TSTP Solution File: ITP126^1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP126^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n019.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 : Thu Aug 31 03:18:27 EDT 2023
% Result : Timeout 299.90s 300.20s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.17 % Problem : ITP126^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.18 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n019.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 14:43:43 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.25/0.56 %----Proving TH0
% 0.25/0.57 %------------------------------------------------------------------------------
% 0.25/0.57 % File : ITP126^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.57 % Domain : Interactive Theorem Proving
% 0.25/0.57 % Problem : Sledgehammer Monitor problem prob_770__6461298_1
% 0.25/0.57 % Version : Especial.
% 0.25/0.57 % English :
% 0.25/0.57
% 0.25/0.57 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.57 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.57 % Source : [Des21]
% 0.25/0.57 % Names : Monitor/prob_770__6461298_1 [Des21]
% 0.25/0.57
% 0.25/0.57 % Status : Theorem
% 0.25/0.57 % Rating : 1.00 v8.1.0, 0.91 v7.5.0
% 0.25/0.57 % Syntax : Number of formulae : 380 ( 210 unt; 51 typ; 0 def)
% 0.25/0.57 % Number of atoms : 729 ( 452 equ; 0 cnn)
% 0.25/0.57 % Maximal formula atoms : 4 ( 2 avg)
% 0.25/0.57 % Number of connectives : 2042 ( 105 ~; 15 |; 53 &;1643 @)
% 0.25/0.57 % ( 0 <=>; 226 =>; 0 <=; 0 <~>)
% 0.25/0.57 % Maximal formula depth : 16 ( 5 avg)
% 0.25/0.57 % Number of types : 10 ( 9 usr)
% 0.25/0.57 % Number of type conns : 123 ( 123 >; 0 *; 0 +; 0 <<)
% 0.25/0.57 % Number of symbols : 45 ( 42 usr; 11 con; 0-3 aty)
% 0.25/0.57 % Number of variables : 780 ( 40 ^; 698 !; 42 ?; 780 :)
% 0.25/0.57 % SPC : TH0_THM_EQU_NAR
% 0.25/0.57
% 0.25/0.57 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:17.167
% 0.25/0.57 %------------------------------------------------------------------------------
% 0.25/0.57 % Could-be-implicit typings (9)
% 0.25/0.57 thf(ty_n_t__Option__Ooption_It__Option__Ooption_Itf__b_J_J,type,
% 0.25/0.57 option_option_b: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_n_t__List__Olist_It__Option__Ooption_Itf__b_J_J,type,
% 0.25/0.57 list_option_b: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.25/0.57 set_nat: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_n_t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 option_b: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_n_t__MFOTL__Oformula_Itf__a_J,type,
% 0.25/0.57 formula_a: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_n_t__List__Olist_Itf__b_J,type,
% 0.25/0.57 list_b: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_n_t__Nat__Onat,type,
% 0.25/0.57 nat: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_n_t__Int__Oint,type,
% 0.25/0.57 int: $tType ).
% 0.25/0.57
% 0.25/0.57 thf(ty_n_tf__b,type,
% 0.25/0.57 b: $tType ).
% 0.25/0.57
% 0.25/0.57 % Explicit typings (42)
% 0.25/0.57 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 0.25/0.57 plus_plus_int: int > int > int ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 0.25/0.57 plus_plus_nat: nat > nat > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.25/0.57 zero_zero_int: int ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.25/0.57 zero_zero_nat: nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_If_001t__Nat__Onat,type,
% 0.25/0.57 if_nat: $o > nat > nat > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Odrop_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 drop_option_b: nat > list_option_b > list_option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Odrop_001tf__b,type,
% 0.25/0.57 drop_b: nat > list_b > list_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Ofind_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 find_option_b: ( option_b > $o ) > list_option_b > option_option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Ofind_001tf__b,type,
% 0.25/0.57 find_b: ( b > $o ) > list_b > option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Ogen__length_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 gen_length_option_b: nat > list_option_b > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Ogen__length_001tf__b,type,
% 0.25/0.57 gen_length_b: nat > list_b > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Olist_OCons_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 cons_option_b: option_b > list_option_b > list_option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Olist_OCons_001tf__b,type,
% 0.25/0.57 cons_b: b > list_b > list_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Olist__ex_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 list_ex_option_b: ( option_b > $o ) > list_option_b > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Olist__ex_001tf__b,type,
% 0.25/0.57 list_ex_b: ( b > $o ) > list_b > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Onth_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 nth_option_b: list_option_b > nat > option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_List_Onth_001tf__b,type,
% 0.25/0.57 nth_b: list_b > nat > b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_MFOTL_Ofvi_001tf__a,type,
% 0.25/0.57 fvi_a: nat > formula_a > set_nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat_OSuc,type,
% 0.25/0.57 suc: nat > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.25/0.57 semiri2019852685at_int: nat > int ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.25/0.57 semiri1382578993at_nat: nat > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Option__Ooption_Itf__b_J_J,type,
% 0.25/0.57 size_s1671393719tion_b: list_option_b > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__b_J,type,
% 0.25/0.57 size_size_list_b: list_b > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Option__Ooption_Itf__b_J_J,type,
% 0.25/0.57 size_s684879735tion_b: option_option_b > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 size_size_option_b: option_b > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.25/0.57 nat_triangle: nat > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 none_option_b: option_option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Option_Ooption_ONone_001tf__b,type,
% 0.25/0.57 none_b: option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 some_option_b: option_b > option_option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Option_Ooption_OSome_001tf__b,type,
% 0.25/0.57 some_b: b > option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Option_Ooption_Osize__option_001t__Option__Ooption_Itf__b_J,type,
% 0.25/0.57 size_option_option_b: ( option_b > nat ) > option_option_b > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Option_Ooption_Osize__option_001tf__b,type,
% 0.25/0.57 size_option_b: ( b > nat ) > option_b > nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.25/0.57 ord_less_int: int > int > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.25/0.57 ord_less_nat: nat > nat > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.25/0.57 ord_less_eq_nat: nat > nat > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.25/0.57 collect_nat: ( nat > $o ) > set_nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_c_member_001t__Nat__Onat,type,
% 0.25/0.57 member_nat: nat > set_nat > $o ).
% 0.25/0.57
% 0.25/0.57 thf(sy_v__092_060phi_062,type,
% 0.25/0.57 phi: formula_a ).
% 0.25/0.57
% 0.25/0.57 thf(sy_v_b,type,
% 0.25/0.57 b2: nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_v_n,type,
% 0.25/0.57 n: nat ).
% 0.25/0.57
% 0.25/0.57 thf(sy_v_v,type,
% 0.25/0.57 v: list_option_b ).
% 0.25/0.57
% 0.25/0.57 thf(sy_v_x,type,
% 0.25/0.57 x: b ).
% 0.25/0.57
% 0.25/0.57 % Relevant facts (323)
% 0.25/0.57 thf(fact_0_nth__Cons__Suc,axiom,
% 0.25/0.57 ! [X: b,Xs: list_b,N: nat] :
% 0.25/0.57 ( ( nth_b @ ( cons_b @ X @ Xs ) @ ( suc @ N ) )
% 0.25/0.57 = ( nth_b @ Xs @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % nth_Cons_Suc
% 0.25/0.57 thf(fact_1_nth__Cons__Suc,axiom,
% 0.25/0.57 ! [X: option_b,Xs: list_option_b,N: nat] :
% 0.25/0.57 ( ( nth_option_b @ ( cons_option_b @ X @ Xs ) @ ( suc @ N ) )
% 0.25/0.57 = ( nth_option_b @ Xs @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % nth_Cons_Suc
% 0.25/0.57 thf(fact_2_nth__Cons__0,axiom,
% 0.25/0.57 ! [X: b,Xs: list_b] :
% 0.25/0.57 ( ( nth_b @ ( cons_b @ X @ Xs ) @ zero_zero_nat )
% 0.25/0.57 = X ) ).
% 0.25/0.57
% 0.25/0.57 % nth_Cons_0
% 0.25/0.57 thf(fact_3_nth__Cons__0,axiom,
% 0.25/0.57 ! [X: option_b,Xs: list_option_b] :
% 0.25/0.57 ( ( nth_option_b @ ( cons_option_b @ X @ Xs ) @ zero_zero_nat )
% 0.25/0.57 = X ) ).
% 0.25/0.57
% 0.25/0.57 % nth_Cons_0
% 0.25/0.57 thf(fact_4_less__Suc0,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.25/0.57 = ( N = zero_zero_nat ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_Suc0
% 0.25/0.57 thf(fact_5_zero__less__Suc,axiom,
% 0.25/0.57 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % zero_less_Suc
% 0.25/0.57 thf(fact_6_not__None__eq,axiom,
% 0.25/0.57 ! [X: option_option_b] :
% 0.25/0.57 ( ( X != none_option_b )
% 0.25/0.57 = ( ? [Y: option_b] :
% 0.25/0.57 ( X
% 0.25/0.57 = ( some_option_b @ Y ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_None_eq
% 0.25/0.57 thf(fact_7_not__None__eq,axiom,
% 0.25/0.57 ! [X: option_b] :
% 0.25/0.57 ( ( X != none_b )
% 0.25/0.57 = ( ? [Y: b] :
% 0.25/0.57 ( X
% 0.25/0.57 = ( some_b @ Y ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_None_eq
% 0.25/0.57 thf(fact_8_not__Some__eq,axiom,
% 0.25/0.57 ! [X: option_option_b] :
% 0.25/0.57 ( ( ! [Y: option_b] :
% 0.25/0.57 ( X
% 0.25/0.57 != ( some_option_b @ Y ) ) )
% 0.25/0.57 = ( X = none_option_b ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_Some_eq
% 0.25/0.57 thf(fact_9_not__Some__eq,axiom,
% 0.25/0.57 ! [X: option_b] :
% 0.25/0.57 ( ( ! [Y: b] :
% 0.25/0.57 ( X
% 0.25/0.57 != ( some_b @ Y ) ) )
% 0.25/0.57 = ( X = none_b ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_Some_eq
% 0.25/0.57 thf(fact_10_lessI,axiom,
% 0.25/0.57 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % lessI
% 0.25/0.57 thf(fact_11_Suc__mono,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M @ N )
% 0.25/0.57 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_mono
% 0.25/0.57 thf(fact_12_Suc__less__eq,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.25/0.57 = ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_less_eq
% 0.25/0.57 thf(fact_13_neq0__conv,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( N != zero_zero_nat )
% 0.25/0.57 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % neq0_conv
% 0.25/0.57 thf(fact_14_less__nat__zero__code,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.25/0.57
% 0.25/0.57 % less_nat_zero_code
% 0.25/0.57 thf(fact_15_bot__nat__0_Onot__eq__extremum,axiom,
% 0.25/0.57 ! [A: nat] :
% 0.25/0.57 ( ( A != zero_zero_nat )
% 0.25/0.57 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % bot_nat_0.not_eq_extremum
% 0.25/0.57 thf(fact_16_list_Oinject,axiom,
% 0.25/0.57 ! [X21: b,X22: list_b,Y21: b,Y22: list_b] :
% 0.25/0.57 ( ( ( cons_b @ X21 @ X22 )
% 0.25/0.57 = ( cons_b @ Y21 @ Y22 ) )
% 0.25/0.57 = ( ( X21 = Y21 )
% 0.25/0.57 & ( X22 = Y22 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.inject
% 0.25/0.57 thf(fact_17_list_Oinject,axiom,
% 0.25/0.57 ! [X21: option_b,X22: list_option_b,Y21: option_b,Y22: list_option_b] :
% 0.25/0.57 ( ( ( cons_option_b @ X21 @ X22 )
% 0.25/0.57 = ( cons_option_b @ Y21 @ Y22 ) )
% 0.25/0.57 = ( ( X21 = Y21 )
% 0.25/0.57 & ( X22 = Y22 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list.inject
% 0.25/0.57 thf(fact_18_old_Onat_Oinject,axiom,
% 0.25/0.57 ! [Nat: nat,Nat2: nat] :
% 0.25/0.57 ( ( ( suc @ Nat )
% 0.25/0.57 = ( suc @ Nat2 ) )
% 0.25/0.57 = ( Nat = Nat2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.nat.inject
% 0.25/0.57 thf(fact_19_nat_Oinject,axiom,
% 0.25/0.57 ! [X2: nat,Y2: nat] :
% 0.25/0.57 ( ( ( suc @ X2 )
% 0.25/0.57 = ( suc @ Y2 ) )
% 0.25/0.57 = ( X2 = Y2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % nat.inject
% 0.25/0.57 thf(fact_20_option_Oinject,axiom,
% 0.25/0.57 ! [X2: option_b,Y2: option_b] :
% 0.25/0.57 ( ( ( some_option_b @ X2 )
% 0.25/0.57 = ( some_option_b @ Y2 ) )
% 0.25/0.57 = ( X2 = Y2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.inject
% 0.25/0.57 thf(fact_21_option_Oinject,axiom,
% 0.25/0.57 ! [X2: b,Y2: b] :
% 0.25/0.57 ( ( ( some_b @ X2 )
% 0.25/0.57 = ( some_b @ Y2 ) )
% 0.25/0.57 = ( X2 = Y2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.inject
% 0.25/0.57 thf(fact_22_not__Cons__self2,axiom,
% 0.25/0.57 ! [X: b,Xs: list_b] :
% 0.25/0.57 ( ( cons_b @ X @ Xs )
% 0.25/0.57 != Xs ) ).
% 0.25/0.57
% 0.25/0.57 % not_Cons_self2
% 0.25/0.57 thf(fact_23_not__Cons__self2,axiom,
% 0.25/0.57 ! [X: option_b,Xs: list_option_b] :
% 0.25/0.57 ( ( cons_option_b @ X @ Xs )
% 0.25/0.57 != Xs ) ).
% 0.25/0.57
% 0.25/0.57 % not_Cons_self2
% 0.25/0.57 thf(fact_24_n__not__Suc__n,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( N
% 0.25/0.57 != ( suc @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % n_not_Suc_n
% 0.25/0.57 thf(fact_25_Suc__inject,axiom,
% 0.25/0.57 ! [X: nat,Y3: nat] :
% 0.25/0.57 ( ( ( suc @ X )
% 0.25/0.57 = ( suc @ Y3 ) )
% 0.25/0.57 => ( X = Y3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_inject
% 0.25/0.57 thf(fact_26_linorder__neqE__nat,axiom,
% 0.25/0.57 ! [X: nat,Y3: nat] :
% 0.25/0.57 ( ( X != Y3 )
% 0.25/0.57 => ( ~ ( ord_less_nat @ X @ Y3 )
% 0.25/0.57 => ( ord_less_nat @ Y3 @ X ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % linorder_neqE_nat
% 0.25/0.57 thf(fact_27_infinite__descent,axiom,
% 0.25/0.57 ! [P: nat > $o,N: nat] :
% 0.25/0.57 ( ! [N2: nat] :
% 0.25/0.57 ( ~ ( P @ N2 )
% 0.25/0.57 => ? [M2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.57 & ~ ( P @ M2 ) ) )
% 0.25/0.57 => ( P @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % infinite_descent
% 0.25/0.57 thf(fact_28_nat__less__induct,axiom,
% 0.25/0.57 ! [P: nat > $o,N: nat] :
% 0.25/0.57 ( ! [N2: nat] :
% 0.25/0.57 ( ! [M2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.57 => ( P @ M2 ) )
% 0.25/0.57 => ( P @ N2 ) )
% 0.25/0.57 => ( P @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % nat_less_induct
% 0.25/0.57 thf(fact_29_less__irrefl__nat,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ~ ( ord_less_nat @ N @ N ) ).
% 0.25/0.57
% 0.25/0.57 % less_irrefl_nat
% 0.25/0.57 thf(fact_30_less__not__refl3,axiom,
% 0.25/0.57 ! [S: nat,T: nat] :
% 0.25/0.57 ( ( ord_less_nat @ S @ T )
% 0.25/0.57 => ( S != T ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_not_refl3
% 0.25/0.57 thf(fact_31_less__not__refl2,axiom,
% 0.25/0.57 ! [N: nat,M: nat] :
% 0.25/0.57 ( ( ord_less_nat @ N @ M )
% 0.25/0.57 => ( M != N ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_not_refl2
% 0.25/0.57 thf(fact_32_less__not__refl,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ~ ( ord_less_nat @ N @ N ) ).
% 0.25/0.57
% 0.25/0.57 % less_not_refl
% 0.25/0.57 thf(fact_33_nat__neq__iff,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( M != N )
% 0.25/0.57 = ( ( ord_less_nat @ M @ N )
% 0.25/0.57 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % nat_neq_iff
% 0.25/0.57 thf(fact_34_size__neq__size__imp__neq,axiom,
% 0.25/0.57 ! [X: option_b,Y3: option_b] :
% 0.25/0.57 ( ( ( size_size_option_b @ X )
% 0.25/0.57 != ( size_size_option_b @ Y3 ) )
% 0.25/0.57 => ( X != Y3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % size_neq_size_imp_neq
% 0.25/0.57 thf(fact_35_size__neq__size__imp__neq,axiom,
% 0.25/0.57 ! [X: list_b,Y3: list_b] :
% 0.25/0.57 ( ( ( size_size_list_b @ X )
% 0.25/0.57 != ( size_size_list_b @ Y3 ) )
% 0.25/0.57 => ( X != Y3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % size_neq_size_imp_neq
% 0.25/0.57 thf(fact_36_size__neq__size__imp__neq,axiom,
% 0.25/0.57 ! [X: list_option_b,Y3: list_option_b] :
% 0.25/0.57 ( ( ( size_s1671393719tion_b @ X )
% 0.25/0.57 != ( size_s1671393719tion_b @ Y3 ) )
% 0.25/0.57 => ( X != Y3 ) ) ).
% 0.25/0.57
% 0.25/0.57 % size_neq_size_imp_neq
% 0.25/0.57 thf(fact_37_neq__if__length__neq,axiom,
% 0.25/0.57 ! [Xs: list_b,Ys: list_b] :
% 0.25/0.57 ( ( ( size_size_list_b @ Xs )
% 0.25/0.57 != ( size_size_list_b @ Ys ) )
% 0.25/0.57 => ( Xs != Ys ) ) ).
% 0.25/0.57
% 0.25/0.57 % neq_if_length_neq
% 0.25/0.57 thf(fact_38_neq__if__length__neq,axiom,
% 0.25/0.57 ! [Xs: list_option_b,Ys: list_option_b] :
% 0.25/0.57 ( ( ( size_s1671393719tion_b @ Xs )
% 0.25/0.57 != ( size_s1671393719tion_b @ Ys ) )
% 0.25/0.57 => ( Xs != Ys ) ) ).
