%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP103^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 : Wed Feb 25 08:55:34 AM UTC 2026
% Result : Theorem 22.71s 4.55s
% Output : Refutation 22.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP103^2 : TPTP v9.2.1. Released v7.5.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:27:10 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.45 thf(spec,logic,$$dhol).
% 0.20/0.45 %------------------------------------------------------------------------------
% 0.20/0.45 % File : ITP103^2 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.45 % Domain : Interactive Theorem Proving
% 0.20/0.45 % Problem : Sledgehammer ListSlice problem prob_142__5617098_1
% 0.20/0.45 % Version : Especial.
% 0.20/0.45 % English :
% 0.20/0.45
% 0.20/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.45 % Source : [Des21]
% 0.20/0.45 % Names : ListSlice/prob_142__5617098_1 [Des21]
% 0.20/0.45
% 0.20/0.45 % Status : Theorem
% 0.20/0.45 % Rating : 0.00 v8.1.0, 0.25 v7.5.0
% 0.20/0.45 % Syntax : Number of formulae : 324 ( 93 unt; 43 typ; 0 def)
% 0.20/0.45 % Number of atoms : 882 ( 307 equ; 0 cnn)
% 0.20/0.45 % Maximal formula atoms : 6 ( 3 avg)
% 0.20/0.45 % Number of connectives : 3563 ( 105 ~; 33 |; 65 &;2956 @)
% 0.20/0.45 % ( 0 <=>; 404 =>; 0 <=; 0 <~>)
% 0.20/0.45 % Maximal formula depth : 16 ( 7 avg)
% 0.20/0.45 % Number of types : 3 ( 2 usr)
% 0.20/0.46 % Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 42 ( 41 usr; 3 con; 0-4 aty)
% 0.20/0.46 % Number of variables : 799 ( 10 ^; 730 !; 23 ?; 799 :)
% 0.20/0.46 % ( 36 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.46 % SPC : TH1_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:25.126
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (4)
% 0.20/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.20/0.46 product_prod: $tType > $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_List_Olist,type,
% 0.20/0.46 list: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Nat_Onat,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_tf_a,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 % Explicit typings (39)
% 0.20/0.46 thf(sy_cl_HOL_Otype,type,
% 0.20/0.46 type:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Nat_Osize,type,
% 0.20/0.46 size:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.20/0.46 zero:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Fields_Ofield,type,
% 0.20/0.46 field:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.20/0.46 order:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Omult__zero,type,
% 0.20/0.46 mult_zero:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.46 linorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Oordered__ring,type,
% 0.20/0.46 ordered_ring:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Owellorder,type,
% 0.20/0.46 wellorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Fields_Odivision__ring,type,
% 0.20/0.46 division_ring:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Parity_Osemiring__bits,type,
% 0.20/0.46 semiring_bits:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Osemidom__divide,type,
% 0.20/0.46 semidom_divide:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.20/0.46 semigroup_mult:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.20/0.46 linordered_idom:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Olinordered__ring,type,
% 0.20/0.46 linordered_ring:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Oordered__semiring,type,
% 0.20/0.46 ordered_semiring:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Fields_Olinordered__field,type,
% 0.30/0.46 linordered_field:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.30/0.46 ab_semigroup_mult:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Oordered__semiring__0,type,
% 0.30/0.46 ordered_semiring_0:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Oordered__comm__semiring,type,
% 0.30/0.46 ordere1490568538miring:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 0.30/0.46 linord581940658strict:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 0.30/0.46 semiri1193490041visors:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Olinordered__semiring__strict,type,
% 0.30/0.46 linord20386208strict:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.30/0.46 linord1659791738miring:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.30/0.46 canoni770627133id_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Olinordered__comm__semiring__strict,type,
% 0.30/0.46 linord893533164strict:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 0.30/0.46 semiri1923998003cancel:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Euclidean__Division_Oeuclidean__semiring__cancel,type,
% 0.30/0.46 euclid191655569cancel:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.30/0.46 times_times:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.30/0.46 zero_zero:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Oproduct,type,
% 0.30/0.46 product:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( list @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_OSuc,type,
% 0.30/0.46 suc: nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.30/0.46 size_size:
% 0.30/0.46 !>[A: $tType] : ( A > nat ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.30/0.46 ord_less:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Rings_Odivide__class_Odivide,type,
% 0.30/0.46 divide_divide:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_k,type,
% 0.30/0.46 k: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_n,type,
% 0.30/0.46 n: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_xs,type,
% 0.30/0.46 xs: list @ a ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (253)
% 0.30/0.46 thf(fact_0_div__mult__self__is__m,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 => ( ( divide_divide @ nat @ ( times_times @ nat @ M @ N ) @ N )
% 0.30/0.46 = M ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult_self_is_m
% 0.30/0.46 thf(fact_1_div__mult__self1__is__m,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 => ( ( divide_divide @ nat @ ( times_times @ nat @ N @ M ) @ N )
% 0.30/0.46 = M ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult_self1_is_m
% 0.30/0.46 thf(fact_2_nat__mult__div__cancel__disj,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ( K
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 => ( ( divide_divide @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( zero_zero @ nat ) ) )
% 0.30/0.46 & ( ( K
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ( ( divide_divide @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( divide_divide @ nat @ M @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_div_cancel_disj
% 0.30/0.46 thf(fact_3_div__less,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 => ( ( divide_divide @ nat @ M @ N )
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_less
% 0.30/0.46 thf(fact_4_div__by__Suc__0,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( divide_divide @ nat @ M @ ( suc @ ( zero_zero @ nat ) ) )
% 0.30/0.46 = M ) ).
% 0.30/0.46
% 0.30/0.46 % div_by_Suc_0
% 0.30/0.46 thf(fact_5_mult__less__cancel2,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 0.30/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 & ( ord_less @ nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel2
% 0.30/0.46 thf(fact_6_nat__0__less__mult__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ M @ N ) )
% 0.30/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.30/0.46 & ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_0_less_mult_iff
% 0.30/0.46 thf(fact_7_nat__mult__less__cancel__disj,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 & ( ord_less @ nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_less_cancel_disj
% 0.30/0.46 thf(fact_8_mult__eq__1__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times @ nat @ M @ N )
% 0.30/0.46 = ( suc @ ( zero_zero @ nat ) ) )
% 0.30/0.46 = ( ( M
% 0.30/0.46 = ( suc @ ( zero_zero @ nat ) ) )
% 0.30/0.46 & ( N
% 0.30/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_eq_1_iff
% 0.30/0.46 thf(fact_9_one__eq__mult__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ( suc @ ( zero_zero @ nat ) )
% 0.30/0.46 = ( times_times @ nat @ M @ N ) )
% 0.30/0.46 = ( ( M
% 0.30/0.46 = ( suc @ ( zero_zero @ nat ) ) )
% 0.30/0.46 & ( N
% 0.30/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % one_eq_mult_iff
% 0.30/0.46 thf(fact_10_less__Suc0,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) )
% 0.30/0.46 = ( N
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc0
% 0.30/0.46 thf(fact_11_zero__less__Suc,axiom,
% 0.30/0.46 ! [N: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_Suc
% 0.30/0.46 thf(fact_12_old_Onat_Oinject,axiom,
% 0.30/0.46 ! [Nat: nat,Nat2: nat] :
% 0.30/0.46 ( ( ( suc @ Nat )
% 0.30/0.46 = ( suc @ Nat2 ) )
% 0.30/0.46 = ( Nat = Nat2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.inject
% 0.30/0.46 thf(fact_13_nat_Oinject,axiom,
% 0.30/0.46 ! [X2: nat,Y2: nat] :
% 0.30/0.46 ( ( ( suc @ X2 )
% 0.30/0.46 = ( suc @ Y2 ) )
% 0.30/0.46 = ( X2 = Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.inject
% 0.30/0.46 thf(fact_14_bot__nat__0_Onot__eq__extremum,axiom,
% 0.30/0.46 ! [A2: nat] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.not_eq_extremum
% 0.30/0.46 thf(fact_15_less__nat__zero__code,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_nat_zero_code
% 0.30/0.46 thf(fact_16_neq0__conv,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( N
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq0_conv
% 0.30/0.46 thf(fact_17_Suc__less__eq,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/0.46 = ( ord_less @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_less_eq
% 0.30/0.46 thf(fact_18_Suc__mono,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_mono
% 0.30/0.46 thf(fact_19_lessI,axiom,
% 0.30/0.46 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % lessI
% 0.30/0.46 thf(fact_20_mult__cancel2,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times @ nat @ M @ K )
% 0.30/0.46 = ( times_times @ nat @ N @ K ) )
% 0.30/0.46 = ( ( M = N )
% 0.30/0.46 | ( K
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel2
% 0.30/0.46 thf(fact_21_mult__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times @ nat @ K @ M )
% 0.30/0.46 = ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( ( M = N )
% 0.30/0.46 | ( K
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel1
% 0.30/0.46 thf(fact_22_mult__0__right,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( times_times @ nat @ M @ ( zero_zero @ nat ) )
% 0.30/0.46 = ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_0_right
% 0.30/0.46 thf(fact_23_mult__is__0,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times @ nat @ M @ N )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 = ( ( M
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 | ( N
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_is_0
% 0.30/0.46 thf(fact_24_div__mult__mult1__if,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid191655569cancel @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ( C
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( zero_zero @ A ) ) )
% 0.30/0.46 & ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult_mult1_if
% 0.30/0.46 thf(fact_25_div__mult__mult2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid191655569cancel @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult_mult2
% 0.30/0.46 thf(fact_26_div__mult__mult1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( euclid191655569cancel @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult_mult1
% 0.30/0.46 thf(fact_27_measure__induct__rule,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( wellorder @ B )
% 0.30/0.46 => ! [F: A > B,P: A > $o,A2: A] :
% 0.30/0.46 ( ! [X: A] :
% 0.30/0.46 ( ! [Y: A] :
% 0.30/0.46 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X ) )
% 0.30/0.46 => ( P @ Y ) )
% 0.30/0.46 => ( P @ X ) )
% 0.30/0.46 => ( P @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % measure_induct_rule
% 0.30/0.46 thf(fact_28_measure__induct,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( wellorder @ B )
% 0.30/0.46 => ! [F: A > B,P: A > $o,A2: A] :
% 0.30/0.46 ( ! [X: A] :
% 0.30/0.46 ( ! [Y: A] :
% 0.30/0.46 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X ) )
% 0.30/0.46 => ( P @ Y ) )
% 0.30/0.46 => ( P @ X ) )
% 0.30/0.46 => ( P @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % measure_induct
% 0.30/0.46 thf(fact_29_n__not__Suc__n,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( N
% 0.30/0.46 != ( suc @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % n_not_Suc_n
% 0.30/0.46 thf(fact_30_Suc__inject,axiom,
% 0.30/0.46 ! [X3: nat,Y3: nat] :
% 0.30/0.46 ( ( ( suc @ X3 )
% 0.30/0.46 = ( suc @ Y3 ) )
% 0.30/0.46 => ( X3 = Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_inject
% 0.30/0.46 thf(fact_31_infinite__descent__measure,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,V: A > nat,X3: A] :
% 0.30/0.46 ( ! [X: A] :
% 0.30/0.46 ( ~ ( P @ X )
% 0.30/0.46 => ? [Y: A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( V @ Y ) @ ( V @ X ) )
% 0.30/0.46 & ~ ( P @ Y ) ) )
% 0.30/0.46 => ( P @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent_measure
% 0.30/0.46 thf(fact_32_linorder__neqE__nat,axiom,
% 0.30/0.46 ! [X3: nat,Y3: nat] :
% 0.30/0.46 ( ( X3 != Y3 )
% 0.30/0.46 => ( ~ ( ord_less @ nat @ X3 @ Y3 )
% 0.30/0.46 => ( ord_less @ nat @ Y3 @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_neqE_nat
% 0.30/0.46 thf(fact_33_infinite__descent,axiom,
% 0.30/0.46 ! [P: nat > $o,N: nat] :
% 0.30/0.46 ( ! [N2: nat] :
% 0.30/0.46 ( ~ ( P @ N2 )
% 0.30/0.46 => ? [M2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.30/0.46 & ~ ( P @ M2 ) ) )
% 0.30/0.46 => ( P @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent
% 0.30/0.46 thf(fact_34_nat__less__induct,axiom,
% 0.30/0.46 ! [P: nat > $o,N: nat] :
% 0.30/0.46 ( ! [N2: nat] :
% 0.30/0.46 ( ! [M2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.30/0.46 => ( P @ M2 ) )
% 0.30/0.46 => ( P @ N2 ) )
% 0.30/0.46 => ( P @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_less_induct
% 0.30/0.46 thf(fact_35_less__irrefl__nat,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N @ N ) ).
% 0.30/0.46
% 0.30/0.46 % less_irrefl_nat
% 0.30/0.46 thf(fact_36_less__not__refl3,axiom,
% 0.30/0.46 ! [S: nat,T: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ S @ T )
% 0.30/0.46 => ( S != T ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl3
% 0.30/0.46 thf(fact_37_less__not__refl2,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N @ M )
% 0.30/0.46 => ( M != N ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl2
% 0.30/0.46 thf(fact_38_less__not__refl,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N @ N ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl
% 0.30/0.46 thf(fact_39_nat__neq__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( M != N )
% 0.30/0.46 = ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_neq_iff
% 0.30/0.46 thf(fact_40_size__neq__size__imp__neq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( size @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ( size_size @ A @ X3 )
% 0.30/0.46 != ( size_size @ A @ Y3 ) )
% 0.30/0.46 => ( X3 != Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % size_neq_size_imp_neq
% 0.30/0.46 thf(fact_41_not0__implies__Suc,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( N
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ? [M3: nat] :
% 0.30/0.46 ( N
% 0.30/0.46 = ( suc @ M3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not0_implies_Suc
% 0.30/0.46 thf(fact_42_old_Onat_Oinducts,axiom,
% 0.30/0.46 ! [P: nat > $o,Nat: nat] :
% 0.30/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [Nat3: nat] :
% 0.30/0.46 ( ( P @ Nat3 )
% 0.30/0.46 => ( P @ ( suc @ Nat3 ) ) )
% 0.30/0.46 => ( P @ Nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.inducts
% 0.30/0.46 thf(fact_43_old_Onat_Oexhaust,axiom,
% 0.30/0.46 ! [Y3: nat] :
% 0.30/0.46 ( ( Y3
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ~ ! [Nat3: nat] :
% 0.30/0.46 ( Y3
% 0.30/0.46 != ( suc @ Nat3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.exhaust
% 0.30/0.46 thf(fact_44_Zero__not__Suc,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % Zero_not_Suc
% 0.30/0.46 thf(fact_45_Zero__neq__Suc,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % Zero_neq_Suc
% 0.30/0.46 thf(fact_46_Suc__neq__Zero,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( suc @ M )
% 0.30/0.46 != ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_neq_Zero
% 0.30/0.46 thf(fact_47_zero__induct,axiom,
% 0.30/0.46 ! [P: nat > $o,K: nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [N2: nat] :
% 0.30/0.46 ( ( P @ ( suc @ N2 ) )
% 0.30/0.46 => ( P @ N2 ) )
% 0.30/0.46 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_induct
% 0.30/0.46 thf(fact_48_diff__induct,axiom,
% 0.30/0.46 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.30/0.46 ( ! [X: nat] : ( P @ X @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [Y4: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y4 ) )
% 0.30/0.46 => ( ! [X: nat,Y4: nat] :
% 0.30/0.46 ( ( P @ X @ Y4 )
% 0.30/0.46 => ( P @ ( suc @ X ) @ ( suc @ Y4 ) ) )
% 0.30/0.46 => ( P @ M @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_induct
% 0.30/0.46 thf(fact_49_nat__induct,axiom,
% 0.30/0.46 ! [P: nat > $o,N: nat] :
% 0.30/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [N2: nat] :
% 0.30/0.46 ( ( P @ N2 )
% 0.30/0.46 => ( P @ ( suc @ N2 ) ) )
% 0.30/0.46 => ( P @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_induct
% 0.30/0.46 thf(fact_50_nat_OdiscI,axiom,
% 0.30/0.46 ! [Nat: nat,X2: nat] :
% 0.30/0.46 ( ( Nat
% 0.30/0.46 = ( suc @ X2 ) )
% 0.30/0.46 => ( Nat
% 0.30/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.discI
% 0.30/0.46 thf(fact_51_old_Onat_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [Nat2: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ Nat2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.distinct(1)
% 0.30/0.46 thf(fact_52_old_Onat_Odistinct_I2_J,axiom,
% 0.30/0.46 ! [Nat4: nat] :
% 0.30/0.46 ( ( suc @ Nat4 )
% 0.30/0.46 != ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.distinct(2)
% 0.30/0.46 thf(fact_53_nat_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X2: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.distinct(1)
% 0.30/0.46 thf(fact_54_infinite__descent0__measure,axiom,
% 0.30/0.46 ! [A: $tType,V: A > nat,P: A > $o,X3: A] :
% 0.30/0.46 ( ! [X: A] :
% 0.30/0.46 ( ( ( V @ X )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 => ( P @ X ) )
% 0.30/0.46 => ( ! [X: A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V @ X ) )
% 0.30/0.46 => ( ~ ( P @ X )
% 0.30/0.46 => ? [Y: A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( V @ Y ) @ ( V @ X ) )
% 0.30/0.46 & ~ ( P @ Y ) ) ) )
% 0.30/0.46 => ( P @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent0_measure
% 0.30/0.46 thf(fact_55_bot__nat__0_Oextremum__strict,axiom,
% 0.30/0.46 ! [A2: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum_strict
% 0.30/0.46 thf(fact_56_infinite__descent0,axiom,
% 0.30/0.46 ! [P: nat > $o,N: nat] :
% 0.30/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ( ~ ( P @ N2 )
% 0.30/0.46 => ? [M2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.30/0.46 & ~ ( P @ M2 ) ) ) )
% 0.30/0.46 => ( P @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent0
% 0.30/0.46 thf(fact_57_gr__implies__not0,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 => ( N
% 0.30/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr_implies_not0
% 0.30/0.46 thf(fact_58_less__zeroE,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_zeroE
% 0.30/0.46 thf(fact_59_not__less0,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less0
% 0.30/0.46 thf(fact_60_not__gr0,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 0.30/0.46 = ( N
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_gr0
% 0.30/0.46 thf(fact_61_gr0I,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( N
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr0I
% 0.30/0.46 thf(fact_62_not__less__less__Suc__eq,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ~ ( ord_less @ nat @ N @ M )
% 0.30/0.46 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.30/0.46 = ( N = M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_less_Suc_eq
% 0.30/0.46 thf(fact_63_strict__inc__induct,axiom,
% 0.30/0.46 ! [I: nat,J: nat,P: nat > $o] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ! [I2: nat] :
% 0.30/0.46 ( ( J
% 0.30/0.46 = ( suc @ I2 ) )
% 0.30/0.46 => ( P @ I2 ) )
% 0.30/0.46 => ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I2 @ J )
% 0.30/0.46 => ( ( P @ ( suc @ I2 ) )
% 0.30/0.46 => ( P @ I2 ) ) )
% 0.30/0.46 => ( P @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_inc_induct
% 0.30/0.46 thf(fact_64_less__Suc__induct,axiom,
% 0.30/0.46 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.30/0.46 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I2 @ J2 )
% 0.30/0.46 => ( ( ord_less @ nat @ J2 @ K2 )
% 0.30/0.46 => ( ( P @ I2 @ J2 )
% 0.30/0.46 => ( ( P @ J2 @ K2 )
% 0.30/0.46 => ( P @ I2 @ K2 ) ) ) ) )
% 0.30/0.46 => ( P @ I @ J ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc_induct
% 0.30/0.46 thf(fact_65_less__trans__Suc,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less @ nat @ J @ K )
% 0.30/0.46 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_trans_Suc
% 0.30/0.46 thf(fact_66_Suc__less__SucD,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.30/0.46 => ( ord_less @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_less_SucD
% 0.30/0.46 thf(fact_67_less__antisym,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ~ ( ord_less @ nat @ N @ M )
% 0.30/0.46 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.30/0.46 => ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_antisym
% 0.30/0.46 thf(fact_68_Suc__less__eq2,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 0.30/0.46 = ( ? [M4: nat] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( suc @ M4 ) )
% 0.30/0.46 & ( ord_less @ nat @ N @ M4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_less_eq2
% 0.30/0.46 thf(fact_69_All__less__Suc,axiom,
% 0.30/0.46 ! [N: nat,P: nat > $o] :
% 0.30/0.46 ( ( ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N ) )
% 0.30/0.46 => ( P @ I3 ) ) )
% 0.30/0.46 = ( ( P @ N )
% 0.30/0.46 & ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ N )
% 0.30/0.46 => ( P @ I3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % All_less_Suc
% 0.30/0.46 thf(fact_70_not__less__eq,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 0.30/0.46 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_eq
% 0.30/0.46 thf(fact_71_less__Suc__eq,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.30/0.46 = ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 | ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc_eq
% 0.30/0.46 thf(fact_72_Ex__less__Suc,axiom,
% 0.30/0.46 ! [N: nat,P: nat > $o] :
% 0.30/0.46 ( ( ? [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N ) )
% 0.30/0.46 & ( P @ I3 ) ) )
% 0.30/0.46 = ( ( P @ N )
% 0.30/0.46 | ? [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ N )
% 0.30/0.46 & ( P @ I3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Ex_less_Suc
% 0.30/0.46 thf(fact_73_less__SucI,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_SucI
% 0.30/0.46 thf(fact_74_less__SucE,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.30/0.46 => ( ~ ( ord_less @ nat @ M @ N )
% 0.30/0.46 => ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_SucE
% 0.30/0.46 thf(fact_75_Suc__lessI,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 => ( ( ( suc @ M )
% 0.30/0.46 != N )
% 0.30/0.46 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_lessI
% 0.30/0.46 thf(fact_76_Suc__lessE,axiom,
% 0.30/0.46 ! [I: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 0.30/0.46 => ~ ! [J2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J2 )
% 0.30/0.46 => ( K
% 0.30/0.46 != ( suc @ J2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_lessE
% 0.30/0.46 thf(fact_77_Suc__lessD,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 0.30/0.46 => ( ord_less @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_lessD
% 0.30/0.46 thf(fact_78_Nat_OlessE,axiom,
% 0.30/0.46 ! [I: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ K )
% 0.30/0.46 => ( ( K
% 0.30/0.46 != ( suc @ I ) )
% 0.30/0.46 => ~ ! [J2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J2 )
% 0.30/0.46 => ( K
% 0.30/0.46 != ( suc @ J2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nat.lessE
% 0.30/0.46 thf(fact_79_nat__mult__eq__cancel__disj,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times @ nat @ K @ M )
% 0.30/0.46 = ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( ( K
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 | ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_eq_cancel_disj
% 0.30/0.46 thf(fact_80_mult__0,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( times_times @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 = ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_0
% 0.30/0.46 thf(fact_81_Suc__mult__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ( times_times @ nat @ ( suc @ K ) @ M )
% 0.30/0.46 = ( times_times @ nat @ ( suc @ K ) @ N ) )
% 0.30/0.46 = ( M = N ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_mult_cancel1
% 0.30/0.46 thf(fact_82_div__mult2__eq,axiom,
% 0.30/0.46 ! [M: nat,N: nat,Q: nat] :
% 0.30/0.46 ( ( divide_divide @ nat @ M @ ( times_times @ nat @ N @ Q ) )
% 0.30/0.46 = ( divide_divide @ nat @ ( divide_divide @ nat @ M @ N ) @ Q ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_mult2_eq
% 0.30/0.46 thf(fact_83_lift__Suc__mono__less__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [F: nat > A,N: nat,M: nat] :
% 0.30/0.46 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 0.30/0.46 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lift_Suc_mono_less_iff
% 0.30/0.46 thf(fact_84_lift__Suc__mono__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [F: nat > A,N: nat,N3: nat] :
% 0.30/0.46 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.30/0.46 => ( ( ord_less @ nat @ N @ N3 )
% 0.30/0.46 => ( ord_less @ A @ ( F @ N ) @ ( F @ N3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lift_Suc_mono_less
% 0.30/0.46 thf(fact_85_less__Suc__eq__0__disj,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.30/0.46 = ( ( M
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 | ? [J3: nat] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( suc @ J3 ) )
% 0.30/0.46 & ( ord_less @ nat @ J3 @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc_eq_0_disj
% 0.30/0.46 thf(fact_86_gr0__implies__Suc,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 => ? [M3: nat] :
% 0.30/0.46 ( N
% 0.30/0.46 = ( suc @ M3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr0_implies_Suc
% 0.30/0.46 thf(fact_87_All__less__Suc2,axiom,
% 0.30/0.46 ! [N: nat,P: nat > $o] :
% 0.30/0.46 ( ( ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N ) )
% 0.30/0.46 => ( P @ I3 ) ) )
% 0.30/0.46 = ( ( P @ ( zero_zero @ nat ) )
% 0.30/0.46 & ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ N )
% 0.30/0.46 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % All_less_Suc2
% 0.30/0.46 thf(fact_88_gr0__conv__Suc,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 = ( ? [M5: nat] :
% 0.30/0.46 ( N
% 0.30/0.46 = ( suc @ M5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr0_conv_Suc
% 0.30/0.46 thf(fact_89_Ex__less__Suc2,axiom,
% 0.30/0.46 ! [N: nat,P: nat > $o] :
% 0.30/0.46 ( ( ? [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N ) )
% 0.30/0.46 & ( P @ I3 ) ) )
% 0.30/0.46 = ( ( P @ ( zero_zero @ nat ) )
% 0.30/0.46 | ? [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ N )
% 0.30/0.46 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Ex_less_Suc2
% 0.30/0.46 thf(fact_90_nat__mult__less__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 => ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( ord_less @ nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_less_cancel1
% 0.30/0.46 thf(fact_91_nat__mult__eq__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 => ( ( ( times_times @ nat @ K @ M )
% 0.30/0.46 = ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_eq_cancel1
% 0.30/0.46 thf(fact_92_mult__less__mono2,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 => ( ord_less @ nat @ ( times_times @ nat @ K @ I ) @ ( times_times @ nat @ K @ J ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_mono2
% 0.30/0.46 thf(fact_93_mult__less__mono1,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 => ( ord_less @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ K ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_mono1
% 0.30/0.46 thf(fact_94_Suc__mult__less__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( times_times @ nat @ ( suc @ K ) @ M ) @ ( times_times @ nat @ ( suc @ K ) @ N ) )
% 0.30/0.46 = ( ord_less @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_mult_less_cancel1
% 0.30/0.46 thf(fact_95_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ( divide_divide @ nat @ M @ N )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 = ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 | ( N
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Euclidean_Division.div_eq_0_iff
% 0.30/0.46 thf(fact_96_Euclidean__Division_Oless__mult__imp__div__less,axiom,
% 0.30/0.46 ! [M: nat,I: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ ( times_times @ nat @ I @ N ) )
% 0.30/0.46 => ( ord_less @ nat @ ( divide_divide @ nat @ M @ N ) @ I ) ) ).
% 0.30/0.46
% 0.30/0.46 % Euclidean_Division.less_mult_imp_div_less
% 0.30/0.46 thf(fact_97_n__less__n__mult__m,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 => ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ M )
% 0.30/0.46 => ( ord_less @ nat @ N @ ( times_times @ nat @ N @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % n_less_n_mult_m
% 0.30/0.46 thf(fact_98_n__less__m__mult__n,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 => ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ M )
% 0.30/0.46 => ( ord_less @ nat @ N @ ( times_times @ nat @ M @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % n_less_m_mult_n
% 0.30/0.46 thf(fact_99_one__less__mult,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ N )
% 0.30/0.46 => ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ M )
% 0.30/0.46 => ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( times_times @ nat @ M @ N ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % one_less_mult
% 0.30/0.46 thf(fact_100_nat__mult__div__cancel1,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 => ( ( divide_divide @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( divide_divide @ nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_div_cancel1
% 0.30/0.46 thf(fact_101_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_divide_mult_cancel_right2
% 0.30/0.46 thf(fact_102_nonzero__mult__div__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semidom_divide @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( B2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ B2 ) @ B2 )
% 0.30/0.46 = A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_div_cancel_right
% 0.30/0.46 thf(fact_103_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_divide_mult_cancel_right
% 0.30/0.46 thf(fact_104_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ B2 @ C ) )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_divide_mult_cancel_left2
% 0.30/0.46 thf(fact_105_nonzero__mult__div__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semidom_divide @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ B2 ) @ A2 )
% 0.30/0.46 = B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_div_cancel_left
% 0.30/0.46 thf(fact_106_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_mult_divide_mult_cancel_left
% 0.30/0.46 thf(fact_107_mult__divide__mult__cancel__left__if,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ( C
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( zero_zero @ A ) ) )
% 0.30/0.46 & ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_divide_mult_cancel_left_if
% 0.30/0.46 thf(fact_108_less__div__Suc__mult,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.30/0.46 => ( ord_less @ nat @ N @ ( times_times @ nat @ ( suc @ ( divide_divide @ nat @ N @ M ) ) @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_div_Suc_mult
% 0.30/0.46 thf(fact_109_times__divide__eq__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( times_times @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_divide_eq_right
% 0.30/0.46 thf(fact_110_divide__divide__eq__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( divide_divide @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_divide_eq_right
% 0.30/0.46 thf(fact_111_divide__divide__eq__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( divide_divide @ A @ A2 @ B2 ) @ C )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_divide_eq_left
% 0.30/0.46 thf(fact_112_mult__zero__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( mult_zero @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( times_times @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_zero_left
% 0.30/0.46 thf(fact_113_mult__zero__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( mult_zero @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_zero_right
% 0.30/0.46 thf(fact_114_mult__eq__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1193490041visors @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A2 @ B2 )
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 = ( ( A2
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( B2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_eq_0_iff
% 0.30/0.46 thf(fact_115_mult__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1923998003cancel @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ C @ A2 )
% 0.30/0.46 = ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( ( C
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel_left
% 0.30/0.46 thf(fact_116_mult__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1923998003cancel @ A )
% 0.30/0.46 => ! [A2: A,C: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A2 @ C )
% 0.30/0.46 = ( times_times @ A @ B2 @ C ) )
% 0.30/0.46 = ( ( C
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel_right
% 0.30/0.46 thf(fact_117_div__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semidom_divide @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_0
% 0.30/0.46 thf(fact_118_divide__eq__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( divide_divide @ A @ A2 @ B2 )
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 = ( ( A2
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( B2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_eq_0_iff
% 0.30/0.46 thf(fact_119_div__by__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semidom_divide @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_by_0
% 0.30/0.46 thf(fact_120_divide__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ( divide_divide @ A @ C @ A2 )
% 0.30/0.46 = ( divide_divide @ A @ C @ B2 ) )
% 0.30/0.46 = ( ( C
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_cancel_left
% 0.30/0.46 thf(fact_121_divide__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [A2: A,C: A,B2: A] :
% 0.30/0.46 ( ( ( divide_divide @ A @ A2 @ C )
% 0.30/0.46 = ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( ( C
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_cancel_right
% 0.30/0.46 thf(fact_122_division__ring__divide__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % division_ring_divide_zero
% 0.30/0.46 thf(fact_123_times__divide__eq__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [B2: A,C: A,A2: A] :
% 0.30/0.46 ( ( times_times @ A @ ( divide_divide @ A @ B2 @ C ) @ A2 )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ B2 @ A2 ) @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_divide_eq_left
% 0.30/0.46 thf(fact_124_linordered__field__no__lb,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ? [Y4: A] : ( ord_less @ A @ Y4 @ X4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_field_no_lb
% 0.30/0.46 thf(fact_125_linordered__field__no__ub,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X4: A] :
% 0.30/0.46 ? [X_1: A] : ( ord_less @ A @ X4 @ X_1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_field_no_ub
% 0.30/0.46 thf(fact_126_linorder__neqE__linordered__idom,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_idom @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( X3 != Y3 )
% 0.30/0.46 => ( ~ ( ord_less @ A @ X3 @ Y3 )
% 0.30/0.46 => ( ord_less @ A @ Y3 @ X3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_neqE_linordered_idom
% 0.30/0.46 thf(fact_127_mult__not__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( mult_zero @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A2 @ B2 )
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( A2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 & ( B2
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_not_zero
% 0.30/0.46 thf(fact_128_divisors__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1193490041visors @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( times_times @ A @ A2 @ B2 )
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( ( A2
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 | ( B2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divisors_zero
% 0.30/0.46 thf(fact_129_no__zero__divisors,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1193490041visors @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( B2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( times_times @ A @ A2 @ B2 )
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % no_zero_divisors
% 0.30/0.46 thf(fact_130_mult__left__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1923998003cancel @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( times_times @ A @ C @ A2 )
% 0.30/0.46 = ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_left_cancel
% 0.30/0.46 thf(fact_131_mult__right__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiri1923998003cancel @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( times_times @ A @ A2 @ C )
% 0.30/0.46 = ( times_times @ A @ B2 @ C ) )
% 0.30/0.46 = ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_right_cancel
% 0.30/0.46 thf(fact_132_times__divide__times__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z: A,W: A] :
% 0.30/0.46 ( ( times_times @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( divide_divide @ A @ Z @ W ) )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ X3 @ Z ) @ ( times_times @ A @ Y3 @ W ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % times_divide_times_eq
% 0.30/0.46 thf(fact_133_divide__divide__times__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A,Z: A,W: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( divide_divide @ A @ Z @ W ) )
% 0.30/0.46 = ( divide_divide @ A @ ( times_times @ A @ X3 @ W ) @ ( times_times @ A @ Y3 @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_divide_times_eq
% 0.30/0.46 thf(fact_134_divide__divide__eq__left_H,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( divide_divide @ A @ A2 @ B2 ) @ C )
% 0.30/0.46 = ( divide_divide @ A @ A2 @ ( times_times @ A @ C @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_divide_eq_left'
% 0.30/0.46 thf(fact_135_mult__neg__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_neg_neg
% 0.30/0.46 thf(fact_136_not__square__less__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_ring @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ~ ( ord_less @ A @ ( times_times @ A @ A2 @ A2 ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_square_less_zero
% 0.30/0.46 thf(fact_137_mult__less__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.30/0.46 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_0_iff
% 0.30/0.46 thf(fact_138_mult__neg__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_neg_pos
% 0.30/0.46 thf(fact_139_mult__pos__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg
% 0.30/0.46 thf(fact_140_mult__pos__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_pos
% 0.30/0.46 thf(fact_141_mult__pos__neg2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ B2 @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_pos_neg2
% 0.30/0.46 thf(fact_142_zero__less__mult__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_iff
% 0.30/0.46 thf(fact_143_zero__less__mult__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos
% 0.30/0.46 thf(fact_144_zero__less__mult__pos2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B2 @ A2 ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_mult_pos2
% 0.30/0.46 thf(fact_145_mult__less__cancel__left__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( ord_less @ A @ B2 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_neg
% 0.30/0.46 thf(fact_146_mult__less__cancel__left__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_pos
% 0.30/0.46 thf(fact_147_mult__strict__left__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono_neg
% 0.30/0.46 thf(fact_148_mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_left_mono
% 0.30/0.46 thf(fact_149_mult__less__cancel__left__disj,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 & ( ord_less @ A @ A2 @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ B2 @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_left_disj
% 0.30/0.46 thf(fact_150_mult__strict__right__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono_neg
% 0.30/0.46 thf(fact_151_mult__strict__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord20386208strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_strict_right_mono
% 0.30/0.46 thf(fact_152_mult__less__cancel__right__disj,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A2: A,C: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 & ( ord_less @ A @ A2 @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ B2 @ A2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_cancel_right_disj
% 0.30/0.46 thf(fact_153_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord893533164strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.46 thf(fact_154_divide__neg__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ Y3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_neg_neg
% 0.30/0.46 thf(fact_155_divide__neg__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ Y3 )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_neg_pos
% 0.30/0.46 thf(fact_156_divide__pos__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ X3 )
% 0.30/0.46 => ( ( ord_less @ A @ Y3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_pos_neg
% 0.30/0.46 thf(fact_157_divide__pos__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ X3 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ Y3 )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_pos_pos
% 0.30/0.46 thf(fact_158_divide__less__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( divide_divide @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.30/0.46 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_less_0_iff
% 0.30/0.46 thf(fact_159_divide__less__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,C: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( divide_divide @ A @ A2 @ C ) @ ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less @ A @ A2 @ B2 ) )
% 0.30/0.46 & ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ B2 @ A2 ) )
% 0.30/0.46 & ( C
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_less_cancel
% 0.30/0.46 thf(fact_160_zero__less__divide__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_divide_iff
% 0.30/0.46 thf(fact_161_divide__strict__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ A2 @ C ) @ ( divide_divide @ A @ B2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_strict_right_mono
% 0.30/0.46 thf(fact_162_divide__strict__right__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ A2 @ C ) @ ( divide_divide @ A @ B2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_strict_right_mono_neg
% 0.30/0.46 thf(fact_163_frac__eq__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( field @ A )
% 0.30/0.46 => ! [Y3: A,Z: A,X3: A,W: A] :
% 0.30/0.46 ( ( Y3
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( Z
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( divide_divide @ A @ X3 @ Y3 )
% 0.30/0.46 = ( divide_divide @ A @ W @ Z ) )
% 0.30/0.46 = ( ( times_times @ A @ X3 @ Z )
% 0.30/0.46 = ( times_times @ A @ W @ Y3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % frac_eq_eq
% 0.30/0.46 thf(fact_164_divide__eq__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [B2: A,C: A,A2: A] :
% 0.30/0.46 ( ( ( divide_divide @ A @ B2 @ C )
% 0.30/0.46 = A2 )
% 0.30/0.46 = ( ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( B2
% 0.30/0.46 = ( times_times @ A @ A2 @ C ) ) )
% 0.30/0.46 & ( ( C
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_eq_eq
% 0.30/0.46 thf(fact_165_eq__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( times_times @ A @ A2 @ C )
% 0.30/0.46 = B2 ) )
% 0.30/0.46 & ( ( C
% 0.30/0.46 = ( zero_zero @ A ) )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_divide_eq
% 0.30/0.46 thf(fact_166_divide__eq__imp,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [C: A,B2: A,A2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( B2
% 0.30/0.46 = ( times_times @ A @ A2 @ C ) )
% 0.30/0.46 => ( ( divide_divide @ A @ B2 @ C )
% 0.30/0.46 = A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_eq_imp
% 0.30/0.46 thf(fact_167_eq__divide__imp,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( times_times @ A @ A2 @ C )
% 0.30/0.46 = B2 )
% 0.30/0.46 => ( A2
% 0.30/0.46 = ( divide_divide @ A @ B2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_divide_imp
% 0.30/0.46 thf(fact_168_nonzero__divide__eq__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [C: A,B2: A,A2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ( divide_divide @ A @ B2 @ C )
% 0.30/0.46 = A2 )
% 0.30/0.46 = ( B2
% 0.30/0.46 = ( times_times @ A @ A2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_divide_eq_eq
% 0.30/0.46 thf(fact_169_nonzero__eq__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( division_ring @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( C
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ( A2
% 0.30/0.46 = ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( ( times_times @ A @ A2 @ C )
% 0.30/0.46 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nonzero_eq_divide_eq
% 0.30/0.46 thf(fact_170_div__eq__0__conv,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ( divide_divide @ nat @ N @ M )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 = ( ( M
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_eq_0_conv
% 0.30/0.46 thf(fact_171_div__eq__0__conv_H,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.30/0.46 => ( ( ( divide_divide @ nat @ N @ M )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 = ( ord_less @ nat @ N @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_eq_0_conv'
% 0.30/0.46 thf(fact_172_Util__Div_Oless__mult__imp__div__less,axiom,
% 0.30/0.46 ! [N: nat,K: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N @ ( times_times @ nat @ K @ M ) )
% 0.30/0.46 => ( ord_less @ nat @ ( divide_divide @ nat @ N @ M ) @ K ) ) ).
