%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP044^2 : 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 : n029.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 08:55:06 AM UTC 2026
% Result : Theorem 23.12s 4.63s
% Output : Refutation 23.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP044^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n029.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
% 0.16/0.33 % DateTime : Tue Feb 24 08:24:29 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : ITP044^2 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.45 % Domain : Interactive Theorem Proving
% 0.29/0.45 % Problem : Sledgehammer Descartes_Sign_Rule problem prob_761__5872108_1
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Des21]
% 0.29/0.45 % Names : Descartes_Sign_Rule/prob_761__5872108_1 [Des21]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.00 v8.1.0, 0.25 v7.5.0
% 0.29/0.45 % Syntax : Number of formulae : 437 ( 94 unt; 72 typ; 0 def)
% 0.29/0.45 % Number of atoms : 901 ( 374 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 11 ( 2 avg)
% 0.29/0.45 % Number of connectives : 3538 ( 96 ~; 27 |; 45 &;2942 @)
% 0.29/0.45 % ( 0 <=>; 428 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 20 ( 6 avg)
% 0.29/0.45 % Number of types : 3 ( 2 usr)
% 0.29/0.45 % Number of type conns : 107 ( 107 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 71 ( 70 usr; 3 con; 0-3 aty)
% 0.29/0.45 % Number of variables : 942 ( 13 ^; 856 !; 9 ?; 942 :)
% 0.29/0.45 % ( 64 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.45 % SPC : TH1_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:26:47.381
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % Could-be-implicit typings (4)
% 0.29/0.45 thf(ty_t_Polynomial_Opoly,type,
% 0.29/0.45 poly: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_List_Olist,type,
% 0.29/0.45 list: $tType > $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_t_Nat_Onat,type,
% 0.29/0.45 nat: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(ty_tf_a,type,
% 0.29/0.45 a: $tType ).
% 0.29/0.45
% 0.29/0.45 % Explicit typings (68)
% 0.29/0.45 thf(sy_cl_Rings_Ocomm__ring__1,type,
% 0.29/0.45 comm_ring_1:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_HOL_Otype,type,
% 0.29/0.45 type:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Oone,type,
% 0.29/0.45 one:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Osgn,type,
% 0.29/0.45 sgn:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Oidom,type,
% 0.29/0.45 idom:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Oring,type,
% 0.29/0.45 ring:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Oplus,type,
% 0.29/0.45 plus:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ozero,type,
% 0.29/0.45 zero:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Oring__1,type,
% 0.29/0.45 ring_1:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ouminus,type,
% 0.29/0.45 uminus:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.29/0.45 ord:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Nat_Oring__char__0,type,
% 0.29/0.45 ring_char_0:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Num_Oneg__numeral,type,
% 0.29/0.45 neg_numeral:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Ocomm__ring,type,
% 0.29/0.45 comm_ring:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Omult__zero,type,
% 0.29/0.45 mult_zero:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ogroup__add,type,
% 0.29/0.45 group_add:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Omonoid__add,type,
% 0.29/0.45 monoid_add:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.29/0.45 monoid_mult:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.29/0.45 linorder:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Oidom__abs__sgn,type,
% 0.29/0.45 idom_abs_sgn:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.29/0.45 zero_neq_one:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Oab__group__add,type,
% 0.29/0.45 ab_group_add:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Orderings_Owellorder,type,
% 0.29/0.45 wellorder:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Ozero__less__one,type,
% 0.29/0.45 zero_less_one:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.29/0.45 semigroup_mult:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Ocomm__semiring__0,type,
% 0.29/0.45 comm_semiring_0:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.29/0.45 comm_semiring_1:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.29/0.45 linordered_idom:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Olinordered__ring,type,
% 0.29/0.45 linordered_ring:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.29/0.45 comm_monoid_add:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 0.29/0.45 comm_monoid_mult:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.29/0.45 ab_semigroup_mult:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.29/0.45 boolean_algebra:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.29/0.45 linordered_semidom:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.29/0.45 ordered_ab_group_add:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 0.29/0.45 linord581940658strict:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Oring__1__no__zero__divisors,type,
% 0.29/0.45 ring_11004092258visors:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.29/0.45 linord219039673up_add:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 0.29/0.45 semiri1193490041visors:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Olinordered__semiring__strict,type,
% 0.29/0.45 linord20386208strict:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.29/0.45 linord1659791738miring:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.29/0.45 canoni770627133id_add:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Olinordered__comm__semiring__strict,type,
% 0.29/0.45 linord893533164strict:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 0.29/0.45 semiri1923998003cancel:
% 0.29/0.45 !>[A: $tType] : $o ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Opsums,type,
% 0.29/0.45 descar1668888542_psums:
% 0.29/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Oreduce__root,type,
% 0.29/0.45 descar316357986e_root:
% 0.29/0.45 !>[A: $tType] : ( A > ( poly @ A ) > ( poly @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Osign__changes,type,
% 0.29/0.45 descar149487500hanges:
% 0.29/0.45 !>[A: $tType] : ( ( list @ A ) > nat ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.29/0.45 one_one:
% 0.29/0.45 !>[A: $tType] : A ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.29/0.45 times_times:
% 0.29/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.29/0.45 uminus_uminus:
% 0.29/0.45 !>[A: $tType] : ( A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.29/0.45 zero_zero:
% 0.29/0.45 !>[A: $tType] : A ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Oappend,type,
% 0.29/0.45 append:
% 0.29/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Olist_OCons,type,
% 0.29/0.45 cons:
% 0.29/0.45 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Olist_ONil,type,
% 0.29/0.45 nil:
% 0.29/0.45 !>[A: $tType] : ( list @ A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_On__lists,type,
% 0.29/0.45 n_lists:
% 0.29/0.45 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_List_Onull,type,
% 0.29/0.45 null:
% 0.29/0.45 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec,type,
% 0.29/0.45 neg_numeral_dbl_dec:
% 0.29/0.45 !>[A: $tType] : ( A > A ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.29/0.45 ord_less:
% 0.29/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Polynomial_OPoly,type,
% 0.29/0.45 poly2:
% 0.29/0.45 !>[A: $tType] : ( ( list @ A ) > ( poly @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Polynomial_Ocoeffs,type,
% 0.29/0.45 coeffs:
% 0.29/0.45 !>[A: $tType] : ( ( poly @ A ) > ( list @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Polynomial_Ois__zero,type,
% 0.29/0.45 is_zero:
% 0.29/0.45 !>[A: $tType] : ( ( poly @ A ) > $o ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Polynomial_OpCons,type,
% 0.29/0.45 pCons:
% 0.29/0.45 !>[A: $tType] : ( A > ( poly @ A ) > ( poly @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Polynomial_Opoly__cutoff,type,
% 0.29/0.45 poly_cutoff:
% 0.29/0.45 !>[A: $tType] : ( nat > ( poly @ A ) > ( poly @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_c_Polynomial_Osmult,type,
% 0.29/0.45 smult:
% 0.29/0.45 !>[A: $tType] : ( A > ( poly @ A ) > ( poly @ A ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_g,type,
% 0.29/0.45 g: poly @ a ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_v,type,
% 0.29/0.45 v: ( poly @ a ) > nat ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_xs____,type,
% 0.29/0.45 xs: list @ a ).
% 0.29/0.45
% 0.29/0.45 thf(sy_v_ys____,type,
% 0.29/0.45 ys: list @ a ).
% 0.29/0.45
% 0.29/0.45 % Relevant facts (252)
% 0.29/0.45 thf(fact_0_v__def,axiom,
% 0.29/0.45 ( v
% 0.29/0.45 = ( ^ [F: poly @ a] : ( descar149487500hanges @ a @ ( coeffs @ a @ F ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % v_def
% 0.29/0.45 thf(fact_1_nz,axiom,
% 0.29/0.45 ( g
% 0.29/0.45 != ( zero_zero @ ( poly @ a ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % nz
% 0.29/0.45 thf(fact_2_coeffs__eq__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ( ( ^ [Y: poly @ A,Z: poly @ A] : ( Y = Z ) )
% 0.29/0.45 = ( ^ [P: poly @ A,Q: poly @ A] :
% 0.29/0.45 ( ( coeffs @ A @ P )
% 0.29/0.45 = ( coeffs @ A @ Q ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % coeffs_eq_iff
% 0.29/0.45 thf(fact_3_ys,axiom,
% 0.29/0.45 ( ys
% 0.29/0.45 = ( descar1668888542_psums @ a @ xs ) ) ).
% 0.29/0.45
% 0.29/0.45 % ys
% 0.29/0.45 thf(fact_4_sign__changes__coeff__sign__changes,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_idom @ A )
% 0.29/0.45 => ! [Xs: list @ A,P2: poly @ A] :
% 0.29/0.45 ( ( ( poly2 @ A @ Xs )
% 0.29/0.45 = P2 )
% 0.29/0.45 => ( ( descar149487500hanges @ A @ Xs )
% 0.29/0.45 = ( descar149487500hanges @ A @ ( coeffs @ A @ P2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sign_changes_coeff_sign_changes
% 0.29/0.45 thf(fact_5_ys__def,axiom,
% 0.29/0.45 ( ys
% 0.29/0.45 = ( append @ a @ ( coeffs @ a @ g ) @ ( cons @ a @ ( zero_zero @ a ) @ ( nil @ a ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ys_def
% 0.29/0.45 thf(fact_6_coeff__sign__changes__reduce__root,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_idom @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A] :
% 0.29/0.45 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.45 => ( ( descar149487500hanges @ A @ ( coeffs @ A @ ( descar316357986e_root @ A @ A2 @ P2 ) ) )
% 0.29/0.45 = ( descar149487500hanges @ A @ ( coeffs @ A @ P2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % coeff_sign_changes_reduce_root
% 0.29/0.45 thf(fact_7_is__zero__def,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ( ( is_zero @ A )
% 0.29/0.45 = ( ^ [P: poly @ A] : ( null @ A @ ( coeffs @ A @ P ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % is_zero_def
% 0.29/0.45 thf(fact_8_Poly__coeffs,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [P2: poly @ A] :
% 0.29/0.45 ( ( poly2 @ A @ ( coeffs @ A @ P2 ) )
% 0.29/0.45 = P2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % Poly_coeffs
% 0.29/0.45 thf(fact_9_sign__changes__Nil,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ( sgn @ A )
% 0.29/0.45 & ( zero @ A ) )
% 0.29/0.45 => ( ( descar149487500hanges @ A @ ( nil @ A ) )
% 0.29/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sign_changes_Nil
% 0.29/0.45 thf(fact_10_xs__def,axiom,
% 0.29/0.45 ( xs
% 0.29/0.45 = ( coeffs @ a @ ( times_times @ ( poly @ a ) @ ( pCons @ a @ ( one_one @ a ) @ ( pCons @ a @ ( uminus_uminus @ a @ ( one_one @ a ) ) @ ( zero_zero @ ( poly @ a ) ) ) ) @ g ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % xs_def
% 0.29/0.45 thf(fact_11_coeff__sign__changes__smult,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_idom @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A] :
% 0.29/0.45 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.45 => ( ( descar149487500hanges @ A @ ( coeffs @ A @ ( smult @ A @ A2 @ P2 ) ) )
% 0.29/0.45 = ( descar149487500hanges @ A @ ( coeffs @ A @ P2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % coeff_sign_changes_smult
% 0.29/0.45 thf(fact_12_sign__changes__0__Cons,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( idom_abs_sgn @ A )
% 0.29/0.45 => ! [Xs: list @ A] :
% 0.29/0.45 ( ( descar149487500hanges @ A @ ( cons @ A @ ( zero_zero @ A ) @ Xs ) )
% 0.29/0.45 = ( descar149487500hanges @ A @ Xs ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sign_changes_0_Cons
% 0.29/0.45 thf(fact_13_sign__changes__Cons__Cons__0,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_idom @ A )
% 0.29/0.45 => ! [X: A,Xs: list @ A] :
% 0.29/0.45 ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( cons @ A @ ( zero_zero @ A ) @ Xs ) ) )
% 0.29/0.45 = ( descar149487500hanges @ A @ ( cons @ A @ X @ Xs ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sign_changes_Cons_Cons_0
% 0.29/0.45 thf(fact_14_pCons__eq__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A,B: A,Q2: poly @ A] :
% 0.29/0.45 ( ( ( pCons @ A @ A2 @ P2 )
% 0.29/0.45 = ( pCons @ A @ B @ Q2 ) )
% 0.29/0.45 = ( ( A2 = B )
% 0.29/0.45 & ( P2 = Q2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % pCons_eq_iff
% 0.29/0.45 thf(fact_15_minus__pCons,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ab_group_add @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A] :
% 0.29/0.45 ( ( uminus_uminus @ ( poly @ A ) @ ( pCons @ A @ A2 @ P2 ) )
% 0.29/0.45 = ( pCons @ A @ ( uminus_uminus @ A @ A2 ) @ ( uminus_uminus @ ( poly @ A ) @ P2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % minus_pCons
% 0.29/0.45 thf(fact_16_smult__smult,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [A2: A,B: A,P2: poly @ A] :
% 0.29/0.45 ( ( smult @ A @ A2 @ ( smult @ A @ B @ P2 ) )
% 0.29/0.45 = ( smult @ A @ ( times_times @ A @ A2 @ B ) @ P2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_smult
% 0.29/0.45 thf(fact_17_smult__1__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A )
% 0.29/0.45 => ! [P2: poly @ A] :
% 0.29/0.45 ( ( smult @ A @ ( one_one @ A ) @ P2 )
% 0.29/0.45 = P2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_1_left
% 0.29/0.45 thf(fact_18_smult__minus__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_ring @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A] :
% 0.29/0.45 ( ( smult @ A @ ( uminus_uminus @ A @ A2 ) @ P2 )
% 0.29/0.45 = ( uminus_uminus @ ( poly @ A ) @ ( smult @ A @ A2 @ P2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_minus_left
% 0.29/0.45 thf(fact_19_smult__0__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( smult @ A @ A2 @ ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_0_right
% 0.29/0.45 thf(fact_20_mult__smult__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A,Q2: poly @ A] :
% 0.29/0.45 ( ( times_times @ ( poly @ A ) @ ( smult @ A @ A2 @ P2 ) @ Q2 )
% 0.29/0.45 = ( smult @ A @ A2 @ ( times_times @ ( poly @ A ) @ P2 @ Q2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_smult_left
% 0.29/0.45 thf(fact_21_mult__smult__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [P2: poly @ A,A2: A,Q2: poly @ A] :
% 0.29/0.45 ( ( times_times @ ( poly @ A ) @ P2 @ ( smult @ A @ A2 @ Q2 ) )
% 0.29/0.45 = ( smult @ A @ A2 @ ( times_times @ ( poly @ A ) @ P2 @ Q2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_smult_right
% 0.29/0.45 thf(fact_22_pCons__0__0,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ( ( pCons @ A @ ( zero_zero @ A ) @ ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % pCons_0_0
% 0.29/0.45 thf(fact_23_pCons__eq__0__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A] :
% 0.29/0.45 ( ( ( pCons @ A @ A2 @ P2 )
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 = ( ( A2
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 & ( P2
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % pCons_eq_0_iff
% 0.29/0.45 thf(fact_24_one__poly__eq__simps_I2_J,axiom,
% 0.29/0.45 ! [B2: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ B2 )
% 0.29/0.45 => ( ( pCons @ B2 @ ( one_one @ B2 ) @ ( zero_zero @ ( poly @ B2 ) ) )
% 0.29/0.45 = ( one_one @ ( poly @ B2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % one_poly_eq_simps(2)
% 0.29/0.45 thf(fact_25_one__poly__eq__simps_I1_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A )
% 0.29/0.45 => ( ( one_one @ ( poly @ A ) )
% 0.29/0.45 = ( pCons @ A @ ( one_one @ A ) @ ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % one_poly_eq_simps(1)
% 0.29/0.45 thf(fact_26_smult__0__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [P2: poly @ A] :
% 0.29/0.45 ( ( smult @ A @ ( zero_zero @ A ) @ P2 )
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_0_left
% 0.29/0.45 thf(fact_27_smult__eq__0__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ( comm_semiring_0 @ A )
% 0.29/0.45 & ( semiri1193490041visors @ A ) )
% 0.29/0.45 => ! [A2: A,P2: poly @ A] :
% 0.29/0.45 ( ( ( smult @ A @ A2 @ P2 )
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 = ( ( A2
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( P2
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_eq_0_iff
% 0.29/0.45 thf(fact_28_smult__pCons,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [A2: A,B: A,P2: poly @ A] :
% 0.29/0.45 ( ( smult @ A @ A2 @ ( pCons @ A @ B @ P2 ) )
% 0.29/0.45 = ( pCons @ A @ ( times_times @ A @ A2 @ B ) @ ( smult @ A @ A2 @ P2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_pCons
% 0.29/0.45 thf(fact_29_coeffs__eq__Nil,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [P2: poly @ A] :
% 0.29/0.45 ( ( ( coeffs @ A @ P2 )
% 0.29/0.45 = ( nil @ A ) )
% 0.29/0.45 = ( P2
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % coeffs_eq_Nil
% 0.29/0.45 thf(fact_30_coeffs__0__eq__Nil,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ( ( coeffs @ A @ ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 = ( nil @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % coeffs_0_eq_Nil
% 0.29/0.45 thf(fact_31_psums__0__Cons,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( monoid_add @ A )
% 0.29/0.45 => ! [Xs: list @ A] :
% 0.29/0.45 ( ( descar1668888542_psums @ A @ ( cons @ A @ ( zero_zero @ A ) @ Xs ) )
% 0.29/0.45 = ( cons @ A @ ( zero_zero @ A ) @ ( descar1668888542_psums @ A @ Xs ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % psums_0_Cons
% 0.29/0.45 thf(fact_32_coeffs__1__eq,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A )
% 0.29/0.45 => ( ( coeffs @ A @ ( one_one @ ( poly @ A ) ) )
% 0.29/0.45 = ( cons @ A @ ( one_one @ A ) @ ( nil @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % coeffs_1_eq
% 0.29/0.45 thf(fact_33_sign__changes__singleton,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ( sgn @ A )
% 0.29/0.45 & ( zero @ A ) )
% 0.29/0.45 => ! [X: A] :
% 0.29/0.45 ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sign_changes_singleton
% 0.29/0.45 thf(fact_34__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062,axiom,
% 0.29/0.45 ( ( descar149487500hanges @ a @ xs )
% 0.29/0.45 = ( v @ ( times_times @ ( poly @ a ) @ ( pCons @ a @ ( one_one @ a ) @ ( pCons @ a @ ( uminus_uminus @ a @ ( one_one @ a ) ) @ ( zero_zero @ ( poly @ a ) ) ) ) @ g ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % \<open>sign_changes xs = v ([:1::'a, - (1::'a):] * g)\<close>
% 0.29/0.45 thf(fact_35_Poly__snoc__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [As: list @ A] :
% 0.29/0.45 ( ( poly2 @ A @ ( append @ A @ As @ ( cons @ A @ ( zero_zero @ A ) @ ( nil @ A ) ) ) )
% 0.29/0.45 = ( poly2 @ A @ As ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Poly_snoc_zero
% 0.29/0.45 thf(fact_36_Poly_Osimps_I2_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [A2: A,As: list @ A] :
% 0.29/0.45 ( ( poly2 @ A @ ( cons @ A @ A2 @ As ) )
% 0.29/0.45 = ( pCons @ A @ A2 @ ( poly2 @ A @ As ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Poly.simps(2)
% 0.29/0.45 thf(fact_37_Poly_Osimps_I1_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ( ( poly2 @ A @ ( nil @ A ) )
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Poly.simps(1)
% 0.29/0.45 thf(fact_38_psums_Osimps_I2_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( plus @ A )
% 0.29/0.45 => ! [X: A] :
% 0.29/0.45 ( ( descar1668888542_psums @ A @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.45 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % psums.simps(2)
% 0.29/0.45 thf(fact_39_psums_Osimps_I1_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( plus @ A )
% 0.29/0.45 => ( ( descar1668888542_psums @ A @ ( nil @ A ) )
% 0.29/0.45 = ( nil @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % psums.simps(1)
% 0.29/0.45 thf(fact_40_pCons__one,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A )
% 0.29/0.45 => ( ( pCons @ A @ ( one_one @ A ) @ ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 = ( one_one @ ( poly @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % pCons_one
% 0.29/0.45 thf(fact_41_pCons__cases,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [P2: poly @ A] :
% 0.29/0.45 ~ ! [A3: A,Q3: poly @ A] :
% 0.29/0.45 ( P2
% 0.29/0.45 != ( pCons @ A @ A3 @ Q3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % pCons_cases
% 0.29/0.45 thf(fact_42_is__zero__null,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ( ( is_zero @ A )
% 0.29/0.45 = ( ^ [P: poly @ A] :
% 0.29/0.45 ( P
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % is_zero_null
% 0.29/0.45 thf(fact_43_pCons__induct,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [P3: ( poly @ A ) > $o,P2: poly @ A] :
% 0.29/0.45 ( ( P3 @ ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 => ( ! [A3: A,P4: poly @ A] :
% 0.29/0.45 ( ( ( A3
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 | ( P4
% 0.29/0.45 != ( zero_zero @ ( poly @ A ) ) ) )
% 0.29/0.45 => ( ( P3 @ P4 )
% 0.29/0.45 => ( P3 @ ( pCons @ A @ A3 @ P4 ) ) ) )
% 0.29/0.45 => ( P3 @ P2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % pCons_induct
% 0.29/0.45 thf(fact_44_pderiv_Ocases,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ( comm_semiring_1 @ A )
% 0.29/0.45 & ( semiri1193490041visors @ A ) )
% 0.29/0.45 => ! [X: poly @ A] :
% 0.29/0.45 ~ ! [A3: A,P4: poly @ A] :
% 0.29/0.45 ( X
% 0.29/0.45 != ( pCons @ A @ A3 @ P4 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % pderiv.cases
% 0.29/0.45 thf(fact_45_ext,axiom,
% 0.29/0.45 ! [B2: $tType,A: $tType,F2: A > B2,G: A > B2] :
% 0.29/0.45 ( ! [X2: A] :
% 0.29/0.45 ( ( F2 @ X2 )
% 0.29/0.45 = ( G @ X2 ) )
% 0.29/0.45 => ( F2 = G ) ) ).
% 0.29/0.45
% 0.29/0.45 % ext
% 0.29/0.45 thf(fact_46_poly__induct2,axiom,
% 0.29/0.45 ! [A: $tType,B2: $tType] :
% 0.29/0.45 ( ( ( zero @ B2 )
% 0.29/0.45 & ( zero @ A ) )
% 0.29/0.45 => ! [P3: ( poly @ A ) > ( poly @ B2 ) > $o,P2: poly @ A,Q2: poly @ B2] :
% 0.29/0.45 ( ( P3 @ ( zero_zero @ ( poly @ A ) ) @ ( zero_zero @ ( poly @ B2 ) ) )
% 0.29/0.45 => ( ! [A3: A,P4: poly @ A,B3: B2,Q3: poly @ B2] :
% 0.29/0.45 ( ( P3 @ P4 @ Q3 )
% 0.29/0.45 => ( P3 @ ( pCons @ A @ A3 @ P4 ) @ ( pCons @ B2 @ B3 @ Q3 ) ) )
% 0.29/0.45 => ( P3 @ P2 @ Q2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % poly_induct2
% 0.29/0.45 thf(fact_47_pderiv_Oinduct,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ( comm_semiring_1 @ A )
% 0.29/0.45 & ( semiri1193490041visors @ A ) )
% 0.29/0.45 => ! [P3: ( poly @ A ) > $o,A0: poly @ A] :
% 0.29/0.45 ( ! [A3: A,P4: poly @ A] :
% 0.29/0.45 ( ( ( P4
% 0.29/0.45 != ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 => ( P3 @ P4 ) )
% 0.29/0.45 => ( P3 @ ( pCons @ A @ A3 @ P4 ) ) )
% 0.29/0.45 => ( P3 @ A0 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % pderiv.induct
% 0.29/0.45 thf(fact_48_mult__poly__0__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [Q2: poly @ A] :
% 0.29/0.45 ( ( times_times @ ( poly @ A ) @ ( zero_zero @ ( poly @ A ) ) @ Q2 )
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_poly_0_left
% 0.29/0.45 thf(fact_49_mult__poly__0__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [P2: poly @ A] :
% 0.29/0.45 ( ( times_times @ ( poly @ A ) @ P2 @ ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_poly_0_right
% 0.29/0.45 thf(fact_50_plus__coeffs_Oinduct,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_monoid_add @ A )
% 0.29/0.45 => ! [P3: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.45 ( ! [Xs2: list @ A] : ( P3 @ Xs2 @ ( nil @ A ) )
% 0.29/0.45 => ( ! [V: A,Va: list @ A] : ( P3 @ ( nil @ A ) @ ( cons @ A @ V @ Va ) )
% 0.29/0.45 => ( ! [X2: A,Xs2: list @ A,Y2: A,Ys: list @ A] :
% 0.29/0.45 ( ( P3 @ Xs2 @ Ys )
% 0.29/0.45 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys ) ) )
% 0.29/0.45 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % plus_coeffs.induct
% 0.29/0.45 thf(fact_51_not__0__coeffs__not__Nil,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [P2: poly @ A] :
% 0.29/0.45 ( ( P2
% 0.29/0.45 != ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 => ( ( coeffs @ A @ P2 )
% 0.29/0.45 != ( nil @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % not_0_coeffs_not_Nil
% 0.29/0.45 thf(fact_52_minus__poly__rev__list_Oinduct,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A )
% 0.29/0.45 => ! [P3: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.45 ( ! [X2: A,Xs2: list @ A,Y2: A,Ys: list @ A] :
% 0.29/0.45 ( ( P3 @ Xs2 @ Ys )
% 0.29/0.45 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys ) ) )
% 0.29/0.45 => ( ! [Xs2: list @ A] : ( P3 @ Xs2 @ ( nil @ A ) )
% 0.29/0.45 => ( ! [Y2: A,Ys: list @ A] : ( P3 @ ( nil @ A ) @ ( cons @ A @ Y2 @ Ys ) )
% 0.29/0.45 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % minus_poly_rev_list.induct
% 0.29/0.45 thf(fact_53_synthetic__div__unique__lemma,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [C: A,P2: poly @ A,A2: A] :
% 0.29/0.45 ( ( ( smult @ A @ C @ P2 )
% 0.29/0.45 = ( pCons @ A @ A2 @ P2 ) )
% 0.29/0.45 => ( P2
% 0.29/0.45 = ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % synthetic_div_unique_lemma
% 0.29/0.45 thf(fact_54_psums_Ocases,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( plus @ A )
% 0.29/0.45 => ! [X: list @ A] :
% 0.29/0.45 ( ( X
% 0.29/0.45 != ( nil @ A ) )
% 0.29/0.45 => ( ! [X2: A] :
% 0.29/0.45 ( X
% 0.29/0.45 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.45 => ~ ! [X2: A,Y2: A,Xs2: list @ A] :
% 0.29/0.45 ( X
% 0.29/0.45 != ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % psums.cases
% 0.29/0.45 thf(fact_55_reduce__root__pCons,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_0 @ A )
% 0.29/0.45 => ! [A2: A,C: A,P2: poly @ A] :
% 0.29/0.45 ( ( descar316357986e_root @ A @ A2 @ ( pCons @ A @ C @ P2 ) )
% 0.29/0.45 = ( pCons @ A @ C @ ( smult @ A @ A2 @ ( descar316357986e_root @ A @ A2 @ P2 ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % reduce_root_pCons
% 0.29/0.45 thf(fact_56_reduce__root__nonzero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( idom @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 => ( ( P2
% 0.29/0.45 != ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.45 => ( ( descar316357986e_root @ A @ A2 @ P2 )
% 0.29/0.45 != ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % reduce_root_nonzero
% 0.29/0.45 thf(fact_57_sign__changes__Cons__Cons__same,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_idom @ A )
% 0.29/0.45 => ! [X: A,Y3: A,Xs: list @ A] :
% 0.29/0.45 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ X @ Y3 ) )
% 0.29/0.45 => ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Xs ) ) )
% 0.29/0.45 = ( descar149487500hanges @ A @ ( cons @ A @ Y3 @ Xs ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sign_changes_Cons_Cons_same
% 0.29/0.45 thf(fact_58_append1__eq__conv,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A,Y3: A] :
% 0.29/0.45 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.29/0.45 = ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 0.29/0.45 = ( ( Xs = Ys2 )
% 0.29/0.45 & ( X = Y3 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % append1_eq_conv
% 0.29/0.45 thf(fact_59_mult__minus1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring_1 @ A )
% 0.29/0.45 => ! [Z2: A] :
% 0.29/0.45 ( ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ Z2 )
% 0.29/0.45 = ( uminus_uminus @ A @ Z2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_minus1
% 0.29/0.45 thf(fact_60_mult__minus1__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring_1 @ A )
% 0.29/0.45 => ! [Z2: A] :
% 0.29/0.45 ( ( times_times @ A @ Z2 @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.29/0.45 = ( uminus_uminus @ A @ Z2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_minus1_right
% 0.29/0.45 thf(fact_61_less__neg__neg,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linord219039673up_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ ( uminus_uminus @ A @ A2 ) )
% 0.29/0.45 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_neg_neg
% 0.29/0.45 thf(fact_62_neg__less__pos,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linord219039673up_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ A2 )
% 0.29/0.45 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neg_less_pos
% 0.29/0.45 thf(fact_63_neg__0__less__iff__less,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ordered_ab_group_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A2 ) )
% 0.29/0.45 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neg_0_less_iff_less
% 0.29/0.45 thf(fact_64_neg__less__0__iff__less,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ordered_ab_group_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ ( zero_zero @ A ) )
% 0.29/0.45 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neg_less_0_iff_less
% 0.29/0.45 thf(fact_65_mult__cancel__left1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring_11004092258visors @ A )
% 0.29/0.45 => ! [C: A,B: A] :
% 0.29/0.45 ( ( C
% 0.29/0.45 = ( times_times @ A @ C @ B ) )
% 0.29/0.45 = ( ( C
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( B
% 0.29/0.45 = ( one_one @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_cancel_left1
% 0.29/0.45 thf(fact_66_mult__cancel__left2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring_11004092258visors @ A )
% 0.29/0.45 => ! [C: A,A2: A] :
% 0.29/0.45 ( ( ( times_times @ A @ C @ A2 )
% 0.29/0.45 = C )
% 0.29/0.45 = ( ( C
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( A2
% 0.29/0.45 = ( one_one @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_cancel_left2
% 0.29/0.45 thf(fact_67_mult__cancel__right1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring_11004092258visors @ A )
% 0.29/0.45 => ! [C: A,B: A] :
% 0.29/0.45 ( ( C
% 0.29/0.45 = ( times_times @ A @ B @ C ) )
% 0.29/0.45 = ( ( C
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( B
% 0.29/0.45 = ( one_one @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_cancel_right1
% 0.29/0.45 thf(fact_68_mult__cancel__right2,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring_11004092258visors @ A )
% 0.29/0.45 => ! [A2: A,C: A] :
% 0.29/0.45 ( ( ( times_times @ A @ A2 @ C )
% 0.29/0.45 = C )
% 0.29/0.45 = ( ( C
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( A2
% 0.29/0.45 = ( one_one @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_cancel_right2
% 0.29/0.45 thf(fact_69_neg__equal__iff__equal,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( ( uminus_uminus @ A @ A2 )
% 0.29/0.45 = ( uminus_uminus @ A @ B ) )
% 0.29/0.45 = ( A2 = B ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neg_equal_iff_equal
% 0.29/0.45 thf(fact_70_add_Oinverse__inverse,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A2 ) )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.inverse_inverse
% 0.29/0.45 thf(fact_71_list_Oinject,axiom,
% 0.29/0.45 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.29/0.45 ( ( ( cons @ A @ X21 @ X22 )
% 0.29/0.45 = ( cons @ A @ Y21 @ Y22 ) )
% 0.29/0.45 = ( ( X21 = Y21 )
% 0.29/0.45 & ( X22 = Y22 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % list.inject
% 0.29/0.45 thf(fact_72_same__append__eq,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.29/0.45 ( ( ( append @ A @ Xs @ Ys2 )
% 0.29/0.45 = ( append @ A @ Xs @ Zs ) )
% 0.29/0.45 = ( Ys2 = Zs ) ) ).
% 0.29/0.45
% 0.29/0.45 % same_append_eq
% 0.29/0.45 thf(fact_73_append__same__eq,axiom,
% 0.29/0.45 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.29/0.45 ( ( ( append @ A @ Ys2 @ Xs )
% 0.29/0.45 = ( append @ A @ Zs @ Xs ) )
% 0.29/0.45 = ( Ys2 = Zs ) ) ).
