5) C_2)) (@ (@ tptp.plus_plus_nat B_6) C_2)) (@ (@ tptp.ord_less_eq_nat A_5) B_6))) (forall ((C_1 tptp.int) (A_4 tptp.int) (B_5 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_1))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A_4)) (@ _let_1 B_5)) (@ (@ tptp.ord_less_eq_int A_4) B_5)))) (forall ((C_1 tptp.nat) (A_4 tptp.nat) (B_5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_1))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_4)) (@ _let_1 B_5)) (@ (@ tptp.ord_less_eq_nat A_4) B_5)))) (forall ((A_3 tptp.int) (B_4 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_3) B_4)) B_4) A_3)) (forall ((A_2 tptp.int) (B_3 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_2) B_3)) B_3) A_2)) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M) K_1))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I_1) K)) J)))) (forall ((J tptp.nat) (K tptp.nat) (I_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I_1) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I_1) K)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) K)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) J)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) N)) N) M))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (= (@ (@ tptp.minus_minus_nat J) I_1) K) (= J (@ (@ tptp.plus_plus_nat K) I_1))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I_1)) K)))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I_1)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I_1)))) (forall ((N tptp.nat)) (= (@ tptp.suc N) (@ (@ 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(forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N_1 tptp.nat)) (@ (@ tptp.ord_less_nat N_1) K))))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ P N) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N) _let_1) (=> (=> (= M N) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N) M) _let_1) _let_1))))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I_1)) K)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((I_1 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J)) I_1))) (forall ((J tptp.nat) (I_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I_1)) I_1))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J)) K) (@ (@ tptp.ord_less_nat I_1) K))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))) (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (not (= M N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((N tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))) (forall ((N_2 (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat N_2) (exists ((M_1 tptp.nat)) (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_2) (@ (@ tptp.ord_less_nat X_1) M_1)))))) (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I tptp.nat)) (@ (@ tptp.ord_less_nat I) N)))) N)) (forall ((P (-> tptp.nat Bool)) (I_1 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ P K_1) (@ (@ tptp.ord_less_nat K_1) I_1)))))) (forall ((I_1 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I_1) (@ tptp.suc (@ (@ tptp.plus_plus_nat I_1) M)))) (forall ((I_1 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I_1) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I_1)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_1)))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) J))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))) (forall ((C tptp.nat) (A_1 tptp.nat) (B_2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_1) B_2) (=> (@ (@ tptp.ord_less_eq_nat C) A_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A_1) C)) (@ (@ tptp.minus_minus_nat B_2) C))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))) (forall ((X_1 tptp.nat)) (= (@ tptp.ord_less_nat X_1) (@ tptp.ord_less_eq_nat (@ tptp.suc X_1)))) (forall ((M tptp.nat) (K tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_1) N_1) (@ (@ tptp.ord_less_nat (@ F M_1)) (@ F N_1)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))) (forall ((P (-> tptp.nat Bool)) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ P J) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ P (@ tptp.suc I)) (@ P I)))) (@ P I_1))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K_1)))))) (forall ((N tptp.nat) (N_2 (-> tptp.nat Bool))) (=> (forall ((X_1 tptp.nat)) (=> (@ (@ tptp.member_nat X_1) N_2) (@ (@ tptp.ord_less_nat X_1) N))) (@ tptp.finite_finite_nat N_2))) (forall ((I_1 tptp.nat) (J tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((I tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J_1) (@ (@ tptp.ord_less_nat (@ F I)) (@ F J_1)))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ F I_1)) (@ F J))))) (forall ((I_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) K) (=> (not (= K (@ tptp.suc I_1))) (not (forall ((J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (not (= K (@ tptp.suc J_1))))))))) (forall ((I_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I_1)) K) (not (forall ((J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (not (= K (@ tptp.suc J_1)))))))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (= tptp.bot_bot_nat tptp.zero_zero_nat) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((Nat_2 tptp.nat)) (not (= (@ tptp.suc Nat_2) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((Nat_1 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat_1)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M_1 tptp.nat)) (= N (@ tptp.suc M_1))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J_1 tptp.nat)) (and (= M (@ tptp.suc J_1)) (@ (@ tptp.ord_less_nat J_1) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (= tptp.one_one_nat _let_15) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.nat_case_nat tptp.zero_zero_nat) (lambda ((K_1 tptp.nat)) K_1)) (@ _let_1 N))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))) (forall ((I_1 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I_1))) N))) (forall ((P (-> tptp.nat Bool)) (A_1 tptp.nat) (B_2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A_1) B_2)) (and (=> (@ (@ tptp.ord_less_nat A_1) B_2) (@ P tptp.zero_zero_nat)) (forall ((D_1 tptp.nat)) (=> (= A_1 (@ (@ tptp.plus_plus_nat B_2) D_1)) (@ P D_1)))))) (forall ((P (-> tptp.nat Bool)) (A_1 tptp.nat) (B_2 tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A_1) B_2)) (not (or (and (@ (@ tptp.ord_less_nat A_1) B_2) (not (@ P tptp.zero_zero_nat))) (exists ((D_1 tptp.nat)) (and (= A_1 (@ (@ tptp.plus_plus_nat B_2) D_1)) (not (@ P D_1)))))))) (forall ((I_1 tptp.nat) (M_2 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M_2) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K_1)) M_2) (@ (@ tptp.ord_less_nat K_1) I_1)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat K_1) M_2) (@ (@ tptp.ord_less_nat K_1) (@ tptp.suc I_1))))))))) (forall ((I_1 tptp.nat) (M_2 (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M_2) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat K_1) M_2) (@ (@ tptp.ord_less_nat K_1) (@ tptp.suc I_1)))))) tptp.zero_zero_nat)))) (forall ((I_1 tptp.nat) (M_2 (-> tptp.nat Bool))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M_2)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K_1)) M_2) (@ (@ tptp.ord_less_nat K_1) I_1))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K_1 tptp.nat)) (and (@ (@ tptp.member_nat K_1) M_2) (@ (@ tptp.ord_less_nat K_1) (@ tptp.suc I_1))))))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N)) (=> (not _let_2) (= _let_1 (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (@ P N) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat K_1) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K_1) (not (@ P I)))) (@ P (@ (@ tptp.plus_plus_nat K_1) tptp.one_one_nat))))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (@ P N) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K_1) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K_1) (not (@ P I)))) (@ P K_1)))))) (forall ((I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (= (@ (@ tptp.plus_plus_nat I_1) K_1) J))))) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M_1 tptp.nat)) (= N (@ tptp.suc M_1))))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat tptp.nat)) (not (= Y (@ tptp.suc Nat))))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N_1 tptp.nat)) (=> (@ P (@ tptp.suc N_1)) (@ P N_1))) (@ P tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M_1 tptp.nat)) (= N (@ tptp.suc M_1))))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N_1 tptp.nat)) (=> (@ P N_1) (@ P (@ tptp.suc N_1)))) (@ P N)))) (forall ((V tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 (@ tptp.suc (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat)))))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) L))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I_1)) (@ _let_1 J))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) K)))) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))) (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I_1)) (@ _let_1 J)))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) K))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M) N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat M) N) (@ (@ tptp.times_times_nat N) M))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ (@ tptp.times_times_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.times_times_nat N) K))))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_int K) L))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))) (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V) W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z1))) (= (@ (@ tptp.times_times_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_int Z2) Z3))))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z2)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z2)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z2))))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z2)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z2))))) (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V) W)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z2)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))) (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I_1) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J)))))) (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))) (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int Z) tptp.zero_zero_int) Z)) (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) Z) Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int K) L) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int K) L)) tptp.zero_zero_int))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))) (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I_1) J) (@ (@ tptp.ord_less_eq_int (@ _let_1 I_1)) (@ _let_1 J))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int Z1))) (= (@ (@ tptp.plus_plus_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.plus_plus_int Z2) Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.plus_plus_int Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int Z) W) (@ (@ tptp.plus_plus_int W) Z))) (forall ((W tptp.int)) (@ (@ tptp.ord_less_eq_int W) W)) (forall ((Z tptp.int) (W tptp.int)) (or (@ (@ tptp.ord_less_eq_int Z) W) (@ (@ tptp.ord_less_eq_int W) Z))) (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_int J) K) (@ _let_1 K))))) (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) W) (=> (@ (@ tptp.ord_less_eq_int W) Z) (= Z W)))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))) (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.ord_less_int Z) W) (and (@ (@ tptp.ord_less_eq_int Z) W) (not (= Z W))))) (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) J) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I_1) K)) (@ (@ tptp.plus_plus_int J) K)))) (forall ((Z_3 tptp.int) (Z tptp.int) (W_1 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int W_1) W) (=> (@ (@ tptp.ord_less_eq_int Z_3) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int W_1) Z_3)) (@ (@ tptp.plus_plus_int W) Z))))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))) (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))) (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))) (forall ((I_1 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I_1) J)) U)) K))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))) (forall ((B_2 tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (B_1 tptp.int) (Q tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q)) R))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_2) Q_1)) R_1) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R_1) B_2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (=> (@ (@ tptp.ord_less_eq_int B_1) B_2) (@ (@ tptp.ord_less_eq_int Q) Q_1))))))))) (forall ((B_2 tptp.int) (Q tptp.int) (R tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B_2))) (let ((_let_2 (@ tptp.times_times_int B_2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q)) R)) (@ (@ tptp.plus_plus_int (@ _let_2 Q_1)) R_1)) (=> (@ (@ tptp.ord_less_eq_int R_1) tptp.zero_zero_int) (=> (@ _let_1 R_1) (=> (@ _let_1 R) (@ (@ tptp.ord_less_eq_int Q_1) Q)))))))) (forall ((K tptp.int)) (= (@ tptp.number_number_of_int K) K)) (not (= tptp.zero_zero_int tptp.one_one_int)) (forall ((R_1 tptp.int) (Q_1 tptp.int) (A_1 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_1) (=> (= A_1 (@ (@ tptp.plus_plus_int R_1) (@ (@ tptp.times_times_int A_1) Q_1))) (=> (@ (@ tptp.ord_less_int R_1) A_1) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Q_1))))) (forall ((R_1 tptp.int) (Q_1 tptp.int) (A_1 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_1) (=> (= A_1 (@ (@ tptp.plus_plus_int R_1) (@ (@ tptp.times_times_int A_1) Q_1))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_1) (@ (@ tptp.ord_less_eq_int Q_1) tptp.one_one_int))))) (forall ((B_1 tptp.int) (Q tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q)) R)) (=> (@ (@ tptp.ord_less_int R) B_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (@ _let_1 Q)))))) (forall ((B_1 tptp.int) (Q tptp.int) (R tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q)) R)) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (@ (@ tptp.ord_less_eq_int Q) tptp.zero_zero_int))))) (forall ((B_2 tptp.int) (Q tptp.int) (R tptp.int) (Q_1 