% 0.30/0.46
% 0.30/0.46 % Util_Div.less_mult_imp_div_less
% 0.30/0.46 thf(fact_173_divide__less__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [B2: A,C: A,A2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C ) @ A2 )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less @ A @ B2 @ ( times_times @ A @ A2 @ C ) ) )
% 0.30/0.46 & ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) )
% 0.30/0.46 & ( ~ ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_less_eq
% 0.30/0.46 thf(fact_174_less__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) )
% 0.30/0.46 & ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ B2 @ ( times_times @ A @ A2 @ C ) ) )
% 0.30/0.46 & ( ~ ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_divide_eq
% 0.30/0.46 thf(fact_175_neg__divide__less__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [C: A,B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C ) @ A2 )
% 0.30/0.46 = ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neg_divide_less_eq
% 0.30/0.46 thf(fact_176_neg__less__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( ord_less @ A @ B2 @ ( times_times @ A @ A2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neg_less_divide_eq
% 0.30/0.46 thf(fact_177_pos__divide__less__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [C: A,B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C ) @ A2 )
% 0.30/0.46 = ( ord_less @ A @ B2 @ ( times_times @ A @ A2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pos_divide_less_eq
% 0.30/0.46 thf(fact_178_pos__less__divide__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [C: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ( ord_less @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 0.30/0.46 = ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pos_less_divide_eq
% 0.30/0.46 thf(fact_179_mult__imp__div__pos__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [Y3: A,X3: A,Z: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ Y3 )
% 0.30/0.46 => ( ( ord_less @ A @ X3 @ ( times_times @ A @ Z @ Y3 ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ Z ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_imp_div_pos_less
% 0.30/0.46 thf(fact_180_mult__imp__less__div__pos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [Y3: A,Z: A,X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ Y3 )
% 0.30/0.46 => ( ( ord_less @ A @ ( times_times @ A @ Z @ Y3 ) @ X3 )
% 0.30/0.46 => ( ord_less @ A @ Z @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_imp_less_div_pos
% 0.30/0.46 thf(fact_181_divide__strict__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ C @ A2 ) @ ( divide_divide @ A @ C @ B2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_strict_left_mono
% 0.30/0.46 thf(fact_182_divide__strict__left__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 0.30/0.46 => ( ord_less @ A @ ( divide_divide @ A @ C @ A2 ) @ ( divide_divide @ A @ C @ B2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_strict_left_mono_neg
% 0.30/0.46 thf(fact_183_div__less__conv,axiom,
% 0.30/0.46 ! [M: nat,N: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.30/0.46 => ( ( ord_less @ nat @ ( divide_divide @ nat @ N @ M ) @ K )
% 0.30/0.46 = ( ord_less @ nat @ N @ ( times_times @ nat @ K @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_less_conv
% 0.30/0.46 thf(fact_184_div__less__imp__less__mult,axiom,
% 0.30/0.46 ! [M: nat,N: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.30/0.46 => ( ( ord_less @ nat @ ( divide_divide @ nat @ N @ M ) @ K )
% 0.30/0.46 => ( ord_less @ nat @ N @ ( times_times @ nat @ K @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % div_less_imp_less_mult
% 0.30/0.46 thf(fact_185_bits__div__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiring_bits @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bits_div_0
% 0.30/0.46 thf(fact_186_bits__div__by__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semiring_bits @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bits_div_by_0
% 0.30/0.46 thf(fact_187_not__gr__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N: A] :
% 0.30/0.46 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.30/0.46 = ( N
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_gr_zero
% 0.30/0.46 thf(fact_188_mult__cancel2__gr0,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 => ( ( ( times_times @ nat @ M @ K )
% 0.30/0.46 = ( times_times @ nat @ N @ K ) )
% 0.30/0.46 = ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_cancel2_gr0
% 0.30/0.46 thf(fact_189_zero__reorient,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( zero @ A )
% 0.30/0.46 => ! [X3: A] :
% 0.30/0.46 ( ( ( zero_zero @ A )
% 0.30/0.46 = X3 )
% 0.30/0.46 = ( X3
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_reorient
% 0.30/0.46 thf(fact_190_mult_Oleft__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_mult @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C: A] :
% 0.30/0.46 ( ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ C ) )
% 0.30/0.46 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult.left_commute
% 0.30/0.46 thf(fact_191_mult_Ocommute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_mult @ A )
% 0.30/0.46 => ( ( times_times @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] : ( times_times @ A @ B3 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult.commute
% 0.30/0.46 thf(fact_192_mult_Oassoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semigroup_mult @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 0.30/0.46 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult.assoc
% 0.30/0.46 thf(fact_193_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_mult @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 0.30/0.46 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ab_semigroup_mult_class.mult_ac(1)
% 0.30/0.46 thf(fact_194_zero__less__iff__neq__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.30/0.46 = ( N
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_iff_neq_zero
% 0.30/0.46 thf(fact_195_gr__implies__not__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [M: A,N: A] :
% 0.30/0.46 ( ( ord_less @ A @ M @ N )
% 0.30/0.46 => ( N
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr_implies_not_zero
% 0.30/0.46 thf(fact_196_not__less__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N: A] :
% 0.30/0.46 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_zero
% 0.30/0.46 thf(fact_197_gr__zeroI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N: A] :
% 0.30/0.46 ( ( N
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr_zeroI
% 0.30/0.46 thf(fact_198_gr__implies__gr0,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr_implies_gr0
% 0.30/0.46 thf(fact_199_nat__lessSucSuc0__conv,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N @ ( suc @ ( suc @ ( zero_zero @ nat ) ) ) )
% 0.30/0.46 = ( ( N
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 | ( N
% 0.30/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_lessSucSuc0_conv
% 0.30/0.46 thf(fact_200_nat__grSuc0__conv,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ N )
% 0.30/0.46 = ( ( N
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 & ( N
% 0.30/0.46 != ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_grSuc0_conv
% 0.30/0.46 thf(fact_201_mult__less__iff1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_idom @ A )
% 0.30/0.46 => ! [Z: A,X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ Z )
% 0.30/0.46 => ( ( ord_less @ A @ ( times_times @ A @ X3 @ Z ) @ ( times_times @ A @ Y3 @ Z ) )
% 0.30/0.46 = ( ord_less @ A @ X3 @ Y3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_less_iff1
% 0.30/0.46 thf(fact_202_length__induct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.30/0.46 ( ! [Xs2: list @ A] :
% 0.30/0.46 ( ! [Ys: list @ A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.30/0.46 => ( P @ Ys ) )
% 0.30/0.46 => ( P @ Xs2 ) )
% 0.30/0.46 => ( P @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % length_induct
% 0.30/0.46 thf(fact_203_Ex__list__of__length,axiom,
% 0.30/0.46 ! [A: $tType,N: nat] :
% 0.30/0.46 ? [Xs2: list @ A] :
% 0.30/0.46 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.30/0.46 = N ) ).
% 0.30/0.46
% 0.30/0.46 % Ex_list_of_length
% 0.30/0.46 thf(fact_204_neq__if__length__neq,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.30/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.30/0.46 != ( size_size @ ( list @ A ) @ Ys2 ) )
% 0.30/0.46 => ( Xs != Ys2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_if_length_neq
% 0.30/0.46 thf(fact_205_list__decode_Ocases,axiom,
% 0.30/0.46 ! [X3: nat] :
% 0.30/0.46 ( ( X3
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ~ ! [N2: nat] :
% 0.30/0.46 ( X3
% 0.30/0.46 != ( suc @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_decode.cases
% 0.30/0.46 thf(fact_206_dependent__nat__choice,axiom,
% 0.30/0.46 ! [A: $tType,P: nat > A > $o,Q2: nat > A > A > $o] :
% 0.30/0.46 ( ? [X_12: A] : ( P @ ( zero_zero @ nat ) @ X_12 )
% 0.30/0.46 => ( ! [X: A,N2: nat] :
% 0.30/0.46 ( ( P @ N2 @ X )
% 0.30/0.46 => ? [Y: A] :
% 0.30/0.46 ( ( P @ ( suc @ N2 ) @ Y )
% 0.30/0.46 & ( Q2 @ N2 @ X @ Y ) ) )
% 0.30/0.46 => ? [F2: nat > A] :
% 0.30/0.46 ! [N4: nat] :
% 0.30/0.46 ( ( P @ N4 @ ( F2 @ N4 ) )
% 0.30/0.46 & ( Q2 @ N4 @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dependent_nat_choice
% 0.30/0.46 thf(fact_207_exists__least__lemma,axiom,
% 0.30/0.46 ! [P: nat > $o] :
% 0.30/0.46 ( ~ ( P @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ? [X_12: nat] : ( P @ X_12 )
% 0.30/0.46 => ? [N2: nat] :
% 0.30/0.46 ( ~ ( P @ N2 )
% 0.30/0.46 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exists_least_lemma
% 0.30/0.46 thf(fact_208_field__lbound__gt__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [D1: A,D2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ D1 )
% 0.30/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ D2 )
% 0.30/0.46 => ? [E: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ E )
% 0.30/0.46 & ( ord_less @ A @ E @ D1 )
% 0.30/0.46 & ( ord_less @ A @ E @ D2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % field_lbound_gt_zero
% 0.30/0.46 thf(fact_209_less__numeral__extra_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_numeral_extra(3)
% 0.30/0.46 thf(fact_210_length__product,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Xs: list @ A,Ys2: list @ B] :
% 0.30/0.46 ( ( size_size @ ( list @ ( product_prod @ A @ B ) ) @ ( product @ A @ B @ Xs @ Ys2 ) )
% 0.30/0.46 = ( times_times @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ B ) @ Ys2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % length_product
% 0.30/0.46 thf(fact_211_split__div_H,axiom,
% 0.30/0.46 ! [P: nat > $o,M: nat,N: nat] :
% 0.30/0.46 ( ( P @ ( divide_divide @ nat @ M @ N ) )
% 0.30/0.46 = ( ( ( N
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 & ( P @ ( zero_zero @ nat ) ) )
% 0.30/0.46 | ? [Q3: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( times_times @ nat @ N @ Q3 ) @ M )
% 0.30/0.46 & ( ord_less @ nat @ M @ ( times_times @ nat @ N @ ( suc @ Q3 ) ) )
% 0.30/0.46 & ( P @ Q3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_div'
% 0.30/0.46 thf(fact_212_le__less__div__conv,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.30/0.46 => ( ( ( ord_less_eq @ nat @ ( times_times @ nat @ K @ M ) @ N )
% 0.30/0.46 & ( ord_less @ nat @ N @ ( times_times @ nat @ ( suc @ K ) @ M ) ) )
% 0.30/0.46 = ( ( divide_divide @ nat @ N @ M )
% 0.30/0.46 = K ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_less_div_conv
% 0.30/0.46 thf(fact_213_le__zero__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.30/0.46 = ( N
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_zero_eq
% 0.30/0.46 thf(fact_214_bot__nat__0_Oextremum,axiom,
% 0.30/0.46 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum
% 0.30/0.46 thf(fact_215_le0,axiom,
% 0.30/0.46 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.30/0.46
% 0.30/0.46 % le0
% 0.30/0.46 thf(fact_216_Suc__le__mono,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.30/0.46 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_le_mono
% 0.30/0.46 thf(fact_217_one__le__mult__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( times_times @ nat @ M @ N ) )
% 0.30/0.46 = ( ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ M )
% 0.30/0.46 & ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % one_le_mult_iff
% 0.30/0.46 thf(fact_218_mult__le__cancel2,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 0.30/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_le_cancel2
% 0.30/0.46 thf(fact_219_nat__mult__le__cancel__disj,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.30/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_mult_le_cancel_disj
% 0.30/0.46 thf(fact_220_le__numeral__extra_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_numeral_extra(3)
% 0.30/0.46 thf(fact_221_zero__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [X3: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_le
% 0.30/0.46 thf(fact_222_ge__less__neq__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A3: A,N5: A] :
% 0.30/0.46 ! [X5: A] :
% 0.30/0.46 ( ( ord_less @ A @ X5 @ A3 )
% 0.30/0.46 => ( N5 != X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ge_less_neq_conv
% 0.30/0.46 thf(fact_223_less__ge__neq__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ( ord_less @ A )
% 0.30/0.46 = ( ^ [N5: A,A3: A] :
% 0.30/0.46 ! [X5: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ X5 )
% 0.30/0.46 => ( N5 != X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_ge_neq_conv
% 0.30/0.46 thf(fact_224_greater__le__neq__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ( ord_less @ A )
% 0.30/0.46 = ( ^ [A3: A,N5: A] :
% 0.30/0.46 ! [X5: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X5 @ A3 )
% 0.30/0.46 => ( N5 != X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % greater_le_neq_conv
% 0.30/0.46 thf(fact_225_le__greater__neq__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [N5: A,A3: A] :
% 0.30/0.46 ! [X5: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ X5 )
% 0.30/0.46 => ( N5 != X5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_greater_neq_conv
% 0.30/0.46 thf(fact_226_nat__geSucSuc0__conv,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ ( suc @ ( zero_zero @ nat ) ) ) @ N )
% 0.30/0.46 = ( ( N
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 & ( N
% 0.30/0.46 != ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_geSucSuc0_conv
% 0.30/0.46 thf(fact_227_nat__leSuc0__conv,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) )
% 0.30/0.46 = ( ( N
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 | ( N
% 0.30/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_leSuc0_conv
% 0.30/0.46 thf(fact_228_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere1490568538miring @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.46 thf(fact_229_zero__le__mult__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_le_mult_iff
% 0.30/0.46 thf(fact_230_mult__nonneg__nonpos2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring_0 @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ B2 @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_nonneg_nonpos2
% 0.30/0.46 thf(fact_231_mult__nonpos__nonneg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring_0 @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_nonpos_nonneg
% 0.30/0.46 thf(fact_232_mult__nonneg__nonpos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring_0 @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_nonneg_nonpos
% 0.30/0.46 thf(fact_233_mult__nonneg__nonneg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring_0 @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_nonneg_nonneg
% 0.30/0.46 thf(fact_234_split__mult__neg__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring_0 @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.30/0.46 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_mult_neg_le
% 0.30/0.46 thf(fact_235_mult__le__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord581940658strict @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 0.30/0.46 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.30/0.46 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_le_0_iff
% 0.30/0.46 thf(fact_236_mult__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_right_mono
% 0.30/0.46 thf(fact_237_mult__right__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ring @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_right_mono_neg
% 0.30/0.46 thf(fact_238_mult__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_left_mono
% 0.30/0.46 thf(fact_239_mult__nonpos__nonpos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ring @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_nonpos_nonpos
% 0.30/0.46 thf(fact_240_mult__left__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ring @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_left_mono_neg
% 0.30/0.46 thf(fact_241_split__mult__pos__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ring @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_mult_pos_le
% 0.30/0.46 thf(fact_242_zero__le__square,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_ring @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_le_square
% 0.30/0.46 thf(fact_243_mult__mono_H,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A,D: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C @ D )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_mono'
% 0.30/0.46 thf(fact_244_mult__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_semiring @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A,D: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C @ D )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mult_mono
% 0.30/0.46 thf(fact_245_divide__right__mono__neg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( divide_divide @ A @ B2 @ C ) @ ( divide_divide @ A @ A2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_right_mono_neg
% 0.30/0.46 thf(fact_246_divide__nonpos__nonpos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_nonpos_nonpos
% 0.30/0.46 thf(fact_247_divide__nonpos__nonneg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_nonpos_nonneg
% 0.30/0.46 thf(fact_248_divide__nonneg__nonpos,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y3 @ ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_nonneg_nonpos
% 0.30/0.46 thf(fact_249_divide__nonneg__nonneg,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [X3: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_nonneg_nonneg
% 0.30/0.46 thf(fact_250_zero__le__divide__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ A2 @ B2 ) )
% 0.30/0.46 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.30/0.46 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_le_divide_iff
% 0.30/0.46 thf(fact_251_divide__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ ( divide_divide @ A @ A2 @ C ) @ ( divide_divide @ A @ B2 @ C ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_right_mono
% 0.30/0.46 thf(fact_252_divide__le__0__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linordered_field @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( divide_divide @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 0.30/0.46 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.30/0.46 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.30/0.46 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.30/0.46 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % divide_le_0_iff
% 0.30/0.46
% 0.30/0.46 % Type constructors (25)
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A4: $tType,A5: $tType] :
% 0.30/0.46 ( ( order @ A5 )
% 0.30/0.46 => ( order @ ( A4 > A5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Euclidean__Division_Oeuclidean__semiring__cancel,axiom,
% 0.30/0.46 euclid191655569cancel @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 0.30/0.46 semiri1923998003cancel @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict,axiom,
% 0.30/0.46 linord893533164strict @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.30/0.46 canoni770627133id_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.30/0.46 linord1659791738miring @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__semiring__strict,axiom,
% 0.30/0.46 linord20386208strict @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors,axiom,
% 0.30/0.46 semiri1193490041visors @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
% 0.30/0.46 ordere1490568538miring @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0,axiom,
% 0.30/0.46 ordered_semiring_0 @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.30/0.46 ab_semigroup_mult @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Oordered__semiring,axiom,
% 0.30/0.46 ordered_semiring @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.30/0.46 semigroup_mult @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Osemidom__divide,axiom,
% 0.30/0.46 semidom_divide @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Parity_Osemiring__bits,axiom,
% 0.30/0.46 semiring_bits @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.30/0.46 wellorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.30/0.46 linorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Omult__zero,axiom,
% 0.30/0.46 mult_zero @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 0.30/0.46 order @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.30/0.46 zero @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.30/0.46 size @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_2,axiom,
% 0.30/0.46 linorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 0.30/0.46 order @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_List_Olist___Nat_Osize_4,axiom,
% 0.30/0.46 ! [A4: $tType] : ( size @ ( list @ A4 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Nat_Osize_5,axiom,
% 0.30/0.46 ! [A4: $tType,A5: $tType] : ( size @ ( product_prod @ A4 @ A5 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (3)
% 0.30/0.46 thf(conj_0,hypothesis,
% 0.30/0.46 ( ( divide_divide @ nat @ ( size_size @ ( list @ a ) @ xs ) @ k )
% 0.30/0.46 = ( suc @ n ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(conj_1,hypothesis,
% 0.30/0.46 ( k
% 0.30/0.46 != ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(conj_2,conjecture,
% 0.30/0.46 ord_less @ nat @ ( times_times @ nat @ n @ k ) @ ( size_size @ ( list @ a ) @ xs ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.46/1.46 ---- Embedded in THF ---
% 2.46/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.46/1.46 %%% Generated on Tue Feb 24 08:27:11 EST 2026
% 2.46/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.46/1.46 %%% Logic specification used:
% 2.46/1.46 %%% thf(spec, logic, $$dhol).
% 2.46/1.46
% 2.46/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2DTF32501.p
% 2.46/1.46 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.46/1.46 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.46/1.46 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.46/1.46 thf(ty_tf_a, type, a: $tType).
% 2.46/1.46 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Fields_Ofield, type, field: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Omult__zero, type, mult_zero: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Oordered__ring, type, ordered_ring: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Fields_Odivision__ring, type, division_ring: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Parity_Osemiring__bits, type, semiring_bits: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Osemidom__divide, type, semidom_divide: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Groups_Osemigroup__mult, type, semigroup_mult: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Olinordered__ring, type, linordered_ring: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Oordered__semiring, type, ordered_semiring: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Groups_Oab__semigroup__mult, type, ab_semigroup_mult: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Oordered__semiring__0, type, ordered_semiring_0: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Oordered__comm__semiring, type, ordere1490568538miring: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Olinordered__ring__strict, type, linord581940658strict: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Osemiring__no__zero__divisors, type, semiri1193490041visors: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Olinordered__semiring__strict, type, linord20386208strict: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Olinordered__comm__semiring__strict, type, linord893533164strict: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel, type, semiri1923998003cancel: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_cl_Euclidean__Division_Oeuclidean__semiring__cancel, type, euclid191655569cancel: (!> [A:$tType]: ($o))).
% 2.46/1.46 thf(sy_c_Groups_Otimes__class_Otimes, type, times_times: (!> [A:$tType]: ((A > (A > A))))).
% 2.46/1.46 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.46/1.46 thf(sy_c_List_Oproduct, type, product: (!> [A:$tType,B:$tType]: (((list @ A) > ((list @ B) > (list @ ((product_prod @ A) @ B))))))).
% 2.46/1.46 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.46/1.46 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.46/1.46 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.46/1.46 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.46/1.46 thf(sy_c_Rings_Odivide__class_Odivide, type, divide_divide: (!> [A:$tType]: ((A > (A > A))))).
% 2.46/1.46 thf(sy_v_k, type, k: nat).
% 2.46/1.46 thf(sy_v_n, type, n: nat).
% 2.46/1.46 thf(sy_v_xs, type, xs: (list @ a)).
% 2.46/1.46 thf(fact_0_div__mult__self__is__m, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((((divide_divide @ nat) @ (((times_times @ nat) @ M) @ N)) @ N) = M))))).
% 2.46/1.46 thf(fact_1_div__mult__self1__is__m, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((((divide_divide @ nat) @ (((times_times @ nat) @ N) @ M)) @ N) = M))))).
% 2.46/1.46 thf(fact_2_nat__mult__div__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: ((((K = (zero_zero @ nat)) => ((((divide_divide @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = (zero_zero @ nat))) & ((K != (zero_zero @ nat)) => ((((divide_divide @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = (((divide_divide @ nat) @ M) @ N))))))).
% 2.46/1.46 thf(fact_3_div__less, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => ((((divide_divide @ nat) @ M) @ N) = (zero_zero @ nat)))))).
% 2.46/1.46 thf(fact_4_div__by__Suc__0, axiom, (! [M:nat]: (((((divide_divide @ nat) @ M) @ (suc @ (zero_zero @ nat))) = M)))).
% 2.46/1.46 thf(fact_5_mult__less__cancel2, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less @ nat) @ (((times_times @ nat) @ M) @ K)) @ (((times_times @ nat) @ N) @ K)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) & (((ord_less @ nat) @ M) @ N)))))).
% 2.46/1.46 thf(fact_6_nat__0__less__mult__iff, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (((times_times @ nat) @ M) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ M) & (((ord_less @ nat) @ (zero_zero @ nat)) @ N)))))).
% 2.46/1.46 thf(fact_7_nat__mult__less__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) & (((ord_less @ nat) @ M) @ N)))))).
% 2.46/1.46 thf(fact_8_mult__eq__1__iff, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (suc @ (zero_zero @ nat))) = ((M = (suc @ (zero_zero @ nat))) & (N = (suc @ (zero_zero @ nat)))))))).
% 2.46/1.46 thf(fact_9_one__eq__mult__iff, axiom, (! [M:nat,N:nat]: ((((suc @ (zero_zero @ nat)) = (((times_times @ nat) @ M) @ N)) = ((M = (suc @ (zero_zero @ nat))) & (N = (suc @ (zero_zero @ nat)))))))).
% 2.46/1.46 thf(fact_10_less__Suc0, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (suc @ (zero_zero @ nat))) = (N = (zero_zero @ nat)))))).
% 2.46/1.46 thf(fact_11_zero__less__Suc, axiom, (! [N:nat]: ((((ord_less @ nat) @ (zero_zero @ nat)) @ (suc @ N))))).
% 2.46/1.46 thf(fact_12_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.46/1.46 thf(fact_13_nat_Oinject, axiom, (! [X2:nat,Y2:nat]: ((((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))).
% 2.46/1.46 thf(fact_14_bot__nat__0_Onot__eq__extremum, axiom, (! [A2:nat]: (((A2 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A2))))).
% 2.46/1.46 thf(fact_15_less__nat__zero__code, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_16_neq0__conv, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.46/1.46 thf(fact_17_Suc__less__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.46/1.46 thf(fact_18_Suc__mono, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ (suc @ M)) @ (suc @ N)))))).
% 2.46/1.46 thf(fact_19_lessI, axiom, (! [N:nat]: ((((ord_less @ nat) @ N) @ (suc @ N))))).
% 2.46/1.46 thf(fact_20_mult__cancel2, axiom, (! [M:nat,K:nat,N:nat]: ((((((times_times @ nat) @ M) @ K) = (((times_times @ nat) @ N) @ K)) = ((M = N) | (K = (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_21_mult__cancel1, axiom, (! [K:nat,M:nat,N:nat]: ((((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = ((M = N) | (K = (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_22_mult__0__right, axiom, (! [M:nat]: (((((times_times @ nat) @ M) @ (zero_zero @ nat)) = (zero_zero @ nat))))).
% 2.46/1.46 thf(fact_23_mult__is__0, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) | (N = (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_24_div__mult__mult1__if, axiom, (! [A:$tType]: (((euclid191655569cancel @ A) => (! [C:A,A2:A,B2:A]: ((((C = (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (zero_zero @ A))) & ((C != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (((divide_divide @ A) @ A2) @ B2)))))))))).
% 2.46/1.46 thf(fact_25_div__mult__mult2, axiom, (! [A:$tType]: (((euclid191655569cancel @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)) = (((divide_divide @ A) @ A2) @ B2))))))))).
% 2.46/1.46 thf(fact_26_div__mult__mult1, axiom, (! [A:$tType]: (((euclid191655569cancel @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (((divide_divide @ A) @ A2) @ B2))))))))).
% 2.46/1.46 thf(fact_27_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P:(A > $o),A2:A]: (((! [X:A]: (((! [Y:A]: (((((ord_less @ B) @ (F @ Y)) @ (F @ X)) => (P @ Y)))) => (P @ X)))) => (P @ A2)))))))).
% 2.46/1.46 thf(fact_28_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P:(A > $o),A2:A]: (((! [X:A]: (((! [Y:A]: (((((ord_less @ B) @ (F @ Y)) @ (F @ X)) => (P @ Y)))) => (P @ X)))) => (P @ A2)))))))).
% 2.46/1.46 thf(fact_29_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 2.46/1.46 thf(fact_30_Suc__inject, axiom, (! [X3:nat,Y3:nat]: ((((suc @ X3) = (suc @ Y3)) => (X3 = Y3))))).
% 2.46/1.46 thf(fact_31_infinite__descent__measure, axiom, (! [A:$tType,P:(A > $o),V:(A > nat),X3:A]: (((! [X:A]: (((~ ((P @ X))) => (? [Y:A]: (((((ord_less @ nat) @ (V @ Y)) @ (V @ X)) & (~ ((P @ Y))))))))) => (P @ X3))))).
% 2.46/1.46 thf(fact_32_linorder__neqE__nat, axiom, (! [X3:nat,Y3:nat]: (((X3 != Y3) => ((~ ((((ord_less @ nat) @ X3) @ Y3))) => (((ord_less @ nat) @ Y3) @ X3)))))).
% 2.46/1.46 thf(fact_33_infinite__descent, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2))))))))) => (P @ N))))).
% 2.46/1.46 thf(fact_34_nat__less__induct, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 2.46/1.46 thf(fact_35_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.46/1.46 thf(fact_36_less__not__refl3, axiom, (! [S:nat,T:nat]: (((((ord_less @ nat) @ S) @ T) => (S != T))))).
% 2.46/1.46 thf(fact_37_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.46/1.46 thf(fact_38_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.46/1.46 thf(fact_39_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.46/1.46 thf(fact_40_size__neq__size__imp__neq, axiom, (! [A:$tType]: (((size @ A) => (! [X3:A,Y3:A]: (((((size_size @ A) @ X3) != ((size_size @ A) @ Y3)) => (X3 != Y3)))))))).
% 2.46/1.46 thf(fact_41_not0__implies__Suc, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (? [M3:nat]: ((N = (suc @ M3)))))))).
% 2.46/1.46 thf(fact_42_old_Onat_Oinducts, axiom, (! [P:(nat > $o),Nat:nat]: (((P @ (zero_zero @ nat)) => ((! [Nat3:nat]: (((P @ Nat3) => (P @ (suc @ Nat3))))) => (P @ Nat)))))).
% 2.46/1.46 thf(fact_43_old_Onat_Oexhaust, axiom, (! [Y3:nat]: (((Y3 != (zero_zero @ nat)) => (~ ((! [Nat3:nat]: ((Y3 != (suc @ Nat3)))))))))).
% 2.46/1.46 thf(fact_44_Zero__not__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.46/1.46 thf(fact_45_Zero__neq__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.46/1.46 thf(fact_46_Suc__neq__Zero, axiom, (! [M:nat]: (((suc @ M) != (zero_zero @ nat))))).
% 2.46/1.46 thf(fact_47_zero__induct, axiom, (! [P:(nat > $o),K:nat]: (((P @ K) => ((! [N2:nat]: (((P @ (suc @ N2)) => (P @ N2)))) => (P @ (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_48_diff__induct, axiom, (! [P:(nat > (nat > $o)),M:nat,N:nat]: (((! [X:nat]: (((P @ X) @ (zero_zero @ nat)))) => ((! [Y4:nat]: (((P @ (zero_zero @ nat)) @ (suc @ Y4)))) => ((! [X:nat,Y4:nat]: ((((P @ X) @ Y4) => ((P @ (suc @ X)) @ (suc @ Y4))))) => ((P @ M) @ N))))))).
% 2.46/1.46 thf(fact_49_nat__induct, axiom, (! [P:(nat > $o),N:nat]: (((P @ (zero_zero @ nat)) => ((! [N2:nat]: (((P @ N2) => (P @ (suc @ N2))))) => (P @ N)))))).
% 2.46/1.46 thf(fact_50_nat_OdiscI, axiom, (! [Nat:nat,X2:nat]: (((Nat = (suc @ X2)) => (Nat != (zero_zero @ nat)))))).
% 2.46/1.46 thf(fact_51_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 2.46/1.46 thf(fact_52_old_Onat_Odistinct_I2_J, axiom, (! [Nat4:nat]: (((suc @ Nat4) != (zero_zero @ nat))))).
% 2.46/1.46 thf(fact_53_nat_Odistinct_I1_J, axiom, (! [X2:nat]: (((zero_zero @ nat) != (suc @ X2))))).
% 2.46/1.46 thf(fact_54_infinite__descent0__measure, axiom, (! [A:$tType,V:(A > nat),P:(A > $o),X3:A]: (((! [X:A]: ((((V @ X) = (zero_zero @ nat)) => (P @ X)))) => ((! [X:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V @ X)) => ((~ ((P @ X))) => (? [Y:A]: (((((ord_less @ nat) @ (V @ Y)) @ (V @ X)) & (~ ((P @ Y)))))))))) => (P @ X3)))))).
% 2.46/1.46 thf(fact_55_bot__nat__0_Oextremum__strict, axiom, (! [A2:nat]: ((~ ((((ord_less @ nat) @ A2) @ (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_56_infinite__descent0, axiom, (! [P:(nat > $o),N:nat]: (((P @ (zero_zero @ nat)) => ((! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2)))))))))) => (P @ N)))))).
% 2.46/1.46 thf(fact_57_gr__implies__not0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (N != (zero_zero @ nat)))))).
% 2.46/1.46 thf(fact_58_less__zeroE, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_59_not__less0, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_60_not__gr0, axiom, (! [N:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N))) = (N = (zero_zero @ nat)))))).
% 2.46/1.46 thf(fact_61_gr0I, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.46/1.46 thf(fact_62_not__less__less__Suc__eq, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) = (N = M)))))).
% 2.46/1.46 thf(fact_63_strict__inc__induct, axiom, (! [I:nat,J:nat,P:(nat > $o)]: (((((ord_less @ nat) @ I) @ J) => ((! [I2:nat]: (((J = (suc @ I2)) => (P @ I2)))) => ((! [I2:nat]: (((((ord_less @ nat) @ I2) @ J) => ((P @ (suc @ I2)) => (P @ I2))))) => (P @ I))))))).
% 2.46/1.46 thf(fact_64_less__Suc__induct, axiom, (! [I:nat,J:nat,P:(nat > (nat > $o))]: (((((ord_less @ nat) @ I) @ J) => ((! [I2:nat]: (((P @ I2) @ (suc @ I2)))) => ((! [I2:nat,J2:nat,K2:nat]: (((((ord_less @ nat) @ I2) @ J2) => ((((ord_less @ nat) @ J2) @ K2) => (((P @ I2) @ J2) => (((P @ J2) @ K2) => ((P @ I2) @ K2))))))) => ((P @ I) @ J))))))).
% 2.46/1.46 thf(fact_65_less__trans__Suc, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (suc @ I)) @ K)))))).
% 2.46/1.46 thf(fact_66_Suc__less__SucD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) => (((ord_less @ nat) @ M) @ N))))).
% 2.46/1.46 thf(fact_67_less__antisym, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) => (M = N)))))).
% 2.46/1.46 thf(fact_68_Suc__less__eq2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (suc @ N)) @ M) = (? [M4:nat]: (((M = (suc @ M4)) & (((ord_less @ nat) @ N) @ M4)))))))).
% 2.46/1.46 thf(fact_69_All__less__Suc, axiom, (! [N:nat,P:(nat > $o)]: (((! [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N)) => (P @ I3)))) = ((P @ N) & (! [I3:nat]: (((((ord_less @ nat) @ I3) @ N) => (P @ I3))))))))).
% 2.46/1.46 thf(fact_70_not__less__eq, axiom, (! [M:nat,N:nat]: (((~ ((((ord_less @ nat) @ M) @ N))) = (((ord_less @ nat) @ N) @ (suc @ M)))))).
% 2.46/1.46 thf(fact_71_less__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = ((((ord_less @ nat) @ M) @ N) | (M = N)))))).
% 2.46/1.46 thf(fact_72_Ex__less__Suc, axiom, (! [N:nat,P:(nat > $o)]: (((? [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N)) & (P @ I3)))) = ((P @ N) | (? [I3:nat]: (((((ord_less @ nat) @ I3) @ N) & (P @ I3))))))))).