% 0.29/0.45
% 0.29/0.45 % append_same_eq
% 0.29/0.45 thf(fact_74_append__assoc,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.29/0.45 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs )
% 0.29/0.45 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % append_assoc
% 0.29/0.45 thf(fact_75_append_Oassoc,axiom,
% 0.29/0.45 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 0.29/0.45 ( ( append @ A @ ( append @ A @ A2 @ B ) @ C )
% 0.29/0.45 = ( append @ A @ A2 @ ( append @ A @ B @ C ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % append.assoc
% 0.29/0.45 thf(fact_76_not__gr__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( canoni770627133id_add @ A )
% 0.29/0.45 => ! [N: A] :
% 0.29/0.45 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.29/0.45 = ( N
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % not_gr_zero
% 0.29/0.45 thf(fact_77_mult__cancel__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiri1923998003cancel @ A )
% 0.29/0.45 => ! [A2: A,C: A,B: A] :
% 0.29/0.45 ( ( ( times_times @ A @ A2 @ C )
% 0.29/0.45 = ( times_times @ A @ B @ C ) )
% 0.29/0.45 = ( ( C
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( A2 = B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_cancel_right
% 0.29/0.45 thf(fact_78_mult__cancel__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiri1923998003cancel @ A )
% 0.29/0.45 => ! [C: A,A2: A,B: A] :
% 0.29/0.45 ( ( ( times_times @ A @ C @ A2 )
% 0.29/0.45 = ( times_times @ A @ C @ B ) )
% 0.29/0.45 = ( ( C
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( A2 = B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_cancel_left
% 0.29/0.45 thf(fact_79_mult__eq__0__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiri1193490041visors @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( ( times_times @ A @ A2 @ B )
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 = ( ( A2
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( B
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_eq_0_iff
% 0.29/0.45 thf(fact_80_mult__zero__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( mult_zero @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.45 = ( zero_zero @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_zero_right
% 0.29/0.45 thf(fact_81_mult__zero__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( mult_zero @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( times_times @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.45 = ( zero_zero @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_zero_left
% 0.29/0.45 thf(fact_82_neg__equal__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linord219039673up_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ( uminus_uminus @ A @ A2 )
% 0.29/0.45 = A2 )
% 0.29/0.45 = ( A2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neg_equal_zero
% 0.29/0.45 thf(fact_83_equal__neg__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linord219039673up_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 = ( uminus_uminus @ A @ A2 ) )
% 0.29/0.45 = ( A2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % equal_neg_zero
% 0.29/0.45 thf(fact_84_neg__equal__0__iff__equal,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ( uminus_uminus @ A @ A2 )
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 = ( A2
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neg_equal_0_iff_equal
% 0.29/0.45 thf(fact_85_neg__0__equal__iff__equal,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( ( zero_zero @ A )
% 0.29/0.45 = ( uminus_uminus @ A @ A2 ) )
% 0.29/0.45 = ( ( zero_zero @ A )
% 0.29/0.45 = A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neg_0_equal_iff_equal
% 0.29/0.45 thf(fact_86_add_Oinverse__neutral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A )
% 0.29/0.45 => ( ( uminus_uminus @ A @ ( zero_zero @ A ) )
% 0.29/0.45 = ( zero_zero @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % add.inverse_neutral
% 0.29/0.45 thf(fact_87_mult_Oright__neutral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( monoid_mult @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult.right_neutral
% 0.29/0.45 thf(fact_88_mult_Oleft__neutral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( monoid_mult @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult.left_neutral
% 0.29/0.45 thf(fact_89_neg__less__iff__less,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ordered_ab_group_add @ A )
% 0.29/0.45 => ! [B: A,A2: A] :
% 0.29/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ B ) @ ( uminus_uminus @ A @ A2 ) )
% 0.29/0.45 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % neg_less_iff_less
% 0.29/0.45 thf(fact_90_mult__minus__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( times_times @ A @ A2 @ ( uminus_uminus @ A @ B ) )
% 0.29/0.45 = ( uminus_uminus @ A @ ( times_times @ A @ A2 @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_minus_right
% 0.29/0.45 thf(fact_91_minus__mult__minus,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( times_times @ A @ ( uminus_uminus @ A @ A2 ) @ ( uminus_uminus @ A @ B ) )
% 0.29/0.45 = ( times_times @ A @ A2 @ B ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % minus_mult_minus
% 0.29/0.45 thf(fact_92_mult__minus__left,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( times_times @ A @ ( uminus_uminus @ A @ A2 ) @ B )
% 0.29/0.45 = ( uminus_uminus @ A @ ( times_times @ A @ A2 @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_minus_left
% 0.29/0.45 thf(fact_93_append_Oright__neutral,axiom,
% 0.29/0.45 ! [A: $tType,A2: list @ A] :
% 0.29/0.45 ( ( append @ A @ A2 @ ( nil @ A ) )
% 0.29/0.45 = A2 ) ).
% 0.29/0.45
% 0.29/0.45 % append.right_neutral
% 0.29/0.45 thf(fact_94_append__is__Nil__conv,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.45 ( ( ( append @ A @ Xs @ Ys2 )
% 0.29/0.45 = ( nil @ A ) )
% 0.29/0.45 = ( ( Xs
% 0.29/0.45 = ( nil @ A ) )
% 0.29/0.45 & ( Ys2
% 0.29/0.45 = ( nil @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % append_is_Nil_conv
% 0.29/0.45 thf(fact_95_Nil__is__append__conv,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.45 ( ( ( nil @ A )
% 0.29/0.45 = ( append @ A @ Xs @ Ys2 ) )
% 0.29/0.45 = ( ( Xs
% 0.29/0.45 = ( nil @ A ) )
% 0.29/0.45 & ( Ys2
% 0.29/0.45 = ( nil @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % Nil_is_append_conv
% 0.29/0.45 thf(fact_96_self__append__conv2,axiom,
% 0.29/0.45 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.29/0.45 ( ( Ys2
% 0.29/0.45 = ( append @ A @ Xs @ Ys2 ) )
% 0.29/0.45 = ( Xs
% 0.29/0.45 = ( nil @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % self_append_conv2
% 0.29/0.45 thf(fact_97_append__self__conv2,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.45 ( ( ( append @ A @ Xs @ Ys2 )
% 0.29/0.45 = Ys2 )
% 0.29/0.45 = ( Xs
% 0.29/0.45 = ( nil @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % append_self_conv2
% 0.29/0.45 thf(fact_98_self__append__conv,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.45 ( ( Xs
% 0.29/0.45 = ( append @ A @ Xs @ Ys2 ) )
% 0.29/0.45 = ( Ys2
% 0.29/0.45 = ( nil @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % self_append_conv
% 0.29/0.45 thf(fact_99_append__self__conv,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.45 ( ( ( append @ A @ Xs @ Ys2 )
% 0.29/0.45 = Xs )
% 0.29/0.45 = ( Ys2
% 0.29/0.45 = ( nil @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % append_self_conv
% 0.29/0.45 thf(fact_100_append__Nil2,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A] :
% 0.29/0.45 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.29/0.45 = Xs ) ).
% 0.29/0.45
% 0.29/0.45 % append_Nil2
% 0.29/0.45 thf(fact_101_smult__minus__right,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_ring @ A )
% 0.29/0.45 => ! [A2: A,P2: poly @ A] :
% 0.29/0.45 ( ( smult @ A @ A2 @ ( uminus_uminus @ ( poly @ A ) @ P2 ) )
% 0.29/0.45 = ( uminus_uminus @ ( poly @ A ) @ ( smult @ A @ A2 @ P2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_minus_right
% 0.29/0.45 thf(fact_102_smult__one,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_semiring_1 @ A )
% 0.29/0.45 => ! [C: A] :
% 0.29/0.45 ( ( smult @ A @ C @ ( one_one @ ( poly @ A ) ) )
% 0.29/0.45 = ( pCons @ A @ C @ ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % smult_one
% 0.29/0.45 thf(fact_103_zero__reorient,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero @ A )
% 0.29/0.45 => ! [X: A] :
% 0.29/0.45 ( ( ( zero_zero @ A )
% 0.29/0.45 = X )
% 0.29/0.45 = ( X
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % zero_reorient
% 0.29/0.45 thf(fact_104_linorder__neqE__linordered__idom,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_idom @ A )
% 0.29/0.45 => ! [X: A,Y3: A] :
% 0.29/0.45 ( ( X != Y3 )
% 0.29/0.45 => ( ~ ( ord_less @ A @ X @ Y3 )
% 0.29/0.45 => ( ord_less @ A @ Y3 @ X ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % linorder_neqE_linordered_idom
% 0.29/0.45 thf(fact_105_mult_Oleft__commute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ab_semigroup_mult @ A )
% 0.29/0.45 => ! [B: A,A2: A,C: A] :
% 0.29/0.45 ( ( times_times @ A @ B @ ( times_times @ A @ A2 @ C ) )
% 0.29/0.45 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult.left_commute
% 0.29/0.45 thf(fact_106_mult_Ocommute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ab_semigroup_mult @ A )
% 0.29/0.45 => ( ( times_times @ A )
% 0.29/0.45 = ( ^ [A4: A,B4: A] : ( times_times @ A @ B4 @ A4 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult.commute
% 0.29/0.45 thf(fact_107_mult_Oassoc,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semigroup_mult @ A )
% 0.29/0.45 => ! [A2: A,B: A,C: A] :
% 0.29/0.45 ( ( times_times @ A @ ( times_times @ A @ A2 @ B ) @ C )
% 0.29/0.45 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult.assoc
% 0.29/0.45 thf(fact_108_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ab_semigroup_mult @ A )
% 0.29/0.45 => ! [A2: A,B: A,C: A] :
% 0.29/0.45 ( ( times_times @ A @ ( times_times @ A @ A2 @ B ) @ C )
% 0.29/0.45 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % ab_semigroup_mult_class.mult_ac(1)
% 0.29/0.45 thf(fact_109_one__reorient,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( one @ A )
% 0.29/0.45 => ! [X: A] :
% 0.29/0.45 ( ( ( one_one @ A )
% 0.29/0.45 = X )
% 0.29/0.45 = ( X
% 0.29/0.45 = ( one_one @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % one_reorient
% 0.29/0.45 thf(fact_110_minus__equation__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( ( uminus_uminus @ A @ A2 )
% 0.29/0.45 = B )
% 0.29/0.45 = ( ( uminus_uminus @ A @ B )
% 0.29/0.45 = A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % minus_equation_iff
% 0.29/0.45 thf(fact_111_equation__minus__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( group_add @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 = ( uminus_uminus @ A @ B ) )
% 0.29/0.45 = ( B
% 0.29/0.45 = ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % equation_minus_iff
% 0.29/0.45 thf(fact_112_not__Cons__self2,axiom,
% 0.29/0.45 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.45 ( ( cons @ A @ X @ Xs )
% 0.29/0.45 != Xs ) ).
% 0.29/0.45
% 0.29/0.45 % not_Cons_self2
% 0.29/0.45 thf(fact_113_append__eq__append__conv2,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A,Ts: list @ A] :
% 0.29/0.45 ( ( ( append @ A @ Xs @ Ys2 )
% 0.29/0.45 = ( append @ A @ Zs @ Ts ) )
% 0.29/0.45 = ( ? [Us: list @ A] :
% 0.29/0.45 ( ( ( Xs
% 0.29/0.45 = ( append @ A @ Zs @ Us ) )
% 0.29/0.45 & ( ( append @ A @ Us @ Ys2 )
% 0.29/0.45 = Ts ) )
% 0.29/0.45 | ( ( ( append @ A @ Xs @ Us )
% 0.29/0.45 = Zs )
% 0.29/0.45 & ( Ys2
% 0.29/0.45 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % append_eq_append_conv2
% 0.29/0.45 thf(fact_114_append__eq__appendI,axiom,
% 0.29/0.45 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys2: list @ A,Us2: list @ A] :
% 0.29/0.45 ( ( ( append @ A @ Xs @ Xs1 )
% 0.29/0.45 = Zs )
% 0.29/0.45 => ( ( Ys2
% 0.29/0.45 = ( append @ A @ Xs1 @ Us2 ) )
% 0.29/0.45 => ( ( append @ A @ Xs @ Ys2 )
% 0.29/0.45 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % append_eq_appendI
% 0.29/0.45 thf(fact_115_sign__changes__two,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linordered_idom @ A )
% 0.29/0.45 => ! [X: A,Y3: A] :
% 0.29/0.45 ( ( ( ( ( ord_less @ A @ ( zero_zero @ A ) @ X )
% 0.29/0.45 & ( ord_less @ A @ Y3 @ ( zero_zero @ A ) ) )
% 0.29/0.45 | ( ( ord_less @ A @ X @ ( zero_zero @ A ) )
% 0.29/0.45 & ( ord_less @ A @ ( zero_zero @ A ) @ Y3 ) ) )
% 0.29/0.45 => ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 0.29/0.45 = ( one_one @ nat ) ) )
% 0.29/0.45 & ( ~ ( ( ( ord_less @ A @ ( zero_zero @ A ) @ X )
% 0.29/0.45 & ( ord_less @ A @ Y3 @ ( zero_zero @ A ) ) )
% 0.29/0.45 | ( ( ord_less @ A @ X @ ( zero_zero @ A ) )
% 0.29/0.45 & ( ord_less @ A @ ( zero_zero @ A ) @ Y3 ) ) )
% 0.29/0.45 => ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 0.29/0.45 = ( zero_zero @ nat ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % sign_changes_two
% 0.29/0.45 thf(fact_116_zero__less__iff__neq__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( canoni770627133id_add @ A )
% 0.29/0.45 => ! [N: A] :
% 0.29/0.45 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.29/0.45 = ( N
% 0.29/0.45 != ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % zero_less_iff_neq_zero
% 0.29/0.45 thf(fact_117_gr__implies__not__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( canoni770627133id_add @ A )
% 0.29/0.45 => ! [M: A,N: A] :
% 0.29/0.45 ( ( ord_less @ A @ M @ N )
% 0.29/0.45 => ( N
% 0.29/0.45 != ( zero_zero @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % gr_implies_not_zero
% 0.29/0.45 thf(fact_118_not__less__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( canoni770627133id_add @ A )
% 0.29/0.45 => ! [N: A] :
% 0.29/0.45 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % not_less_zero
% 0.29/0.45 thf(fact_119_gr__zeroI,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( canoni770627133id_add @ A )
% 0.29/0.45 => ! [N: A] :
% 0.29/0.45 ( ( N
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % gr_zeroI
% 0.29/0.45 thf(fact_120_less__numeral__extra_I3_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linord1659791738miring @ A )
% 0.29/0.45 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_numeral_extra(3)
% 0.29/0.45 thf(fact_121_mult__right__cancel,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiri1923998003cancel @ A )
% 0.29/0.45 => ! [C: A,A2: A,B: A] :
% 0.29/0.45 ( ( C
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 => ( ( ( times_times @ A @ A2 @ C )
% 0.29/0.45 = ( times_times @ A @ B @ C ) )
% 0.29/0.45 = ( A2 = B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_right_cancel
% 0.29/0.45 thf(fact_122_mult__left__cancel,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiri1923998003cancel @ A )
% 0.29/0.45 => ! [C: A,A2: A,B: A] :
% 0.29/0.45 ( ( C
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 => ( ( ( times_times @ A @ C @ A2 )
% 0.29/0.45 = ( times_times @ A @ C @ B ) )
% 0.29/0.45 = ( A2 = B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_left_cancel
% 0.29/0.45 thf(fact_123_no__zero__divisors,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiri1193490041visors @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( A2
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 => ( ( B
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 => ( ( times_times @ A @ A2 @ B )
% 0.29/0.45 != ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % no_zero_divisors
% 0.29/0.45 thf(fact_124_divisors__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( semiri1193490041visors @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( ( times_times @ A @ A2 @ B )
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 => ( ( A2
% 0.29/0.45 = ( zero_zero @ A ) )
% 0.29/0.45 | ( B
% 0.29/0.45 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % divisors_zero
% 0.29/0.45 thf(fact_125_mult__not__zero,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( mult_zero @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( ( times_times @ A @ A2 @ B )
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 => ( ( A2
% 0.29/0.45 != ( zero_zero @ A ) )
% 0.29/0.45 & ( B
% 0.29/0.45 != ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult_not_zero
% 0.29/0.45 thf(fact_126_zero__neq__one,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( zero_neq_one @ A )
% 0.29/0.45 => ( ( zero_zero @ A )
% 0.29/0.45 != ( one_one @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % zero_neq_one
% 0.29/0.45 thf(fact_127_less__numeral__extra_I4_J,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linord1659791738miring @ A )
% 0.29/0.45 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_numeral_extra(4)
% 0.29/0.45 thf(fact_128_mult_Ocomm__neutral,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_monoid_mult @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % mult.comm_neutral
% 0.29/0.45 thf(fact_129_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( comm_monoid_mult @ A )
% 0.29/0.45 => ! [A2: A] :
% 0.29/0.45 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.29/0.45 = A2 ) ) ).
% 0.29/0.45
% 0.29/0.45 % comm_monoid_mult_class.mult_1
% 0.29/0.45 thf(fact_130_minus__less__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ordered_ab_group_add @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ B )
% 0.29/0.45 = ( ord_less @ A @ ( uminus_uminus @ A @ B ) @ A2 ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % minus_less_iff
% 0.29/0.45 thf(fact_131_less__minus__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ordered_ab_group_add @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( ord_less @ A @ A2 @ ( uminus_uminus @ A @ B ) )
% 0.29/0.45 = ( ord_less @ A @ B @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % less_minus_iff
% 0.29/0.45 thf(fact_132_minus__mult__commute,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( times_times @ A @ ( uminus_uminus @ A @ A2 ) @ B )
% 0.29/0.45 = ( times_times @ A @ A2 @ ( uminus_uminus @ A @ B ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % minus_mult_commute
% 0.29/0.45 thf(fact_133_square__eq__iff,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( idom @ A )
% 0.29/0.45 => ! [A2: A,B: A] :
% 0.29/0.45 ( ( ( times_times @ A @ A2 @ A2 )
% 0.29/0.45 = ( times_times @ A @ B @ B ) )
% 0.29/0.45 = ( ( A2 = B )
% 0.29/0.45 | ( A2
% 0.29/0.45 = ( uminus_uminus @ A @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % square_eq_iff
% 0.29/0.45 thf(fact_134_one__neq__neg__one,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( ring_char_0 @ A )
% 0.29/0.45 => ( ( one_one @ A )
% 0.29/0.45 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % one_neq_neg_one
% 0.29/0.45 thf(fact_135_strict__sorted_Oinduct,axiom,
% 0.29/0.45 ! [A: $tType] :
% 0.29/0.45 ( ( linorder @ A )
% 0.29/0.45 => ! [P3: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.45 ( ( P3 @ ( nil @ A ) )
% 0.29/0.45 => ( ! [X2: A,Ys: list @ A] :
% 0.29/0.45 ( ( P3 @ Ys )
% 0.29/0.45 => ( P3 @ ( cons @ A @ X2 @ Ys ) ) )
% 0.29/0.45 => ( P3 @ A0 ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 % strict_sorted.induct
% 0.29/0.46 thf(fact_136_strict__sorted_Ocases,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X: list @ A] :
% 0.29/0.46 ( ( X
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ~ ! [X2: A,Ys: list @ A] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ A @ X2 @ Ys ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % strict_sorted.cases
% 0.29/0.46 thf(fact_137_map__tailrec__rev_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,B2: $tType,P3: ( A > B2 ) > ( list @ A ) > ( list @ B2 ) > $o,A0: A > B2,A1: list @ A,A22: list @ B2] :
% 0.29/0.46 ( ! [F3: A > B2,X_1: list @ B2] : ( P3 @ F3 @ ( nil @ A ) @ X_1 )
% 0.29/0.46 => ( ! [F3: A > B2,A3: A,As2: list @ A,Bs: list @ B2] :
% 0.29/0.46 ( ( P3 @ F3 @ As2 @ ( cons @ B2 @ ( F3 @ A3 ) @ Bs ) )
% 0.29/0.46 => ( P3 @ F3 @ ( cons @ A @ A3 @ As2 ) @ Bs ) )
% 0.29/0.46 => ( P3 @ A0 @ A1 @ A22 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % map_tailrec_rev.induct
% 0.29/0.46 thf(fact_138_list__nonempty__induct,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A,P3: ( list @ A ) > $o] :
% 0.29/0.46 ( ( Xs
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A] : ( P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A] :
% 0.29/0.46 ( ( Xs2
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ( P3 @ Xs2 )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 0.29/0.46 => ( P3 @ Xs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list_nonempty_induct
% 0.29/0.46 thf(fact_139_successively_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P3: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.29/0.46 ( ! [P5: A > A > $o] : ( P3 @ P5 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [P5: A > A > $o,X2: A] : ( P3 @ P5 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [P5: A > A > $o,X2: A,Y2: A,Xs2: list @ A] :
% 0.29/0.46 ( ( P3 @ P5 @ ( cons @ A @ Y2 @ Xs2 ) )
% 0.29/0.46 => ( P3 @ P5 @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) )
% 0.29/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % successively.induct
% 0.29/0.46 thf(fact_140_arg__min__list_Oinduct,axiom,
% 0.29/0.46 ! [B2: $tType,A: $tType] :
% 0.29/0.46 ( ( linorder @ B2 )
% 0.29/0.46 => ! [P3: ( A > B2 ) > ( list @ A ) > $o,A0: A > B2,A1: list @ A] :
% 0.29/0.46 ( ! [F3: A > B2,X2: A] : ( P3 @ F3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [F3: A > B2,X2: A,Y2: A,Zs2: list @ A] :
% 0.29/0.46 ( ( P3 @ F3 @ ( cons @ A @ Y2 @ Zs2 ) )
% 0.29/0.46 => ( P3 @ F3 @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Zs2 ) ) ) )
% 0.29/0.46 => ( ! [A3: A > B2] : ( P3 @ A3 @ ( nil @ A ) )
% 0.29/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % arg_min_list.induct
% 0.29/0.46 thf(fact_141_remdups__adj_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P3: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.46 ( ( P3 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A] : ( P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X2: A,Y2: A,Xs2: list @ A] :
% 0.29/0.46 ( ( ( X2 = Y2 )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.29/0.46 => ( ( ( X2 != Y2 )
% 0.29/0.46 => ( P3 @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.29/0.46 => ( P3 @ A0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % remdups_adj.induct
% 0.29/0.46 thf(fact_142_sorted__wrt_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P3: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.29/0.46 ( ! [P5: A > A > $o] : ( P3 @ P5 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [P5: A > A > $o,X2: A,Ys: list @ A] :
% 0.29/0.46 ( ( P3 @ P5 @ Ys )
% 0.29/0.46 => ( P3 @ P5 @ ( cons @ A @ X2 @ Ys ) ) )
% 0.29/0.46 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sorted_wrt.induct
% 0.29/0.46 thf(fact_143_remdups__adj_Ocases,axiom,
% 0.29/0.46 ! [A: $tType,X: list @ A] :
% 0.29/0.46 ( ( X
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ~ ! [X2: A,Y2: A,Xs2: list @ A] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % remdups_adj.cases
% 0.29/0.46 thf(fact_144_transpose_Ocases,axiom,
% 0.29/0.46 ! [A: $tType,X: list @ ( list @ A )] :
% 0.29/0.46 ( ( X
% 0.29/0.46 != ( nil @ ( list @ A ) ) )
% 0.29/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.29/0.46 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % transpose.cases
% 0.29/0.46 thf(fact_145_shuffles_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P3: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.46 ( ! [X_1: list @ A] : ( P3 @ ( nil @ A ) @ X_1 )
% 0.29/0.46 => ( ! [Xs2: list @ A] : ( P3 @ Xs2 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A,Y2: A,Ys: list @ A] :
% 0.29/0.46 ( ( P3 @ Xs2 @ ( cons @ A @ Y2 @ Ys ) )
% 0.29/0.46 => ( ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ Ys )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys ) ) ) )
% 0.29/0.46 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % shuffles.induct
% 0.29/0.46 thf(fact_146_min__list_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [P3: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.46 ( ! [X2: A,Xs2: list @ A] :
% 0.29/0.46 ( ! [X212: A,X222: list @ A] :
% 0.29/0.46 ( ( Xs2
% 0.29/0.46 = ( cons @ A @ X212 @ X222 ) )
% 0.29/0.46 => ( P3 @ Xs2 ) )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.29/0.46 => ( ( P3 @ ( nil @ A ) )
% 0.29/0.46 => ( P3 @ A0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % min_list.induct
% 0.29/0.46 thf(fact_147_min__list_Ocases,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ord @ A )
% 0.29/0.46 => ! [X: list @ A] :
% 0.29/0.46 ( ! [X2: A,Xs2: list @ A] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ A @ X2 @ Xs2 ) )
% 0.29/0.46 => ( X
% 0.29/0.46 = ( nil @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % min_list.cases
% 0.29/0.46 thf(fact_148_induct__list012,axiom,
% 0.29/0.46 ! [A: $tType,P3: ( list @ A ) > $o,Xs: list @ A] :
% 0.29/0.46 ( ( P3 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A] : ( P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X2: A,Y2: A,Zs2: list @ A] :
% 0.29/0.46 ( ( P3 @ Zs2 )
% 0.29/0.46 => ( ( P3 @ ( cons @ A @ Y2 @ Zs2 ) )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Zs2 ) ) ) ) )
% 0.29/0.46 => ( P3 @ Xs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % induct_list012
% 0.29/0.46 thf(fact_149_splice_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P3: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.46 ( ! [X_1: list @ A] : ( P3 @ ( nil @ A ) @ X_1 )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A,Ys: list @ A] :
% 0.29/0.46 ( ( P3 @ Ys @ Xs2 )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ Ys ) )
% 0.29/0.46 => ( P3 @ A0 @ A1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % splice.induct
% 0.29/0.46 thf(fact_150_list__induct2_H,axiom,
% 0.29/0.46 ! [A: $tType,B2: $tType,P3: ( list @ A ) > ( list @ B2 ) > $o,Xs: list @ A,Ys2: list @ B2] :
% 0.29/0.46 ( ( P3 @ ( nil @ A ) @ ( nil @ B2 ) )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A] : ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B2 ) )
% 0.29/0.46 => ( ! [Y2: B2,Ys: list @ B2] : ( P3 @ ( nil @ A ) @ ( cons @ B2 @ Y2 @ Ys ) )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A,Y2: B2,Ys: list @ B2] :
% 0.29/0.46 ( ( P3 @ Xs2 @ Ys )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B2 @ Y2 @ Ys ) ) )
% 0.29/0.46 => ( P3 @ Xs @ Ys2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list_induct2'
% 0.29/0.46 thf(fact_151_neq__Nil__conv,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A] :
% 0.29/0.46 ( ( Xs
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 = ( ? [Y4: A,Ys3: list @ A] :
% 0.29/0.46 ( Xs
% 0.29/0.46 = ( cons @ A @ Y4 @ Ys3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % neq_Nil_conv
% 0.29/0.46 thf(fact_152_list_Oinducts,axiom,
% 0.29/0.46 ! [A: $tType,P3: ( list @ A ) > $o,List: list @ A] :
% 0.29/0.46 ( ( P3 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X1: A,X23: list @ A] :
% 0.29/0.46 ( ( P3 @ X23 )
% 0.29/0.46 => ( P3 @ ( cons @ A @ X1 @ X23 ) ) )
% 0.29/0.46 => ( P3 @ List ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.inducts
% 0.29/0.46 thf(fact_153_list_Oexhaust,axiom,
% 0.29/0.46 ! [A: $tType,Y3: list @ A] :
% 0.29/0.46 ( ( Y3
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ~ ! [X213: A,X223: list @ A] :
% 0.29/0.46 ( Y3
% 0.29/0.46 != ( cons @ A @ X213 @ X223 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.exhaust
% 0.29/0.46 thf(fact_154_list_OdiscI,axiom,
% 0.29/0.46 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.29/0.46 ( ( List
% 0.29/0.46 = ( cons @ A @ X21 @ X22 ) )
% 0.29/0.46 => ( List
% 0.29/0.46 != ( nil @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.discI
% 0.29/0.46 thf(fact_155_list_Odistinct_I1_J,axiom,
% 0.29/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.29/0.46 ( ( nil @ A )
% 0.29/0.46 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.distinct(1)
% 0.29/0.46 thf(fact_156_append__Cons,axiom,
% 0.29/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.46 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys2 )
% 0.29/0.46 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % append_Cons
% 0.29/0.46 thf(fact_157_Cons__eq__appendI,axiom,
% 0.29/0.46 ! [A: $tType,X: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.29/0.46 ( ( ( cons @ A @ X @ Xs1 )
% 0.29/0.46 = Ys2 )
% 0.29/0.46 => ( ( Xs
% 0.29/0.46 = ( append @ A @ Xs1 @ Zs ) )
% 0.29/0.46 => ( ( cons @ A @ X @ Xs )
% 0.29/0.46 = ( append @ A @ Ys2 @ Zs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Cons_eq_appendI
% 0.29/0.46 thf(fact_158_append_Oleft__neutral,axiom,
% 0.29/0.46 ! [A: $tType,A2: list @ A] :
% 0.29/0.46 ( ( append @ A @ ( nil @ A ) @ A2 )
% 0.29/0.46 = A2 ) ).
% 0.29/0.46
% 0.29/0.46 % append.left_neutral
% 0.29/0.46 thf(fact_159_append__Nil,axiom,
% 0.29/0.46 ! [A: $tType,Ys2: list @ A] :
% 0.29/0.46 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 0.29/0.46 = Ys2 ) ).
% 0.29/0.46
% 0.29/0.46 % append_Nil
% 0.29/0.46 thf(fact_160_eq__Nil__appendI,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.46 ( ( Xs = Ys2 )
% 0.29/0.46 => ( Xs
% 0.29/0.46 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_Nil_appendI
% 0.29/0.46 thf(fact_161_null__rec_I1_J,axiom,
% 0.29/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.46 ~ ( null @ A @ ( cons @ A @ X @ Xs ) ) ).
% 0.29/0.46
% 0.29/0.46 % null_rec(1)
% 0.29/0.46 thf(fact_162_eq__Nil__null,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A] :
% 0.29/0.46 ( ( Xs
% 0.29/0.46 = ( nil @ A ) )
% 0.29/0.46 = ( null @ A @ Xs ) ) ).