% 0.25/0.57
% 0.25/0.57 % neq_if_length_neq
% 0.25/0.57 thf(fact_39_Ex__list__of__length,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ? [Xs2: list_b] :
% 0.25/0.57 ( ( size_size_list_b @ Xs2 )
% 0.25/0.57 = N ) ).
% 0.25/0.57
% 0.25/0.57 % Ex_list_of_length
% 0.25/0.57 thf(fact_40_Ex__list__of__length,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ? [Xs2: list_option_b] :
% 0.25/0.57 ( ( size_s1671393719tion_b @ Xs2 )
% 0.25/0.57 = N ) ).
% 0.25/0.57
% 0.25/0.57 % Ex_list_of_length
% 0.25/0.57 thf(fact_41_not0__implies__Suc,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( N != zero_zero_nat )
% 0.25/0.57 => ? [M3: nat] :
% 0.25/0.57 ( N
% 0.25/0.57 = ( suc @ M3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % not0_implies_Suc
% 0.25/0.57 thf(fact_42_old_Onat_Oinducts,axiom,
% 0.25/0.57 ! [P: nat > $o,Nat: nat] :
% 0.25/0.57 ( ( P @ zero_zero_nat )
% 0.25/0.57 => ( ! [Nat3: nat] :
% 0.25/0.57 ( ( P @ Nat3 )
% 0.25/0.57 => ( P @ ( suc @ Nat3 ) ) )
% 0.25/0.57 => ( P @ Nat ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.nat.inducts
% 0.25/0.57 thf(fact_43_old_Onat_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: nat] :
% 0.25/0.57 ( ( Y3 != zero_zero_nat )
% 0.25/0.57 => ~ ! [Nat3: nat] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( suc @ Nat3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.nat.exhaust
% 0.25/0.57 thf(fact_44_Zero__not__Suc,axiom,
% 0.25/0.57 ! [M: nat] :
% 0.25/0.57 ( zero_zero_nat
% 0.25/0.57 != ( suc @ M ) ) ).
% 0.25/0.57
% 0.25/0.57 % Zero_not_Suc
% 0.25/0.57 thf(fact_45_Zero__neq__Suc,axiom,
% 0.25/0.57 ! [M: nat] :
% 0.25/0.57 ( zero_zero_nat
% 0.25/0.57 != ( suc @ M ) ) ).
% 0.25/0.57
% 0.25/0.57 % Zero_neq_Suc
% 0.25/0.57 thf(fact_46_Suc__neq__Zero,axiom,
% 0.25/0.57 ! [M: nat] :
% 0.25/0.57 ( ( suc @ M )
% 0.25/0.57 != zero_zero_nat ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_neq_Zero
% 0.25/0.57 thf(fact_47_zero__induct,axiom,
% 0.25/0.57 ! [P: nat > $o,K: nat] :
% 0.25/0.57 ( ( P @ K )
% 0.25/0.57 => ( ! [N2: nat] :
% 0.25/0.57 ( ( P @ ( suc @ N2 ) )
% 0.25/0.57 => ( P @ N2 ) )
% 0.25/0.57 => ( P @ zero_zero_nat ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % zero_induct
% 0.25/0.57 thf(fact_48_diff__induct,axiom,
% 0.25/0.57 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.25/0.57 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 0.25/0.57 => ( ! [Y4: nat] : ( P @ zero_zero_nat @ ( suc @ Y4 ) )
% 0.25/0.57 => ( ! [X3: nat,Y4: nat] :
% 0.25/0.57 ( ( P @ X3 @ Y4 )
% 0.25/0.57 => ( P @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 0.25/0.57 => ( P @ M @ N ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % diff_induct
% 0.25/0.57 thf(fact_49_nat__induct,axiom,
% 0.25/0.57 ! [P: nat > $o,N: nat] :
% 0.25/0.57 ( ( P @ zero_zero_nat )
% 0.25/0.57 => ( ! [N2: nat] :
% 0.25/0.57 ( ( P @ N2 )
% 0.25/0.57 => ( P @ ( suc @ N2 ) ) )
% 0.25/0.57 => ( P @ N ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % nat_induct
% 0.25/0.57 thf(fact_50_mem__Collect__eq,axiom,
% 0.25/0.57 ! [A: nat,P: nat > $o] :
% 0.25/0.57 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.25/0.57 = ( P @ A ) ) ).
% 0.25/0.57
% 0.25/0.57 % mem_Collect_eq
% 0.25/0.57 thf(fact_51_Collect__mem__eq,axiom,
% 0.25/0.57 ! [A2: set_nat] :
% 0.25/0.57 ( ( collect_nat
% 0.25/0.57 @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 0.25/0.57 = A2 ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_mem_eq
% 0.25/0.57 thf(fact_52_Collect__cong,axiom,
% 0.25/0.57 ! [P: nat > $o,Q: nat > $o] :
% 0.25/0.57 ( ! [X3: nat] :
% 0.25/0.57 ( ( P @ X3 )
% 0.25/0.57 = ( Q @ X3 ) )
% 0.25/0.57 => ( ( collect_nat @ P )
% 0.25/0.57 = ( collect_nat @ Q ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Collect_cong
% 0.25/0.57 thf(fact_53_nat_OdiscI,axiom,
% 0.25/0.57 ! [Nat: nat,X2: nat] :
% 0.25/0.57 ( ( Nat
% 0.25/0.57 = ( suc @ X2 ) )
% 0.25/0.57 => ( Nat != zero_zero_nat ) ) ).
% 0.25/0.57
% 0.25/0.57 % nat.discI
% 0.25/0.57 thf(fact_54_old_Onat_Odistinct_I1_J,axiom,
% 0.25/0.57 ! [Nat2: nat] :
% 0.25/0.57 ( zero_zero_nat
% 0.25/0.57 != ( suc @ Nat2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % old.nat.distinct(1)
% 0.25/0.57 thf(fact_55_old_Onat_Odistinct_I2_J,axiom,
% 0.25/0.57 ! [Nat2: nat] :
% 0.25/0.57 ( ( suc @ Nat2 )
% 0.25/0.57 != zero_zero_nat ) ).
% 0.25/0.57
% 0.25/0.57 % old.nat.distinct(2)
% 0.25/0.57 thf(fact_56_nat_Odistinct_I1_J,axiom,
% 0.25/0.57 ! [X2: nat] :
% 0.25/0.57 ( zero_zero_nat
% 0.25/0.57 != ( suc @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % nat.distinct(1)
% 0.25/0.57 thf(fact_57_bot__nat__0_Oextremum__strict,axiom,
% 0.25/0.57 ! [A: nat] :
% 0.25/0.57 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.25/0.57
% 0.25/0.57 % bot_nat_0.extremum_strict
% 0.25/0.57 thf(fact_58_infinite__descent0,axiom,
% 0.25/0.57 ! [P: nat > $o,N: nat] :
% 0.25/0.57 ( ( P @ zero_zero_nat )
% 0.25/0.57 => ( ! [N2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.57 => ( ~ ( P @ N2 )
% 0.25/0.57 => ? [M2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M2 @ N2 )
% 0.25/0.57 & ~ ( P @ M2 ) ) ) )
% 0.25/0.57 => ( P @ N ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % infinite_descent0
% 0.25/0.57 thf(fact_59_gr__implies__not0,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M @ N )
% 0.25/0.57 => ( N != zero_zero_nat ) ) ).
% 0.25/0.57
% 0.25/0.57 % gr_implies_not0
% 0.25/0.57 thf(fact_60_less__zeroE,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.25/0.57
% 0.25/0.57 % less_zeroE
% 0.25/0.57 thf(fact_61_not__less0,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.25/0.57
% 0.25/0.57 % not_less0
% 0.25/0.57 thf(fact_62_not__gr0,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.25/0.57 = ( N = zero_zero_nat ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_gr0
% 0.25/0.57 thf(fact_63_gr0I,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( N != zero_zero_nat )
% 0.25/0.57 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % gr0I
% 0.25/0.57 thf(fact_64_not__less__less__Suc__eq,axiom,
% 0.25/0.57 ! [N: nat,M: nat] :
% 0.25/0.57 ( ~ ( ord_less_nat @ N @ M )
% 0.25/0.57 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.25/0.57 = ( N = M ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_less_less_Suc_eq
% 0.25/0.57 thf(fact_65_strict__inc__induct,axiom,
% 0.25/0.57 ! [I: nat,J: nat,P: nat > $o] :
% 0.25/0.57 ( ( ord_less_nat @ I @ J )
% 0.25/0.57 => ( ! [I2: nat] :
% 0.25/0.57 ( ( J
% 0.25/0.57 = ( suc @ I2 ) )
% 0.25/0.57 => ( P @ I2 ) )
% 0.25/0.57 => ( ! [I2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I2 @ J )
% 0.25/0.57 => ( ( P @ ( suc @ I2 ) )
% 0.25/0.57 => ( P @ I2 ) ) )
% 0.25/0.57 => ( P @ I ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % strict_inc_induct
% 0.25/0.57 thf(fact_66_less__Suc__induct,axiom,
% 0.25/0.57 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.25/0.57 ( ( ord_less_nat @ I @ J )
% 0.25/0.57 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.25/0.57 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I2 @ J2 )
% 0.25/0.57 => ( ( ord_less_nat @ J2 @ K2 )
% 0.25/0.57 => ( ( P @ I2 @ J2 )
% 0.25/0.57 => ( ( P @ J2 @ K2 )
% 0.25/0.57 => ( P @ I2 @ K2 ) ) ) ) )
% 0.25/0.57 => ( P @ I @ J ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_Suc_induct
% 0.25/0.57 thf(fact_67_less__trans__Suc,axiom,
% 0.25/0.57 ! [I: nat,J: nat,K: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I @ J )
% 0.25/0.57 => ( ( ord_less_nat @ J @ K )
% 0.25/0.57 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_trans_Suc
% 0.25/0.57 thf(fact_68_Suc__less__SucD,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.25/0.57 => ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_less_SucD
% 0.25/0.57 thf(fact_69_less__antisym,axiom,
% 0.25/0.57 ! [N: nat,M: nat] :
% 0.25/0.57 ( ~ ( ord_less_nat @ N @ M )
% 0.25/0.57 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.25/0.57 => ( M = N ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_antisym
% 0.25/0.57 thf(fact_70_Suc__less__eq2,axiom,
% 0.25/0.57 ! [N: nat,M: nat] :
% 0.25/0.57 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.25/0.57 = ( ? [M4: nat] :
% 0.25/0.57 ( ( M
% 0.25/0.57 = ( suc @ M4 ) )
% 0.25/0.57 & ( ord_less_nat @ N @ M4 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_less_eq2
% 0.25/0.57 thf(fact_71_All__less__Suc,axiom,
% 0.25/0.57 ! [N: nat,P: nat > $o] :
% 0.25/0.57 ( ( ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.25/0.57 => ( P @ I3 ) ) )
% 0.25/0.57 = ( ( P @ N )
% 0.25/0.57 & ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ N )
% 0.25/0.57 => ( P @ I3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % All_less_Suc
% 0.25/0.57 thf(fact_72_not__less__eq,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.25/0.57 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % not_less_eq
% 0.25/0.57 thf(fact_73_less__Suc__eq,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.25/0.57 = ( ( ord_less_nat @ M @ N )
% 0.25/0.57 | ( M = N ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_Suc_eq
% 0.25/0.57 thf(fact_74_Ex__less__Suc,axiom,
% 0.25/0.57 ! [N: nat,P: nat > $o] :
% 0.25/0.57 ( ( ? [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.25/0.57 & ( P @ I3 ) ) )
% 0.25/0.57 = ( ( P @ N )
% 0.25/0.57 | ? [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ N )
% 0.25/0.57 & ( P @ I3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Ex_less_Suc
% 0.25/0.57 thf(fact_75_less__SucI,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M @ N )
% 0.25/0.57 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_SucI
% 0.25/0.57 thf(fact_76_less__SucE,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.25/0.57 => ( ~ ( ord_less_nat @ M @ N )
% 0.25/0.57 => ( M = N ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_SucE
% 0.25/0.57 thf(fact_77_Suc__lessI,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M @ N )
% 0.25/0.57 => ( ( ( suc @ M )
% 0.25/0.57 != N )
% 0.25/0.57 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_lessI
% 0.25/0.57 thf(fact_78_Suc__lessE,axiom,
% 0.25/0.57 ! [I: nat,K: nat] :
% 0.25/0.57 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.25/0.57 => ~ ! [J2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I @ J2 )
% 0.25/0.57 => ( K
% 0.25/0.57 != ( suc @ J2 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_lessE
% 0.25/0.57 thf(fact_79_Suc__lessD,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.25/0.57 => ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_lessD
% 0.25/0.57 thf(fact_80_Nat_OlessE,axiom,
% 0.25/0.57 ! [I: nat,K: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I @ K )
% 0.25/0.57 => ( ( K
% 0.25/0.57 != ( suc @ I ) )
% 0.25/0.57 => ~ ! [J2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I @ J2 )
% 0.25/0.57 => ( K
% 0.25/0.57 != ( suc @ J2 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Nat.lessE
% 0.25/0.57 thf(fact_81_length__induct,axiom,
% 0.25/0.57 ! [P: list_b > $o,Xs: list_b] :
% 0.25/0.57 ( ! [Xs2: list_b] :
% 0.25/0.57 ( ! [Ys2: list_b] :
% 0.25/0.57 ( ( ord_less_nat @ ( size_size_list_b @ Ys2 ) @ ( size_size_list_b @ Xs2 ) )
% 0.25/0.57 => ( P @ Ys2 ) )
% 0.25/0.57 => ( P @ Xs2 ) )
% 0.25/0.57 => ( P @ Xs ) ) ).
% 0.25/0.57
% 0.25/0.57 % length_induct
% 0.25/0.57 thf(fact_82_length__induct,axiom,
% 0.25/0.57 ! [P: list_option_b > $o,Xs: list_option_b] :
% 0.25/0.57 ( ! [Xs2: list_option_b] :
% 0.25/0.57 ( ! [Ys2: list_option_b] :
% 0.25/0.57 ( ( ord_less_nat @ ( size_s1671393719tion_b @ Ys2 ) @ ( size_s1671393719tion_b @ Xs2 ) )
% 0.25/0.57 => ( P @ Ys2 ) )
% 0.25/0.57 => ( P @ Xs2 ) )
% 0.25/0.57 => ( P @ Xs ) ) ).
% 0.25/0.57
% 0.25/0.57 % length_induct
% 0.25/0.57 thf(fact_83_combine__options__cases,axiom,
% 0.25/0.57 ! [X: option_b,P: option_b > option_option_b > $o,Y3: option_option_b] :
% 0.25/0.57 ( ( ( X = none_b )
% 0.25/0.57 => ( P @ X @ Y3 ) )
% 0.25/0.57 => ( ( ( Y3 = none_option_b )
% 0.25/0.57 => ( P @ X @ Y3 ) )
% 0.25/0.57 => ( ! [A3: b,B: option_b] :
% 0.25/0.57 ( ( X
% 0.25/0.57 = ( some_b @ A3 ) )
% 0.25/0.57 => ( ( Y3
% 0.25/0.57 = ( some_option_b @ B ) )
% 0.25/0.57 => ( P @ X @ Y3 ) ) )
% 0.25/0.57 => ( P @ X @ Y3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % combine_options_cases
% 0.25/0.57 thf(fact_84_combine__options__cases,axiom,
% 0.25/0.57 ! [X: option_option_b,P: option_option_b > option_b > $o,Y3: option_b] :
% 0.25/0.57 ( ( ( X = none_option_b )
% 0.25/0.57 => ( P @ X @ Y3 ) )
% 0.25/0.57 => ( ( ( Y3 = none_b )
% 0.25/0.57 => ( P @ X @ Y3 ) )
% 0.25/0.57 => ( ! [A3: option_b,B: b] :
% 0.25/0.57 ( ( X
% 0.25/0.57 = ( some_option_b @ A3 ) )
% 0.25/0.57 => ( ( Y3
% 0.25/0.57 = ( some_b @ B ) )
% 0.25/0.57 => ( P @ X @ Y3 ) ) )
% 0.25/0.57 => ( P @ X @ Y3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % combine_options_cases
% 0.25/0.57 thf(fact_85_combine__options__cases,axiom,
% 0.25/0.57 ! [X: option_option_b,P: option_option_b > option_option_b > $o,Y3: option_option_b] :
% 0.25/0.57 ( ( ( X = none_option_b )
% 0.25/0.57 => ( P @ X @ Y3 ) )
% 0.25/0.57 => ( ( ( Y3 = none_option_b )
% 0.25/0.57 => ( P @ X @ Y3 ) )
% 0.25/0.57 => ( ! [A3: option_b,B: option_b] :
% 0.25/0.57 ( ( X
% 0.25/0.57 = ( some_option_b @ A3 ) )
% 0.25/0.57 => ( ( Y3
% 0.25/0.57 = ( some_option_b @ B ) )
% 0.25/0.57 => ( P @ X @ Y3 ) ) )
% 0.25/0.57 => ( P @ X @ Y3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % combine_options_cases
% 0.25/0.57 thf(fact_86_combine__options__cases,axiom,
% 0.25/0.57 ! [X: option_b,P: option_b > option_b > $o,Y3: option_b] :
% 0.25/0.57 ( ( ( X = none_b )
% 0.25/0.57 => ( P @ X @ Y3 ) )
% 0.25/0.57 => ( ( ( Y3 = none_b )
% 0.25/0.57 => ( P @ X @ Y3 ) )
% 0.25/0.57 => ( ! [A3: b,B: b] :
% 0.25/0.57 ( ( X
% 0.25/0.57 = ( some_b @ A3 ) )
% 0.25/0.57 => ( ( Y3
% 0.25/0.57 = ( some_b @ B ) )
% 0.25/0.57 => ( P @ X @ Y3 ) ) )
% 0.25/0.57 => ( P @ X @ Y3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % combine_options_cases
% 0.25/0.57 thf(fact_87_split__option__all,axiom,
% 0.25/0.57 ( ( ^ [P2: option_option_b > $o] :
% 0.25/0.57 ! [X5: option_option_b] : ( P2 @ X5 ) )
% 0.25/0.57 = ( ^ [P3: option_option_b > $o] :
% 0.25/0.57 ( ( P3 @ none_option_b )
% 0.25/0.57 & ! [X4: option_b] : ( P3 @ ( some_option_b @ X4 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_option_all
% 0.25/0.57 thf(fact_88_split__option__all,axiom,
% 0.25/0.57 ( ( ^ [P2: option_b > $o] :
% 0.25/0.57 ! [X5: option_b] : ( P2 @ X5 ) )
% 0.25/0.57 = ( ^ [P3: option_b > $o] :
% 0.25/0.57 ( ( P3 @ none_b )
% 0.25/0.57 & ! [X4: b] : ( P3 @ ( some_b @ X4 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_option_all
% 0.25/0.57 thf(fact_89_split__option__ex,axiom,
% 0.25/0.57 ( ( ^ [P2: option_option_b > $o] :
% 0.25/0.57 ? [X5: option_option_b] : ( P2 @ X5 ) )
% 0.25/0.57 = ( ^ [P3: option_option_b > $o] :
% 0.25/0.57 ( ( P3 @ none_option_b )
% 0.25/0.57 | ? [X4: option_b] : ( P3 @ ( some_option_b @ X4 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_option_ex
% 0.25/0.57 thf(fact_90_split__option__ex,axiom,
% 0.25/0.57 ( ( ^ [P2: option_b > $o] :
% 0.25/0.57 ? [X5: option_b] : ( P2 @ X5 ) )
% 0.25/0.57 = ( ^ [P3: option_b > $o] :
% 0.25/0.57 ( ( P3 @ none_b )
% 0.25/0.57 | ? [X4: b] : ( P3 @ ( some_b @ X4 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % split_option_ex
% 0.25/0.57 thf(fact_91_option_Oinducts,axiom,
% 0.25/0.57 ! [P: option_option_b > $o,Option: option_option_b] :
% 0.25/0.57 ( ( P @ none_option_b )
% 0.25/0.57 => ( ! [X3: option_b] : ( P @ ( some_option_b @ X3 ) )
% 0.25/0.57 => ( P @ Option ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.inducts
% 0.25/0.57 thf(fact_92_option_Oinducts,axiom,
% 0.25/0.57 ! [P: option_b > $o,Option: option_b] :
% 0.25/0.57 ( ( P @ none_b )
% 0.25/0.57 => ( ! [X3: b] : ( P @ ( some_b @ X3 ) )
% 0.25/0.57 => ( P @ Option ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.inducts
% 0.25/0.57 thf(fact_93_option_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: option_option_b] :
% 0.25/0.57 ( ( Y3 != none_option_b )
% 0.25/0.57 => ~ ! [X23: option_b] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( some_option_b @ X23 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.exhaust
% 0.25/0.57 thf(fact_94_option_Oexhaust,axiom,
% 0.25/0.57 ! [Y3: option_b] :
% 0.25/0.57 ( ( Y3 != none_b )
% 0.25/0.57 => ~ ! [X23: b] :
% 0.25/0.57 ( Y3
% 0.25/0.57 != ( some_b @ X23 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.exhaust
% 0.25/0.57 thf(fact_95_option_OdiscI,axiom,
% 0.25/0.57 ! [Option: option_option_b,X2: option_b] :
% 0.25/0.57 ( ( Option
% 0.25/0.57 = ( some_option_b @ X2 ) )
% 0.25/0.57 => ( Option != none_option_b ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.discI
% 0.25/0.57 thf(fact_96_option_OdiscI,axiom,
% 0.25/0.57 ! [Option: option_b,X2: b] :
% 0.25/0.57 ( ( Option
% 0.25/0.57 = ( some_b @ X2 ) )
% 0.25/0.57 => ( Option != none_b ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.discI
% 0.25/0.57 thf(fact_97_option_Odistinct_I1_J,axiom,
% 0.25/0.57 ! [X2: option_b] :
% 0.25/0.57 ( none_option_b
% 0.25/0.57 != ( some_option_b @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.distinct(1)
% 0.25/0.57 thf(fact_98_option_Odistinct_I1_J,axiom,
% 0.25/0.57 ! [X2: b] :
% 0.25/0.57 ( none_b
% 0.25/0.57 != ( some_b @ X2 ) ) ).