% 2.46/1.46 thf(fact_73_less__SucI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ M) @ (suc @ N)))))).
% 2.46/1.46 thf(fact_74_less__SucE, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) => ((~ ((((ord_less @ nat) @ M) @ N))) => (M = N)))))).
% 2.46/1.46 thf(fact_75_Suc__lessI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((suc @ M) != N) => (((ord_less @ nat) @ (suc @ M)) @ N)))))).
% 2.46/1.46 thf(fact_76_Suc__lessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ (suc @ I)) @ K) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2))))))))))).
% 2.46/1.46 thf(fact_77_Suc__lessD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ N) => (((ord_less @ nat) @ M) @ N))))).
% 2.46/1.46 thf(fact_78_Nat_OlessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ I) @ K) => ((K != (suc @ I)) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2)))))))))))).
% 2.46/1.46 thf(fact_79_nat__mult__eq__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: ((((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = ((K = (zero_zero @ nat)) | (M = N)))))).
% 2.46/1.46 thf(fact_80_mult__0, axiom, (! [N:nat]: (((((times_times @ nat) @ (zero_zero @ nat)) @ N) = (zero_zero @ nat))))).
% 2.46/1.46 thf(fact_81_Suc__mult__cancel1, axiom, (! [K:nat,M:nat,N:nat]: ((((((times_times @ nat) @ (suc @ K)) @ M) = (((times_times @ nat) @ (suc @ K)) @ N)) = (M = N))))).
% 2.46/1.46 thf(fact_82_div__mult2__eq, axiom, (! [M:nat,N:nat,Q:nat]: (((((divide_divide @ nat) @ M) @ (((times_times @ nat) @ N) @ Q)) = (((divide_divide @ nat) @ (((divide_divide @ nat) @ M) @ N)) @ Q))))).
% 2.46/1.46 thf(fact_83_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,M:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ A) @ (F @ N)) @ (F @ M)) = (((ord_less @ nat) @ N) @ M))))))))).
% 2.46/1.46 thf(fact_84_lift__Suc__mono__less, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N3:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ nat) @ N) @ N3) => (((ord_less @ A) @ (F @ N)) @ (F @ N3)))))))))).
% 2.46/1.46 thf(fact_85_less__Suc__eq__0__disj, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = ((M = (zero_zero @ nat)) | (? [J3:nat]: (((M = (suc @ J3)) & (((ord_less @ nat) @ J3) @ N))))))))).
% 2.46/1.46 thf(fact_86_gr0__implies__Suc, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (? [M3:nat]: ((N = (suc @ M3)))))))).
% 2.46/1.46 thf(fact_87_All__less__Suc2, axiom, (! [N:nat,P:(nat > $o)]: (((! [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N)) => (P @ I3)))) = ((P @ (zero_zero @ nat)) & (! [I3:nat]: (((((ord_less @ nat) @ I3) @ N) => (P @ (suc @ I3)))))))))).
% 2.46/1.46 thf(fact_88_gr0__conv__Suc, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) = (? [M5:nat]: ((N = (suc @ M5)))))))).
% 2.46/1.46 thf(fact_89_Ex__less__Suc2, axiom, (! [N:nat,P:(nat > $o)]: (((? [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N)) & (P @ I3)))) = ((P @ (zero_zero @ nat)) | (? [I3:nat]: (((((ord_less @ nat) @ I3) @ N) & (P @ (suc @ I3)))))))))).
% 2.46/1.46 thf(fact_90_nat__mult__less__cancel1, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => ((((ord_less @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = (((ord_less @ nat) @ M) @ N)))))).
% 2.46/1.46 thf(fact_91_nat__mult__eq__cancel1, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = (M = N)))))).
% 2.46/1.46 thf(fact_92_mult__less__mono2, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((ord_less @ nat) @ (((times_times @ nat) @ K) @ I)) @ (((times_times @ nat) @ K) @ J))))))).
% 2.46/1.46 thf(fact_93_mult__less__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((ord_less @ nat) @ (((times_times @ nat) @ I) @ K)) @ (((times_times @ nat) @ J) @ K))))))).
% 2.46/1.46 thf(fact_94_Suc__mult__less__cancel1, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((times_times @ nat) @ (suc @ K)) @ M)) @ (((times_times @ nat) @ (suc @ K)) @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.46/1.46 thf(fact_95_Euclidean__Division_Odiv__eq__0__iff, axiom, (! [M:nat,N:nat]: ((((((divide_divide @ nat) @ M) @ N) = (zero_zero @ nat)) = ((((ord_less @ nat) @ M) @ N) | (N = (zero_zero @ nat))))))).
% 2.46/1.46 thf(fact_96_Euclidean__Division_Oless__mult__imp__div__less, axiom, (! [M:nat,I:nat,N:nat]: (((((ord_less @ nat) @ M) @ (((times_times @ nat) @ I) @ N)) => (((ord_less @ nat) @ (((divide_divide @ nat) @ M) @ N)) @ I))))).
% 2.46/1.46 thf(fact_97_n__less__n__mult__m, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((((ord_less @ nat) @ (suc @ (zero_zero @ nat))) @ M) => (((ord_less @ nat) @ N) @ (((times_times @ nat) @ N) @ M))))))).
% 2.46/1.46 thf(fact_98_n__less__m__mult__n, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((((ord_less @ nat) @ (suc @ (zero_zero @ nat))) @ M) => (((ord_less @ nat) @ N) @ (((times_times @ nat) @ M) @ N))))))).
% 2.46/1.46 thf(fact_99_one__less__mult, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (suc @ (zero_zero @ nat))) @ N) => ((((ord_less @ nat) @ (suc @ (zero_zero @ nat))) @ M) => (((ord_less @ nat) @ (suc @ (zero_zero @ nat))) @ (((times_times @ nat) @ M) @ N))))))).
% 2.46/1.46 thf(fact_100_nat__mult__div__cancel1, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => ((((divide_divide @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = (((divide_divide @ nat) @ M) @ N)))))).
% 2.46/1.46 thf(fact_101_nonzero__mult__divide__mult__cancel__right2, axiom, (! [A:$tType]: (((field @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ C) @ B2)) = (((divide_divide @ A) @ A2) @ B2))))))))).
% 2.46/1.46 thf(fact_102_nonzero__mult__div__cancel__right, axiom, (! [A:$tType]: (((semidom_divide @ A) => (! [B2:A,A2:A]: (((B2 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A2) @ B2)) @ B2) = A2)))))))).
% 2.46/1.46 thf(fact_103_nonzero__mult__divide__mult__cancel__right, axiom, (! [A:$tType]: (((field @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)) = (((divide_divide @ A) @ A2) @ B2))))))))).
% 2.46/1.46 thf(fact_104_nonzero__mult__divide__mult__cancel__left2, axiom, (! [A:$tType]: (((field @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ B2) @ C)) = (((divide_divide @ A) @ A2) @ B2))))))))).
% 2.46/1.46 thf(fact_105_nonzero__mult__div__cancel__left, axiom, (! [A:$tType]: (((semidom_divide @ A) => (! [A2:A,B2:A]: (((A2 != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ A2) @ B2)) @ A2) = B2)))))))).
% 2.46/1.46 thf(fact_106_nonzero__mult__divide__mult__cancel__left, axiom, (! [A:$tType]: (((field @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (((divide_divide @ A) @ A2) @ B2))))))))).
% 2.46/1.46 thf(fact_107_mult__divide__mult__cancel__left__if, axiom, (! [A:$tType]: (((field @ A) => (! [C:A,A2:A,B2:A]: ((((C = (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (zero_zero @ A))) & ((C != (zero_zero @ A)) => ((((divide_divide @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (((divide_divide @ A) @ A2) @ B2)))))))))).
% 2.46/1.46 thf(fact_108_less__div__Suc__mult, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ M) => (((ord_less @ nat) @ N) @ (((times_times @ nat) @ (suc @ (((divide_divide @ nat) @ N) @ M))) @ M)))))).
% 2.46/1.46 thf(fact_109_times__divide__eq__right, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A2:A,B2:A,C:A]: (((((times_times @ A) @ A2) @ (((divide_divide @ A) @ B2) @ C)) = (((divide_divide @ A) @ (((times_times @ A) @ A2) @ B2)) @ C)))))))).
% 2.46/1.46 thf(fact_110_divide__divide__eq__right, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,B2:A,C:A]: (((((divide_divide @ A) @ A2) @ (((divide_divide @ A) @ B2) @ C)) = (((divide_divide @ A) @ (((times_times @ A) @ A2) @ C)) @ B2)))))))).
% 2.46/1.46 thf(fact_111_divide__divide__eq__left, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,B2:A,C:A]: (((((divide_divide @ A) @ (((divide_divide @ A) @ A2) @ B2)) @ C) = (((divide_divide @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 2.46/1.46 thf(fact_112_mult__zero__left, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A]: (((((times_times @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.46/1.46 thf(fact_113_mult__zero__right, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.46/1.46 thf(fact_114_mult__eq__0__iff, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) = (zero_zero @ A)) = ((A2 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_115_mult__cancel__left, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B2:A]: ((((((times_times @ A) @ C) @ A2) = (((times_times @ A) @ C) @ B2)) = ((C = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.46/1.46 thf(fact_116_mult__cancel__right, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [A2:A,C:A,B2:A]: ((((((times_times @ A) @ A2) @ C) = (((times_times @ A) @ B2) @ C)) = ((C = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.46/1.46 thf(fact_117_div__0, axiom, (! [A:$tType]: (((semidom_divide @ A) => (! [A2:A]: (((((divide_divide @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.46/1.46 thf(fact_118_divide__eq__0__iff, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,B2:A]: ((((((divide_divide @ A) @ A2) @ B2) = (zero_zero @ A)) = ((A2 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_119_div__by__0, axiom, (! [A:$tType]: (((semidom_divide @ A) => (! [A2:A]: (((((divide_divide @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.46/1.46 thf(fact_120_divide__cancel__left, axiom, (! [A:$tType]: (((field @ A) => (! [C:A,A2:A,B2:A]: ((((((divide_divide @ A) @ C) @ A2) = (((divide_divide @ A) @ C) @ B2)) = ((C = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.46/1.46 thf(fact_121_divide__cancel__right, axiom, (! [A:$tType]: (((field @ A) => (! [A2:A,C:A,B2:A]: ((((((divide_divide @ A) @ A2) @ C) = (((divide_divide @ A) @ B2) @ C)) = ((C = (zero_zero @ A)) | (A2 = B2))))))))).
% 2.46/1.46 thf(fact_122_division__ring__divide__zero, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A2:A]: (((((divide_divide @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.46/1.46 thf(fact_123_times__divide__eq__left, axiom, (! [A:$tType]: (((field @ A) => (! [B2:A,C:A,A2:A]: (((((times_times @ A) @ (((divide_divide @ A) @ B2) @ C)) @ A2) = (((divide_divide @ A) @ (((times_times @ A) @ B2) @ A2)) @ C)))))))).
% 2.46/1.46 thf(fact_124_linordered__field__no__lb, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X4:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X4))))))))).
% 2.46/1.46 thf(fact_125_linordered__field__no__ub, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X4:A]: ((? [X_1:A]: ((((ord_less @ A) @ X4) @ X_1))))))))).
% 2.46/1.46 thf(fact_126_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X3:A,Y3:A]: (((X3 != Y3) => ((~ ((((ord_less @ A) @ X3) @ Y3))) => (((ord_less @ A) @ Y3) @ X3))))))))).
% 2.46/1.46 thf(fact_127_mult__not__zero, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) != (zero_zero @ A)) => ((A2 != (zero_zero @ A)) & (B2 != (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_128_divisors__zero, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: ((((((times_times @ A) @ A2) @ B2) = (zero_zero @ A)) => ((A2 = (zero_zero @ A)) | (B2 = (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_129_no__zero__divisors, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B2:A]: (((A2 != (zero_zero @ A)) => ((B2 != (zero_zero @ A)) => ((((times_times @ A) @ A2) @ B2) != (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_130_mult__left__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => (((((times_times @ A) @ C) @ A2) = (((times_times @ A) @ C) @ B2)) = (A2 = B2))))))))).
% 2.46/1.46 thf(fact_131_mult__right__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => (((((times_times @ A) @ A2) @ C) = (((times_times @ A) @ B2) @ C)) = (A2 = B2))))))))).
% 2.46/1.46 thf(fact_132_times__divide__times__eq, axiom, (! [A:$tType]: (((field @ A) => (! [X3:A,Y3:A,Z:A,W:A]: (((((times_times @ A) @ (((divide_divide @ A) @ X3) @ Y3)) @ (((divide_divide @ A) @ Z) @ W)) = (((divide_divide @ A) @ (((times_times @ A) @ X3) @ Z)) @ (((times_times @ A) @ Y3) @ W))))))))).
% 2.46/1.46 thf(fact_133_divide__divide__times__eq, axiom, (! [A:$tType]: (((field @ A) => (! [X3:A,Y3:A,Z:A,W:A]: (((((divide_divide @ A) @ (((divide_divide @ A) @ X3) @ Y3)) @ (((divide_divide @ A) @ Z) @ W)) = (((divide_divide @ A) @ (((times_times @ A) @ X3) @ W)) @ (((times_times @ A) @ Y3) @ Z))))))))).
% 2.46/1.46 thf(fact_134_divide__divide__eq__left_H, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A2:A,B2:A,C:A]: (((((divide_divide @ A) @ (((divide_divide @ A) @ A2) @ B2)) @ C) = (((divide_divide @ A) @ A2) @ (((times_times @ A) @ C) @ B2))))))))).
% 2.46/1.46 thf(fact_135_mult__neg__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)))))))))).
% 2.46/1.46 thf(fact_136_not__square__less__zero, axiom, (! [A:$tType]: (((linordered_ring @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ (((times_times @ A) @ A2) @ A2)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_137_mult__less__0__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A2) & (((ord_less @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less @ A) @ A2) @ (zero_zero @ A)) & (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))))).
% 2.46/1.46 thf(fact_138_mult__neg__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_139_mult__pos__neg, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_140_mult__pos__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)))))))))).
% 2.46/1.46 thf(fact_141_mult__pos__neg2, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ B2) @ A2)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_142_zero__less__mult__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A2) & (((ord_less @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less @ A) @ A2) @ (zero_zero @ A)) & (((ord_less @ A) @ B2) @ (zero_zero @ A))))))))))).
% 2.46/1.46 thf(fact_143_zero__less__mult__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)) => ((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((ord_less @ A) @ (zero_zero @ A)) @ B2))))))))).
% 2.46/1.46 thf(fact_144_zero__less__mult__pos2, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ B2) @ A2)) => ((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((ord_less @ A) @ (zero_zero @ A)) @ B2))))))))).
% 2.46/1.46 thf(fact_145_mult__less__cancel__left__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ C) @ (zero_zero @ A)) => ((((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (((ord_less @ A) @ B2) @ A2))))))))).
% 2.46/1.46 thf(fact_146_mult__less__cancel__left__pos, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ C) => ((((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (((ord_less @ A) @ A2) @ B2))))))))).
% 2.46/1.46 thf(fact_147_mult__strict__left__mono__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.46/1.46 thf(fact_148_mult__strict__left__mono, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.46/1.46 thf(fact_149_mult__less__cancel__left__disj, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) & (((ord_less @ A) @ A2) @ B2)) | ((((ord_less @ A) @ C) @ (zero_zero @ A)) & (((ord_less @ A) @ B2) @ A2)))))))))).
% 2.46/1.46 thf(fact_150_mult__strict__right__mono__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)))))))))).
% 2.46/1.46 thf(fact_151_mult__strict__right__mono, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)))))))))).
% 2.46/1.46 thf(fact_152_mult__less__cancel__right__disj, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) & (((ord_less @ A) @ A2) @ B2)) | ((((ord_less @ A) @ C) @ (zero_zero @ A)) & (((ord_less @ A) @ B2) @ A2)))))))))).
% 2.46/1.46 thf(fact_153_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom, (! [A:$tType]: (((linord893533164strict @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.46/1.46 thf(fact_154_divide__neg__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ (zero_zero @ A)) => ((((ord_less @ A) @ Y3) @ (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ X3) @ Y3)))))))))).
% 2.46/1.46 thf(fact_155_divide__neg__pos, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ (zero_zero @ A)) => ((((ord_less @ A) @ (zero_zero @ A)) @ Y3) => (((ord_less @ A) @ (((divide_divide @ A) @ X3) @ Y3)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_156_divide__pos__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ X3) => ((((ord_less @ A) @ Y3) @ (zero_zero @ A)) => (((ord_less @ A) @ (((divide_divide @ A) @ X3) @ Y3)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_157_divide__pos__pos, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ X3) => ((((ord_less @ A) @ (zero_zero @ A)) @ Y3) => (((ord_less @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ X3) @ Y3)))))))))).
% 2.46/1.46 thf(fact_158_divide__less__0__iff, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (((divide_divide @ A) @ A2) @ B2)) @ (zero_zero @ A)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A2) & (((ord_less @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less @ A) @ A2) @ (zero_zero @ A)) & (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))))).
% 2.46/1.46 thf(fact_159_divide__less__cancel, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less @ A) @ (((divide_divide @ A) @ A2) @ C)) @ (((divide_divide @ A) @ B2) @ C)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ A2) @ B2)) & (((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less @ A) @ B2) @ A2)) & (C != (zero_zero @ A))))))))))).
% 2.46/1.46 thf(fact_160_zero__less__divide__iff, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ A2) @ B2)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A2) & (((ord_less @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less @ A) @ A2) @ (zero_zero @ A)) & (((ord_less @ A) @ B2) @ (zero_zero @ A))))))))))).
% 2.46/1.46 thf(fact_161_divide__strict__right__mono, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ (((divide_divide @ A) @ A2) @ C)) @ (((divide_divide @ A) @ B2) @ C)))))))))).
% 2.46/1.46 thf(fact_162_divide__strict__right__mono__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less @ A) @ (((divide_divide @ A) @ A2) @ C)) @ (((divide_divide @ A) @ B2) @ C)))))))))).
% 2.46/1.46 thf(fact_163_frac__eq__eq, axiom, (! [A:$tType]: (((field @ A) => (! [Y3:A,Z:A,X3:A,W:A]: (((Y3 != (zero_zero @ A)) => ((Z != (zero_zero @ A)) => (((((divide_divide @ A) @ X3) @ Y3) = (((divide_divide @ A) @ W) @ Z)) = ((((times_times @ A) @ X3) @ Z) = (((times_times @ A) @ W) @ Y3))))))))))).
% 2.46/1.46 thf(fact_164_divide__eq__eq, axiom, (! [A:$tType]: (((division_ring @ A) => (! [B2:A,C:A,A2:A]: ((((((divide_divide @ A) @ B2) @ C) = A2) = (((C != (zero_zero @ A)) => (B2 = (((times_times @ A) @ A2) @ C))) & ((C = (zero_zero @ A)) => (A2 = (zero_zero @ A))))))))))).
% 2.46/1.46 thf(fact_165_eq__divide__eq, axiom, (! [A:$tType]: (((division_ring @ A) => (! [A2:A,B2:A,C:A]: (((A2 = (((divide_divide @ A) @ B2) @ C)) = (((C != (zero_zero @ A)) => ((((times_times @ A) @ A2) @ C) = B2)) & ((C = (zero_zero @ A)) => (A2 = (zero_zero @ A))))))))))).
% 2.46/1.46 thf(fact_166_divide__eq__imp, axiom, (! [A:$tType]: (((division_ring @ A) => (! [C:A,B2:A,A2:A]: (((C != (zero_zero @ A)) => ((B2 = (((times_times @ A) @ A2) @ C)) => ((((divide_divide @ A) @ B2) @ C) = A2))))))))).
% 2.46/1.46 thf(fact_167_eq__divide__imp, axiom, (! [A:$tType]: (((division_ring @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => (((((times_times @ A) @ A2) @ C) = B2) => (A2 = (((divide_divide @ A) @ B2) @ C)))))))))).
% 2.46/1.46 thf(fact_168_nonzero__divide__eq__eq, axiom, (! [A:$tType]: (((division_ring @ A) => (! [C:A,B2:A,A2:A]: (((C != (zero_zero @ A)) => (((((divide_divide @ A) @ B2) @ C) = A2) = (B2 = (((times_times @ A) @ A2) @ C)))))))))).
% 2.46/1.46 thf(fact_169_nonzero__eq__divide__eq, axiom, (! [A:$tType]: (((division_ring @ A) => (! [C:A,A2:A,B2:A]: (((C != (zero_zero @ A)) => ((A2 = (((divide_divide @ A) @ B2) @ C)) = ((((times_times @ A) @ A2) @ C) = B2))))))))).
% 2.46/1.46 thf(fact_170_div__eq__0__conv, axiom, (! [N:nat,M:nat]: ((((((divide_divide @ nat) @ N) @ M) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) | (((ord_less @ nat) @ N) @ M)))))).
% 2.46/1.46 thf(fact_171_div__eq__0__conv_H, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ M) => (((((divide_divide @ nat) @ N) @ M) = (zero_zero @ nat)) = (((ord_less @ nat) @ N) @ M)))))).
% 2.46/1.46 thf(fact_172_Util__Div_Oless__mult__imp__div__less, axiom, (! [N:nat,K:nat,M:nat]: (((((ord_less @ nat) @ N) @ (((times_times @ nat) @ K) @ M)) => (((ord_less @ nat) @ (((divide_divide @ nat) @ N) @ M)) @ K))))).
% 2.46/1.46 thf(fact_173_divide__less__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [B2:A,C:A,A2:A]: (((((ord_less @ A) @ (((divide_divide @ A) @ B2) @ C)) @ A2) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ B2) @ (((times_times @ A) @ A2) @ C))) & ((~ ((((ord_less @ A) @ (zero_zero @ A)) @ C))) => (((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ B2)) & ((~ ((((ord_less @ A) @ C) @ (zero_zero @ A)))) => (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))))))).
% 2.46/1.46 thf(fact_174_less__divide__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ (((divide_divide @ A) @ B2) @ C)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ B2)) & ((~ ((((ord_less @ A) @ (zero_zero @ A)) @ C))) => (((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less @ A) @ B2) @ (((times_times @ A) @ A2) @ C))) & ((~ ((((ord_less @ A) @ C) @ (zero_zero @ A)))) => (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))))))).
% 2.46/1.46 thf(fact_175_neg__divide__less__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [C:A,B2:A,A2:A]: (((((ord_less @ A) @ C) @ (zero_zero @ A)) => ((((ord_less @ A) @ (((divide_divide @ A) @ B2) @ C)) @ A2) = (((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ B2))))))))).
% 2.46/1.46 thf(fact_176_neg__less__divide__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ C) @ (zero_zero @ A)) => ((((ord_less @ A) @ A2) @ (((divide_divide @ A) @ B2) @ C)) = (((ord_less @ A) @ B2) @ (((times_times @ A) @ A2) @ C)))))))))).
% 2.46/1.46 thf(fact_177_pos__divide__less__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [C:A,B2:A,A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ C) => ((((ord_less @ A) @ (((divide_divide @ A) @ B2) @ C)) @ A2) = (((ord_less @ A) @ B2) @ (((times_times @ A) @ A2) @ C)))))))))).
% 2.46/1.46 thf(fact_178_pos__less__divide__eq, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ C) => ((((ord_less @ A) @ A2) @ (((divide_divide @ A) @ B2) @ C)) = (((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ B2))))))))).
% 2.46/1.46 thf(fact_179_mult__imp__div__pos__less, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [Y3:A,X3:A,Z:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ Y3) => ((((ord_less @ A) @ X3) @ (((times_times @ A) @ Z) @ Y3)) => (((ord_less @ A) @ (((divide_divide @ A) @ X3) @ Y3)) @ Z))))))))).
% 2.46/1.46 thf(fact_180_mult__imp__less__div__pos, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [Y3:A,Z:A,X3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ Y3) => ((((ord_less @ A) @ (((times_times @ A) @ Z) @ Y3)) @ X3) => (((ord_less @ A) @ Z) @ (((divide_divide @ A) @ X3) @ Y3)))))))))).
% 2.46/1.46 thf(fact_181_divide__strict__left__mono, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ C) => ((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)) => (((ord_less @ A) @ (((divide_divide @ A) @ C) @ A2)) @ (((divide_divide @ A) @ C) @ B2))))))))))).
% 2.46/1.46 thf(fact_182_divide__strict__left__mono__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ C) @ (zero_zero @ A)) => ((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)) => (((ord_less @ A) @ (((divide_divide @ A) @ C) @ A2)) @ (((divide_divide @ A) @ C) @ B2))))))))))).
% 2.46/1.46 thf(fact_183_div__less__conv, axiom, (! [M:nat,N:nat,K:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ M) => ((((ord_less @ nat) @ (((divide_divide @ nat) @ N) @ M)) @ K) = (((ord_less @ nat) @ N) @ (((times_times @ nat) @ K) @ M))))))).
% 2.46/1.46 thf(fact_184_div__less__imp__less__mult, axiom, (! [M:nat,N:nat,K:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ M) => ((((ord_less @ nat) @ (((divide_divide @ nat) @ N) @ M)) @ K) => (((ord_less @ nat) @ N) @ (((times_times @ nat) @ K) @ M))))))).
% 2.46/1.46 thf(fact_185_bits__div__0, axiom, (! [A:$tType]: (((semiring_bits @ A) => (! [A2:A]: (((((divide_divide @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.46/1.46 thf(fact_186_bits__div__by__0, axiom, (! [A:$tType]: (((semiring_bits @ A) => (! [A2:A]: (((((divide_divide @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.46/1.46 thf(fact_187_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.46/1.46 thf(fact_188_mult__cancel2__gr0, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((((times_times @ nat) @ M) @ K) = (((times_times @ nat) @ N) @ K)) = (M = N)))))).
% 2.46/1.46 thf(fact_189_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X3:A]: ((((zero_zero @ A) = X3) = (X3 = (zero_zero @ A))))))))).
% 2.46/1.46 thf(fact_190_mult_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [B2:A,A2:A,C:A]: (((((times_times @ A) @ B2) @ (((times_times @ A) @ A2) @ C)) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 2.46/1.46 thf(fact_191_mult_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => ((times_times @ A) = (^ [A3:A,B3:A]: ((((times_times @ A) @ B3) @ A3)))))))).
% 2.46/1.46 thf(fact_192_mult_Oassoc, axiom, (! [A:$tType]: (((semigroup_mult @ A) => (! [A2:A,B2:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 2.46/1.46 thf(fact_193_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [A2:A,B2:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 2.46/1.46 thf(fact_194_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.46/1.46 thf(fact_195_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.46/1.46 thf(fact_196_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_197_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.46/1.46 thf(fact_198_gr__implies__gr0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.46/1.46 thf(fact_199_nat__lessSucSuc0__conv, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (suc @ (suc @ (zero_zero @ nat)))) = ((N = (zero_zero @ nat)) | (N = (suc @ (zero_zero @ nat)))))))).
% 2.46/1.46 thf(fact_200_nat__grSuc0__conv, axiom, (! [N:nat]: (((((ord_less @ nat) @ (suc @ (zero_zero @ nat))) @ N) = ((N != (zero_zero @ nat)) & (N != (suc @ (zero_zero @ nat)))))))).
% 2.46/1.46 thf(fact_201_mult__less__iff1, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z:A,X3:A,Y3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ Z) => ((((ord_less @ A) @ (((times_times @ A) @ X3) @ Z)) @ (((times_times @ A) @ Y3) @ Z)) = (((ord_less @ A) @ X3) @ Y3))))))))).
% 2.46/1.46 thf(fact_202_length__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((! [Xs2:(list @ A)]: (((! [Ys:(list @ A)]: (((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ys)) @ ((size_size @ (list @ A)) @ Xs2)) => (P @ Ys)))) => (P @ Xs2)))) => (P @ Xs))))).
% 2.46/1.46 thf(fact_203_Ex__list__of__length, axiom, (! [A:$tType,N:nat]: ((? [Xs2:(list @ A)]: ((((size_size @ (list @ A)) @ Xs2) = N)))))).
% 2.46/1.46 thf(fact_204_neq__if__length__neq, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) != ((size_size @ (list @ A)) @ Ys2)) => (Xs != Ys2))))).
% 2.46/1.46 thf(fact_205_list__decode_Ocases, axiom, (! [X3:nat]: (((X3 != (zero_zero @ nat)) => (~ ((! [N2:nat]: ((X3 != (suc @ N2)))))))))).
% 2.46/1.46 thf(fact_206_dependent__nat__choice, axiom, (! [A:$tType,P:(nat > (A > $o)),Q2:(nat > (A > (A > $o)))]: (((? [X_12:A]: (((P @ (zero_zero @ nat)) @ X_12))) => ((! [X:A,N2:nat]: ((((P @ N2) @ X) => (? [Y:A]: ((((P @ (suc @ N2)) @ Y) & (((Q2 @ N2) @ X) @ Y))))))) => (? [F2:(nat > A)]: ((! [N4:nat]: ((((P @ N4) @ (F2 @ N4)) & (((Q2 @ N4) @ (F2 @ N4)) @ (F2 @ (suc @ N4))))))))))))).
% 2.46/1.46 thf(fact_207_exists__least__lemma, axiom, (! [P:(nat > $o)]: (((~ ((P @ (zero_zero @ nat)))) => ((? [X_12:nat]: ((P @ X_12))) => (? [N2:nat]: (((~ ((P @ N2))) & (P @ (suc @ N2)))))))))).
% 2.46/1.46 thf(fact_208_field__lbound__gt__zero, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [D1:A,D2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ D1) => ((((ord_less @ A) @ (zero_zero @ A)) @ D2) => (? [E:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ E) & ((((ord_less @ A) @ E) @ D1) & (((ord_less @ A) @ E) @ D2))))))))))))).
% 2.46/1.46 thf(fact_209_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 2.46/1.46 thf(fact_210_length__product, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Ys2:(list @ B)]: ((((size_size @ (list @ ((product_prod @ A) @ B))) @ ((((product @ A) @ B) @ Xs) @ Ys2)) = (((times_times @ nat) @ ((size_size @ (list @ A)) @ Xs)) @ ((size_size @ (list @ B)) @ Ys2)))))).
% 2.46/1.46 thf(fact_211_split__div_H, axiom, (! [P:(nat > $o),M:nat,N:nat]: (((P @ (((divide_divide @ nat) @ M) @ N)) = (((N = (zero_zero @ nat)) & (P @ (zero_zero @ nat))) | (? [Q3:nat]: (((((ord_less_eq @ nat) @ (((times_times @ nat) @ N) @ Q3)) @ M) & ((((ord_less @ nat) @ M) @ (((times_times @ nat) @ N) @ (suc @ Q3))) & (P @ Q3)))))))))).
% 2.46/1.46 thf(fact_212_le__less__div__conv, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ M) => (((((ord_less_eq @ nat) @ (((times_times @ nat) @ K) @ M)) @ N) & (((ord_less @ nat) @ N) @ (((times_times @ nat) @ (suc @ K)) @ M))) = ((((divide_divide @ nat) @ N) @ M) = K)))))).
% 2.46/1.46 thf(fact_213_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.46/1.46 thf(fact_214_bot__nat__0_Oextremum, axiom, (! [A2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A2)))).
% 2.46/1.46 thf(fact_215_le0, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.46/1.46 thf(fact_216_Suc__le__mono, axiom, (! [N:nat,M:nat]: (((((ord_less_eq @ nat) @ (suc @ N)) @ (suc @ M)) = (((ord_less_eq @ nat) @ N) @ M))))).
% 2.46/1.46 thf(fact_217_one__le__mult__iff, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ (zero_zero @ nat))) @ (((times_times @ nat) @ M) @ N)) = ((((ord_less_eq @ nat) @ (suc @ (zero_zero @ nat))) @ M) & (((ord_less_eq @ nat) @ (suc @ (zero_zero @ nat))) @ N)))))).
% 2.46/1.46 thf(fact_218_mult__le__cancel2, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((times_times @ nat) @ M) @ K)) @ (((times_times @ nat) @ N) @ K)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((ord_less_eq @ nat) @ M) @ N)))))).
% 2.46/1.46 thf(fact_219_nat__mult__le__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((ord_less_eq @ nat) @ M) @ N)))))).
% 2.46/1.46 thf(fact_220_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.46/1.46 thf(fact_221_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X3))))))).
% 2.46/1.46 thf(fact_222_ge__less__neq__conv, axiom, (! [A:$tType]: (((linorder @ A) => ((ord_less_eq @ A) = (^ [A3:A,N5:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ A3) => (N5 != X5))))))))))).
% 2.46/1.46 thf(fact_223_less__ge__neq__conv, axiom, (! [A:$tType]: (((linorder @ A) => ((ord_less @ A) = (^ [N5:A,A3:A]: ((! [X5:A]: (((((ord_less_eq @ A) @ A3) @ X5) => (N5 != X5))))))))))).
% 2.46/1.46 thf(fact_224_greater__le__neq__conv, axiom, (! [A:$tType]: (((linorder @ A) => ((ord_less @ A) = (^ [A3:A,N5:A]: ((! [X5:A]: (((((ord_less_eq @ A) @ X5) @ A3) => (N5 != X5))))))))))).
% 2.46/1.46 thf(fact_225_le__greater__neq__conv, axiom, (! [A:$tType]: (((linorder @ A) => ((ord_less_eq @ A) = (^ [N5:A,A3:A]: ((! [X5:A]: (((((ord_less @ A) @ A3) @ X5) => (N5 != X5))))))))))).
% 2.46/1.46 thf(fact_226_nat__geSucSuc0__conv, axiom, (! [N:nat]: (((((ord_less_eq @ nat) @ (suc @ (suc @ (zero_zero @ nat)))) @ N) = ((N != (zero_zero @ nat)) & (N != (suc @ (zero_zero @ nat)))))))).
% 2.46/1.46 thf(fact_227_nat__leSuc0__conv, axiom, (! [N:nat]: (((((ord_less_eq @ nat) @ N) @ (suc @ (zero_zero @ nat))) = ((N = (zero_zero @ nat)) | (N = (suc @ (zero_zero @ nat)))))))).
% 2.46/1.46 thf(fact_228_ordered__comm__semiring__class_Ocomm__mult__left__mono, axiom, (! [A:$tType]: (((ordere1490568538miring @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.46/1.46 thf(fact_229_zero__le__mult__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)) = (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))))))))))).
% 2.46/1.46 thf(fact_230_mult__nonneg__nonpos2, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ B2) @ A2)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_231_mult__nonpos__nonneg, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_232_mult__nonneg__nonpos, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_233_mult__nonneg__nonneg, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)))))))))).
% 2.46/1.46 thf(fact_234_split__mult__neg__le, axiom, (! [A:$tType]: (((ordered_semiring_0 @ A) => (! [A2:A,B2:A]: (((((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2))) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A))))))))).
% 2.46/1.46 thf(fact_235_mult__le__0__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ B2)) @ (zero_zero @ A)) = (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))))).
% 2.46/1.46 thf(fact_236_mult__right__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)))))))))).
% 2.46/1.46 thf(fact_237_mult__right__mono__neg, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ C)))))))))).
% 2.46/1.46 thf(fact_238_mult__left__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.46/1.46 thf(fact_239_mult__nonpos__nonpos, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2)))))))))).
% 2.46/1.46 thf(fact_240_mult__left__mono__neg, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B2)))))))))).
% 2.46/1.46 thf(fact_241_split__mult__pos__le, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [A2:A,B2:A]: (((((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A)))) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B2))))))))).
% 2.46/1.46 thf(fact_242_zero__le__square, axiom, (! [A:$tType]: (((linordered_ring @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ A2)))))))).
% 2.46/1.46 thf(fact_243_mult__mono_H, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ D)))))))))))).
% 2.46/1.46 thf(fact_244_mult__mono, axiom, (! [A:$tType]: (((ordered_semiring @ A) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B2) @ D)))))))))))).
% 2.46/1.46 thf(fact_245_divide__right__mono__neg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((divide_divide @ A) @ B2) @ C)) @ (((divide_divide @ A) @ A2) @ C)))))))))).
% 2.46/1.46 thf(fact_246_divide__nonpos__nonpos, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ Y3) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ X3) @ Y3)))))))))).
% 2.46/1.46 thf(fact_247_divide__nonpos__nonneg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y3) => (((ord_less_eq @ A) @ (((divide_divide @ A) @ X3) @ Y3)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_248_divide__nonneg__nonpos, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X3) => ((((ord_less_eq @ A) @ Y3) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((divide_divide @ A) @ X3) @ Y3)) @ (zero_zero @ A)))))))))).
% 2.46/1.46 thf(fact_249_divide__nonneg__nonneg, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X3) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y3) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ X3) @ Y3)))))))))).