% 0.29/0.46
% 0.29/0.46 % eq_Nil_null
% 0.29/0.46 thf(fact_163_null__rec_I2_J,axiom,
% 0.29/0.46 ! [B2: $tType] : ( null @ B2 @ ( nil @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % null_rec(2)
% 0.29/0.46 thf(fact_164_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord893533164strict @ A )
% 0.29/0.46 => ! [A2: A,B: A,C: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.29/0.46 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.29/0.46 thf(fact_165_mult__less__cancel__right__disj,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [A2: A,C: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) )
% 0.29/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.29/0.46 & ( ord_less @ A @ A2 @ B ) )
% 0.29/0.46 | ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.29/0.46 & ( ord_less @ A @ B @ A2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_cancel_right_disj
% 0.29/0.46 thf(fact_166_mult__strict__right__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord20386208strict @ A )
% 0.29/0.46 => ! [A2: A,B: A,C: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.29/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_strict_right_mono
% 0.29/0.46 thf(fact_167_mult__strict__right__mono__neg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [B: A,A2: A,C: A] :
% 0.29/0.46 ( ( ord_less @ A @ B @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_strict_right_mono_neg
% 0.29/0.46 thf(fact_168_mult__less__cancel__left__disj,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [C: A,A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) )
% 0.29/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.29/0.46 & ( ord_less @ A @ A2 @ B ) )
% 0.29/0.46 | ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.29/0.46 & ( ord_less @ A @ B @ A2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_cancel_left_disj
% 0.29/0.46 thf(fact_169_mult__strict__left__mono,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord20386208strict @ A )
% 0.29/0.46 => ! [A2: A,B: A,C: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ B )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.29/0.46 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_strict_left_mono
% 0.29/0.46 thf(fact_170_mult__strict__left__mono__neg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [B: A,A2: A,C: A] :
% 0.29/0.46 ( ( ord_less @ A @ B @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_strict_left_mono_neg
% 0.29/0.46 thf(fact_171_mult__less__cancel__left__pos,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [C: A,A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 0.29/0.46 => ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) )
% 0.29/0.46 = ( ord_less @ A @ A2 @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_cancel_left_pos
% 0.29/0.46 thf(fact_172_mult__less__cancel__left__neg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [C: A,A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) )
% 0.29/0.46 = ( ord_less @ A @ B @ A2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_cancel_left_neg
% 0.29/0.46 thf(fact_173_zero__less__mult__pos2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord20386208strict @ A )
% 0.29/0.46 => ! [B: A,A2: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B @ A2 ) )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_mult_pos2
% 0.29/0.46 thf(fact_174_zero__less__mult__pos,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord20386208strict @ A )
% 0.29/0.46 => ! [A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B ) )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_mult_pos
% 0.29/0.46 thf(fact_175_zero__less__mult__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B ) )
% 0.29/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B ) )
% 0.29/0.46 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 & ( ord_less @ A @ B @ ( zero_zero @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_mult_iff
% 0.29/0.46 thf(fact_176_mult__pos__neg2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord20386208strict @ A )
% 0.29/0.46 => ! [A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( times_times @ A @ B @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_pos_neg2
% 0.29/0.46 thf(fact_177_mult__pos__pos,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord20386208strict @ A )
% 0.29/0.46 => ! [A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_pos_pos
% 0.29/0.46 thf(fact_178_mult__pos__neg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord20386208strict @ A )
% 0.29/0.46 => ! [A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 => ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ B ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_pos_neg
% 0.29/0.46 thf(fact_179_mult__neg__pos,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord20386208strict @ A )
% 0.29/0.46 => ! [A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B )
% 0.29/0.46 => ( ord_less @ A @ ( times_times @ A @ A2 @ B ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_neg_pos
% 0.29/0.46 thf(fact_180_mult__less__0__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( times_times @ A @ A2 @ B ) @ ( zero_zero @ A ) )
% 0.29/0.46 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.46 & ( ord_less @ A @ B @ ( zero_zero @ A ) ) )
% 0.29/0.46 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 & ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_0_iff
% 0.29/0.46 thf(fact_181_not__square__less__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_ring @ A )
% 0.29/0.46 => ! [A2: A] :
% 0.29/0.46 ~ ( ord_less @ A @ ( times_times @ A @ A2 @ A2 ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_square_less_zero
% 0.29/0.46 thf(fact_182_mult__neg__neg,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord581940658strict @ A )
% 0.29/0.46 => ! [A2: A,B: A] :
% 0.29/0.46 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_neg_neg
% 0.29/0.46 thf(fact_183_not__one__less__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_one_less_zero
% 0.29/0.46 thf(fact_184_zero__less__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( zero_less_one @ A )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_one
% 0.29/0.46 thf(fact_185_less__numeral__extra_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linord1659791738miring @ A )
% 0.29/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_numeral_extra(1)
% 0.29/0.46 thf(fact_186_less__1__mult,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_semidom @ A )
% 0.29/0.46 => ! [M: A,N: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( one_one @ A ) @ M )
% 0.29/0.46 => ( ( ord_less @ A @ ( one_one @ A ) @ N )
% 0.29/0.46 => ( ord_less @ A @ ( one_one @ A ) @ ( times_times @ A @ M @ N ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_1_mult
% 0.29/0.46 thf(fact_187_zero__neq__neg__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ring_char_0 @ A )
% 0.29/0.46 => ( ( zero_zero @ A )
% 0.29/0.46 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_neq_neg_one
% 0.29/0.46 thf(fact_188_less__minus__one__simps_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_minus_one_simps(2)
% 0.29/0.46 thf(fact_189_less__minus__one__simps_I4_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_minus_one_simps(4)
% 0.29/0.46 thf(fact_190_square__eq__1__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( ring_11004092258visors @ A )
% 0.29/0.46 => ! [X: A] :
% 0.29/0.46 ( ( ( times_times @ A @ X @ X )
% 0.29/0.46 = ( one_one @ A ) )
% 0.29/0.46 = ( ( X
% 0.29/0.46 = ( one_one @ A ) )
% 0.29/0.46 | ( X
% 0.29/0.46 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % square_eq_1_iff
% 0.29/0.46 thf(fact_191_rev__nonempty__induct,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A,P3: ( list @ A ) > $o] :
% 0.29/0.46 ( ( Xs
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A] : ( P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A] :
% 0.29/0.46 ( ( Xs2
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ( P3 @ Xs2 )
% 0.29/0.46 => ( P3 @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ) )
% 0.29/0.46 => ( P3 @ Xs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rev_nonempty_induct
% 0.29/0.46 thf(fact_192_append__eq__Cons__conv,axiom,
% 0.29/0.46 ! [A: $tType,Ys2: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.29/0.46 ( ( ( append @ A @ Ys2 @ Zs )
% 0.29/0.46 = ( cons @ A @ X @ Xs ) )
% 0.29/0.46 = ( ( ( Ys2
% 0.29/0.46 = ( nil @ A ) )
% 0.29/0.46 & ( Zs
% 0.29/0.46 = ( cons @ A @ X @ Xs ) ) )
% 0.29/0.46 | ? [Ys4: list @ A] :
% 0.29/0.46 ( ( Ys2
% 0.29/0.46 = ( cons @ A @ X @ Ys4 ) )
% 0.29/0.46 & ( ( append @ A @ Ys4 @ Zs )
% 0.29/0.46 = Xs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % append_eq_Cons_conv
% 0.29/0.46 thf(fact_193_Cons__eq__append__conv,axiom,
% 0.29/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.29/0.46 ( ( ( cons @ A @ X @ Xs )
% 0.29/0.46 = ( append @ A @ Ys2 @ Zs ) )
% 0.29/0.46 = ( ( ( Ys2
% 0.29/0.46 = ( nil @ A ) )
% 0.29/0.46 & ( ( cons @ A @ X @ Xs )
% 0.29/0.46 = Zs ) )
% 0.29/0.46 | ? [Ys4: list @ A] :
% 0.29/0.46 ( ( ( cons @ A @ X @ Ys4 )
% 0.29/0.46 = Ys2 )
% 0.29/0.46 & ( Xs
% 0.29/0.46 = ( append @ A @ Ys4 @ Zs ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Cons_eq_append_conv
% 0.29/0.46 thf(fact_194_rev__exhaust,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A] :
% 0.29/0.46 ( ( Xs
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ~ ! [Ys: list @ A,Y2: A] :
% 0.29/0.46 ( Xs
% 0.29/0.46 != ( append @ A @ Ys @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rev_exhaust
% 0.29/0.46 thf(fact_195_rev__induct,axiom,
% 0.29/0.46 ! [A: $tType,P3: ( list @ A ) > $o,Xs: list @ A] :
% 0.29/0.46 ( ( P3 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A] :
% 0.29/0.46 ( ( P3 @ Xs2 )
% 0.29/0.46 => ( P3 @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) )
% 0.29/0.46 => ( P3 @ Xs ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % rev_induct
% 0.29/0.46 thf(fact_196_less__minus__one__simps_I1_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_minus_one_simps(1)
% 0.29/0.46 thf(fact_197_less__minus__one__simps_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_minus_one_simps(3)
% 0.29/0.46 thf(fact_198_poly__cutoff__1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( comm_semiring_1 @ A )
% 0.29/0.46 => ! [N: nat] :
% 0.29/0.46 ( ( ( N
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 => ( ( poly_cutoff @ A @ N @ ( one_one @ ( poly @ A ) ) )
% 0.29/0.46 = ( zero_zero @ ( poly @ A ) ) ) )
% 0.29/0.46 & ( ( N
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 => ( ( poly_cutoff @ A @ N @ ( one_one @ ( poly @ A ) ) )
% 0.29/0.46 = ( one_one @ ( poly @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % poly_cutoff_1
% 0.29/0.46 thf(fact_199_mult__less__iff1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ! [Z2: A,X: A,Y3: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ Z2 )
% 0.29/0.46 => ( ( ord_less @ A @ ( times_times @ A @ X @ Z2 ) @ ( times_times @ A @ Y3 @ Z2 ) )
% 0.29/0.46 = ( ord_less @ A @ X @ Y3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_iff1
% 0.29/0.46 thf(fact_200_dbl__dec__simps_I2_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( neg_numeral @ A )
% 0.29/0.46 => ( ( neg_numeral_dbl_dec @ A @ ( zero_zero @ A ) )
% 0.29/0.46 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dbl_dec_simps(2)
% 0.29/0.46 thf(fact_201_nat__mult__less__cancel__disj,axiom,
% 0.29/0.46 ! [K: nat,M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.29/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.29/0.46 & ( ord_less @ nat @ M @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_mult_less_cancel_disj
% 0.29/0.46 thf(fact_202_nat__0__less__mult__iff,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ M @ N ) )
% 0.29/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.29/0.46 & ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_0_less_mult_iff
% 0.29/0.46 thf(fact_203_mult__less__cancel2,axiom,
% 0.29/0.46 ! [M: nat,K: nat,N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 0.29/0.46 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.29/0.46 & ( ord_less @ nat @ M @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_cancel2
% 0.29/0.46 thf(fact_204_mult__cancel2,axiom,
% 0.29/0.46 ! [M: nat,K: nat,N: nat] :
% 0.29/0.46 ( ( ( times_times @ nat @ M @ K )
% 0.29/0.46 = ( times_times @ nat @ N @ K ) )
% 0.29/0.46 = ( ( M = N )
% 0.29/0.46 | ( K
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_cancel2
% 0.29/0.46 thf(fact_205_neq0__conv,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( N
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % neq0_conv
% 0.29/0.46 thf(fact_206_less__nat__zero__code,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_nat_zero_code
% 0.29/0.46 thf(fact_207_bot__nat__0_Onot__eq__extremum,axiom,
% 0.29/0.46 ! [A2: nat] :
% 0.29/0.46 ( ( A2
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_nat_0.not_eq_extremum
% 0.29/0.46 thf(fact_208_mult__is__0,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ( times_times @ nat @ M @ N )
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 = ( ( M
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 | ( N
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_is_0
% 0.29/0.46 thf(fact_209_mult__0__right,axiom,
% 0.29/0.46 ! [M: nat] :
% 0.29/0.46 ( ( times_times @ nat @ M @ ( zero_zero @ nat ) )
% 0.29/0.46 = ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_0_right
% 0.29/0.46 thf(fact_210_mult__cancel1,axiom,
% 0.29/0.46 ! [K: nat,M: nat,N: nat] :
% 0.29/0.46 ( ( ( times_times @ nat @ K @ M )
% 0.29/0.46 = ( times_times @ nat @ K @ N ) )
% 0.29/0.46 = ( ( M = N )
% 0.29/0.46 | ( K
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_cancel1
% 0.29/0.46 thf(fact_211_nat__1__eq__mult__iff,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ( one_one @ nat )
% 0.29/0.46 = ( times_times @ nat @ M @ N ) )
% 0.29/0.46 = ( ( M
% 0.29/0.46 = ( one_one @ nat ) )
% 0.29/0.46 & ( N
% 0.29/0.46 = ( one_one @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_1_eq_mult_iff
% 0.29/0.46 thf(fact_212_nat__mult__eq__1__iff,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ( times_times @ nat @ M @ N )
% 0.29/0.46 = ( one_one @ nat ) )
% 0.29/0.46 = ( ( M
% 0.29/0.46 = ( one_one @ nat ) )
% 0.29/0.46 & ( N
% 0.29/0.46 = ( one_one @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_mult_eq_1_iff
% 0.29/0.46 thf(fact_213_dbl__dec__simps_I3_J,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( neg_numeral @ A )
% 0.29/0.46 => ( ( neg_numeral_dbl_dec @ A @ ( one_one @ A ) )
% 0.29/0.46 = ( one_one @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % dbl_dec_simps(3)
% 0.29/0.46 thf(fact_214_poly__cutoff__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( zero @ A )
% 0.29/0.46 => ! [N: nat] :
% 0.29/0.46 ( ( poly_cutoff @ A @ N @ ( zero_zero @ ( poly @ A ) ) )
% 0.29/0.46 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % poly_cutoff_0
% 0.29/0.46 thf(fact_215_less__one,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 0.29/0.46 = ( N
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_one
% 0.29/0.46 thf(fact_216_nat__mult__1,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( times_times @ nat @ ( one_one @ nat ) @ N )
% 0.29/0.46 = N ) ).
% 0.29/0.46
% 0.29/0.46 % nat_mult_1
% 0.29/0.46 thf(fact_217_nat__mult__1__right,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( times_times @ nat @ N @ ( one_one @ nat ) )
% 0.29/0.46 = N ) ).
% 0.29/0.46
% 0.29/0.46 % nat_mult_1_right
% 0.29/0.46 thf(fact_218_infinite__descent__measure,axiom,
% 0.29/0.46 ! [A: $tType,P3: A > $o,V2: A > nat,X: A] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ~ ( P3 @ X2 )
% 0.29/0.46 => ? [Y5: A] :
% 0.29/0.46 ( ( ord_less @ nat @ ( V2 @ Y5 ) @ ( V2 @ X2 ) )
% 0.29/0.46 & ~ ( P3 @ Y5 ) ) )
% 0.29/0.46 => ( P3 @ X ) ) ).
% 0.29/0.46
% 0.29/0.46 % infinite_descent_measure
% 0.29/0.46 thf(fact_219_linorder__neqE__nat,axiom,
% 0.29/0.46 ! [X: nat,Y3: nat] :
% 0.29/0.46 ( ( X != Y3 )
% 0.29/0.46 => ( ~ ( ord_less @ nat @ X @ Y3 )
% 0.29/0.46 => ( ord_less @ nat @ Y3 @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % linorder_neqE_nat
% 0.29/0.46 thf(fact_220_infinite__descent,axiom,
% 0.29/0.46 ! [P3: nat > $o,N: nat] :
% 0.29/0.46 ( ! [N2: nat] :
% 0.29/0.46 ( ~ ( P3 @ N2 )
% 0.29/0.46 => ? [M2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.29/0.46 & ~ ( P3 @ M2 ) ) )
% 0.29/0.46 => ( P3 @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % infinite_descent
% 0.29/0.46 thf(fact_221_nat__less__induct,axiom,
% 0.29/0.46 ! [P3: nat > $o,N: nat] :
% 0.29/0.46 ( ! [N2: nat] :
% 0.29/0.46 ( ! [M2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.29/0.46 => ( P3 @ M2 ) )
% 0.29/0.46 => ( P3 @ N2 ) )
% 0.29/0.46 => ( P3 @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_less_induct
% 0.29/0.46 thf(fact_222_less__irrefl__nat,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N @ N ) ).
% 0.29/0.46
% 0.29/0.46 % less_irrefl_nat
% 0.29/0.46 thf(fact_223_less__not__refl3,axiom,
% 0.29/0.46 ! [S: nat,T: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ S @ T )
% 0.29/0.46 => ( S != T ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_not_refl3
% 0.29/0.46 thf(fact_224_less__not__refl2,axiom,
% 0.29/0.46 ! [N: nat,M: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ N @ M )
% 0.29/0.46 => ( M != N ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_not_refl2
% 0.29/0.46 thf(fact_225_less__not__refl,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N @ N ) ).
% 0.29/0.46
% 0.29/0.46 % less_not_refl
% 0.29/0.46 thf(fact_226_nat__neq__iff,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( M != N )
% 0.29/0.46 = ( ( ord_less @ nat @ M @ N )
% 0.29/0.46 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_neq_iff
% 0.29/0.46 thf(fact_227_measure__induct,axiom,
% 0.29/0.46 ! [B2: $tType,A: $tType] :
% 0.29/0.46 ( ( wellorder @ B2 )
% 0.29/0.46 => ! [F2: A > B2,P3: A > $o,A2: A] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ! [Y5: A] :
% 0.29/0.46 ( ( ord_less @ B2 @ ( F2 @ Y5 ) @ ( F2 @ X2 ) )
% 0.29/0.46 => ( P3 @ Y5 ) )
% 0.29/0.46 => ( P3 @ X2 ) )
% 0.29/0.46 => ( P3 @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measure_induct
% 0.29/0.46 thf(fact_228_measure__induct__rule,axiom,
% 0.29/0.46 ! [B2: $tType,A: $tType] :
% 0.29/0.46 ( ( wellorder @ B2 )
% 0.29/0.46 => ! [F2: A > B2,P3: A > $o,A2: A] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ! [Y5: A] :
% 0.29/0.46 ( ( ord_less @ B2 @ ( F2 @ Y5 ) @ ( F2 @ X2 ) )
% 0.29/0.46 => ( P3 @ Y5 ) )
% 0.29/0.46 => ( P3 @ X2 ) )
% 0.29/0.46 => ( P3 @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measure_induct_rule
% 0.29/0.46 thf(fact_229_gr0I,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( N
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.29/0.46
% 0.29/0.46 % gr0I
% 0.29/0.46 thf(fact_230_not__gr0,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 0.29/0.46 = ( N
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_gr0
% 0.29/0.46 thf(fact_231_not__less0,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_less0
% 0.29/0.46 thf(fact_232_less__zeroE,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_zeroE
% 0.29/0.46 thf(fact_233_gr__implies__not0,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M @ N )
% 0.29/0.46 => ( N
% 0.29/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % gr_implies_not0
% 0.29/0.46 thf(fact_234_infinite__descent0,axiom,
% 0.29/0.46 ! [P3: nat > $o,N: nat] :
% 0.29/0.46 ( ( P3 @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [N2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.29/0.46 => ( ~ ( P3 @ N2 )
% 0.29/0.46 => ? [M2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.29/0.46 & ~ ( P3 @ M2 ) ) ) )
% 0.29/0.46 => ( P3 @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % infinite_descent0
% 0.29/0.46 thf(fact_235_bot__nat__0_Oextremum__strict,axiom,
% 0.29/0.46 ! [A2: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_nat_0.extremum_strict
% 0.29/0.46 thf(fact_236_infinite__descent0__measure,axiom,
% 0.29/0.46 ! [A: $tType,V2: A > nat,P3: A > $o,X: A] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ( ( V2 @ X2 )
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 => ( P3 @ X2 ) )
% 0.29/0.46 => ( ! [X2: A] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X2 ) )
% 0.29/0.46 => ( ~ ( P3 @ X2 )
% 0.29/0.46 => ? [Y5: A] :
% 0.29/0.46 ( ( ord_less @ nat @ ( V2 @ Y5 ) @ ( V2 @ X2 ) )
% 0.29/0.46 & ~ ( P3 @ Y5 ) ) ) )
% 0.29/0.46 => ( P3 @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % infinite_descent0_measure
% 0.29/0.46 thf(fact_237_mult__less__mono1,axiom,
% 0.29/0.46 ! [I: nat,J: nat,K: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I @ J )
% 0.29/0.46 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.29/0.46 => ( ord_less @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ K ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_mono1
% 0.29/0.46 thf(fact_238_mult__less__mono2,axiom,
% 0.29/0.46 ! [I: nat,J: nat,K: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I @ J )
% 0.29/0.46 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.29/0.46 => ( ord_less @ nat @ ( times_times @ nat @ K @ I ) @ ( times_times @ nat @ K @ J ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_less_mono2
% 0.29/0.46 thf(fact_239_mult__0,axiom,
% 0.29/0.46 ! [N: nat] :
% 0.29/0.46 ( ( times_times @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.46 = ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_0
% 0.29/0.46 thf(fact_240_nat__mult__eq__cancel1,axiom,
% 0.29/0.46 ! [K: nat,M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.29/0.46 => ( ( ( times_times @ nat @ K @ M )
% 0.29/0.46 = ( times_times @ nat @ K @ N ) )
% 0.29/0.46 = ( M = N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_mult_eq_cancel1
% 0.29/0.46 thf(fact_241_nat__mult__less__cancel1,axiom,
% 0.29/0.46 ! [K: nat,M: nat,N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 0.29/0.46 => ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 0.29/0.46 = ( ord_less @ nat @ M @ N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_mult_less_cancel1
% 0.29/0.46 thf(fact_242_nat__mult__eq__cancel__disj,axiom,
% 0.29/0.46 ! [K: nat,M: nat,N: nat] :
% 0.29/0.46 ( ( ( times_times @ nat @ K @ M )
% 0.29/0.46 = ( times_times @ nat @ K @ N ) )
% 0.29/0.46 = ( ( K
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 | ( M = N ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_mult_eq_cancel_disj
% 0.29/0.46 thf(fact_243_mult__eq__self__implies__10,axiom,
% 0.29/0.46 ! [M: nat,N: nat] :
% 0.29/0.46 ( ( M
% 0.29/0.46 = ( times_times @ nat @ M @ N ) )
% 0.29/0.46 => ( ( N
% 0.29/0.46 = ( one_one @ nat ) )
% 0.29/0.46 | ( M
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % mult_eq_self_implies_10
% 0.29/0.46 thf(fact_244_n__lists__Nil,axiom,
% 0.29/0.46 ! [A: $tType,N: nat] :
% 0.29/0.46 ( ( ( N
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.29/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.29/0.46 & ( ( N
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 0.29/0.46 = ( nil @ ( list @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % n_lists_Nil
% 0.29/0.46 thf(fact_245_n__lists_Osimps_I1_J,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A] :
% 0.29/0.46 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 0.29/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % n_lists.simps(1)
% 0.29/0.46 thf(fact_246_compl__eq__compl__iff,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( boolean_algebra @ A )
% 0.29/0.46 => ! [X: A,Y3: A] :
% 0.29/0.46 ( ( ( uminus_uminus @ A @ X )
% 0.29/0.46 = ( uminus_uminus @ A @ Y3 ) )
% 0.29/0.46 = ( X = Y3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_eq_compl_iff
% 0.29/0.46 thf(fact_247_double__compl,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( boolean_algebra @ A )
% 0.29/0.46 => ! [X: A] :
% 0.29/0.46 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.29/0.46 = X ) ) ).
% 0.29/0.46
% 0.29/0.46 % double_compl
% 0.29/0.46 thf(fact_248_uminus__apply,axiom,
% 0.29/0.46 ! [B2: $tType,A: $tType] :
% 0.29/0.46 ( ( uminus @ B2 )
% 0.29/0.46 => ( ( uminus_uminus @ ( A > B2 ) )
% 0.29/0.46 = ( ^ [A5: A > B2,X3: A] : ( uminus_uminus @ B2 @ ( A5 @ X3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % uminus_apply
% 0.29/0.46 thf(fact_249_fun__Compl__def,axiom,
% 0.29/0.46 ! [B2: $tType,A: $tType] :
% 0.29/0.46 ( ( uminus @ B2 )
% 0.29/0.46 => ( ( uminus_uminus @ ( A > B2 ) )
% 0.29/0.46 = ( ^ [A5: A > B2,X3: A] : ( uminus_uminus @ B2 @ ( A5 @ X3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % fun_Compl_def
% 0.29/0.46 thf(fact_250_compl__less__swap1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( boolean_algebra @ A )
% 0.29/0.46 => ! [Y3: A,X: A] :
% 0.29/0.46 ( ( ord_less @ A @ Y3 @ ( uminus_uminus @ A @ X ) )
% 0.29/0.46 => ( ord_less @ A @ X @ ( uminus_uminus @ A @ Y3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_less_swap1
% 0.29/0.46 thf(fact_251_compl__less__swap2,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( boolean_algebra @ A )
% 0.29/0.46 => ! [Y3: A,X: A] :
% 0.29/0.46 ( ( ord_less @ A @ ( uminus_uminus @ A @ Y3 ) @ X )
% 0.29/0.46 => ( ord_less @ A @ ( uminus_uminus @ A @ X ) @ Y3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % compl_less_swap2
% 0.29/0.46
% 0.29/0.46 % Subclasses (40)
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__ring__1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( comm_ring_1 @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___HOL_Otype,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( type @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Oone,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( one @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Osgn,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( sgn @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Oidom,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( idom @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Oring,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ring @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Oplus,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( plus @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Ozero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( zero @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Oring__1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ring_1 @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Ouminus,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( uminus @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Orderings_Oord,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ord @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Nat_Oring__char__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ring_char_0 @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Num_Oneg__numeral,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( neg_numeral @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__ring,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( comm_ring @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Omult__zero,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( mult_zero @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Ogroup__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( group_add @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Omonoid__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( monoid_add @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Omonoid__mult,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( monoid_mult @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Orderings_Olinorder,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( linorder @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Oidom__abs__sgn,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( idom_abs_sgn @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Ozero__neq__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( zero_neq_one @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Oab__group__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ab_group_add @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Ozero__less__one,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( zero_less_one @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Osemigroup__mult,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( semigroup_mult @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__0,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( comm_semiring_0 @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__1,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( comm_semiring_1 @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__ring,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( linordered_ring @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( comm_monoid_add @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__mult,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( comm_monoid_mult @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__mult,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ab_semigroup_mult @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__semidom,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( linordered_semidom @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__group__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ordered_ab_group_add @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__ring__strict,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( linord581940658strict @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Oring__1__no__zero__divisors,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( ring_11004092258visors @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Groups_Olinordered__ab__group__add,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( linord219039673up_add @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( semiri1193490041visors @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__semiring__strict,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( linord20386208strict @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__nonzero__semiring,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( linord1659791738miring @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__comm__semiring__strict,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( linord893533164strict @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A )
% 0.29/0.46 => ( semiri1923998003cancel @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 % Type constructors (71)
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring__1,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_ring_1 @ A6 )
% 0.29/0.46 => ( comm_ring_1 @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( boolean_algebra @ A7 )
% 0.29/0.46 => ( boolean_algebra @ ( A6 > A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( ord @ A7 )
% 0.29/0.46 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.29/0.46 ! [A6: $tType,A7: $tType] :
% 0.29/0.46 ( ( uminus @ A7 )
% 0.29/0.46 => ( uminus @ ( A6 > A7 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 0.29/0.46 semiri1923998003cancel @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict,axiom,
% 0.29/0.46 linord893533164strict @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.29/0.46 canoni770627133id_add @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.29/0.46 linord1659791738miring @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__semiring__strict,axiom,
% 0.29/0.46 linord20386208strict @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors,axiom,
% 0.29/0.46 semiri1193490041visors @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.29/0.46 linordered_semidom @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.29/0.46 ab_semigroup_mult @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 0.29/0.46 comm_monoid_mult @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.29/0.46 comm_monoid_add @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.29/0.46 comm_semiring_1 @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0,axiom,
% 0.29/0.46 comm_semiring_0 @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.29/0.46 semigroup_mult @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Ozero__less__one,axiom,
% 0.29/0.46 zero_less_one @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.29/0.46 wellorder @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 0.29/0.46 zero_neq_one @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.29/0.46 linorder @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.29/0.46 monoid_mult @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 0.29/0.46 monoid_add @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Rings_Omult__zero,axiom,
% 0.29/0.46 mult_zero @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 0.29/0.46 ord @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.29/0.46 zero @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Oplus,axiom,
% 0.29/0.46 plus @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.29/0.46 one @ nat ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_2,axiom,
% 0.29/0.46 boolean_algebra @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_3,axiom,
% 0.29/0.46 linorder @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.29/0.46 ord @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_HOL_Obool___Groups_Ouminus_5,axiom,
% 0.29/0.46 uminus @ $o ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors__cancel_6,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( idom @ A6 )
% 0.29/0.46 => ( semiri1923998003cancel @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Olinordered__comm__semiring__strict_7,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linord893533164strict @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_8,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linord1659791738miring @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Olinordered__semiring__strict_9,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linord20386208strict @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors_10,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( ( comm_semiring_0 @ A6 )
% 0.29/0.46 & ( semiri1193490041visors @ A6 ) )
% 0.29/0.46 => ( semiri1193490041visors @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Olinordered__ab__group__add,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linord219039673up_add @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Oring__1__no__zero__divisors,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( idom @ A6 )
% 0.29/0.46 => ( ring_11004092258visors @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Olinordered__ring__strict,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linord581940658strict @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( ordered_ab_group_add @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Olinordered__semidom_11,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linordered_semidom @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Oab__semigroup__mult_12,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_0 @ A6 )
% 0.29/0.46 => ( ab_semigroup_mult @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__mult_13,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_1 @ A6 )
% 0.29/0.46 => ( comm_monoid_mult @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_14,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A6 )
% 0.29/0.46 => ( comm_monoid_add @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Olinordered__ring,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linordered_ring @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Olinordered__idom,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linordered_idom @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_15,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_1 @ A6 )
% 0.29/0.46 => ( comm_semiring_1 @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_16,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_0 @ A6 )
% 0.29/0.46 => ( comm_semiring_0 @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Osemigroup__mult_17,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_0 @ A6 )
% 0.29/0.46 => ( semigroup_mult @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Ozero__less__one_18,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( zero_less_one @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Oab__group__add,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A6 )
% 0.29/0.46 => ( ab_group_add @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Ozero__neq__one_19,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_1 @ A6 )
% 0.29/0.46 => ( zero_neq_one @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Oidom__abs__sgn,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( idom_abs_sgn @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Orderings_Olinorder_20,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( linorder @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Omonoid__mult_21,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_1 @ A6 )
% 0.29/0.46 => ( monoid_mult @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Omonoid__add_22,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A6 )
% 0.29/0.46 => ( monoid_add @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Ogroup__add,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A6 )
% 0.29/0.46 => ( group_add @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Omult__zero_23,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_0 @ A6 )
% 0.29/0.46 => ( mult_zero @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_ring @ A6 )
% 0.29/0.46 => ( comm_ring @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Num_Oneg__numeral,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_ring_1 @ A6 )
% 0.29/0.46 => ( neg_numeral @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Nat_Oring__char__0,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( ( ring_char_0 @ A6 )
% 0.29/0.46 & ( comm_ring_1 @ A6 ) )
% 0.29/0.46 => ( ring_char_0 @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Orderings_Oord_24,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( ord @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Ouminus_25,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( ab_group_add @ A6 )
% 0.29/0.46 => ( uminus @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Oring__1,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_ring_1 @ A6 )
% 0.29/0.46 => ( ring_1 @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Ozero_26,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( zero @ A6 )
% 0.29/0.46 => ( zero @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Oplus_27,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_monoid_add @ A6 )
% 0.29/0.46 => ( plus @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Oring,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_ring @ A6 )
% 0.29/0.46 => ( ring @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Rings_Oidom,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( idom @ A6 )
% 0.29/0.46 => ( idom @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Osgn,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( linordered_idom @ A6 )
% 0.29/0.46 => ( sgn @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(tcon_Polynomial_Opoly___Groups_Oone_28,axiom,
% 0.29/0.46 ! [A6: $tType] :
% 0.29/0.46 ( ( comm_semiring_1 @ A6 )
% 0.29/0.46 => ( one @ ( poly @ A6 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Free types (1)
% 0.29/0.46 thf(tfree_0,hypothesis,
% 0.29/0.46 linordered_idom @ a ).
% 0.29/0.46
% 0.29/0.46 % Conjectures (1)
% 0.29/0.46 thf(conj_0,conjecture,
% 0.29/0.46 ( ( descar149487500hanges @ a @ ys )
% 0.29/0.46 = ( descar149487500hanges @ a @ ( coeffs @ a @ g ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.81/1.53 ---- Embedded in THF ---
% 2.81/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.81/1.53 %%% Generated on Tue Feb 24 08:24:30 EST 2026
% 2.81/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.81/1.53 %%% Logic specification used:
% 2.81/1.53 %%% thf(spec, logic, $$dhol).
% 2.81/1.53
% 2.81/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2DTF578.p
% 2.81/1.53 thf(ty_t_Polynomial_Opoly, type, poly: ($tType > $tType)).
% 2.81/1.53 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.81/1.53 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.81/1.53 thf(ty_tf_a, type, a: $tType).
% 2.81/1.53 thf(sy_cl_Rings_Ocomm__ring__1, type, comm_ring_1: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Osgn, type, sgn: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Oidom, type, idom: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Oring, type, ring: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Oplus, type, plus: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Oring__1, type, ring_1: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Ouminus, type, uminus: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Nat_Oring__char__0, type, ring_char_0: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Ocomm__ring, type, comm_ring: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Omult__zero, type, mult_zero: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Omonoid__mult, type, monoid_mult: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Oidom__abs__sgn, type, idom_abs_sgn: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Oab__group__add, type, ab_group_add: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Ozero__less__one, type, zero_less_one: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Osemigroup__mult, type, semigroup_mult: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Ocomm__semiring__0, type, comm_semiring_0: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Olinordered__ring, type, linordered_ring: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Ocomm__monoid__mult, type, comm_monoid_mult: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Oab__semigroup__mult, type, ab_semigroup_mult: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Olinordered__ring__strict, type, linord581940658strict: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Oring__1__no__zero__divisors, type, ring_11004092258visors: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Osemiring__no__zero__divisors, type, semiri1193490041visors: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Olinordered__semiring__strict, type, linord20386208strict: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Olinordered__comm__semiring__strict, type, linord893533164strict: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel, type, semiri1923998003cancel: (!> [A:$tType]: ($o))).
% 2.81/1.53 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Opsums, type, descar1668888542_psums: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.81/1.53 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Oreduce__root, type, descar316357986e_root: (!> [A:$tType]: ((A > ((poly @ A) > (poly @ A)))))).
% 2.81/1.53 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Osign__changes, type, descar149487500hanges: (!> [A:$tType]: (((list @ A) > nat)))).
% 2.81/1.53 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.81/1.53 thf(sy_c_Groups_Otimes__class_Otimes, type, times_times: (!> [A:$tType]: ((A > (A > A))))).
% 2.81/1.53 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.81/1.53 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.81/1.53 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.81/1.53 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.81/1.53 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.81/1.53 thf(sy_c_List_On__lists, type, n_lists: (!> [A:$tType]: ((nat > ((list @ A) > (list @ (list @ A))))))).
% 2.81/1.53 thf(sy_c_List_Onull, type, null: (!> [A:$tType]: (((list @ A) > $o)))).
% 2.81/1.53 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec, type, neg_numeral_dbl_dec: (!> [A:$tType]: ((A > A)))).
% 2.81/1.53 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.81/1.53 thf(sy_c_Polynomial_OPoly, type, poly2: (!> [A:$tType]: (((list @ A) > (poly @ A))))).
% 2.81/1.53 thf(sy_c_Polynomial_Ocoeffs, type, coeffs: (!> [A:$tType]: (((poly @ A) > (list @ A))))).
% 2.81/1.53 thf(sy_c_Polynomial_Ois__zero, type, is_zero: (!> [A:$tType]: (((poly @ A) > $o)))).
% 2.81/1.53 thf(sy_c_Polynomial_OpCons, type, pCons: (!> [A:$tType]: ((A > ((poly @ A) > (poly @ A)))))).
% 2.81/1.53 thf(sy_c_Polynomial_Opoly__cutoff, type, poly_cutoff: (!> [A:$tType]: ((nat > ((poly @ A) > (poly @ A)))))).
% 2.81/1.53 thf(sy_c_Polynomial_Osmult, type, smult: (!> [A:$tType]: ((A > ((poly @ A) > (poly @ A)))))).
% 2.81/1.53 thf(sy_v_g, type, g: (poly @ a)).
% 2.81/1.53 thf(sy_v_v, type, v: ((poly @ a) > nat)).
% 2.81/1.53 thf(sy_v_xs____, type, xs: (list @ a)).
% 2.81/1.53 thf(sy_v_ys____, type, ys: (list @ a)).
% 2.81/1.53 thf(fact_0_v__def, axiom, (v = (^ [F:(poly @ a)]: (((descar149487500hanges @ a) @ ((coeffs @ a) @ F)))))).
% 2.81/1.53 thf(fact_1_nz, axiom, (g != (zero_zero @ (poly @ a)))).
% 2.81/1.53 thf(fact_2_coeffs__eq__iff, axiom, (! [A:$tType]: (((zero @ A) => ((^ [Y:(poly @ A),Z:(poly @ A)]: ((Y = Z))) = (^ [P:(poly @ A),Q:(poly @ A)]: ((((coeffs @ A) @ P) = ((coeffs @ A) @ Q))))))))).
% 2.81/1.53 thf(fact_3_ys, axiom, (ys = ((descar1668888542_psums @ a) @ xs))).
% 2.81/1.53 thf(fact_4_sign__changes__coeff__sign__changes, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Xs:(list @ A),P2:(poly @ A)]: (((((poly2 @ A) @ Xs) = P2) => (((descar149487500hanges @ A) @ Xs) = ((descar149487500hanges @ A) @ ((coeffs @ A) @ P2)))))))))).
% 2.81/1.53 thf(fact_5_ys__def, axiom, (ys = (((append @ a) @ ((coeffs @ a) @ g)) @ (((cons @ a) @ (zero_zero @ a)) @ (nil @ a))))).