% 0.25/0.57
% 0.25/0.57 % option.distinct(1)
% 0.25/0.57 thf(fact_99_lift__Suc__mono__less__iff,axiom,
% 0.25/0.57 ! [F: nat > nat,N: nat,M: nat] :
% 0.25/0.57 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.25/0.57 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.25/0.57 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lift_Suc_mono_less_iff
% 0.25/0.57 thf(fact_100_lift__Suc__mono__less__iff,axiom,
% 0.25/0.57 ! [F: nat > int,N: nat,M: nat] :
% 0.25/0.57 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.25/0.57 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 0.25/0.57 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lift_Suc_mono_less_iff
% 0.25/0.57 thf(fact_101_lift__Suc__mono__less,axiom,
% 0.25/0.57 ! [F: nat > nat,N: nat,N3: nat] :
% 0.25/0.57 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.25/0.57 => ( ( ord_less_nat @ N @ N3 )
% 0.25/0.57 => ( ord_less_nat @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lift_Suc_mono_less
% 0.25/0.57 thf(fact_102_lift__Suc__mono__less,axiom,
% 0.25/0.57 ! [F: nat > int,N: nat,N3: nat] :
% 0.25/0.57 ( ! [N2: nat] : ( ord_less_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.25/0.57 => ( ( ord_less_nat @ N @ N3 )
% 0.25/0.57 => ( ord_less_int @ ( F @ N ) @ ( F @ N3 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % lift_Suc_mono_less
% 0.25/0.57 thf(fact_103_less__Suc__eq__0__disj,axiom,
% 0.25/0.57 ! [M: nat,N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.25/0.57 = ( ( M = zero_zero_nat )
% 0.25/0.57 | ? [J3: nat] :
% 0.25/0.57 ( ( M
% 0.25/0.57 = ( suc @ J3 ) )
% 0.25/0.57 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % less_Suc_eq_0_disj
% 0.25/0.57 thf(fact_104_gr0__implies__Suc,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.25/0.57 => ? [M3: nat] :
% 0.25/0.57 ( N
% 0.25/0.57 = ( suc @ M3 ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % gr0_implies_Suc
% 0.25/0.57 thf(fact_105_All__less__Suc2,axiom,
% 0.25/0.57 ! [N: nat,P: nat > $o] :
% 0.25/0.57 ( ( ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.25/0.57 => ( P @ I3 ) ) )
% 0.25/0.57 = ( ( P @ zero_zero_nat )
% 0.25/0.57 & ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ N )
% 0.25/0.57 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % All_less_Suc2
% 0.25/0.57 thf(fact_106_gr0__conv__Suc,axiom,
% 0.25/0.57 ! [N: nat] :
% 0.25/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.25/0.57 = ( ? [M5: nat] :
% 0.25/0.57 ( N
% 0.25/0.57 = ( suc @ M5 ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % gr0_conv_Suc
% 0.25/0.57 thf(fact_107_Ex__less__Suc2,axiom,
% 0.25/0.57 ! [N: nat,P: nat > $o] :
% 0.25/0.57 ( ( ? [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ ( suc @ N ) )
% 0.25/0.57 & ( P @ I3 ) ) )
% 0.25/0.57 = ( ( P @ zero_zero_nat )
% 0.25/0.57 | ? [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ N )
% 0.25/0.57 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Ex_less_Suc2
% 0.25/0.57 thf(fact_108_length__Suc__conv,axiom,
% 0.25/0.57 ! [Xs: list_b,N: nat] :
% 0.25/0.57 ( ( ( size_size_list_b @ Xs )
% 0.25/0.57 = ( suc @ N ) )
% 0.25/0.57 = ( ? [Y: b,Ys3: list_b] :
% 0.25/0.57 ( ( Xs
% 0.25/0.57 = ( cons_b @ Y @ Ys3 ) )
% 0.25/0.57 & ( ( size_size_list_b @ Ys3 )
% 0.25/0.57 = N ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % length_Suc_conv
% 0.25/0.57 thf(fact_109_length__Suc__conv,axiom,
% 0.25/0.57 ! [Xs: list_option_b,N: nat] :
% 0.25/0.57 ( ( ( size_s1671393719tion_b @ Xs )
% 0.25/0.57 = ( suc @ N ) )
% 0.25/0.57 = ( ? [Y: option_b,Ys3: list_option_b] :
% 0.25/0.57 ( ( Xs
% 0.25/0.57 = ( cons_option_b @ Y @ Ys3 ) )
% 0.25/0.57 & ( ( size_s1671393719tion_b @ Ys3 )
% 0.25/0.57 = N ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % length_Suc_conv
% 0.25/0.57 thf(fact_110_Suc__length__conv,axiom,
% 0.25/0.57 ! [N: nat,Xs: list_b] :
% 0.25/0.57 ( ( ( suc @ N )
% 0.25/0.57 = ( size_size_list_b @ Xs ) )
% 0.25/0.57 = ( ? [Y: b,Ys3: list_b] :
% 0.25/0.57 ( ( Xs
% 0.25/0.57 = ( cons_b @ Y @ Ys3 ) )
% 0.25/0.57 & ( ( size_size_list_b @ Ys3 )
% 0.25/0.57 = N ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_length_conv
% 0.25/0.57 thf(fact_111_Suc__length__conv,axiom,
% 0.25/0.57 ! [N: nat,Xs: list_option_b] :
% 0.25/0.57 ( ( ( suc @ N )
% 0.25/0.57 = ( size_s1671393719tion_b @ Xs ) )
% 0.25/0.57 = ( ? [Y: option_b,Ys3: list_option_b] :
% 0.25/0.57 ( ( Xs
% 0.25/0.57 = ( cons_option_b @ Y @ Ys3 ) )
% 0.25/0.57 & ( ( size_s1671393719tion_b @ Ys3 )
% 0.25/0.57 = N ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Suc_length_conv
% 0.25/0.57 thf(fact_112_list__eq__iff__nth__eq,axiom,
% 0.25/0.57 ( ( ^ [Y5: list_b,Z: list_b] : ( Y5 = Z ) )
% 0.25/0.57 = ( ^ [Xs3: list_b,Ys3: list_b] :
% 0.25/0.57 ( ( ( size_size_list_b @ Xs3 )
% 0.25/0.57 = ( size_size_list_b @ Ys3 ) )
% 0.25/0.57 & ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ ( size_size_list_b @ Xs3 ) )
% 0.25/0.57 => ( ( nth_b @ Xs3 @ I3 )
% 0.25/0.57 = ( nth_b @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_eq_iff_nth_eq
% 0.25/0.57 thf(fact_113_list__eq__iff__nth__eq,axiom,
% 0.25/0.57 ( ( ^ [Y5: list_option_b,Z: list_option_b] : ( Y5 = Z ) )
% 0.25/0.57 = ( ^ [Xs3: list_option_b,Ys3: list_option_b] :
% 0.25/0.57 ( ( ( size_s1671393719tion_b @ Xs3 )
% 0.25/0.57 = ( size_s1671393719tion_b @ Ys3 ) )
% 0.25/0.57 & ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ ( size_s1671393719tion_b @ Xs3 ) )
% 0.25/0.57 => ( ( nth_option_b @ Xs3 @ I3 )
% 0.25/0.57 = ( nth_option_b @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % list_eq_iff_nth_eq
% 0.25/0.57 thf(fact_114_Skolem__list__nth,axiom,
% 0.25/0.57 ! [K: nat,P: nat > b > $o] :
% 0.25/0.57 ( ( ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ K )
% 0.25/0.57 => ? [X5: b] : ( P @ I3 @ X5 ) ) )
% 0.25/0.57 = ( ? [Xs3: list_b] :
% 0.25/0.57 ( ( ( size_size_list_b @ Xs3 )
% 0.25/0.57 = K )
% 0.25/0.57 & ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ K )
% 0.25/0.57 => ( P @ I3 @ ( nth_b @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Skolem_list_nth
% 0.25/0.57 thf(fact_115_Skolem__list__nth,axiom,
% 0.25/0.57 ! [K: nat,P: nat > option_b > $o] :
% 0.25/0.57 ( ( ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ K )
% 0.25/0.57 => ? [X5: option_b] : ( P @ I3 @ X5 ) ) )
% 0.25/0.57 = ( ? [Xs3: list_option_b] :
% 0.25/0.57 ( ( ( size_s1671393719tion_b @ Xs3 )
% 0.25/0.57 = K )
% 0.25/0.57 & ! [I3: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I3 @ K )
% 0.25/0.57 => ( P @ I3 @ ( nth_option_b @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % Skolem_list_nth
% 0.25/0.57 thf(fact_116_nth__equalityI,axiom,
% 0.25/0.57 ! [Xs: list_b,Ys: list_b] :
% 0.25/0.57 ( ( ( size_size_list_b @ Xs )
% 0.25/0.57 = ( size_size_list_b @ Ys ) )
% 0.25/0.57 => ( ! [I2: nat] :
% 0.25/0.57 ( ( ord_less_nat @ I2 @ ( size_size_list_b @ Xs ) )
% 0.25/0.57 => ( ( nth_b @ Xs @ I2 )
% 0.25/0.57 = ( nth_b @ Ys @ I2 ) ) )
% 0.25/0.57 => ( Xs = Ys ) ) ) ).