% 2.46/1.46 thf(fact_250_zero__le__divide__iff, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((divide_divide @ A) @ A2) @ B2)) = (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))))))))))).
% 2.46/1.46 thf(fact_251_divide__right__mono, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((divide_divide @ A) @ A2) @ C)) @ (((divide_divide @ A) @ B2) @ C)))))))))).
% 2.46/1.46 thf(fact_252_divide__le__0__iff, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (((divide_divide @ A) @ A2) @ B2)) @ (zero_zero @ A)) = (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | ((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))))).
% 2.46/1.46 thf(tcon_fun___Orderings_Oorder, axiom, (! [A4:$tType,A5:$tType]: (((order @ A5) => (order @ (A4 > A5)))))).
% 2.46/1.46 thf(tcon_Nat_Onat___Euclidean__Division_Oeuclidean__semiring__cancel, axiom, (euclid191655569cancel @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel, axiom, (semiri1923998003cancel @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict, axiom, (linord893533164strict @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Olinordered__semiring__strict, axiom, (linord20386208strict @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors, axiom, (semiri1193490041visors @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring, axiom, (ordere1490568538miring @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0, axiom, (ordered_semiring_0 @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult, axiom, (ab_semigroup_mult @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Oordered__semiring, axiom, (ordered_semiring @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Groups_Osemigroup__mult, axiom, (semigroup_mult @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Osemidom__divide, axiom, (semidom_divide @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Parity_Osemiring__bits, axiom, (semiring_bits @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Rings_Omult__zero, axiom, (mult_zero @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Orderings_Oorder_1, axiom, (order @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.46/1.46 thf(tcon_Nat_Onat___Nat_Osize, axiom, (size @ nat)).
% 2.46/1.46 thf(tcon_HOL_Obool___Orderings_Olinorder_2, axiom, (linorder @ $o)).
% 2.46/1.46 thf(tcon_HOL_Obool___Orderings_Oorder_3, axiom, (order @ $o)).
% 2.46/1.46 thf(tcon_List_Olist___Nat_Osize_4, axiom, (! [A4:$tType]: ((size @ (list @ A4))))).
% 2.46/1.46 thf(tcon_Product__Type_Oprod___Nat_Osize_5, axiom, (! [A4:$tType,A5:$tType]: ((size @ ((product_prod @ A4) @ A5))))).
% 2.46/1.46 thf(conj_0, hypothesis, ((((divide_divide @ nat) @ ((size_size @ (list @ a)) @ xs)) @ k) = (suc @ n))).
% 2.46/1.46 thf(conj_1, hypothesis, (k != (zero_zero @ nat))).
% 2.46/1.46 thf(conj_2, conjecture, (((ord_less @ nat) @ (((times_times @ nat) @ n) @ k)) @ ((size_size @ (list @ a)) @ xs))).
% 2.46/1.46 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2DTF32501.p
% 2.46/1.46 ------------------------
% 2.46/1.49 ---- Cleaned THF ---
% 2.46/1.49 thf(ty_t_Product__Type_Oprod,type,
% 2.46/1.49 product_prod: $tType > $tType > $tType ).
% 2.46/1.49
% 2.46/1.49 thf(ty_t_List_Olist,type,
% 2.46/1.49 list: $tType > $tType ).
% 2.46/1.49
% 2.46/1.49 thf(ty_t_Nat_Onat,type,
% 2.46/1.49 nat: $tType ).
% 2.46/1.49
% 2.46/1.49 thf(ty_tf_a,type,
% 2.46/1.49 a: $tType ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_HOL_Otype,type,
% 2.46/1.49 type:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Nat_Osize,type,
% 2.46/1.49 size:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Groups_Ozero,type,
% 2.46/1.49 zero:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Fields_Ofield,type,
% 2.46/1.49 field:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Orderings_Oorder,type,
% 2.46/1.49 order:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Omult__zero,type,
% 2.46/1.49 mult_zero:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Orderings_Olinorder,type,
% 2.46/1.49 linorder:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Oordered__ring,type,
% 2.46/1.49 ordered_ring:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Orderings_Owellorder,type,
% 2.46/1.49 wellorder:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Fields_Odivision__ring,type,
% 2.46/1.49 division_ring:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Parity_Osemiring__bits,type,
% 2.46/1.49 semiring_bits:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Osemidom__divide,type,
% 2.46/1.49 semidom_divide:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Groups_Osemigroup__mult,type,
% 2.46/1.49 semigroup_mult:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.46/1.49 linordered_idom:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Olinordered__ring,type,
% 2.46/1.49 linordered_ring:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Oordered__semiring,type,
% 2.46/1.49 ordered_semiring:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Fields_Olinordered__field,type,
% 2.46/1.49 linordered_field:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 2.46/1.49 ab_semigroup_mult:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Oordered__semiring__0,type,
% 2.46/1.49 ordered_semiring_0:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Oordered__comm__semiring,type,
% 2.46/1.49 ordere1490568538miring:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 2.46/1.49 linord581940658strict:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 2.46/1.49 semiri1193490041visors:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Olinordered__semiring__strict,type,
% 2.46/1.49 linord20386208strict:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.46/1.49 linord1659791738miring:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.46/1.49 canoni770627133id_add:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Olinordered__comm__semiring__strict,type,
% 2.46/1.49 linord893533164strict:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 2.46/1.49 semiri1923998003cancel:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_cl_Euclidean__Division_Oeuclidean__semiring__cancel,type,
% 2.46/1.49 euclid191655569cancel:
% 2.46/1.49 !>[A: $tType] : $o ).
% 2.46/1.49
% 2.46/1.49 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 2.46/1.49 times_times:
% 2.46/1.49 !>[A: $tType] : ( A > A > A ) ).
% 2.46/1.49
% 2.46/1.49 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.46/1.49 zero_zero:
% 2.46/1.49 !>[A: $tType] : A ).
% 2.46/1.49
% 2.46/1.49 thf(sy_c_List_Oproduct,type,
% 2.46/1.49 product:
% 2.46/1.49 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( list @ B ) > ( list @ ( product_prod @ A @ B ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(sy_c_Nat_OSuc,type,
% 2.46/1.49 suc: nat > nat ).
% 2.46/1.49
% 2.46/1.49 thf(sy_c_Nat_Osize__class_Osize,type,
% 2.46/1.49 size_size:
% 2.46/1.49 !>[A: $tType] : ( A > nat ) ).
% 2.46/1.49
% 2.46/1.49 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.46/1.49 ord_less:
% 2.46/1.49 !>[A: $tType] : ( A > A > $o ) ).
% 2.46/1.49
% 2.46/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.46/1.49 ord_less_eq:
% 2.46/1.49 !>[A: $tType] : ( A > A > $o ) ).
% 2.46/1.49
% 2.46/1.49 thf(sy_c_Rings_Odivide__class_Odivide,type,
% 2.46/1.49 divide_divide:
% 2.46/1.49 !>[A: $tType] : ( A > A > A ) ).
% 2.46/1.49
% 2.46/1.49 thf(sy_v_k,type,
% 2.46/1.49 k: nat ).
% 2.46/1.49
% 2.46/1.49 thf(sy_v_n,type,
% 2.46/1.49 n: nat ).
% 2.46/1.49
% 2.46/1.49 thf(sy_v_xs,type,
% 2.46/1.49 xs: list @ a ).
% 2.46/1.49
% 2.46/1.49 thf(fact_0_div__mult__self__is__m,axiom,
% 2.46/1.49 ! [N: nat,M: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.46/1.49 => ( ( divide_divide @ nat @ ( times_times @ nat @ M @ N ) @ N )
% 2.46/1.49 = M ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_1_div__mult__self1__is__m,axiom,
% 2.46/1.49 ! [N: nat,M: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.46/1.49 => ( ( divide_divide @ nat @ ( times_times @ nat @ N @ M ) @ N )
% 2.46/1.49 = M ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_2_nat__mult__div__cancel__disj,axiom,
% 2.46/1.49 ! [K: nat,M: nat,N: nat] :
% 2.46/1.49 ( ( ( K
% 2.46/1.49 = ( zero_zero @ nat ) )
% 2.46/1.49 => ( ( divide_divide @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.46/1.49 = ( zero_zero @ nat ) ) )
% 2.46/1.49 & ( ( K
% 2.46/1.49 != ( zero_zero @ nat ) )
% 2.46/1.49 => ( ( divide_divide @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.46/1.49 = ( divide_divide @ nat @ M @ N ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_3_div__less,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ M @ N )
% 2.46/1.49 => ( ( divide_divide @ nat @ M @ N )
% 2.46/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_4_div__by__Suc__0,axiom,
% 2.46/1.49 ! [M: nat] :
% 2.46/1.49 ( ( divide_divide @ nat @ M @ ( suc @ ( zero_zero @ nat ) ) )
% 2.46/1.49 = M ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_5_mult__less__cancel2,axiom,
% 2.46/1.49 ! [M: nat,K: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 2.46/1.49 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.46/1.49 & ( ord_less @ nat @ M @ N ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_6_nat__0__less__mult__iff,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ M @ N ) )
% 2.46/1.49 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.46/1.49 & ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_7_nat__mult__less__cancel__disj,axiom,
% 2.46/1.49 ! [K: nat,M: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.46/1.49 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.46/1.49 & ( ord_less @ nat @ M @ N ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_8_mult__eq__1__iff,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ( times_times @ nat @ M @ N )
% 2.46/1.49 = ( suc @ ( zero_zero @ nat ) ) )
% 2.46/1.49 = ( ( M
% 2.46/1.49 = ( suc @ ( zero_zero @ nat ) ) )
% 2.46/1.49 & ( N
% 2.46/1.49 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_9_one__eq__mult__iff,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ( suc @ ( zero_zero @ nat ) )
% 2.46/1.49 = ( times_times @ nat @ M @ N ) )
% 2.46/1.49 = ( ( M
% 2.46/1.49 = ( suc @ ( zero_zero @ nat ) ) )
% 2.46/1.49 & ( N
% 2.46/1.49 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_10_less__Suc0,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) )
% 2.46/1.49 = ( N
% 2.46/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_11_zero__less__Suc,axiom,
% 2.46/1.49 ! [N: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_12_old_Onat_Oinject,axiom,
% 2.46/1.49 ! [Nat: nat,Nat2: nat] :
% 2.46/1.49 ( ( ( suc @ Nat )
% 2.46/1.49 = ( suc @ Nat2 ) )
% 2.46/1.49 = ( Nat = Nat2 ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_13_nat_Oinject,axiom,
% 2.46/1.49 ! [X2: nat,Y2: nat] :
% 2.46/1.49 ( ( ( suc @ X2 )
% 2.46/1.49 = ( suc @ Y2 ) )
% 2.46/1.49 = ( X2 = Y2 ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_14_bot__nat__0_Onot__eq__extremum,axiom,
% 2.46/1.49 ! [A2: nat] :
% 2.46/1.49 ( ( A2
% 2.46/1.49 != ( zero_zero @ nat ) )
% 2.46/1.49 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_15_less__nat__zero__code,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_16_neq0__conv,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ( ( N
% 2.46/1.49 != ( zero_zero @ nat ) )
% 2.46/1.49 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_17_Suc__less__eq,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.46/1.49 = ( ord_less @ nat @ M @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_18_Suc__mono,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ M @ N )
% 2.46/1.49 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_19_lessI,axiom,
% 2.46/1.49 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_20_mult__cancel2,axiom,
% 2.46/1.49 ! [M: nat,K: nat,N: nat] :
% 2.46/1.49 ( ( ( times_times @ nat @ M @ K )
% 2.46/1.49 = ( times_times @ nat @ N @ K ) )
% 2.46/1.49 = ( ( M = N )
% 2.46/1.49 | ( K
% 2.46/1.49 = ( zero_zero @ nat ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_21_mult__cancel1,axiom,
% 2.46/1.49 ! [K: nat,M: nat,N: nat] :
% 2.46/1.49 ( ( ( times_times @ nat @ K @ M )
% 2.46/1.49 = ( times_times @ nat @ K @ N ) )
% 2.46/1.49 = ( ( M = N )
% 2.46/1.49 | ( K
% 2.46/1.49 = ( zero_zero @ nat ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_22_mult__0__right,axiom,
% 2.46/1.49 ! [M: nat] :
% 2.46/1.49 ( ( times_times @ nat @ M @ ( zero_zero @ nat ) )
% 2.46/1.49 = ( zero_zero @ nat ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_23_mult__is__0,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ( times_times @ nat @ M @ N )
% 2.46/1.49 = ( zero_zero @ nat ) )
% 2.46/1.49 = ( ( M
% 2.46/1.49 = ( zero_zero @ nat ) )
% 2.46/1.49 | ( N
% 2.46/1.49 = ( zero_zero @ nat ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_24_div__mult__mult1__if,axiom,
% 2.46/1.49 ! [A: $tType] :
% 2.46/1.49 ( ( euclid191655569cancel @ A )
% 2.46/1.49 => ! [C: A,A2: A,B2: A] :
% 2.46/1.49 ( ( ( C
% 2.46/1.49 = ( zero_zero @ A ) )
% 2.46/1.49 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.46/1.49 = ( zero_zero @ A ) ) )
% 2.46/1.49 & ( ( C
% 2.46/1.49 != ( zero_zero @ A ) )
% 2.46/1.49 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.46/1.49 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_25_div__mult__mult2,axiom,
% 2.46/1.49 ! [A: $tType] :
% 2.46/1.49 ( ( euclid191655569cancel @ A )
% 2.46/1.49 => ! [C: A,A2: A,B2: A] :
% 2.46/1.49 ( ( C
% 2.46/1.49 != ( zero_zero @ A ) )
% 2.46/1.49 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) )
% 2.46/1.49 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_26_div__mult__mult1,axiom,
% 2.46/1.49 ! [A: $tType] :
% 2.46/1.49 ( ( euclid191655569cancel @ A )
% 2.46/1.49 => ! [C: A,A2: A,B2: A] :
% 2.46/1.49 ( ( C
% 2.46/1.49 != ( zero_zero @ A ) )
% 2.46/1.49 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.46/1.49 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_27_measure__induct__rule,axiom,
% 2.46/1.49 ! [B: $tType,A: $tType] :
% 2.46/1.49 ( ( wellorder @ B )
% 2.46/1.49 => ! [F: A > B,P: A > $o,A2: A] :
% 2.46/1.49 ( ! [X: A] :
% 2.46/1.49 ( ! [Y: A] :
% 2.46/1.49 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X ) )
% 2.46/1.49 => ( P @ Y ) )
% 2.46/1.49 => ( P @ X ) )
% 2.46/1.49 => ( P @ A2 ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_28_measure__induct,axiom,
% 2.46/1.49 ! [B: $tType,A: $tType] :
% 2.46/1.49 ( ( wellorder @ B )
% 2.46/1.49 => ! [F: A > B,P: A > $o,A2: A] :
% 2.46/1.49 ( ! [X: A] :
% 2.46/1.49 ( ! [Y: A] :
% 2.46/1.49 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X ) )
% 2.46/1.49 => ( P @ Y ) )
% 2.46/1.49 => ( P @ X ) )
% 2.46/1.49 => ( P @ A2 ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_29_n__not__Suc__n,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ( N
% 2.46/1.49 != ( suc @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_30_Suc__inject,axiom,
% 2.46/1.49 ! [X3: nat,Y3: nat] :
% 2.46/1.49 ( ( ( suc @ X3 )
% 2.46/1.49 = ( suc @ Y3 ) )
% 2.46/1.49 => ( X3 = Y3 ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_31_infinite__descent__measure,axiom,
% 2.46/1.49 ! [A: $tType,P: A > $o,V: A > nat,X3: A] :
% 2.46/1.49 ( ! [X: A] :
% 2.46/1.49 ( ~ ( P @ X )
% 2.46/1.49 => ? [Y: A] :
% 2.46/1.49 ( ( ord_less @ nat @ ( V @ Y ) @ ( V @ X ) )
% 2.46/1.49 & ~ ( P @ Y ) ) )
% 2.46/1.49 => ( P @ X3 ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_32_linorder__neqE__nat,axiom,
% 2.46/1.49 ! [X3: nat,Y3: nat] :
% 2.46/1.49 ( ( X3 != Y3 )
% 2.46/1.49 => ( ~ ( ord_less @ nat @ X3 @ Y3 )
% 2.46/1.49 => ( ord_less @ nat @ Y3 @ X3 ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_33_infinite__descent,axiom,
% 2.46/1.49 ! [P: nat > $o,N: nat] :
% 2.46/1.49 ( ! [N2: nat] :
% 2.46/1.49 ( ~ ( P @ N2 )
% 2.46/1.49 => ? [M2: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ M2 @ N2 )
% 2.46/1.49 & ~ ( P @ M2 ) ) )
% 2.46/1.49 => ( P @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_34_nat__less__induct,axiom,
% 2.46/1.49 ! [P: nat > $o,N: nat] :
% 2.46/1.49 ( ! [N2: nat] :
% 2.46/1.49 ( ! [M2: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ M2 @ N2 )
% 2.46/1.49 => ( P @ M2 ) )
% 2.46/1.49 => ( P @ N2 ) )
% 2.46/1.49 => ( P @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_35_less__irrefl__nat,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ~ ( ord_less @ nat @ N @ N ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_36_less__not__refl3,axiom,
% 2.46/1.49 ! [S: nat,T: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ S @ T )
% 2.46/1.49 => ( S != T ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_37_less__not__refl2,axiom,
% 2.46/1.49 ! [N: nat,M: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ N @ M )
% 2.46/1.49 => ( M != N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_38_less__not__refl,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ~ ( ord_less @ nat @ N @ N ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_39_nat__neq__iff,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( M != N )
% 2.46/1.49 = ( ( ord_less @ nat @ M @ N )
% 2.46/1.49 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_40_size__neq__size__imp__neq,axiom,
% 2.46/1.49 ! [A: $tType] :
% 2.46/1.49 ( ( size @ A )
% 2.46/1.49 => ! [X3: A,Y3: A] :
% 2.46/1.49 ( ( ( size_size @ A @ X3 )
% 2.46/1.49 != ( size_size @ A @ Y3 ) )
% 2.46/1.49 => ( X3 != Y3 ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_41_not0__implies__Suc,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ( ( N
% 2.46/1.49 != ( zero_zero @ nat ) )
% 2.46/1.49 => ? [M3: nat] :
% 2.46/1.49 ( N
% 2.46/1.49 = ( suc @ M3 ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_42_old_Onat_Oinducts,axiom,
% 2.46/1.49 ! [P: nat > $o,Nat: nat] :
% 2.46/1.49 ( ( P @ ( zero_zero @ nat ) )
% 2.46/1.49 => ( ! [Nat3: nat] :
% 2.46/1.49 ( ( P @ Nat3 )
% 2.46/1.49 => ( P @ ( suc @ Nat3 ) ) )
% 2.46/1.49 => ( P @ Nat ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_43_old_Onat_Oexhaust,axiom,
% 2.46/1.49 ! [Y3: nat] :
% 2.46/1.49 ( ( Y3
% 2.46/1.49 != ( zero_zero @ nat ) )
% 2.46/1.49 => ~ ! [Nat3: nat] :
% 2.46/1.49 ( Y3
% 2.46/1.49 != ( suc @ Nat3 ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_44_Zero__not__Suc,axiom,
% 2.46/1.49 ! [M: nat] :
% 2.46/1.49 ( ( zero_zero @ nat )
% 2.46/1.49 != ( suc @ M ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_45_Zero__neq__Suc,axiom,
% 2.46/1.49 ! [M: nat] :
% 2.46/1.49 ( ( zero_zero @ nat )
% 2.46/1.49 != ( suc @ M ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_46_Suc__neq__Zero,axiom,
% 2.46/1.49 ! [M: nat] :
% 2.46/1.49 ( ( suc @ M )
% 2.46/1.49 != ( zero_zero @ nat ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_47_zero__induct,axiom,
% 2.46/1.49 ! [P: nat > $o,K: nat] :
% 2.46/1.49 ( ( P @ K )
% 2.46/1.49 => ( ! [N2: nat] :
% 2.46/1.49 ( ( P @ ( suc @ N2 ) )
% 2.46/1.49 => ( P @ N2 ) )
% 2.46/1.49 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_48_diff__induct,axiom,
% 2.46/1.49 ! [P: nat > nat > $o,M: nat,N: nat] :
% 2.46/1.49 ( ! [X: nat] : ( P @ X @ ( zero_zero @ nat ) )
% 2.46/1.49 => ( ! [Y4: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y4 ) )
% 2.46/1.49 => ( ! [X: nat,Y4: nat] :
% 2.46/1.49 ( ( P @ X @ Y4 )
% 2.46/1.49 => ( P @ ( suc @ X ) @ ( suc @ Y4 ) ) )
% 2.46/1.49 => ( P @ M @ N ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_49_nat__induct,axiom,
% 2.46/1.49 ! [P: nat > $o,N: nat] :
% 2.46/1.49 ( ( P @ ( zero_zero @ nat ) )
% 2.46/1.49 => ( ! [N2: nat] :
% 2.46/1.49 ( ( P @ N2 )
% 2.46/1.49 => ( P @ ( suc @ N2 ) ) )
% 2.46/1.49 => ( P @ N ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_50_nat_OdiscI,axiom,
% 2.46/1.49 ! [Nat: nat,X2: nat] :
% 2.46/1.49 ( ( Nat
% 2.46/1.49 = ( suc @ X2 ) )
% 2.46/1.49 => ( Nat
% 2.46/1.49 != ( zero_zero @ nat ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_51_old_Onat_Odistinct_I1_J,axiom,
% 2.46/1.49 ! [Nat2: nat] :
% 2.46/1.49 ( ( zero_zero @ nat )
% 2.46/1.49 != ( suc @ Nat2 ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_52_old_Onat_Odistinct_I2_J,axiom,
% 2.46/1.49 ! [Nat4: nat] :
% 2.46/1.49 ( ( suc @ Nat4 )
% 2.46/1.49 != ( zero_zero @ nat ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_53_nat_Odistinct_I1_J,axiom,
% 2.46/1.49 ! [X2: nat] :
% 2.46/1.49 ( ( zero_zero @ nat )
% 2.46/1.49 != ( suc @ X2 ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_54_infinite__descent0__measure,axiom,
% 2.46/1.49 ! [A: $tType,V: A > nat,P: A > $o,X3: A] :
% 2.46/1.49 ( ! [X: A] :
% 2.46/1.49 ( ( ( V @ X )
% 2.46/1.49 = ( zero_zero @ nat ) )
% 2.46/1.49 => ( P @ X ) )
% 2.46/1.49 => ( ! [X: A] :
% 2.46/1.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V @ X ) )
% 2.46/1.49 => ( ~ ( P @ X )
% 2.46/1.49 => ? [Y: A] :
% 2.46/1.49 ( ( ord_less @ nat @ ( V @ Y ) @ ( V @ X ) )
% 2.46/1.49 & ~ ( P @ Y ) ) ) )
% 2.46/1.49 => ( P @ X3 ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_55_bot__nat__0_Oextremum__strict,axiom,
% 2.46/1.49 ! [A2: nat] :
% 2.46/1.49 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_56_infinite__descent0,axiom,
% 2.46/1.49 ! [P: nat > $o,N: nat] :
% 2.46/1.49 ( ( P @ ( zero_zero @ nat ) )
% 2.46/1.49 => ( ! [N2: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.46/1.49 => ( ~ ( P @ N2 )
% 2.46/1.49 => ? [M2: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ M2 @ N2 )
% 2.46/1.49 & ~ ( P @ M2 ) ) ) )
% 2.46/1.49 => ( P @ N ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_57_gr__implies__not0,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ M @ N )
% 2.46/1.49 => ( N
% 2.46/1.49 != ( zero_zero @ nat ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_58_less__zeroE,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_59_not__less0,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_60_not__gr0,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 2.46/1.49 = ( N
% 2.46/1.49 = ( zero_zero @ nat ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_61_gr0I,axiom,
% 2.46/1.49 ! [N: nat] :
% 2.46/1.49 ( ( N
% 2.46/1.49 != ( zero_zero @ nat ) )
% 2.46/1.49 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_62_not__less__less__Suc__eq,axiom,
% 2.46/1.49 ! [N: nat,M: nat] :
% 2.46/1.49 ( ~ ( ord_less @ nat @ N @ M )
% 2.46/1.49 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.46/1.49 = ( N = M ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_63_strict__inc__induct,axiom,
% 2.46/1.49 ! [I: nat,J: nat,P: nat > $o] :
% 2.46/1.49 ( ( ord_less @ nat @ I @ J )
% 2.46/1.49 => ( ! [I2: nat] :
% 2.46/1.49 ( ( J
% 2.46/1.49 = ( suc @ I2 ) )
% 2.46/1.49 => ( P @ I2 ) )
% 2.46/1.49 => ( ! [I2: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ I2 @ J )
% 2.46/1.49 => ( ( P @ ( suc @ I2 ) )
% 2.46/1.49 => ( P @ I2 ) ) )
% 2.46/1.49 => ( P @ I ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_64_less__Suc__induct,axiom,
% 2.46/1.49 ! [I: nat,J: nat,P: nat > nat > $o] :
% 2.46/1.49 ( ( ord_less @ nat @ I @ J )
% 2.46/1.49 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 2.46/1.49 => ( ! [I2: nat,J2: nat,K2: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ I2 @ J2 )
% 2.46/1.49 => ( ( ord_less @ nat @ J2 @ K2 )
% 2.46/1.49 => ( ( P @ I2 @ J2 )
% 2.46/1.49 => ( ( P @ J2 @ K2 )
% 2.46/1.49 => ( P @ I2 @ K2 ) ) ) ) )
% 2.46/1.49 => ( P @ I @ J ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_65_less__trans__Suc,axiom,
% 2.46/1.49 ! [I: nat,J: nat,K: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ I @ J )
% 2.46/1.49 => ( ( ord_less @ nat @ J @ K )
% 2.46/1.49 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_66_Suc__less__SucD,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.46/1.49 => ( ord_less @ nat @ M @ N ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_67_less__antisym,axiom,
% 2.46/1.49 ! [N: nat,M: nat] :
% 2.46/1.49 ( ~ ( ord_less @ nat @ N @ M )
% 2.46/1.49 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.46/1.49 => ( M = N ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_68_Suc__less__eq2,axiom,
% 2.46/1.49 ! [N: nat,M: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 2.46/1.49 = ( ? [M4: nat] :
% 2.46/1.49 ( ( M
% 2.46/1.49 = ( suc @ M4 ) )
% 2.46/1.49 & ( ord_less @ nat @ N @ M4 ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_69_All__less__Suc,axiom,
% 2.46/1.49 ! [N: nat,P: nat > $o] :
% 2.46/1.49 ( ( ! [I3: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ I3 @ ( suc @ N ) )
% 2.46/1.49 => ( P @ I3 ) ) )
% 2.46/1.49 = ( ( P @ N )
% 2.46/1.49 & ! [I3: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ I3 @ N )
% 2.46/1.49 => ( P @ I3 ) ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_70_not__less__eq,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 2.46/1.49 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_71_less__Suc__eq,axiom,
% 2.46/1.49 ! [M: nat,N: nat] :
% 2.46/1.49 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.46/1.49 = ( ( ord_less @ nat @ M @ N )
% 2.46/1.49 | ( M = N ) ) ) ).
% 2.46/1.49
% 2.46/1.49 thf(fact_72_Ex__less__Suc,axiom,
% 2.46/1.49 ! [N: nat,P: nat > $o] :
% 2.46/1.49 ( ( ? [I3: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I3 @ ( suc @ N ) )
% 2.46/1.50 & ( P @ I3 ) ) )
% 2.46/1.50 = ( ( P @ N )
% 2.46/1.50 | ? [I3: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I3 @ N )
% 2.46/1.50 & ( P @ I3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_73_less__SucI,axiom,
% 2.46/1.50 ! [M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ M @ N )
% 2.46/1.50 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_74_less__SucE,axiom,
% 2.46/1.50 ! [M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.46/1.50 => ( ~ ( ord_less @ nat @ M @ N )
% 2.46/1.50 => ( M = N ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_75_Suc__lessI,axiom,
% 2.46/1.50 ! [M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ M @ N )
% 2.46/1.50 => ( ( ( suc @ M )
% 2.46/1.50 != N )
% 2.46/1.50 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_76_Suc__lessE,axiom,
% 2.46/1.50 ! [I: nat,K: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 2.46/1.50 => ~ ! [J2: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I @ J2 )
% 2.46/1.50 => ( K
% 2.46/1.50 != ( suc @ J2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_77_Suc__lessD,axiom,
% 2.46/1.50 ! [M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 2.46/1.50 => ( ord_less @ nat @ M @ N ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_78_Nat_OlessE,axiom,
% 2.46/1.50 ! [I: nat,K: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I @ K )
% 2.46/1.50 => ( ( K
% 2.46/1.50 != ( suc @ I ) )
% 2.46/1.50 => ~ ! [J2: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I @ J2 )
% 2.46/1.50 => ( K
% 2.46/1.50 != ( suc @ J2 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_79_nat__mult__eq__cancel__disj,axiom,
% 2.46/1.50 ! [K: nat,M: nat,N: nat] :
% 2.46/1.50 ( ( ( times_times @ nat @ K @ M )
% 2.46/1.50 = ( times_times @ nat @ K @ N ) )
% 2.46/1.50 = ( ( K
% 2.46/1.50 = ( zero_zero @ nat ) )
% 2.46/1.50 | ( M = N ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_80_mult__0,axiom,
% 2.46/1.50 ! [N: nat] :
% 2.46/1.50 ( ( times_times @ nat @ ( zero_zero @ nat ) @ N )
% 2.46/1.50 = ( zero_zero @ nat ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_81_Suc__mult__cancel1,axiom,
% 2.46/1.50 ! [K: nat,M: nat,N: nat] :
% 2.46/1.50 ( ( ( times_times @ nat @ ( suc @ K ) @ M )
% 2.46/1.50 = ( times_times @ nat @ ( suc @ K ) @ N ) )
% 2.46/1.50 = ( M = N ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_82_div__mult2__eq,axiom,
% 2.46/1.50 ! [M: nat,N: nat,Q: nat] :
% 2.46/1.50 ( ( divide_divide @ nat @ M @ ( times_times @ nat @ N @ Q ) )
% 2.46/1.50 = ( divide_divide @ nat @ ( divide_divide @ nat @ M @ N ) @ Q ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_83_lift__Suc__mono__less__iff,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( order @ A )
% 2.46/1.50 => ! [F: nat > A,N: nat,M: nat] :
% 2.46/1.50 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.46/1.50 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 2.46/1.50 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_84_lift__Suc__mono__less,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( order @ A )
% 2.46/1.50 => ! [F: nat > A,N: nat,N3: nat] :
% 2.46/1.50 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.46/1.50 => ( ( ord_less @ nat @ N @ N3 )
% 2.46/1.50 => ( ord_less @ A @ ( F @ N ) @ ( F @ N3 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_85_less__Suc__eq__0__disj,axiom,
% 2.46/1.50 ! [M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.46/1.50 = ( ( M
% 2.46/1.50 = ( zero_zero @ nat ) )
% 2.46/1.50 | ? [J3: nat] :
% 2.46/1.50 ( ( M
% 2.46/1.50 = ( suc @ J3 ) )
% 2.46/1.50 & ( ord_less @ nat @ J3 @ N ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_86_gr0__implies__Suc,axiom,
% 2.46/1.50 ! [N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.46/1.50 => ? [M3: nat] :
% 2.46/1.50 ( N
% 2.46/1.50 = ( suc @ M3 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_87_All__less__Suc2,axiom,
% 2.46/1.50 ! [N: nat,P: nat > $o] :
% 2.46/1.50 ( ( ! [I3: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I3 @ ( suc @ N ) )
% 2.46/1.50 => ( P @ I3 ) ) )
% 2.46/1.50 = ( ( P @ ( zero_zero @ nat ) )
% 2.46/1.50 & ! [I3: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I3 @ N )
% 2.46/1.50 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_88_gr0__conv__Suc,axiom,
% 2.46/1.50 ! [N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.46/1.50 = ( ? [M5: nat] :
% 2.46/1.50 ( N
% 2.46/1.50 = ( suc @ M5 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_89_Ex__less__Suc2,axiom,
% 2.46/1.50 ! [N: nat,P: nat > $o] :
% 2.46/1.50 ( ( ? [I3: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I3 @ ( suc @ N ) )
% 2.46/1.50 & ( P @ I3 ) ) )
% 2.46/1.50 = ( ( P @ ( zero_zero @ nat ) )
% 2.46/1.50 | ? [I3: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I3 @ N )
% 2.46/1.50 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_90_nat__mult__less__cancel1,axiom,
% 2.46/1.50 ! [K: nat,M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.46/1.50 => ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.46/1.50 = ( ord_less @ nat @ M @ N ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_91_nat__mult__eq__cancel1,axiom,
% 2.46/1.50 ! [K: nat,M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.46/1.50 => ( ( ( times_times @ nat @ K @ M )
% 2.46/1.50 = ( times_times @ nat @ K @ N ) )
% 2.46/1.50 = ( M = N ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_92_mult__less__mono2,axiom,
% 2.46/1.50 ! [I: nat,J: nat,K: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I @ J )
% 2.46/1.50 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.46/1.50 => ( ord_less @ nat @ ( times_times @ nat @ K @ I ) @ ( times_times @ nat @ K @ J ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_93_mult__less__mono1,axiom,
% 2.46/1.50 ! [I: nat,J: nat,K: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ I @ J )
% 2.46/1.50 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.46/1.50 => ( ord_less @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ K ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_94_Suc__mult__less__cancel1,axiom,
% 2.46/1.50 ! [K: nat,M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( times_times @ nat @ ( suc @ K ) @ M ) @ ( times_times @ nat @ ( suc @ K ) @ N ) )
% 2.46/1.50 = ( ord_less @ nat @ M @ N ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_95_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 2.46/1.50 ! [M: nat,N: nat] :
% 2.46/1.50 ( ( ( divide_divide @ nat @ M @ N )
% 2.46/1.50 = ( zero_zero @ nat ) )
% 2.46/1.50 = ( ( ord_less @ nat @ M @ N )
% 2.46/1.50 | ( N
% 2.46/1.50 = ( zero_zero @ nat ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_96_Euclidean__Division_Oless__mult__imp__div__less,axiom,
% 2.46/1.50 ! [M: nat,I: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ M @ ( times_times @ nat @ I @ N ) )
% 2.46/1.50 => ( ord_less @ nat @ ( divide_divide @ nat @ M @ N ) @ I ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_97_n__less__n__mult__m,axiom,
% 2.46/1.50 ! [N: nat,M: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.46/1.50 => ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ M )
% 2.46/1.50 => ( ord_less @ nat @ N @ ( times_times @ nat @ N @ M ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_98_n__less__m__mult__n,axiom,
% 2.46/1.50 ! [N: nat,M: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.46/1.50 => ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ M )
% 2.46/1.50 => ( ord_less @ nat @ N @ ( times_times @ nat @ M @ N ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_99_one__less__mult,axiom,
% 2.46/1.50 ! [N: nat,M: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ N )
% 2.46/1.50 => ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ M )
% 2.46/1.50 => ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( times_times @ nat @ M @ N ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_100_nat__mult__div__cancel1,axiom,
% 2.46/1.50 ! [K: nat,M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.46/1.50 => ( ( divide_divide @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.46/1.50 = ( divide_divide @ nat @ M @ N ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_101_nonzero__mult__divide__mult__cancel__right2,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( C
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ C @ B2 ) )
% 2.46/1.50 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_102_nonzero__mult__div__cancel__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semidom_divide @ A )
% 2.46/1.50 => ! [B2: A,A2: A] :
% 2.46/1.50 ( ( B2
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ B2 ) @ B2 )
% 2.46/1.50 = A2 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_103_nonzero__mult__divide__mult__cancel__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( C
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) )
% 2.46/1.50 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_104_nonzero__mult__divide__mult__cancel__left2,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( C
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ B2 @ C ) )
% 2.46/1.50 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_105_nonzero__mult__div__cancel__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semidom_divide @ A )
% 2.46/1.50 => ! [A2: A,B2: A] :
% 2.46/1.50 ( ( A2
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( divide_divide @ A @ ( times_times @ A @ A2 @ B2 ) @ A2 )
% 2.46/1.50 = B2 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_106_nonzero__mult__divide__mult__cancel__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( C
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.46/1.50 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_107_mult__divide__mult__cancel__left__if,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( ( C
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.46/1.50 = ( zero_zero @ A ) ) )
% 2.46/1.50 & ( ( C
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( divide_divide @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.46/1.50 = ( divide_divide @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_108_less__div__Suc__mult,axiom,
% 2.46/1.50 ! [M: nat,N: nat] :
% 2.46/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.46/1.50 => ( ord_less @ nat @ N @ ( times_times @ nat @ ( suc @ ( divide_divide @ nat @ N @ M ) ) @ M ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_109_times__divide__eq__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( division_ring @ A )
% 2.46/1.50 => ! [A2: A,B2: A,C: A] :
% 2.46/1.50 ( ( times_times @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 2.46/1.50 = ( divide_divide @ A @ ( times_times @ A @ A2 @ B2 ) @ C ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_110_divide__divide__eq__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [A2: A,B2: A,C: A] :
% 2.46/1.50 ( ( divide_divide @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 2.46/1.50 = ( divide_divide @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_111_divide__divide__eq__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [A2: A,B2: A,C: A] :
% 2.46/1.50 ( ( divide_divide @ A @ ( divide_divide @ A @ A2 @ B2 ) @ C )
% 2.46/1.50 = ( divide_divide @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_112_mult__zero__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( mult_zero @ A )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( times_times @ A @ ( zero_zero @ A ) @ A2 )
% 2.46/1.50 = ( zero_zero @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_113_mult__zero__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( mult_zero @ A )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 2.46/1.50 = ( zero_zero @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_114_mult__eq__0__iff,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semiri1193490041visors @ A )
% 2.46/1.50 => ! [A2: A,B2: A] :
% 2.46/1.50 ( ( ( times_times @ A @ A2 @ B2 )
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 = ( ( A2
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 | ( B2
% 2.46/1.50 = ( zero_zero @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_115_mult__cancel__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semiri1923998003cancel @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( ( times_times @ A @ C @ A2 )
% 2.46/1.50 = ( times_times @ A @ C @ B2 ) )
% 2.46/1.50 = ( ( C
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 | ( A2 = B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_116_mult__cancel__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semiri1923998003cancel @ A )
% 2.46/1.50 => ! [A2: A,C: A,B2: A] :
% 2.46/1.50 ( ( ( times_times @ A @ A2 @ C )
% 2.46/1.50 = ( times_times @ A @ B2 @ C ) )
% 2.46/1.50 = ( ( C
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 | ( A2 = B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_117_div__0,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semidom_divide @ A )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
% 2.46/1.50 = ( zero_zero @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_118_divide__eq__0__iff,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [A2: A,B2: A] :
% 2.46/1.50 ( ( ( divide_divide @ A @ A2 @ B2 )
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 = ( ( A2
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 | ( B2
% 2.46/1.50 = ( zero_zero @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_119_div__by__0,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semidom_divide @ A )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 2.46/1.50 = ( zero_zero @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_120_divide__cancel__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( ( divide_divide @ A @ C @ A2 )
% 2.46/1.50 = ( divide_divide @ A @ C @ B2 ) )
% 2.46/1.50 = ( ( C
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 | ( A2 = B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_121_divide__cancel__right,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [A2: A,C: A,B2: A] :
% 2.46/1.50 ( ( ( divide_divide @ A @ A2 @ C )
% 2.46/1.50 = ( divide_divide @ A @ B2 @ C ) )
% 2.46/1.50 = ( ( C
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 | ( A2 = B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_122_division__ring__divide__zero,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( division_ring @ A )
% 2.46/1.50 => ! [A2: A] :
% 2.46/1.50 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 2.46/1.50 = ( zero_zero @ A ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_123_times__divide__eq__left,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [B2: A,C: A,A2: A] :
% 2.46/1.50 ( ( times_times @ A @ ( divide_divide @ A @ B2 @ C ) @ A2 )
% 2.46/1.50 = ( divide_divide @ A @ ( times_times @ A @ B2 @ A2 ) @ C ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_124_linordered__field__no__lb,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( linordered_field @ A )
% 2.46/1.50 => ! [X4: A] :
% 2.46/1.50 ? [Y4: A] : ( ord_less @ A @ Y4 @ X4 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_125_linordered__field__no__ub,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( linordered_field @ A )
% 2.46/1.50 => ! [X4: A] :
% 2.46/1.50 ? [X_1: A] : ( ord_less @ A @ X4 @ X_1 ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_126_linorder__neqE__linordered__idom,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( linordered_idom @ A )
% 2.46/1.50 => ! [X3: A,Y3: A] :
% 2.46/1.50 ( ( X3 != Y3 )
% 2.46/1.50 => ( ~ ( ord_less @ A @ X3 @ Y3 )
% 2.46/1.50 => ( ord_less @ A @ Y3 @ X3 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_127_mult__not__zero,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( mult_zero @ A )
% 2.46/1.50 => ! [A2: A,B2: A] :
% 2.46/1.50 ( ( ( times_times @ A @ A2 @ B2 )
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( A2
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 & ( B2
% 2.46/1.50 != ( zero_zero @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_128_divisors__zero,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semiri1193490041visors @ A )
% 2.46/1.50 => ! [A2: A,B2: A] :
% 2.46/1.50 ( ( ( times_times @ A @ A2 @ B2 )
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 => ( ( A2
% 2.46/1.50 = ( zero_zero @ A ) )
% 2.46/1.50 | ( B2
% 2.46/1.50 = ( zero_zero @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_129_no__zero__divisors,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semiri1193490041visors @ A )
% 2.46/1.50 => ! [A2: A,B2: A] :
% 2.46/1.50 ( ( A2
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( B2
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( times_times @ A @ A2 @ B2 )
% 2.46/1.50 != ( zero_zero @ A ) ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_130_mult__left__cancel,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semiri1923998003cancel @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( C
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( ( times_times @ A @ C @ A2 )
% 2.46/1.50 = ( times_times @ A @ C @ B2 ) )
% 2.46/1.50 = ( A2 = B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_131_mult__right__cancel,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( semiri1923998003cancel @ A )
% 2.46/1.50 => ! [C: A,A2: A,B2: A] :
% 2.46/1.50 ( ( C
% 2.46/1.50 != ( zero_zero @ A ) )
% 2.46/1.50 => ( ( ( times_times @ A @ A2 @ C )
% 2.46/1.50 = ( times_times @ A @ B2 @ C ) )
% 2.46/1.50 = ( A2 = B2 ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_132_times__divide__times__eq,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [X3: A,Y3: A,Z: A,W: A] :
% 2.46/1.50 ( ( times_times @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( divide_divide @ A @ Z @ W ) )
% 2.46/1.50 = ( divide_divide @ A @ ( times_times @ A @ X3 @ Z ) @ ( times_times @ A @ Y3 @ W ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_133_divide__divide__times__eq,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( field @ A )
% 2.46/1.50 => ! [X3: A,Y3: A,Z: A,W: A] :
% 2.46/1.50 ( ( divide_divide @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( divide_divide @ A @ Z @ W ) )
% 2.46/1.50 = ( divide_divide @ A @ ( times_times @ A @ X3 @ W ) @ ( times_times @ A @ Y3 @ Z ) ) ) ) ).