% 2.81/1.53 thf(fact_6_coeff__sign__changes__reduce__root, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [A2:A,P2:(poly @ A)]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((descar149487500hanges @ A) @ ((coeffs @ A) @ (((descar316357986e_root @ A) @ A2) @ P2))) = ((descar149487500hanges @ A) @ ((coeffs @ A) @ P2)))))))))).
% 2.81/1.53 thf(fact_7_is__zero__def, axiom, (! [A:$tType]: (((zero @ A) => ((is_zero @ A) = (^ [P:(poly @ A)]: (((null @ A) @ ((coeffs @ A) @ P))))))))).
% 2.81/1.53 thf(fact_8_Poly__coeffs, axiom, (! [A:$tType]: (((zero @ A) => (! [P2:(poly @ A)]: ((((poly2 @ A) @ ((coeffs @ A) @ P2)) = P2))))))).
% 2.81/1.53 thf(fact_9_sign__changes__Nil, axiom, (! [A:$tType]: ((((sgn @ A) & (zero @ A)) => (((descar149487500hanges @ A) @ (nil @ A)) = (zero_zero @ nat)))))).
% 2.81/1.53 thf(fact_10_xs__def, axiom, (xs = ((coeffs @ a) @ (((times_times @ (poly @ a)) @ (((pCons @ a) @ (one_one @ a)) @ (((pCons @ a) @ ((uminus_uminus @ a) @ (one_one @ a))) @ (zero_zero @ (poly @ a))))) @ g)))).
% 2.81/1.53 thf(fact_11_coeff__sign__changes__smult, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [A2:A,P2:(poly @ A)]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((descar149487500hanges @ A) @ ((coeffs @ A) @ (((smult @ A) @ A2) @ P2))) = ((descar149487500hanges @ A) @ ((coeffs @ A) @ P2)))))))))).
% 2.81/1.53 thf(fact_12_sign__changes__0__Cons, axiom, (! [A:$tType]: (((idom_abs_sgn @ A) => (! [Xs:(list @ A)]: ((((descar149487500hanges @ A) @ (((cons @ A) @ (zero_zero @ A)) @ Xs)) = ((descar149487500hanges @ A) @ Xs)))))))).
% 2.81/1.53 thf(fact_13_sign__changes__Cons__Cons__0, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Xs:(list @ A)]: ((((descar149487500hanges @ A) @ (((cons @ A) @ X) @ (((cons @ A) @ (zero_zero @ A)) @ Xs))) = ((descar149487500hanges @ A) @ (((cons @ A) @ X) @ Xs))))))))).
% 2.81/1.53 thf(fact_14_pCons__eq__iff, axiom, (! [A:$tType]: (((zero @ A) => (! [A2:A,P2:(poly @ A),B:A,Q2:(poly @ A)]: ((((((pCons @ A) @ A2) @ P2) = (((pCons @ A) @ B) @ Q2)) = ((A2 = B) & (P2 = Q2))))))))).
% 2.81/1.53 thf(fact_15_minus__pCons, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,P2:(poly @ A)]: ((((uminus_uminus @ (poly @ A)) @ (((pCons @ A) @ A2) @ P2)) = (((pCons @ A) @ ((uminus_uminus @ A) @ A2)) @ ((uminus_uminus @ (poly @ A)) @ P2))))))))).
% 2.81/1.53 thf(fact_16_smult__smult, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [A2:A,B:A,P2:(poly @ A)]: (((((smult @ A) @ A2) @ (((smult @ A) @ B) @ P2)) = (((smult @ A) @ (((times_times @ A) @ A2) @ B)) @ P2)))))))).
% 2.81/1.53 thf(fact_17_smult__1__left, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => (! [P2:(poly @ A)]: (((((smult @ A) @ (one_one @ A)) @ P2) = P2))))))).
% 2.81/1.53 thf(fact_18_smult__minus__left, axiom, (! [A:$tType]: (((comm_ring @ A) => (! [A2:A,P2:(poly @ A)]: (((((smult @ A) @ ((uminus_uminus @ A) @ A2)) @ P2) = ((uminus_uminus @ (poly @ A)) @ (((smult @ A) @ A2) @ P2))))))))).
% 2.81/1.53 thf(fact_19_smult__0__right, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [A2:A]: (((((smult @ A) @ A2) @ (zero_zero @ (poly @ A))) = (zero_zero @ (poly @ A))))))))).
% 2.81/1.53 thf(fact_20_mult__smult__left, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [A2:A,P2:(poly @ A),Q2:(poly @ A)]: (((((times_times @ (poly @ A)) @ (((smult @ A) @ A2) @ P2)) @ Q2) = (((smult @ A) @ A2) @ (((times_times @ (poly @ A)) @ P2) @ Q2))))))))).
% 2.81/1.53 thf(fact_21_mult__smult__right, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [P2:(poly @ A),A2:A,Q2:(poly @ A)]: (((((times_times @ (poly @ A)) @ P2) @ (((smult @ A) @ A2) @ Q2)) = (((smult @ A) @ A2) @ (((times_times @ (poly @ A)) @ P2) @ Q2))))))))).
% 2.81/1.53 thf(fact_22_pCons__0__0, axiom, (! [A:$tType]: (((zero @ A) => ((((pCons @ A) @ (zero_zero @ A)) @ (zero_zero @ (poly @ A))) = (zero_zero @ (poly @ A))))))).
% 2.81/1.53 thf(fact_23_pCons__eq__0__iff, axiom, (! [A:$tType]: (((zero @ A) => (! [A2:A,P2:(poly @ A)]: ((((((pCons @ A) @ A2) @ P2) = (zero_zero @ (poly @ A))) = ((A2 = (zero_zero @ A)) & (P2 = (zero_zero @ (poly @ A))))))))))).
% 2.81/1.53 thf(fact_24_one__poly__eq__simps_I2_J, axiom, (! [B2:$tType]: (((comm_semiring_1 @ B2) => ((((pCons @ B2) @ (one_one @ B2)) @ (zero_zero @ (poly @ B2))) = (one_one @ (poly @ B2))))))).
% 2.81/1.53 thf(fact_25_one__poly__eq__simps_I1_J, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => ((one_one @ (poly @ A)) = (((pCons @ A) @ (one_one @ A)) @ (zero_zero @ (poly @ A)))))))).
% 2.81/1.53 thf(fact_26_smult__0__left, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [P2:(poly @ A)]: (((((smult @ A) @ (zero_zero @ A)) @ P2) = (zero_zero @ (poly @ A))))))))).
% 2.81/1.53 thf(fact_27_smult__eq__0__iff, axiom, (! [A:$tType]: ((((comm_semiring_0 @ A) & (semiri1193490041visors @ A)) => (! [A2:A,P2:(poly @ A)]: ((((((smult @ A) @ A2) @ P2) = (zero_zero @ (poly @ A))) = ((A2 = (zero_zero @ A)) | (P2 = (zero_zero @ (poly @ A))))))))))).
% 2.81/1.53 thf(fact_28_smult__pCons, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [A2:A,B:A,P2:(poly @ A)]: (((((smult @ A) @ A2) @ (((pCons @ A) @ B) @ P2)) = (((pCons @ A) @ (((times_times @ A) @ A2) @ B)) @ (((smult @ A) @ A2) @ P2))))))))).
% 2.81/1.53 thf(fact_29_coeffs__eq__Nil, axiom, (! [A:$tType]: (((zero @ A) => (! [P2:(poly @ A)]: (((((coeffs @ A) @ P2) = (nil @ A)) = (P2 = (zero_zero @ (poly @ A)))))))))).
% 2.81/1.53 thf(fact_30_coeffs__0__eq__Nil, axiom, (! [A:$tType]: (((zero @ A) => (((coeffs @ A) @ (zero_zero @ (poly @ A))) = (nil @ A)))))).
% 2.81/1.53 thf(fact_31_psums__0__Cons, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [Xs:(list @ A)]: ((((descar1668888542_psums @ A) @ (((cons @ A) @ (zero_zero @ A)) @ Xs)) = (((cons @ A) @ (zero_zero @ A)) @ ((descar1668888542_psums @ A) @ Xs))))))))).
% 2.81/1.53 thf(fact_32_coeffs__1__eq, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => (((coeffs @ A) @ (one_one @ (poly @ A))) = (((cons @ A) @ (one_one @ A)) @ (nil @ A))))))).
% 2.81/1.53 thf(fact_33_sign__changes__singleton, axiom, (! [A:$tType]: ((((sgn @ A) & (zero @ A)) => (! [X:A]: ((((descar149487500hanges @ A) @ (((cons @ A) @ X) @ (nil @ A))) = (zero_zero @ nat)))))))).
% 2.81/1.53 thf(fact_34__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062, axiom, (((descar149487500hanges @ a) @ xs) = (v @ (((times_times @ (poly @ a)) @ (((pCons @ a) @ (one_one @ a)) @ (((pCons @ a) @ ((uminus_uminus @ a) @ (one_one @ a))) @ (zero_zero @ (poly @ a))))) @ g)))).
% 2.81/1.53 thf(fact_35_Poly__snoc__zero, axiom, (! [A:$tType]: (((zero @ A) => (! [As:(list @ A)]: ((((poly2 @ A) @ (((append @ A) @ As) @ (((cons @ A) @ (zero_zero @ A)) @ (nil @ A)))) = ((poly2 @ A) @ As)))))))).
% 2.81/1.53 thf(fact_36_Poly_Osimps_I2_J, axiom, (! [A:$tType]: (((zero @ A) => (! [A2:A,As:(list @ A)]: ((((poly2 @ A) @ (((cons @ A) @ A2) @ As)) = (((pCons @ A) @ A2) @ ((poly2 @ A) @ As))))))))).
% 2.81/1.53 thf(fact_37_Poly_Osimps_I1_J, axiom, (! [A:$tType]: (((zero @ A) => (((poly2 @ A) @ (nil @ A)) = (zero_zero @ (poly @ A))))))).
% 2.81/1.53 thf(fact_38_psums_Osimps_I2_J, axiom, (! [A:$tType]: (((plus @ A) => (! [X:A]: ((((descar1668888542_psums @ A) @ (((cons @ A) @ X) @ (nil @ A))) = (((cons @ A) @ X) @ (nil @ A))))))))).
% 2.81/1.53 thf(fact_39_psums_Osimps_I1_J, axiom, (! [A:$tType]: (((plus @ A) => (((descar1668888542_psums @ A) @ (nil @ A)) = (nil @ A)))))).
% 2.81/1.53 thf(fact_40_pCons__one, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => ((((pCons @ A) @ (one_one @ A)) @ (zero_zero @ (poly @ A))) = (one_one @ (poly @ A))))))).
% 2.81/1.53 thf(fact_41_pCons__cases, axiom, (! [A:$tType]: (((zero @ A) => (! [P2:(poly @ A)]: ((~ ((! [A3:A,Q3:(poly @ A)]: ((P2 != (((pCons @ A) @ A3) @ Q3)))))))))))).
% 2.81/1.53 thf(fact_42_is__zero__null, axiom, (! [A:$tType]: (((zero @ A) => ((is_zero @ A) = (^ [P:(poly @ A)]: ((P = (zero_zero @ (poly @ A)))))))))).
% 2.81/1.53 thf(fact_43_pCons__induct, axiom, (! [A:$tType]: (((zero @ A) => (! [P3:((poly @ A) > $o),P2:(poly @ A)]: (((P3 @ (zero_zero @ (poly @ A))) => ((! [A3:A,P4:(poly @ A)]: ((((A3 != (zero_zero @ A)) | (P4 != (zero_zero @ (poly @ A)))) => ((P3 @ P4) => (P3 @ (((pCons @ A) @ A3) @ P4)))))) => (P3 @ P2))))))))).
% 2.81/1.53 thf(fact_44_pderiv_Ocases, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) & (semiri1193490041visors @ A)) => (! [X:(poly @ A)]: ((~ ((! [A3:A,P4:(poly @ A)]: ((X != (((pCons @ A) @ A3) @ P4)))))))))))).
% 2.81/1.53 thf(fact_45_ext, axiom, (! [B2:$tType,A:$tType,F2:(A > B2),G:(A > B2)]: (((! [X2:A]: (((F2 @ X2) = (G @ X2)))) => (F2 = G))))).
% 2.81/1.53 thf(fact_46_poly__induct2, axiom, (! [A:$tType,B2:$tType]: ((((zero @ B2) & (zero @ A)) => (! [P3:((poly @ A) > ((poly @ B2) > $o)),P2:(poly @ A),Q2:(poly @ B2)]: ((((P3 @ (zero_zero @ (poly @ A))) @ (zero_zero @ (poly @ B2))) => ((! [A3:A,P4:(poly @ A),B3:B2,Q3:(poly @ B2)]: ((((P3 @ P4) @ Q3) => ((P3 @ (((pCons @ A) @ A3) @ P4)) @ (((pCons @ B2) @ B3) @ Q3))))) => ((P3 @ P2) @ Q2))))))))).
% 2.81/1.53 thf(fact_47_pderiv_Oinduct, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) & (semiri1193490041visors @ A)) => (! [P3:((poly @ A) > $o),A0:(poly @ A)]: (((! [A3:A,P4:(poly @ A)]: ((((P4 != (zero_zero @ (poly @ A))) => (P3 @ P4)) => (P3 @ (((pCons @ A) @ A3) @ P4))))) => (P3 @ A0)))))))).
% 2.81/1.53 thf(fact_48_mult__poly__0__left, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [Q2:(poly @ A)]: (((((times_times @ (poly @ A)) @ (zero_zero @ (poly @ A))) @ Q2) = (zero_zero @ (poly @ A))))))))).
% 2.81/1.53 thf(fact_49_mult__poly__0__right, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [P2:(poly @ A)]: (((((times_times @ (poly @ A)) @ P2) @ (zero_zero @ (poly @ A))) = (zero_zero @ (poly @ A))))))))).
% 2.81/1.53 thf(fact_50_plus__coeffs_Oinduct, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [P3:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [Xs2:(list @ A)]: (((P3 @ Xs2) @ (nil @ A)))) => ((! [V:A,Va:(list @ A)]: (((P3 @ (nil @ A)) @ (((cons @ A) @ V) @ Va)))) => ((! [X2:A,Xs2:(list @ A),Y2:A,Ys:(list @ A)]: ((((P3 @ Xs2) @ Ys) => ((P3 @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys))))) => ((P3 @ A0) @ A1)))))))))).
% 2.81/1.53 thf(fact_51_not__0__coeffs__not__Nil, axiom, (! [A:$tType]: (((zero @ A) => (! [P2:(poly @ A)]: (((P2 != (zero_zero @ (poly @ A))) => (((coeffs @ A) @ P2) != (nil @ A))))))))).
% 2.81/1.53 thf(fact_52_minus__poly__rev__list_Oinduct, axiom, (! [A:$tType]: (((group_add @ A) => (! [P3:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X2:A,Xs2:(list @ A),Y2:A,Ys:(list @ A)]: ((((P3 @ Xs2) @ Ys) => ((P3 @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys))))) => ((! [Xs2:(list @ A)]: (((P3 @ Xs2) @ (nil @ A)))) => ((! [Y2:A,Ys:(list @ A)]: (((P3 @ (nil @ A)) @ (((cons @ A) @ Y2) @ Ys)))) => ((P3 @ A0) @ A1)))))))))).
% 2.81/1.53 thf(fact_53_synthetic__div__unique__lemma, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [C:A,P2:(poly @ A),A2:A]: ((((((smult @ A) @ C) @ P2) = (((pCons @ A) @ A2) @ P2)) => (P2 = (zero_zero @ (poly @ A)))))))))).
% 2.81/1.53 thf(fact_54_psums_Ocases, axiom, (! [A:$tType]: (((plus @ A) => (! [X:(list @ A)]: (((X != (nil @ A)) => ((! [X2:A]: ((X != (((cons @ A) @ X2) @ (nil @ A))))) => (~ ((! [X2:A,Y2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Xs2))))))))))))))).
% 2.81/1.53 thf(fact_55_reduce__root__pCons, axiom, (! [A:$tType]: (((comm_semiring_0 @ A) => (! [A2:A,C:A,P2:(poly @ A)]: (((((descar316357986e_root @ A) @ A2) @ (((pCons @ A) @ C) @ P2)) = (((pCons @ A) @ C) @ (((smult @ A) @ A2) @ (((descar316357986e_root @ A) @ A2) @ P2)))))))))).
% 2.81/1.53 thf(fact_56_reduce__root__nonzero, axiom, (! [A:$tType]: (((idom @ A) => (! [A2:A,P2:(poly @ A)]: (((A2 != (zero_zero @ A)) => ((P2 != (zero_zero @ (poly @ A))) => ((((descar316357986e_root @ A) @ A2) @ P2) != (zero_zero @ (poly @ A))))))))))).
% 2.81/1.53 thf(fact_57_sign__changes__Cons__Cons__same, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y3:A,Xs:(list @ A)]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ X) @ Y3)) => (((descar149487500hanges @ A) @ (((cons @ A) @ X) @ (((cons @ A) @ Y3) @ Xs))) = ((descar149487500hanges @ A) @ (((cons @ A) @ Y3) @ Xs)))))))))).
% 2.81/1.53 thf(fact_58_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys2:(list @ A),Y3:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys2) @ (((cons @ A) @ Y3) @ (nil @ A)))) = ((Xs = Ys2) & (X = Y3)))))).
% 2.81/1.53 thf(fact_59_mult__minus1, axiom, (! [A:$tType]: (((ring_1 @ A) => (! [Z2:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ Z2) = ((uminus_uminus @ A) @ Z2)))))))).
% 2.81/1.53 thf(fact_60_mult__minus1__right, axiom, (! [A:$tType]: (((ring_1 @ A) => (! [Z2:A]: (((((times_times @ A) @ Z2) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ Z2)))))))).
% 2.81/1.53 thf(fact_61_less__neg__neg, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less @ A) @ A2) @ ((uminus_uminus @ A) @ A2)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_62_neg__less__pos, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A2)) @ A2) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.81/1.53 thf(fact_63_neg__0__less__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((uminus_uminus @ A) @ A2)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_64_neg__less__0__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A2)) @ (zero_zero @ A)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 2.81/1.53 thf(fact_65_mult__cancel__left1, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C:A,B:A]: (((C = (((times_times @ A) @ C) @ B)) = ((C = (zero_zero @ A)) | (B = (one_one @ A)))))))))).
% 2.81/1.53 thf(fact_66_mult__cancel__left2, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C:A,A2:A]: ((((((times_times @ A) @ C) @ A2) = C) = ((C = (zero_zero @ A)) | (A2 = (one_one @ A)))))))))).
% 2.81/1.53 thf(fact_67_mult__cancel__right1, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [C:A,B:A]: (((C = (((times_times @ A) @ B) @ C)) = ((C = (zero_zero @ A)) | (B = (one_one @ A)))))))))).
% 2.81/1.53 thf(fact_68_mult__cancel__right2, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [A2:A,C:A]: ((((((times_times @ A) @ A2) @ C) = C) = ((C = (zero_zero @ A)) | (A2 = (one_one @ A)))))))))).
% 2.81/1.53 thf(fact_69_neg__equal__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A]: (((((uminus_uminus @ A) @ A2) = ((uminus_uminus @ A) @ B)) = (A2 = B)))))))).
% 2.81/1.53 thf(fact_70_add_Oinverse__inverse, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A2)) = A2))))))).
% 2.81/1.53 thf(fact_71_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.81/1.53 thf(fact_72_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Xs) @ Zs)) = (Ys2 = Zs))))).
% 2.81/1.53 thf(fact_73_append__same__eq, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys2) @ Xs) = (((append @ A) @ Zs) @ Xs)) = (Ys2 = Zs))))).
% 2.81/1.53 thf(fact_74_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys2)) @ Zs) = (((append @ A) @ Xs) @ (((append @ A) @ Ys2) @ Zs)))))).
% 2.81/1.53 thf(fact_75_append_Oassoc, axiom, (! [A:$tType,A2:(list @ A),B:(list @ A),C:(list @ A)]: (((((append @ A) @ (((append @ A) @ A2) @ B)) @ C) = (((append @ A) @ A2) @ (((append @ A) @ B) @ C)))))).
% 2.81/1.53 thf(fact_76_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_77_mult__cancel__right, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [A2:A,C:A,B:A]: ((((((times_times @ A) @ A2) @ C) = (((times_times @ A) @ B) @ C)) = ((C = (zero_zero @ A)) | (A2 = B))))))))).
% 2.81/1.53 thf(fact_78_mult__cancel__left, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B:A]: ((((((times_times @ A) @ C) @ A2) = (((times_times @ A) @ C) @ B)) = ((C = (zero_zero @ A)) | (A2 = B))))))))).
% 2.81/1.53 thf(fact_79_mult__eq__0__iff, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B:A]: ((((((times_times @ A) @ A2) @ B) = (zero_zero @ A)) = ((A2 = (zero_zero @ A)) | (B = (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_80_mult__zero__right, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 2.81/1.53 thf(fact_81_mult__zero__left, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A]: (((((times_times @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.81/1.53 thf(fact_82_neg__equal__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((uminus_uminus @ A) @ A2) = A2) = (A2 = (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_83_equal__neg__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((A2 = ((uminus_uminus @ A) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_84_neg__equal__0__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((uminus_uminus @ A) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_85_neg__0__equal__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: ((((zero_zero @ A) = ((uminus_uminus @ A) @ A2)) = ((zero_zero @ A) = A2)))))))).
% 2.81/1.53 thf(fact_86_add_Oinverse__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (((uminus_uminus @ A) @ (zero_zero @ A)) = (zero_zero @ A)))))).
% 2.81/1.53 thf(fact_87_mult_Oright__neutral, axiom, (! [A:$tType]: (((monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 2.81/1.53 thf(fact_88_mult_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 2.81/1.53 thf(fact_89_neg__less__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B:A,A2:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ B)) @ ((uminus_uminus @ A) @ A2)) = (((ord_less @ A) @ A2) @ B)))))))).
% 2.81/1.53 thf(fact_90_mult__minus__right, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,B:A]: (((((times_times @ A) @ A2) @ ((uminus_uminus @ A) @ B)) = ((uminus_uminus @ A) @ (((times_times @ A) @ A2) @ B))))))))).
% 2.81/1.53 thf(fact_91_minus__mult__minus, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,B:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A2)) @ ((uminus_uminus @ A) @ B)) = (((times_times @ A) @ A2) @ B)))))))).
% 2.81/1.53 thf(fact_92_mult__minus__left, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,B:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A2)) @ B) = ((uminus_uminus @ A) @ (((times_times @ A) @ A2) @ B))))))))).
% 2.81/1.53 thf(fact_93_append_Oright__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ A2) @ (nil @ A)) = A2)))).
% 2.81/1.53 thf(fact_94_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.81/1.53 thf(fact_95_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys2)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.81/1.53 thf(fact_96_self__append__conv2, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 = (((append @ A) @ Xs) @ Ys2)) = (Xs = (nil @ A)))))).
% 2.81/1.53 thf(fact_97_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Ys2) = (Xs = (nil @ A)))))).
% 2.81/1.53 thf(fact_98_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys2)) = (Ys2 = (nil @ A)))))).
% 2.81/1.53 thf(fact_99_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Xs) = (Ys2 = (nil @ A)))))).
% 2.81/1.53 thf(fact_100_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.81/1.53 thf(fact_101_smult__minus__right, axiom, (! [A:$tType]: (((comm_ring @ A) => (! [A2:A,P2:(poly @ A)]: (((((smult @ A) @ A2) @ ((uminus_uminus @ (poly @ A)) @ P2)) = ((uminus_uminus @ (poly @ A)) @ (((smult @ A) @ A2) @ P2))))))))).
% 2.81/1.53 thf(fact_102_smult__one, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => (! [C:A]: (((((smult @ A) @ C) @ (one_one @ (poly @ A))) = (((pCons @ A) @ C) @ (zero_zero @ (poly @ A)))))))))).
% 2.81/1.53 thf(fact_103_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_104_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y3:A]: (((X != Y3) => ((~ ((((ord_less @ A) @ X) @ Y3))) => (((ord_less @ A) @ Y3) @ X))))))))).
% 2.81/1.53 thf(fact_105_mult_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [B:A,A2:A,C:A]: (((((times_times @ A) @ B) @ (((times_times @ A) @ A2) @ C)) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B) @ C))))))))).
% 2.81/1.53 thf(fact_106_mult_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => ((times_times @ A) = (^ [A4:A,B4:A]: ((((times_times @ A) @ B4) @ A4)))))))).
% 2.81/1.53 thf(fact_107_mult_Oassoc, axiom, (! [A:$tType]: (((semigroup_mult @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B) @ C))))))))).
% 2.81/1.53 thf(fact_108_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B) @ C))))))))).
% 2.81/1.53 thf(fact_109_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 2.81/1.53 thf(fact_110_minus__equation__iff, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A]: (((((uminus_uminus @ A) @ A2) = B) = (((uminus_uminus @ A) @ B) = A2)))))))).
% 2.81/1.53 thf(fact_111_equation__minus__iff, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A]: (((A2 = ((uminus_uminus @ A) @ B)) = (B = ((uminus_uminus @ A) @ A2))))))))).
% 2.81/1.53 thf(fact_112_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.81/1.53 thf(fact_113_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs) @ Us)) & ((((append @ A) @ Us) @ Ys2) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs) & (Ys2 = (((append @ A) @ Us) @ Ts)))))))))).
% 2.81/1.53 thf(fact_114_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs:(list @ A),Ys2:(list @ A),Us2:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs) => ((Ys2 = (((append @ A) @ Xs1) @ Us2)) => ((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs) @ Us2))))))).
% 2.81/1.53 thf(fact_115_sign__changes__two, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y3:A]: ((((((((ord_less @ A) @ (zero_zero @ A)) @ X) & (((ord_less @ A) @ Y3) @ (zero_zero @ A))) | ((((ord_less @ A) @ X) @ (zero_zero @ A)) & (((ord_less @ A) @ (zero_zero @ A)) @ Y3))) => (((descar149487500hanges @ A) @ (((cons @ A) @ X) @ (((cons @ A) @ Y3) @ (nil @ A)))) = (one_one @ nat))) & ((~ ((((((ord_less @ A) @ (zero_zero @ A)) @ X) & (((ord_less @ A) @ Y3) @ (zero_zero @ A))) | ((((ord_less @ A) @ X) @ (zero_zero @ A)) & (((ord_less @ A) @ (zero_zero @ A)) @ Y3))))) => (((descar149487500hanges @ A) @ (((cons @ A) @ X) @ (((cons @ A) @ Y3) @ (nil @ A)))) = (zero_zero @ nat)))))))))).
% 2.81/1.53 thf(fact_116_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_117_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.81/1.53 thf(fact_118_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_119_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.81/1.53 thf(fact_120_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 2.81/1.53 thf(fact_121_mult__right__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B:A]: (((C != (zero_zero @ A)) => (((((times_times @ A) @ A2) @ C) = (((times_times @ A) @ B) @ C)) = (A2 = B))))))))).
% 2.81/1.53 thf(fact_122_mult__left__cancel, axiom, (! [A:$tType]: (((semiri1923998003cancel @ A) => (! [C:A,A2:A,B:A]: (((C != (zero_zero @ A)) => (((((times_times @ A) @ C) @ A2) = (((times_times @ A) @ C) @ B)) = (A2 = B))))))))).
% 2.81/1.53 thf(fact_123_no__zero__divisors, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B:A]: (((A2 != (zero_zero @ A)) => ((B != (zero_zero @ A)) => ((((times_times @ A) @ A2) @ B) != (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_124_divisors__zero, axiom, (! [A:$tType]: (((semiri1193490041visors @ A) => (! [A2:A,B:A]: ((((((times_times @ A) @ A2) @ B) = (zero_zero @ A)) => ((A2 = (zero_zero @ A)) | (B = (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_125_mult__not__zero, axiom, (! [A:$tType]: (((mult_zero @ A) => (! [A2:A,B:A]: ((((((times_times @ A) @ A2) @ B) != (zero_zero @ A)) => ((A2 != (zero_zero @ A)) & (B != (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_126_zero__neq__one, axiom, (! [A:$tType]: (((zero_neq_one @ A) => ((zero_zero @ A) != (one_one @ A)))))).
% 2.81/1.53 thf(fact_127_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.81/1.53 thf(fact_128_mult_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 2.81/1.53 thf(fact_129_comm__monoid__mult__class_Omult__1, axiom, (! [A:$tType]: (((comm_monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 2.81/1.53 thf(fact_130_minus__less__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A2)) @ B) = (((ord_less @ A) @ ((uminus_uminus @ A) @ B)) @ A2)))))))).
% 2.81/1.53 thf(fact_131_less__minus__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ ((uminus_uminus @ A) @ B)) = (((ord_less @ A) @ B) @ ((uminus_uminus @ A) @ A2))))))))).
% 2.81/1.53 thf(fact_132_minus__mult__commute, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,B:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A2)) @ B) = (((times_times @ A) @ A2) @ ((uminus_uminus @ A) @ B))))))))).
% 2.81/1.53 thf(fact_133_square__eq__iff, axiom, (! [A:$tType]: (((idom @ A) => (! [A2:A,B:A]: ((((((times_times @ A) @ A2) @ A2) = (((times_times @ A) @ B) @ B)) = ((A2 = B) | (A2 = ((uminus_uminus @ A) @ B)))))))))).
% 2.81/1.53 thf(fact_134_one__neq__neg__one, axiom, (! [A:$tType]: (((ring_char_0 @ A) => ((one_one @ A) != ((uminus_uminus @ A) @ (one_one @ A))))))).
% 2.81/1.53 thf(fact_135_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P3:((list @ A) > $o),A0:(list @ A)]: (((P3 @ (nil @ A)) => ((! [X2:A,Ys:(list @ A)]: (((P3 @ Ys) => (P3 @ (((cons @ A) @ X2) @ Ys))))) => (P3 @ A0))))))))).
% 2.81/1.53 thf(fact_136_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(list @ A)]: (((X != (nil @ A)) => (~ ((! [X2:A,Ys:(list @ A)]: ((X != (((cons @ A) @ X2) @ Ys))))))))))))).
% 2.81/1.53 thf(fact_137_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B2:$tType,P3:((A > B2) > ((list @ A) > ((list @ B2) > $o))),A0:(A > B2),A1:(list @ A),A22:(list @ B2)]: (((! [F3:(A > B2),X_1:(list @ B2)]: ((((P3 @ F3) @ (nil @ A)) @ X_1))) => ((! [F3:(A > B2),A3:A,As2:(list @ A),Bs:(list @ B2)]: (((((P3 @ F3) @ As2) @ (((cons @ B2) @ (F3 @ A3)) @ Bs)) => (((P3 @ F3) @ (((cons @ A) @ A3) @ As2)) @ Bs)))) => (((P3 @ A0) @ A1) @ A22)))))).
% 2.81/1.53 thf(fact_138_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P3:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P3 @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P3 @ Xs2) => (P3 @ (((cons @ A) @ X2) @ Xs2)))))) => (P3 @ Xs))))))).
% 2.81/1.53 thf(fact_139_successively_Oinduct, axiom, (! [A:$tType,P3:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P5:(A > (A > $o))]: (((P3 @ P5) @ (nil @ A)))) => ((! [P5:(A > (A > $o)),X2:A]: (((P3 @ P5) @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [P5:(A > (A > $o)),X2:A,Y2:A,Xs2:(list @ A)]: ((((P3 @ P5) @ (((cons @ A) @ Y2) @ Xs2)) => ((P3 @ P5) @ (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Xs2)))))) => ((P3 @ A0) @ A1))))))).
% 2.81/1.53 thf(fact_140_arg__min__list_Oinduct, axiom, (! [B2:$tType,A:$tType]: (((linorder @ B2) => (! [P3:((A > B2) > ((list @ A) > $o)),A0:(A > B2),A1:(list @ A)]: (((! [F3:(A > B2),X2:A]: (((P3 @ F3) @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [F3:(A > B2),X2:A,Y2:A,Zs2:(list @ A)]: ((((P3 @ F3) @ (((cons @ A) @ Y2) @ Zs2)) => ((P3 @ F3) @ (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Zs2)))))) => ((! [A3:(A > B2)]: (((P3 @ A3) @ (nil @ A)))) => ((P3 @ A0) @ A1)))))))))).
% 2.81/1.53 thf(fact_141_remdups__adj_Oinduct, axiom, (! [A:$tType,P3:((list @ A) > $o),A0:(list @ A)]: (((P3 @ (nil @ A)) => ((! [X2:A]: ((P3 @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Y2:A,Xs2:(list @ A)]: ((((X2 = Y2) => (P3 @ (((cons @ A) @ X2) @ Xs2))) => (((X2 != Y2) => (P3 @ (((cons @ A) @ Y2) @ Xs2))) => (P3 @ (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Xs2))))))) => (P3 @ A0))))))).
% 2.81/1.53 thf(fact_142_sorted__wrt_Oinduct, axiom, (! [A:$tType,P3:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P5:(A > (A > $o))]: (((P3 @ P5) @ (nil @ A)))) => ((! [P5:(A > (A > $o)),X2:A,Ys:(list @ A)]: ((((P3 @ P5) @ Ys) => ((P3 @ P5) @ (((cons @ A) @ X2) @ Ys))))) => ((P3 @ A0) @ A1)))))).
% 2.81/1.53 thf(fact_143_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X2:A]: ((X != (((cons @ A) @ X2) @ (nil @ A))))) => (~ ((! [X2:A,Y2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Xs2)))))))))))).
% 2.81/1.53 thf(fact_144_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X2:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X2) @ Xs2)) @ Xss))))))))))).