% 0.25/0.57
% 0.25/0.57 % nth_equalityI
% 0.25/0.57 thf(fact_117_nth__equalityI,axiom,
% 0.25/0.57 ! [Xs: list_option_b,Ys: list_option_b] :
% 0.25/0.58 ( ( ( size_s1671393719tion_b @ Xs )
% 0.25/0.58 = ( size_s1671393719tion_b @ Ys ) )
% 0.25/0.58 => ( ! [I2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I2 @ ( size_s1671393719tion_b @ Xs ) )
% 0.25/0.58 => ( ( nth_option_b @ Xs @ I2 )
% 0.25/0.58 = ( nth_option_b @ Ys @ I2 ) ) )
% 0.25/0.58 => ( Xs = Ys ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % nth_equalityI
% 0.25/0.58 thf(fact_118_not__gr__zero,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.25/0.58 = ( N = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % not_gr_zero
% 0.25/0.58 thf(fact_119_fvi__Suc__bound,axiom,
% 0.25/0.58 ! [B2: nat,Phi: formula_a,N: nat] :
% 0.25/0.58 ( ! [X3: nat] :
% 0.25/0.58 ( ( member_nat @ X3 @ ( fvi_a @ ( suc @ B2 ) @ Phi ) )
% 0.25/0.58 => ( ord_less_nat @ X3 @ N ) )
% 0.25/0.58 => ! [X6: nat] :
% 0.25/0.58 ( ( member_nat @ X6 @ ( fvi_a @ B2 @ Phi ) )
% 0.25/0.58 => ( ord_less_nat @ X6 @ ( suc @ N ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fvi_Suc_bound
% 0.25/0.58 thf(fact_120_length__Cons,axiom,
% 0.25/0.58 ! [X: b,Xs: list_b] :
% 0.25/0.58 ( ( size_size_list_b @ ( cons_b @ X @ Xs ) )
% 0.25/0.58 = ( suc @ ( size_size_list_b @ Xs ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_Cons
% 0.25/0.58 thf(fact_121_length__Cons,axiom,
% 0.25/0.58 ! [X: option_b,Xs: list_option_b] :
% 0.25/0.58 ( ( size_s1671393719tion_b @ ( cons_option_b @ X @ Xs ) )
% 0.25/0.58 = ( suc @ ( size_s1671393719tion_b @ Xs ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_Cons
% 0.25/0.58 thf(fact_122_option_Osize__gen_I1_J,axiom,
% 0.25/0.58 ! [X: b > nat] :
% 0.25/0.58 ( ( size_option_b @ X @ none_b )
% 0.25/0.58 = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % option.size_gen(1)
% 0.25/0.58 thf(fact_123_fvi__Suc,axiom,
% 0.25/0.58 ! [X: nat,B2: nat,Phi: formula_a] :
% 0.25/0.58 ( ( member_nat @ X @ ( fvi_a @ ( suc @ B2 ) @ Phi ) )
% 0.25/0.58 = ( member_nat @ ( suc @ X ) @ ( fvi_a @ B2 @ Phi ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % fvi_Suc
% 0.25/0.58 thf(fact_124_option_Osize_I4_J,axiom,
% 0.25/0.58 ! [X2: option_b] :
% 0.25/0.58 ( ( size_s684879735tion_b @ ( some_option_b @ X2 ) )
% 0.25/0.58 = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % option.size(4)
% 0.25/0.58 thf(fact_125_option_Osize_I4_J,axiom,
% 0.25/0.58 ! [X2: b] :
% 0.25/0.58 ( ( size_size_option_b @ ( some_b @ X2 ) )
% 0.25/0.58 = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % option.size(4)
% 0.25/0.58 thf(fact_126_option_Osize_I3_J,axiom,
% 0.25/0.58 ( ( size_size_option_b @ none_b )
% 0.25/0.58 = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % option.size(3)
% 0.25/0.58 thf(fact_127_find__Some__iff,axiom,
% 0.25/0.58 ! [P: b > $o,Xs: list_b,X: b] :
% 0.25/0.58 ( ( ( find_b @ P @ Xs )
% 0.25/0.58 = ( some_b @ X ) )
% 0.25/0.58 = ( ? [I3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I3 @ ( size_size_list_b @ Xs ) )
% 0.25/0.58 & ( P @ ( nth_b @ Xs @ I3 ) )
% 0.25/0.58 & ( X
% 0.25/0.58 = ( nth_b @ Xs @ I3 ) )
% 0.25/0.58 & ! [J3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ J3 @ I3 )
% 0.25/0.58 => ~ ( P @ ( nth_b @ Xs @ J3 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % find_Some_iff
% 0.25/0.58 thf(fact_128_find__Some__iff,axiom,
% 0.25/0.58 ! [P: option_b > $o,Xs: list_option_b,X: option_b] :
% 0.25/0.58 ( ( ( find_option_b @ P @ Xs )
% 0.25/0.58 = ( some_option_b @ X ) )
% 0.25/0.58 = ( ? [I3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I3 @ ( size_s1671393719tion_b @ Xs ) )
% 0.25/0.58 & ( P @ ( nth_option_b @ Xs @ I3 ) )
% 0.25/0.58 & ( X
% 0.25/0.58 = ( nth_option_b @ Xs @ I3 ) )
% 0.25/0.58 & ! [J3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ J3 @ I3 )
% 0.25/0.58 => ~ ( P @ ( nth_option_b @ Xs @ J3 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % find_Some_iff
% 0.25/0.58 thf(fact_129_exists__least__lemma,axiom,
% 0.25/0.58 ! [P: nat > $o] :
% 0.25/0.58 ( ~ ( P @ zero_zero_nat )
% 0.25/0.58 => ( ? [X_1: nat] : ( P @ X_1 )
% 0.25/0.58 => ? [N2: nat] :
% 0.25/0.58 ( ~ ( P @ N2 )
% 0.25/0.58 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % exists_least_lemma
% 0.25/0.58 thf(fact_130_option_Osize__neq,axiom,
% 0.25/0.58 ! [X: option_b] :
% 0.25/0.58 ( ( size_size_option_b @ X )
% 0.25/0.58 != zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % option.size_neq
% 0.25/0.58 thf(fact_131_zero__reorient,axiom,
% 0.25/0.58 ! [X: nat] :
% 0.25/0.58 ( ( zero_zero_nat = X )
% 0.25/0.58 = ( X = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % zero_reorient
% 0.25/0.58 thf(fact_132_zero__reorient,axiom,
% 0.25/0.58 ! [X: int] :
% 0.25/0.58 ( ( zero_zero_int = X )
% 0.25/0.58 = ( X = zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % zero_reorient
% 0.25/0.58 thf(fact_133_find_Osimps_I2_J,axiom,
% 0.25/0.58 ! [P: option_b > $o,X: option_b,Xs: list_option_b] :
% 0.25/0.58 ( ( ( P @ X )
% 0.25/0.58 => ( ( find_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 0.25/0.58 = ( some_option_b @ X ) ) )
% 0.25/0.58 & ( ~ ( P @ X )
% 0.25/0.58 => ( ( find_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 0.25/0.58 = ( find_option_b @ P @ Xs ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % find.simps(2)
% 0.25/0.58 thf(fact_134_find_Osimps_I2_J,axiom,
% 0.25/0.58 ! [P: b > $o,X: b,Xs: list_b] :
% 0.25/0.58 ( ( ( P @ X )
% 0.25/0.58 => ( ( find_b @ P @ ( cons_b @ X @ Xs ) )
% 0.25/0.58 = ( some_b @ X ) ) )
% 0.25/0.58 & ( ~ ( P @ X )
% 0.25/0.58 => ( ( find_b @ P @ ( cons_b @ X @ Xs ) )
% 0.25/0.58 = ( find_b @ P @ Xs ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % find.simps(2)
% 0.25/0.58 thf(fact_135_gr__zeroI,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( N != zero_zero_nat )
% 0.25/0.58 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.25/0.58
% 0.25/0.58 % gr_zeroI
% 0.25/0.58 thf(fact_136_not__less__zero,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % not_less_zero
% 0.25/0.58 thf(fact_137_gr__implies__not__zero,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N )
% 0.25/0.58 => ( N != zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % gr_implies_not_zero
% 0.25/0.58 thf(fact_138_zero__less__iff__neq__zero,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.25/0.58 = ( N != zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % zero_less_iff_neq_zero
% 0.25/0.58 thf(fact_139_list__decode_Ocases,axiom,
% 0.25/0.58 ! [X: nat] :
% 0.25/0.58 ( ( X != zero_zero_nat )
% 0.25/0.58 => ~ ! [N2: nat] :
% 0.25/0.58 ( X
% 0.25/0.58 != ( suc @ N2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_decode.cases
% 0.25/0.58 thf(fact_140_less__numeral__extra_I3_J,axiom,
% 0.25/0.58 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % less_numeral_extra(3)
% 0.25/0.58 thf(fact_141_less__numeral__extra_I3_J,axiom,
% 0.25/0.58 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.25/0.58
% 0.25/0.58 % less_numeral_extra(3)
% 0.25/0.58 thf(fact_142_length__code,axiom,
% 0.25/0.58 ( size_size_list_b
% 0.25/0.58 = ( gen_length_b @ zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_code
% 0.25/0.58 thf(fact_143_length__code,axiom,
% 0.25/0.58 ( size_s1671393719tion_b
% 0.25/0.58 = ( gen_length_option_b @ zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_code
% 0.25/0.58 thf(fact_144_gen__length__code_I2_J,axiom,
% 0.25/0.58 ! [N: nat,X: b,Xs: list_b] :
% 0.25/0.58 ( ( gen_length_b @ N @ ( cons_b @ X @ Xs ) )
% 0.25/0.58 = ( gen_length_b @ ( suc @ N ) @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % gen_length_code(2)
% 0.25/0.58 thf(fact_145_gen__length__code_I2_J,axiom,
% 0.25/0.58 ! [N: nat,X: option_b,Xs: list_option_b] :
% 0.25/0.58 ( ( gen_length_option_b @ N @ ( cons_option_b @ X @ Xs ) )
% 0.25/0.58 = ( gen_length_option_b @ ( suc @ N ) @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % gen_length_code(2)
% 0.25/0.58 thf(fact_146_option_Osize__gen_I2_J,axiom,
% 0.25/0.58 ! [X: option_b > nat,X2: option_b] :
% 0.25/0.58 ( ( size_option_option_b @ X @ ( some_option_b @ X2 ) )
% 0.25/0.58 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % option.size_gen(2)
% 0.25/0.58 thf(fact_147_option_Osize__gen_I2_J,axiom,
% 0.25/0.58 ! [X: b > nat,X2: b] :
% 0.25/0.58 ( ( size_option_b @ X @ ( some_b @ X2 ) )
% 0.25/0.58 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % option.size_gen(2)
% 0.25/0.58 thf(fact_148_Cons__nth__drop__Suc,axiom,
% 0.25/0.58 ! [I: nat,Xs: list_b] :
% 0.25/0.58 ( ( ord_less_nat @ I @ ( size_size_list_b @ Xs ) )
% 0.25/0.58 => ( ( cons_b @ ( nth_b @ Xs @ I ) @ ( drop_b @ ( suc @ I ) @ Xs ) )
% 0.25/0.58 = ( drop_b @ I @ Xs ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Cons_nth_drop_Suc
% 0.25/0.58 thf(fact_149_Cons__nth__drop__Suc,axiom,
% 0.25/0.58 ! [I: nat,Xs: list_option_b] :
% 0.25/0.58 ( ( ord_less_nat @ I @ ( size_s1671393719tion_b @ Xs ) )
% 0.25/0.58 => ( ( cons_option_b @ ( nth_option_b @ Xs @ I ) @ ( drop_option_b @ ( suc @ I ) @ Xs ) )
% 0.25/0.58 = ( drop_option_b @ I @ Xs ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Cons_nth_drop_Suc
% 0.25/0.58 thf(fact_150_list__ex__length,axiom,
% 0.25/0.58 ( list_ex_b
% 0.25/0.58 = ( ^ [P3: b > $o,Xs3: list_b] :
% 0.25/0.58 ? [N4: nat] :
% 0.25/0.58 ( ( ord_less_nat @ N4 @ ( size_size_list_b @ Xs3 ) )
% 0.25/0.58 & ( P3 @ ( nth_b @ Xs3 @ N4 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_ex_length
% 0.25/0.58 thf(fact_151_list__ex__length,axiom,
% 0.25/0.58 ( list_ex_option_b
% 0.25/0.58 = ( ^ [P3: option_b > $o,Xs3: list_option_b] :
% 0.25/0.58 ? [N4: nat] :
% 0.25/0.58 ( ( ord_less_nat @ N4 @ ( size_s1671393719tion_b @ Xs3 ) )
% 0.25/0.58 & ( P3 @ ( nth_option_b @ Xs3 @ N4 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_ex_length
% 0.25/0.58 thf(fact_152_of__nat__0__less__iff,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N ) )
% 0.25/0.58 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_0_less_iff
% 0.25/0.58 thf(fact_153_of__nat__0__less__iff,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N ) )
% 0.25/0.58 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_0_less_iff
% 0.25/0.58 thf(fact_154_add__left__cancel,axiom,
% 0.25/0.58 ! [A: nat,B2: nat,C: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ A @ B2 )
% 0.25/0.58 = ( plus_plus_nat @ A @ C ) )
% 0.25/0.58 = ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_left_cancel
% 0.25/0.58 thf(fact_155_add__left__cancel,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ A @ B2 )
% 0.25/0.58 = ( plus_plus_int @ A @ C ) )
% 0.25/0.58 = ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_left_cancel
% 0.25/0.58 thf(fact_156_add__right__cancel,axiom,
% 0.25/0.58 ! [B2: nat,A: nat,C: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ B2 @ A )
% 0.25/0.58 = ( plus_plus_nat @ C @ A ) )
% 0.25/0.58 = ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_right_cancel
% 0.25/0.58 thf(fact_157_add__right__cancel,axiom,
% 0.25/0.58 ! [B2: int,A: int,C: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ B2 @ A )
% 0.25/0.58 = ( plus_plus_int @ C @ A ) )
% 0.25/0.58 = ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_right_cancel
% 0.25/0.58 thf(fact_158_of__nat__eq__iff,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ( semiri1382578993at_nat @ M )
% 0.25/0.58 = ( semiri1382578993at_nat @ N ) )
% 0.25/0.58 = ( M = N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_eq_iff
% 0.25/0.58 thf(fact_159_of__nat__eq__iff,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ( semiri2019852685at_int @ M )
% 0.25/0.58 = ( semiri2019852685at_int @ N ) )
% 0.25/0.58 = ( M = N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_eq_iff
% 0.25/0.58 thf(fact_160_zero__eq__add__iff__both__eq__0,axiom,
% 0.25/0.58 ! [X: nat,Y3: nat] :
% 0.25/0.58 ( ( zero_zero_nat
% 0.25/0.58 = ( plus_plus_nat @ X @ Y3 ) )
% 0.25/0.58 = ( ( X = zero_zero_nat )
% 0.25/0.58 & ( Y3 = zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % zero_eq_add_iff_both_eq_0
% 0.25/0.58 thf(fact_161_add__eq__0__iff__both__eq__0,axiom,
% 0.25/0.58 ! [X: nat,Y3: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ X @ Y3 )
% 0.25/0.58 = zero_zero_nat )
% 0.25/0.58 = ( ( X = zero_zero_nat )
% 0.25/0.58 & ( Y3 = zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_eq_0_iff_both_eq_0
% 0.25/0.58 thf(fact_162_add__cancel__right__right,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( A
% 0.25/0.58 = ( plus_plus_nat @ A @ B2 ) )
% 0.25/0.58 = ( B2 = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_cancel_right_right
% 0.25/0.58 thf(fact_163_add__cancel__right__right,axiom,
% 0.25/0.58 ! [A: int,B2: int] :
% 0.25/0.58 ( ( A
% 0.25/0.58 = ( plus_plus_int @ A @ B2 ) )
% 0.25/0.58 = ( B2 = zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_cancel_right_right
% 0.25/0.58 thf(fact_164_add__cancel__right__left,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( A
% 0.25/0.58 = ( plus_plus_nat @ B2 @ A ) )
% 0.25/0.58 = ( B2 = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_cancel_right_left
% 0.25/0.58 thf(fact_165_add__cancel__right__left,axiom,
% 0.25/0.58 ! [A: int,B2: int] :
% 0.25/0.58 ( ( A
% 0.25/0.58 = ( plus_plus_int @ B2 @ A ) )
% 0.25/0.58 = ( B2 = zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_cancel_right_left
% 0.25/0.58 thf(fact_166_add__cancel__left__right,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ A @ B2 )
% 0.25/0.58 = A )
% 0.25/0.58 = ( B2 = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_cancel_left_right
% 0.25/0.58 thf(fact_167_add__cancel__left__right,axiom,
% 0.25/0.58 ! [A: int,B2: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ A @ B2 )
% 0.25/0.58 = A )
% 0.25/0.58 = ( B2 = zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_cancel_left_right
% 0.25/0.58 thf(fact_168_add__cancel__left__left,axiom,
% 0.25/0.58 ! [B2: nat,A: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ B2 @ A )
% 0.25/0.58 = A )
% 0.25/0.58 = ( B2 = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_cancel_left_left
% 0.25/0.58 thf(fact_169_add__cancel__left__left,axiom,
% 0.25/0.58 ! [B2: int,A: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ B2 @ A )
% 0.25/0.58 = A )
% 0.25/0.58 = ( B2 = zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_cancel_left_left
% 0.25/0.58 thf(fact_170_double__zero__sym,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( zero_zero_int
% 0.25/0.58 = ( plus_plus_int @ A @ A ) )
% 0.25/0.58 = ( A = zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % double_zero_sym
% 0.25/0.58 thf(fact_171_double__zero,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ A @ A )
% 0.25/0.58 = zero_zero_int )
% 0.25/0.58 = ( A = zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % double_zero
% 0.25/0.58 thf(fact_172_add_Oright__neutral,axiom,
% 0.25/0.58 ! [A: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % add.right_neutral
% 0.25/0.58 thf(fact_173_add_Oright__neutral,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % add.right_neutral
% 0.25/0.58 thf(fact_174_add_Oleft__neutral,axiom,
% 0.25/0.58 ! [A: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % add.left_neutral
% 0.25/0.58 thf(fact_175_add_Oleft__neutral,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % add.left_neutral
% 0.25/0.58 thf(fact_176_add__less__cancel__right,axiom,
% 0.25/0.58 ! [A: nat,C: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 0.25/0.58 = ( ord_less_nat @ A @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_cancel_right
% 0.25/0.58 thf(fact_177_add__less__cancel__right,axiom,
% 0.25/0.58 ! [A: int,C: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 0.25/0.58 = ( ord_less_int @ A @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_cancel_right
% 0.25/0.58 thf(fact_178_add__less__cancel__left,axiom,
% 0.25/0.58 ! [C: nat,A: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 0.25/0.58 = ( ord_less_nat @ A @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_cancel_left
% 0.25/0.58 thf(fact_179_add__less__cancel__left,axiom,
% 0.25/0.58 ! [C: int,A: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 0.25/0.58 = ( ord_less_int @ A @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_cancel_left
% 0.25/0.58 thf(fact_180_add__is__0,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ M @ N )
% 0.25/0.58 = zero_zero_nat )
% 0.25/0.58 = ( ( M = zero_zero_nat )
% 0.25/0.58 & ( N = zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_is_0
% 0.25/0.58 thf(fact_181_Nat_Oadd__0__right,axiom,
% 0.25/0.58 ! [M: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.25/0.58 = M ) ).
% 0.25/0.58
% 0.25/0.58 % Nat.add_0_right
% 0.25/0.58 thf(fact_182_add__Suc__right,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 0.25/0.58 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_Suc_right
% 0.25/0.58 thf(fact_183_nat__add__left__cancel__less,axiom,
% 0.25/0.58 ! [K: nat,M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.25/0.58 = ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat_add_left_cancel_less
% 0.25/0.58 thf(fact_184_drop0,axiom,
% 0.25/0.58 ( ( drop_option_b @ zero_zero_nat )
% 0.25/0.58 = ( ^ [X4: list_option_b] : X4 ) ) ).