% 2.46/1.50
% 2.46/1.50 thf(fact_134_divide__divide__eq__left_H,axiom,
% 2.46/1.50 ! [A: $tType] :
% 2.46/1.50 ( ( division_ring @ A )
% 2.46/1.50 => ! [A2: A,B2: A,C: A] :
% 2.46/1.50 ( ( divide_divide @ A @ ( divide_divide @ A @ A2 @ B2 ) @ C )
% 2.68/1.50 = ( divide_divide @ A @ A2 @ ( times_times @ A @ C @ B2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_135_mult__neg__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_136_not__square__less__zero,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_ring @ A )
% 2.68/1.50 => ! [A2: A] :
% 2.68/1.50 ~ ( ord_less @ A @ ( times_times @ A @ A2 @ A2 ) @ ( zero_zero @ A ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_137_mult__less__0__iff,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.68/1.50 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_138_mult__neg__pos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord20386208strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_139_mult__pos__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord20386208strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_140_mult__pos__pos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord20386208strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 2.68/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_141_mult__pos__neg2,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord20386208strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ B2 @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_142_zero__less__mult__iff,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.68/1.50 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_143_zero__less__mult__pos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord20386208strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_144_zero__less__mult__pos2,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord20386208strict @ A )
% 2.68/1.50 => ! [B2: A,A2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B2 @ A2 ) )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_145_mult__less__cancel__left__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [C: A,A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.68/1.50 = ( ord_less @ A @ B2 @ A2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_146_mult__less__cancel__left__pos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [C: A,A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.68/1.50 = ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_147_mult__strict__left__mono__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [B2: A,A2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ B2 @ A2 )
% 2.68/1.50 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_148_mult__strict__left__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord20386208strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_149_mult__less__cancel__left__disj,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [C: A,A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 & ( ord_less @ A @ A2 @ B2 ) )
% 2.68/1.50 | ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less @ A @ B2 @ A2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_150_mult__strict__right__mono__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [B2: A,A2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ B2 @ A2 )
% 2.68/1.50 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_151_mult__strict__right__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord20386208strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_152_mult__less__cancel__right__disj,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [A2: A,C: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 & ( ord_less @ A @ A2 @ B2 ) )
% 2.68/1.50 | ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less @ A @ B2 @ A2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_153_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord893533164strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_154_divide__neg__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less @ A @ X3 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less @ A @ Y3 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_155_divide__neg__pos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less @ A @ X3 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ Y3 )
% 2.68/1.50 => ( ord_less @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_156_divide__pos__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ X3 )
% 2.68/1.50 => ( ( ord_less @ A @ Y3 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_157_divide__pos__pos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ X3 )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ Y3 )
% 2.68/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_158_divide__less__0__iff,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( divide_divide @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.68/1.50 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_159_divide__less__cancel,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,C: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( divide_divide @ A @ A2 @ C ) @ ( divide_divide @ A @ B2 @ C ) )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less @ A @ A2 @ B2 ) )
% 2.68/1.50 & ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ B2 @ A2 ) )
% 2.68/1.50 & ( C
% 2.68/1.50 != ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_160_zero__less__divide__iff,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ A2 @ B2 ) )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.68/1.50 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_161_divide__strict__right__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less @ A @ ( divide_divide @ A @ A2 @ C ) @ ( divide_divide @ A @ B2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_162_divide__strict__right__mono__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [B2: A,A2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ B2 @ A2 )
% 2.68/1.50 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( divide_divide @ A @ A2 @ C ) @ ( divide_divide @ A @ B2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_163_frac__eq__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( field @ A )
% 2.68/1.50 => ! [Y3: A,Z: A,X3: A,W: A] :
% 2.68/1.50 ( ( Y3
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( ( Z
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ( divide_divide @ A @ X3 @ Y3 )
% 2.68/1.50 = ( divide_divide @ A @ W @ Z ) )
% 2.68/1.50 = ( ( times_times @ A @ X3 @ Z )
% 2.68/1.50 = ( times_times @ A @ W @ Y3 ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_164_divide__eq__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( division_ring @ A )
% 2.68/1.50 => ! [B2: A,C: A,A2: A] :
% 2.68/1.50 ( ( ( divide_divide @ A @ B2 @ C )
% 2.68/1.50 = A2 )
% 2.68/1.50 = ( ( ( C
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( B2
% 2.68/1.50 = ( times_times @ A @ A2 @ C ) ) )
% 2.68/1.50 & ( ( C
% 2.68/1.50 = ( zero_zero @ A ) )
% 2.68/1.50 => ( A2
% 2.68/1.50 = ( zero_zero @ A ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_165_eq__divide__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( division_ring @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( A2
% 2.68/1.50 = ( divide_divide @ A @ B2 @ C ) )
% 2.68/1.50 = ( ( ( C
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( ( times_times @ A @ A2 @ C )
% 2.68/1.50 = B2 ) )
% 2.68/1.50 & ( ( C
% 2.68/1.50 = ( zero_zero @ A ) )
% 2.68/1.50 => ( A2
% 2.68/1.50 = ( zero_zero @ A ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_166_divide__eq__imp,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( division_ring @ A )
% 2.68/1.50 => ! [C: A,B2: A,A2: A] :
% 2.68/1.50 ( ( C
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( ( B2
% 2.68/1.50 = ( times_times @ A @ A2 @ C ) )
% 2.68/1.50 => ( ( divide_divide @ A @ B2 @ C )
% 2.68/1.50 = A2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_167_eq__divide__imp,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( division_ring @ A )
% 2.68/1.50 => ! [C: A,A2: A,B2: A] :
% 2.68/1.50 ( ( C
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ( times_times @ A @ A2 @ C )
% 2.68/1.50 = B2 )
% 2.68/1.50 => ( A2
% 2.68/1.50 = ( divide_divide @ A @ B2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_168_nonzero__divide__eq__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( division_ring @ A )
% 2.68/1.50 => ! [C: A,B2: A,A2: A] :
% 2.68/1.50 ( ( C
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ( divide_divide @ A @ B2 @ C )
% 2.68/1.50 = A2 )
% 2.68/1.50 = ( B2
% 2.68/1.50 = ( times_times @ A @ A2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_169_nonzero__eq__divide__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( division_ring @ A )
% 2.68/1.50 => ! [C: A,A2: A,B2: A] :
% 2.68/1.50 ( ( C
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( ( A2
% 2.68/1.50 = ( divide_divide @ A @ B2 @ C ) )
% 2.68/1.50 = ( ( times_times @ A @ A2 @ C )
% 2.68/1.50 = B2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_170_div__eq__0__conv,axiom,
% 2.68/1.50 ! [N: nat,M: nat] :
% 2.68/1.50 ( ( ( divide_divide @ nat @ N @ M )
% 2.68/1.50 = ( zero_zero @ nat ) )
% 2.68/1.50 = ( ( M
% 2.68/1.50 = ( zero_zero @ nat ) )
% 2.68/1.50 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_171_div__eq__0__conv_H,axiom,
% 2.68/1.50 ! [M: nat,N: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.68/1.50 => ( ( ( divide_divide @ nat @ N @ M )
% 2.68/1.50 = ( zero_zero @ nat ) )
% 2.68/1.50 = ( ord_less @ nat @ N @ M ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_172_Util__Div_Oless__mult__imp__div__less,axiom,
% 2.68/1.50 ! [N: nat,K: nat,M: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ N @ ( times_times @ nat @ K @ M ) )
% 2.68/1.50 => ( ord_less @ nat @ ( divide_divide @ nat @ N @ M ) @ K ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_173_divide__less__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [B2: A,C: A,A2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C ) @ A2 )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less @ A @ B2 @ ( times_times @ A @ A2 @ C ) ) )
% 2.68/1.50 & ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) )
% 2.68/1.50 & ( ~ ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_174_less__divide__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 2.68/1.50 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) )
% 2.68/1.50 & ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ B2 @ ( times_times @ A @ A2 @ C ) ) )
% 2.68/1.50 & ( ~ ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_175_neg__divide__less__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [C: A,B2: A,A2: A] :
% 2.68/1.50 ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C ) @ A2 )
% 2.68/1.50 = ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_176_neg__less__divide__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [C: A,A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 2.68/1.50 = ( ord_less @ A @ B2 @ ( times_times @ A @ A2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_177_pos__divide__less__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [C: A,B2: A,A2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ( ord_less @ A @ ( divide_divide @ A @ B2 @ C ) @ A2 )
% 2.68/1.50 = ( ord_less @ A @ B2 @ ( times_times @ A @ A2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_178_pos__less__divide__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [C: A,A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ( ord_less @ A @ A2 @ ( divide_divide @ A @ B2 @ C ) )
% 2.68/1.50 = ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ B2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_179_mult__imp__div__pos__less,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [Y3: A,X3: A,Z: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ Y3 )
% 2.68/1.50 => ( ( ord_less @ A @ X3 @ ( times_times @ A @ Z @ Y3 ) )
% 2.68/1.50 => ( ord_less @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ Z ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_180_mult__imp__less__div__pos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [Y3: A,Z: A,X3: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ Y3 )
% 2.68/1.50 => ( ( ord_less @ A @ ( times_times @ A @ Z @ Y3 ) @ X3 )
% 2.68/1.50 => ( ord_less @ A @ Z @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_181_divide__strict__left__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [B2: A,A2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ B2 @ A2 )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 2.68/1.50 => ( ord_less @ A @ ( divide_divide @ A @ C @ A2 ) @ ( divide_divide @ A @ C @ B2 ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_182_divide__strict__left__mono__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 2.68/1.50 => ( ord_less @ A @ ( divide_divide @ A @ C @ A2 ) @ ( divide_divide @ A @ C @ B2 ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_183_div__less__conv,axiom,
% 2.68/1.50 ! [M: nat,N: nat,K: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.68/1.50 => ( ( ord_less @ nat @ ( divide_divide @ nat @ N @ M ) @ K )
% 2.68/1.50 = ( ord_less @ nat @ N @ ( times_times @ nat @ K @ M ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_184_div__less__imp__less__mult,axiom,
% 2.68/1.50 ! [M: nat,N: nat,K: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.68/1.50 => ( ( ord_less @ nat @ ( divide_divide @ nat @ N @ M ) @ K )
% 2.68/1.50 => ( ord_less @ nat @ N @ ( times_times @ nat @ K @ M ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_185_bits__div__0,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( semiring_bits @ A )
% 2.68/1.50 => ! [A2: A] :
% 2.68/1.50 ( ( divide_divide @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 = ( zero_zero @ A ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_186_bits__div__by__0,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( semiring_bits @ A )
% 2.68/1.50 => ! [A2: A] :
% 2.68/1.50 ( ( divide_divide @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 = ( zero_zero @ A ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_187_not__gr__zero,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( canoni770627133id_add @ A )
% 2.68/1.50 => ! [N: A] :
% 2.68/1.50 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.68/1.50 = ( N
% 2.68/1.50 = ( zero_zero @ A ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_188_mult__cancel2__gr0,axiom,
% 2.68/1.50 ! [K: nat,M: nat,N: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.68/1.50 => ( ( ( times_times @ nat @ M @ K )
% 2.68/1.50 = ( times_times @ nat @ N @ K ) )
% 2.68/1.50 = ( M = N ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_189_zero__reorient,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( zero @ A )
% 2.68/1.50 => ! [X3: A] :
% 2.68/1.50 ( ( ( zero_zero @ A )
% 2.68/1.50 = X3 )
% 2.68/1.50 = ( X3
% 2.68/1.50 = ( zero_zero @ A ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_190_mult_Oleft__commute,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ab_semigroup_mult @ A )
% 2.68/1.50 => ! [B2: A,A2: A,C: A] :
% 2.68/1.50 ( ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ C ) )
% 2.68/1.50 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_191_mult_Ocommute,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ab_semigroup_mult @ A )
% 2.68/1.50 => ( ( times_times @ A )
% 2.68/1.50 = ( ^ [A3: A,B3: A] : ( times_times @ A @ B3 @ A3 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_192_mult_Oassoc,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( semigroup_mult @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 2.68/1.50 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_193_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ab_semigroup_mult @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 2.68/1.50 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_194_zero__less__iff__neq__zero,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( canoni770627133id_add @ A )
% 2.68/1.50 => ! [N: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.68/1.50 = ( N
% 2.68/1.50 != ( zero_zero @ A ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_195_gr__implies__not__zero,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( canoni770627133id_add @ A )
% 2.68/1.50 => ! [M: A,N: A] :
% 2.68/1.50 ( ( ord_less @ A @ M @ N )
% 2.68/1.50 => ( N
% 2.68/1.50 != ( zero_zero @ A ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_196_not__less__zero,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( canoni770627133id_add @ A )
% 2.68/1.50 => ! [N: A] :
% 2.68/1.50 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_197_gr__zeroI,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( canoni770627133id_add @ A )
% 2.68/1.50 => ! [N: A] :
% 2.68/1.50 ( ( N
% 2.68/1.50 != ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_198_gr__implies__gr0,axiom,
% 2.68/1.50 ! [M: nat,N: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ M @ N )
% 2.68/1.50 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_199_nat__lessSucSuc0__conv,axiom,
% 2.68/1.50 ! [N: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ N @ ( suc @ ( suc @ ( zero_zero @ nat ) ) ) )
% 2.68/1.50 = ( ( N
% 2.68/1.50 = ( zero_zero @ nat ) )
% 2.68/1.50 | ( N
% 2.68/1.50 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_200_nat__grSuc0__conv,axiom,
% 2.68/1.50 ! [N: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ N )
% 2.68/1.50 = ( ( N
% 2.68/1.50 != ( zero_zero @ nat ) )
% 2.68/1.50 & ( N
% 2.68/1.50 != ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_201_mult__less__iff1,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_idom @ A )
% 2.68/1.50 => ! [Z: A,X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ Z )
% 2.68/1.50 => ( ( ord_less @ A @ ( times_times @ A @ X3 @ Z ) @ ( times_times @ A @ Y3 @ Z ) )
% 2.68/1.50 = ( ord_less @ A @ X3 @ Y3 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_202_length__induct,axiom,
% 2.68/1.50 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.68/1.50 ( ! [Xs2: list @ A] :
% 2.68/1.50 ( ! [Ys: list @ A] :
% 2.68/1.50 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 2.68/1.50 => ( P @ Ys ) )
% 2.68/1.50 => ( P @ Xs2 ) )
% 2.68/1.50 => ( P @ Xs ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_203_Ex__list__of__length,axiom,
% 2.68/1.50 ! [A: $tType,N: nat] :
% 2.68/1.50 ? [Xs2: list @ A] :
% 2.68/1.50 ( ( size_size @ ( list @ A ) @ Xs2 )
% 2.68/1.50 = N ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_204_neq__if__length__neq,axiom,
% 2.68/1.50 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.68/1.50 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.68/1.50 != ( size_size @ ( list @ A ) @ Ys2 ) )
% 2.68/1.50 => ( Xs != Ys2 ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_205_list__decode_Ocases,axiom,
% 2.68/1.50 ! [X3: nat] :
% 2.68/1.50 ( ( X3
% 2.68/1.50 != ( zero_zero @ nat ) )
% 2.68/1.50 => ~ ! [N2: nat] :
% 2.68/1.50 ( X3
% 2.68/1.50 != ( suc @ N2 ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_206_dependent__nat__choice,axiom,
% 2.68/1.50 ! [A: $tType,P: nat > A > $o,Q2: nat > A > A > $o] :
% 2.68/1.50 ( ? [X_12: A] : ( P @ ( zero_zero @ nat ) @ X_12 )
% 2.68/1.50 => ( ! [X: A,N2: nat] :
% 2.68/1.50 ( ( P @ N2 @ X )
% 2.68/1.50 => ? [Y: A] :
% 2.68/1.50 ( ( P @ ( suc @ N2 ) @ Y )
% 2.68/1.50 & ( Q2 @ N2 @ X @ Y ) ) )
% 2.68/1.50 => ? [F2: nat > A] :
% 2.68/1.50 ! [N4: nat] :
% 2.68/1.50 ( ( P @ N4 @ ( F2 @ N4 ) )
% 2.68/1.50 & ( Q2 @ N4 @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_207_exists__least__lemma,axiom,
% 2.68/1.50 ! [P: nat > $o] :
% 2.68/1.50 ( ~ ( P @ ( zero_zero @ nat ) )
% 2.68/1.50 => ( ? [X_12: nat] : ( P @ X_12 )
% 2.68/1.50 => ? [N2: nat] :
% 2.68/1.50 ( ~ ( P @ N2 )
% 2.68/1.50 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_208_field__lbound__gt__zero,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [D1: A,D2: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ D1 )
% 2.68/1.50 => ( ( ord_less @ A @ ( zero_zero @ A ) @ D2 )
% 2.68/1.50 => ? [E: A] :
% 2.68/1.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ E )
% 2.68/1.50 & ( ord_less @ A @ E @ D1 )
% 2.68/1.50 & ( ord_less @ A @ E @ D2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_209_less__numeral__extra_I3_J,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord1659791738miring @ A )
% 2.68/1.50 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_210_length__product,axiom,
% 2.68/1.50 ! [A: $tType,B: $tType,Xs: list @ A,Ys2: list @ B] :
% 2.68/1.50 ( ( size_size @ ( list @ ( product_prod @ A @ B ) ) @ ( product @ A @ B @ Xs @ Ys2 ) )
% 2.68/1.50 = ( times_times @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( size_size @ ( list @ B ) @ Ys2 ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_211_split__div_H,axiom,
% 2.68/1.50 ! [P: nat > $o,M: nat,N: nat] :
% 2.68/1.50 ( ( P @ ( divide_divide @ nat @ M @ N ) )
% 2.68/1.50 = ( ( ( N
% 2.68/1.50 = ( zero_zero @ nat ) )
% 2.68/1.50 & ( P @ ( zero_zero @ nat ) ) )
% 2.68/1.50 | ? [Q3: nat] :
% 2.68/1.50 ( ( ord_less_eq @ nat @ ( times_times @ nat @ N @ Q3 ) @ M )
% 2.68/1.50 & ( ord_less @ nat @ M @ ( times_times @ nat @ N @ ( suc @ Q3 ) ) )
% 2.68/1.50 & ( P @ Q3 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_212_le__less__div__conv,axiom,
% 2.68/1.50 ! [M: nat,K: nat,N: nat] :
% 2.68/1.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.68/1.50 => ( ( ( ord_less_eq @ nat @ ( times_times @ nat @ K @ M ) @ N )
% 2.68/1.50 & ( ord_less @ nat @ N @ ( times_times @ nat @ ( suc @ K ) @ M ) ) )
% 2.68/1.50 = ( ( divide_divide @ nat @ N @ M )
% 2.68/1.50 = K ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_213_le__zero__eq,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( canoni770627133id_add @ A )
% 2.68/1.50 => ! [N: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.68/1.50 = ( N
% 2.68/1.50 = ( zero_zero @ A ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_214_bot__nat__0_Oextremum,axiom,
% 2.68/1.50 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_215_le0,axiom,
% 2.68/1.50 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_216_Suc__le__mono,axiom,
% 2.68/1.50 ! [N: nat,M: nat] :
% 2.68/1.50 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 2.68/1.50 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_217_one__le__mult__iff,axiom,
% 2.68/1.50 ! [M: nat,N: nat] :
% 2.68/1.50 ( ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( times_times @ nat @ M @ N ) )
% 2.68/1.50 = ( ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ M )
% 2.68/1.50 & ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ N ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_218_mult__le__cancel2,axiom,
% 2.68/1.50 ! [M: nat,K: nat,N: nat] :
% 2.68/1.50 ( ( ord_less_eq @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 2.68/1.50 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.68/1.50 => ( ord_less_eq @ nat @ M @ N ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_219_nat__mult__le__cancel__disj,axiom,
% 2.68/1.50 ! [K: nat,M: nat,N: nat] :
% 2.68/1.50 ( ( ord_less_eq @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.68/1.50 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.68/1.50 => ( ord_less_eq @ nat @ M @ N ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_220_le__numeral__extra_I3_J,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord1659791738miring @ A )
% 2.68/1.50 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_221_zero__le,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( canoni770627133id_add @ A )
% 2.68/1.50 => ! [X3: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_222_ge__less__neq__conv,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linorder @ A )
% 2.68/1.50 => ( ( ord_less_eq @ A )
% 2.68/1.50 = ( ^ [A3: A,N5: A] :
% 2.68/1.50 ! [X5: A] :
% 2.68/1.50 ( ( ord_less @ A @ X5 @ A3 )
% 2.68/1.50 => ( N5 != X5 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_223_less__ge__neq__conv,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linorder @ A )
% 2.68/1.50 => ( ( ord_less @ A )
% 2.68/1.50 = ( ^ [N5: A,A3: A] :
% 2.68/1.50 ! [X5: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A3 @ X5 )
% 2.68/1.50 => ( N5 != X5 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_224_greater__le__neq__conv,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linorder @ A )
% 2.68/1.50 => ( ( ord_less @ A )
% 2.68/1.50 = ( ^ [A3: A,N5: A] :
% 2.68/1.50 ! [X5: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ X5 @ A3 )
% 2.68/1.50 => ( N5 != X5 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_225_le__greater__neq__conv,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linorder @ A )
% 2.68/1.50 => ( ( ord_less_eq @ A )
% 2.68/1.50 = ( ^ [N5: A,A3: A] :
% 2.68/1.50 ! [X5: A] :
% 2.68/1.50 ( ( ord_less @ A @ A3 @ X5 )
% 2.68/1.50 => ( N5 != X5 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_226_nat__geSucSuc0__conv,axiom,
% 2.68/1.50 ! [N: nat] :
% 2.68/1.50 ( ( ord_less_eq @ nat @ ( suc @ ( suc @ ( zero_zero @ nat ) ) ) @ N )
% 2.68/1.50 = ( ( N
% 2.68/1.50 != ( zero_zero @ nat ) )
% 2.68/1.50 & ( N
% 2.68/1.50 != ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_227_nat__leSuc0__conv,axiom,
% 2.68/1.50 ! [N: nat] :
% 2.68/1.50 ( ( ord_less_eq @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) )
% 2.68/1.50 = ( ( N
% 2.68/1.50 = ( zero_zero @ nat ) )
% 2.68/1.50 | ( N
% 2.68/1.50 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_228_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordere1490568538miring @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_229_zero__le__mult__iff,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) )
% 2.68/1.50 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.68/1.50 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_230_mult__nonneg__nonpos2,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring_0 @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ B2 @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_231_mult__nonpos__nonneg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring_0 @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_232_mult__nonneg__nonpos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring_0 @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_233_mult__nonneg__nonneg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring_0 @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.68/1.50 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_234_split__mult__neg__le,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring_0 @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.68/1.50 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_235_mult__le__0__iff,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linord581940658strict @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( times_times @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 2.68/1.50 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.68/1.50 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_236_mult__right__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_237_mult__right__mono__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_ring @ A )
% 2.68/1.50 => ! [B2: A,A2: A,C: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_238_mult__left__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_239_mult__nonpos__nonpos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_ring @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_240_mult__left__mono__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_ring @ A )
% 2.68/1.50 => ! [B2: A,A2: A,C: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_241_split__mult__pos__le,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_ring @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.68/1.50 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B2 ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_242_zero__le__square,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_ring @ A )
% 2.68/1.50 => ! [A2: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ A2 ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_243_mult__mono_H,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A,D: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ C @ D )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_244_mult__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( ordered_semiring @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A,D: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ C @ D )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less_eq @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_245_divide__right__mono__neg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( divide_divide @ A @ B2 @ C ) @ ( divide_divide @ A @ A2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_246_divide__nonpos__nonpos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ X3 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less_eq @ A @ Y3 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_247_divide__nonpos__nonneg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ X3 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y3 )
% 2.68/1.50 => ( ord_less_eq @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_248_divide__nonneg__nonpos,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ Y3 @ ( zero_zero @ A ) )
% 2.68/1.50 => ( ord_less_eq @ A @ ( divide_divide @ A @ X3 @ Y3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_249_divide__nonneg__nonneg,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [X3: A,Y3: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y3 )
% 2.68/1.50 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ X3 @ Y3 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_250_zero__le__divide__iff,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( divide_divide @ A @ A2 @ B2 ) )
% 2.68/1.50 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 2.68/1.50 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_251_divide__right__mono,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A,C: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.68/1.50 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 2.68/1.50 => ( ord_less_eq @ A @ ( divide_divide @ A @ A2 @ C ) @ ( divide_divide @ A @ B2 @ C ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(fact_252_divide__le__0__iff,axiom,
% 2.68/1.50 ! [A: $tType] :
% 2.68/1.50 ( ( linordered_field @ A )
% 2.68/1.50 => ! [A2: A,B2: A] :
% 2.68/1.50 ( ( ord_less_eq @ A @ ( divide_divide @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 2.68/1.50 = ( ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 2.68/1.50 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 2.68/1.50 | ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 2.68/1.50 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.68/1.50 ! [A4: $tType,A5: $tType] :
% 2.68/1.50 ( ( order @ A5 )
% 2.68/1.50 => ( order @ ( A4 > A5 ) ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Euclidean__Division_Oeuclidean__semiring__cancel,axiom,
% 2.68/1.50 euclid191655569cancel @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 2.68/1.50 semiri1923998003cancel @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict,axiom,
% 2.68/1.50 linord893533164strict @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.68/1.50 canoni770627133id_add @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 2.68/1.50 linord1659791738miring @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__semiring__strict,axiom,
% 2.68/1.50 linord20386208strict @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors,axiom,
% 2.68/1.50 semiri1193490041visors @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Oordered__comm__semiring,axiom,
% 2.68/1.50 ordere1490568538miring @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Oordered__semiring__0,axiom,
% 2.68/1.50 ordered_semiring_0 @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 2.68/1.50 ab_semigroup_mult @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Oordered__semiring,axiom,
% 2.68/1.50 ordered_semiring @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 2.68/1.50 semigroup_mult @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Osemidom__divide,axiom,
% 2.68/1.50 semidom_divide @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Parity_Osemiring__bits,axiom,
% 2.68/1.50 semiring_bits @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.68/1.50 wellorder @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.68/1.50 linorder @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Rings_Omult__zero,axiom,
% 2.68/1.50 mult_zero @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 2.68/1.50 order @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.68/1.50 zero @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 2.68/1.50 size @ nat ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder_2,axiom,
% 2.68/1.50 linorder @ $o ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 2.68/1.50 order @ $o ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_List_Olist___Nat_Osize_4,axiom,
% 2.68/1.50 ! [A4: $tType] : ( size @ ( list @ A4 ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(tcon_Product__Type_Oprod___Nat_Osize_5,axiom,
% 2.68/1.50 ! [A4: $tType,A5: $tType] : ( size @ ( product_prod @ A4 @ A5 ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(conj_0,hypothesis,
% 2.68/1.50 ( ( divide_divide @ nat @ ( size_size @ ( list @ a ) @ xs ) @ k )
% 2.68/1.50 = ( suc @ n ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(conj_1,hypothesis,
% 2.68/1.50 ( k
% 2.68/1.50 != ( zero_zero @ nat ) ) ).
% 2.68/1.50
% 2.68/1.50 thf(conj_2,conjecture,
% 2.68/1.50 ord_less @ nat @ ( times_times @ nat @ n @ k ) @ ( size_size @ ( list @ a ) @ xs ) ).
% 2.68/1.50 ------------------------
% 2.68/1.52 % (32693)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/183Mi)
% 2.68/1.52 % (32697)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/2Mi)
% 2.68/1.52 % (32699)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/18Mi)
% 2.68/1.52 % (32697)Instruction limit reached!
% 2.68/1.52 % (32697)------------------------------
% 2.68/1.52 % (32697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.52 % (32697)Termination reason: Unknown
% 2.68/1.52 % (32697)Termination phase: shuffling
% 2.68/1.52
% 2.68/1.52 % (32697)Memory used [KB]: 1407
% 2.68/1.52 % (32697)Time elapsed: 0.002 s
% 2.68/1.52 % (32697)Instructions burned: 4 (million)
% 2.68/1.52 % (32697)------------------------------
% 2.68/1.52 % (32697)------------------------------
% 2.68/1.52 % (32698)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/275Mi)
% 2.68/1.52 % (32695)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/27Mi)
% 2.68/1.53 % (32699)Instruction limit reached!
% 2.68/1.53 % (32699)------------------------------
% 2.68/1.53 % (32699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.53 % (32699)Termination reason: Unknown
% 2.68/1.53 % (32699)Termination phase: Property scanning
% 2.68/1.53
% 2.68/1.53 % (32699)Memory used [KB]: 1663
% 2.68/1.53 % (32699)Time elapsed: 0.008 s
% 2.68/1.53 % (32699)Instructions burned: 20 (million)
% 2.68/1.53 % (32699)------------------------------
% 2.68/1.53 % (32699)------------------------------
% 2.68/1.53 % (32696)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/2Mi)
% 2.68/1.53 % (32696)Instruction limit reached!
% 2.68/1.53 % (32696)------------------------------
% 2.68/1.53 % (32696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.53 % (32696)Termination reason: Unknown
% 2.68/1.53 % (32696)Termination phase: shuffling
% 2.68/1.53
% 2.68/1.53 % (32696)Memory used [KB]: 1279
% 2.68/1.53 % (32696)Time elapsed: 0.002 s
% 2.68/1.53 % (32696)Instructions burned: 2 (million)
% 2.68/1.53 % (32696)------------------------------
% 2.68/1.53 % (32696)------------------------------
% 2.68/1.53 % (32694)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/4Mi)
% 2.68/1.53 % (32694)Instruction limit reached!
% 2.68/1.53 % (32694)------------------------------
% 2.68/1.53 % (32694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.53 % (32694)Termination reason: Unknown
% 2.68/1.53 % (32694)Termination phase: shuffling
% 2.68/1.53
% 2.68/1.53 % (32694)Memory used [KB]: 1407
% 2.68/1.53 % (32694)Time elapsed: 0.003 s
% 2.68/1.53 % (32694)Instructions burned: 5 (million)
% 2.68/1.53 % (32694)------------------------------
% 2.68/1.53 % (32694)------------------------------
% 2.68/1.53 % (32700)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/3Mi)
% 2.68/1.53 % (32700)Instruction limit reached!