% 2.81/1.53 thf(fact_145_shuffles_Oinduct, axiom, (! [A:$tType,P3:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P3 @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P3 @ Xs2) @ (nil @ A)))) => ((! [X2:A,Xs2:(list @ A),Y2:A,Ys:(list @ A)]: ((((P3 @ Xs2) @ (((cons @ A) @ Y2) @ Ys)) => (((P3 @ (((cons @ A) @ X2) @ Xs2)) @ Ys) => ((P3 @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys)))))) => ((P3 @ A0) @ A1))))))).
% 2.81/1.53 thf(fact_146_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P3:((list @ A) > $o),A0:(list @ A)]: (((! [X2:A,Xs2:(list @ A)]: (((! [X212:A,X222:(list @ A)]: (((Xs2 = (((cons @ A) @ X212) @ X222)) => (P3 @ Xs2)))) => (P3 @ (((cons @ A) @ X2) @ Xs2))))) => ((P3 @ (nil @ A)) => (P3 @ A0))))))))).
% 2.81/1.53 thf(fact_147_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X:(list @ A)]: (((! [X2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ Xs2)))) => (X = (nil @ A))))))))).
% 2.81/1.53 thf(fact_148_induct__list012, axiom, (! [A:$tType,P3:((list @ A) > $o),Xs:(list @ A)]: (((P3 @ (nil @ A)) => ((! [X2:A]: ((P3 @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Y2:A,Zs2:(list @ A)]: (((P3 @ Zs2) => ((P3 @ (((cons @ A) @ Y2) @ Zs2)) => (P3 @ (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Zs2))))))) => (P3 @ Xs))))))).
% 2.81/1.53 thf(fact_149_splice_Oinduct, axiom, (! [A:$tType,P3:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P3 @ (nil @ A)) @ X_1))) => ((! [X2:A,Xs2:(list @ A),Ys:(list @ A)]: ((((P3 @ Ys) @ Xs2) => ((P3 @ (((cons @ A) @ X2) @ Xs2)) @ Ys)))) => ((P3 @ A0) @ A1)))))).
% 2.81/1.53 thf(fact_150_list__induct2_H, axiom, (! [A:$tType,B2:$tType,P3:((list @ A) > ((list @ B2) > $o)),Xs:(list @ A),Ys2:(list @ B2)]: ((((P3 @ (nil @ A)) @ (nil @ B2)) => ((! [X2:A,Xs2:(list @ A)]: (((P3 @ (((cons @ A) @ X2) @ Xs2)) @ (nil @ B2)))) => ((! [Y2:B2,Ys:(list @ B2)]: (((P3 @ (nil @ A)) @ (((cons @ B2) @ Y2) @ Ys)))) => ((! [X2:A,Xs2:(list @ A),Y2:B2,Ys:(list @ B2)]: ((((P3 @ Xs2) @ Ys) => ((P3 @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B2) @ Y2) @ Ys))))) => ((P3 @ Xs) @ Ys2)))))))).
% 2.81/1.53 thf(fact_151_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y4:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y4) @ Ys3)))))))).
% 2.81/1.53 thf(fact_152_list_Oinducts, axiom, (! [A:$tType,P3:((list @ A) > $o),List:(list @ A)]: (((P3 @ (nil @ A)) => ((! [X1:A,X23:(list @ A)]: (((P3 @ X23) => (P3 @ (((cons @ A) @ X1) @ X23))))) => (P3 @ List)))))).
% 2.81/1.53 thf(fact_153_list_Oexhaust, axiom, (! [A:$tType,Y3:(list @ A)]: (((Y3 != (nil @ A)) => (~ ((! [X213:A,X223:(list @ A)]: ((Y3 != (((cons @ A) @ X213) @ X223)))))))))).
% 2.81/1.53 thf(fact_154_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.81/1.53 thf(fact_155_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.81/1.53 thf(fact_156_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys2:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys2) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys2)))))).
% 2.81/1.53 thf(fact_157_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys2:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys2) => ((Xs = (((append @ A) @ Xs1) @ Zs)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys2) @ Zs))))))).
% 2.81/1.53 thf(fact_158_append_Oleft__neutral, axiom, (! [A:$tType,A2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A2) = A2)))).
% 2.81/1.53 thf(fact_159_append__Nil, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.81/1.53 thf(fact_160_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = Ys2) => (Xs = (((append @ A) @ (nil @ A)) @ Ys2)))))).
% 2.81/1.53 thf(fact_161_null__rec_I1_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((~ (((null @ A) @ (((cons @ A) @ X) @ Xs))))))).
% 2.81/1.53 thf(fact_162_eq__Nil__null, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs = (nil @ A)) = ((null @ A) @ Xs))))).
% 2.81/1.53 thf(fact_163_null__rec_I2_J, axiom, (! [B2:$tType]: (((null @ B2) @ (nil @ B2))))).
% 2.81/1.53 thf(fact_164_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom, (! [A:$tType]: (((linord893533164strict @ A) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B)))))))))).
% 2.81/1.53 thf(fact_165_mult__less__cancel__right__disj, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,C:A,B:A]: (((((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B) @ C)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) & (((ord_less @ A) @ A2) @ B)) | ((((ord_less @ A) @ C) @ (zero_zero @ A)) & (((ord_less @ A) @ B) @ A2)))))))))).
% 2.81/1.53 thf(fact_166_mult__strict__right__mono, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B) @ C)))))))))).
% 2.81/1.53 thf(fact_167_mult__strict__right__mono__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [B:A,A2:A,C:A]: (((((ord_less @ A) @ B) @ A2) => ((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B) @ C)))))))))).
% 2.81/1.53 thf(fact_168_mult__less__cancel__left__disj, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B)) = (((((ord_less @ A) @ (zero_zero @ A)) @ C) & (((ord_less @ A) @ A2) @ B)) | ((((ord_less @ A) @ C) @ (zero_zero @ A)) & (((ord_less @ A) @ B) @ A2)))))))))).
% 2.81/1.53 thf(fact_169_mult__strict__left__mono, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ (zero_zero @ A)) @ C) => (((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B)))))))))).
% 2.81/1.53 thf(fact_170_mult__strict__left__mono__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [B:A,A2:A,C:A]: (((((ord_less @ A) @ B) @ A2) => ((((ord_less @ A) @ C) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B)))))))))).
% 2.81/1.53 thf(fact_171_mult__less__cancel__left__pos, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ C) => ((((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B)) = (((ord_less @ A) @ A2) @ B))))))))).
% 2.81/1.53 thf(fact_172_mult__less__cancel__left__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ C) @ (zero_zero @ A)) => ((((ord_less @ A) @ (((times_times @ A) @ C) @ A2)) @ (((times_times @ A) @ C) @ B)) = (((ord_less @ A) @ B) @ A2))))))))).
% 2.81/1.53 thf(fact_173_zero__less__mult__pos2, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [B:A,A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ B) @ A2)) => ((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((ord_less @ A) @ (zero_zero @ A)) @ B))))))))).
% 2.81/1.53 thf(fact_174_zero__less__mult__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B)) => ((((ord_less @ A) @ (zero_zero @ A)) @ A2) => (((ord_less @ A) @ (zero_zero @ A)) @ B))))))))).
% 2.81/1.53 thf(fact_175_zero__less__mult__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A2) & (((ord_less @ A) @ (zero_zero @ A)) @ B)) | ((((ord_less @ A) @ A2) @ (zero_zero @ A)) & (((ord_less @ A) @ B) @ (zero_zero @ A))))))))))).
% 2.81/1.53 thf(fact_176_mult__pos__neg2, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ B) @ A2)) @ (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_177_mult__pos__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ B) => (((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B)))))))))).
% 2.81/1.53 thf(fact_178_mult__pos__neg, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B) @ (zero_zero @ A)) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ B)) @ (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_179_mult__neg__pos, axiom, (! [A:$tType]: (((linord20386208strict @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ (zero_zero @ A)) @ B) => (((ord_less @ A) @ (((times_times @ A) @ A2) @ B)) @ (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_180_mult__less__0__iff, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ (((times_times @ A) @ A2) @ B)) @ (zero_zero @ A)) = (((((ord_less @ A) @ (zero_zero @ A)) @ A2) & (((ord_less @ A) @ B) @ (zero_zero @ A))) | ((((ord_less @ A) @ A2) @ (zero_zero @ A)) & (((ord_less @ A) @ (zero_zero @ A)) @ B)))))))))).
% 2.81/1.53 thf(fact_181_not__square__less__zero, axiom, (! [A:$tType]: (((linordered_ring @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ (((times_times @ A) @ A2) @ A2)) @ (zero_zero @ A)))))))))).
% 2.81/1.53 thf(fact_182_mult__neg__neg, axiom, (! [A:$tType]: (((linord581940658strict @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ B) @ (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ (((times_times @ A) @ A2) @ B)))))))))).
% 2.81/1.53 thf(fact_183_not__one__less__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 2.81/1.53 thf(fact_184_zero__less__one, axiom, (! [A:$tType]: (((zero_less_one @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.81/1.53 thf(fact_185_less__numeral__extra_I1_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.81/1.53 thf(fact_186_less__1__mult, axiom, (! [A:$tType]: (((linordered_semidom @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ (one_one @ A)) @ M) => ((((ord_less @ A) @ (one_one @ A)) @ N) => (((ord_less @ A) @ (one_one @ A)) @ (((times_times @ A) @ M) @ N)))))))))).
% 2.81/1.53 thf(fact_187_zero__neq__neg__one, axiom, (! [A:$tType]: (((ring_char_0 @ A) => ((zero_zero @ A) != ((uminus_uminus @ A) @ (one_one @ A))))))).
% 2.81/1.53 thf(fact_188_less__minus__one__simps_I2_J, axiom, (! [A:$tType]: (((linordered_idom @ A) => (((ord_less @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ (one_one @ A)))))).
% 2.81/1.53 thf(fact_189_less__minus__one__simps_I4_J, axiom, (! [A:$tType]: (((linordered_idom @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ ((uminus_uminus @ A) @ (one_one @ A))))))))).
% 2.81/1.53 thf(fact_190_square__eq__1__iff, axiom, (! [A:$tType]: (((ring_11004092258visors @ A) => (! [X:A]: ((((((times_times @ A) @ X) @ X) = (one_one @ A)) = ((X = (one_one @ A)) | (X = ((uminus_uminus @ A) @ (one_one @ A))))))))))).
% 2.81/1.53 thf(fact_191_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P3:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P3 @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P3 @ Xs2) => (P3 @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))))))) => (P3 @ Xs))))))).
% 2.81/1.53 thf(fact_192_append__eq__Cons__conv, axiom, (! [A:$tType,Ys2:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys2) @ Zs) = (((cons @ A) @ X) @ Xs)) = (((Ys2 = (nil @ A)) & (Zs = (((cons @ A) @ X) @ Xs))) | (? [Ys4:(list @ A)]: (((Ys2 = (((cons @ A) @ X) @ Ys4)) & ((((append @ A) @ Ys4) @ Zs) = Xs))))))))).
% 2.81/1.53 thf(fact_193_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys2) @ Zs)) = (((Ys2 = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs)) | (? [Ys4:(list @ A)]: ((((((cons @ A) @ X) @ Ys4) = Ys2) & (Xs = (((append @ A) @ Ys4) @ Zs)))))))))).
% 2.81/1.53 thf(fact_194_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys:(list @ A),Y2:A]: ((Xs != (((append @ A) @ Ys) @ (((cons @ A) @ Y2) @ (nil @ A)))))))))))).
% 2.81/1.53 thf(fact_195_rev__induct, axiom, (! [A:$tType,P3:((list @ A) > $o),Xs:(list @ A)]: (((P3 @ (nil @ A)) => ((! [X2:A,Xs2:(list @ A)]: (((P3 @ Xs2) => (P3 @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A))))))) => (P3 @ Xs)))))).
% 2.81/1.53 thf(fact_196_less__minus__one__simps_I1_J, axiom, (! [A:$tType]: (((linordered_idom @ A) => (((ord_less @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ (zero_zero @ A)))))).
% 2.81/1.53 thf(fact_197_less__minus__one__simps_I3_J, axiom, (! [A:$tType]: (((linordered_idom @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ ((uminus_uminus @ A) @ (one_one @ A))))))))).
% 2.81/1.53 thf(fact_198_poly__cutoff__1, axiom, (! [A:$tType]: (((comm_semiring_1 @ A) => (! [N:nat]: ((((N = (zero_zero @ nat)) => ((((poly_cutoff @ A) @ N) @ (one_one @ (poly @ A))) = (zero_zero @ (poly @ A)))) & ((N != (zero_zero @ nat)) => ((((poly_cutoff @ A) @ N) @ (one_one @ (poly @ A))) = (one_one @ (poly @ A))))))))))).
% 2.81/1.53 thf(fact_199_mult__less__iff1, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:A,X:A,Y3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ Z2) => ((((ord_less @ A) @ (((times_times @ A) @ X) @ Z2)) @ (((times_times @ A) @ Y3) @ Z2)) = (((ord_less @ A) @ X) @ Y3))))))))).
% 2.81/1.53 thf(fact_200_dbl__dec__simps_I2_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (((neg_numeral_dbl_dec @ A) @ (zero_zero @ A)) = ((uminus_uminus @ A) @ (one_one @ A))))))).
% 2.81/1.53 thf(fact_201_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)))))).
% 2.81/1.53 thf(fact_202_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)))))).
% 2.81/1.53 thf(fact_203_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)))))).
% 2.81/1.53 thf(fact_204_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))))))).
% 2.81/1.53 thf(fact_205_neq0__conv, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.81/1.53 thf(fact_206_less__nat__zero__code, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.81/1.53 thf(fact_207_bot__nat__0_Onot__eq__extremum, axiom, (! [A2:nat]: (((A2 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A2))))).
% 2.81/1.53 thf(fact_208_mult__is__0, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) | (N = (zero_zero @ nat))))))).
% 2.81/1.53 thf(fact_209_mult__0__right, axiom, (! [M:nat]: (((((times_times @ nat) @ M) @ (zero_zero @ nat)) = (zero_zero @ nat))))).
% 2.81/1.53 thf(fact_210_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))))))).
% 2.81/1.53 thf(fact_211_nat__1__eq__mult__iff, axiom, (! [M:nat,N:nat]: ((((one_one @ nat) = (((times_times @ nat) @ M) @ N)) = ((M = (one_one @ nat)) & (N = (one_one @ nat))))))).
% 2.81/1.53 thf(fact_212_nat__mult__eq__1__iff, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (one_one @ nat)) = ((M = (one_one @ nat)) & (N = (one_one @ nat))))))).
% 2.81/1.53 thf(fact_213_dbl__dec__simps_I3_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (((neg_numeral_dbl_dec @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 2.81/1.53 thf(fact_214_poly__cutoff__0, axiom, (! [A:$tType]: (((zero @ A) => (! [N:nat]: (((((poly_cutoff @ A) @ N) @ (zero_zero @ (poly @ A))) = (zero_zero @ (poly @ A))))))))).
% 2.81/1.53 thf(fact_215_less__one, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (one_one @ nat)) = (N = (zero_zero @ nat)))))).
% 2.81/1.53 thf(fact_216_nat__mult__1, axiom, (! [N:nat]: (((((times_times @ nat) @ (one_one @ nat)) @ N) = N)))).
% 2.81/1.53 thf(fact_217_nat__mult__1__right, axiom, (! [N:nat]: (((((times_times @ nat) @ N) @ (one_one @ nat)) = N)))).
% 2.81/1.53 thf(fact_218_infinite__descent__measure, axiom, (! [A:$tType,P3:(A > $o),V2:(A > nat),X:A]: (((! [X2:A]: (((~ ((P3 @ X2))) => (? [Y5:A]: (((((ord_less @ nat) @ (V2 @ Y5)) @ (V2 @ X2)) & (~ ((P3 @ Y5))))))))) => (P3 @ X))))).
% 2.81/1.53 thf(fact_219_linorder__neqE__nat, axiom, (! [X:nat,Y3:nat]: (((X != Y3) => ((~ ((((ord_less @ nat) @ X) @ Y3))) => (((ord_less @ nat) @ Y3) @ X)))))).
% 2.81/1.53 thf(fact_220_infinite__descent, axiom, (! [P3:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P3 @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P3 @ M2))))))))) => (P3 @ N))))).
% 2.81/1.53 thf(fact_221_nat__less__induct, axiom, (! [P3:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) => (P3 @ M2)))) => (P3 @ N2)))) => (P3 @ N))))).
% 2.81/1.53 thf(fact_222_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.81/1.53 thf(fact_223_less__not__refl3, axiom, (! [S:nat,T:nat]: (((((ord_less @ nat) @ S) @ T) => (S != T))))).
% 2.81/1.53 thf(fact_224_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.81/1.53 thf(fact_225_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.81/1.53 thf(fact_226_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.81/1.53 thf(fact_227_measure__induct, axiom, (! [B2:$tType,A:$tType]: (((wellorder @ B2) => (! [F2:(A > B2),P3:(A > $o),A2:A]: (((! [X2:A]: (((! [Y5:A]: (((((ord_less @ B2) @ (F2 @ Y5)) @ (F2 @ X2)) => (P3 @ Y5)))) => (P3 @ X2)))) => (P3 @ A2)))))))).
% 2.81/1.53 thf(fact_228_measure__induct__rule, axiom, (! [B2:$tType,A:$tType]: (((wellorder @ B2) => (! [F2:(A > B2),P3:(A > $o),A2:A]: (((! [X2:A]: (((! [Y5:A]: (((((ord_less @ B2) @ (F2 @ Y5)) @ (F2 @ X2)) => (P3 @ Y5)))) => (P3 @ X2)))) => (P3 @ A2)))))))).
% 2.81/1.53 thf(fact_229_gr0I, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.81/1.53 thf(fact_230_not__gr0, axiom, (! [N:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N))) = (N = (zero_zero @ nat)))))).
% 2.81/1.53 thf(fact_231_not__less0, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.81/1.53 thf(fact_232_less__zeroE, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.81/1.53 thf(fact_233_gr__implies__not0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (N != (zero_zero @ nat)))))).
% 2.81/1.53 thf(fact_234_infinite__descent0, axiom, (! [P3:(nat > $o),N:nat]: (((P3 @ (zero_zero @ nat)) => ((! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((~ ((P3 @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P3 @ M2)))))))))) => (P3 @ N)))))).
% 2.81/1.53 thf(fact_235_bot__nat__0_Oextremum__strict, axiom, (! [A2:nat]: ((~ ((((ord_less @ nat) @ A2) @ (zero_zero @ nat))))))).
% 2.81/1.53 thf(fact_236_infinite__descent0__measure, axiom, (! [A:$tType,V2:(A > nat),P3:(A > $o),X:A]: (((! [X2:A]: ((((V2 @ X2) = (zero_zero @ nat)) => (P3 @ X2)))) => ((! [X2:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V2 @ X2)) => ((~ ((P3 @ X2))) => (? [Y5:A]: (((((ord_less @ nat) @ (V2 @ Y5)) @ (V2 @ X2)) & (~ ((P3 @ Y5)))))))))) => (P3 @ X)))))).
% 2.81/1.53 thf(fact_237_mult__less__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((ord_less @ nat) @ (((times_times @ nat) @ I) @ K)) @ (((times_times @ nat) @ J) @ K))))))).
% 2.81/1.53 thf(fact_238_mult__less__mono2, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((ord_less @ nat) @ (((times_times @ nat) @ K) @ I)) @ (((times_times @ nat) @ K) @ J))))))).
% 2.81/1.53 thf(fact_239_mult__0, axiom, (! [N:nat]: (((((times_times @ nat) @ (zero_zero @ nat)) @ N) = (zero_zero @ nat))))).
% 2.81/1.53 thf(fact_240_nat__mult__eq__cancel1, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => (((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = (M = N)))))).
% 2.81/1.53 thf(fact_241_nat__mult__less__cancel1, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ K) => ((((ord_less @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)) = (((ord_less @ nat) @ M) @ N)))))).
% 2.81/1.53 thf(fact_242_nat__mult__eq__cancel__disj, axiom, (! [K:nat,M:nat,N:nat]: ((((((times_times @ nat) @ K) @ M) = (((times_times @ nat) @ K) @ N)) = ((K = (zero_zero @ nat)) | (M = N)))))).
% 2.81/1.53 thf(fact_243_mult__eq__self__implies__10, axiom, (! [M:nat,N:nat]: (((M = (((times_times @ nat) @ M) @ N)) => ((N = (one_one @ nat)) | (M = (zero_zero @ nat))))))).
% 2.81/1.53 thf(fact_244_n__lists__Nil, axiom, (! [A:$tType,N:nat]: ((((N = (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))) & ((N != (zero_zero @ nat)) => ((((n_lists @ A) @ N) @ (nil @ A)) = (nil @ (list @ A)))))))).
% 2.81/1.53 thf(fact_245_n__lists_Osimps_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: (((((n_lists @ A) @ (zero_zero @ nat)) @ Xs) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.81/1.53 thf(fact_246_compl__eq__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X:A,Y3:A]: (((((uminus_uminus @ A) @ X) = ((uminus_uminus @ A) @ Y3)) = (X = Y3)))))))).
% 2.81/1.53 thf(fact_247_double__compl, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ X)) = X))))))).
% 2.81/1.53 thf(fact_248_uminus__apply, axiom, (! [B2:$tType,A:$tType]: (((uminus @ B2) => ((uminus_uminus @ (A > B2)) = (^ [A5:(A > B2),X3:A]: (((uminus_uminus @ B2) @ (A5 @ X3))))))))).
% 2.81/1.53 thf(fact_249_fun__Compl__def, axiom, (! [B2:$tType,A:$tType]: (((uminus @ B2) => ((uminus_uminus @ (A > B2)) = (^ [A5:(A > B2),X3:A]: (((uminus_uminus @ B2) @ (A5 @ X3))))))))).
% 2.81/1.53 thf(fact_250_compl__less__swap1, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y3:A,X:A]: (((((ord_less @ A) @ Y3) @ ((uminus_uminus @ A) @ X)) => (((ord_less @ A) @ X) @ ((uminus_uminus @ A) @ Y3))))))))).
% 2.81/1.53 thf(fact_251_compl__less__swap2, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y3:A,X:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ Y3)) @ X) => (((ord_less @ A) @ ((uminus_uminus @ A) @ X)) @ Y3)))))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__ring__1, axiom, (! [A:$tType]: (((linordered_idom @ A) => (comm_ring_1 @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___HOL_Otype, axiom, (! [A:$tType]: (((linordered_idom @ A) => (type @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Oone, axiom, (! [A:$tType]: (((linordered_idom @ A) => (one @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Osgn, axiom, (! [A:$tType]: (((linordered_idom @ A) => (sgn @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Oidom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (idom @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Oring, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ring @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Oplus, axiom, (! [A:$tType]: (((linordered_idom @ A) => (plus @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Ozero, axiom, (! [A:$tType]: (((linordered_idom @ A) => (zero @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Oring__1, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ring_1 @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Ouminus, axiom, (! [A:$tType]: (((linordered_idom @ A) => (uminus @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Orderings_Oord, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ord @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Nat_Oring__char__0, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ring_char_0 @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Num_Oneg__numeral, axiom, (! [A:$tType]: (((linordered_idom @ A) => (neg_numeral @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__ring, axiom, (! [A:$tType]: (((linordered_idom @ A) => (comm_ring @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Omult__zero, axiom, (! [A:$tType]: (((linordered_idom @ A) => (mult_zero @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Ogroup__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (group_add @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Omonoid__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (monoid_add @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Omonoid__mult, axiom, (! [A:$tType]: (((linordered_idom @ A) => (monoid_mult @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Orderings_Olinorder, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linorder @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Oidom__abs__sgn, axiom, (! [A:$tType]: (((linordered_idom @ A) => (idom_abs_sgn @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Ozero__neq__one, axiom, (! [A:$tType]: (((linordered_idom @ A) => (zero_neq_one @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Oab__group__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ab_group_add @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Ozero__less__one, axiom, (! [A:$tType]: (((linordered_idom @ A) => (zero_less_one @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Osemigroup__mult, axiom, (! [A:$tType]: (((linordered_idom @ A) => (semigroup_mult @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__0, axiom, (! [A:$tType]: (((linordered_idom @ A) => (comm_semiring_0 @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__1, axiom, (! [A:$tType]: (((linordered_idom @ A) => (comm_semiring_1 @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__ring, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linordered_ring @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (comm_monoid_add @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__mult, axiom, (! [A:$tType]: (((linordered_idom @ A) => (comm_monoid_mult @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__mult, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ab_semigroup_mult @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__semidom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linordered_semidom @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__group__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ordered_ab_group_add @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__ring__strict, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linord581940658strict @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Oring__1__no__zero__divisors, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ring_11004092258visors @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Groups_Olinordered__ab__group__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linord219039673up_add @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors, axiom, (! [A:$tType]: (((linordered_idom @ A) => (semiri1193490041visors @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__semiring__strict, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linord20386208strict @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__nonzero__semiring, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linord1659791738miring @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__comm__semiring__strict, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linord893533164strict @ A))))).
% 2.81/1.53 thf(subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors__cancel, axiom, (! [A:$tType]: (((linordered_idom @ A) => (semiri1923998003cancel @ A))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring__1, axiom, (! [A6:$tType]: (((comm_ring_1 @ A6) => (comm_ring_1 @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A6:$tType,A7:$tType]: (((boolean_algebra @ A7) => (boolean_algebra @ (A6 > A7)))))).
% 2.81/1.53 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.81/1.53 thf(tcon_fun___Groups_Ouminus, axiom, (! [A6:$tType,A7:$tType]: (((uminus @ A7) => (uminus @ (A6 > A7)))))).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel, axiom, (semiri1923998003cancel @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict, axiom, (linord893533164strict @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Olinordered__semiring__strict, axiom, (linord20386208strict @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors, axiom, (semiri1193490041visors @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, (linordered_semidom @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult, axiom, (ab_semigroup_mult @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult, axiom, (comm_monoid_mult @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1, axiom, (comm_semiring_1 @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0, axiom, (comm_semiring_0 @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Osemigroup__mult, axiom, (semigroup_mult @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Ozero__less__one, axiom, (zero_less_one @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Ozero__neq__one, axiom, (zero_neq_one @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Omonoid__mult, axiom, (monoid_mult @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Omonoid__add, axiom, (monoid_add @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Rings_Omult__zero, axiom, (mult_zero @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Oord_1, axiom, (ord @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Oplus, axiom, (plus @ nat)).
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 2.81/1.53 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_2, axiom, (boolean_algebra @ $o)).
% 2.81/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder_3, axiom, (linorder @ $o)).
% 2.81/1.53 thf(tcon_HOL_Obool___Orderings_Oord_4, axiom, (ord @ $o)).
% 2.81/1.53 thf(tcon_HOL_Obool___Groups_Ouminus_5, axiom, (uminus @ $o)).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors__cancel_6, axiom, (! [A6:$tType]: (((idom @ A6) => (semiri1923998003cancel @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Olinordered__comm__semiring__strict_7, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linord893533164strict @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_8, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linord1659791738miring @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Olinordered__semiring__strict_9, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linord20386208strict @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors_10, axiom, (! [A6:$tType]: ((((comm_semiring_0 @ A6) & (semiri1193490041visors @ A6)) => (semiri1193490041visors @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Olinordered__ab__group__add, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linord219039673up_add @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Oring__1__no__zero__divisors, axiom, (! [A6:$tType]: (((idom @ A6) => (ring_11004092258visors @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Olinordered__ring__strict, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linord581940658strict @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (ordered_ab_group_add @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Olinordered__semidom_11, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linordered_semidom @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Oab__semigroup__mult_12, axiom, (! [A6:$tType]: (((comm_semiring_0 @ A6) => (ab_semigroup_mult @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__mult_13, axiom, (! [A6:$tType]: (((comm_semiring_1 @ A6) => (comm_monoid_mult @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_14, axiom, (! [A6:$tType]: (((comm_monoid_add @ A6) => (comm_monoid_add @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Olinordered__ring, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linordered_ring @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Olinordered__idom, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linordered_idom @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_15, axiom, (! [A6:$tType]: (((comm_semiring_1 @ A6) => (comm_semiring_1 @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_16, axiom, (! [A6:$tType]: (((comm_semiring_0 @ A6) => (comm_semiring_0 @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Osemigroup__mult_17, axiom, (! [A6:$tType]: (((comm_semiring_0 @ A6) => (semigroup_mult @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Ozero__less__one_18, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (zero_less_one @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Oab__group__add, axiom, (! [A6:$tType]: (((ab_group_add @ A6) => (ab_group_add @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Ozero__neq__one_19, axiom, (! [A6:$tType]: (((comm_semiring_1 @ A6) => (zero_neq_one @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Oidom__abs__sgn, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (idom_abs_sgn @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Orderings_Olinorder_20, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (linorder @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Omonoid__mult_21, axiom, (! [A6:$tType]: (((comm_semiring_1 @ A6) => (monoid_mult @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Omonoid__add_22, axiom, (! [A6:$tType]: (((comm_monoid_add @ A6) => (monoid_add @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Ogroup__add, axiom, (! [A6:$tType]: (((ab_group_add @ A6) => (group_add @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Omult__zero_23, axiom, (! [A6:$tType]: (((comm_semiring_0 @ A6) => (mult_zero @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring, axiom, (! [A6:$tType]: (((comm_ring @ A6) => (comm_ring @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Num_Oneg__numeral, axiom, (! [A6:$tType]: (((comm_ring_1 @ A6) => (neg_numeral @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Nat_Oring__char__0, axiom, (! [A6:$tType]: ((((ring_char_0 @ A6) & (comm_ring_1 @ A6)) => (ring_char_0 @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Orderings_Oord_24, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (ord @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Ouminus_25, axiom, (! [A6:$tType]: (((ab_group_add @ A6) => (uminus @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Oring__1, axiom, (! [A6:$tType]: (((comm_ring_1 @ A6) => (ring_1 @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Ozero_26, axiom, (! [A6:$tType]: (((zero @ A6) => (zero @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Oplus_27, axiom, (! [A6:$tType]: (((comm_monoid_add @ A6) => (plus @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Oring, axiom, (! [A6:$tType]: (((comm_ring @ A6) => (ring @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Rings_Oidom, axiom, (! [A6:$tType]: (((idom @ A6) => (idom @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Osgn, axiom, (! [A6:$tType]: (((linordered_idom @ A6) => (sgn @ (poly @ A6)))))).
% 2.81/1.53 thf(tcon_Polynomial_Opoly___Groups_Oone_28, axiom, (! [A6:$tType]: (((comm_semiring_1 @ A6) => (one @ (poly @ A6)))))).
% 2.81/1.53 thf(tfree_0, hypothesis, (linordered_idom @ a)).
% 2.81/1.53 thf(conj_0, conjecture, (((descar149487500hanges @ a) @ ys) = ((descar149487500hanges @ a) @ ((coeffs @ a) @ g)))).
% 2.81/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2DTF578.p
% 2.81/1.53 ------------------------
% 2.81/1.56 ---- Cleaned THF ---
% 2.81/1.56 thf(ty_t_Polynomial_Opoly,type,
% 2.81/1.56 poly: $tType > $tType ).
% 2.81/1.56
% 2.81/1.56 thf(ty_t_List_Olist,type,
% 2.81/1.56 list: $tType > $tType ).
% 2.81/1.56
% 2.81/1.56 thf(ty_t_Nat_Onat,type,
% 2.81/1.56 nat: $tType ).