% 0.25/0.58
% 0.25/0.58 % drop0
% 0.25/0.58 thf(fact_185_drop__drop,axiom,
% 0.25/0.58 ! [N: nat,M: nat,Xs: list_option_b] :
% 0.25/0.58 ( ( drop_option_b @ N @ ( drop_option_b @ M @ Xs ) )
% 0.25/0.58 = ( drop_option_b @ ( plus_plus_nat @ N @ M ) @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % drop_drop
% 0.25/0.58 thf(fact_186_list__ex__simps_I1_J,axiom,
% 0.25/0.58 ! [P: b > $o,X: b,Xs: list_b] :
% 0.25/0.58 ( ( list_ex_b @ P @ ( cons_b @ X @ Xs ) )
% 0.25/0.58 = ( ( P @ X )
% 0.25/0.58 | ( list_ex_b @ P @ Xs ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_ex_simps(1)
% 0.25/0.58 thf(fact_187_list__ex__simps_I1_J,axiom,
% 0.25/0.58 ! [P: option_b > $o,X: option_b,Xs: list_option_b] :
% 0.25/0.58 ( ( list_ex_option_b @ P @ ( cons_option_b @ X @ Xs ) )
% 0.25/0.58 = ( ( P @ X )
% 0.25/0.58 | ( list_ex_option_b @ P @ Xs ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_ex_simps(1)
% 0.25/0.58 thf(fact_188_add__less__same__cancel1,axiom,
% 0.25/0.58 ! [B2: nat,A: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ B2 @ A ) @ B2 )
% 0.25/0.58 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_same_cancel1
% 0.25/0.58 thf(fact_189_add__less__same__cancel1,axiom,
% 0.25/0.58 ! [B2: int,A: int] :
% 0.25/0.58 ( ( ord_less_int @ ( plus_plus_int @ B2 @ A ) @ B2 )
% 0.25/0.58 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_same_cancel1
% 0.25/0.58 thf(fact_190_add__less__same__cancel2,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ B2 )
% 0.25/0.58 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_same_cancel2
% 0.25/0.58 thf(fact_191_add__less__same__cancel2,axiom,
% 0.25/0.58 ! [A: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ B2 )
% 0.25/0.58 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_same_cancel2
% 0.25/0.58 thf(fact_192_less__add__same__cancel1,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B2 ) )
% 0.25/0.58 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_add_same_cancel1
% 0.25/0.58 thf(fact_193_less__add__same__cancel1,axiom,
% 0.25/0.58 ! [A: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B2 ) )
% 0.25/0.58 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_add_same_cancel1
% 0.25/0.58 thf(fact_194_less__add__same__cancel2,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B2 @ A ) )
% 0.25/0.58 = ( ord_less_nat @ zero_zero_nat @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_add_same_cancel2
% 0.25/0.58 thf(fact_195_less__add__same__cancel2,axiom,
% 0.25/0.58 ! [A: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ A @ ( plus_plus_int @ B2 @ A ) )
% 0.25/0.58 = ( ord_less_int @ zero_zero_int @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_add_same_cancel2
% 0.25/0.58 thf(fact_196_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.25/0.58 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % double_add_less_zero_iff_single_add_less_zero
% 0.25/0.58 thf(fact_197_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.25/0.58 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.25/0.58
% 0.25/0.58 % zero_less_double_add_iff_zero_less_single_add
% 0.25/0.58 thf(fact_198_of__nat__0,axiom,
% 0.25/0.58 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 0.25/0.58 = zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_0
% 0.25/0.58 thf(fact_199_of__nat__0,axiom,
% 0.25/0.58 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.25/0.58 = zero_zero_int ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_0
% 0.25/0.58 thf(fact_200_of__nat__0__eq__iff,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( zero_zero_nat
% 0.25/0.58 = ( semiri1382578993at_nat @ N ) )
% 0.25/0.58 = ( zero_zero_nat = N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_0_eq_iff
% 0.25/0.58 thf(fact_201_of__nat__0__eq__iff,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( zero_zero_int
% 0.25/0.58 = ( semiri2019852685at_int @ N ) )
% 0.25/0.58 = ( zero_zero_nat = N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_0_eq_iff
% 0.25/0.58 thf(fact_202_of__nat__eq__0__iff,axiom,
% 0.25/0.58 ! [M: nat] :
% 0.25/0.58 ( ( ( semiri1382578993at_nat @ M )
% 0.25/0.58 = zero_zero_nat )
% 0.25/0.58 = ( M = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_eq_0_iff
% 0.25/0.58 thf(fact_203_of__nat__eq__0__iff,axiom,
% 0.25/0.58 ! [M: nat] :
% 0.25/0.58 ( ( ( semiri2019852685at_int @ M )
% 0.25/0.58 = zero_zero_int )
% 0.25/0.58 = ( M = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_eq_0_iff
% 0.25/0.58 thf(fact_204_of__nat__less__iff,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 0.25/0.58 = ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_less_iff
% 0.25/0.58 thf(fact_205_of__nat__less__iff,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 0.25/0.58 = ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_less_iff
% 0.25/0.58 thf(fact_206_of__nat__add,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( semiri1382578993at_nat @ ( plus_plus_nat @ M @ N ) )
% 0.25/0.58 = ( plus_plus_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_add
% 0.25/0.58 thf(fact_207_of__nat__add,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) )
% 0.25/0.58 = ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_add
% 0.25/0.58 thf(fact_208_add__gr__0,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.25/0.58 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.25/0.58 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_gr_0
% 0.25/0.58 thf(fact_209_drop__Suc__Cons,axiom,
% 0.25/0.58 ! [N: nat,X: b,Xs: list_b] :
% 0.25/0.58 ( ( drop_b @ ( suc @ N ) @ ( cons_b @ X @ Xs ) )
% 0.25/0.58 = ( drop_b @ N @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % drop_Suc_Cons
% 0.25/0.58 thf(fact_210_drop__Suc__Cons,axiom,
% 0.25/0.58 ! [N: nat,X: option_b,Xs: list_option_b] :
% 0.25/0.58 ( ( drop_option_b @ ( suc @ N ) @ ( cons_option_b @ X @ Xs ) )
% 0.25/0.58 = ( drop_option_b @ N @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % drop_Suc_Cons
% 0.25/0.58 thf(fact_211_is__num__normalize_I1_J,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 0.25/0.58 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % is_num_normalize(1)
% 0.25/0.58 thf(fact_212_less__add__eq__less,axiom,
% 0.25/0.58 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ K @ L )
% 0.25/0.58 => ( ( ( plus_plus_nat @ M @ L )
% 0.25/0.58 = ( plus_plus_nat @ K @ N ) )
% 0.25/0.58 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_add_eq_less
% 0.25/0.58 thf(fact_213_trans__less__add2,axiom,
% 0.25/0.58 ! [I: nat,J: nat,M: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J )
% 0.25/0.58 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % trans_less_add2
% 0.25/0.58 thf(fact_214_trans__less__add1,axiom,
% 0.25/0.58 ! [I: nat,J: nat,M: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J )
% 0.25/0.58 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % trans_less_add1
% 0.25/0.58 thf(fact_215_add__less__mono1,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_mono1
% 0.25/0.58 thf(fact_216_not__add__less2,axiom,
% 0.25/0.58 ! [J: nat,I: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 0.25/0.58
% 0.25/0.58 % not_add_less2
% 0.25/0.58 thf(fact_217_not__add__less1,axiom,
% 0.25/0.58 ! [I: nat,J: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 0.25/0.58
% 0.25/0.58 % not_add_less1
% 0.25/0.58 thf(fact_218_add__less__mono,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J )
% 0.25/0.58 => ( ( ord_less_nat @ K @ L )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_mono
% 0.25/0.58 thf(fact_219_add__lessD1,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 0.25/0.58 => ( ord_less_nat @ I @ K ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_lessD1
% 0.25/0.58 thf(fact_220_add__Suc,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.25/0.58 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_Suc
% 0.25/0.58 thf(fact_221_nat__arith_Osuc1,axiom,
% 0.25/0.58 ! [A2: nat,K: nat,A: nat] :
% 0.25/0.58 ( ( A2
% 0.25/0.58 = ( plus_plus_nat @ K @ A ) )
% 0.25/0.58 => ( ( suc @ A2 )
% 0.25/0.58 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat_arith.suc1
% 0.25/0.58 thf(fact_222_add__Suc__shift,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 0.25/0.58 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_Suc_shift
% 0.25/0.58 thf(fact_223_add__eq__self__zero,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ M @ N )
% 0.25/0.58 = M )
% 0.25/0.58 => ( N = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_eq_self_zero
% 0.25/0.58 thf(fact_224_plus__nat_Oadd__0,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.25/0.58 = N ) ).
% 0.25/0.58
% 0.25/0.58 % plus_nat.add_0
% 0.25/0.58 thf(fact_225_drop__0,axiom,
% 0.25/0.58 ! [Xs: list_option_b] :
% 0.25/0.58 ( ( drop_option_b @ zero_zero_nat @ Xs )
% 0.25/0.58 = Xs ) ).
% 0.25/0.58
% 0.25/0.58 % drop_0
% 0.25/0.58 thf(fact_226_add__less__imp__less__right,axiom,
% 0.25/0.58 ! [A: nat,C: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) )
% 0.25/0.58 => ( ord_less_nat @ A @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_imp_less_right
% 0.25/0.58 thf(fact_227_add__less__imp__less__right,axiom,
% 0.25/0.58 ! [A: int,C: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) )
% 0.25/0.58 => ( ord_less_int @ A @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_imp_less_right
% 0.25/0.58 thf(fact_228_add__less__imp__less__left,axiom,
% 0.25/0.58 ! [C: nat,A: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) )
% 0.25/0.58 => ( ord_less_nat @ A @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_imp_less_left
% 0.25/0.58 thf(fact_229_add__less__imp__less__left,axiom,
% 0.25/0.58 ! [C: int,A: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) )
% 0.25/0.58 => ( ord_less_int @ A @ B2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_imp_less_left
% 0.25/0.58 thf(fact_230_add__strict__right__mono,axiom,
% 0.25/0.58 ! [A: nat,B2: nat,C: nat] :
% 0.25/0.58 ( ( ord_less_nat @ A @ B2 )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_strict_right_mono
% 0.25/0.58 thf(fact_231_add__strict__right__mono,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( ord_less_int @ A @ B2 )
% 0.25/0.58 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_strict_right_mono
% 0.25/0.58 thf(fact_232_add__strict__left__mono,axiom,
% 0.25/0.58 ! [A: nat,B2: nat,C: nat] :
% 0.25/0.58 ( ( ord_less_nat @ A @ B2 )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_strict_left_mono
% 0.25/0.58 thf(fact_233_add__strict__left__mono,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( ord_less_int @ A @ B2 )
% 0.25/0.58 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_strict_left_mono
% 0.25/0.58 thf(fact_234_add__strict__mono,axiom,
% 0.25/0.58 ! [A: nat,B2: nat,C: nat,D: nat] :
% 0.25/0.58 ( ( ord_less_nat @ A @ B2 )
% 0.25/0.58 => ( ( ord_less_nat @ C @ D )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B2 @ D ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_strict_mono
% 0.25/0.58 thf(fact_235_add__strict__mono,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int,D: int] :
% 0.25/0.58 ( ( ord_less_int @ A @ B2 )
% 0.25/0.58 => ( ( ord_less_int @ C @ D )
% 0.25/0.58 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B2 @ D ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_strict_mono
% 0.25/0.58 thf(fact_236_add__mono__thms__linordered__field_I1_J,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.58 ( ( ( ord_less_nat @ I @ J )
% 0.25/0.58 & ( K = L ) )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_mono_thms_linordered_field(1)
% 0.25/0.58 thf(fact_237_add__mono__thms__linordered__field_I1_J,axiom,
% 0.25/0.58 ! [I: int,J: int,K: int,L: int] :
% 0.25/0.58 ( ( ( ord_less_int @ I @ J )
% 0.25/0.58 & ( K = L ) )
% 0.25/0.58 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_mono_thms_linordered_field(1)
% 0.25/0.58 thf(fact_238_add__mono__thms__linordered__field_I2_J,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.58 ( ( ( I = J )
% 0.25/0.58 & ( ord_less_nat @ K @ L ) )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_mono_thms_linordered_field(2)
% 0.25/0.58 thf(fact_239_add__mono__thms__linordered__field_I2_J,axiom,
% 0.25/0.58 ! [I: int,J: int,K: int,L: int] :
% 0.25/0.58 ( ( ( I = J )
% 0.25/0.58 & ( ord_less_int @ K @ L ) )
% 0.25/0.58 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_mono_thms_linordered_field(2)
% 0.25/0.58 thf(fact_240_add__mono__thms__linordered__field_I5_J,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.58 ( ( ( ord_less_nat @ I @ J )
% 0.25/0.58 & ( ord_less_nat @ K @ L ) )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_mono_thms_linordered_field(5)
% 0.25/0.58 thf(fact_241_add__mono__thms__linordered__field_I5_J,axiom,
% 0.25/0.58 ! [I: int,J: int,K: int,L: int] :
% 0.25/0.58 ( ( ( ord_less_int @ I @ J )
% 0.25/0.58 & ( ord_less_int @ K @ L ) )
% 0.25/0.58 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_mono_thms_linordered_field(5)
% 0.25/0.58 thf(fact_242_add_Ogroup__left__neutral,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % add.group_left_neutral
% 0.25/0.58 thf(fact_243_add_Ocomm__neutral,axiom,
% 0.25/0.58 ! [A: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % add.comm_neutral
% 0.25/0.58 thf(fact_244_add_Ocomm__neutral,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % add.comm_neutral
% 0.25/0.58 thf(fact_245_comm__monoid__add__class_Oadd__0,axiom,
% 0.25/0.58 ! [A: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % comm_monoid_add_class.add_0
% 0.25/0.58 thf(fact_246_comm__monoid__add__class_Oadd__0,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % comm_monoid_add_class.add_0
% 0.25/0.58 thf(fact_247_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.25/0.58 ! [A: nat,B2: nat,C: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 0.25/0.58 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % ab_semigroup_add_class.add_ac(1)
% 0.25/0.58 thf(fact_248_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 0.25/0.58 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % ab_semigroup_add_class.add_ac(1)
% 0.25/0.58 thf(fact_249_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.25/0.58 ( ( ( I = J )
% 0.25/0.58 & ( K = L ) )
% 0.25/0.58 => ( ( plus_plus_nat @ I @ K )
% 0.25/0.58 = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_mono_thms_linordered_semiring(4)
% 0.25/0.58 thf(fact_250_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.25/0.58 ! [I: int,J: int,K: int,L: int] :
% 0.25/0.58 ( ( ( I = J )
% 0.25/0.58 & ( K = L ) )
% 0.25/0.58 => ( ( plus_plus_int @ I @ K )
% 0.25/0.58 = ( plus_plus_int @ J @ L ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_mono_thms_linordered_semiring(4)
% 0.25/0.58 thf(fact_251_group__cancel_Oadd1,axiom,
% 0.25/0.58 ! [A2: nat,K: nat,A: nat,B2: nat] :
% 0.25/0.58 ( ( A2
% 0.25/0.58 = ( plus_plus_nat @ K @ A ) )
% 0.25/0.58 => ( ( plus_plus_nat @ A2 @ B2 )
% 0.25/0.58 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % group_cancel.add1
% 0.25/0.58 thf(fact_252_group__cancel_Oadd1,axiom,
% 0.25/0.58 ! [A2: int,K: int,A: int,B2: int] :
% 0.25/0.58 ( ( A2
% 0.25/0.58 = ( plus_plus_int @ K @ A ) )
% 0.25/0.58 => ( ( plus_plus_int @ A2 @ B2 )
% 0.25/0.58 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % group_cancel.add1
% 0.25/0.58 thf(fact_253_group__cancel_Oadd2,axiom,
% 0.25/0.58 ! [B3: nat,K: nat,B2: nat,A: nat] :
% 0.25/0.58 ( ( B3
% 0.25/0.58 = ( plus_plus_nat @ K @ B2 ) )
% 0.25/0.58 => ( ( plus_plus_nat @ A @ B3 )
% 0.25/0.58 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % group_cancel.add2
% 0.25/0.58 thf(fact_254_group__cancel_Oadd2,axiom,
% 0.25/0.58 ! [B3: int,K: int,B2: int,A: int] :
% 0.25/0.58 ( ( B3
% 0.25/0.58 = ( plus_plus_int @ K @ B2 ) )
% 0.25/0.58 => ( ( plus_plus_int @ A @ B3 )
% 0.25/0.58 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % group_cancel.add2
% 0.25/0.58 thf(fact_255_add_Oassoc,axiom,
% 0.25/0.58 ! [A: nat,B2: nat,C: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B2 ) @ C )
% 0.25/0.58 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add.assoc
% 0.25/0.58 thf(fact_256_add_Oassoc,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( plus_plus_int @ ( plus_plus_int @ A @ B2 ) @ C )
% 0.25/0.58 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add.assoc
% 0.25/0.58 thf(fact_257_add_Oleft__cancel,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ A @ B2 )
% 0.25/0.58 = ( plus_plus_int @ A @ C ) )
% 0.25/0.58 = ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add.left_cancel
% 0.25/0.58 thf(fact_258_add_Oright__cancel,axiom,
% 0.25/0.58 ! [B2: int,A: int,C: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ B2 @ A )
% 0.25/0.58 = ( plus_plus_int @ C @ A ) )
% 0.25/0.58 = ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add.right_cancel
% 0.25/0.58 thf(fact_259_add_Ocommute,axiom,
% 0.25/0.58 ( plus_plus_nat
% 0.25/0.58 = ( ^ [A4: nat,B4: nat] : ( plus_plus_nat @ B4 @ A4 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add.commute
% 0.25/0.58 thf(fact_260_add_Ocommute,axiom,
% 0.25/0.58 ( plus_plus_int
% 0.25/0.58 = ( ^ [A4: int,B4: int] : ( plus_plus_int @ B4 @ A4 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add.commute
% 0.25/0.58 thf(fact_261_add_Oleft__commute,axiom,
% 0.25/0.58 ! [B2: nat,A: nat,C: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ B2 @ ( plus_plus_nat @ A @ C ) )
% 0.25/0.58 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add.left_commute
% 0.25/0.58 thf(fact_262_add_Oleft__commute,axiom,
% 0.25/0.58 ! [B2: int,A: int,C: int] :
% 0.25/0.58 ( ( plus_plus_int @ B2 @ ( plus_plus_int @ A @ C ) )
% 0.25/0.58 = ( plus_plus_int @ A @ ( plus_plus_int @ B2 @ C ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add.left_commute
% 0.25/0.58 thf(fact_263_add__left__imp__eq,axiom,
% 0.25/0.58 ! [A: nat,B2: nat,C: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ A @ B2 )
% 0.25/0.58 = ( plus_plus_nat @ A @ C ) )
% 0.25/0.58 => ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_left_imp_eq
% 0.25/0.58 thf(fact_264_add__left__imp__eq,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ A @ B2 )
% 0.25/0.58 = ( plus_plus_int @ A @ C ) )
% 0.25/0.58 => ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_left_imp_eq
% 0.25/0.58 thf(fact_265_add__right__imp__eq,axiom,
% 0.25/0.58 ! [B2: nat,A: nat,C: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ B2 @ A )
% 0.25/0.58 = ( plus_plus_nat @ C @ A ) )
% 0.25/0.58 => ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_right_imp_eq
% 0.25/0.58 thf(fact_266_add__right__imp__eq,axiom,
% 0.25/0.58 ! [B2: int,A: int,C: int] :
% 0.25/0.58 ( ( ( plus_plus_int @ B2 @ A )
% 0.25/0.58 = ( plus_plus_int @ C @ A ) )
% 0.25/0.58 => ( B2 = C ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_right_imp_eq
% 0.25/0.58 thf(fact_267_of__nat__less__0__iff,axiom,
% 0.25/0.58 ! [M: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_less_0_iff
% 0.25/0.58 thf(fact_268_of__nat__less__0__iff,axiom,
% 0.25/0.58 ! [M: nat] :
% 0.25/0.58 ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_less_0_iff
% 0.25/0.58 thf(fact_269_of__nat__neq__0,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( semiri1382578993at_nat @ ( suc @ N ) )
% 0.25/0.58 != zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_neq_0
% 0.25/0.58 thf(fact_270_of__nat__neq__0,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( semiri2019852685at_int @ ( suc @ N ) )
% 0.25/0.58 != zero_zero_int ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_neq_0
% 0.25/0.58 thf(fact_271_less__imp__of__nat__less,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N )
% 0.25/0.58 => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_imp_of_nat_less
% 0.25/0.58 thf(fact_272_less__imp__of__nat__less,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N )
% 0.25/0.58 => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_imp_of_nat_less
% 0.25/0.58 thf(fact_273_of__nat__less__imp__less,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N ) )
% 0.25/0.58 => ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_less_imp_less
% 0.25/0.58 thf(fact_274_of__nat__less__imp__less,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N ) )
% 0.25/0.58 => ( ord_less_nat @ M @ N ) ) ).