% 2.68/1.53 % (32700)------------------------------
% 2.68/1.53 % (32700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.53 % (32700)Termination reason: Unknown
% 2.68/1.53 % (32700)Termination phase: shuffling
% 2.68/1.53
% 2.68/1.53 % (32700)Memory used [KB]: 1279
% 2.68/1.53 % (32700)Time elapsed: 0.003 s
% 2.68/1.53 % (32700)Instructions burned: 3 (million)
% 2.68/1.53 % (32700)------------------------------
% 2.68/1.53 % (32700)------------------------------
% 2.68/1.53 % (32701)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/37Mi)
% 2.68/1.54 % (32703)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/3Mi)
% 2.68/1.54 % (32702)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/15Mi)
% 2.68/1.54 % (32703)Instruction limit reached!
% 2.68/1.54 % (32703)------------------------------
% 2.68/1.54 % (32703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.54 % (32703)Termination reason: Unknown
% 2.68/1.54 % (32703)Termination phase: shuffling
% 2.68/1.54
% 2.68/1.54 % (32703)Memory used [KB]: 1279
% 2.68/1.54 % (32703)Time elapsed: 0.002 s
% 2.68/1.54 % (32703)Instructions burned: 3 (million)
% 2.68/1.54 % (32703)------------------------------
% 2.68/1.54 % (32703)------------------------------
% 2.68/1.54 % (32695)Instruction limit reached!
% 2.68/1.54 % (32695)------------------------------
% 2.68/1.54 % (32695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.54 % (32695)Termination reason: Unknown
% 2.68/1.54 % (32695)Termination phase: Property scanning
% 2.68/1.54
% 2.68/1.54 % (32695)Memory used [KB]: 1663
% 2.68/1.54 % (32695)Time elapsed: 0.018 s
% 2.68/1.54 % (32695)Instructions burned: 28 (million)
% 2.68/1.54 % (32695)------------------------------
% 2.68/1.54 % (32695)------------------------------
% 2.68/1.55 % (32701)Instruction limit reached!
% 2.68/1.55 % (32701)------------------------------
% 2.68/1.55 % (32701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.55 % (32701)Termination reason: Unknown
% 2.68/1.55 % (32701)Termination phase: Property scanning
% 2.68/1.55
% 2.68/1.55 % (32701)Memory used [KB]: 2046
% 2.68/1.55 % (32701)Time elapsed: 0.012 s
% 2.68/1.55 % (32701)Instructions burned: 39 (million)
% 2.68/1.55 % (32701)------------------------------
% 2.68/1.55 % (32701)------------------------------
% 2.68/1.55 % (32702)Instruction limit reached!
% 2.68/1.55 % (32702)------------------------------
% 2.68/1.55 % (32702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.55 % (32702)Termination reason: Unknown
% 2.68/1.55 % (32702)Termination phase: shuffling
% 2.68/1.55
% 2.68/1.55 % (32702)Memory used [KB]: 1663
% 2.68/1.55 % (32702)Time elapsed: 0.008 s
% 2.68/1.55 % (32702)Instructions burned: 17 (million)
% 2.68/1.55 % (32702)------------------------------
% 2.68/1.55 % (32702)------------------------------
% 2.68/1.55 % (32704)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/1041Mi)
% 2.68/1.55 % (32706)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/7Mi)
% 2.68/1.55 % (32706)Instruction limit reached!
% 2.68/1.55 % (32706)------------------------------
% 2.68/1.55 % (32706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.55 % (32706)Termination reason: Unknown
% 2.68/1.55 % (32706)Termination phase: shuffling
% 2.68/1.55
% 2.68/1.55 % (32706)Memory used [KB]: 1407
% 2.68/1.55 % (32706)Time elapsed: 0.005 s
% 2.68/1.55 % (32706)Instructions burned: 9 (million)
% 2.68/1.55 % (32706)------------------------------
% 2.68/1.55 % (32706)------------------------------
% 2.68/1.55 % (32712)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/3Mi)
% 2.68/1.56 % (32712)Instruction limit reached!
% 2.68/1.56 % (32712)------------------------------
% 2.68/1.56 % (32712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.56 % (32712)Termination reason: Unknown
% 2.68/1.56 % (32712)Termination phase: shuffling
% 2.68/1.56
% 2.68/1.56 % (32712)Memory used [KB]: 1279
% 2.68/1.56 % (32712)Time elapsed: 0.002 s
% 2.68/1.56 % (32712)Instructions burned: 3 (million)
% 2.68/1.56 % (32712)------------------------------
% 2.68/1.56 % (32712)------------------------------
% 2.68/1.56 % (32713)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/3Mi)
% 2.68/1.56 % (32707)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/16Mi)
% 2.68/1.56 % (32713)Instruction limit reached!
% 2.68/1.56 % (32713)------------------------------
% 2.68/1.56 % (32713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.56 % (32713)Termination reason: Unknown
% 2.68/1.56 % (32713)Termination phase: shuffling
% 2.68/1.56
% 2.68/1.56 % (32713)Memory used [KB]: 1279
% 2.68/1.56 % (32713)Time elapsed: 0.003 s
% 2.68/1.56 % (32713)Instructions burned: 3 (million)
% 2.68/1.56 % (32713)------------------------------
% 2.68/1.56 % (32713)------------------------------
% 2.68/1.56 % (32707)Instruction limit reached!
% 2.68/1.56 % (32707)------------------------------
% 2.68/1.56 % (32707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.56 % (32707)Termination reason: Unknown
% 2.68/1.56 % (32707)Termination phase: shuffling
% 2.68/1.56
% 2.68/1.56 % (32707)Memory used [KB]: 1663
% 2.68/1.56 % (32707)Time elapsed: 0.009 s
% 2.68/1.56 % (32707)Instructions burned: 17 (million)
% 2.68/1.56 % (32707)------------------------------
% 2.68/1.56 % (32707)------------------------------
% 2.68/1.56 % (32714)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/7Mi)
% 2.68/1.57 % (32715)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/3Mi)
% 2.68/1.57 % (32714)Instruction limit reached!
% 2.68/1.57 % (32714)------------------------------
% 2.68/1.57 % (32714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.57 % (32714)Termination reason: Unknown
% 2.68/1.57 % (32714)Termination phase: shuffling
% 2.68/1.57
% 2.68/1.57 % (32714)Memory used [KB]: 1407
% 2.68/1.57 % (32714)Time elapsed: 0.005 s
% 2.68/1.57 % (32714)Instructions burned: 9 (million)
% 2.68/1.57 % (32714)------------------------------
% 2.68/1.57 % (32714)------------------------------
% 2.68/1.57 % (32715)Instruction limit reached!
% 2.68/1.57 % (32715)------------------------------
% 2.68/1.57 % (32715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.57 % (32715)Termination reason: Unknown
% 2.68/1.57 % (32715)Termination phase: shuffling
% 2.68/1.57
% 2.68/1.57 % (32715)Memory used [KB]: 1407
% 2.68/1.57 % (32715)Time elapsed: 0.003 s
% 2.68/1.57 % (32715)Instructions burned: 6 (million)
% 2.68/1.57 % (32715)------------------------------
% 2.68/1.57 % (32715)------------------------------
% 2.68/1.57 % (32716)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/4Mi)
% 2.68/1.57 % (32716)Instruction limit reached!
% 2.68/1.57 % (32716)------------------------------
% 2.68/1.57 % (32716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.57 % (32716)Termination reason: Unknown
% 2.68/1.57 % (32716)Termination phase: shuffling
% 2.68/1.57
% 2.68/1.57 % (32716)Memory used [KB]: 1279
% 2.68/1.57 % (32716)Time elapsed: 0.003 s
% 2.68/1.57 % (32716)Instructions burned: 4 (million)
% 2.68/1.57 % (32716)------------------------------
% 2.68/1.57 % (32716)------------------------------
% 2.68/1.57 % (32718)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/18Mi)
% 2.68/1.58 % (32720)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/6Mi)
% 2.68/1.58 % (32719)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/710Mi)
% 2.68/1.58 % (32720)Instruction limit reached!
% 2.68/1.58 % (32720)------------------------------
% 2.68/1.58 % (32720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.58 % (32720)Termination reason: Unknown
% 2.68/1.58 % (32720)Termination phase: shuffling
% 2.68/1.58
% 2.68/1.58 % (32720)Memory used [KB]: 1407
% 2.68/1.58 % (32720)Time elapsed: 0.003 s
% 2.68/1.58 % (32720)Instructions burned: 6 (million)
% 2.68/1.58 % (32720)------------------------------
% 2.68/1.58 % (32720)------------------------------
% 2.68/1.58 % (32721)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/902Mi)
% 2.68/1.58 % (32718)Instruction limit reached!
% 2.68/1.58 % (32718)------------------------------
% 2.68/1.58 % (32718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.58 % (32718)Termination reason: Unknown
% 2.68/1.58 % (32718)Termination phase: shuffling
% 2.68/1.58
% 2.68/1.58 % (32718)Memory used [KB]: 1663
% 2.68/1.58 % (32718)Time elapsed: 0.008 s
% 2.68/1.58 % (32718)Instructions burned: 19 (million)
% 2.68/1.58 % (32718)------------------------------
% 2.68/1.58 % (32718)------------------------------
% 2.68/1.59 % (32722)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/21Mi)
% 2.68/1.59 % (32693)Instruction limit reached!
% 2.68/1.59 % (32693)------------------------------
% 2.68/1.59 % (32693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.59 % (32693)Termination reason: Unknown
% 2.68/1.59 % (32693)Termination phase: Saturation
% 2.68/1.59
% 2.68/1.59 % (32693)Memory used [KB]: 6908
% 2.68/1.59 % (32693)Time elapsed: 0.073 s
% 2.68/1.59 % (32693)Instructions burned: 184 (million)
% 2.68/1.59 % (32693)------------------------------
% 2.68/1.59 % (32693)------------------------------
% 2.68/1.59 % (32724)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/5Mi)
% 2.68/1.59 % (32724)Instruction limit reached!
% 2.68/1.59 % (32724)------------------------------
% 2.68/1.59 % (32724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.59 % (32724)Termination reason: Unknown
% 2.68/1.59 % (32724)Termination phase: shuffling
% 2.68/1.59
% 2.68/1.59 % (32724)Memory used [KB]: 1407
% 2.68/1.59 % (32724)Time elapsed: 0.004 s
% 2.68/1.59 % (32724)Instructions burned: 8 (million)
% 2.68/1.59 % (32724)------------------------------
% 2.68/1.59 % (32724)------------------------------
% 2.68/1.59 % (32722)Instruction limit reached!
% 2.68/1.59 % (32722)------------------------------
% 2.68/1.59 % (32722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.59 % (32722)Termination reason: Unknown
% 2.68/1.59 % (32722)Termination phase: shuffling
% 2.68/1.59
% 2.68/1.59 % (32722)Memory used [KB]: 1663
% 2.68/1.59 % (32722)Time elapsed: 0.008 s
% 2.68/1.59 % (32722)Instructions burned: 21 (million)
% 2.68/1.59 % (32722)------------------------------
% 2.68/1.59 % (32722)------------------------------
% 2.68/1.60 % (32726)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/6Mi)
% 2.68/1.60 % (32726)Instruction limit reached!
% 2.68/1.60 % (32726)------------------------------
% 2.68/1.60 % (32726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.60 % (32726)Termination reason: Unknown
% 2.68/1.60 % (32726)Termination phase: shuffling
% 2.68/1.60
% 2.68/1.60 % (32726)Memory used [KB]: 1407
% 2.68/1.60 % (32726)Time elapsed: 0.004 s
% 2.68/1.60 % (32726)Instructions burned: 6 (million)
% 2.68/1.60 % (32726)------------------------------
% 2.68/1.60 % (32726)------------------------------
% 2.68/1.61 % (32727)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32501 for (2999ds/377Mi)
% 2.68/1.61 % (32735)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_32501 for (2998ds/779Mi)
% 2.68/1.62 % (32736)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_32501 for (2998ds/19Mi)
% 2.68/1.63 % (32698)Instruction limit reached!
% 2.68/1.63 % (32698)------------------------------
% 2.68/1.63 % (32698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.63 % (32698)Termination reason: Unknown
% 2.68/1.63 % (32698)Termination phase: Saturation
% 2.68/1.63
% 2.68/1.63 % (32698)Memory used [KB]: 7036
% 2.68/1.63 % (32698)Time elapsed: 0.108 s
% 2.68/1.63 % (32698)Instructions burned: 275 (million)
% 2.68/1.63 % (32698)------------------------------
% 2.68/1.63 % (32698)------------------------------
% 2.68/1.63 % (32736)Instruction limit reached!
% 2.68/1.63 % (32736)------------------------------
% 2.68/1.63 % (32736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.63 % (32736)Termination reason: Unknown
% 2.68/1.63 % (32736)Termination phase: shuffling
% 2.68/1.63
% 2.68/1.63 % (32736)Memory used [KB]: 1663
% 2.68/1.63 % (32736)Time elapsed: 0.011 s
% 2.68/1.63 % (32736)Instructions burned: 20 (million)
% 2.68/1.63 % (32736)------------------------------
% 2.68/1.63 % (32736)------------------------------
% 2.68/1.64 % (32742)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32501 for (2998ds/879Mi)
% 2.68/1.65 % (32743)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32501 for (2998ds/17Mi)
% 2.68/1.65 % (32743)Instruction limit reached!
% 2.68/1.65 % (32743)------------------------------
% 2.68/1.65 % (32743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.65 % (32743)Termination reason: Unknown
% 2.68/1.65 % (32743)Termination phase: shuffling
% 2.68/1.65
% 2.68/1.65 % (32743)Memory used [KB]: 1663
% 2.68/1.65 % (32743)Time elapsed: 0.011 s
% 2.68/1.65 % (32743)Instructions burned: 17 (million)
% 2.68/1.65 % (32743)------------------------------
% 2.68/1.65 % (32743)------------------------------
% 2.68/1.67 % (32749)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32501 for (2998ds/3Mi)
% 2.68/1.67 % (32749)Instruction limit reached!
% 2.68/1.67 % (32749)------------------------------
% 2.68/1.67 % (32749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.67 % (32749)Termination reason: Unknown
% 2.68/1.67 % (32749)Termination phase: shuffling
% 2.68/1.67
% 2.68/1.67 % (32749)Memory used [KB]: 1407
% 2.68/1.67 % (32749)Time elapsed: 0.003 s
% 2.68/1.67 % (32749)Instructions burned: 5 (million)
% 2.68/1.67 % (32749)------------------------------
% 2.68/1.67 % (32749)------------------------------
% 2.68/1.69 % (32755)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32501 for (2998ds/30Mi)
% 2.68/1.70 % (32755)Instruction limit reached!
% 2.68/1.70 % (32755)------------------------------
% 2.68/1.70 % (32755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.70 % (32755)Termination reason: Unknown
% 2.68/1.70 % (32755)Termination phase: Property scanning
% 2.68/1.70
% 2.68/1.70 % (32755)Memory used [KB]: 1663
% 2.68/1.70 % (32755)Time elapsed: 0.016 s
% 2.68/1.70 % (32755)Instructions burned: 30 (million)
% 2.68/1.70 % (32755)------------------------------
% 2.68/1.70 % (32755)------------------------------
% 2.68/1.72 % (32760)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32501 for (2997ds/127Mi)
% 2.68/1.76 % (32727)Instruction limit reached!
% 2.68/1.76 % (32727)------------------------------
% 2.68/1.76 % (32727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.76 % (32727)Termination reason: Unknown
% 2.68/1.76 % (32727)Termination phase: Saturation
% 2.68/1.76
% 2.68/1.76 % (32727)Memory used [KB]: 7547
% 2.68/1.76 % (32727)Time elapsed: 0.154 s
% 2.68/1.76 % (32727)Instructions burned: 379 (million)
% 2.68/1.76 % (32727)------------------------------
% 2.68/1.76 % (32727)------------------------------
% 2.68/1.78 % (32760)Instruction limit reached!
% 2.68/1.78 % (32760)------------------------------
% 2.68/1.78 % (32760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.78 % (32760)Termination reason: Unknown
% 2.68/1.78 % (32760)Termination phase: Saturation
% 2.68/1.78
% 2.68/1.78 % (32760)Memory used [KB]: 6780
% 2.68/1.78 % (32760)Time elapsed: 0.058 s
% 2.68/1.78 % (32760)Instructions burned: 129 (million)
% 2.68/1.78 % (32760)------------------------------
% 2.68/1.78 % (32760)------------------------------
% 2.68/1.78 % (32767)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_32501 for (2997ds/100Mi)
% 2.68/1.79 % (301)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_32501 for (2997ds/3Mi)
% 2.68/1.79 % (301)Instruction limit reached!
% 2.68/1.79 % (301)------------------------------
% 2.68/1.79 % (301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.79 % (301)Termination reason: Unknown
% 2.68/1.79 % (301)Termination phase: shuffling
% 2.68/1.79
% 2.68/1.79 % (301)Memory used [KB]: 1407
% 2.68/1.79 % (301)Time elapsed: 0.003 s
% 2.68/1.79 % (301)Instructions burned: 3 (million)
% 2.68/1.79 % (301)------------------------------
% 2.68/1.79 % (301)------------------------------
% 2.68/1.81 % (32767)Instruction limit reached!
% 2.68/1.81 % (32767)------------------------------
% 2.68/1.81 % (32767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.81 % (32767)Termination reason: Unknown
% 2.68/1.81 % (32767)Termination phase: Saturation
% 2.68/1.81
% 2.68/1.81 % (32767)Memory used [KB]: 6652
% 2.68/1.81 % (32767)Time elapsed: 0.029 s
% 2.68/1.81 % (32767)Instructions burned: 103 (million)
% 2.68/1.81 % (32767)------------------------------
% 2.68/1.81 % (32767)------------------------------
% 2.68/1.81 % (303)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_32501 for (2997ds/20Mi)
% 2.68/1.82 % (305)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_32501 for (2996ds/86Mi)
% 2.68/1.82 % (303)Instruction limit reached!
% 2.68/1.82 % (303)------------------------------
% 2.68/1.82 % (303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.82 % (303)Termination reason: Unknown
% 2.68/1.82 % (303)Termination phase: Property scanning
% 2.68/1.82
% 2.68/1.82 % (303)Memory used [KB]: 1663
% 2.68/1.82 % (303)Time elapsed: 0.012 s
% 2.68/1.82 % (303)Instructions burned: 20 (million)
% 2.68/1.82 % (303)------------------------------
% 2.68/1.82 % (303)------------------------------
% 2.68/1.83 % (306)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_32501 for (2996ds/107Mi)
% 2.68/1.84 % (305)Instruction limit reached!
% 2.68/1.84 % (305)------------------------------
% 2.68/1.84 % (305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.84 % (305)Termination reason: Unknown
% 2.68/1.84 % (305)Termination phase: Saturation
% 2.68/1.84
% 2.68/1.84 % (305)Memory used [KB]: 6524
% 2.68/1.84 % (305)Time elapsed: 0.026 s
% 2.68/1.84 % (305)Instructions burned: 87 (million)
% 2.68/1.84 % (305)------------------------------
% 2.68/1.84 % (305)------------------------------
% 2.68/1.85 % (307)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_32501 for (2996ds/39Mi)
% 2.68/1.86 % (307)Instruction limit reached!
% 2.68/1.86 % (307)------------------------------
% 2.68/1.86 % (307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.86 % (307)Termination reason: Unknown
% 2.68/1.86 % (307)Termination phase: Property scanning
% 2.68/1.86
% 2.68/1.86 % (307)Memory used [KB]: 2046
% 2.68/1.86 % (307)Time elapsed: 0.012 s
% 2.68/1.86 % (307)Instructions burned: 39 (million)
% 2.68/1.86 % (307)------------------------------
% 2.68/1.86 % (307)------------------------------
% 2.68/1.87 % (309)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_32501 for (2996ds/448Mi)
% 2.68/1.89 % (306)Instruction limit reached!
% 2.68/1.89 % (306)------------------------------
% 2.68/1.89 % (306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.89 % (306)Termination reason: Unknown
% 2.68/1.89 % (306)Termination phase: Saturation
% 2.68/1.89
% 2.68/1.89 % (306)Memory used [KB]: 6780
% 2.68/1.89 % (306)Time elapsed: 0.053 s
% 2.68/1.89 % (306)Instructions burned: 107 (million)
% 2.68/1.89 % (306)------------------------------
% 2.68/1.89 % (306)------------------------------
% 2.68/1.90 % (311)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_32501 for (2996ds/46Mi)
% 2.68/1.91 % (32719)Instruction limit reached!
% 2.68/1.91 % (32719)------------------------------
% 2.68/1.91 % (32719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.91 % (32719)Termination reason: Unknown
% 2.68/1.91 % (32719)Termination phase: Saturation
% 2.68/1.91
% 2.68/1.91 % (32719)Memory used [KB]: 7547
% 2.68/1.91 % (32719)Time elapsed: 0.357 s
% 2.68/1.91 % (32719)Instructions burned: 711 (million)
% 2.68/1.91 % (32719)------------------------------
% 2.68/1.91 % (32719)------------------------------
% 2.68/1.93 % (311)Instruction limit reached!
% 2.68/1.93 % (311)------------------------------
% 2.68/1.93 % (311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.93 % (311)Termination reason: Unknown
% 2.68/1.93 % (311)Termination phase: Property scanning
% 2.68/1.93
% 2.68/1.93 % (311)Memory used [KB]: 1918
% 2.68/1.93 % (311)Time elapsed: 0.024 s
% 2.68/1.93 % (311)Instructions burned: 48 (million)
% 2.68/1.93 % (311)------------------------------
% 2.68/1.93 % (311)------------------------------
% 2.68/1.93 % (313)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_32501 for (2995ds/98Mi)
% 2.68/1.96 % (315)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_32501 for (2995ds/507Mi)
% 2.68/1.98 % (313)Instruction limit reached!
% 2.68/1.98 % (313)------------------------------
% 2.68/1.98 % (313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.98 % (313)Termination reason: Unknown
% 2.68/1.98 % (313)Termination phase: Saturation
% 2.68/1.98
% 2.68/1.98 % (313)Memory used [KB]: 2174
% 2.68/1.98 % (313)Time elapsed: 0.045 s
% 2.68/1.98 % (313)Instructions burned: 98 (million)
% 2.68/1.98 % (313)------------------------------
% 2.68/1.98 % (313)------------------------------
% 2.68/1.98 % (32735)Instruction limit reached!
% 2.68/1.98 % (32735)------------------------------
% 2.68/1.98 % (32735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.98 % (32735)Termination reason: Unknown
% 2.68/1.98 % (32735)Termination phase: Saturation
% 2.68/1.98
% 2.68/1.98 % (32735)Memory used [KB]: 7675
% 2.68/1.98 % (32735)Time elapsed: 0.369 s
% 2.68/1.98 % (32735)Instructions burned: 780 (million)
% 2.68/1.98 % (32735)------------------------------
% 2.68/1.98 % (32735)------------------------------
% 2.68/1.99 % (318)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_32501 for (2995ds/149Mi)
% 2.68/1.99 % (320)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_32501 for (2995ds/39Mi)
% 2.68/2.00 % (32721)Instruction limit reached!
% 2.68/2.00 % (32721)------------------------------
% 2.68/2.00 % (32721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.00 % (32721)Termination reason: Unknown
% 2.68/2.00 % (32721)Termination phase: Saturation
% 2.68/2.00
% 2.68/2.00 % (32721)Memory used [KB]: 9594
% 2.68/2.00 % (32721)Time elapsed: 0.415 s
% 2.68/2.00 % (32721)Instructions burned: 902 (million)
% 2.68/2.00 % (32721)------------------------------
% 2.68/2.00 % (32721)------------------------------
% 2.68/2.01 % (32704)Instruction limit reached!
% 2.68/2.01 % (32704)------------------------------
% 2.68/2.01 % (32704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.01 % (32704)Termination reason: Unknown
% 2.68/2.01 % (32704)Termination phase: Saturation
% 2.68/2.01
% 2.68/2.01 % (32704)Memory used [KB]: 9466
% 2.68/2.01 % (32704)Time elapsed: 0.465 s
% 2.68/2.01 % (32704)Instructions burned: 1042 (million)
% 2.68/2.01 % (32704)------------------------------
% 2.68/2.01 % (32704)------------------------------
% 2.68/2.01 % (320)Instruction limit reached!
% 2.68/2.01 % (320)------------------------------
% 2.68/2.01 % (320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.01 % (320)Termination reason: Unknown
% 2.68/2.01 % (320)Termination phase: Preprocessing 3
% 2.68/2.01
% 2.68/2.01 % (320)Memory used [KB]: 1918
% 2.68/2.01 % (320)Time elapsed: 0.021 s
% 2.68/2.01 % (320)Instructions burned: 40 (million)
% 2.68/2.01 % (320)------------------------------
% 2.68/2.01 % (320)------------------------------
% 2.68/2.02 % (322)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_32501 for (2995ds/6Mi)
% 2.68/2.02 % (322)Instruction limit reached!
% 2.68/2.02 % (322)------------------------------
% 2.68/2.02 % (322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.02 % (322)Termination reason: Unknown
% 2.68/2.02 % (322)Termination phase: shuffling
% 2.68/2.02
% 2.68/2.02 % (322)Memory used [KB]: 1407
% 2.68/2.02 % (322)Time elapsed: 0.005 s
% 2.68/2.02 % (322)Instructions burned: 7 (million)
% 2.68/2.02 % (322)------------------------------
% 2.68/2.02 % (322)------------------------------
% 6.11/2.03 % (324)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/1087Mi)
% 6.11/2.04 % (326)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/44Mi)
% 6.11/2.04 % (325)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/47Mi)
% 6.11/2.04 % (32742)Instruction limit reached!
% 6.11/2.04 % (32742)------------------------------
% 6.11/2.04 % (32742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.04 % (32742)Termination reason: Unknown
% 6.11/2.04 % (32742)Termination phase: Saturation
% 6.11/2.04
% 6.11/2.04 % (32742)Memory used [KB]: 7547
% 6.11/2.04 % (32742)Time elapsed: 0.388 s
% 6.11/2.04 % (32742)Instructions burned: 879 (million)
% 6.11/2.04 % (32742)------------------------------
% 6.11/2.04 % (32742)------------------------------
% 6.11/2.05 % (318)Instruction limit reached!
% 6.11/2.05 % (318)------------------------------
% 6.11/2.05 % (318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.05 % (318)Termination reason: Unknown
% 6.11/2.05 % (318)Termination phase: Saturation
% 6.11/2.05
% 6.11/2.05 % (318)Memory used [KB]: 6908
% 6.11/2.05 % (318)Time elapsed: 0.054 s
% 6.11/2.05 % (318)Instructions burned: 150 (million)
% 6.11/2.05 % (318)------------------------------
% 6.11/2.05 % (318)------------------------------
% 6.11/2.06 % (326)Instruction limit reached!
% 6.11/2.06 % (326)------------------------------
% 6.11/2.06 % (326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.06 % (326)Termination reason: Unknown
% 6.11/2.06 % (326)Termination phase: Property scanning
% 6.11/2.06
% 6.11/2.06 % (326)Memory used [KB]: 2046
% 6.11/2.06 % (326)Time elapsed: 0.022 s
% 6.11/2.06 % (326)Instructions burned: 45 (million)
% 6.11/2.06 % (326)------------------------------
% 6.11/2.06 % (326)------------------------------
% 6.11/2.06 % (328)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/432Mi)
% 6.11/2.06 % (325)Instruction limit reached!
% 6.11/2.06 % (325)------------------------------
% 6.11/2.06 % (325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.06 % (325)Termination reason: Unknown
% 6.11/2.06 % (325)Termination phase: Property scanning
% 6.11/2.06
% 6.11/2.06 % (325)Memory used [KB]: 1918
% 6.11/2.06 % (325)Time elapsed: 0.024 s
% 6.11/2.06 % (325)Instructions burned: 47 (million)
% 6.11/2.06 % (325)------------------------------
% 6.11/2.06 % (325)------------------------------
% 6.11/2.06 % (329)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/62Mi)
% 6.11/2.08 % (332)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/96Mi)
% 6.11/2.08 % (330)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/31Mi)
% 6.11/2.09 % (309)Instruction limit reached!
% 6.11/2.09 % (309)------------------------------
% 6.11/2.09 % (309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.09 % (309)Termination reason: Unknown
% 6.11/2.09 % (309)Termination phase: Saturation
% 6.11/2.09
% 6.11/2.09 % (309)Memory used [KB]: 7675
% 6.11/2.09 % (309)Time elapsed: 0.219 s
% 6.11/2.09 % (309)Instructions burned: 449 (million)
% 6.11/2.09 % (309)------------------------------
% 6.11/2.09 % (309)------------------------------
% 6.11/2.09 % (329)Instruction limit reached!
% 6.11/2.09 % (329)------------------------------
% 6.11/2.09 % (329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.09 % (329)Termination reason: Unknown
% 6.11/2.09 % (329)Termination phase: Preprocessing 1
% 6.11/2.09
% 6.11/2.09 % (329)Memory used [KB]: 2046
% 6.11/2.09 % (329)Time elapsed: 0.029 s
% 6.11/2.09 % (329)Instructions burned: 63 (million)
% 6.11/2.09 % (329)------------------------------
% 6.11/2.09 % (329)------------------------------
% 6.11/2.10 % (334)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/453Mi)
% 6.11/2.11 % (336)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/71Mi)
% 6.11/2.11 % (330)Instruction limit reached!
% 6.11/2.11 % (330)------------------------------
% 6.11/2.11 % (330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.11 % (330)Termination reason: Unknown
% 6.11/2.11 % (330)Termination phase: Property scanning
% 6.11/2.11
% 6.11/2.11 % (330)Memory used [KB]: 1663
% 6.11/2.11 % (330)Time elapsed: 0.015 s
% 6.11/2.11 % (330)Instructions burned: 31 (million)
% 6.11/2.11 % (330)------------------------------
% 6.11/2.11 % (330)------------------------------
% 6.11/2.12 % (332)Instruction limit reached!
% 6.11/2.12 % (332)------------------------------
% 6.11/2.12 % (332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.12 % (332)Termination reason: Unknown
% 6.11/2.12 % (332)Termination phase: Saturation
% 6.11/2.12
% 6.11/2.12 % (332)Memory used [KB]: 6652
% 6.11/2.12 % (332)Time elapsed: 0.046 s
% 6.11/2.12 % (332)Instructions burned: 96 (million)
% 6.11/2.12 % (332)------------------------------
% 6.11/2.12 % (332)------------------------------
% 6.11/2.12 % (337)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_32501 for (2994ds/83Mi)
% 6.56/2.13 % (336)Instruction limit reached!
% 6.56/2.13 % (336)------------------------------
% 6.56/2.13 % (336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.13 % (336)Termination reason: Unknown
% 6.56/2.13 % (336)Termination phase: Saturation
% 6.56/2.13
% 6.56/2.13 % (336)Memory used [KB]: 6396
% 6.56/2.13 % (336)Time elapsed: 0.022 s
% 6.56/2.13 % (336)Instructions burned: 72 (million)
% 6.56/2.13 % (336)------------------------------
% 6.56/2.13 % (336)------------------------------
% 6.56/2.14 % (342)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_32501 for (2993ds/41Mi)
% 6.56/2.14 % (341)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_32501 for (2993ds/11Mi)
% 6.56/2.14 % (341)Instruction limit reached!
% 6.56/2.14 % (341)------------------------------
% 6.56/2.14 % (341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.14 % (341)Termination reason: Unknown
% 6.56/2.14 % (341)Termination phase: shuffling
% 6.56/2.14
% 6.56/2.14 % (341)Memory used [KB]: 1535
% 6.56/2.14 % (341)Time elapsed: 0.007 s
% 6.56/2.14 % (341)Instructions burned: 12 (million)
% 6.56/2.14 % (341)------------------------------
% 6.56/2.14 % (341)------------------------------
% 6.56/2.16 % (342)Instruction limit reached!
% 6.56/2.16 % (342)------------------------------
% 6.56/2.16 % (342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.16 % (342)Termination reason: Unknown
% 6.56/2.16 % (342)Termination phase: Property scanning
% 6.56/2.16
% 6.56/2.16 % (342)Memory used [KB]: 2046
% 6.56/2.16 % (342)Time elapsed: 0.021 s
% 6.56/2.16 % (342)Instructions burned: 43 (million)
% 6.56/2.16 % (342)------------------------------
% 6.56/2.16 % (342)------------------------------
% 6.56/2.16 % (345)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32501 for (2993ds/6Mi)
% 6.56/2.16 % (345)Instruction limit reached!
% 6.56/2.16 % (345)------------------------------
% 6.56/2.16 % (345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.16 % (345)Termination reason: Unknown
% 6.56/2.16 % (345)Termination phase: shuffling
% 6.56/2.16
% 6.56/2.16 % (345)Memory used [KB]: 1407
% 6.56/2.16 % (345)Time elapsed: 0.005 s
% 6.56/2.16 % (345)Instructions burned: 7 (million)
% 6.56/2.16 % (345)------------------------------
% 6.56/2.16 % (345)------------------------------
% 6.56/2.16 % (337)Instruction limit reached!
% 6.56/2.16 % (337)------------------------------
% 6.56/2.16 % (337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.16 % (337)Termination reason: Unknown
% 6.56/2.17 % (337)Termination phase: Saturation
% 6.56/2.17
% 6.56/2.17 % (337)Memory used [KB]: 6524
% 6.56/2.17 % (337)Time elapsed: 0.043 s
% 6.56/2.17 % (337)Instructions burned: 83 (million)
% 6.56/2.17 % (337)------------------------------
% 6.56/2.17 % (337)------------------------------
% 6.56/2.17 % (347)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_32501 for (2993ds/150Mi)
% 6.56/2.18 % (315)Instruction limit reached!
% 6.56/2.18 % (315)------------------------------
% 6.56/2.18 % (315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.18 % (315)Termination reason: Unknown
% 6.56/2.18 % (315)Termination phase: Saturation
% 6.56/2.18
% 6.56/2.18 % (315)Memory used [KB]: 7931
% 6.56/2.18 % (315)Time elapsed: 0.252 s
% 6.56/2.18 % (315)Instructions burned: 507 (million)
% 6.56/2.18 % (315)------------------------------
% 6.56/2.18 % (315)------------------------------
% 6.56/2.18 % (348)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_32501 for (2993ds/343Mi)
% 6.56/2.18 % (349)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_32501 for (2993ds/109Mi)
% 6.56/2.19 % (352)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_32501 for (2993ds/253Mi)
% 6.79/2.23 % (328)Instruction limit reached!
% 6.79/2.23 % (328)------------------------------
% 6.79/2.23 % (328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.23 % (328)Termination reason: Unknown
% 6.79/2.23 % (328)Termination phase: Saturation
% 6.79/2.23
% 6.79/2.23 % (328)Memory used [KB]: 3837
% 6.79/2.23 % (328)Time elapsed: 0.195 s
% 6.79/2.23 % (328)Instructions burned: 433 (million)
% 6.79/2.23 % (328)------------------------------
% 6.79/2.23 % (328)------------------------------
% 6.79/2.23 % (349)Instruction limit reached!
% 6.79/2.23 % (349)------------------------------
% 6.79/2.23 % (349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.23 % (349)Termination reason: Unknown
% 6.79/2.23 % (349)Termination phase: Saturation
% 6.79/2.23
% 6.79/2.23 % (349)Memory used [KB]: 6780
% 6.79/2.23 % (349)Time elapsed: 0.053 s
% 6.79/2.23 % (349)Instructions burned: 109 (million)
% 6.79/2.23 % (349)------------------------------
% 6.79/2.23 % (349)------------------------------
% 6.79/2.24 % (355)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_32501 for (2992ds/140Mi)
% 6.79/2.24 % (347)Instruction limit reached!
% 6.79/2.24 % (347)------------------------------
% 6.79/2.24 % (347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.24 % (347)Termination reason: Unknown
% 6.79/2.24 % (347)Termination phase: Saturation
% 6.79/2.24
% 6.79/2.24 % (347)Memory used [KB]: 7036
% 6.79/2.24 % (347)Time elapsed: 0.096 s
% 6.79/2.24 % (347)Instructions burned: 150 (million)
% 6.79/2.24 % (347)------------------------------
% 6.79/2.24 % (347)------------------------------
% 6.79/2.25 % (356)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_32501 for (2992ds/614Mi)
% 6.79/2.26 % (359)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_32501 for (2992ds/202Mi)
% 6.79/2.29 % (355)Instruction limit reached!
% 6.79/2.29 % (355)------------------------------
% 6.79/2.29 % (355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.29 % (355)Termination reason: Unknown
% 6.79/2.29 % (355)Termination phase: Saturation
% 6.79/2.29
% 6.79/2.29 % (355)Memory used [KB]: 6780
% 6.79/2.29 % (355)Time elapsed: 0.075 s
% 6.79/2.29 % (355)Instructions burned: 142 (million)
% 6.79/2.29 % (355)------------------------------
% 6.79/2.29 % (355)------------------------------
% 6.79/2.29 % (334)Instruction limit reached!