% 2.81/1.56
% 2.81/1.56 thf(ty_tf_a,type,
% 2.81/1.56 a: $tType ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Ocomm__ring__1,type,
% 2.81/1.56 comm_ring_1:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_HOL_Otype,type,
% 2.81/1.56 type:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Oone,type,
% 2.81/1.56 one:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Osgn,type,
% 2.81/1.56 sgn:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Oidom,type,
% 2.81/1.56 idom:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Oring,type,
% 2.81/1.56 ring:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Oplus,type,
% 2.81/1.56 plus:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Ozero,type,
% 2.81/1.56 zero:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Oring__1,type,
% 2.81/1.56 ring_1:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Ouminus,type,
% 2.81/1.56 uminus:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Orderings_Oord,type,
% 2.81/1.56 ord:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Nat_Oring__char__0,type,
% 2.81/1.56 ring_char_0:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Num_Oneg__numeral,type,
% 2.81/1.56 neg_numeral:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Ocomm__ring,type,
% 2.81/1.56 comm_ring:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Omult__zero,type,
% 2.81/1.56 mult_zero:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Ogroup__add,type,
% 2.81/1.56 group_add:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Omonoid__add,type,
% 2.81/1.56 monoid_add:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Omonoid__mult,type,
% 2.81/1.56 monoid_mult:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Orderings_Olinorder,type,
% 2.81/1.56 linorder:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Oidom__abs__sgn,type,
% 2.81/1.56 idom_abs_sgn:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Ozero__neq__one,type,
% 2.81/1.56 zero_neq_one:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Oab__group__add,type,
% 2.81/1.56 ab_group_add:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Orderings_Owellorder,type,
% 2.81/1.56 wellorder:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Ozero__less__one,type,
% 2.81/1.56 zero_less_one:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Osemigroup__mult,type,
% 2.81/1.56 semigroup_mult:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Ocomm__semiring__0,type,
% 2.81/1.56 comm_semiring_0:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 2.81/1.56 comm_semiring_1:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.81/1.56 linordered_idom:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Olinordered__ring,type,
% 2.81/1.56 linordered_ring:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.81/1.56 comm_monoid_add:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 2.81/1.56 comm_monoid_mult:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 2.81/1.56 ab_semigroup_mult:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 2.81/1.56 boolean_algebra:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Olinordered__semidom,type,
% 2.81/1.56 linordered_semidom:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.81/1.56 ordered_ab_group_add:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Olinordered__ring__strict,type,
% 2.81/1.56 linord581940658strict:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Oring__1__no__zero__divisors,type,
% 2.81/1.56 ring_11004092258visors:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.81/1.56 linord219039673up_add:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Osemiring__no__zero__divisors,type,
% 2.81/1.56 semiri1193490041visors:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Olinordered__semiring__strict,type,
% 2.81/1.56 linord20386208strict:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.81/1.56 linord1659791738miring:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.81/1.56 canoni770627133id_add:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Olinordered__comm__semiring__strict,type,
% 2.81/1.56 linord893533164strict:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_cl_Rings_Osemiring__no__zero__divisors__cancel,type,
% 2.81/1.56 semiri1923998003cancel:
% 2.81/1.56 !>[A: $tType] : $o ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Opsums,type,
% 2.81/1.56 descar1668888542_psums:
% 2.81/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Oreduce__root,type,
% 2.81/1.56 descar316357986e_root:
% 2.81/1.56 !>[A: $tType] : ( A > ( poly @ A ) > ( poly @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Descartes__Sign__Rule__Mirabelle__vuqjybseel_Osign__changes,type,
% 2.81/1.56 descar149487500hanges:
% 2.81/1.56 !>[A: $tType] : ( ( list @ A ) > nat ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.81/1.56 one_one:
% 2.81/1.56 !>[A: $tType] : A ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 2.81/1.56 times_times:
% 2.81/1.56 !>[A: $tType] : ( A > A > A ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.81/1.56 uminus_uminus:
% 2.81/1.56 !>[A: $tType] : ( A > A ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.81/1.56 zero_zero:
% 2.81/1.56 !>[A: $tType] : A ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_List_Oappend,type,
% 2.81/1.56 append:
% 2.81/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_List_Olist_OCons,type,
% 2.81/1.56 cons:
% 2.81/1.56 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_List_Olist_ONil,type,
% 2.81/1.56 nil:
% 2.81/1.56 !>[A: $tType] : ( list @ A ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_List_On__lists,type,
% 2.81/1.56 n_lists:
% 2.81/1.56 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_List_Onull,type,
% 2.81/1.56 null:
% 2.81/1.56 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec,type,
% 2.81/1.56 neg_numeral_dbl_dec:
% 2.81/1.56 !>[A: $tType] : ( A > A ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.81/1.56 ord_less:
% 2.81/1.56 !>[A: $tType] : ( A > A > $o ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Polynomial_OPoly,type,
% 2.81/1.56 poly2:
% 2.81/1.56 !>[A: $tType] : ( ( list @ A ) > ( poly @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Polynomial_Ocoeffs,type,
% 2.81/1.56 coeffs:
% 2.81/1.56 !>[A: $tType] : ( ( poly @ A ) > ( list @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Polynomial_Ois__zero,type,
% 2.81/1.56 is_zero:
% 2.81/1.56 !>[A: $tType] : ( ( poly @ A ) > $o ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Polynomial_OpCons,type,
% 2.81/1.56 pCons:
% 2.81/1.56 !>[A: $tType] : ( A > ( poly @ A ) > ( poly @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Polynomial_Opoly__cutoff,type,
% 2.81/1.56 poly_cutoff:
% 2.81/1.56 !>[A: $tType] : ( nat > ( poly @ A ) > ( poly @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_c_Polynomial_Osmult,type,
% 2.81/1.56 smult:
% 2.81/1.56 !>[A: $tType] : ( A > ( poly @ A ) > ( poly @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(sy_v_g,type,
% 2.81/1.56 g: poly @ a ).
% 2.81/1.56
% 2.81/1.56 thf(sy_v_v,type,
% 2.81/1.56 v: ( poly @ a ) > nat ).
% 2.81/1.56
% 2.81/1.56 thf(sy_v_xs____,type,
% 2.81/1.56 xs: list @ a ).
% 2.81/1.56
% 2.81/1.56 thf(sy_v_ys____,type,
% 2.81/1.56 ys: list @ a ).
% 2.81/1.56
% 2.81/1.56 thf(fact_0_v__def,axiom,
% 2.81/1.56 ( v
% 2.81/1.56 = ( ^ [F: poly @ a] : ( descar149487500hanges @ a @ ( coeffs @ a @ F ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_1_nz,axiom,
% 2.81/1.56 ( g
% 2.81/1.56 != ( zero_zero @ ( poly @ a ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_2_coeffs__eq__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ( ( ^ [Y: poly @ A,Z: poly @ A] : ( Y = Z ) )
% 2.81/1.56 = ( ^ [P: poly @ A,Q: poly @ A] :
% 2.81/1.56 ( ( coeffs @ A @ P )
% 2.81/1.56 = ( coeffs @ A @ Q ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_3_ys,axiom,
% 2.81/1.56 ( ys
% 2.81/1.56 = ( descar1668888542_psums @ a @ xs ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_4_sign__changes__coeff__sign__changes,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ! [Xs: list @ A,P2: poly @ A] :
% 2.81/1.56 ( ( ( poly2 @ A @ Xs )
% 2.81/1.56 = P2 )
% 2.81/1.56 => ( ( descar149487500hanges @ A @ Xs )
% 2.81/1.56 = ( descar149487500hanges @ A @ ( coeffs @ A @ P2 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_5_ys__def,axiom,
% 2.81/1.56 ( ys
% 2.81/1.56 = ( append @ a @ ( coeffs @ a @ g ) @ ( cons @ a @ ( zero_zero @ a ) @ ( nil @ a ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_6_coeff__sign__changes__reduce__root,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 => ( ( descar149487500hanges @ A @ ( coeffs @ A @ ( descar316357986e_root @ A @ A2 @ P2 ) ) )
% 2.81/1.56 = ( descar149487500hanges @ A @ ( coeffs @ A @ P2 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_7_is__zero__def,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ( ( is_zero @ A )
% 2.81/1.56 = ( ^ [P: poly @ A] : ( null @ A @ ( coeffs @ A @ P ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_8_Poly__coeffs,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [P2: poly @ A] :
% 2.81/1.56 ( ( poly2 @ A @ ( coeffs @ A @ P2 ) )
% 2.81/1.56 = P2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_9_sign__changes__Nil,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ( sgn @ A )
% 2.81/1.56 & ( zero @ A ) )
% 2.81/1.56 => ( ( descar149487500hanges @ A @ ( nil @ A ) )
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_10_xs__def,axiom,
% 2.81/1.56 ( xs
% 2.81/1.56 = ( coeffs @ a @ ( times_times @ ( poly @ a ) @ ( pCons @ a @ ( one_one @ a ) @ ( pCons @ a @ ( uminus_uminus @ a @ ( one_one @ a ) ) @ ( zero_zero @ ( poly @ a ) ) ) ) @ g ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_11_coeff__sign__changes__smult,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 => ( ( descar149487500hanges @ A @ ( coeffs @ A @ ( smult @ A @ A2 @ P2 ) ) )
% 2.81/1.56 = ( descar149487500hanges @ A @ ( coeffs @ A @ P2 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_12_sign__changes__0__Cons,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( idom_abs_sgn @ A )
% 2.81/1.56 => ! [Xs: list @ A] :
% 2.81/1.56 ( ( descar149487500hanges @ A @ ( cons @ A @ ( zero_zero @ A ) @ Xs ) )
% 2.81/1.56 = ( descar149487500hanges @ A @ Xs ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_13_sign__changes__Cons__Cons__0,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ! [X: A,Xs: list @ A] :
% 2.81/1.56 ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( cons @ A @ ( zero_zero @ A ) @ Xs ) ) )
% 2.81/1.56 = ( descar149487500hanges @ A @ ( cons @ A @ X @ Xs ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_14_pCons__eq__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A,B: A,Q2: poly @ A] :
% 2.81/1.56 ( ( ( pCons @ A @ A2 @ P2 )
% 2.81/1.56 = ( pCons @ A @ B @ Q2 ) )
% 2.81/1.56 = ( ( A2 = B )
% 2.81/1.56 & ( P2 = Q2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_15_minus__pCons,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ab_group_add @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A] :
% 2.81/1.56 ( ( uminus_uminus @ ( poly @ A ) @ ( pCons @ A @ A2 @ P2 ) )
% 2.81/1.56 = ( pCons @ A @ ( uminus_uminus @ A @ A2 ) @ ( uminus_uminus @ ( poly @ A ) @ P2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_16_smult__smult,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [A2: A,B: A,P2: poly @ A] :
% 2.81/1.56 ( ( smult @ A @ A2 @ ( smult @ A @ B @ P2 ) )
% 2.81/1.56 = ( smult @ A @ ( times_times @ A @ A2 @ B ) @ P2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_17_smult__1__left,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_1 @ A )
% 2.81/1.56 => ! [P2: poly @ A] :
% 2.81/1.56 ( ( smult @ A @ ( one_one @ A ) @ P2 )
% 2.81/1.56 = P2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_18_smult__minus__left,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_ring @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A] :
% 2.81/1.56 ( ( smult @ A @ ( uminus_uminus @ A @ A2 ) @ P2 )
% 2.81/1.56 = ( uminus_uminus @ ( poly @ A ) @ ( smult @ A @ A2 @ P2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_19_smult__0__right,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( smult @ A @ A2 @ ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_20_mult__smult__left,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A,Q2: poly @ A] :
% 2.81/1.56 ( ( times_times @ ( poly @ A ) @ ( smult @ A @ A2 @ P2 ) @ Q2 )
% 2.81/1.56 = ( smult @ A @ A2 @ ( times_times @ ( poly @ A ) @ P2 @ Q2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_21_mult__smult__right,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [P2: poly @ A,A2: A,Q2: poly @ A] :
% 2.81/1.56 ( ( times_times @ ( poly @ A ) @ P2 @ ( smult @ A @ A2 @ Q2 ) )
% 2.81/1.56 = ( smult @ A @ A2 @ ( times_times @ ( poly @ A ) @ P2 @ Q2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_22_pCons__0__0,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ( ( pCons @ A @ ( zero_zero @ A ) @ ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_23_pCons__eq__0__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A] :
% 2.81/1.56 ( ( ( pCons @ A @ A2 @ P2 )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 = ( ( A2
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 & ( P2
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_24_one__poly__eq__simps_I2_J,axiom,
% 2.81/1.56 ! [B2: $tType] :
% 2.81/1.56 ( ( comm_semiring_1 @ B2 )
% 2.81/1.56 => ( ( pCons @ B2 @ ( one_one @ B2 ) @ ( zero_zero @ ( poly @ B2 ) ) )
% 2.81/1.56 = ( one_one @ ( poly @ B2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_25_one__poly__eq__simps_I1_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_1 @ A )
% 2.81/1.56 => ( ( one_one @ ( poly @ A ) )
% 2.81/1.56 = ( pCons @ A @ ( one_one @ A ) @ ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_26_smult__0__left,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [P2: poly @ A] :
% 2.81/1.56 ( ( smult @ A @ ( zero_zero @ A ) @ P2 )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_27_smult__eq__0__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ( comm_semiring_0 @ A )
% 2.81/1.56 & ( semiri1193490041visors @ A ) )
% 2.81/1.56 => ! [A2: A,P2: poly @ A] :
% 2.81/1.56 ( ( ( smult @ A @ A2 @ P2 )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 = ( ( A2
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( P2
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_28_smult__pCons,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [A2: A,B: A,P2: poly @ A] :
% 2.81/1.56 ( ( smult @ A @ A2 @ ( pCons @ A @ B @ P2 ) )
% 2.81/1.56 = ( pCons @ A @ ( times_times @ A @ A2 @ B ) @ ( smult @ A @ A2 @ P2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_29_coeffs__eq__Nil,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [P2: poly @ A] :
% 2.81/1.56 ( ( ( coeffs @ A @ P2 )
% 2.81/1.56 = ( nil @ A ) )
% 2.81/1.56 = ( P2
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_30_coeffs__0__eq__Nil,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ( ( coeffs @ A @ ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 = ( nil @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_31_psums__0__Cons,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( monoid_add @ A )
% 2.81/1.56 => ! [Xs: list @ A] :
% 2.81/1.56 ( ( descar1668888542_psums @ A @ ( cons @ A @ ( zero_zero @ A ) @ Xs ) )
% 2.81/1.56 = ( cons @ A @ ( zero_zero @ A ) @ ( descar1668888542_psums @ A @ Xs ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_32_coeffs__1__eq,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_1 @ A )
% 2.81/1.56 => ( ( coeffs @ A @ ( one_one @ ( poly @ A ) ) )
% 2.81/1.56 = ( cons @ A @ ( one_one @ A ) @ ( nil @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_33_sign__changes__singleton,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ( sgn @ A )
% 2.81/1.56 & ( zero @ A ) )
% 2.81/1.56 => ! [X: A] :
% 2.81/1.56 ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_34__092_060open_062sign__changes_Axs_A_061_Av_A_I_091_0581_058_058_Ha_M_A_N_A_I1_058_058_Ha_J_058_093_A_K_Ag_J_092_060close_062,axiom,
% 2.81/1.56 ( ( descar149487500hanges @ a @ xs )
% 2.81/1.56 = ( v @ ( times_times @ ( poly @ a ) @ ( pCons @ a @ ( one_one @ a ) @ ( pCons @ a @ ( uminus_uminus @ a @ ( one_one @ a ) ) @ ( zero_zero @ ( poly @ a ) ) ) ) @ g ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_35_Poly__snoc__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [As: list @ A] :
% 2.81/1.56 ( ( poly2 @ A @ ( append @ A @ As @ ( cons @ A @ ( zero_zero @ A ) @ ( nil @ A ) ) ) )
% 2.81/1.56 = ( poly2 @ A @ As ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_36_Poly_Osimps_I2_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [A2: A,As: list @ A] :
% 2.81/1.56 ( ( poly2 @ A @ ( cons @ A @ A2 @ As ) )
% 2.81/1.56 = ( pCons @ A @ A2 @ ( poly2 @ A @ As ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_37_Poly_Osimps_I1_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ( ( poly2 @ A @ ( nil @ A ) )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_38_psums_Osimps_I2_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( plus @ A )
% 2.81/1.56 => ! [X: A] :
% 2.81/1.56 ( ( descar1668888542_psums @ A @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.81/1.56 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_39_psums_Osimps_I1_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( plus @ A )
% 2.81/1.56 => ( ( descar1668888542_psums @ A @ ( nil @ A ) )
% 2.81/1.56 = ( nil @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_40_pCons__one,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_1 @ A )
% 2.81/1.56 => ( ( pCons @ A @ ( one_one @ A ) @ ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 = ( one_one @ ( poly @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_41_pCons__cases,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [P2: poly @ A] :
% 2.81/1.56 ~ ! [A3: A,Q3: poly @ A] :
% 2.81/1.56 ( P2
% 2.81/1.56 != ( pCons @ A @ A3 @ Q3 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_42_is__zero__null,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ( ( is_zero @ A )
% 2.81/1.56 = ( ^ [P: poly @ A] :
% 2.81/1.56 ( P
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_43_pCons__induct,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [P3: ( poly @ A ) > $o,P2: poly @ A] :
% 2.81/1.56 ( ( P3 @ ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 => ( ! [A3: A,P4: poly @ A] :
% 2.81/1.56 ( ( ( A3
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 | ( P4
% 2.81/1.56 != ( zero_zero @ ( poly @ A ) ) ) )
% 2.81/1.56 => ( ( P3 @ P4 )
% 2.81/1.56 => ( P3 @ ( pCons @ A @ A3 @ P4 ) ) ) )
% 2.81/1.56 => ( P3 @ P2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_44_pderiv_Ocases,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ( comm_semiring_1 @ A )
% 2.81/1.56 & ( semiri1193490041visors @ A ) )
% 2.81/1.56 => ! [X: poly @ A] :
% 2.81/1.56 ~ ! [A3: A,P4: poly @ A] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( pCons @ A @ A3 @ P4 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_45_ext,axiom,
% 2.81/1.56 ! [B2: $tType,A: $tType,F2: A > B2,G: A > B2] :
% 2.81/1.56 ( ! [X2: A] :
% 2.81/1.56 ( ( F2 @ X2 )
% 2.81/1.56 = ( G @ X2 ) )
% 2.81/1.56 => ( F2 = G ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_46_poly__induct2,axiom,
% 2.81/1.56 ! [A: $tType,B2: $tType] :
% 2.81/1.56 ( ( ( zero @ B2 )
% 2.81/1.56 & ( zero @ A ) )
% 2.81/1.56 => ! [P3: ( poly @ A ) > ( poly @ B2 ) > $o,P2: poly @ A,Q2: poly @ B2] :
% 2.81/1.56 ( ( P3 @ ( zero_zero @ ( poly @ A ) ) @ ( zero_zero @ ( poly @ B2 ) ) )
% 2.81/1.56 => ( ! [A3: A,P4: poly @ A,B3: B2,Q3: poly @ B2] :
% 2.81/1.56 ( ( P3 @ P4 @ Q3 )
% 2.81/1.56 => ( P3 @ ( pCons @ A @ A3 @ P4 ) @ ( pCons @ B2 @ B3 @ Q3 ) ) )
% 2.81/1.56 => ( P3 @ P2 @ Q2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_47_pderiv_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ( comm_semiring_1 @ A )
% 2.81/1.56 & ( semiri1193490041visors @ A ) )
% 2.81/1.56 => ! [P3: ( poly @ A ) > $o,A0: poly @ A] :
% 2.81/1.56 ( ! [A3: A,P4: poly @ A] :
% 2.81/1.56 ( ( ( P4
% 2.81/1.56 != ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 => ( P3 @ P4 ) )
% 2.81/1.56 => ( P3 @ ( pCons @ A @ A3 @ P4 ) ) )
% 2.81/1.56 => ( P3 @ A0 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_48_mult__poly__0__left,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [Q2: poly @ A] :
% 2.81/1.56 ( ( times_times @ ( poly @ A ) @ ( zero_zero @ ( poly @ A ) ) @ Q2 )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_49_mult__poly__0__right,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [P2: poly @ A] :
% 2.81/1.56 ( ( times_times @ ( poly @ A ) @ P2 @ ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_50_plus__coeffs_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_monoid_add @ A )
% 2.81/1.56 => ! [P3: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.81/1.56 ( ! [Xs2: list @ A] : ( P3 @ Xs2 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [V: A,Va: list @ A] : ( P3 @ ( nil @ A ) @ ( cons @ A @ V @ Va ) )
% 2.81/1.56 => ( ! [X2: A,Xs2: list @ A,Y2: A,Ys: list @ A] :
% 2.81/1.56 ( ( P3 @ Xs2 @ Ys )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys ) ) )
% 2.81/1.56 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_51_not__0__coeffs__not__Nil,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [P2: poly @ A] :
% 2.81/1.56 ( ( P2
% 2.81/1.56 != ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 => ( ( coeffs @ A @ P2 )
% 2.81/1.56 != ( nil @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_52_minus__poly__rev__list_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( group_add @ A )
% 2.81/1.56 => ! [P3: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.81/1.56 ( ! [X2: A,Xs2: list @ A,Y2: A,Ys: list @ A] :
% 2.81/1.56 ( ( P3 @ Xs2 @ Ys )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys ) ) )
% 2.81/1.56 => ( ! [Xs2: list @ A] : ( P3 @ Xs2 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [Y2: A,Ys: list @ A] : ( P3 @ ( nil @ A ) @ ( cons @ A @ Y2 @ Ys ) )
% 2.81/1.56 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_53_synthetic__div__unique__lemma,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [C: A,P2: poly @ A,A2: A] :
% 2.81/1.56 ( ( ( smult @ A @ C @ P2 )
% 2.81/1.56 = ( pCons @ A @ A2 @ P2 ) )
% 2.81/1.56 => ( P2
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_54_psums_Ocases,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( plus @ A )
% 2.81/1.56 => ! [X: list @ A] :
% 2.81/1.56 ( ( X
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.81/1.56 => ~ ! [X2: A,Y2: A,Xs2: list @ A] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_55_reduce__root__pCons,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_0 @ A )
% 2.81/1.56 => ! [A2: A,C: A,P2: poly @ A] :
% 2.81/1.56 ( ( descar316357986e_root @ A @ A2 @ ( pCons @ A @ C @ P2 ) )
% 2.81/1.56 = ( pCons @ A @ C @ ( smult @ A @ A2 @ ( descar316357986e_root @ A @ A2 @ P2 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_56_reduce__root__nonzero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( idom @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A] :
% 2.81/1.56 ( ( A2
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 => ( ( P2
% 2.81/1.56 != ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 => ( ( descar316357986e_root @ A @ A2 @ P2 )
% 2.81/1.56 != ( zero_zero @ ( poly @ A ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_57_sign__changes__Cons__Cons__same,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ! [X: A,Y3: A,Xs: list @ A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ X @ Y3 ) )
% 2.81/1.56 => ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Xs ) ) )
% 2.81/1.56 = ( descar149487500hanges @ A @ ( cons @ A @ Y3 @ Xs ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_58_append1__eq__conv,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A,Y3: A] :
% 2.81/1.56 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.81/1.56 = ( append @ A @ Ys2 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 2.81/1.56 = ( ( Xs = Ys2 )
% 2.81/1.56 & ( X = Y3 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_59_mult__minus1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_1 @ A )
% 2.81/1.56 => ! [Z2: A] :
% 2.81/1.56 ( ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ Z2 )
% 2.81/1.56 = ( uminus_uminus @ A @ Z2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_60_mult__minus1__right,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_1 @ A )
% 2.81/1.56 => ! [Z2: A] :
% 2.81/1.56 ( ( times_times @ A @ Z2 @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.81/1.56 = ( uminus_uminus @ A @ Z2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_61_less__neg__neg,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord219039673up_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( ord_less @ A @ A2 @ ( uminus_uminus @ A @ A2 ) )
% 2.81/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_62_neg__less__pos,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord219039673up_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ A2 )
% 2.81/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_63_neg__0__less__iff__less,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ordered_ab_group_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A2 ) )
% 2.81/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_64_neg__less__0__iff__less,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ordered_ab_group_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ ( zero_zero @ A ) )
% 2.81/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_65_mult__cancel__left1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_11004092258visors @ A )
% 2.81/1.56 => ! [C: A,B: A] :
% 2.81/1.56 ( ( C
% 2.81/1.56 = ( times_times @ A @ C @ B ) )
% 2.81/1.56 = ( ( C
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( B
% 2.81/1.56 = ( one_one @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_66_mult__cancel__left2,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_11004092258visors @ A )
% 2.81/1.56 => ! [C: A,A2: A] :
% 2.81/1.56 ( ( ( times_times @ A @ C @ A2 )
% 2.81/1.56 = C )
% 2.81/1.56 = ( ( C
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( A2
% 2.81/1.56 = ( one_one @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_67_mult__cancel__right1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_11004092258visors @ A )
% 2.81/1.56 => ! [C: A,B: A] :
% 2.81/1.56 ( ( C
% 2.81/1.56 = ( times_times @ A @ B @ C ) )
% 2.81/1.56 = ( ( C
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( B
% 2.81/1.56 = ( one_one @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_68_mult__cancel__right2,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_11004092258visors @ A )
% 2.81/1.56 => ! [A2: A,C: A] :
% 2.81/1.56 ( ( ( times_times @ A @ A2 @ C )
% 2.81/1.56 = C )
% 2.81/1.56 = ( ( C
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( A2
% 2.81/1.56 = ( one_one @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_69_neg__equal__iff__equal,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( group_add @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ( uminus_uminus @ A @ A2 )
% 2.81/1.56 = ( uminus_uminus @ A @ B ) )
% 2.81/1.56 = ( A2 = B ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_70_add_Oinverse__inverse,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( group_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A2 ) )
% 2.81/1.56 = A2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_71_list_Oinject,axiom,
% 2.81/1.56 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.81/1.56 ( ( ( cons @ A @ X21 @ X22 )
% 2.81/1.56 = ( cons @ A @ Y21 @ Y22 ) )
% 2.81/1.56 = ( ( X21 = Y21 )
% 2.81/1.56 & ( X22 = Y22 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_72_same__append__eq,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 2.81/1.56 ( ( ( append @ A @ Xs @ Ys2 )
% 2.81/1.56 = ( append @ A @ Xs @ Zs ) )
% 2.81/1.56 = ( Ys2 = Zs ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_73_append__same__eq,axiom,
% 2.81/1.56 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.81/1.56 ( ( ( append @ A @ Ys2 @ Xs )
% 2.81/1.56 = ( append @ A @ Zs @ Xs ) )
% 2.81/1.56 = ( Ys2 = Zs ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_74_append__assoc,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 2.81/1.56 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs )
% 2.81/1.56 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_75_append_Oassoc,axiom,
% 2.81/1.56 ! [A: $tType,A2: list @ A,B: list @ A,C: list @ A] :
% 2.81/1.56 ( ( append @ A @ ( append @ A @ A2 @ B ) @ C )
% 2.81/1.56 = ( append @ A @ A2 @ ( append @ A @ B @ C ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_76_not__gr__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( canoni770627133id_add @ A )
% 2.81/1.56 => ! [N: A] :
% 2.81/1.56 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.81/1.56 = ( N
% 2.81/1.56 = ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_77_mult__cancel__right,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( semiri1923998003cancel @ A )
% 2.81/1.56 => ! [A2: A,C: A,B: A] :
% 2.81/1.56 ( ( ( times_times @ A @ A2 @ C )
% 2.81/1.56 = ( times_times @ A @ B @ C ) )
% 2.81/1.56 = ( ( C
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( A2 = B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_78_mult__cancel__left,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( semiri1923998003cancel @ A )
% 2.81/1.56 => ! [C: A,A2: A,B: A] :
% 2.81/1.56 ( ( ( times_times @ A @ C @ A2 )
% 2.81/1.56 = ( times_times @ A @ C @ B ) )
% 2.81/1.56 = ( ( C
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( A2 = B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_79_mult__eq__0__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( semiri1193490041visors @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ( times_times @ A @ A2 @ B )
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 = ( ( A2
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( B
% 2.81/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_80_mult__zero__right,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( mult_zero @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( times_times @ A @ A2 @ ( zero_zero @ A ) )
% 2.81/1.56 = ( zero_zero @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_81_mult__zero__left,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( mult_zero @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( times_times @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 = ( zero_zero @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_82_neg__equal__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord219039673up_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( ( uminus_uminus @ A @ A2 )
% 2.81/1.56 = A2 )
% 2.81/1.56 = ( A2
% 2.81/1.56 = ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_83_equal__neg__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord219039673up_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( A2
% 2.81/1.56 = ( uminus_uminus @ A @ A2 ) )
% 2.81/1.56 = ( A2
% 2.81/1.56 = ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_84_neg__equal__0__iff__equal,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( group_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( ( uminus_uminus @ A @ A2 )
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 = ( A2
% 2.81/1.56 = ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_85_neg__0__equal__iff__equal,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( group_add @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( ( zero_zero @ A )
% 2.81/1.56 = ( uminus_uminus @ A @ A2 ) )
% 2.81/1.56 = ( ( zero_zero @ A )
% 2.81/1.56 = A2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_86_add_Oinverse__neutral,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( group_add @ A )
% 2.81/1.56 => ( ( uminus_uminus @ A @ ( zero_zero @ A ) )
% 2.81/1.56 = ( zero_zero @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_87_mult_Oright__neutral,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( monoid_mult @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 2.81/1.56 = A2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_88_mult_Oleft__neutral,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( monoid_mult @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 2.81/1.56 = A2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_89_neg__less__iff__less,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ordered_ab_group_add @ A )
% 2.81/1.56 => ! [B: A,A2: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( uminus_uminus @ A @ B ) @ ( uminus_uminus @ A @ A2 ) )
% 2.81/1.56 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_90_mult__minus__right,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( times_times @ A @ A2 @ ( uminus_uminus @ A @ B ) )
% 2.81/1.56 = ( uminus_uminus @ A @ ( times_times @ A @ A2 @ B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_91_minus__mult__minus,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( times_times @ A @ ( uminus_uminus @ A @ A2 ) @ ( uminus_uminus @ A @ B ) )
% 2.81/1.56 = ( times_times @ A @ A2 @ B ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_92_mult__minus__left,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( times_times @ A @ ( uminus_uminus @ A @ A2 ) @ B )
% 2.81/1.56 = ( uminus_uminus @ A @ ( times_times @ A @ A2 @ B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_93_append_Oright__neutral,axiom,
% 2.81/1.56 ! [A: $tType,A2: list @ A] :
% 2.81/1.56 ( ( append @ A @ A2 @ ( nil @ A ) )
% 2.81/1.56 = A2 ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_94_append__is__Nil__conv,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.81/1.56 ( ( ( append @ A @ Xs @ Ys2 )
% 2.81/1.56 = ( nil @ A ) )
% 2.81/1.56 = ( ( Xs
% 2.81/1.56 = ( nil @ A ) )
% 2.81/1.56 & ( Ys2
% 2.81/1.56 = ( nil @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_95_Nil__is__append__conv,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.81/1.56 ( ( ( nil @ A )
% 2.81/1.56 = ( append @ A @ Xs @ Ys2 ) )
% 2.81/1.56 = ( ( Xs
% 2.81/1.56 = ( nil @ A ) )
% 2.81/1.56 & ( Ys2
% 2.81/1.56 = ( nil @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_96_self__append__conv2,axiom,
% 2.81/1.56 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.81/1.56 ( ( Ys2
% 2.81/1.56 = ( append @ A @ Xs @ Ys2 ) )
% 2.81/1.56 = ( Xs
% 2.81/1.56 = ( nil @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_97_append__self__conv2,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.81/1.56 ( ( ( append @ A @ Xs @ Ys2 )
% 2.81/1.56 = Ys2 )
% 2.81/1.56 = ( Xs
% 2.81/1.56 = ( nil @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_98_self__append__conv,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.81/1.56 ( ( Xs
% 2.81/1.56 = ( append @ A @ Xs @ Ys2 ) )
% 2.81/1.56 = ( Ys2
% 2.81/1.56 = ( nil @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_99_append__self__conv,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.81/1.56 ( ( ( append @ A @ Xs @ Ys2 )
% 2.81/1.56 = Xs )
% 2.81/1.56 = ( Ys2
% 2.81/1.56 = ( nil @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_100_append__Nil2,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A] :
% 2.81/1.56 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.81/1.56 = Xs ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_101_smult__minus__right,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_ring @ A )
% 2.81/1.56 => ! [A2: A,P2: poly @ A] :
% 2.81/1.56 ( ( smult @ A @ A2 @ ( uminus_uminus @ ( poly @ A ) @ P2 ) )
% 2.81/1.56 = ( uminus_uminus @ ( poly @ A ) @ ( smult @ A @ A2 @ P2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_102_smult__one,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_1 @ A )
% 2.81/1.56 => ! [C: A] :
% 2.81/1.56 ( ( smult @ A @ C @ ( one_one @ ( poly @ A ) ) )
% 2.81/1.56 = ( pCons @ A @ C @ ( zero_zero @ ( poly @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_103_zero__reorient,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [X: A] :
% 2.81/1.56 ( ( ( zero_zero @ A )
% 2.81/1.56 = X )
% 2.81/1.56 = ( X
% 2.81/1.56 = ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_104_linorder__neqE__linordered__idom,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ! [X: A,Y3: A] :
% 2.81/1.56 ( ( X != Y3 )
% 2.81/1.56 => ( ~ ( ord_less @ A @ X @ Y3 )
% 2.81/1.56 => ( ord_less @ A @ Y3 @ X ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_105_mult_Oleft__commute,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ab_semigroup_mult @ A )
% 2.81/1.56 => ! [B: A,A2: A,C: A] :
% 2.81/1.56 ( ( times_times @ A @ B @ ( times_times @ A @ A2 @ C ) )
% 2.81/1.56 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_106_mult_Ocommute,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ab_semigroup_mult @ A )
% 2.81/1.56 => ( ( times_times @ A )
% 2.81/1.56 = ( ^ [A4: A,B4: A] : ( times_times @ A @ B4 @ A4 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_107_mult_Oassoc,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( semigroup_mult @ A )
% 2.81/1.56 => ! [A2: A,B: A,C: A] :
% 2.81/1.56 ( ( times_times @ A @ ( times_times @ A @ A2 @ B ) @ C )
% 2.81/1.56 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_108_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ab_semigroup_mult @ A )
% 2.81/1.56 => ! [A2: A,B: A,C: A] :
% 2.81/1.56 ( ( times_times @ A @ ( times_times @ A @ A2 @ B ) @ C )
% 2.81/1.56 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_109_one__reorient,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( one @ A )
% 2.81/1.56 => ! [X: A] :
% 2.81/1.56 ( ( ( one_one @ A )
% 2.81/1.56 = X )
% 2.81/1.56 = ( X
% 2.81/1.56 = ( one_one @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_110_minus__equation__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( group_add @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ( uminus_uminus @ A @ A2 )
% 2.81/1.56 = B )
% 2.81/1.56 = ( ( uminus_uminus @ A @ B )
% 2.81/1.56 = A2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_111_equation__minus__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( group_add @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( A2
% 2.81/1.56 = ( uminus_uminus @ A @ B ) )
% 2.81/1.56 = ( B
% 2.81/1.56 = ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_112_not__Cons__self2,axiom,
% 2.81/1.56 ! [A: $tType,X: A,Xs: list @ A] :
% 2.81/1.56 ( ( cons @ A @ X @ Xs )
% 2.81/1.56 != Xs ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_113_append__eq__append__conv2,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A,Ts: list @ A] :
% 2.81/1.56 ( ( ( append @ A @ Xs @ Ys2 )
% 2.81/1.56 = ( append @ A @ Zs @ Ts ) )
% 2.81/1.56 = ( ? [Us: list @ A] :
% 2.81/1.56 ( ( ( Xs
% 2.81/1.56 = ( append @ A @ Zs @ Us ) )
% 2.81/1.56 & ( ( append @ A @ Us @ Ys2 )
% 2.81/1.56 = Ts ) )
% 2.81/1.56 | ( ( ( append @ A @ Xs @ Us )
% 2.81/1.56 = Zs )
% 2.81/1.56 & ( Ys2
% 2.81/1.56 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_114_append__eq__appendI,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys2: list @ A,Us2: list @ A] :
% 2.81/1.56 ( ( ( append @ A @ Xs @ Xs1 )
% 2.81/1.56 = Zs )
% 2.81/1.56 => ( ( Ys2
% 2.81/1.56 = ( append @ A @ Xs1 @ Us2 ) )
% 2.81/1.56 => ( ( append @ A @ Xs @ Ys2 )
% 2.81/1.56 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_115_sign__changes__two,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ! [X: A,Y3: A] :
% 2.81/1.56 ( ( ( ( ( ord_less @ A @ ( zero_zero @ A ) @ X )
% 2.81/1.56 & ( ord_less @ A @ Y3 @ ( zero_zero @ A ) ) )
% 2.81/1.56 | ( ( ord_less @ A @ X @ ( zero_zero @ A ) )
% 2.81/1.56 & ( ord_less @ A @ ( zero_zero @ A ) @ Y3 ) ) )
% 2.81/1.56 => ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 2.81/1.56 = ( one_one @ nat ) ) )
% 2.81/1.56 & ( ~ ( ( ( ord_less @ A @ ( zero_zero @ A ) @ X )
% 2.81/1.56 & ( ord_less @ A @ Y3 @ ( zero_zero @ A ) ) )
% 2.81/1.56 | ( ( ord_less @ A @ X @ ( zero_zero @ A ) )
% 2.81/1.56 & ( ord_less @ A @ ( zero_zero @ A ) @ Y3 ) ) )
% 2.81/1.56 => ( ( descar149487500hanges @ A @ ( cons @ A @ X @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) )
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_116_zero__less__iff__neq__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( canoni770627133id_add @ A )
% 2.81/1.56 => ! [N: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.81/1.56 = ( N
% 2.81/1.56 != ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_117_gr__implies__not__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( canoni770627133id_add @ A )
% 2.81/1.56 => ! [M: A,N: A] :
% 2.81/1.56 ( ( ord_less @ A @ M @ N )
% 2.81/1.56 => ( N
% 2.81/1.56 != ( zero_zero @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_118_not__less__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( canoni770627133id_add @ A )
% 2.81/1.56 => ! [N: A] :
% 2.81/1.56 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_119_gr__zeroI,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( canoni770627133id_add @ A )
% 2.81/1.56 => ! [N: A] :
% 2.81/1.56 ( ( N
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_120_less__numeral__extra_I3_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord1659791738miring @ A )