tptp.int) (R_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B_2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q)) R)) (@ (@ tptp.plus_plus_int (@ _let_1 Q_1)) R_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B_2) (=> (@ (@ tptp.ord_less_int R_1) B_2) (@ (@ tptp.ord_less_eq_int Q) Q_1))))))) (forall ((B_2 tptp.int) (Q_1 tptp.int) (R_1 tptp.int) (B_1 tptp.int) (Q tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q)) R))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_2) Q_1)) R_1) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R) B_1) (=> (@ _let_1 R_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (=> (@ (@ tptp.ord_less_eq_int B_1) B_2) (@ (@ tptp.ord_less_eq_int Q_1) Q)))))))))) (forall ((P (-> tptp.int Bool)) (I_1 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P I) (@ P (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P I_1))))) (forall ((P (-> tptp.int Bool)) (I_1 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I_1) K) (=> (@ P K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P I) (@ P (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P I_1))))) (forall ((P (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I_1) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P I) (@ P (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P I_1))))) (forall ((P (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I_1) (=> (@ P K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P I) (@ P (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P I_1))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.times_times_int X) Y)))))) (@ _let_11 tptp.zero_zero_int) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_int X) Y)))))) (@ _let_11 tptp.one_one_int) (forall ((P_1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (= (@ P X_1) (@ P_1 X_1)))) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1)))) (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P_1 X_1))))))) (forall ((K tptp.int) (P (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.minus_minus_int X_1) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.minus_minus_int X_1) (@ (@ tptp.times_times_int K) D))))))))) (forall ((P_1 Bool) (P Bool) (X tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (=> (=> _let_1 (= P P_1)) (= (and _let_1 P) (and _let_1 P_1))))) (forall ((P_1 Bool) (P Bool) (X tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (=> (=> _let_1 (= P P_1)) (= (=> _let_1 P) (=> _let_1 P_1))))) (forall ((K tptp.int) (P (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.plus_plus_int X_1) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.plus_plus_int X_1) (@ (@ tptp.times_times_int K) D))))))))) (forall ((I_1 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P I) (@ P (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P I) (@ P (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P I_1))))) (forall ((P (-> tptp.int Bool)) (P1 (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int) (K_1 tptp.int)) (= (@ P1 X_1) (@ P1 (@ (@ tptp.minus_minus_int X_1) (@ (@ tptp.times_times_int K_1) D))))) (=> (exists ((Z_2 tptp.int)) (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_int X_1) Z_2) (= (@ P X_1) (@ P1 X_1))))) (=> (@ tptp.ex P1) (@ tptp.ex P)))))) (forall ((P (-> tptp.int Bool)) (P_1 (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int) (K_1 tptp.int)) (= (@ P_1 X_1) (@ P_1 (@ (@ tptp.minus_minus_int X_1) (@ (@ tptp.times_times_int K_1) D))))) (=> (exists ((Z_2 tptp.int)) (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_int Z_2) X_1) (= (@ P X_1) (@ P_1 X_1))))) (=> (@ tptp.ex P_1) (@ tptp.ex P)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.nat_tsub X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int Y) X))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_int X) Y))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N))) (forall ((K tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int K)) tptp.zero_zero_int))) (= _let_18 tptp.one_one_int) (= _let_17 tptp.zero_zero_int) (forall ((N tptp.nat)) (= (= (@ tptp.semiri1621563631at_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M) N))) Z))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) Z) (exists ((N_1 tptp.nat)) (= Z (@ (@ tptp.plus_plus_int W) (@ tptp.semiri1621563631at_int N_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.ord_less_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.nat_tsub (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat X) Y)))) (forall ((A (-> tptp.nat Bool))) (= (@ tptp.finite_card_nat A) (@ tptp.finite_card_int (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) A)))) (forall ((A (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat A) (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) A)))) (= tptp.one_one_int _let_18) (= tptp.zero_zero_int _let_17) (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1)))) (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) (@ tptp.collect_nat (lambda ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))))) (forall ((Z tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int Z))) (forall ((P (-> tptp.int Bool))) (= (exists ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1))) (exists ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))) (forall ((P (-> tptp.int Bool))) (= (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1))) (forall ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int N)) tptp.zero_zero_int) (= N tptp.zero_zero_nat))) (= (@ tptp.semiri1621563631at_int _let_15) tptp.one_one_int) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) Z) (exists ((N_1 tptp.nat)) (= Z (@ (@ tptp.plus_plus_int W) (@ tptp.semiri1621563631at_int (@ tptp.suc N_1))))))) (forall ((M tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int M)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat M) N))))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((K tptp.nat) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1621563631at_int K)))) (=> (@ (@ tptp.ord_less_int I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.nat_tsub X) Y)))))) (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.nat_tsub X) Y) (@ (@ tptp.minus_minus_int X) Y)))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1) (= K (@ tptp.semiri1621563631at_int N_1)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1621563631at_int M) (@ tptp.semiri1621563631at_int N)) (= M N))) (forall ((A (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int tptp.semiri1621563631at_int))) (= (@ (@ tptp.ord_less_nat_o A) B) (@ (@ tptp.ord_less_int_o (@ _let_1 A)) (@ _let_1 B))))) (forall ((A (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int tptp.semiri1621563631at_int))) (= (@ (@ tptp.ord_less_eq_nat_o A) B) (@ (@ tptp.ord_less_eq_int_o (@ _let_1 A)) (@ _let_1 B))))) (= tptp.bot_bot_int_o (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) tptp.bot_bot_nat_o)) (forall ((A (-> tptp.nat Bool)) (B (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.image_nat_int tptp.semiri1621563631at_int))) (= (= A B) (= (@ _let_1 A) (@ _let_1 B))))) (forall ((X tptp.nat) (A (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_int (@ tptp.semiri1621563631at_int X)) (@ (@ tptp.image_nat_int tptp.semiri1621563631at_int) A)))) (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (let ((_let_1 (@ tptp.semiri1621563631at_int (@ (@ (@ tptp.if_nat P) X) Y)))) (and (=> P (= (@ tptp.semiri1621563631at_int X) _let_1)) (=> (not P) (= (@ tptp.semiri1621563631at_int Y) _let_1))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.semiri1621563631at_int X) (@ tptp.semiri1621563631at_int Y)) (= X Y))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N_1 tptp.nat)) (not (= K (@ tptp.semiri1621563631at_int N_1))))))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (not (forall ((M_1 tptp.nat)) (not (= Z (@ tptp.semiri1621563631at_int M_1))))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N_1 tptp.nat)) (= K (@ tptp.semiri1621563631at_int N_1))))) (forall ((Z tptp.int)) (not (forall ((M_1 tptp.nat) (N_1 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int M_1)) (@ tptp.semiri1621563631at_int N_1))))))) (forall ((X tptp.int) (Z tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))) (forall ((Z_1 tptp.int)) (= (@ tptp.nat_neg Z_1) (@ (@ tptp.ord_less_int Z_1) tptp.zero_zero_int))) (forall ((X tptp.int)) (= (not (@ tptp.nat_neg X)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (not (@ tptp.nat_neg tptp.one_one_int)) (not (@ tptp.nat_neg tptp.zero_zero_int)) (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))) (forall ((N tptp.nat)) (not (@ tptp.nat_neg (@ tptp.semiri1621563631at_int N)))) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.semiri1621563631at_int M))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((V tptp.int)) (=> (@ tptp.nat_neg (@ tptp.number_number_of_int V)) (= (@ tptp.number_number_of_nat V) tptp.zero_zero_nat))) (forall ((V tptp.int) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_1))) (let ((_let_2 (@ tptp.nat_neg _let_1))) (let ((_let_3 (@ tptp.number_number_of_int V))) (let ((_let_4 (@ tptp.nat_neg _let_3))) (= (= (@ tptp.number_number_of_nat V) (@ tptp.number_number_of_nat V_1)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (=> (not _let_4) (and (=> _let_2 (= _let_3 tptp.zero_zero_int)) (=> (not _let_2) (= V V_1))))))))))) (forall ((V_1 tptp.int) (K tptp.nat) (V tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V_1)) K))) (let ((_let_2 (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V)))) (let ((_let_3 (@ _let_2 _let_1))) (let ((_let_4 (@ tptp.nat_neg (@ tptp.number_number_of_int V_1)))) (let ((_let_5 (@ tptp.nat_neg (@ tptp.number_number_of_int V)))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_2 K))) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V) V_1))) K)))))))))))) (forall ((V tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V))) (let ((_let_2 (@ tptp.semiri1621563631at_int (@ tptp.number_number_of_nat V)))) (let ((_let_3 (@ tptp.nat_neg _let_1))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((Z tptp.int) (X tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D))))) (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K))))))) (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K))))))) (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((I tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I) (@ (@ tptp.ord_less_nat I) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I) (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K)))))))) (forall ((N tptp.nat) (V tptp.int)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V)) N)))) (let ((_let_2 (@ tptp.nat_neg (@ tptp.number_number_of_int V)))) (and (=> _let_2 (= _let_1 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) N))) (=> (not _let_2) (= _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat (@ tptp.succ V))) N))))))) (forall ((K tptp.int)) (= (@ tptp.succ K) (@ (@ tptp.plus_plus_int K) tptp.one_one_int))) (forall ((V tptp.int)) (let ((_let_1 (@ tptp.suc (@ tptp.number_number_of_nat V)))) (let ((_let_2 (@ tptp.nat_neg (@ tptp.number_number_of_int V)))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ tptp.succ V)))))))) (forall ((W tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W))) (let ((_let_2 (@ tptp.number_number_of_nat (@ tptp.bit1 W)))) (let ((_let_3 (@ tptp.nat_neg (@ tptp.number_number_of_int W)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ tptp.suc (@ (@ tptp.plus_plus_nat _let_1) _let_1))))))))) (forall ((V tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.number_number_of_nat V)))) (let ((_let_2 (@ (@ tptp.ord_less_int V) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ tptp.succ V)))))))) (= (@ tptp.succ tptp.pls) _let_8) (forall ((W tptp.int)) (= (@ tptp.nat_neg (@ tptp.number_number_of_int (@ tptp.bit1 W))) (@ tptp.nat_neg (@ tptp.number_number_of_int W)))) (not (@ tptp.nat_neg _let_13)) (= _let_10 (@ tptp.semiri1621563631at_int _let_16)) (= _let_14 _let_15) (= _let_16 (@ tptp.suc (@ tptp.suc _let_15))) (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) N))) (= tptp.one_one_nat _let_14) (= _let_14 tptp.one_one_nat) (= tptp.one_one_int (@ tptp.number_number_of_int _let_8)) (= tptp.zero_zero_int _let_13) (forall ((K tptp.int)) (= (@ tptp.bit1 K) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) K)) K))) (= _let_12 tptp.zero_zero_nat) (= tptp.zero_zero_nat _let_12) (= tptp.pls tptp.zero_zero_int) (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit1 K) (@ tptp.bit1 L)) (= K L))) (forall ((K tptp.int)) (not (= (@ tptp.bit1 K) tptp.pls))) (forall ((L tptp.int)) (not (= tptp.pls (@ tptp.bit1 L)))) (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.pls) K)) (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.pls) K) K)) (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.pls) K)) (forall ((W tptp.int)) (= (@ (@ tptp.times_times_int tptp.pls) W) tptp.pls)) (@ _let_11 _let_10) (@ (@ tptp.ord_less_eq_int tptp.pls) tptp.pls) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (not (@ (@ tptp.ord_less_int tptp.pls) tptp.pls)) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_int K) L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_int K1) K2))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int tptp.pls) (@ tptp.bit1 K)) (@ (@ tptp.ord_less_eq_int tptp.pls) K))) (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (@ (@ tptp.fequal_a X) Y)) (= X Y))) (forall ((X tptp.x_a) (Y tptp.x_a)) (or (not (= X Y)) (@ (@ tptp.fequal_a X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X tptp.int) (Y tptp.int)) (or (not (@ (@ tptp.fequal_int X) Y)) (= X Y))) (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (@ (@ tptp.fequal_int X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (@ (@ tptp.fequal_nat X) Y)) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (@ (@ tptp.fequal_nat X) Y))) (@ tptp.finite_finite_pname tptp.u) _let_7 (@ (@ tptp.ord_less_eq_nat _let_5) _let_6) (= (@ tptp.finite_card_a tptp.g) (@ (@ tptp.minus_minus_nat _let_6) _let_5)) _let_4 (not (@ (@ tptp.member_a _let_2) tptp.g)) _let_3 true))))))))))))))))))))))))))))))))))))))))
% 1.73/1.96 )
% 1.73/1.96 % SZS output end Proof for SWW473^3
% 1.73/1.96 % cvc5---1.0.5 exiting
% 1.73/1.96 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------