% 6.79/2.29 % (334)------------------------------
% 6.79/2.29 % (334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.79/2.29 % (334)Termination reason: Unknown
% 6.79/2.29 % (334)Termination phase: Saturation
% 6.79/2.29
% 6.79/2.29 % (334)Memory used [KB]: 7419
% 6.79/2.29 % (334)Time elapsed: 0.191 s
% 6.79/2.29 % (334)Instructions burned: 454 (million)
% 6.79/2.29 % (334)------------------------------
% 6.79/2.29 % (334)------------------------------
% 7.37/2.31 % (364)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_32501 for (2992ds/339Mi)
% 7.37/2.31 % (352)Instruction limit reached!
% 7.37/2.31 % (352)------------------------------
% 7.37/2.31 % (352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.37/2.31 % (352)Termination reason: Unknown
% 7.37/2.31 % (352)Termination phase: Saturation
% 7.37/2.31
% 7.37/2.31 % (352)Memory used [KB]: 7291
% 7.37/2.31 % (352)Time elapsed: 0.142 s
% 7.37/2.31 % (352)Instructions burned: 254 (million)
% 7.37/2.31 % (352)------------------------------
% 7.37/2.31 % (352)------------------------------
% 7.37/2.31 % (366)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_32501 for (2992ds/283Mi)
% 7.37/2.32 % (367)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_32501 for (2991ds/134Mi)
% 7.37/2.35 % (348)Instruction limit reached!
% 7.37/2.35 % (348)------------------------------
% 7.37/2.35 % (348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.37/2.35 % (348)Termination reason: Unknown
% 7.37/2.35 % (348)Termination phase: Saturation
% 7.37/2.35
% 7.37/2.35 % (348)Memory used [KB]: 6780
% 7.37/2.35 % (348)Time elapsed: 0.198 s
% 7.37/2.35 % (348)Instructions burned: 343 (million)
% 7.37/2.35 % (348)------------------------------
% 7.37/2.35 % (348)------------------------------
% 7.37/2.36 % (359)Instruction limit reached!
% 7.37/2.36 % (359)------------------------------
% 7.37/2.36 % (359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.37/2.36 % (359)Termination reason: Unknown
% 7.37/2.36 % (359)Termination phase: Saturation
% 7.37/2.36
% 7.37/2.36 % (359)Memory used [KB]: 7036
% 7.37/2.36 % (359)Time elapsed: 0.103 s
% 7.37/2.36 % (359)Instructions burned: 203 (million)
% 7.37/2.36 % (359)------------------------------
% 7.37/2.36 % (359)------------------------------
% 7.37/2.37 % (371)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_32501 for (2991ds/298Mi)
% 7.37/2.37 % (367)Instruction limit reached!
% 7.37/2.37 % (367)------------------------------
% 7.37/2.37 % (367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.37/2.37 % (367)Termination reason: Unknown
% 7.37/2.37 % (367)Termination phase: Saturation
% 7.37/2.37
% 7.37/2.37 % (367)Memory used [KB]: 6780
% 7.37/2.37 % (367)Time elapsed: 0.049 s
% 7.37/2.37 % (367)Instructions burned: 134 (million)
% 7.37/2.37 % (367)------------------------------
% 7.37/2.37 % (367)------------------------------
% 7.37/2.38 % (372)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_32501 for (2991ds/192Mi)
% 7.37/2.38 % (373)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_32501 for (2991ds/258Mi)
% 7.87/2.42 % (366)Instruction limit reached!
% 7.87/2.42 % (366)------------------------------
% 7.87/2.42 % (366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.42 % (366)Termination reason: Unknown
% 7.87/2.42 % (366)Termination phase: Saturation
% 7.87/2.42
% 7.87/2.42 % (366)Memory used [KB]: 7291
% 7.87/2.42 % (366)Time elapsed: 0.115 s
% 7.87/2.42 % (366)Instructions burned: 283 (million)
% 7.87/2.42 % (366)------------------------------
% 7.87/2.42 % (366)------------------------------
% 7.87/2.44 % (377)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_32501 for (2990ds/90Mi)
% 7.87/2.47 % (364)Instruction limit reached!
% 7.87/2.47 % (364)------------------------------
% 7.87/2.47 % (364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.47 % (364)Termination reason: Unknown
% 7.87/2.47 % (364)Termination phase: Saturation
% 7.87/2.47
% 7.87/2.47 % (364)Memory used [KB]: 7419
% 7.87/2.47 % (364)Time elapsed: 0.163 s
% 7.87/2.47 % (364)Instructions burned: 339 (million)
% 7.87/2.47 % (364)------------------------------
% 7.87/2.47 % (364)------------------------------
% 7.87/2.47 % (372)Instruction limit reached!
% 7.87/2.47 % (372)------------------------------
% 7.87/2.47 % (372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.47 % (372)Termination reason: Unknown
% 7.87/2.47 % (372)Termination phase: Saturation
% 7.87/2.47
% 7.87/2.47 % (372)Memory used [KB]: 7547
% 7.87/2.47 % (372)Time elapsed: 0.098 s
% 7.87/2.47 % (372)Instructions burned: 192 (million)
% 7.87/2.47 % (372)------------------------------
% 7.87/2.47 % (372)------------------------------
% 7.87/2.48 % (377)Instruction limit reached!
% 7.87/2.48 % (377)------------------------------
% 7.87/2.48 % (377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.48 % (377)Termination reason: Unknown
% 7.87/2.48 % (377)Termination phase: Saturation
% 7.87/2.48
% 7.87/2.48 % (377)Memory used [KB]: 6524
% 7.87/2.48 % (377)Time elapsed: 0.045 s
% 7.87/2.48 % (377)Instructions burned: 91 (million)
% 7.87/2.48 % (377)------------------------------
% 7.87/2.48 % (377)------------------------------
% 7.87/2.49 % (371)Instruction limit reached!
% 7.87/2.49 % (371)------------------------------
% 7.87/2.49 % (371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.49 % (371)Termination reason: Unknown
% 7.87/2.49 % (371)Termination phase: Saturation
% 7.87/2.49
% 7.87/2.49 % (371)Memory used [KB]: 7675
% 7.87/2.49 % (371)Time elapsed: 0.123 s
% 7.87/2.49 % (371)Instructions burned: 299 (million)
% 7.87/2.49 % (371)------------------------------
% 7.87/2.49 % (371)------------------------------
% 7.87/2.49 % (381)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_32501 for (2990ds/231Mi)
% 8.49/2.50 % (382)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_32501 for (2990ds/458Mi)
% 8.49/2.50 % (383)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32501 for (2990ds/31Mi)
% 8.49/2.50 % (373)Instruction limit reached!
% 8.49/2.50 % (373)------------------------------
% 8.49/2.50 % (373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.50 % (373)Termination reason: Unknown
% 8.49/2.50 % (373)Termination phase: Saturation
% 8.49/2.50
% 8.49/2.50 % (373)Memory used [KB]: 6908
% 8.49/2.50 % (373)Time elapsed: 0.118 s
% 8.49/2.50 % (373)Instructions burned: 258 (million)
% 8.49/2.50 % (373)------------------------------
% 8.49/2.50 % (373)------------------------------
% 8.49/2.50 % (384)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_32501 for (2990ds/297Mi)
% 8.49/2.52 % (383)Instruction limit reached!
% 8.49/2.52 % (383)------------------------------
% 8.49/2.52 % (383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.52 % (383)Termination reason: Unknown
% 8.49/2.52 % (383)Termination phase: shuffling
% 8.49/2.52
% 8.49/2.52 % (383)Memory used [KB]: 1663
% 8.49/2.52 % (383)Time elapsed: 0.017 s
% 8.49/2.52 % (383)Instructions burned: 32 (million)
% 8.49/2.52 % (383)------------------------------
% 8.49/2.52 % (383)------------------------------
% 8.49/2.52 % (386)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_32501 for (2990ds/987Mi)
% 8.49/2.54 % (387)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_32501 for (2989ds/182Mi)
% 8.49/2.55 % (324)Instruction limit reached!
% 8.49/2.55 % (324)------------------------------
% 8.49/2.55 % (324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.55 % (356)Instruction limit reached!
% 8.49/2.55 % (356)------------------------------
% 8.49/2.55 % (356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.55 % (356)Termination reason: Unknown
% 8.49/2.55 % (356)Termination phase: Saturation
% 8.49/2.55
% 8.49/2.55 % (356)Memory used [KB]: 8059
% 8.49/2.55 % (356)Time elapsed: 0.307 s
% 8.49/2.55 % (356)Instructions burned: 614 (million)
% 8.49/2.55 % (356)------------------------------
% 8.49/2.55 % (356)------------------------------
% 8.49/2.55 % (324)Termination reason: Unknown
% 8.49/2.55 % (324)Termination phase: Saturation
% 8.49/2.55
% 8.49/2.55 % (324)Memory used [KB]: 8827
% 8.49/2.55 % (324)Time elapsed: 0.525 s
% 8.49/2.55 % (324)Instructions burned: 1087 (million)
% 8.49/2.55 % (324)------------------------------
% 8.49/2.55 % (324)------------------------------
% 8.49/2.57 % (391)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_32501 for (2989ds/182Mi)
% 8.49/2.57 % (392)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_32501 for (2989ds/154Mi)
% 8.49/2.57 % (381)Instruction limit reached!
% 8.49/2.57 % (381)------------------------------
% 8.49/2.57 % (381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.49/2.57 % (381)Termination reason: Unknown
% 8.49/2.57 % (381)Termination phase: Saturation
% 8.49/2.57
% 8.49/2.57 % (381)Memory used [KB]: 6780
% 8.49/2.57 % (381)Time elapsed: 0.089 s
% 8.49/2.57 % (381)Instructions burned: 234 (million)
% 8.49/2.57 % (381)------------------------------
% 8.49/2.57 % (381)------------------------------
% 8.49/2.59 % (393)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_32501 for (2989ds/79Mi)
% 9.61/2.62 % (387)Instruction limit reached!
% 9.61/2.62 % (387)------------------------------
% 9.61/2.62 % (387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.62 % (387)Termination reason: Unknown
% 9.61/2.62 % (387)Termination phase: Saturation
% 9.61/2.62
% 9.61/2.62 % (387)Memory used [KB]: 6908
% 9.61/2.62 % (387)Time elapsed: 0.083 s
% 9.61/2.62 % (387)Instructions burned: 183 (million)
% 9.61/2.62 % (387)------------------------------
% 9.61/2.62 % (387)------------------------------
% 9.61/2.63 % (393)Instruction limit reached!
% 9.61/2.63 % (393)------------------------------
% 9.61/2.63 % (393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.63 % (393)Termination reason: Unknown
% 9.61/2.63 % (393)Termination phase: Saturation
% 9.61/2.63
% 9.61/2.63 % (393)Memory used [KB]: 6524
% 9.61/2.63 % (393)Time elapsed: 0.039 s
% 9.61/2.63 % (393)Instructions burned: 79 (million)
% 9.61/2.63 % (393)------------------------------
% 9.61/2.63 % (393)------------------------------
% 9.61/2.64 % (399)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/216Mi)
% 9.61/2.64 % (392)Instruction limit reached!
% 9.61/2.64 % (392)------------------------------
% 9.61/2.64 % (392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.64 % (392)Termination reason: Unknown
% 9.61/2.64 % (392)Termination phase: Saturation
% 9.61/2.64
% 9.61/2.64 % (392)Memory used [KB]: 2558
% 9.61/2.64 % (392)Time elapsed: 0.071 s
% 9.61/2.64 % (392)Instructions burned: 154 (million)
% 9.61/2.64 % (392)------------------------------
% 9.61/2.64 % (392)------------------------------
% 9.61/2.64 % (384)Instruction limit reached!
% 9.61/2.64 % (384)------------------------------
% 9.61/2.64 % (384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.64 % (384)Termination reason: Unknown
% 9.61/2.64 % (384)Termination phase: Saturation
% 9.61/2.64
% 9.61/2.64 % (384)Memory used [KB]: 7036
% 9.61/2.64 % (384)Time elapsed: 0.142 s
% 9.61/2.64 % (384)Instructions burned: 299 (million)
% 9.61/2.64 % (384)------------------------------
% 9.61/2.64 % (384)------------------------------
% 9.61/2.65 % (400)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/114Mi)
% 9.61/2.65 % (402)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/922Mi)
% 9.61/2.65 % (403)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/182Mi)
% 9.61/2.65 % (391)Instruction limit reached!
% 9.61/2.65 % (391)------------------------------
% 9.61/2.65 % (391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.65 % (391)Termination reason: Unknown
% 9.61/2.65 % (391)Termination phase: Saturation
% 9.61/2.65
% 9.61/2.65 % (391)Memory used [KB]: 7036
% 9.61/2.65 % (391)Time elapsed: 0.085 s
% 9.61/2.65 % (391)Instructions burned: 184 (million)
% 9.61/2.65 % (391)------------------------------
% 9.61/2.65 % (391)------------------------------
% 9.61/2.66 % (404)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/164Mi)
% 9.61/2.67 % (382)Instruction limit reached!
% 9.61/2.67 % (382)------------------------------
% 9.61/2.67 % (382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.67 % (382)Termination reason: Unknown
% 9.61/2.67 % (382)Termination phase: Saturation
% 9.61/2.67
% 9.61/2.67 % (382)Memory used [KB]: 7419
% 9.61/2.67 % (382)Time elapsed: 0.195 s
% 9.61/2.67 % (382)Instructions burned: 460 (million)
% 9.61/2.67 % (382)------------------------------
% 9.61/2.67 % (382)------------------------------
% 9.61/2.68 % (405)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/50Mi)
% 9.61/2.68 % (400)Instruction limit reached!
% 9.61/2.68 % (400)------------------------------
% 9.61/2.68 % (400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.68 % (400)Termination reason: Unknown
% 9.61/2.68 % (400)Termination phase: Saturation
% 9.61/2.68
% 9.61/2.68 % (400)Memory used [KB]: 6780
% 9.61/2.68 % (400)Time elapsed: 0.036 s
% 9.61/2.68 % (400)Instructions burned: 116 (million)
% 9.61/2.68 % (400)------------------------------
% 9.61/2.68 % (400)------------------------------
% 9.61/2.69 % (406)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/368Mi)
% 9.61/2.69 % (405)Instruction limit reached!
% 9.61/2.69 % (405)------------------------------
% 9.61/2.69 % (405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.69 % (405)Termination reason: Unknown
% 9.61/2.69 % (405)Termination phase: Property scanning
% 9.61/2.69
% 9.61/2.69 % (405)Memory used [KB]: 2046
% 9.61/2.69 % (405)Time elapsed: 0.015 s
% 9.61/2.69 % (405)Instructions burned: 53 (million)
% 9.61/2.69 % (405)------------------------------
% 9.61/2.69 % (405)------------------------------
% 10.35/2.70 % (399)Instruction limit reached!
% 10.35/2.70 % (399)------------------------------
% 10.35/2.70 % (399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.70 % (399)Termination reason: Unknown
% 10.35/2.70 % (399)Termination phase: Saturation
% 10.35/2.70
% 10.35/2.70 % (399)Memory used [KB]: 7291
% 10.35/2.70 % (399)Time elapsed: 0.065 s
% 10.35/2.70 % (399)Instructions burned: 217 (million)
% 10.35/2.70 % (399)------------------------------
% 10.35/2.70 % (399)------------------------------
% 10.35/2.70 % (407)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/1021Mi)
% 10.35/2.71 % (403)Instruction limit reached!
% 10.35/2.71 % (403)------------------------------
% 10.35/2.71 % (403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.71 % (403)Termination reason: Unknown
% 10.35/2.71 % (403)Termination phase: Saturation
% 10.35/2.71
% 10.35/2.71 % (403)Memory used [KB]: 6908
% 10.35/2.71 % (403)Time elapsed: 0.053 s
% 10.35/2.71 % (403)Instructions burned: 185 (million)
% 10.35/2.71 % (403)------------------------------
% 10.35/2.71 % (403)------------------------------
% 10.35/2.71 % (408)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/267Mi)
% 10.35/2.71 % (404)Instruction limit reached!
% 10.35/2.71 % (404)------------------------------
% 10.35/2.71 % (404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.71 % (404)Termination reason: Unknown
% 10.35/2.71 % (404)Termination phase: Saturation
% 10.35/2.71
% 10.35/2.71 % (404)Memory used [KB]: 2302
% 10.35/2.71 % (404)Time elapsed: 0.047 s
% 10.35/2.71 % (404)Instructions burned: 164 (million)
% 10.35/2.71 % (404)------------------------------
% 10.35/2.71 % (404)------------------------------
% 10.35/2.71 % (409)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/204Mi)
% 10.35/2.72 % (410)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_32501 for (2988ds/26Mi)
% 10.35/2.73 % (410)Instruction limit reached!
% 10.35/2.73 % (410)------------------------------
% 10.35/2.73 % (410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.73 % (410)Termination reason: Unknown
% 10.35/2.73 % (410)Termination phase: shuffling
% 10.35/2.73
% 10.35/2.73 % (410)Memory used [KB]: 1791
% 10.35/2.73 % (410)Time elapsed: 0.008 s
% 10.35/2.73 % (410)Instructions burned: 26 (million)
% 10.35/2.73 % (410)------------------------------
% 10.35/2.73 % (410)------------------------------
% 10.35/2.74 % (415)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_32501 for (2987ds/53Mi)
% 10.35/2.75 % (415)Instruction limit reached!
% 10.35/2.75 % (415)------------------------------
% 10.35/2.75 % (415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.75 % (415)Termination reason: Unknown
% 10.35/2.75 % (415)Termination phase: Property scanning
% 10.35/2.75
% 10.35/2.75 % (415)Memory used [KB]: 2046
% 10.35/2.75 % (415)Time elapsed: 0.016 s
% 10.35/2.75 % (415)Instructions burned: 56 (million)
% 10.35/2.75 % (415)------------------------------
% 10.35/2.75 % (415)------------------------------
% 10.35/2.76 % (425)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_32501 for (2987ds/4436Mi)
% 10.35/2.78 % (409)Instruction limit reached!
% 10.35/2.78 % (409)------------------------------
% 10.35/2.78 % (409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.78 % (409)Termination reason: Unknown
% 10.35/2.78 % (409)Termination phase: Saturation
% 10.35/2.78
% 10.35/2.78 % (409)Memory used [KB]: 6780
% 10.35/2.78 % (409)Time elapsed: 0.066 s
% 10.35/2.78 % (409)Instructions burned: 206 (million)
% 10.35/2.78 % (409)------------------------------
% 10.35/2.78 % (409)------------------------------
% 10.35/2.79 % (437)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_32501 for (2987ds/1539Mi)
% 10.35/2.79 % (408)Instruction limit reached!
% 10.35/2.79 % (408)------------------------------
% 10.35/2.79 % (408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.79 % (408)Termination reason: Unknown
% 10.35/2.79 % (408)Termination phase: Saturation
% 10.35/2.79
% 10.35/2.79 % (408)Memory used [KB]: 7291
% 10.35/2.79 % (408)Time elapsed: 0.084 s
% 10.35/2.79 % (408)Instructions burned: 269 (million)
% 10.35/2.79 % (408)------------------------------
% 10.35/2.79 % (408)------------------------------
% 10.35/2.79 % (406)Instruction limit reached!
% 10.35/2.79 % (406)------------------------------
% 10.35/2.79 % (406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.35/2.79 % (406)Termination reason: Unknown
% 10.35/2.79 % (406)Termination phase: Saturation
% 10.35/2.79
% 10.35/2.79 % (406)Memory used [KB]: 7164
% 10.35/2.79 % (406)Time elapsed: 0.103 s
% 10.35/2.79 % (406)Instructions burned: 371 (million)
% 10.35/2.79 % (406)------------------------------
% 10.35/2.79 % (406)------------------------------
% 10.87/2.80 % (447)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_32501 for (2987ds/408Mi)
% 10.87/2.80 % (450)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_32501 for (2987ds/5205Mi)
% 10.87/2.87 % (386)Instruction limit reached!
% 10.87/2.87 % (386)------------------------------
% 10.87/2.87 % (386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.87/2.87 % (386)Termination reason: Unknown
% 10.87/2.87 % (386)Termination phase: Saturation
% 10.87/2.87
% 10.87/2.87 % (386)Memory used [KB]: 8571
% 10.87/2.87 % (386)Time elapsed: 0.350 s
% 10.87/2.87 % (386)Instructions burned: 989 (million)
% 10.87/2.87 % (386)------------------------------
% 10.87/2.87 % (386)------------------------------
% 10.87/2.88 % (479)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_32501 for (2986ds/1913Mi)
% 11.23/2.93 % (447)Instruction limit reached!
% 11.23/2.93 % (447)------------------------------
% 11.23/2.93 % (447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.23/2.93 % (447)Termination reason: Unknown
% 11.23/2.93 % (447)Termination phase: Saturation
% 11.23/2.93
% 11.23/2.93 % (447)Memory used [KB]: 7931
% 11.23/2.93 % (447)Time elapsed: 0.131 s
% 11.23/2.93 % (447)Instructions burned: 409 (million)
% 11.23/2.93 % (447)------------------------------
% 11.23/2.93 % (447)------------------------------
% 11.23/2.94 % (527)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_32501 for (2985ds/4350Mi)
% 11.23/2.95 % (402)Instruction limit reached!
% 11.23/2.95 % (402)------------------------------
% 11.23/2.95 % (402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.23/2.95 % (402)Termination reason: Unknown
% 11.23/2.95 % (402)Termination phase: Saturation
% 11.23/2.95
% 11.23/2.95 % (402)Memory used [KB]: 8571
% 11.23/2.95 % (402)Time elapsed: 0.303 s
% 11.23/2.95 % (402)Instructions burned: 923 (million)
% 11.23/2.95 % (402)------------------------------
% 11.23/2.95 % (402)------------------------------
% 11.23/2.96 % (536)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_32501 for (2985ds/68Mi)
% 11.23/2.98 % (536)Instruction limit reached!
% 11.23/2.98 % (536)------------------------------
% 11.23/2.98 % (536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.23/2.98 % (536)Termination reason: Unknown
% 11.23/2.98 % (536)Termination phase: Saturation
% 11.23/2.98
% 11.23/2.98 % (536)Memory used [KB]: 6396
% 11.23/2.98 % (536)Time elapsed: 0.021 s
% 11.23/2.98 % (536)Instructions burned: 69 (million)
% 11.23/2.98 % (536)------------------------------
% 11.23/2.98 % (536)------------------------------
% 11.23/2.99 % (553)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_32501 for (2985ds/358Mi)
% 12.93/3.03 % (407)Instruction limit reached!
% 12.93/3.03 % (407)------------------------------
% 12.93/3.03 % (407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.03 % (407)Termination reason: Unknown
% 12.93/3.03 % (407)Termination phase: Saturation
% 12.93/3.03
% 12.93/3.03 % (407)Memory used [KB]: 8955
% 12.93/3.03 % (407)Time elapsed: 0.324 s
% 12.93/3.03 % (407)Instructions burned: 1021 (million)
% 12.93/3.03 % (407)------------------------------
% 12.93/3.03 % (407)------------------------------
% 12.93/3.04 % (575)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_32501 for (2984ds/31Mi)
% 12.93/3.05 % (575)Instruction limit reached!
% 12.93/3.05 % (575)------------------------------
% 12.93/3.05 % (575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.05 % (575)Termination reason: Unknown
% 12.93/3.05 % (575)Termination phase: Preprocessing 1
% 12.93/3.05
% 12.93/3.05 % (575)Memory used [KB]: 1663
% 12.93/3.05 % (575)Time elapsed: 0.011 s
% 12.93/3.05 % (575)Instructions burned: 33 (million)
% 12.93/3.05 % (575)------------------------------
% 12.93/3.05 % (575)------------------------------
% 12.93/3.06 % (586)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_32501 for (2984ds/279Mi)
% 12.93/3.09 % (586)Refutation not found, incomplete strategy
% 12.93/3.09 % (586)------------------------------
% 12.93/3.09 % (586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.09 % (586)Termination reason: Refutation not found, incomplete strategy
% 12.93/3.09
% 12.93/3.09
% 12.93/3.09 % (586)Memory used [KB]: 6780
% 12.93/3.09 % (586)Time elapsed: 0.030 s
% 12.93/3.09 % (586)Instructions burned: 109 (million)
% 12.93/3.09 % (586)------------------------------
% 12.93/3.09 % (586)------------------------------
% 12.93/3.10 % (599)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_32501 for (2984ds/258Mi)
% 12.93/3.11 % (553)Instruction limit reached!
% 12.93/3.11 % (553)------------------------------
% 12.93/3.11 % (553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.11 % (553)Termination reason: Unknown
% 12.93/3.11 % (553)Termination phase: Saturation
% 12.93/3.11
% 12.93/3.11 % (553)Memory used [KB]: 7036
% 12.93/3.11 % (553)Time elapsed: 0.115 s
% 12.93/3.11 % (553)Instructions burned: 360 (million)
% 12.93/3.11 % (553)------------------------------
% 12.93/3.11 % (553)------------------------------
% 12.93/3.12 % (606)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_32501 for (2984ds/26Mi)
% 12.93/3.12 % (606)Instruction limit reached!
% 12.93/3.12 % (606)------------------------------
% 12.93/3.12 % (606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.12 % (606)Termination reason: Unknown
% 12.93/3.12 % (606)Termination phase: shuffling
% 12.93/3.12
% 12.93/3.12 % (606)Memory used [KB]: 1791
% 12.93/3.12 % (606)Time elapsed: 0.009 s
% 12.93/3.12 % (606)Instructions burned: 29 (million)
% 12.93/3.12 % (606)------------------------------
% 12.93/3.12 % (606)------------------------------
% 13.73/3.13 % (614)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_32501 for (2983ds/995Mi)
% 13.73/3.18 % (599)Instruction limit reached!
% 13.73/3.18 % (599)------------------------------
% 13.73/3.18 % (599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.18 % (599)Termination reason: Unknown
% 13.73/3.18 % (599)Termination phase: Saturation
% 13.73/3.18
% 13.73/3.18 % (599)Memory used [KB]: 7164
% 13.73/3.18 % (599)Time elapsed: 0.082 s
% 13.73/3.18 % (599)Instructions burned: 259 (million)
% 13.73/3.18 % (599)------------------------------
% 13.73/3.18 % (599)------------------------------
% 13.73/3.19 % (629)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_32501 for (2983ds/373Mi)
% 14.17/3.28 % (437)Instruction limit reached!
% 14.17/3.28 % (437)------------------------------
% 14.17/3.28 % (437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.17/3.28 % (437)Termination reason: Unknown
% 14.17/3.28 % (437)Termination phase: Saturation
% 14.17/3.28
% 14.17/3.28 % (437)Memory used [KB]: 9594
% 14.17/3.28 % (437)Time elapsed: 0.488 s
% 14.17/3.28 % (437)Instructions burned: 1540 (million)
% 14.17/3.28 % (437)------------------------------
% 14.17/3.28 % (437)------------------------------
% 14.17/3.29 % (693)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_32501 for (2982ds/253Mi)
% 14.66/3.30 % (629)Instruction limit reached!
% 14.66/3.30 % (629)------------------------------
% 14.66/3.30 % (629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.30 % (629)Termination reason: Unknown
% 14.66/3.30 % (629)Termination phase: Saturation
% 14.66/3.30
% 14.66/3.30 % (629)Memory used [KB]: 7291
% 14.66/3.30 % (629)Time elapsed: 0.118 s
% 14.66/3.30 % (629)Instructions burned: 375 (million)
% 14.66/3.30 % (629)------------------------------
% 14.66/3.30 % (629)------------------------------
% 14.66/3.31 % (705)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_32501 for (2982ds/832Mi)
% 14.66/3.36 % (693)Instruction limit reached!
% 14.66/3.36 % (693)------------------------------
% 14.66/3.36 % (693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.36 % (693)Termination reason: Unknown
% 14.66/3.36 % (693)Termination phase: Saturation
% 14.66/3.36
% 14.66/3.36 % (693)Memory used [KB]: 7291
% 14.66/3.36 % (693)Time elapsed: 0.074 s
% 14.66/3.36 % (693)Instructions burned: 254 (million)
% 14.66/3.36 % (693)------------------------------
% 14.66/3.36 % (693)------------------------------
% 14.66/3.37 % (711)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_32501 for (2981ds/668Mi)
% 15.27/3.44 % (614)Instruction limit reached!
% 15.27/3.44 % (614)------------------------------
% 15.27/3.44 % (614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.27/3.44 % (614)Termination reason: Unknown
% 15.27/3.44 % (614)Termination phase: Saturation
% 15.27/3.44
% 15.27/3.44 % (614)Memory used [KB]: 9083
% 15.27/3.44 % (614)Time elapsed: 0.310 s
% 15.27/3.44 % (614)Instructions burned: 995 (million)
% 15.27/3.44 % (614)------------------------------
% 15.27/3.44 % (614)------------------------------
% 15.27/3.45 % (712)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_32501 for (2980ds/40Mi)
% 15.27/3.46 % (712)Instruction limit reached!
% 15.27/3.46 % (712)------------------------------
% 15.27/3.46 % (712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.27/3.46 % (712)Termination reason: Unknown
% 15.27/3.46 % (712)Termination phase: Property scanning
% 15.27/3.46
% 15.27/3.46 % (712)Memory used [KB]: 2046
% 15.27/3.46 % (712)Time elapsed: 0.013 s
% 15.27/3.46 % (712)Instructions burned: 43 (million)
% 15.27/3.46 % (712)------------------------------
% 15.27/3.46 % (712)------------------------------
% 15.27/3.47 % (713)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_32501 for (2980ds/294Mi)
% 15.27/3.47 % (479)Instruction limit reached!
% 15.27/3.47 % (479)------------------------------
% 15.27/3.47 % (479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.27/3.47 % (479)Termination reason: Unknown
% 15.27/3.47 % (479)Termination phase: Saturation
% 15.27/3.47
% 15.27/3.47 % (479)Memory used [KB]: 3709
% 15.27/3.47 % (479)Time elapsed: 0.600 s
% 15.27/3.47 % (479)Instructions burned: 1914 (million)
% 15.27/3.47 % (479)------------------------------
% 15.27/3.47 % (479)------------------------------
% 15.27/3.48 % (714)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_32501 for (2980ds/187Mi)
% 15.27/3.50 % (713)Refutation not found, incomplete strategy
% 15.27/3.50 % (713)------------------------------
% 15.27/3.50 % (713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.27/3.50 % (713)Termination reason: Refutation not found, incomplete strategy
% 15.27/3.50
% 15.27/3.50
% 15.27/3.50 % (713)Memory used [KB]: 6652
% 15.27/3.50 % (713)Time elapsed: 0.023 s
% 15.27/3.50 % (713)Instructions burned: 80 (million)
% 15.27/3.50 % (713)------------------------------
% 15.27/3.50 % (713)------------------------------
% 16.04/3.51 % (715)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_32501 for (2980ds/371Mi)
% 16.04/3.54 % (714)Instruction limit reached!
% 16.04/3.54 % (714)------------------------------
% 16.04/3.54 % (714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.04/3.54 % (714)Termination reason: Unknown
% 16.04/3.54 % (714)Termination phase: Saturation
% 16.04/3.54
% 16.04/3.54 % (714)Memory used [KB]: 6908
% 16.04/3.54 % (714)Time elapsed: 0.059 s
% 16.04/3.54 % (714)Instructions burned: 188 (million)
% 16.04/3.54 % (714)------------------------------
% 16.04/3.54 % (714)------------------------------
% 16.04/3.55 % (716)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_32501 for (2979ds/1827Mi)
% 16.04/3.57 % (705)Instruction limit reached!
% 16.04/3.57 % (705)------------------------------
% 16.04/3.57 % (705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.04/3.57 % (705)Termination reason: Unknown
% 16.04/3.57 % (705)Termination phase: Saturation
% 16.04/3.57
% 16.04/3.57 % (705)Memory used [KB]: 8059
% 16.04/3.57 % (705)Time elapsed: 0.257 s
% 16.04/3.57 % (705)Instructions burned: 832 (million)
% 16.04/3.57 % (705)------------------------------
% 16.04/3.57 % (705)------------------------------
% 16.04/3.57 % (711)Instruction limit reached!
% 16.04/3.57 % (711)------------------------------
% 16.04/3.57 % (711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.04/3.57 % (711)Termination reason: Unknown
% 16.04/3.57 % (711)Termination phase: Saturation
% 16.04/3.57
% 16.04/3.57 % (711)Memory used [KB]: 13944
% 16.04/3.57 % (711)Time elapsed: 0.205 s
% 16.04/3.57 % (711)Instructions burned: 671 (million)
% 16.04/3.57 % (711)------------------------------
% 16.04/3.57 % (711)------------------------------
% 16.04/3.58 % (717)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_32501 for (2979ds/70Mi)
% 16.04/3.58 % (718)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_32501 for (2979ds/316Mi)
% 16.04/3.60 % (717)Instruction limit reached!
% 16.04/3.60 % (717)------------------------------
% 16.04/3.60 % (717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.04/3.60 % (717)Termination reason: Unknown
% 16.04/3.60 % (717)Termination phase: Property scanning
% 16.04/3.60
% 16.04/3.60 % (717)Memory used [KB]: 2174
% 16.04/3.60 % (717)Time elapsed: 0.020 s
% 16.04/3.60 % (717)Instructions burned: 71 (million)
% 16.04/3.60 % (717)------------------------------
% 16.04/3.60 % (717)------------------------------
% 16.89/3.61 % (719)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_32501 for (2978ds/932Mi)
% 16.89/3.63 % (715)Instruction limit reached!
% 16.89/3.63 % (715)------------------------------
% 16.89/3.63 % (715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.89/3.63 % (715)Termination reason: Unknown
% 16.89/3.63 % (715)Termination phase: Saturation
% 16.89/3.63
% 16.89/3.63 % (715)Memory used [KB]: 6908
% 16.89/3.63 % (715)Time elapsed: 0.142 s
% 16.89/3.63 % (715)Instructions burned: 372 (million)
% 16.89/3.63 % (715)------------------------------
% 16.89/3.63 % (715)------------------------------
% 16.89/3.63 % (718)Refutation not found, incomplete strategy
% 16.89/3.63 % (718)------------------------------
% 16.89/3.63 % (718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.89/3.63 % (718)Termination reason: Refutation not found, incomplete strategy
% 16.89/3.63
% 16.89/3.63
% 16.89/3.63 % (718)Memory used [KB]: 6908
% 16.89/3.63 % (718)Time elapsed: 0.046 s
% 16.89/3.63 % (718)Instructions burned: 170 (million)
% 16.89/3.63 % (718)------------------------------
% 16.89/3.63 % (718)------------------------------
% 16.89/3.64 % (720)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_32501 for (2978ds/4714Mi)
% 16.89/3.64 % (721)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_32501 for (2978ds/8250Mi)
% 16.89/3.68 % (720)Refutation not found, incomplete strategy
% 16.89/3.68 % (720)------------------------------
% 16.89/3.68 % (720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.89/3.68 % (720)Termination reason: Refutation not found, incomplete strategy
% 16.89/3.68
% 16.89/3.68
% 16.89/3.68 % (720)Memory used [KB]: 7164
% 16.89/3.68 % (720)Time elapsed: 0.045 s
% 16.89/3.68 % (720)Instructions burned: 160 (million)
% 16.89/3.68 % (720)------------------------------
% 16.89/3.68 % (720)------------------------------
% 16.89/3.69 % (722)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_32501 for (2978ds/770Mi)
% 17.75/3.89 % (719)Instruction limit reached!
% 17.75/3.89 % (719)------------------------------
% 17.75/3.89 % (719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.75/3.89 % (719)Termination reason: Unknown
% 17.75/3.89 % (719)Termination phase: Saturation
% 17.75/3.89
% 17.75/3.89 % (719)Memory used [KB]: 9210
% 17.75/3.89 % (719)Time elapsed: 0.282 s
% 17.75/3.89 % (719)Instructions burned: 932 (million)
% 17.75/3.89 % (719)------------------------------
% 17.75/3.89 % (719)------------------------------
% 18.33/3.90 % (723)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_32501 for (2976ds/794Mi)
% 18.33/3.93 % (722)Instruction limit reached!
% 18.33/3.93 % (722)------------------------------
% 18.33/3.93 % (722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.33/3.93 % (722)Termination reason: Unknown
% 18.33/3.93 % (722)Termination phase: Saturation
% 18.33/3.93
% 18.33/3.93 % (722)Memory used [KB]: 7675
% 18.33/3.93 % (722)Time elapsed: 0.245 s
% 18.33/3.93 % (722)Instructions burned: 771 (million)
% 18.33/3.93 % (722)------------------------------
% 18.33/3.93 % (722)------------------------------
% 18.33/3.94 % (724)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_32501 for (2975ds/464Mi)
% 19.96/4.09 % (724)Instruction limit reached!