% 2.81/1.56 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_121_mult__right__cancel,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( semiri1923998003cancel @ A )
% 2.81/1.56 => ! [C: A,A2: A,B: A] :
% 2.81/1.56 ( ( C
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 => ( ( ( times_times @ A @ A2 @ C )
% 2.81/1.56 = ( times_times @ A @ B @ C ) )
% 2.81/1.56 = ( A2 = B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_122_mult__left__cancel,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( semiri1923998003cancel @ A )
% 2.81/1.56 => ! [C: A,A2: A,B: A] :
% 2.81/1.56 ( ( C
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 => ( ( ( times_times @ A @ C @ A2 )
% 2.81/1.56 = ( times_times @ A @ C @ B ) )
% 2.81/1.56 = ( A2 = B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_123_no__zero__divisors,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( semiri1193490041visors @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( A2
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 => ( ( B
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 => ( ( times_times @ A @ A2 @ B )
% 2.81/1.56 != ( zero_zero @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_124_divisors__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( semiri1193490041visors @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ( times_times @ A @ A2 @ B )
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 => ( ( A2
% 2.81/1.56 = ( zero_zero @ A ) )
% 2.81/1.56 | ( B
% 2.81/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_125_mult__not__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( mult_zero @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ( times_times @ A @ A2 @ B )
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 => ( ( A2
% 2.81/1.56 != ( zero_zero @ A ) )
% 2.81/1.56 & ( B
% 2.81/1.56 != ( zero_zero @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_126_zero__neq__one,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero_neq_one @ A )
% 2.81/1.56 => ( ( zero_zero @ A )
% 2.81/1.56 != ( one_one @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_127_less__numeral__extra_I4_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord1659791738miring @ A )
% 2.81/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_128_mult_Ocomm__neutral,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_monoid_mult @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 2.81/1.56 = A2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_129_comm__monoid__mult__class_Omult__1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_monoid_mult @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 2.81/1.56 = A2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_130_minus__less__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ordered_ab_group_add @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( uminus_uminus @ A @ A2 ) @ B )
% 2.81/1.56 = ( ord_less @ A @ ( uminus_uminus @ A @ B ) @ A2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_131_less__minus__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ordered_ab_group_add @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ A2 @ ( uminus_uminus @ A @ B ) )
% 2.81/1.56 = ( ord_less @ A @ B @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_132_minus__mult__commute,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( times_times @ A @ ( uminus_uminus @ A @ A2 ) @ B )
% 2.81/1.56 = ( times_times @ A @ A2 @ ( uminus_uminus @ A @ B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_133_square__eq__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( idom @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ( times_times @ A @ A2 @ A2 )
% 2.81/1.56 = ( times_times @ A @ B @ B ) )
% 2.81/1.56 = ( ( A2 = B )
% 2.81/1.56 | ( A2
% 2.81/1.56 = ( uminus_uminus @ A @ B ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_134_one__neq__neg__one,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_char_0 @ A )
% 2.81/1.56 => ( ( one_one @ A )
% 2.81/1.56 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_135_strict__sorted_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linorder @ A )
% 2.81/1.56 => ! [P3: ( list @ A ) > $o,A0: list @ A] :
% 2.81/1.56 ( ( P3 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A,Ys: list @ A] :
% 2.81/1.56 ( ( P3 @ Ys )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Ys ) ) )
% 2.81/1.56 => ( P3 @ A0 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_136_strict__sorted_Ocases,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linorder @ A )
% 2.81/1.56 => ! [X: list @ A] :
% 2.81/1.56 ( ( X
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ~ ! [X2: A,Ys: list @ A] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( cons @ A @ X2 @ Ys ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_137_map__tailrec__rev_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType,B2: $tType,P3: ( A > B2 ) > ( list @ A ) > ( list @ B2 ) > $o,A0: A > B2,A1: list @ A,A22: list @ B2] :
% 2.81/1.56 ( ! [F3: A > B2,X_1: list @ B2] : ( P3 @ F3 @ ( nil @ A ) @ X_1 )
% 2.81/1.56 => ( ! [F3: A > B2,A3: A,As2: list @ A,Bs: list @ B2] :
% 2.81/1.56 ( ( P3 @ F3 @ As2 @ ( cons @ B2 @ ( F3 @ A3 ) @ Bs ) )
% 2.81/1.56 => ( P3 @ F3 @ ( cons @ A @ A3 @ As2 ) @ Bs ) )
% 2.81/1.56 => ( P3 @ A0 @ A1 @ A22 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_138_list__nonempty__induct,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,P3: ( list @ A ) > $o] :
% 2.81/1.56 ( ( Xs
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A] : ( P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.81/1.56 => ( ! [X2: A,Xs2: list @ A] :
% 2.81/1.56 ( ( Xs2
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ( ( P3 @ Xs2 )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 2.81/1.56 => ( P3 @ Xs ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_139_successively_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType,P3: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.81/1.56 ( ! [P5: A > A > $o] : ( P3 @ P5 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [P5: A > A > $o,X2: A] : ( P3 @ P5 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.81/1.56 => ( ! [P5: A > A > $o,X2: A,Y2: A,Xs2: list @ A] :
% 2.81/1.56 ( ( P3 @ P5 @ ( cons @ A @ Y2 @ Xs2 ) )
% 2.81/1.56 => ( P3 @ P5 @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) )
% 2.81/1.56 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_140_arg__min__list_Oinduct,axiom,
% 2.81/1.56 ! [B2: $tType,A: $tType] :
% 2.81/1.56 ( ( linorder @ B2 )
% 2.81/1.56 => ! [P3: ( A > B2 ) > ( list @ A ) > $o,A0: A > B2,A1: list @ A] :
% 2.81/1.56 ( ! [F3: A > B2,X2: A] : ( P3 @ F3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.81/1.56 => ( ! [F3: A > B2,X2: A,Y2: A,Zs2: list @ A] :
% 2.81/1.56 ( ( P3 @ F3 @ ( cons @ A @ Y2 @ Zs2 ) )
% 2.81/1.56 => ( P3 @ F3 @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Zs2 ) ) ) )
% 2.81/1.56 => ( ! [A3: A > B2] : ( P3 @ A3 @ ( nil @ A ) )
% 2.81/1.56 => ( P3 @ A0 @ A1 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_141_remdups__adj_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType,P3: ( list @ A ) > $o,A0: list @ A] :
% 2.81/1.56 ( ( P3 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A] : ( P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.81/1.56 => ( ! [X2: A,Y2: A,Xs2: list @ A] :
% 2.81/1.56 ( ( ( X2 = Y2 )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.81/1.56 => ( ( ( X2 != Y2 )
% 2.81/1.56 => ( P3 @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 2.81/1.56 => ( P3 @ A0 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_142_sorted__wrt_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType,P3: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.81/1.56 ( ! [P5: A > A > $o] : ( P3 @ P5 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [P5: A > A > $o,X2: A,Ys: list @ A] :
% 2.81/1.56 ( ( P3 @ P5 @ Ys )
% 2.81/1.56 => ( P3 @ P5 @ ( cons @ A @ X2 @ Ys ) ) )
% 2.81/1.56 => ( P3 @ A0 @ A1 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_143_remdups__adj_Ocases,axiom,
% 2.81/1.56 ! [A: $tType,X: list @ A] :
% 2.81/1.56 ( ( X
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.81/1.56 => ~ ! [X2: A,Y2: A,Xs2: list @ A] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_144_transpose_Ocases,axiom,
% 2.81/1.56 ! [A: $tType,X: list @ ( list @ A )] :
% 2.81/1.56 ( ( X
% 2.81/1.56 != ( nil @ ( list @ A ) ) )
% 2.81/1.56 => ( ! [Xss: list @ ( list @ A )] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.81/1.56 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_145_shuffles_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType,P3: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.81/1.56 ( ! [X_1: list @ A] : ( P3 @ ( nil @ A ) @ X_1 )
% 2.81/1.56 => ( ! [Xs2: list @ A] : ( P3 @ Xs2 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A,Xs2: list @ A,Y2: A,Ys: list @ A] :
% 2.81/1.56 ( ( P3 @ Xs2 @ ( cons @ A @ Y2 @ Ys ) )
% 2.81/1.56 => ( ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ Ys )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys ) ) ) )
% 2.81/1.56 => ( P3 @ A0 @ A1 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_146_min__list_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ord @ A )
% 2.81/1.56 => ! [P3: ( list @ A ) > $o,A0: list @ A] :
% 2.81/1.56 ( ! [X2: A,Xs2: list @ A] :
% 2.81/1.56 ( ! [X212: A,X222: list @ A] :
% 2.81/1.56 ( ( Xs2
% 2.81/1.56 = ( cons @ A @ X212 @ X222 ) )
% 2.81/1.56 => ( P3 @ Xs2 ) )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.81/1.56 => ( ( P3 @ ( nil @ A ) )
% 2.81/1.56 => ( P3 @ A0 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_147_min__list_Ocases,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ord @ A )
% 2.81/1.56 => ! [X: list @ A] :
% 2.81/1.56 ( ! [X2: A,Xs2: list @ A] :
% 2.81/1.56 ( X
% 2.81/1.56 != ( cons @ A @ X2 @ Xs2 ) )
% 2.81/1.56 => ( X
% 2.81/1.56 = ( nil @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_148_induct__list012,axiom,
% 2.81/1.56 ! [A: $tType,P3: ( list @ A ) > $o,Xs: list @ A] :
% 2.81/1.56 ( ( P3 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A] : ( P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.81/1.56 => ( ! [X2: A,Y2: A,Zs2: list @ A] :
% 2.81/1.56 ( ( P3 @ Zs2 )
% 2.81/1.56 => ( ( P3 @ ( cons @ A @ Y2 @ Zs2 ) )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Zs2 ) ) ) ) )
% 2.81/1.56 => ( P3 @ Xs ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_149_splice_Oinduct,axiom,
% 2.81/1.56 ! [A: $tType,P3: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.81/1.56 ( ! [X_1: list @ A] : ( P3 @ ( nil @ A ) @ X_1 )
% 2.81/1.56 => ( ! [X2: A,Xs2: list @ A,Ys: list @ A] :
% 2.81/1.56 ( ( P3 @ Ys @ Xs2 )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ Ys ) )
% 2.81/1.56 => ( P3 @ A0 @ A1 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_150_list__induct2_H,axiom,
% 2.81/1.56 ! [A: $tType,B2: $tType,P3: ( list @ A ) > ( list @ B2 ) > $o,Xs: list @ A,Ys2: list @ B2] :
% 2.81/1.56 ( ( P3 @ ( nil @ A ) @ ( nil @ B2 ) )
% 2.81/1.56 => ( ! [X2: A,Xs2: list @ A] : ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B2 ) )
% 2.81/1.56 => ( ! [Y2: B2,Ys: list @ B2] : ( P3 @ ( nil @ A ) @ ( cons @ B2 @ Y2 @ Ys ) )
% 2.81/1.56 => ( ! [X2: A,Xs2: list @ A,Y2: B2,Ys: list @ B2] :
% 2.81/1.56 ( ( P3 @ Xs2 @ Ys )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B2 @ Y2 @ Ys ) ) )
% 2.81/1.56 => ( P3 @ Xs @ Ys2 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_151_neq__Nil__conv,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A] :
% 2.81/1.56 ( ( Xs
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 = ( ? [Y4: A,Ys3: list @ A] :
% 2.81/1.56 ( Xs
% 2.81/1.56 = ( cons @ A @ Y4 @ Ys3 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_152_list_Oinducts,axiom,
% 2.81/1.56 ! [A: $tType,P3: ( list @ A ) > $o,List: list @ A] :
% 2.81/1.56 ( ( P3 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [X1: A,X23: list @ A] :
% 2.81/1.56 ( ( P3 @ X23 )
% 2.81/1.56 => ( P3 @ ( cons @ A @ X1 @ X23 ) ) )
% 2.81/1.56 => ( P3 @ List ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_153_list_Oexhaust,axiom,
% 2.81/1.56 ! [A: $tType,Y3: list @ A] :
% 2.81/1.56 ( ( Y3
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ~ ! [X213: A,X223: list @ A] :
% 2.81/1.56 ( Y3
% 2.81/1.56 != ( cons @ A @ X213 @ X223 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_154_list_OdiscI,axiom,
% 2.81/1.56 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.81/1.56 ( ( List
% 2.81/1.56 = ( cons @ A @ X21 @ X22 ) )
% 2.81/1.56 => ( List
% 2.81/1.56 != ( nil @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_155_list_Odistinct_I1_J,axiom,
% 2.81/1.56 ! [A: $tType,X21: A,X22: list @ A] :
% 2.81/1.56 ( ( nil @ A )
% 2.81/1.56 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_156_append__Cons,axiom,
% 2.81/1.56 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A] :
% 2.81/1.56 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys2 )
% 2.81/1.56 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_157_Cons__eq__appendI,axiom,
% 2.81/1.56 ! [A: $tType,X: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.81/1.56 ( ( ( cons @ A @ X @ Xs1 )
% 2.81/1.56 = Ys2 )
% 2.81/1.56 => ( ( Xs
% 2.81/1.56 = ( append @ A @ Xs1 @ Zs ) )
% 2.81/1.56 => ( ( cons @ A @ X @ Xs )
% 2.81/1.56 = ( append @ A @ Ys2 @ Zs ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_158_append_Oleft__neutral,axiom,
% 2.81/1.56 ! [A: $tType,A2: list @ A] :
% 2.81/1.56 ( ( append @ A @ ( nil @ A ) @ A2 )
% 2.81/1.56 = A2 ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_159_append__Nil,axiom,
% 2.81/1.56 ! [A: $tType,Ys2: list @ A] :
% 2.81/1.56 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 2.81/1.56 = Ys2 ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_160_eq__Nil__appendI,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.81/1.56 ( ( Xs = Ys2 )
% 2.81/1.56 => ( Xs
% 2.81/1.56 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_161_null__rec_I1_J,axiom,
% 2.81/1.56 ! [A: $tType,X: A,Xs: list @ A] :
% 2.81/1.56 ~ ( null @ A @ ( cons @ A @ X @ Xs ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_162_eq__Nil__null,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A] :
% 2.81/1.56 ( ( Xs
% 2.81/1.56 = ( nil @ A ) )
% 2.81/1.56 = ( null @ A @ Xs ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_163_null__rec_I2_J,axiom,
% 2.81/1.56 ! [B2: $tType] : ( null @ B2 @ ( nil @ B2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_164_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord893533164strict @ A )
% 2.81/1.56 => ! [A2: A,B: A,C: A] :
% 2.81/1.56 ( ( ord_less @ A @ A2 @ B )
% 2.81/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.81/1.56 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_165_mult__less__cancel__right__disj,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [A2: A,C: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) )
% 2.81/1.56 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.81/1.56 & ( ord_less @ A @ A2 @ B ) )
% 2.81/1.56 | ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.81/1.56 & ( ord_less @ A @ B @ A2 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_166_mult__strict__right__mono,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord20386208strict @ A )
% 2.81/1.56 => ! [A2: A,B: A,C: A] :
% 2.81/1.56 ( ( ord_less @ A @ A2 @ B )
% 2.81/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.81/1.56 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_167_mult__strict__right__mono__neg,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [B: A,A2: A,C: A] :
% 2.81/1.56 ( ( ord_less @ A @ B @ A2 )
% 2.81/1.56 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.81/1.56 => ( ord_less @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_168_mult__less__cancel__left__disj,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [C: A,A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) )
% 2.81/1.56 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.81/1.56 & ( ord_less @ A @ A2 @ B ) )
% 2.81/1.56 | ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.81/1.56 & ( ord_less @ A @ B @ A2 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_169_mult__strict__left__mono,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord20386208strict @ A )
% 2.81/1.56 => ! [A2: A,B: A,C: A] :
% 2.81/1.56 ( ( ord_less @ A @ A2 @ B )
% 2.81/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.81/1.56 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_170_mult__strict__left__mono__neg,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [B: A,A2: A,C: A] :
% 2.81/1.56 ( ( ord_less @ A @ B @ A2 )
% 2.81/1.56 => ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.81/1.56 => ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_171_mult__less__cancel__left__pos,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [C: A,A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ C )
% 2.81/1.56 => ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) )
% 2.81/1.56 = ( ord_less @ A @ A2 @ B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_172_mult__less__cancel__left__neg,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [C: A,A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ C @ ( zero_zero @ A ) )
% 2.81/1.56 => ( ( ord_less @ A @ ( times_times @ A @ C @ A2 ) @ ( times_times @ A @ C @ B ) )
% 2.81/1.56 = ( ord_less @ A @ B @ A2 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_173_zero__less__mult__pos2,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord20386208strict @ A )
% 2.81/1.56 => ! [B: A,A2: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ B @ A2 ) )
% 2.81/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_174_zero__less__mult__pos,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord20386208strict @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B ) )
% 2.81/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_175_zero__less__mult__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B ) )
% 2.81/1.56 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 & ( ord_less @ A @ ( zero_zero @ A ) @ B ) )
% 2.81/1.56 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.81/1.56 & ( ord_less @ A @ B @ ( zero_zero @ A ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_176_mult__pos__neg2,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord20386208strict @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 => ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
% 2.81/1.56 => ( ord_less @ A @ ( times_times @ A @ B @ A2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_177_mult__pos__pos,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord20386208strict @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B )
% 2.81/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_178_mult__pos__neg,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord20386208strict @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 => ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
% 2.81/1.56 => ( ord_less @ A @ ( times_times @ A @ A2 @ B ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_179_mult__neg__pos,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord20386208strict @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.81/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B )
% 2.81/1.56 => ( ord_less @ A @ ( times_times @ A @ A2 @ B ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_180_mult__less__0__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( times_times @ A @ A2 @ B ) @ ( zero_zero @ A ) )
% 2.81/1.56 = ( ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 2.81/1.56 & ( ord_less @ A @ B @ ( zero_zero @ A ) ) )
% 2.81/1.56 | ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.81/1.56 & ( ord_less @ A @ ( zero_zero @ A ) @ B ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_181_not__square__less__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_ring @ A )
% 2.81/1.56 => ! [A2: A] :
% 2.81/1.56 ~ ( ord_less @ A @ ( times_times @ A @ A2 @ A2 ) @ ( zero_zero @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_182_mult__neg__neg,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord581940658strict @ A )
% 2.81/1.56 => ! [A2: A,B: A] :
% 2.81/1.56 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 2.81/1.56 => ( ( ord_less @ A @ B @ ( zero_zero @ A ) )
% 2.81/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( times_times @ A @ A2 @ B ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_183_not__one__less__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord1659791738miring @ A )
% 2.81/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_184_zero__less__one,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero_less_one @ A )
% 2.81/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_185_less__numeral__extra_I1_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linord1659791738miring @ A )
% 2.81/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_186_less__1__mult,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_semidom @ A )
% 2.81/1.56 => ! [M: A,N: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ M )
% 2.81/1.56 => ( ( ord_less @ A @ ( one_one @ A ) @ N )
% 2.81/1.56 => ( ord_less @ A @ ( one_one @ A ) @ ( times_times @ A @ M @ N ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_187_zero__neq__neg__one,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_char_0 @ A )
% 2.81/1.56 => ( ( zero_zero @ A )
% 2.81/1.56 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_188_less__minus__one__simps_I2_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( one_one @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_189_less__minus__one__simps_I4_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_190_square__eq__1__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( ring_11004092258visors @ A )
% 2.81/1.56 => ! [X: A] :
% 2.81/1.56 ( ( ( times_times @ A @ X @ X )
% 2.81/1.56 = ( one_one @ A ) )
% 2.81/1.56 = ( ( X
% 2.81/1.56 = ( one_one @ A ) )
% 2.81/1.56 | ( X
% 2.81/1.56 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_191_rev__nonempty__induct,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A,P3: ( list @ A ) > $o] :
% 2.81/1.56 ( ( Xs
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A] : ( P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.81/1.56 => ( ! [X2: A,Xs2: list @ A] :
% 2.81/1.56 ( ( Xs2
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ( ( P3 @ Xs2 )
% 2.81/1.56 => ( P3 @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ) )
% 2.81/1.56 => ( P3 @ Xs ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_192_append__eq__Cons__conv,axiom,
% 2.81/1.56 ! [A: $tType,Ys2: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.81/1.56 ( ( ( append @ A @ Ys2 @ Zs )
% 2.81/1.56 = ( cons @ A @ X @ Xs ) )
% 2.81/1.56 = ( ( ( Ys2
% 2.81/1.56 = ( nil @ A ) )
% 2.81/1.56 & ( Zs
% 2.81/1.56 = ( cons @ A @ X @ Xs ) ) )
% 2.81/1.56 | ? [Ys4: list @ A] :
% 2.81/1.56 ( ( Ys2
% 2.81/1.56 = ( cons @ A @ X @ Ys4 ) )
% 2.81/1.56 & ( ( append @ A @ Ys4 @ Zs )
% 2.81/1.56 = Xs ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_193_Cons__eq__append__conv,axiom,
% 2.81/1.56 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 2.81/1.56 ( ( ( cons @ A @ X @ Xs )
% 2.81/1.56 = ( append @ A @ Ys2 @ Zs ) )
% 2.81/1.56 = ( ( ( Ys2
% 2.81/1.56 = ( nil @ A ) )
% 2.81/1.56 & ( ( cons @ A @ X @ Xs )
% 2.81/1.56 = Zs ) )
% 2.81/1.56 | ? [Ys4: list @ A] :
% 2.81/1.56 ( ( ( cons @ A @ X @ Ys4 )
% 2.81/1.56 = Ys2 )
% 2.81/1.56 & ( Xs
% 2.81/1.56 = ( append @ A @ Ys4 @ Zs ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_194_rev__exhaust,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A] :
% 2.81/1.56 ( ( Xs
% 2.81/1.56 != ( nil @ A ) )
% 2.81/1.56 => ~ ! [Ys: list @ A,Y2: A] :
% 2.81/1.56 ( Xs
% 2.81/1.56 != ( append @ A @ Ys @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_195_rev__induct,axiom,
% 2.81/1.56 ! [A: $tType,P3: ( list @ A ) > $o,Xs: list @ A] :
% 2.81/1.56 ( ( P3 @ ( nil @ A ) )
% 2.81/1.56 => ( ! [X2: A,Xs2: list @ A] :
% 2.81/1.56 ( ( P3 @ Xs2 )
% 2.81/1.56 => ( P3 @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) )
% 2.81/1.56 => ( P3 @ Xs ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_196_less__minus__one__simps_I1_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( zero_zero @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_197_less__minus__one__simps_I3_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_198_poly__cutoff__1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( comm_semiring_1 @ A )
% 2.81/1.56 => ! [N: nat] :
% 2.81/1.56 ( ( ( N
% 2.81/1.56 = ( zero_zero @ nat ) )
% 2.81/1.56 => ( ( poly_cutoff @ A @ N @ ( one_one @ ( poly @ A ) ) )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) )
% 2.81/1.56 & ( ( N
% 2.81/1.56 != ( zero_zero @ nat ) )
% 2.81/1.56 => ( ( poly_cutoff @ A @ N @ ( one_one @ ( poly @ A ) ) )
% 2.81/1.56 = ( one_one @ ( poly @ A ) ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_199_mult__less__iff1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ! [Z2: A,X: A,Y3: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ Z2 )
% 2.81/1.56 => ( ( ord_less @ A @ ( times_times @ A @ X @ Z2 ) @ ( times_times @ A @ Y3 @ Z2 ) )
% 2.81/1.56 = ( ord_less @ A @ X @ Y3 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_200_dbl__dec__simps_I2_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( neg_numeral @ A )
% 2.81/1.56 => ( ( neg_numeral_dbl_dec @ A @ ( zero_zero @ A ) )
% 2.81/1.56 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_201_nat__mult__less__cancel__disj,axiom,
% 2.81/1.56 ! [K: nat,M: nat,N: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.81/1.56 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.81/1.56 & ( ord_less @ nat @ M @ N ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_202_nat__0__less__mult__iff,axiom,
% 2.81/1.56 ! [M: nat,N: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ M @ N ) )
% 2.81/1.56 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.81/1.56 & ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_203_mult__less__cancel2,axiom,
% 2.81/1.56 ! [M: nat,K: nat,N: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) )
% 2.81/1.56 = ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.81/1.56 & ( ord_less @ nat @ M @ N ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_204_mult__cancel2,axiom,
% 2.81/1.56 ! [M: nat,K: nat,N: nat] :
% 2.81/1.56 ( ( ( times_times @ nat @ M @ K )
% 2.81/1.56 = ( times_times @ nat @ N @ K ) )
% 2.81/1.56 = ( ( M = N )
% 2.81/1.56 | ( K
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_205_neq0__conv,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ( ( N
% 2.81/1.56 != ( zero_zero @ nat ) )
% 2.81/1.56 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_206_less__nat__zero__code,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_207_bot__nat__0_Onot__eq__extremum,axiom,
% 2.81/1.56 ! [A2: nat] :
% 2.81/1.56 ( ( A2
% 2.81/1.56 != ( zero_zero @ nat ) )
% 2.81/1.56 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_208_mult__is__0,axiom,
% 2.81/1.56 ! [M: nat,N: nat] :
% 2.81/1.56 ( ( ( times_times @ nat @ M @ N )
% 2.81/1.56 = ( zero_zero @ nat ) )
% 2.81/1.56 = ( ( M
% 2.81/1.56 = ( zero_zero @ nat ) )
% 2.81/1.56 | ( N
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_209_mult__0__right,axiom,
% 2.81/1.56 ! [M: nat] :
% 2.81/1.56 ( ( times_times @ nat @ M @ ( zero_zero @ nat ) )
% 2.81/1.56 = ( zero_zero @ nat ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_210_mult__cancel1,axiom,
% 2.81/1.56 ! [K: nat,M: nat,N: nat] :
% 2.81/1.56 ( ( ( times_times @ nat @ K @ M )
% 2.81/1.56 = ( times_times @ nat @ K @ N ) )
% 2.81/1.56 = ( ( M = N )
% 2.81/1.56 | ( K
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_211_nat__1__eq__mult__iff,axiom,
% 2.81/1.56 ! [M: nat,N: nat] :
% 2.81/1.56 ( ( ( one_one @ nat )
% 2.81/1.56 = ( times_times @ nat @ M @ N ) )
% 2.81/1.56 = ( ( M
% 2.81/1.56 = ( one_one @ nat ) )
% 2.81/1.56 & ( N
% 2.81/1.56 = ( one_one @ nat ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_212_nat__mult__eq__1__iff,axiom,
% 2.81/1.56 ! [M: nat,N: nat] :
% 2.81/1.56 ( ( ( times_times @ nat @ M @ N )
% 2.81/1.56 = ( one_one @ nat ) )
% 2.81/1.56 = ( ( M
% 2.81/1.56 = ( one_one @ nat ) )
% 2.81/1.56 & ( N
% 2.81/1.56 = ( one_one @ nat ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_213_dbl__dec__simps_I3_J,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( neg_numeral @ A )
% 2.81/1.56 => ( ( neg_numeral_dbl_dec @ A @ ( one_one @ A ) )
% 2.81/1.56 = ( one_one @ A ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_214_poly__cutoff__0,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( zero @ A )
% 2.81/1.56 => ! [N: nat] :
% 2.81/1.56 ( ( poly_cutoff @ A @ N @ ( zero_zero @ ( poly @ A ) ) )
% 2.81/1.56 = ( zero_zero @ ( poly @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_215_less__one,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 2.81/1.56 = ( N
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_216_nat__mult__1,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ( ( times_times @ nat @ ( one_one @ nat ) @ N )
% 2.81/1.56 = N ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_217_nat__mult__1__right,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ( ( times_times @ nat @ N @ ( one_one @ nat ) )
% 2.81/1.56 = N ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_218_infinite__descent__measure,axiom,
% 2.81/1.56 ! [A: $tType,P3: A > $o,V2: A > nat,X: A] :
% 2.81/1.56 ( ! [X2: A] :
% 2.81/1.56 ( ~ ( P3 @ X2 )
% 2.81/1.56 => ? [Y5: A] :
% 2.81/1.56 ( ( ord_less @ nat @ ( V2 @ Y5 ) @ ( V2 @ X2 ) )
% 2.81/1.56 & ~ ( P3 @ Y5 ) ) )
% 2.81/1.56 => ( P3 @ X ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_219_linorder__neqE__nat,axiom,
% 2.81/1.56 ! [X: nat,Y3: nat] :
% 2.81/1.56 ( ( X != Y3 )
% 2.81/1.56 => ( ~ ( ord_less @ nat @ X @ Y3 )
% 2.81/1.56 => ( ord_less @ nat @ Y3 @ X ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_220_infinite__descent,axiom,
% 2.81/1.56 ! [P3: nat > $o,N: nat] :
% 2.81/1.56 ( ! [N2: nat] :
% 2.81/1.56 ( ~ ( P3 @ N2 )
% 2.81/1.56 => ? [M2: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ M2 @ N2 )
% 2.81/1.56 & ~ ( P3 @ M2 ) ) )
% 2.81/1.56 => ( P3 @ N ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_221_nat__less__induct,axiom,
% 2.81/1.56 ! [P3: nat > $o,N: nat] :
% 2.81/1.56 ( ! [N2: nat] :
% 2.81/1.56 ( ! [M2: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ M2 @ N2 )
% 2.81/1.56 => ( P3 @ M2 ) )
% 2.81/1.56 => ( P3 @ N2 ) )
% 2.81/1.56 => ( P3 @ N ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_222_less__irrefl__nat,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ~ ( ord_less @ nat @ N @ N ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_223_less__not__refl3,axiom,
% 2.81/1.56 ! [S: nat,T: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ S @ T )
% 2.81/1.56 => ( S != T ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_224_less__not__refl2,axiom,
% 2.81/1.56 ! [N: nat,M: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ N @ M )
% 2.81/1.56 => ( M != N ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_225_less__not__refl,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ~ ( ord_less @ nat @ N @ N ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_226_nat__neq__iff,axiom,
% 2.81/1.56 ! [M: nat,N: nat] :
% 2.81/1.56 ( ( M != N )
% 2.81/1.56 = ( ( ord_less @ nat @ M @ N )
% 2.81/1.56 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_227_measure__induct,axiom,
% 2.81/1.56 ! [B2: $tType,A: $tType] :
% 2.81/1.56 ( ( wellorder @ B2 )
% 2.81/1.56 => ! [F2: A > B2,P3: A > $o,A2: A] :
% 2.81/1.56 ( ! [X2: A] :
% 2.81/1.56 ( ! [Y5: A] :
% 2.81/1.56 ( ( ord_less @ B2 @ ( F2 @ Y5 ) @ ( F2 @ X2 ) )
% 2.81/1.56 => ( P3 @ Y5 ) )
% 2.81/1.56 => ( P3 @ X2 ) )
% 2.81/1.56 => ( P3 @ A2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_228_measure__induct__rule,axiom,
% 2.81/1.56 ! [B2: $tType,A: $tType] :
% 2.81/1.56 ( ( wellorder @ B2 )
% 2.81/1.56 => ! [F2: A > B2,P3: A > $o,A2: A] :
% 2.81/1.56 ( ! [X2: A] :
% 2.81/1.56 ( ! [Y5: A] :
% 2.81/1.56 ( ( ord_less @ B2 @ ( F2 @ Y5 ) @ ( F2 @ X2 ) )
% 2.81/1.56 => ( P3 @ Y5 ) )
% 2.81/1.56 => ( P3 @ X2 ) )
% 2.81/1.56 => ( P3 @ A2 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_229_gr0I,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ( ( N
% 2.81/1.56 != ( zero_zero @ nat ) )
% 2.81/1.56 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_230_not__gr0,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 2.81/1.56 = ( N
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_231_not__less0,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_232_less__zeroE,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_233_gr__implies__not0,axiom,
% 2.81/1.56 ! [M: nat,N: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ M @ N )
% 2.81/1.56 => ( N
% 2.81/1.56 != ( zero_zero @ nat ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_234_infinite__descent0,axiom,
% 2.81/1.56 ! [P3: nat > $o,N: nat] :
% 2.81/1.56 ( ( P3 @ ( zero_zero @ nat ) )
% 2.81/1.56 => ( ! [N2: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.81/1.56 => ( ~ ( P3 @ N2 )
% 2.81/1.56 => ? [M2: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ M2 @ N2 )
% 2.81/1.56 & ~ ( P3 @ M2 ) ) ) )
% 2.81/1.56 => ( P3 @ N ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_235_bot__nat__0_Oextremum__strict,axiom,
% 2.81/1.56 ! [A2: nat] :
% 2.81/1.56 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_236_infinite__descent0__measure,axiom,
% 2.81/1.56 ! [A: $tType,V2: A > nat,P3: A > $o,X: A] :
% 2.81/1.56 ( ! [X2: A] :
% 2.81/1.56 ( ( ( V2 @ X2 )
% 2.81/1.56 = ( zero_zero @ nat ) )
% 2.81/1.56 => ( P3 @ X2 ) )
% 2.81/1.56 => ( ! [X2: A] :
% 2.81/1.56 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X2 ) )
% 2.81/1.56 => ( ~ ( P3 @ X2 )
% 2.81/1.56 => ? [Y5: A] :
% 2.81/1.56 ( ( ord_less @ nat @ ( V2 @ Y5 ) @ ( V2 @ X2 ) )
% 2.81/1.56 & ~ ( P3 @ Y5 ) ) ) )
% 2.81/1.56 => ( P3 @ X ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_237_mult__less__mono1,axiom,
% 2.81/1.56 ! [I: nat,J: nat,K: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ I @ J )
% 2.81/1.56 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.81/1.56 => ( ord_less @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ K ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_238_mult__less__mono2,axiom,
% 2.81/1.56 ! [I: nat,J: nat,K: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ I @ J )
% 2.81/1.56 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.81/1.56 => ( ord_less @ nat @ ( times_times @ nat @ K @ I ) @ ( times_times @ nat @ K @ J ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_239_mult__0,axiom,
% 2.81/1.56 ! [N: nat] :
% 2.81/1.56 ( ( times_times @ nat @ ( zero_zero @ nat ) @ N )
% 2.81/1.56 = ( zero_zero @ nat ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_240_nat__mult__eq__cancel1,axiom,
% 2.81/1.56 ! [K: nat,M: nat,N: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.81/1.56 => ( ( ( times_times @ nat @ K @ M )
% 2.81/1.56 = ( times_times @ nat @ K @ N ) )
% 2.81/1.56 = ( M = N ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_241_nat__mult__less__cancel1,axiom,
% 2.81/1.56 ! [K: nat,M: nat,N: nat] :
% 2.81/1.56 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ K )
% 2.81/1.56 => ( ( ord_less @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) )
% 2.81/1.56 = ( ord_less @ nat @ M @ N ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_242_nat__mult__eq__cancel__disj,axiom,
% 2.81/1.56 ! [K: nat,M: nat,N: nat] :
% 2.81/1.56 ( ( ( times_times @ nat @ K @ M )
% 2.81/1.56 = ( times_times @ nat @ K @ N ) )
% 2.81/1.56 = ( ( K
% 2.81/1.56 = ( zero_zero @ nat ) )
% 2.81/1.56 | ( M = N ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_243_mult__eq__self__implies__10,axiom,
% 2.81/1.56 ! [M: nat,N: nat] :
% 2.81/1.56 ( ( M
% 2.81/1.56 = ( times_times @ nat @ M @ N ) )
% 2.81/1.56 => ( ( N
% 2.81/1.56 = ( one_one @ nat ) )
% 2.81/1.56 | ( M
% 2.81/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_244_n__lists__Nil,axiom,
% 2.81/1.56 ! [A: $tType,N: nat] :
% 2.81/1.56 ( ( ( N
% 2.81/1.56 = ( zero_zero @ nat ) )
% 2.81/1.56 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 2.81/1.56 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 2.81/1.56 & ( ( N
% 2.81/1.56 != ( zero_zero @ nat ) )
% 2.81/1.56 => ( ( n_lists @ A @ N @ ( nil @ A ) )
% 2.81/1.56 = ( nil @ ( list @ A ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_245_n__lists_Osimps_I1_J,axiom,
% 2.81/1.56 ! [A: $tType,Xs: list @ A] :
% 2.81/1.56 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 2.81/1.56 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_246_compl__eq__compl__iff,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( boolean_algebra @ A )
% 2.81/1.56 => ! [X: A,Y3: A] :
% 2.81/1.56 ( ( ( uminus_uminus @ A @ X )
% 2.81/1.56 = ( uminus_uminus @ A @ Y3 ) )
% 2.81/1.56 = ( X = Y3 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_247_double__compl,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( boolean_algebra @ A )
% 2.81/1.56 => ! [X: A] :
% 2.81/1.56 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 2.81/1.56 = X ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_248_uminus__apply,axiom,
% 2.81/1.56 ! [B2: $tType,A: $tType] :
% 2.81/1.56 ( ( uminus @ B2 )
% 2.81/1.56 => ( ( uminus_uminus @ ( A > B2 ) )
% 2.81/1.56 = ( ^ [A5: A > B2,X3: A] : ( uminus_uminus @ B2 @ ( A5 @ X3 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_249_fun__Compl__def,axiom,
% 2.81/1.56 ! [B2: $tType,A: $tType] :
% 2.81/1.56 ( ( uminus @ B2 )
% 2.81/1.56 => ( ( uminus_uminus @ ( A > B2 ) )
% 2.81/1.56 = ( ^ [A5: A > B2,X3: A] : ( uminus_uminus @ B2 @ ( A5 @ X3 ) ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_250_compl__less__swap1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( boolean_algebra @ A )
% 2.81/1.56 => ! [Y3: A,X: A] :
% 2.81/1.56 ( ( ord_less @ A @ Y3 @ ( uminus_uminus @ A @ X ) )
% 2.81/1.56 => ( ord_less @ A @ X @ ( uminus_uminus @ A @ Y3 ) ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(fact_251_compl__less__swap2,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( boolean_algebra @ A )
% 2.81/1.56 => ! [Y3: A,X: A] :
% 2.81/1.56 ( ( ord_less @ A @ ( uminus_uminus @ A @ Y3 ) @ X )
% 2.81/1.56 => ( ord_less @ A @ ( uminus_uminus @ A @ X ) @ Y3 ) ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__ring__1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( comm_ring_1 @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___HOL_Otype,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( type @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Oone,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( one @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Osgn,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( sgn @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Rings_Oidom,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( idom @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Rings_Oring,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( ring @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Oplus,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( plus @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Ozero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( zero @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Rings_Oring__1,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( ring_1 @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Ouminus,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( uminus @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Orderings_Oord,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( ord @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Nat_Oring__char__0,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( ring_char_0 @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Num_Oneg__numeral,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( neg_numeral @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__ring,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( comm_ring @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Rings_Omult__zero,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( mult_zero @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Ogroup__add,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( group_add @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Omonoid__add,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( monoid_add @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Omonoid__mult,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( monoid_mult @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Orderings_Olinorder,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( linorder @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Rings_Oidom__abs__sgn,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( idom_abs_sgn @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Rings_Ozero__neq__one,axiom,
% 2.81/1.56 ! [A: $tType] :
% 2.81/1.56 ( ( linordered_idom @ A )
% 2.81/1.56 => ( zero_neq_one @ A ) ) ).