% 0.25/0.58
% 0.25/0.58 % of_nat_less_imp_less
% 0.25/0.58 thf(fact_275_add__neg__neg,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.25/0.58 => ( ( ord_less_nat @ B2 @ zero_zero_nat )
% 0.25/0.58 => ( ord_less_nat @ ( plus_plus_nat @ A @ B2 ) @ zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_neg_neg
% 0.25/0.58 thf(fact_276_add__neg__neg,axiom,
% 0.25/0.58 ! [A: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ A @ zero_zero_int )
% 0.25/0.58 => ( ( ord_less_int @ B2 @ zero_zero_int )
% 0.25/0.58 => ( ord_less_int @ ( plus_plus_int @ A @ B2 ) @ zero_zero_int ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_neg_neg
% 0.25/0.58 thf(fact_277_add__pos__pos,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.58 => ( ( ord_less_nat @ zero_zero_nat @ B2 )
% 0.25/0.58 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_pos_pos
% 0.25/0.58 thf(fact_278_add__pos__pos,axiom,
% 0.25/0.58 ! [A: int,B2: int] :
% 0.25/0.58 ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.58 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.25/0.58 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_pos_pos
% 0.25/0.58 thf(fact_279_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ A @ B2 )
% 0.25/0.58 => ~ ! [C2: nat] :
% 0.25/0.58 ( ( B2
% 0.25/0.58 = ( plus_plus_nat @ A @ C2 ) )
% 0.25/0.58 => ( C2 = zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % canonically_ordered_monoid_add_class.lessE
% 0.25/0.58 thf(fact_280_pos__add__strict,axiom,
% 0.25/0.58 ! [A: nat,B2: nat,C: nat] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.25/0.58 => ( ( ord_less_nat @ B2 @ C )
% 0.25/0.58 => ( ord_less_nat @ B2 @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % pos_add_strict
% 0.25/0.58 thf(fact_281_pos__add__strict,axiom,
% 0.25/0.58 ! [A: int,B2: int,C: int] :
% 0.25/0.58 ( ( ord_less_int @ zero_zero_int @ A )
% 0.25/0.58 => ( ( ord_less_int @ B2 @ C )
% 0.25/0.58 => ( ord_less_int @ B2 @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % pos_add_strict
% 0.25/0.58 thf(fact_282_nth__via__drop,axiom,
% 0.25/0.58 ! [N: nat,Xs: list_b,Y3: b,Ys: list_b] :
% 0.25/0.58 ( ( ( drop_b @ N @ Xs )
% 0.25/0.58 = ( cons_b @ Y3 @ Ys ) )
% 0.25/0.58 => ( ( nth_b @ Xs @ N )
% 0.25/0.58 = Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % nth_via_drop
% 0.25/0.58 thf(fact_283_nth__via__drop,axiom,
% 0.25/0.58 ! [N: nat,Xs: list_option_b,Y3: option_b,Ys: list_option_b] :
% 0.25/0.58 ( ( ( drop_option_b @ N @ Xs )
% 0.25/0.58 = ( cons_option_b @ Y3 @ Ys ) )
% 0.25/0.58 => ( ( nth_option_b @ Xs @ N )
% 0.25/0.58 = Y3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % nth_via_drop
% 0.25/0.58 thf(fact_284_add__is__1,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ( plus_plus_nat @ M @ N )
% 0.25/0.58 = ( suc @ zero_zero_nat ) )
% 0.25/0.58 = ( ( ( M
% 0.25/0.58 = ( suc @ zero_zero_nat ) )
% 0.25/0.58 & ( N = zero_zero_nat ) )
% 0.25/0.58 | ( ( M = zero_zero_nat )
% 0.25/0.58 & ( N
% 0.25/0.58 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_is_1
% 0.25/0.58 thf(fact_285_one__is__add,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ( suc @ zero_zero_nat )
% 0.25/0.58 = ( plus_plus_nat @ M @ N ) )
% 0.25/0.58 = ( ( ( M
% 0.25/0.58 = ( suc @ zero_zero_nat ) )
% 0.25/0.58 & ( N = zero_zero_nat ) )
% 0.25/0.58 | ( ( M = zero_zero_nat )
% 0.25/0.58 & ( N
% 0.25/0.58 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % one_is_add
% 0.25/0.58 thf(fact_286_less__imp__add__positive,axiom,
% 0.25/0.58 ! [I: nat,J: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J )
% 0.25/0.58 => ? [K2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.25/0.58 & ( ( plus_plus_nat @ I @ K2 )
% 0.25/0.58 = J ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_imp_add_positive
% 0.25/0.58 thf(fact_287_less__natE,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N )
% 0.25/0.58 => ~ ! [Q2: nat] :
% 0.25/0.58 ( N
% 0.25/0.58 != ( suc @ ( plus_plus_nat @ M @ Q2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_natE
% 0.25/0.58 thf(fact_288_less__add__Suc1,axiom,
% 0.25/0.58 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_add_Suc1
% 0.25/0.58 thf(fact_289_less__add__Suc2,axiom,
% 0.25/0.58 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_add_Suc2
% 0.25/0.58 thf(fact_290_less__iff__Suc__add,axiom,
% 0.25/0.58 ( ord_less_nat
% 0.25/0.58 = ( ^ [M5: nat,N4: nat] :
% 0.25/0.58 ? [K3: nat] :
% 0.25/0.58 ( N4
% 0.25/0.58 = ( suc @ ( plus_plus_nat @ M5 @ K3 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_iff_Suc_add
% 0.25/0.58 thf(fact_291_less__imp__Suc__add,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N )
% 0.25/0.58 => ? [K2: nat] :
% 0.25/0.58 ( N
% 0.25/0.58 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_imp_Suc_add
% 0.25/0.58 thf(fact_292_gen__length__def,axiom,
% 0.25/0.58 ( gen_length_b
% 0.25/0.58 = ( ^ [N4: nat,Xs3: list_b] : ( plus_plus_nat @ N4 @ ( size_size_list_b @ Xs3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % gen_length_def
% 0.25/0.58 thf(fact_293_gen__length__def,axiom,
% 0.25/0.58 ( gen_length_option_b
% 0.25/0.58 = ( ^ [N4: nat,Xs3: list_option_b] : ( plus_plus_nat @ N4 @ ( size_s1671393719tion_b @ Xs3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % gen_length_def
% 0.25/0.58 thf(fact_294_list_Osize_I4_J,axiom,
% 0.25/0.58 ! [X21: b,X22: list_b] :
% 0.25/0.58 ( ( size_size_list_b @ ( cons_b @ X21 @ X22 ) )
% 0.25/0.58 = ( plus_plus_nat @ ( size_size_list_b @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list.size(4)
% 0.25/0.58 thf(fact_295_list_Osize_I4_J,axiom,
% 0.25/0.58 ! [X21: option_b,X22: list_option_b] :
% 0.25/0.58 ( ( size_s1671393719tion_b @ ( cons_option_b @ X21 @ X22 ) )
% 0.25/0.58 = ( plus_plus_nat @ ( size_s1671393719tion_b @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list.size(4)
% 0.25/0.58 thf(fact_296_add__less__zeroD,axiom,
% 0.25/0.58 ! [X: int,Y3: int] :
% 0.25/0.58 ( ( ord_less_int @ ( plus_plus_int @ X @ Y3 ) @ zero_zero_int )
% 0.25/0.58 => ( ( ord_less_int @ X @ zero_zero_int )
% 0.25/0.58 | ( ord_less_int @ Y3 @ zero_zero_int ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_less_zeroD
% 0.25/0.58 thf(fact_297_Euclid__induct,axiom,
% 0.25/0.58 ! [P: nat > nat > $o,A: nat,B2: nat] :
% 0.25/0.58 ( ! [A3: nat,B: nat] :
% 0.25/0.58 ( ( P @ A3 @ B )
% 0.25/0.58 = ( P @ B @ A3 ) )
% 0.25/0.58 => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
% 0.25/0.58 => ( ! [A3: nat,B: nat] :
% 0.25/0.58 ( ( P @ A3 @ B )
% 0.25/0.58 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B ) ) )
% 0.25/0.58 => ( P @ A @ B2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Euclid_induct
% 0.25/0.58 thf(fact_298_pos__int__cases,axiom,
% 0.25/0.58 ! [K: int] :
% 0.25/0.58 ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.58 => ~ ! [N2: nat] :
% 0.25/0.58 ( ( K
% 0.25/0.58 = ( semiri2019852685at_int @ N2 ) )
% 0.25/0.58 => ~ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % pos_int_cases
% 0.25/0.58 thf(fact_299_zero__less__imp__eq__int,axiom,
% 0.25/0.58 ! [K: int] :
% 0.25/0.58 ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.58 => ? [N2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.58 & ( K
% 0.25/0.58 = ( semiri2019852685at_int @ N2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % zero_less_imp_eq_int
% 0.25/0.58 thf(fact_300_zadd__int__left,axiom,
% 0.25/0.58 ! [M: nat,N: nat,Z2: int] :
% 0.25/0.58 ( ( plus_plus_int @ ( semiri2019852685at_int @ M ) @ ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ Z2 ) )
% 0.25/0.58 = ( plus_plus_int @ ( semiri2019852685at_int @ ( plus_plus_nat @ M @ N ) ) @ Z2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % zadd_int_left
% 0.25/0.58 thf(fact_301_int__int__eq,axiom,
% 0.25/0.58 ! [M: nat,N: nat] :
% 0.25/0.58 ( ( ( semiri2019852685at_int @ M )
% 0.25/0.58 = ( semiri2019852685at_int @ N ) )
% 0.25/0.58 = ( M = N ) ) ).
% 0.25/0.58
% 0.25/0.58 % int_int_eq
% 0.25/0.58 thf(fact_302_plus__int__code_I2_J,axiom,
% 0.25/0.58 ! [L: int] :
% 0.25/0.58 ( ( plus_plus_int @ zero_zero_int @ L )
% 0.25/0.58 = L ) ).
% 0.25/0.58
% 0.25/0.58 % plus_int_code(2)
% 0.25/0.58 thf(fact_303_plus__int__code_I1_J,axiom,
% 0.25/0.58 ! [K: int] :
% 0.25/0.58 ( ( plus_plus_int @ K @ zero_zero_int )
% 0.25/0.58 = K ) ).
% 0.25/0.58
% 0.25/0.58 % plus_int_code(1)
% 0.25/0.58 thf(fact_304_zless__iff__Suc__zadd,axiom,
% 0.25/0.58 ( ord_less_int
% 0.25/0.58 = ( ^ [W: int,Z3: int] :
% 0.25/0.58 ? [N4: nat] :
% 0.25/0.58 ( Z3
% 0.25/0.58 = ( plus_plus_int @ W @ ( semiri2019852685at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % zless_iff_Suc_zadd
% 0.25/0.58 thf(fact_305_less__int__code_I1_J,axiom,
% 0.25/0.58 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.25/0.58
% 0.25/0.58 % less_int_code(1)
% 0.25/0.58 thf(fact_306_linorder__neqE__linordered__idom,axiom,
% 0.25/0.58 ! [X: int,Y3: int] :
% 0.25/0.58 ( ( X != Y3 )
% 0.25/0.58 => ( ~ ( ord_less_int @ X @ Y3 )
% 0.25/0.58 => ( ord_less_int @ Y3 @ X ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % linorder_neqE_linordered_idom
% 0.25/0.58 thf(fact_307_nat__int__comparison_I2_J,axiom,
% 0.25/0.58 ( ord_less_nat
% 0.25/0.58 = ( ^ [A4: nat,B4: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A4 ) @ ( semiri2019852685at_int @ B4 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat_int_comparison(2)
% 0.25/0.58 thf(fact_308_int__ops_I1_J,axiom,
% 0.25/0.58 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.25/0.58 = zero_zero_int ) ).
% 0.25/0.58
% 0.25/0.58 % int_ops(1)
% 0.25/0.58 thf(fact_309_verit__comp__simplify1_I1_J,axiom,
% 0.25/0.58 ! [A: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ A @ A ) ).
% 0.25/0.58
% 0.25/0.58 % verit_comp_simplify1(1)
% 0.25/0.58 thf(fact_310_verit__comp__simplify1_I1_J,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ~ ( ord_less_int @ A @ A ) ).
% 0.25/0.58
% 0.25/0.58 % verit_comp_simplify1(1)
% 0.25/0.58 thf(fact_311_nat__int__comparison_I1_J,axiom,
% 0.25/0.58 ( ( ^ [Y5: nat,Z: nat] : ( Y5 = Z ) )
% 0.25/0.58 = ( ^ [A4: nat,B4: nat] :
% 0.25/0.58 ( ( semiri2019852685at_int @ A4 )
% 0.25/0.58 = ( semiri2019852685at_int @ B4 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat_int_comparison(1)
% 0.25/0.58 thf(fact_312_int__if,axiom,
% 0.25/0.58 ! [P: $o,A: nat,B2: nat] :
% 0.25/0.58 ( ( P
% 0.25/0.58 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B2 ) )
% 0.25/0.58 = ( semiri2019852685at_int @ A ) ) )
% 0.25/0.58 & ( ~ P
% 0.25/0.58 => ( ( semiri2019852685at_int @ ( if_nat @ P @ A @ B2 ) )
% 0.25/0.58 = ( semiri2019852685at_int @ B2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % int_if
% 0.25/0.58 thf(fact_313_verit__sum__simplify,axiom,
% 0.25/0.58 ! [A: nat] :
% 0.25/0.58 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % verit_sum_simplify
% 0.25/0.58 thf(fact_314_verit__sum__simplify,axiom,
% 0.25/0.58 ! [A: int] :
% 0.25/0.58 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.25/0.58 = A ) ).
% 0.25/0.58
% 0.25/0.58 % verit_sum_simplify
% 0.25/0.58 thf(fact_315_int__ops_I5_J,axiom,
% 0.25/0.58 ! [A: nat,B2: nat] :
% 0.25/0.58 ( ( semiri2019852685at_int @ ( plus_plus_nat @ A @ B2 ) )
% 0.25/0.58 = ( plus_plus_int @ ( semiri2019852685at_int @ A ) @ ( semiri2019852685at_int @ B2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % int_ops(5)
% 0.25/0.58 thf(fact_316_int__plus,axiom,
% 0.25/0.58 ! [N: nat,M: nat] :
% 0.25/0.58 ( ( semiri2019852685at_int @ ( plus_plus_nat @ N @ M ) )
% 0.25/0.58 = ( plus_plus_int @ ( semiri2019852685at_int @ N ) @ ( semiri2019852685at_int @ M ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % int_plus
% 0.25/0.58 thf(fact_317_triangle__Suc,axiom,
% 0.25/0.58 ! [N: nat] :
% 0.25/0.58 ( ( nat_triangle @ ( suc @ N ) )
% 0.25/0.58 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % triangle_Suc
% 0.25/0.58 thf(fact_318_add__0__iff,axiom,
% 0.25/0.58 ! [B2: nat,A: nat] :
% 0.25/0.58 ( ( B2
% 0.25/0.58 = ( plus_plus_nat @ B2 @ A ) )
% 0.25/0.58 = ( A = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_0_iff
% 0.25/0.58 thf(fact_319_add__0__iff,axiom,
% 0.25/0.58 ! [B2: int,A: int] :
% 0.25/0.58 ( ( B2
% 0.25/0.58 = ( plus_plus_int @ B2 @ A ) )
% 0.25/0.58 = ( A = zero_zero_int ) ) ).
% 0.25/0.58
% 0.25/0.58 % add_0_iff
% 0.25/0.58 thf(fact_320_triangle__0,axiom,
% 0.25/0.58 ( ( nat_triangle @ zero_zero_nat )
% 0.25/0.64 = zero_zero_nat ) ).
% 0.25/0.64
% 0.25/0.64 % triangle_0
% 0.25/0.64 thf(fact_321_nth__drop,axiom,
% 0.25/0.64 ! [N: nat,Xs: list_b,I: nat] :
% 0.25/0.64 ( ( ord_less_eq_nat @ N @ ( size_size_list_b @ Xs ) )
% 0.25/0.64 => ( ( nth_b @ ( drop_b @ N @ Xs ) @ I )
% 0.25/0.64 = ( nth_b @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % nth_drop
% 0.25/0.64 thf(fact_322_nth__drop,axiom,
% 0.25/0.64 ! [N: nat,Xs: list_option_b,I: nat] :
% 0.25/0.64 ( ( ord_less_eq_nat @ N @ ( size_s1671393719tion_b @ Xs ) )
% 0.25/0.64 => ( ( nth_option_b @ ( drop_option_b @ N @ Xs ) @ I )
% 0.25/0.64 = ( nth_option_b @ Xs @ ( plus_plus_nat @ N @ I ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 % nth_drop
% 0.25/0.64
% 0.25/0.64 % Helper facts (3)
% 0.25/0.64 thf(help_If_3_1_If_001t__Nat__Onat_T,axiom,
% 0.25/0.64 ! [P: $o] :
% 0.25/0.64 ( ( P = $true )
% 0.25/0.64 | ( P = $false ) ) ).
% 0.25/0.64
% 0.25/0.64 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.25/0.64 ! [X: nat,Y3: nat] :
% 0.25/0.64 ( ( if_nat @ $false @ X @ Y3 )
% 0.25/0.64 = Y3 ) ).
% 0.25/0.64
% 0.25/0.64 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.25/0.64 ! [X: nat,Y3: nat] :
% 0.25/0.64 ( ( if_nat @ $true @ X @ Y3 )
% 0.25/0.64 = X ) ).
% 0.25/0.64
% 0.25/0.64 % Conjectures (3)
% 0.25/0.64 thf(conj_0,hypothesis,
% 0.25/0.64 member_nat @ zero_zero_nat @ ( fvi_a @ b2 @ phi ) ).
% 0.25/0.64
% 0.25/0.64 thf(conj_1,hypothesis,
% 0.25/0.64 ( ( ( size_s1671393719tion_b @ v )
% 0.25/0.64 = n )
% 0.25/0.64 & ! [I4: nat] :
% 0.25/0.64 ( ( ord_less_nat @ I4 @ n )
% 0.25/0.64 => ( ( ( nth_option_b @ v @ I4 )
% 0.25/0.64 = none_b )
% 0.25/0.64 = ( ~ ( member_nat @ I4 @ ( fvi_a @ ( suc @ b2 ) @ phi ) ) ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 thf(conj_2,conjecture,
% 0.25/0.64 ( ( ( size_s1671393719tion_b @ ( cons_option_b @ ( some_b @ x ) @ v ) )
% 0.25/0.64 = ( suc @ n ) )
% 0.25/0.64 & ! [I2: nat] :
% 0.25/0.64 ( ~ ( ord_less_nat @ I2 @ ( suc @ n ) )
% 0.25/0.64 | ( ( ( nth_option_b @ ( cons_option_b @ ( some_b @ x ) @ v ) @ I2 )
% 0.25/0.64 = none_b )
% 0.25/0.64 = ( ~ ( member_nat @ I2 @ ( fvi_a @ b2 @ phi ) ) ) ) ) ) ).
% 0.25/0.64
% 0.25/0.64 %------------------------------------------------------------------------------
% 0.25/0.64 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.9D3BjHyerS/cvc5---1.0.5_12933.p...