% 19.96/4.09 % (724)------------------------------
% 19.96/4.09 % (724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.96/4.09 % (724)Termination reason: Unknown
% 19.96/4.09 % (724)Termination phase: Saturation
% 19.96/4.09
% 19.96/4.09 % (724)Memory used [KB]: 7419
% 19.96/4.09 % (724)Time elapsed: 0.147 s
% 19.96/4.09 % (724)Instructions burned: 464 (million)
% 19.96/4.09 % (724)------------------------------
% 19.96/4.09 % (724)------------------------------
% 19.96/4.10 % (725)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_32501 for (2974ds/1376Mi)
% 20.74/4.14 % (723)Instruction limit reached!
% 20.74/4.14 % (723)------------------------------
% 20.74/4.14 % (723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.14 % (723)Termination reason: Unknown
% 20.74/4.14 % (723)Termination phase: Saturation
% 20.74/4.14
% 20.74/4.14 % (723)Memory used [KB]: 5117
% 20.74/4.14 % (723)Time elapsed: 0.246 s
% 20.74/4.14 % (723)Instructions burned: 797 (million)
% 20.74/4.14 % (723)------------------------------
% 20.74/4.14 % (723)------------------------------
% 20.74/4.14 % (716)Instruction limit reached!
% 20.74/4.14 % (716)------------------------------
% 20.74/4.14 % (716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.14 % (716)Termination reason: Unknown
% 20.74/4.14 % (716)Termination phase: Saturation
% 20.74/4.14
% 20.74/4.14 % (716)Memory used [KB]: 9083
% 20.74/4.14 % (716)Time elapsed: 0.614 s
% 20.74/4.14 % (716)Instructions burned: 1829 (million)
% 20.74/4.14 % (716)------------------------------
% 20.74/4.14 % (716)------------------------------
% 20.74/4.15 % (727)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_32501 for (2973ds/906Mi)
% 20.74/4.15 % (728)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_32501 for (2973ds/434Mi)
% 20.74/4.18 % (425)Instruction limit reached!
% 20.74/4.18 % (425)------------------------------
% 20.74/4.18 % (425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.18 % (425)Termination reason: Unknown
% 20.74/4.18 % (425)Termination phase: Saturation
% 20.74/4.18
% 20.74/4.18 % (425)Memory used [KB]: 13304
% 20.74/4.18 % (425)Time elapsed: 1.419 s
% 20.74/4.18 % (425)Instructions burned: 4437 (million)
% 20.74/4.18 % (425)------------------------------
% 20.74/4.18 % (425)------------------------------
% 20.74/4.19 % (729)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_32501 for (2973ds/865Mi)
% 21.08/4.28 % (527)Instruction limit reached!
% 21.08/4.28 % (527)------------------------------
% 21.08/4.28 % (527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.28 % (527)Termination reason: Unknown
% 21.08/4.28 % (527)Termination phase: Saturation
% 21.08/4.28
% 21.08/4.28 % (527)Memory used [KB]: 10490
% 21.08/4.28 % (527)Time elapsed: 1.357 s
% 21.08/4.28 % (527)Instructions burned: 4351 (million)
% 21.08/4.28 % (527)------------------------------
% 21.08/4.28 % (527)------------------------------
% 21.08/4.28 % (728)Instruction limit reached!
% 21.08/4.28 % (728)------------------------------
% 21.08/4.28 % (728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.28 % (728)Termination reason: Unknown
% 21.08/4.28 % (728)Termination phase: Saturation
% 21.08/4.28
% 21.08/4.28 % (728)Memory used [KB]: 7803
% 21.08/4.28 % (728)Time elapsed: 0.153 s
% 21.08/4.28 % (728)Instructions burned: 436 (million)
% 21.08/4.28 % (728)------------------------------
% 21.08/4.28 % (728)------------------------------
% 21.08/4.29 % (730)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_32501 for (2972ds/593Mi)
% 21.08/4.29 % (731)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_32501 for (2972ds/443Mi)
% 21.50/4.36 % (450)Instruction limit reached!
% 21.50/4.36 % (450)------------------------------
% 21.50/4.36 % (450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.50/4.36 % (450)Termination reason: Unknown
% 21.50/4.36 % (450)Termination phase: Saturation
% 21.50/4.36
% 21.50/4.36 % (450)Memory used [KB]: 13816
% 21.50/4.36 % (450)Time elapsed: 1.562 s
% 21.50/4.36 % (450)Instructions burned: 5205 (million)
% 21.50/4.36 % (450)------------------------------
% 21.50/4.36 % (450)------------------------------
% 21.50/4.38 % (732)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_32501 for (2971ds/594Mi)
% 21.68/4.43 % (731)Instruction limit reached!
% 21.68/4.43 % (731)------------------------------
% 21.68/4.43 % (731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/4.43 % (731)Termination reason: Unknown
% 21.68/4.43 % (731)Termination phase: Saturation
% 21.68/4.43
% 21.68/4.43 % (731)Memory used [KB]: 7419
% 21.68/4.43 % (731)Time elapsed: 0.141 s
% 21.68/4.43 % (731)Instructions burned: 444 (million)
% 21.68/4.43 % (731)------------------------------
% 21.68/4.43 % (731)------------------------------
% 21.68/4.44 % (733)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_32501 for (2970ds/327Mi)
% 21.68/4.46 % (729)Instruction limit reached!
% 21.68/4.46 % (729)------------------------------
% 21.68/4.46 % (729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/4.46 % (729)Termination reason: Unknown
% 21.68/4.46 % (729)Termination phase: Saturation
% 21.68/4.46
% 21.68/4.46 % (729)Memory used [KB]: 8571
% 21.68/4.46 % (729)Time elapsed: 0.291 s
% 21.68/4.46 % (729)Instructions burned: 865 (million)
% 21.68/4.46 % (729)------------------------------
% 21.68/4.46 % (729)------------------------------
% 21.68/4.47 % (734)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_32501 for (2970ds/5411Mi)
% 21.68/4.47 % (727)Instruction limit reached!
% 21.68/4.47 % (727)------------------------------
% 21.68/4.47 % (727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/4.47 % (727)Termination reason: Unknown
% 21.68/4.47 % (727)Termination phase: Saturation
% 21.68/4.47
% 21.68/4.47 % (727)Memory used [KB]: 10746
% 21.68/4.47 % (727)Time elapsed: 0.337 s
% 21.68/4.47 % (727)Instructions burned: 906 (million)
% 21.68/4.47 % (727)------------------------------
% 21.68/4.47 % (727)------------------------------
% 21.68/4.47 % (730)Instruction limit reached!
% 21.68/4.47 % (730)------------------------------
% 21.68/4.47 % (730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.68/4.47 % (730)Termination reason: Unknown
% 21.68/4.47 % (730)Termination phase: Saturation
% 21.68/4.47
% 21.68/4.47 % (730)Memory used [KB]: 8187
% 21.68/4.47 % (730)Time elapsed: 0.206 s
% 21.68/4.47 % (730)Instructions burned: 593 (million)
% 21.68/4.47 % (730)------------------------------
% 21.68/4.47 % (730)------------------------------
% 21.68/4.48 % (735)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_32501 for (2970ds/1762Mi)
% 21.68/4.48 % (736)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_32501 for (2970ds/96Mi)
% 22.71/4.50 % (736)Instruction limit reached!
% 22.71/4.50 % (736)------------------------------
% 22.71/4.50 % (736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.71/4.50 % (736)Termination reason: Unknown
% 22.71/4.50 % (736)Termination phase: Saturation
% 22.71/4.50
% 22.71/4.50 % (736)Memory used [KB]: 6652
% 22.71/4.50 % (736)Time elapsed: 0.027 s
% 22.71/4.50 % (736)Instructions burned: 99 (million)
% 22.71/4.50 % (736)------------------------------
% 22.71/4.50 % (736)------------------------------
% 22.71/4.51 % (737)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_32501 for (2969ds/503Mi)
% 22.71/4.52 % (725)Instruction limit reached!
% 22.71/4.52 % (725)------------------------------
% 22.71/4.52 % (725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.71/4.52 % (725)Termination reason: Unknown
% 22.71/4.52 % (725)Termination phase: Saturation
% 22.71/4.52
% 22.71/4.52 % (725)Memory used [KB]: 11769
% 22.71/4.52 % (725)Time elapsed: 0.419 s
% 22.71/4.52 % (725)Instructions burned: 1377 (million)
% 22.71/4.52 % (725)------------------------------
% 22.71/4.52 % (725)------------------------------
% 22.71/4.53 % (738)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_32501 for (2969ds/90Mi)
% 22.71/4.55 % (733)Instruction limit reached!
% 22.71/4.55 % (733)------------------------------
% 22.71/4.55 % (733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.71/4.55 % (733)Termination reason: Unknown
% 22.71/4.55 % (733)Termination phase: Saturation
% 22.71/4.55
% 22.71/4.55 % (733)Memory used [KB]: 7675
% 22.71/4.55 % (733)Time elapsed: 0.105 s
% 22.71/4.55 % (733)Instructions burned: 329 (million)
% 22.71/4.55 % (733)------------------------------
% 22.71/4.55 % (733)------------------------------
% 22.71/4.55 % (734)First to succeed.
% 22.71/4.55 % (738)Instruction limit reached!
% 22.71/4.55 % (738)------------------------------
% 22.71/4.55 % (738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.71/4.55 % (738)Termination reason: Unknown
% 22.71/4.55 % (738)Termination phase: Saturation
% 22.71/4.55
% 22.71/4.55 % (738)Memory used [KB]: 6524
% 22.71/4.55 % (738)Time elapsed: 0.027 s
% 22.71/4.55 % (738)Instructions burned: 90 (million)
% 22.71/4.55 % (738)------------------------------
% 22.71/4.55 % (738)------------------------------
% 22.71/4.55 % (734)Refutation found. Thanks to Tanya!
% 22.71/4.55 % SZS status Theorem for DTF2THF_32501
% 22.71/4.55 % SZS output start Proof for DTF2THF_32501
% 22.71/4.55 thf(type_def_6, type, list: ($tType) > $tType).
% 22.71/4.55 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 22.71/4.55 thf(type_def_8, type, nat: $tType).
% 22.71/4.55 thf(type_def_9, type, a: $tType).
% 22.71/4.55 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 22.71/4.55 thf(func_def_1, type, list: ($tType) > $tType).
% 22.71/4.55 thf(func_def_2, type, nat: $tType).
% 22.71/4.55 thf(func_def_3, type, a: $tType).
% 22.71/4.55 thf(func_def_4, type, type: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_5, type, size: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_6, type, zero: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_7, type, field: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_8, type, order: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_9, type, mult_zero: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_11, type, ordered_ring: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_12, type, wellorder: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_13, type, division_ring: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_14, type, semiring_bits: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_15, type, semidom_divide: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_16, type, semigroup_mult: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_17, type, linordered_idom: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_18, type, linordered_ring: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_19, type, ordered_semiring: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_20, type, linordered_field: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_21, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_22, type, ordered_semiring_0: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_23, type, ordere1490568538miring: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_24, type, linord581940658strict: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_25, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_26, type, linord20386208strict: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_27, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_28, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_29, type, linord893533164strict: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_30, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_31, type, euclid191655569cancel: !>[X0: $tType]:($o)).
% 22.71/4.55 thf(func_def_32, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 22.71/4.55 thf(func_def_33, type, zero_zero: !>[X0: $tType]:(X0)).
% 22.71/4.55 thf(func_def_34, type, product: !>[X0: $tType, X1: $tType]:(list @ X0 > list @ X1 > list @ product_prod @ X0 @ X1)).
% 22.71/4.55 thf(func_def_35, type, suc: nat > nat).
% 22.71/4.55 thf(func_def_36, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 22.71/4.55 thf(func_def_37, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 22.71/4.55 thf(func_def_38, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 22.71/4.55 thf(func_def_39, type, divide_divide: !>[X0: $tType]:(X0 > X0 > X0)).
% 22.71/4.55 thf(func_def_40, type, k: nat).
% 22.71/4.55 thf(func_def_41, type, n: nat).
% 22.71/4.55 thf(func_def_42, type, xs: list @ a).
% 22.71/4.55 thf(func_def_54, type, sK0: nat > nat).
% 22.71/4.55 thf(func_def_55, type, sK1: (nat > nat > $o) > nat).
% 22.71/4.55 thf(func_def_56, type, sK2: (nat > nat > $o) > nat).
% 22.71/4.55 thf(func_def_57, type, sK3: (nat > nat > $o) > nat).
% 22.71/4.55 thf(func_def_58, type, sK4: (nat > nat > $o) > nat).
% 22.71/4.55 thf(func_def_59, type, sK5: nat > nat > nat).
% 22.71/4.55 thf(func_def_60, type, sK6: (nat > $o) > nat).
% 22.71/4.55 thf(func_def_61, type, sK7: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_62, type, sK8: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_63, type, sK9: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_64, type, sK10: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_65, type, sK11: (nat > $o) > nat).
% 22.71/4.55 thf(func_def_66, type, sK12: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_67, type, sK13: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_68, type, sK14: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_69, type, sK15: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_70, type, sK16: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_71, type, sK17: (nat > $o) > nat > nat).
% 22.71/4.55 thf(func_def_72, type, sK18: (nat > $o) > nat).
% 22.71/4.55 thf(func_def_73, type, sK19: nat > nat).
% 22.71/4.55 thf(func_def_74, type, sK20: nat > nat > nat).
% 22.71/4.55 thf(func_def_75, type, sK21: !>[X0: $tType]:(nat > list @ X0)).
% 22.71/4.55 thf(func_def_76, type, sK22: nat > nat).
% 22.71/4.55 thf(func_def_77, type, sK23: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 22.71/4.55 thf(func_def_78, type, sK24: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 22.71/4.55 thf(func_def_79, type, sK25: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 22.71/4.55 thf(func_def_80, type, sK26: nat > nat > nat).
% 22.71/4.55 thf(func_def_81, type, sK27: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 22.71/4.55 thf(func_def_82, type, sK28: (nat > $o) > nat).
% 22.71/4.55 thf(func_def_83, type, sK29: nat > nat > nat).
% 22.71/4.55 thf(func_def_84, type, sK30: (nat > $o) > nat).
% 22.71/4.55 thf(func_def_85, type, sK31: (nat > nat > $o) > nat).
% 22.71/4.55 thf(func_def_86, type, sK32: (nat > nat > $o) > nat).
% 22.71/4.55 thf(func_def_87, type, sK33: (nat > nat > $o) > nat).
% 22.71/4.55 thf(func_def_88, type, sK34: (nat > nat > $o) > nat).
% 22.71/4.55 thf(func_def_89, type, sK35: nat > nat).
% 22.71/4.55 thf(func_def_90, type, sK36: (nat > $o) > nat).
% 22.71/4.55 thf(func_def_91, type, sK37: nat > nat).
% 22.71/4.55 thf(func_def_92, type, sK38: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0)).
% 22.71/4.55 thf(func_def_93, type, sK39: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat)).
% 22.71/4.55 thf(func_def_94, type, sK40: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0)).
% 22.71/4.55 thf(func_def_95, type, sK41: (nat > $o) > nat).
% 22.71/4.55 thf(func_def_97, type, ph43: !>[X0: $tType]:(X0)).
% 22.71/4.55 thf(f1939,plain,(
% 22.71/4.55 $false),
% 22.71/4.55 inference(avatar_sat_refutation,[status(thm)],[f1364,f1378,f1767,f1938])).
% 22.71/4.55 thf(f1938,plain,(
% 22.71/4.55 ~spl42_5),
% 22.71/4.55 inference(avatar_contradiction_clause,[status(thm)],[f1937])).
% 22.71/4.55 thf(f1937,plain,(
% 22.71/4.55 $false | ~spl42_5),
% 22.71/4.55 inference(subsumption_resolution,[status(thm)],[f1934,f1285])).
% 22.71/4.55 thf(f1285,plain,(
% 22.71/4.55 ( ! [X1 : nat] : (((ord_less @ nat @ X1 @ X1) != $true)) )),
% 22.71/4.55 inference(equality_resolution,[status(thm)],[f1196])).
% 22.71/4.55 thf(f1196,plain,(
% 22.71/4.55 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($true != (ord_less @ nat @ X1 @ X0))) )),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f1013])).
% 22.71/4.55 thf(f1013,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (((X0 != X1) | (($true != (ord_less @ nat @ X1 @ X0)) & ((ord_less @ nat @ X0 @ X1) != $true))) & (($true = (ord_less @ nat @ X1 @ X0)) | ((ord_less @ nat @ X0 @ X1) = $true) | (X0 = X1)))),
% 22.71/4.55 inference(flattening,[status(thm)],[f1012])).
% 22.71/4.55 thf(f1012,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (((X0 != X1) | (($true != (ord_less @ nat @ X1 @ X0)) & ((ord_less @ nat @ X0 @ X1) != $true))) & ((($true = (ord_less @ nat @ X1 @ X0)) | ((ord_less @ nat @ X0 @ X1) = $true)) | (X0 = X1)))),
% 22.71/4.55 inference(nnf_transformation,[status(thm)],[f399])).
% 22.71/4.55 thf(f399,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((X0 != X1) <=> (($true = (ord_less @ nat @ X1 @ X0)) | ((ord_less @ nat @ X0 @ X1) = $true)))),
% 22.71/4.55 inference(fool_elimination,[status(thm)],[f398])).
% 22.71/4.55 thf(f398,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X1 @ X0) | (ord_less @ nat @ X0 @ X1) = (X0 != X1))),
% 22.71/4.55 inference(rectify,[status(thm)],[f40])).
% 22.71/4.55 thf(f40,axiom,(
% 22.71/4.55 ! [X3 : nat,X2 : nat] : ((ord_less @ nat @ X2 @ X3) | (ord_less @ nat @ X3 @ X2) = (X2 != X3))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',fact_39_nat__neq__iff)).
% 22.71/4.55 thf(f1934,plain,(
% 22.71/4.55 ($true = (ord_less @ nat @ n @ n)) | ~spl42_5),
% 22.71/4.55 inference(trivial_inequality_removal,[status(thm)],[f1932])).
% 22.71/4.55 thf(f1932,plain,(
% 22.71/4.55 ($true != $true) | ($true = (ord_less @ nat @ n @ n)) | ~spl42_5),
% 22.71/4.55 inference(superposition,[status(thm)],[f1179,f1781])).
% 22.71/4.55 thf(f1781,plain,(
% 22.71/4.55 ((ord_less @ nat @ (suc @ n) @ n) = $true) | ~spl42_5),
% 22.71/4.55 inference(trivial_inequality_removal,[status(thm)],[f1780])).
% 22.71/4.55 thf(f1780,plain,(
% 22.71/4.55 ((ord_less @ nat @ (suc @ n) @ n) = $true) | ($true != $true) | ~spl42_5),
% 22.71/4.55 inference(superposition,[status(thm)],[f1305,f1372])).
% 22.71/4.55 thf(f1372,plain,(
% 22.71/4.55 ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)) = $true) | ~spl42_5),
% 22.71/4.55 inference(avatar_component_clause,[status(thm)],[f1370])).
% 22.71/4.55 thf(f1370,definition,(
% 22.71/4.55 spl42_5 <=> ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)) = $true)),
% 22.71/4.55 introduced(definition,[new_symbols(naming,[spl42_5])],[avatar_definition])).
% 22.71/4.55 thf(f1305,plain,(
% 22.71/4.55 ( ! [X0 : nat] : (($true != (ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ X0 @ k))) | ($true = (ord_less @ nat @ (suc @ n) @ X0))) )),
% 22.71/4.55 inference(superposition,[status(thm)],[f1152,f1219])).
% 22.71/4.55 thf(f1219,plain,(
% 22.71/4.55 ((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k) = (suc @ n))),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f279])).
% 22.71/4.55 thf(f279,axiom,(
% 22.71/4.55 ((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k) = (suc @ n))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',conj_0)).
% 22.71/4.55 thf(f1152,plain,(
% 22.71/4.55 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1) = $true) | ((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2)) != $true)) )),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f849])).
% 22.71/4.55 thf(f849,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1) = $true) | ((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2)) != $true))),
% 22.71/4.55 inference(ennf_transformation,[status(thm)],[f409])).
% 22.71/4.55 thf(f409,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2)) = $true) => ((ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1) = $true))),
% 22.71/4.55 inference(fool_elimination,[status(thm)],[f408])).
% 22.71/4.55 thf(f408,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less @ nat @ X0 @ (times_times @ nat @ X1 @ X2)) => (ord_less @ nat @ (divide_divide @ nat @ X0 @ X2) @ X1))),
% 22.71/4.55 inference(rectify,[status(thm)],[f97])).
% 22.71/4.55 thf(f97,axiom,(
% 22.71/4.55 ! [X3 : nat,X27 : nat,X2 : nat] : ((ord_less @ nat @ X3 @ (times_times @ nat @ X27 @ X2)) => (ord_less @ nat @ (divide_divide @ nat @ X3 @ X2) @ X27))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',fact_96_Euclidean__Division_Oless__mult__imp__div__less)).
% 22.71/4.55 thf(f1179,plain,(
% 22.71/4.55 ( ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ (suc @ X0) @ X1) != $true) | ((ord_less @ nat @ X0 @ X1) = $true)) )),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f852])).
% 22.71/4.55 thf(f852,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ (suc @ X0) @ X1) != $true) | ((ord_less @ nat @ X0 @ X1) = $true))),
% 22.71/4.55 inference(ennf_transformation,[status(thm)],[f411])).
% 22.71/4.55 thf(f411,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ (suc @ X0) @ X1) = $true) => ((ord_less @ nat @ X0 @ X1) = $true))),
% 22.71/4.55 inference(fool_elimination,[status(thm)],[f410])).
% 22.71/4.55 thf(f410,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ (suc @ X0) @ X1) => (ord_less @ nat @ X0 @ X1))),
% 22.71/4.55 inference(rectify,[status(thm)],[f78])).
% 22.71/4.55 thf(f78,axiom,(
% 22.71/4.55 ! [X3 : nat,X2 : nat] : ((ord_less @ nat @ (suc @ X3) @ X2) => (ord_less @ nat @ X3 @ X2))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',fact_77_Suc__lessD)).
% 22.71/4.55 thf(f1767,plain,(
% 22.71/4.55 ~spl42_2 | ~spl42_6),
% 22.71/4.55 inference(avatar_contradiction_clause,[status(thm)],[f1766])).
% 22.71/4.55 thf(f1766,plain,(
% 22.71/4.55 $false | (~spl42_2 | ~spl42_6)),
% 22.71/4.55 inference(subsumption_resolution,[status(thm)],[f1765,f1285])).
% 22.71/4.55 thf(f1765,plain,(
% 22.71/4.55 ((ord_less @ nat @ (suc @ n) @ (suc @ n)) = $true) | (~spl42_2 | ~spl42_6)),
% 22.71/4.55 inference(forward_demodulation,[status(thm)],[f1764,f1532])).
% 22.71/4.55 thf(f1532,plain,(
% 22.71/4.55 ((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k) = n) | (~spl42_2 | ~spl42_6)),
% 22.71/4.55 inference(subsumption_resolution,[status(thm)],[f1419,f1324])).
% 22.71/4.55 thf(f1324,plain,(
% 22.71/4.55 ($true = (ord_less @ nat @ zero_zero @ nat @ k)) | ~spl42_2),
% 22.71/4.55 inference(avatar_component_clause,[status(thm)],[f1323])).
% 22.71/4.55 thf(f1323,definition,(
% 22.71/4.55 spl42_2 <=> ($true = (ord_less @ nat @ zero_zero @ nat @ k))),
% 22.71/4.55 introduced(definition,[new_symbols(naming,[spl42_2])],[avatar_definition])).
% 22.71/4.55 thf(f1419,plain,(
% 22.71/4.55 ((divide_divide @ nat @ (size_size @ list @ a @ xs) @ k) = n) | ($true != (ord_less @ nat @ zero_zero @ nat @ k)) | ~spl42_6),
% 22.71/4.55 inference(superposition,[status(thm)],[f1209,f1376])).
% 22.71/4.55 thf(f1376,plain,(
% 22.71/4.55 ((size_size @ list @ a @ xs) = (times_times @ nat @ n @ k)) | ~spl42_6),
% 22.71/4.55 inference(avatar_component_clause,[status(thm)],[f1374])).
% 22.71/4.55 thf(f1374,definition,(
% 22.71/4.55 spl42_6 <=> ((size_size @ list @ a @ xs) = (times_times @ nat @ n @ k))),
% 22.71/4.55 introduced(definition,[new_symbols(naming,[spl42_6])],[avatar_definition])).
% 22.71/4.55 thf(f1209,plain,(
% 22.71/4.55 ( ! [X0 : nat,X1 : nat] : (((divide_divide @ nat @ (times_times @ nat @ X1 @ X0) @ X0) = X1) | ($true != (ord_less @ nat @ zero_zero @ nat @ X0))) )),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f897])).
% 22.71/4.55 thf(f897,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (($true != (ord_less @ nat @ zero_zero @ nat @ X0)) | ((divide_divide @ nat @ (times_times @ nat @ X1 @ X0) @ X0) = X1))),
% 22.71/4.55 inference(ennf_transformation,[status(thm)],[f511])).
% 22.71/4.55 thf(f511,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ zero_zero @ nat @ X0)) => ((divide_divide @ nat @ (times_times @ nat @ X1 @ X0) @ X0) = X1))),
% 22.71/4.55 inference(fool_elimination,[status(thm)],[f510])).
% 22.71/4.55 thf(f510,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ zero_zero @ nat @ X0) => ((divide_divide @ nat @ (times_times @ nat @ X1 @ X0) @ X0) = X1))),
% 22.71/4.55 inference(rectify,[status(thm)],[f1])).
% 22.71/4.55 thf(f1,axiom,(
% 22.71/4.55 ! [X2 : nat,X3 : nat] : ((ord_less @ nat @ zero_zero @ nat @ X2) => ((divide_divide @ nat @ (times_times @ nat @ X3 @ X2) @ X2) = X3))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',fact_0_div__mult__self__is__m)).
% 22.71/4.55 thf(f1764,plain,(
% 22.71/4.55 ($true = (ord_less @ nat @ (suc @ n) @ (suc @ (divide_divide @ nat @ (size_size @ list @ a @ xs) @ k)))) | ~spl42_2),
% 22.71/4.55 inference(subsumption_resolution,[status(thm)],[f1753,f1324])).
% 22.71/4.55 thf(f1753,plain,(
% 22.71/4.55 ($true != (ord_less @ nat @ zero_zero @ nat @ k)) | ($true = (ord_less @ nat @ (suc @ n) @ (suc @ (divide_divide @ nat @ (size_size @ list @ a @ xs) @ k))))),
% 22.71/4.55 inference(trivial_inequality_removal,[status(thm)],[f1748])).
% 22.71/4.55 thf(f1748,plain,(
% 22.71/4.55 ($true != $true) | ($true != (ord_less @ nat @ zero_zero @ nat @ k)) | ($true = (ord_less @ nat @ (suc @ n) @ (suc @ (divide_divide @ nat @ (size_size @ list @ a @ xs) @ k))))),
% 22.71/4.55 inference(superposition,[status(thm)],[f1305,f1255])).
% 22.71/4.55 thf(f1255,plain,(
% 22.71/4.55 ( ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ X1 @ (times_times @ nat @ (suc @ (divide_divide @ nat @ X1 @ X0)) @ X0)) = $true) | ($true != (ord_less @ nat @ zero_zero @ nat @ X0))) )),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f835])).
% 22.71/4.55 thf(f835,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ X1 @ (times_times @ nat @ (suc @ (divide_divide @ nat @ X1 @ X0)) @ X0)) = $true) | ($true != (ord_less @ nat @ zero_zero @ nat @ X0)))),
% 22.71/4.55 inference(ennf_transformation,[status(thm)],[f549])).
% 22.71/4.55 thf(f549,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ zero_zero @ nat @ X0)) => ((ord_less @ nat @ X1 @ (times_times @ nat @ (suc @ (divide_divide @ nat @ X1 @ X0)) @ X0)) = $true))),
% 22.71/4.55 inference(fool_elimination,[status(thm)],[f548])).
% 22.71/4.55 thf(f548,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ zero_zero @ nat @ X0) => (ord_less @ nat @ X1 @ (times_times @ nat @ (suc @ (divide_divide @ nat @ X1 @ X0)) @ X0)))),
% 22.71/4.55 inference(rectify,[status(thm)],[f109])).
% 22.71/4.55 thf(f109,axiom,(
% 22.71/4.55 ! [X3 : nat,X2 : nat] : ((ord_less @ nat @ zero_zero @ nat @ X3) => (ord_less @ nat @ X2 @ (times_times @ nat @ (suc @ (divide_divide @ nat @ X2 @ X3)) @ X3)))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',fact_108_less__div__Suc__mult)).
% 22.71/4.55 thf(f1378,plain,(
% 22.71/4.55 spl42_5 | spl42_6),
% 22.71/4.55 inference(avatar_split_clause,[status(thm)],[f1367,f1374,f1370])).
% 22.71/4.55 thf(f1367,plain,(
% 22.71/4.55 ((size_size @ list @ a @ xs) = (times_times @ nat @ n @ k)) | ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)) = $true)),
% 22.71/4.55 inference(trivial_inequality_removal,[status(thm)],[f1365])).
% 22.71/4.55 thf(f1365,plain,(
% 22.71/4.55 ((ord_less @ nat @ (size_size @ list @ a @ xs) @ (times_times @ nat @ n @ k)) = $true) | ((size_size @ list @ a @ xs) = (times_times @ nat @ n @ k)) | ($true != $true)),
% 22.71/4.55 inference(superposition,[status(thm)],[f1224,f1119])).
% 22.71/4.55 thf(f1119,plain,(
% 22.71/4.55 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ X1 @ X0)) | (X0 = X1) | ((ord_less @ nat @ X0 @ X1) = $true)) )),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f894])).
% 22.71/4.55 thf(f894,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ X1 @ X0)) | ((ord_less @ nat @ X0 @ X1) = $true) | (X0 = X1))),
% 22.71/4.55 inference(flattening,[status(thm)],[f893])).
% 22.71/4.55 thf(f893,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((($true = (ord_less @ nat @ X1 @ X0)) | ((ord_less @ nat @ X0 @ X1) = $true)) | (X0 = X1))),
% 22.71/4.55 inference(ennf_transformation,[status(thm)],[f802])).
% 22.71/4.55 thf(f802,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (((ord_less @ nat @ X0 @ X1) != $true) => ($true = (ord_less @ nat @ X1 @ X0))))),
% 22.71/4.55 inference(flattening,[status(thm)],[f741])).
% 22.71/4.55 thf(f741,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~((ord_less @ nat @ X0 @ X1) = $true) => ($true = (ord_less @ nat @ X1 @ X0))))),
% 22.71/4.55 inference(fool_elimination,[status(thm)],[f740])).
% 22.71/4.55 thf(f740,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X1 @ X0)))),
% 22.71/4.55 inference(rectify,[status(thm)],[f33])).
% 22.71/4.55 thf(f33,axiom,(
% 22.71/4.55 ! [X16 : nat,X17 : nat] : ((X16 != X17) => (~(ord_less @ nat @ X16 @ X17) => (ord_less @ nat @ X17 @ X16)))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',fact_32_linorder__neqE__nat)).
% 22.71/4.55 thf(f1224,plain,(
% 22.71/4.55 ((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs)) != $true)),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f796])).
% 22.71/4.55 thf(f796,plain,(
% 22.71/4.55 ((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs)) != $true)),
% 22.71/4.55 inference(flattening,[status(thm)],[f309])).
% 22.71/4.55 thf(f309,plain,(
% 22.71/4.55 ~((ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs)) = $true)),
% 22.71/4.55 inference(fool_elimination,[status(thm)],[f308])).
% 22.71/4.55 thf(f308,plain,(
% 22.71/4.55 ~(ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 22.71/4.55 inference(rectify,[status(thm)],[f282])).
% 22.71/4.55 thf(f282,negated_conjecture,(
% 22.71/4.55 ~(ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 22.71/4.55 inference(negated_conjecture,[status(cth)],[f281])).
% 22.71/4.55 thf(f281,conjecture,(
% 22.71/4.55 (ord_less @ nat @ (times_times @ nat @ n @ k) @ (size_size @ list @ a @ xs))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',conj_2)).
% 22.71/4.55 thf(f1364,plain,(
% 22.71/4.55 spl42_2),
% 22.71/4.55 inference(avatar_contradiction_clause,[status(thm)],[f1363])).
% 22.71/4.55 thf(f1363,plain,(
% 22.71/4.55 $false | spl42_2),
% 22.71/4.55 inference(subsumption_resolution,[status(thm)],[f1362,f1264])).
% 22.71/4.55 thf(f1264,plain,(
% 22.71/4.55 ( ! [X0 : nat] : (((ord_less @ nat @ X0 @ zero_zero @ nat) != $true)) )),
% 22.71/4.55 inference(equality_resolution,[status(thm)],[f1065])).
% 22.71/4.55 thf(f1065,plain,(
% 22.71/4.55 ( ! [X0 : nat,X1 : nat] : ((zero_zero @ nat != X1) | ((ord_less @ nat @ X0 @ X1) != $true)) )),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f890])).
% 22.71/4.55 thf(f890,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((zero_zero @ nat != X1) | ((ord_less @ nat @ X0 @ X1) != $true))),
% 22.71/4.55 inference(ennf_transformation,[status(thm)],[f751])).
% 22.71/4.55 thf(f751,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ X0 @ X1) = $true) => (zero_zero @ nat != X1))),
% 22.71/4.55 inference(fool_elimination,[status(thm)],[f750])).
% 22.71/4.55 thf(f750,plain,(
% 22.71/4.55 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (zero_zero @ nat != X1))),
% 22.71/4.55 inference(rectify,[status(thm)],[f58])).
% 22.71/4.55 thf(f58,axiom,(
% 22.71/4.55 ! [X3 : nat,X2 : nat] : ((ord_less @ nat @ X3 @ X2) => (zero_zero @ nat != X2))),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',fact_57_gr__implies__not0)).
% 22.71/4.55 thf(f1362,plain,(
% 22.71/4.55 ((ord_less @ nat @ k @ zero_zero @ nat) = $true) | spl42_2),
% 22.71/4.55 inference(subsumption_resolution,[status(thm)],[f1344,f1105])).
% 22.71/4.55 thf(f1105,plain,(
% 22.71/4.55 (zero_zero @ nat != k)),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f280])).
% 22.71/4.55 thf(f280,axiom,(
% 22.71/4.55 (zero_zero @ nat != k)),
% 22.71/4.55 file('/export/starexec/sandbox/tmp/tmp.mVZc4CeeSp/DTF2THF_32501.p',conj_1)).
% 22.71/4.55 thf(f1344,plain,(
% 22.71/4.55 (zero_zero @ nat = k) | ((ord_less @ nat @ k @ zero_zero @ nat) = $true) | spl42_2),
% 22.71/4.55 inference(trivial_inequality_removal,[status(thm)],[f1343])).
% 22.71/4.55 thf(f1343,plain,(
% 22.71/4.55 (zero_zero @ nat = k) | ($true != $true) | ((ord_less @ nat @ k @ zero_zero @ nat) = $true) | spl42_2),
% 22.71/4.55 inference(superposition,[status(thm)],[f1325,f1194])).
% 22.71/4.55 thf(f1194,plain,(
% 22.71/4.55 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ X1 @ X0)) | ((ord_less @ nat @ X0 @ X1) = $true) | (X0 = X1)) )),
% 22.71/4.55 inference(cnf_transformation,[status(thm)],[f1013])).
% 22.71/4.55 thf(f1325,plain,(
% 22.71/4.55 ($true != (ord_less @ nat @ zero_zero @ nat @ k)) | spl42_2),
% 22.71/4.55 inference(avatar_component_clause,[status(thm)],[f1323])).
% 22.71/4.55 % SZS output end Proof for DTF2THF_32501
% 22.71/4.55 % (734)------------------------------
% 22.71/4.55 % (734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.71/4.55 % (734)Termination reason: Refutation
% 22.71/4.55
% 22.71/4.55 % (734)Memory used [KB]: 7036
% 22.71/4.55 % (734)Time elapsed: 0.087 s
% 22.71/4.55 % (734)Instructions burned: 266 (million)
% 22.71/4.55 % (734)------------------------------
% 22.71/4.55 % (734)------------------------------
% 22.71/4.55 % (32692)Success in time 3.053 s
%------------------------------------------------------------------------------