% 0.25/0.64 (declare-sort $$unsorted 0)
% 0.25/0.64 (declare-sort tptp.option_option_b 0)
% 0.25/0.64 (declare-sort tptp.list_option_b 0)
% 0.25/0.64 (declare-sort tptp.set_nat 0)
% 0.25/0.64 (declare-sort tptp.option_b 0)
% 0.25/0.64 (declare-sort tptp.formula_a 0)
% 0.25/0.64 (declare-sort tptp.list_b 0)
% 0.25/0.64 (declare-sort tptp.nat 0)
% 0.25/0.64 (declare-sort tptp.int 0)
% 0.25/0.64 (declare-sort tptp.b 0)
% 0.25/0.64 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 0.25/0.64 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.25/0.64 (declare-fun tptp.zero_zero_int () tptp.int)
% 0.25/0.64 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.25/0.64 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 0.25/0.64 (declare-fun tptp.drop_option_b (tptp.nat tptp.list_option_b) tptp.list_option_b)
% 0.25/0.64 (declare-fun tptp.drop_b (tptp.nat tptp.list_b) tptp.list_b)
% 0.25/0.64 (declare-fun tptp.find_option_b ((-> tptp.option_b Bool) tptp.list_option_b) tptp.option_option_b)
% 0.25/0.64 (declare-fun tptp.find_b ((-> tptp.b Bool) tptp.list_b) tptp.option_b)
% 0.25/0.64 (declare-fun tptp.gen_length_option_b (tptp.nat tptp.list_option_b) tptp.nat)
% 0.25/0.64 (declare-fun tptp.gen_length_b (tptp.nat tptp.list_b) tptp.nat)
% 0.25/0.64 (declare-fun tptp.cons_option_b (tptp.option_b tptp.list_option_b) tptp.list_option_b)
% 0.25/0.64 (declare-fun tptp.cons_b (tptp.b tptp.list_b) tptp.list_b)
% 0.25/0.64 (declare-fun tptp.list_ex_option_b ((-> tptp.option_b Bool) tptp.list_option_b) Bool)
% 0.25/0.64 (declare-fun tptp.list_ex_b ((-> tptp.b Bool) tptp.list_b) Bool)
% 0.25/0.64 (declare-fun tptp.nth_option_b (tptp.list_option_b tptp.nat) tptp.option_b)
% 0.25/0.64 (declare-fun tptp.nth_b (tptp.list_b tptp.nat) tptp.b)
% 0.25/0.64 (declare-fun tptp.fvi_a (tptp.nat tptp.formula_a) tptp.set_nat)
% 0.25/0.64 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.25/0.64 (declare-fun tptp.semiri2019852685at_int (tptp.nat) tptp.int)
% 0.25/0.64 (declare-fun tptp.semiri1382578993at_nat (tptp.nat) tptp.nat)
% 0.25/0.64 (declare-fun tptp.size_s1671393719tion_b (tptp.list_option_b) tptp.nat)
% 0.25/0.64 (declare-fun tptp.size_size_list_b (tptp.list_b) tptp.nat)
% 0.25/0.64 (declare-fun tptp.size_s684879735tion_b (tptp.option_option_b) tptp.nat)
% 0.25/0.64 (declare-fun tptp.size_size_option_b (tptp.option_b) tptp.nat)
% 0.25/0.64 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 0.25/0.64 (declare-fun tptp.none_option_b () tptp.option_option_b)
% 0.25/0.64 (declare-fun tptp.none_b () tptp.option_b)
% 0.25/0.64 (declare-fun tptp.some_option_b (tptp.option_b) tptp.option_option_b)
% 0.25/0.64 (declare-fun tptp.some_b (tptp.b) tptp.option_b)
% 0.25/0.64 (declare-fun tptp.size_option_option_b ((-> tptp.option_b tptp.nat) tptp.option_option_b) tptp.nat)
% 0.25/0.64 (declare-fun tptp.size_option_b ((-> tptp.b tptp.nat) tptp.option_b) tptp.nat)
% 0.25/0.64 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.64 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.64 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.25/0.64 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.25/0.64 (declare-fun tptp.phi () tptp.formula_a)
% 0.25/0.64 (declare-fun tptp.b2 () tptp.nat)
% 0.25/0.64 (declare-fun tptp.n () tptp.nat)
% 0.25/0.64 (declare-fun tptp.v () tptp.list_option_b)
% 0.25/0.64 (declare-fun tptp.x () tptp.b)
% 0.25/0.64 (assert (forall ((X tptp.b) (Xs tptp.list_b) (N tptp.nat)) (= (@ (@ tptp.nth_b (@ (@ tptp.cons_b X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_b Xs) N))))
% 0.25/0.64 (assert (forall ((X tptp.option_b) (Xs tptp.list_option_b) (N tptp.nat)) (= (@ (@ tptp.nth_option_b (@ (@ tptp.cons_option_b X) Xs)) (@ tptp.suc N)) (@ (@ tptp.nth_option_b Xs) N))))
% 0.25/0.64 (assert (forall ((X tptp.b) (Xs tptp.list_b)) (= (@ (@ tptp.nth_b (@ (@ tptp.cons_b X) Xs)) tptp.zero_zero_nat) X)))
% 0.25/0.64 (assert (forall ((X tptp.option_b) (Xs tptp.list_option_b)) (= (@ (@ tptp.nth_option_b (@ (@ tptp.cons_option_b X) Xs)) tptp.zero_zero_nat) X)))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 0.25/0.64 (assert (forall ((X tptp.option_option_b)) (= (not (= X tptp.none_option_b)) (exists ((Y tptp.option_b)) (= X (@ tptp.some_option_b Y))))))
% 0.25/0.64 (assert (forall ((X tptp.option_b)) (= (not (= X tptp.none_b)) (exists ((Y tptp.b)) (= X (@ tptp.some_b Y))))))
% 0.25/0.64 (assert (forall ((X tptp.option_option_b)) (= (forall ((Y tptp.option_b)) (not (= X (@ tptp.some_option_b Y)))) (= X tptp.none_option_b))))
% 0.25/0.64 (assert (forall ((X tptp.option_b)) (= (forall ((Y tptp.b)) (not (= X (@ tptp.some_b Y)))) (= X tptp.none_b))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 0.25/0.64 (assert (forall ((X21 tptp.b) (X22 tptp.list_b) (Y21 tptp.b) (Y22 tptp.list_b)) (= (= (@ (@ tptp.cons_b X21) X22) (@ (@ tptp.cons_b Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.64 (assert (forall ((X21 tptp.option_b) (X22 tptp.list_option_b) (Y21 tptp.option_b) (Y22 tptp.list_option_b)) (= (= (@ (@ tptp.cons_option_b X21) X22) (@ (@ tptp.cons_option_b Y21) Y22)) (and (= X21 Y21) (= X22 Y22)))))
% 0.25/0.64 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 0.25/0.64 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 0.25/0.64 (assert (forall ((X2 tptp.option_b) (Y2 tptp.option_b)) (= (= (@ tptp.some_option_b X2) (@ tptp.some_option_b Y2)) (= X2 Y2))))
% 0.25/0.64 (assert (forall ((X2 tptp.b) (Y2 tptp.b)) (= (= (@ tptp.some_b X2) (@ tptp.some_b Y2)) (= X2 Y2))))
% 0.25/0.64 (assert (forall ((X tptp.b) (Xs tptp.list_b)) (not (= (@ (@ tptp.cons_b X) Xs) Xs))))
% 0.25/0.64 (assert (forall ((X tptp.option_b) (Xs tptp.list_option_b)) (not (= (@ (@ tptp.cons_option_b X) Xs) Xs))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 0.25/0.64 (assert (forall ((X tptp.nat) (Y3 tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y3)) (= X Y3))))
% 0.25/0.64 (assert (forall ((X tptp.nat) (Y3 tptp.nat)) (=> (not (= X Y3)) (=> (not (@ (@ tptp.ord_less_nat X) Y3)) (@ (@ tptp.ord_less_nat Y3) X)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2)))))) (@ P N))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (@ P M2))) (@ P N2))) (@ P N))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.25/0.64 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.25/0.64 (assert (forall ((X tptp.option_b) (Y3 tptp.option_b)) (=> (not (= (@ tptp.size_size_option_b X) (@ tptp.size_size_option_b Y3))) (not (= X Y3)))))
% 0.25/0.64 (assert (forall ((X tptp.list_b) (Y3 tptp.list_b)) (=> (not (= (@ tptp.size_size_list_b X) (@ tptp.size_size_list_b Y3))) (not (= X Y3)))))
% 0.25/0.64 (assert (forall ((X tptp.list_option_b) (Y3 tptp.list_option_b)) (=> (not (= (@ tptp.size_s1671393719tion_b X) (@ tptp.size_s1671393719tion_b Y3))) (not (= X Y3)))))
% 0.25/0.64 (assert (forall ((Xs tptp.list_b) (Ys tptp.list_b)) (=> (not (= (@ tptp.size_size_list_b Xs) (@ tptp.size_size_list_b Ys))) (not (= Xs Ys)))))
% 0.25/0.64 (assert (forall ((Xs tptp.list_option_b) (Ys tptp.list_option_b)) (=> (not (= (@ tptp.size_s1671393719tion_b Xs) (@ tptp.size_s1671393719tion_b Ys))) (not (= Xs Ys)))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_b)) (= (@ tptp.size_size_list_b Xs2) N))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_option_b)) (= (@ tptp.size_s1671393719tion_b Xs2) N))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P Nat3) (@ P (@ tptp.suc Nat3)))) (@ P Nat)))))
% 0.25/0.64 (assert (forall ((Y3 tptp.nat)) (=> (not (= Y3 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y3 (@ tptp.suc Nat3))))))))
% 0.25/0.64 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.25/0.64 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.25/0.64 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y4 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y4))) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ P X3) Y4) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y4)))) (@ (@ P M) N))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ P N2) (@ P (@ tptp.suc N2)))) (@ P N)))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 0.25/0.64 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A2))) A2)))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 0.25/0.64 (assert (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 0.25/0.64 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))))
% 0.25/0.64 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ P N2)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (not (@ P M2))))))) (@ P N)))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.25/0.64 (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))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (=> (= J (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I) J))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.25/0.64 (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))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M4 tptp.nat)) (and (= M (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N) M4))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P N) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 0.25/0.64 (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))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P N) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P I3)))))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.25/0.64 (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))))))
% 0.25/0.64 (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))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.list_b Bool)) (Xs tptp.list_b)) (=> (forall ((Xs2 tptp.list_b)) (=> (forall ((Ys2 tptp.list_b)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_b Ys2)) (@ tptp.size_size_list_b Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 0.25/0.64 (assert (forall ((P (-> tptp.list_option_b Bool)) (Xs tptp.list_option_b)) (=> (forall ((Xs2 tptp.list_option_b)) (=> (forall ((Ys2 tptp.list_option_b)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1671393719tion_b Ys2)) (@ tptp.size_s1671393719tion_b Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 0.25/0.64 (assert (forall ((X tptp.option_b) (P (-> tptp.option_b tptp.option_option_b Bool)) (Y3 tptp.option_option_b)) (let ((_let_1 (@ (@ P X) Y3))) (=> (=> (= X tptp.none_b) _let_1) (=> (=> (= Y3 tptp.none_option_b) _let_1) (=> (forall ((A3 tptp.b) (B tptp.option_b)) (=> (= X (@ tptp.some_b A3)) (=> (= Y3 (@ tptp.some_option_b B)) (@ (@ P X) Y3)))) _let_1))))))
% 0.25/0.64 (assert (forall ((X tptp.option_option_b) (P (-> tptp.option_option_b tptp.option_b Bool)) (Y3 tptp.option_b)) (let ((_let_1 (@ (@ P X) Y3))) (=> (=> (= X tptp.none_option_b) _let_1) (=> (=> (= Y3 tptp.none_b) _let_1) (=> (forall ((A3 tptp.option_b) (B tptp.b)) (=> (= X (@ tptp.some_option_b A3)) (=> (= Y3 (@ tptp.some_b B)) (@ (@ P X) Y3)))) _let_1))))))
% 0.25/0.64 (assert (forall ((X tptp.option_option_b) (P (-> tptp.option_option_b tptp.option_option_b Bool)) (Y3 tptp.option_option_b)) (let ((_let_1 (@ (@ P X) Y3))) (=> (=> (= X tptp.none_option_b) _let_1) (=> (=> (= Y3 tptp.none_option_b) _let_1) (=> (forall ((A3 tptp.option_b) (B tptp.option_b)) (=> (= X (@ tptp.some_option_b A3)) (=> (= Y3 (@ tptp.some_option_b B)) (@ (@ P X) Y3)))) _let_1))))))
% 0.25/0.64 (assert (forall ((X tptp.option_b) (P (-> tptp.option_b tptp.option_b Bool)) (Y3 tptp.option_b)) (let ((_let_1 (@ (@ P X) Y3))) (=> (=> (= X tptp.none_b) _let_1) (=> (=> (= Y3 tptp.none_b) _let_1) (=> (forall ((A3 tptp.b) (B tptp.b)) (=> (= X (@ tptp.some_b A3)) (=> (= Y3 (@ tptp.some_b B)) (@ (@ P X) Y3)))) _let_1))))))
% 0.25/0.64 (assert (= (lambda ((P2 (-> tptp.option_option_b Bool))) (forall ((X5 tptp.option_option_b)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_option_b Bool))) (and (@ P3 tptp.none_option_b) (forall ((X4 tptp.option_b)) (@ P3 (@ tptp.some_option_b X4)))))))
% 0.25/0.64 (assert (= (lambda ((P2 (-> tptp.option_b Bool))) (forall ((X5 tptp.option_b)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_b Bool))) (and (@ P3 tptp.none_b) (forall ((X4 tptp.b)) (@ P3 (@ tptp.some_b X4)))))))
% 0.25/0.64 (assert (= (lambda ((P2 (-> tptp.option_option_b Bool))) (exists ((X5 tptp.option_option_b)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_option_b Bool))) (or (@ P3 tptp.none_option_b) (exists ((X4 tptp.option_b)) (@ P3 (@ tptp.some_option_b X4)))))))
% 0.25/0.64 (assert (= (lambda ((P2 (-> tptp.option_b Bool))) (exists ((X5 tptp.option_b)) (@ P2 X5))) (lambda ((P3 (-> tptp.option_b Bool))) (or (@ P3 tptp.none_b) (exists ((X4 tptp.b)) (@ P3 (@ tptp.some_b X4)))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.option_option_b Bool)) (Option tptp.option_option_b)) (=> (@ P tptp.none_option_b) (=> (forall ((X3 tptp.option_b)) (@ P (@ tptp.some_option_b X3))) (@ P Option)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.option_b Bool)) (Option tptp.option_b)) (=> (@ P tptp.none_b) (=> (forall ((X3 tptp.b)) (@ P (@ tptp.some_b X3))) (@ P Option)))))
% 0.25/0.64 (assert (forall ((Y3 tptp.option_option_b)) (=> (not (= Y3 tptp.none_option_b)) (not (forall ((X23 tptp.option_b)) (not (= Y3 (@ tptp.some_option_b X23))))))))
% 0.25/0.64 (assert (forall ((Y3 tptp.option_b)) (=> (not (= Y3 tptp.none_b)) (not (forall ((X23 tptp.b)) (not (= Y3 (@ tptp.some_b X23))))))))
% 0.25/0.64 (assert (forall ((Option tptp.option_option_b) (X2 tptp.option_b)) (=> (= Option (@ tptp.some_option_b X2)) (not (= Option tptp.none_option_b)))))
% 0.25/0.64 (assert (forall ((Option tptp.option_b) (X2 tptp.b)) (=> (= Option (@ tptp.some_b X2)) (not (= Option tptp.none_b)))))
% 0.25/0.64 (assert (forall ((X2 tptp.option_b)) (not (= tptp.none_option_b (@ tptp.some_option_b X2)))))
% 0.25/0.64 (assert (forall ((X2 tptp.b)) (not (= tptp.none_b (@ tptp.some_b X2)))))
% 0.25/0.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 0.25/0.64 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 0.25/0.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N3))))))
% 0.25/0.64 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N3 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N3) (@ (@ tptp.ord_less_int (@ F N)) (@ F N3))))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M5 tptp.nat)) (= N (@ tptp.suc M5))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N) (@ P (@ tptp.suc I3))))))))
% 0.25/0.64 (assert (forall ((Xs tptp.list_b) (N tptp.nat)) (= (= (@ tptp.size_size_list_b Xs) (@ tptp.suc N)) (exists ((Y tptp.b) (Ys3 tptp.list_b)) (and (= Xs (@ (@ tptp.cons_b Y) Ys3)) (= (@ tptp.size_size_list_b Ys3) N))))))
% 0.25/0.64 (assert (forall ((Xs tptp.list_option_b) (N tptp.nat)) (= (= (@ tptp.size_s1671393719tion_b Xs) (@ tptp.suc N)) (exists ((Y tptp.option_b) (Ys3 tptp.list_option_b)) (and (= Xs (@ (@ tptp.cons_option_b Y) Ys3)) (= (@ tptp.size_s1671393719tion_b Ys3) N))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (Xs tptp.list_b)) (= (= (@ tptp.suc N) (@ tptp.size_size_list_b Xs)) (exists ((Y tptp.b) (Ys3 tptp.list_b)) (and (= Xs (@ (@ tptp.cons_b Y) Ys3)) (= (@ tptp.size_size_list_b Ys3) N))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (Xs tptp.list_option_b)) (= (= (@ tptp.suc N) (@ tptp.size_s1671393719tion_b Xs)) (exists ((Y tptp.option_b) (Ys3 tptp.list_option_b)) (and (= Xs (@ (@ tptp.cons_option_b Y) Ys3)) (= (@ tptp.size_s1671393719tion_b Ys3) N))))))
% 0.25/0.64 (assert (= (lambda ((Y5 tptp.list_b) (Z tptp.list_b)) (= Y5 Z)) (lambda ((Xs3 tptp.list_b) (Ys3 tptp.list_b)) (and (= (@ tptp.size_size_list_b Xs3) (@ tptp.size_size_list_b Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_b Xs3)) (= (@ (@ tptp.nth_b Xs3) I3) (@ (@ tptp.nth_b Ys3) I3))))))))
% 0.25/0.64 (assert (= (lambda ((Y5 tptp.list_option_b) (Z tptp.list_option_b)) (= Y5 Z)) (lambda ((Xs3 tptp.list_option_b) (Ys3 tptp.list_option_b)) (and (= (@ tptp.size_s1671393719tion_b Xs3) (@ tptp.size_s1671393719tion_b Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1671393719tion_b Xs3)) (= (@ (@ tptp.nth_option_b Xs3) I3) (@ (@ tptp.nth_option_b Ys3) I3))))))))
% 0.25/0.64 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.b Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X5 tptp.b)) (@ (@ P I3) X5)))) (exists ((Xs3 tptp.list_b)) (and (= (@ tptp.size_size_list_b Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_b Xs3) I3)))))))))
% 0.25/0.64 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.option_b Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X5 tptp.option_b)) (@ (@ P I3) X5)))) (exists ((Xs3 tptp.list_option_b)) (and (= (@ tptp.size_s1671393719tion_b Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_option_b Xs3) I3)))))))))
% 0.25/0.64 (assert (forall ((Xs tptp.list_b) (Ys tptp.list_b)) (=> (= (@ tptp.size_size_list_b Xs) (@ tptp.size_size_list_b Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_b Xs)) (= (@ (@ tptp.nth_b Xs) I2) (@ (@ tptp.nth_b Ys) I2)))) (= Xs Ys)))))
% 0.25/0.64 (assert (forall ((Xs tptp.list_option_b) (Ys tptp.list_option_b)) (=> (= (@ tptp.size_s1671393719tion_b Xs) (@ tptp.size_s1671393719tion_b Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1671393719tion_b Xs)) (= (@ (@ tptp.nth_option_b Xs) I2) (@ (@ tptp.nth_option_b Ys) I2)))) (= Xs Ys)))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((B2 tptp.nat) (Phi tptp.formula_a) (N tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.fvi_a (@ tptp.suc B2)) Phi)) (@ (@ tptp.ord_less_nat X3) N))) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.fvi_a B2) Phi)) (@ (@ tptp.ord_less_nat X6) (@ tptp.suc N)))))))
% 0.25/0.64 (assert (forall ((X tptp.b) (Xs tptp.list_b)) (= (@ tptp.size_size_list_b (@ (@ tptp.cons_b X) Xs)) (@ tptp.suc (@ tptp.size_size_list_b Xs)))))
% 0.25/0.64 (assert (forall ((X tptp.option_b) (Xs tptp.list_option_b)) (= (@ tptp.size_s1671393719tion_b (@ (@ tptp.cons_option_b X) Xs)) (@ tptp.suc (@ tptp.size_s1671393719tion_b Xs)))))
% 0.25/0.64 (assert (forall ((X (-> tptp.b tptp.nat))) (= (@ (@ tptp.size_option_b X) tptp.none_b) (@ tptp.suc tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((X tptp.nat) (B2 tptp.nat) (Phi tptp.formula_a)) (= (@ (@ tptp.member_nat X) (@ (@ tptp.fvi_a (@ tptp.suc B2)) Phi)) (@ (@ tptp.member_nat (@ tptp.suc X)) (@ (@ tptp.fvi_a B2) Phi)))))
% 0.25/0.64 (assert (forall ((X2 tptp.option_b)) (= (@ tptp.size_s684879735tion_b (@ tptp.some_option_b X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((X2 tptp.b)) (= (@ tptp.size_size_option_b (@ tptp.some_b X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 0.25/0.64 (assert (= (@ tptp.size_size_option_b tptp.none_b) (@ tptp.suc tptp.zero_zero_nat)))
% 0.25/0.64 (assert (forall ((P (-> tptp.b Bool)) (Xs tptp.list_b) (X tptp.b)) (= (= (@ (@ tptp.find_b P) Xs) (@ tptp.some_b X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_b Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_b Xs)) (@ P _let_1) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I3) (not (@ P (@ (@ tptp.nth_b Xs) J3)))))))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.option_b Bool)) (Xs tptp.list_option_b) (X tptp.option_b)) (= (= (@ (@ tptp.find_option_b P) Xs) (@ tptp.some_option_b X)) (exists ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_option_b Xs) I3))) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1671393719tion_b Xs)) (@ P _let_1) (= X _let_1) (forall ((J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) I3) (not (@ P (@ (@ tptp.nth_option_b Xs) J3)))))))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (exists ((N2 tptp.nat)) (and (not (@ P N2)) (@ P (@ tptp.suc N2))))))))
% 0.25/0.64 (assert (forall ((X tptp.option_b)) (not (= (@ tptp.size_size_option_b X) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((P (-> tptp.option_b Bool)) (X tptp.option_b) (Xs tptp.list_option_b)) (let ((_let_1 (@ tptp.find_option_b P))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_option_b X) Xs)))) (let ((_let_3 (@ P X))) (and (=> _let_3 (= _let_2 (@ tptp.some_option_b X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.b Bool)) (X tptp.b) (Xs tptp.list_b)) (let ((_let_1 (@ tptp.find_b P))) (let ((_let_2 (@ _let_1 (@ (@ tptp.cons_b X) Xs)))) (let ((_let_3 (@ P X))) (and (=> _let_3 (= _let_2 (@ tptp.some_b X))) (=> (not _let_3) (= _let_2 (@ _let_1 Xs)))))))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N2 tptp.nat)) (not (= X (@ tptp.suc N2))))))))
% 0.25/0.64 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.25/0.64 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.25/0.64 (assert (= tptp.size_size_list_b (@ tptp.gen_length_b tptp.zero_zero_nat)))
% 0.25/0.64 (assert (= tptp.size_s1671393719tion_b (@ tptp.gen_length_option_b tptp.zero_zero_nat)))
% 0.25/0.64 (assert (forall ((N tptp.nat) (X tptp.b) (Xs tptp.list_b)) (= (@ (@ tptp.gen_length_b N) (@ (@ tptp.cons_b X) Xs)) (@ (@ tptp.gen_length_b (@ tptp.suc N)) Xs))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (X tptp.option_b) (Xs tptp.list_option_b)) (= (@ (@ tptp.gen_length_option_b N) (@ (@ tptp.cons_option_b X) Xs)) (@ (@ tptp.gen_length_option_b (@ tptp.suc N)) Xs))))
% 0.25/0.64 (assert (forall ((X (-> tptp.option_b tptp.nat)) (X2 tptp.option_b)) (= (@ (@ tptp.size_option_option_b X) (@ tptp.some_option_b X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((X (-> tptp.b tptp.nat)) (X2 tptp.b)) (= (@ (@ tptp.size_option_b X) (@ tptp.some_b X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (Xs tptp.list_b)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_b Xs)) (= (@ (@ tptp.cons_b (@ (@ tptp.nth_b Xs) I)) (@ (@ tptp.drop_b (@ tptp.suc I)) Xs)) (@ (@ tptp.drop_b I) Xs)))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (Xs tptp.list_option_b)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1671393719tion_b Xs)) (= (@ (@ tptp.cons_option_b (@ (@ tptp.nth_option_b Xs) I)) (@ (@ tptp.drop_option_b (@ tptp.suc I)) Xs)) (@ (@ tptp.drop_option_b I) Xs)))))
% 0.25/0.64 (assert (= tptp.list_ex_b (lambda ((P3 (-> tptp.b Bool)) (Xs3 tptp.list_b)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat N4) (@ tptp.size_size_list_b Xs3)) (@ P3 (@ (@ tptp.nth_b Xs3) N4)))))))
% 0.25/0.64 (assert (= tptp.list_ex_option_b (lambda ((P3 (-> tptp.option_b Bool)) (Xs3 tptp.list_option_b)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_nat N4) (@ tptp.size_s1671393719tion_b Xs3)) (@ P3 (@ (@ tptp.nth_option_b Xs3) N4)))))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1382578993at_nat N)) (@ _let_1 N)))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri2019852685at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 0.25/0.64 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A) (@ (@ tptp.plus_plus_nat C) A)) (= B2 C))))
% 0.25/0.64 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1382578993at_nat M) (@ tptp.semiri1382578993at_nat N)) (= M N))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri2019852685at_int M) (@ tptp.semiri2019852685at_int N)) (= M N))))
% 0.25/0.64 (assert (forall ((X tptp.nat) (Y3 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y3)) (and (= X tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((X tptp.nat) (Y3 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y3) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y3 tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B2)) (= B2 tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B2)) (= B2 tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B2) A)) (= B2 tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B2) A)) (= B2 tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B2) A) (= B2 tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B2) A) (= B2 tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B2) A) A) (= B2 tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) A) (= B2 tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 0.25/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 0.25/0.64 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A) B2))))
% 0.25/0.64 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A) B2))))
% 0.25/0.64 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A) B2)))))
% 0.25/0.64 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2)))))
% 0.25/0.64 (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)))))
% 0.25/0.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 0.25/0.64 (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))))))
% 0.25/0.64 (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)))))
% 0.25/0.64 (assert (= (@ tptp.drop_option_b tptp.zero_zero_nat) (lambda ((X4 tptp.list_option_b)) X4)))
% 0.25/0.64 (assert (forall ((N tptp.nat) (M tptp.nat) (Xs tptp.list_option_b)) (= (@ (@ tptp.drop_option_b N) (@ (@ tptp.drop_option_b M) Xs)) (@ (@ tptp.drop_option_b (@ (@ tptp.plus_plus_nat N) M)) Xs))))
% 0.25/0.64 (assert (forall ((P (-> tptp.b Bool)) (X tptp.b) (Xs tptp.list_b)) (let ((_let_1 (@ tptp.list_ex_b P))) (= (@ _let_1 (@ (@ tptp.cons_b X) Xs)) (or (@ P X) (@ _let_1 Xs))))))
% 0.25/0.64 (assert (forall ((P (-> tptp.option_b Bool)) (X tptp.option_b) (Xs tptp.list_option_b)) (let ((_let_1 (@ tptp.list_ex_option_b P))) (= (@ _let_1 (@ (@ tptp.cons_option_b X) Xs)) (or (@ P X) (@ _let_1 Xs))))))
% 0.25/0.64 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B2) A)) B2) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B2) A)) B2) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) B2) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) B2) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B2) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B2))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B2) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2))))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 0.25/0.64 (assert (= (@ tptp.semiri1382578993at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 0.25/0.64 (assert (= (@ tptp.semiri2019852685at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1382578993at_nat N)) (= tptp.zero_zero_nat N))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri2019852685at_int N)) (= tptp.zero_zero_nat N))))
% 0.25/0.64 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1382578993at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri2019852685at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1382578993at_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N)))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri2019852685at_int (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N)))))
% 0.25/0.64 (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))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (X tptp.b) (Xs tptp.list_b)) (= (@ (@ tptp.drop_b (@ tptp.suc N)) (@ (@ tptp.cons_b X) Xs)) (@ (@ tptp.drop_b N) Xs))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (X tptp.option_b) (Xs tptp.list_option_b)) (= (@ (@ tptp.drop_option_b (@ tptp.suc N)) (@ (@ tptp.cons_option_b X) Xs)) (@ (@ tptp.drop_option_b N) Xs))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 0.25/0.64 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N 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)))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.25/0.64 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) K) (@ (@ tptp.ord_less_nat I) K))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 0.25/0.64 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 0.25/0.64 (assert (forall ((Xs tptp.list_option_b)) (= (@ (@ tptp.drop_option_b tptp.zero_zero_nat) Xs) Xs)))
% 0.25/0.64 (assert (forall ((A tptp.nat) (C tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)) (@ (@ tptp.ord_less_nat A) B2))))
% 0.25/0.64 (assert (forall ((A tptp.int) (C tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)) (@ (@ tptp.ord_less_int A) B2))))
% 0.25/0.64 (assert (forall ((C tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_nat A) B2)))))
% 0.25/0.64 (assert (forall ((C tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2)) (@ (@ tptp.ord_less_int A) B2)))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) C)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) C)))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B2) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B2))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B2))))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B2) D))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B2) D))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.25/0.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.25/0.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.25/0.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 0.25/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 0.25/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 0.25/0.64 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L)))))
% 0.25/0.64 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 0.25/0.64 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 0.25/0.64 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B3 (@ _let_2 B2)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B2))))))))
% 0.25/0.64 (assert (forall ((B3 tptp.int) (K tptp.int) (B2 tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B3 (@ _let_2 B2)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B2))))))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B2) C))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B2)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B2) C))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 0.25/0.64 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 0.25/0.64 (assert (= tptp.plus_plus_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.plus_plus_nat B4) A4))))
% 0.25/0.64 (assert (= tptp.plus_plus_int (lambda ((A4 tptp.int) (B4 tptp.int)) (@ (@ tptp.plus_plus_int B4) A4))))
% 0.25/0.64 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B2))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.25/0.64 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B2))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B2) (@ _let_1 C)) (= B2 C)))))
% 0.25/0.64 (assert (forall ((B2 tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B2) A) (@ (@ tptp.plus_plus_nat C) A)) (= B2 C))))
% 0.25/0.64 (assert (forall ((B2 tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B2) A) (@ (@ tptp.plus_plus_int C) A)) (= B2 C))))
% 0.25/0.64 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1382578993at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri2019852685at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N)))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N)))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B2)) tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B2)) tptp.zero_zero_int)))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B2)))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B2) (@ _let_1 (@ (@ tptp.plus_plus_int A) B2)))))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B2) (not (forall ((C2 tptp.nat)) (=> (= B2 (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 0.25/0.64 (assert (forall ((A tptp.int) (B2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (Xs tptp.list_b) (Y3 tptp.b) (Ys tptp.list_b)) (=> (= (@ (@ tptp.drop_b N) Xs) (@ (@ tptp.cons_b Y3) Ys)) (= (@ (@ tptp.nth_b Xs) N) Y3))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (Xs tptp.list_option_b) (Y3 tptp.option_b) (Ys tptp.list_option_b)) (=> (= (@ (@ tptp.drop_option_b N) Xs) (@ (@ tptp.cons_option_b Y3) Ys)) (= (@ (@ tptp.nth_option_b Xs) N) Y3))))
% 0.25/0.64 (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)))))))
% 0.25/0.64 (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)))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I) K2) J))))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q2 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q2)))))))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 0.25/0.64 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 0.25/0.64 (assert (= tptp.ord_less_nat (lambda ((M5 tptp.nat) (N4 tptp.nat)) (exists ((K3 tptp.nat)) (= N4 (@ tptp.suc (@ (@ tptp.plus_plus_nat M5) K3)))))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K2 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 0.25/0.64 (assert (= tptp.gen_length_b (lambda ((N4 tptp.nat) (Xs3 tptp.list_b)) (@ (@ tptp.plus_plus_nat N4) (@ tptp.size_size_list_b Xs3)))))
% 0.25/0.64 (assert (= tptp.gen_length_option_b (lambda ((N4 tptp.nat) (Xs3 tptp.list_option_b)) (@ (@ tptp.plus_plus_nat N4) (@ tptp.size_s1671393719tion_b Xs3)))))
% 0.25/0.64 (assert (forall ((X21 tptp.b) (X22 tptp.list_b)) (= (@ tptp.size_size_list_b (@ (@ tptp.cons_b X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_list_b X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((X21 tptp.option_b) (X22 tptp.list_option_b)) (= (@ tptp.size_s1671393719tion_b (@ (@ tptp.cons_option_b X21) X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_s1671393719tion_b X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 0.25/0.64 (assert (forall ((X tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y3)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y3) tptp.zero_zero_int)))))
% 0.25/0.64 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B2 tptp.nat)) (=> (forall ((A3 tptp.nat) (B tptp.nat)) (= (@ (@ P A3) B) (@ (@ P B) A3))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) tptp.zero_zero_nat)) (=> (forall ((A3 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ P A3))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A3) B))))) (@ (@ P A) B2))))))
% 0.25/0.64 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N2 tptp.nat)) (=> (= K (@ tptp.semiri2019852685at_int N2)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))))
% 0.25/0.64 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= K (@ tptp.semiri2019852685at_int N2)))))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat) (Z2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri2019852685at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri2019852685at_int N)) Z2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri2019852685at_int (@ (@ tptp.plus_plus_nat M) N))) Z2))))
% 0.25/0.64 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri2019852685at_int M) (@ tptp.semiri2019852685at_int N)) (= M N))))
% 0.25/0.64 (assert (forall ((L tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L) L)))
% 0.25/0.64 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 0.25/0.64 (assert (= tptp.ord_less_int (lambda ((W tptp.int) (Z3 tptp.int)) (exists ((N4 tptp.nat)) (= Z3 (@ (@ tptp.plus_plus_int W) (@ tptp.semiri2019852685at_int (@ tptp.suc N4))))))))
% 0.25/0.64 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.25/0.64 (assert (forall ((X tptp.int) (Y3 tptp.int)) (=> (not (= X Y3)) (=> (not (@ (@ tptp.ord_less_int X) Y3)) (@ (@ tptp.ord_less_int Y3) X)))))
% 0.25/0.64 (assert (= tptp.ord_less_nat (lambda ((A4 tptp.nat) (B4 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int A4)) (@ tptp.semiri2019852685at_int B4)))))
% 0.25/0.64 (assert (= (@ tptp.semiri2019852685at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 0.25/0.64 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 0.25/0.64 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 0.25/0.64 (assert (= (lambda ((Y5 tptp.nat) (Z tptp.nat)) (= Y5 Z)) (lambda ((A4 tptp.nat) (B4 tptp.nat)) (= (@ tptp.semiri2019852685at_int A4) (@ tptp.semiri2019852685at_int B4)))))
% 0.25/0.64 (assert (forall ((P Bool) (A tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.semiri2019852685at_int (@ (@ (@ tptp.if_nat P) A) B2)))) (and (=> P (= _let_1 (@ tptp.semiri2019852685at_int A))) (=> (not P) (= _let_1 (@ tptp.semiri2019852685at_int B2)))))))
% 0.25/0.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 0.25/0.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 0.25/0.64 (assert (forall ((A tptp.nat) (B2 tptp.nat)) (= (@ tptp.semiri2019852685at_int (@ (@ tptp.plus_plus_nat A) B2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri2019852685at_int A)) (@ tptp.semiri2019852685at_int B2)))))
% 0.25/0.64 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri2019852685at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri2019852685at_int N)) (@ tptp.semiri2019852685at_int M)))))
% 0.25/0.64 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 0.25/0.64 (assert (forall ((B2 tptp.nat) (A tptp.nat)) (= (= B2 (@ (@ tptp.plus_plus_nat B2) A)) (= A tptp.zero_zero_nat))))
% 0.25/0.64 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (= B2 (@ (@ tptp.plus/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 13124 Alarm clock ( read result; case "$result" in
% 299.90/300.20 unsat)
% 299.90/300.20 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.90/300.20 ;;
% 299.90/300.20 sat)
% 299.90/300.20 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.90/300.20 ;;
% 299.90/300.20 esac; exit 1 )
% 299.90/300.21 Alarm clock
% 299.90/300.21 % cvc5---1.0.5 exiting
% 299.90/300.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------