% 2.81/1.56
% 2.81/1.56 thf(subcl_Rings_Olinordered__idom___Groups_Oab__group__add,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( ab_group_add @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Ozero__less__one,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( zero_less_one @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Groups_Osemigroup__mult,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( semigroup_mult @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__0,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( comm_semiring_0 @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Ocomm__semiring__1,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( comm_semiring_1 @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__ring,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( linordered_ring @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( comm_monoid_add @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__mult,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( comm_monoid_mult @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__mult,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( ab_semigroup_mult @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__semidom,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( linordered_semidom @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__group__add,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( ordered_ab_group_add @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__ring__strict,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( linord581940658strict @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Oring__1__no__zero__divisors,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( ring_11004092258visors @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Groups_Olinordered__ab__group__add,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( linord219039673up_add @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( semiri1193490041visors @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__semiring__strict,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( linord20386208strict @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__nonzero__semiring,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( linord1659791738miring @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Olinordered__comm__semiring__strict,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( linord893533164strict @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(subcl_Rings_Olinordered__idom___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 2.81/1.57 ! [A: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A )
% 2.81/1.57 => ( semiri1923998003cancel @ A ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring__1,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_ring_1 @ A6 )
% 2.81/1.57 => ( comm_ring_1 @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 2.81/1.57 ! [A6: $tType,A7: $tType] :
% 2.81/1.57 ( ( boolean_algebra @ A7 )
% 2.81/1.57 => ( boolean_algebra @ ( A6 > A7 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_fun___Orderings_Oord,axiom,
% 2.81/1.57 ! [A6: $tType,A7: $tType] :
% 2.81/1.57 ( ( ord @ A7 )
% 2.81/1.57 => ( ord @ ( A6 > A7 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_fun___Groups_Ouminus,axiom,
% 2.81/1.57 ! [A6: $tType,A7: $tType] :
% 2.81/1.57 ( ( uminus @ A7 )
% 2.81/1.57 => ( uminus @ ( A6 > A7 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors__cancel,axiom,
% 2.81/1.57 semiri1923998003cancel @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Olinordered__comm__semiring__strict,axiom,
% 2.81/1.57 linord893533164strict @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.81/1.57 canoni770627133id_add @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 2.81/1.57 linord1659791738miring @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Olinordered__semiring__strict,axiom,
% 2.81/1.57 linord20386208strict @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors,axiom,
% 2.81/1.57 semiri1193490041visors @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 2.81/1.57 linordered_semidom @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 2.81/1.57 ab_semigroup_mult @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 2.81/1.57 comm_monoid_mult @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 2.81/1.57 comm_monoid_add @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 2.81/1.57 comm_semiring_1 @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__0,axiom,
% 2.81/1.57 comm_semiring_0 @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 2.81/1.57 semigroup_mult @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Ozero__less__one,axiom,
% 2.81/1.57 zero_less_one @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.81/1.57 wellorder @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Ozero__neq__one,axiom,
% 2.81/1.57 zero_neq_one @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.81/1.57 linorder @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 2.81/1.57 monoid_mult @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 2.81/1.57 monoid_add @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Rings_Omult__zero,axiom,
% 2.81/1.57 mult_zero @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Orderings_Oord_1,axiom,
% 2.81/1.57 ord @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.81/1.57 zero @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Oplus,axiom,
% 2.81/1.57 plus @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.81/1.57 one @ nat ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_2,axiom,
% 2.81/1.57 boolean_algebra @ $o ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_HOL_Obool___Orderings_Olinorder_3,axiom,
% 2.81/1.57 linorder @ $o ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 2.81/1.57 ord @ $o ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_HOL_Obool___Groups_Ouminus_5,axiom,
% 2.81/1.57 uminus @ $o ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors__cancel_6,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( idom @ A6 )
% 2.81/1.57 => ( semiri1923998003cancel @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Olinordered__comm__semiring__strict_7,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linord893533164strict @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Olinordered__nonzero__semiring_8,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linord1659791738miring @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Olinordered__semiring__strict_9,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linord20386208strict @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors_10,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( ( comm_semiring_0 @ A6 )
% 2.81/1.57 & ( semiri1193490041visors @ A6 ) )
% 2.81/1.57 => ( semiri1193490041visors @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Olinordered__ab__group__add,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linord219039673up_add @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Oring__1__no__zero__divisors,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( idom @ A6 )
% 2.81/1.57 => ( ring_11004092258visors @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Olinordered__ring__strict,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linord581940658strict @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( ordered_ab_group_add @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Olinordered__semidom_11,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linordered_semidom @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Oab__semigroup__mult_12,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_0 @ A6 )
% 2.81/1.57 => ( ab_semigroup_mult @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__mult_13,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_1 @ A6 )
% 2.81/1.57 => ( comm_monoid_mult @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Ocomm__monoid__add_14,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_monoid_add @ A6 )
% 2.81/1.57 => ( comm_monoid_add @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Olinordered__ring,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linordered_ring @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Olinordered__idom,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linordered_idom @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_15,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_1 @ A6 )
% 2.81/1.57 => ( comm_semiring_1 @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_16,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_0 @ A6 )
% 2.81/1.57 => ( comm_semiring_0 @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Osemigroup__mult_17,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_0 @ A6 )
% 2.81/1.57 => ( semigroup_mult @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Ozero__less__one_18,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( zero_less_one @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Oab__group__add,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( ab_group_add @ A6 )
% 2.81/1.57 => ( ab_group_add @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Ozero__neq__one_19,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_1 @ A6 )
% 2.81/1.57 => ( zero_neq_one @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Oidom__abs__sgn,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( idom_abs_sgn @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Orderings_Olinorder_20,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( linorder @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Omonoid__mult_21,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_1 @ A6 )
% 2.81/1.57 => ( monoid_mult @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Omonoid__add_22,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_monoid_add @ A6 )
% 2.81/1.57 => ( monoid_add @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Ogroup__add,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( ab_group_add @ A6 )
% 2.81/1.57 => ( group_add @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Omult__zero_23,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_0 @ A6 )
% 2.81/1.57 => ( mult_zero @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Ocomm__ring,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_ring @ A6 )
% 2.81/1.57 => ( comm_ring @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Num_Oneg__numeral,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_ring_1 @ A6 )
% 2.81/1.57 => ( neg_numeral @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Nat_Oring__char__0,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( ( ring_char_0 @ A6 )
% 2.81/1.57 & ( comm_ring_1 @ A6 ) )
% 2.81/1.57 => ( ring_char_0 @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Orderings_Oord_24,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( ord @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Ouminus_25,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( ab_group_add @ A6 )
% 2.81/1.57 => ( uminus @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Oring__1,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_ring_1 @ A6 )
% 2.81/1.57 => ( ring_1 @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Ozero_26,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( zero @ A6 )
% 2.81/1.57 => ( zero @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Oplus_27,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_monoid_add @ A6 )
% 2.81/1.57 => ( plus @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Oring,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_ring @ A6 )
% 2.81/1.57 => ( ring @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Rings_Oidom,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( idom @ A6 )
% 2.81/1.57 => ( idom @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Osgn,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( linordered_idom @ A6 )
% 2.81/1.57 => ( sgn @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tcon_Polynomial_Opoly___Groups_Oone_28,axiom,
% 2.81/1.57 ! [A6: $tType] :
% 2.81/1.57 ( ( comm_semiring_1 @ A6 )
% 2.81/1.57 => ( one @ ( poly @ A6 ) ) ) ).
% 2.81/1.57
% 2.81/1.57 thf(tfree_0,hypothesis,
% 2.81/1.57 linordered_idom @ a ).
% 2.81/1.57
% 2.81/1.57 thf(conj_0,conjecture,
% 2.81/1.57 ( ( descar149487500hanges @ a @ ys )
% 2.81/1.57 = ( descar149487500hanges @ a @ ( coeffs @ a @ g ) ) ) ).
% 2.81/1.57 ------------------------
% 2.81/1.59 % (700)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/2Mi)
% 2.81/1.59 % (700)Instruction limit reached!
% 2.81/1.59 % (700)------------------------------
% 2.81/1.59 % (700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.59 % (700)Termination reason: Unknown
% 2.81/1.59 % (700)Termination phase: shuffling
% 2.81/1.59
% 2.81/1.59 % (700)Memory used [KB]: 1407
% 2.81/1.59 % (700)Time elapsed: 0.002 s
% 2.81/1.59 % (698)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_578 for (2999ds/4Mi)
% 2.81/1.59 % (700)Instructions burned: 2 (million)
% 2.81/1.59 % (700)------------------------------
% 2.81/1.59 % (700)------------------------------
% 2.81/1.59 % (703)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/18Mi)
% 2.81/1.60 % (698)Instruction limit reached!
% 2.81/1.60 % (698)------------------------------
% 2.81/1.60 % (698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.60 % (698)Termination reason: Unknown
% 2.81/1.60 % (698)Termination phase: shuffling
% 2.81/1.60
% 2.81/1.60 % (698)Memory used [KB]: 1535
% 2.81/1.60 % (698)Time elapsed: 0.003 s
% 2.81/1.60 % (698)Instructions burned: 6 (million)
% 2.81/1.60 % (698)------------------------------
% 2.81/1.60 % (698)------------------------------
% 2.91/1.60 % (701)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_578 for (2999ds/2Mi)
% 2.91/1.60 % (701)Instruction limit reached!
% 2.91/1.60 % (701)------------------------------
% 2.91/1.60 % (701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (701)Termination reason: Unknown
% 2.91/1.60 % (701)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (701)Memory used [KB]: 1407
% 2.91/1.60 % (701)Time elapsed: 0.004 s
% 2.91/1.60 % (701)Instructions burned: 2 (million)
% 2.91/1.60 % (701)------------------------------
% 2.91/1.60 % (701)------------------------------
% 2.91/1.60 % (703)Instruction limit reached!
% 2.91/1.60 % (703)------------------------------
% 2.91/1.60 % (703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (703)Termination reason: Unknown
% 2.91/1.60 % (703)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (703)Memory used [KB]: 1791
% 2.91/1.60 % (703)Time elapsed: 0.007 s
% 2.91/1.60 % (703)Instructions burned: 18 (million)
% 2.91/1.60 % (703)------------------------------
% 2.91/1.60 % (703)------------------------------
% 2.91/1.60 % (699)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_578 for (2999ds/27Mi)
% 2.91/1.60 % (697)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/183Mi)
% 2.91/1.60 % (702)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_578 for (2999ds/275Mi)
% 2.91/1.60 % (704)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/3Mi)
% 2.91/1.60 % (704)Instruction limit reached!
% 2.91/1.60 % (704)------------------------------
% 2.91/1.60 % (704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.60 % (704)Termination reason: Unknown
% 2.91/1.60 % (704)Termination phase: shuffling
% 2.91/1.60
% 2.91/1.60 % (704)Memory used [KB]: 1407
% 2.91/1.60 % (704)Time elapsed: 0.002 s
% 2.91/1.60 % (704)Instructions burned: 3 (million)
% 2.91/1.60 % (704)------------------------------
% 2.91/1.60 % (704)------------------------------
% 2.91/1.61 % (705)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_578 for (2999ds/37Mi)
% 2.91/1.61 % (707)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_578 for (2999ds/3Mi)
% 2.91/1.61 % (707)Instruction limit reached!
% 2.91/1.61 % (707)------------------------------
% 2.91/1.61 % (707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.61 % (707)Termination reason: Unknown
% 2.91/1.61 % (707)Termination phase: shuffling
% 2.91/1.61
% 2.91/1.61 % (707)Memory used [KB]: 1407
% 2.91/1.61 % (707)Time elapsed: 0.002 s
% 2.91/1.61 % (707)Instructions burned: 3 (million)
% 2.91/1.61 % (707)------------------------------
% 2.91/1.61 % (707)------------------------------
% 2.91/1.61 % (708)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_578 for (2999ds/1041Mi)
% 2.91/1.62 % (706)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_578 for (2999ds/15Mi)
% 2.91/1.62 % (699)Instruction limit reached!
% 2.91/1.62 % (699)------------------------------
% 2.91/1.62 % (699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.62 % (699)Termination reason: Unknown
% 2.91/1.62 % (699)Termination phase: Property scanning
% 2.91/1.62
% 2.91/1.62 % (699)Memory used [KB]: 1791
% 2.91/1.62 % (699)Time elapsed: 0.018 s
% 2.91/1.62 % (699)Instructions burned: 29 (million)
% 2.91/1.62 % (699)------------------------------
% 2.91/1.62 % (699)------------------------------
% 2.91/1.62 % (705)Instruction limit reached!
% 2.91/1.62 % (705)------------------------------
% 2.91/1.62 % (705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.62 % (705)Termination reason: Unknown
% 2.91/1.62 % (705)Termination phase: Property scanning
% 2.91/1.62
% 2.91/1.62 % (705)Memory used [KB]: 2174
% 2.91/1.62 % (705)Time elapsed: 0.013 s
% 2.91/1.62 % (705)Instructions burned: 38 (million)
% 2.91/1.62 % (705)------------------------------
% 2.91/1.62 % (705)------------------------------
% 2.91/1.62 % (709)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/7Mi)
% 2.91/1.62 % (706)Instruction limit reached!
% 2.91/1.62 % (706)------------------------------
% 2.91/1.62 % (706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.62 % (706)Termination reason: Unknown
% 2.91/1.62 % (706)Termination phase: shuffling
% 2.91/1.62
% 2.91/1.62 % (706)Memory used [KB]: 1791
% 2.91/1.62 % (706)Time elapsed: 0.010 s
% 2.91/1.62 % (706)Instructions burned: 15 (million)
% 2.91/1.62 % (706)------------------------------
% 2.91/1.62 % (706)------------------------------
% 2.91/1.62 % (709)Instruction limit reached!
% 2.91/1.62 % (709)------------------------------
% 2.91/1.62 % (709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.62 % (709)Termination reason: Unknown
% 2.91/1.62 % (709)Termination phase: shuffling
% 2.91/1.62
% 2.91/1.62 % (709)Memory used [KB]: 1663
% 2.91/1.62 % (709)Time elapsed: 0.004 s
% 2.91/1.62 % (709)Instructions burned: 10 (million)
% 2.91/1.62 % (709)------------------------------
% 2.91/1.62 % (709)------------------------------
% 2.91/1.63 % (712)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_578 for (2999ds/3Mi)
% 2.91/1.63 % (710)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/16Mi)
% 2.91/1.63 % (712)Instruction limit reached!
% 2.91/1.63 % (712)------------------------------
% 2.91/1.63 % (712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.63 % (712)Termination reason: Unknown
% 2.91/1.63 % (712)Termination phase: shuffling
% 2.91/1.63
% 2.91/1.63 % (712)Memory used [KB]: 1407
% 2.91/1.63 % (712)Time elapsed: 0.003 s
% 2.91/1.63 % (712)Instructions burned: 3 (million)
% 2.91/1.63 % (712)------------------------------
% 2.91/1.63 % (712)------------------------------
% 2.91/1.63 % (713)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_578 for (2999ds/3Mi)
% 2.91/1.63 % (714)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/7Mi)
% 2.91/1.63 % (713)Instruction limit reached!
% 2.91/1.63 % (713)------------------------------
% 2.91/1.63 % (713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.63 % (713)Termination reason: Unknown
% 2.91/1.63 % (713)Termination phase: shuffling
% 2.91/1.63
% 2.91/1.63 % (713)Memory used [KB]: 1407
% 2.91/1.63 % (713)Time elapsed: 0.002 s
% 2.91/1.63 % (713)Instructions burned: 3 (million)
% 2.91/1.63 % (713)------------------------------
% 2.91/1.63 % (713)------------------------------
% 2.91/1.63 % (710)Instruction limit reached!
% 2.91/1.63 % (710)------------------------------
% 2.91/1.63 % (710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.63 % (710)Termination reason: Unknown
% 2.91/1.63 % (710)Termination phase: shuffling
% 2.91/1.63
% 2.91/1.63 % (710)Memory used [KB]: 1791
% 2.91/1.63 % (710)Time elapsed: 0.008 s
% 2.91/1.63 % (710)Instructions burned: 17 (million)
% 2.91/1.63 % (710)------------------------------
% 2.91/1.63 % (710)------------------------------
% 2.91/1.64 % (714)Instruction limit reached!
% 2.91/1.64 % (714)------------------------------
% 2.91/1.64 % (714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.64 % (714)Termination reason: Unknown
% 2.91/1.64 % (714)Termination phase: shuffling
% 2.91/1.64
% 2.91/1.64 % (714)Memory used [KB]: 1535
% 2.91/1.64 % (714)Time elapsed: 0.004 s
% 2.91/1.64 % (714)Instructions burned: 7 (million)
% 2.91/1.64 % (714)------------------------------
% 2.91/1.64 % (714)------------------------------
% 2.91/1.64 % (715)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/3Mi)
% 2.91/1.64 % (715)Instruction limit reached!
% 2.91/1.64 % (715)------------------------------
% 2.91/1.64 % (715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.64 % (715)Termination reason: Unknown
% 2.91/1.64 % (715)Termination phase: shuffling
% 2.91/1.64
% 2.91/1.64 % (715)Memory used [KB]: 1407
% 2.91/1.64 % (715)Time elapsed: 0.003 s
% 2.91/1.64 % (715)Instructions burned: 4 (million)
% 2.91/1.64 % (715)------------------------------
% 2.91/1.64 % (715)------------------------------
% 2.91/1.64 % (716)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/4Mi)
% 2.91/1.64 % (719)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/18Mi)
% 2.91/1.64 % (716)Instruction limit reached!
% 2.91/1.64 % (716)------------------------------
% 2.91/1.64 % (716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.64 % (716)Termination reason: Unknown
% 2.91/1.64 % (716)Termination phase: shuffling
% 2.91/1.64
% 2.91/1.64 % (716)Memory used [KB]: 1535
% 2.91/1.64 % (716)Time elapsed: 0.003 s
% 2.91/1.64 % (716)Instructions burned: 7 (million)
% 2.91/1.64 % (716)------------------------------
% 2.91/1.64 % (716)------------------------------
% 2.91/1.64 % (720)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/710Mi)
% 2.91/1.65 % (702)Refutation not found, incomplete strategy
% 2.91/1.65 % (702)------------------------------
% 2.91/1.65 % (702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.65 % (702)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.65
% 2.91/1.65
% 2.91/1.65 % (702)Memory used [KB]: 6908
% 2.91/1.65 % (702)Time elapsed: 0.046 s
% 2.91/1.65 % (702)Instructions burned: 78 (million)
% 2.91/1.65 % (702)------------------------------
% 2.91/1.65 % (702)------------------------------
% 2.91/1.65 % (721)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/6Mi)
% 2.91/1.65 % (719)Instruction limit reached!
% 2.91/1.65 % (719)------------------------------
% 2.91/1.65 % (719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.65 % (719)Termination reason: Unknown
% 2.91/1.65 % (719)Termination phase: shuffling
% 2.91/1.65
% 2.91/1.65 % (719)Memory used [KB]: 1791
% 2.91/1.65 % (719)Time elapsed: 0.008 s
% 2.91/1.65 % (719)Instructions burned: 18 (million)
% 2.91/1.65 % (719)------------------------------
% 2.91/1.65 % (719)------------------------------
% 2.91/1.65 % (721)Instruction limit reached!
% 2.91/1.65 % (721)------------------------------
% 2.91/1.65 % (721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.65 % (721)Termination reason: Unknown
% 2.91/1.65 % (721)Termination phase: shuffling
% 2.91/1.65
% 2.91/1.65 % (721)Memory used [KB]: 1535
% 2.91/1.65 % (721)Time elapsed: 0.004 s
% 2.91/1.65 % (721)Instructions burned: 6 (million)
% 2.91/1.65 % (721)------------------------------
% 2.91/1.65 % (721)------------------------------
% 2.91/1.65 % (722)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_578 for (2999ds/902Mi)
% 2.91/1.66 % (723)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_578 for (2999ds/21Mi)
% 2.91/1.66 % (724)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/5Mi)
% 2.91/1.66 % (725)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_578 for (2999ds/6Mi)
% 2.91/1.66 % (724)Instruction limit reached!
% 2.91/1.66 % (724)------------------------------
% 2.91/1.66 % (724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.66 % (724)Termination reason: Unknown
% 2.91/1.66 % (724)Termination phase: shuffling
% 2.91/1.66
% 2.91/1.66 % (724)Memory used [KB]: 1535
% 2.91/1.66 % (724)Time elapsed: 0.004 s
% 2.91/1.66 % (724)Instructions burned: 7 (million)
% 2.91/1.66 % (724)------------------------------
% 2.91/1.66 % (724)------------------------------
% 2.91/1.66 % (723)Instruction limit reached!
% 2.91/1.66 % (723)------------------------------
% 2.91/1.66 % (723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.66 % (725)Instruction limit reached!
% 2.91/1.66 % (725)------------------------------
% 2.91/1.66 % (725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.66 % (723)Termination reason: Unknown
% 2.91/1.66 % (723)Termination phase: Property scanning
% 2.91/1.66
% 2.91/1.66 % (723)Memory used [KB]: 1918
% 2.91/1.66 % (723)Time elapsed: 0.009 s
% 2.91/1.66 % (723)Instructions burned: 22 (million)
% 2.91/1.66 % (723)------------------------------
% 2.91/1.66 % (723)------------------------------
% 2.91/1.66 % (725)Termination reason: Unknown
% 2.91/1.66 % (725)Termination phase: shuffling
% 2.91/1.66
% 2.91/1.66 % (725)Memory used [KB]: 1535
% 2.91/1.67 % (725)Time elapsed: 0.004 s
% 2.91/1.67 % (725)Instructions burned: 7 (million)
% 2.91/1.67 % (725)------------------------------
% 2.91/1.67 % (725)------------------------------
% 2.91/1.67 % (726)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/377Mi)
% 2.91/1.68 % (728)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_578 for (2999ds/19Mi)
% 2.91/1.68 % (727)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_578 for (2999ds/779Mi)
% 2.91/1.68 % (728)Instruction limit reached!
% 2.91/1.68 % (728)------------------------------
% 2.91/1.68 % (728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.68 % (728)Termination reason: Unknown
% 2.91/1.68 % (728)Termination phase: shuffling
% 2.91/1.68
% 2.91/1.68 % (728)Memory used [KB]: 1791
% 2.91/1.68 % (728)Time elapsed: 0.008 s
% 2.91/1.68 % (728)Instructions burned: 21 (million)
% 2.91/1.68 % (728)------------------------------
% 2.91/1.68 % (728)------------------------------
% 2.91/1.69 % (722)Refutation not found, incomplete strategy
% 2.91/1.69 % (722)------------------------------
% 2.91/1.69 % (722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.69 % (722)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.69
% 2.91/1.69
% 2.91/1.69 % (722)Memory used [KB]: 7291
% 2.91/1.69 % (722)Time elapsed: 0.033 s
% 2.91/1.69 % (722)Instructions burned: 105 (million)
% 2.91/1.69 % (722)------------------------------
% 2.91/1.69 % (722)------------------------------
% 2.91/1.69 % (729)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_578 for (2999ds/879Mi)
% 2.91/1.70 % (730)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_578 for (2998ds/17Mi)
% 2.91/1.70 % (730)Instruction limit reached!
% 2.91/1.70 % (730)------------------------------
% 2.91/1.70 % (730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.70 % (730)Termination reason: Unknown
% 2.91/1.70 % (730)Termination phase: shuffling
% 2.91/1.70
% 2.91/1.70 % (730)Memory used [KB]: 1791
% 2.91/1.70 % (730)Time elapsed: 0.007 s
% 2.91/1.70 % (730)Instructions burned: 18 (million)
% 2.91/1.70 % (730)------------------------------
% 2.91/1.70 % (730)------------------------------
% 2.91/1.71 % (697)Instruction limit reached!
% 2.91/1.71 % (697)------------------------------
% 2.91/1.71 % (697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.71 % (697)Termination reason: Unknown
% 2.91/1.71 % (697)Termination phase: Saturation
% 2.91/1.71
% 2.91/1.71 % (697)Memory used [KB]: 7419
% 2.91/1.71 % (697)Time elapsed: 0.107 s
% 2.91/1.71 % (697)Instructions burned: 184 (million)
% 2.91/1.71 % (697)------------------------------
% 2.91/1.71 % (697)------------------------------
% 2.91/1.71 % (731)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_578 for (2998ds/3Mi)
% 2.91/1.71 % (731)Instruction limit reached!
% 2.91/1.71 % (731)------------------------------
% 2.91/1.71 % (731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.71 % (731)Termination reason: Unknown
% 2.91/1.71 % (731)Termination phase: shuffling
% 2.91/1.71
% 2.91/1.71 % (731)Memory used [KB]: 1407
% 2.91/1.71 % (731)Time elapsed: 0.002 s
% 2.91/1.71 % (731)Instructions burned: 3 (million)
% 2.91/1.71 % (731)------------------------------
% 2.91/1.71 % (731)------------------------------
% 2.91/1.72 % (734)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_578 for (2998ds/127Mi)
% 2.91/1.72 % (732)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_578 for (2998ds/30Mi)
% 2.91/1.73 % (732)Instruction limit reached!
% 2.91/1.73 % (732)------------------------------
% 2.91/1.73 % (732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.73 % (732)Termination reason: Unknown
% 2.91/1.73 % (732)Termination phase: Preprocessing 1
% 2.91/1.73
% 2.91/1.73 % (732)Memory used [KB]: 1918
% 2.91/1.73 % (732)Time elapsed: 0.013 s
% 2.91/1.73 % (732)Instructions burned: 31 (million)
% 2.91/1.73 % (732)------------------------------
% 2.91/1.73 % (732)------------------------------
% 2.91/1.75 % (735)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_578 for (2998ds/100Mi)
% 2.91/1.76 % (734)Instruction limit reached!
% 2.91/1.76 % (734)------------------------------
% 2.91/1.76 % (734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.76 % (734)Termination reason: Unknown
% 2.91/1.76 % (734)Termination phase: Saturation
% 2.91/1.76
% 2.91/1.76 % (734)Memory used [KB]: 7164
% 2.91/1.76 % (734)Time elapsed: 0.063 s
% 2.91/1.76 % (734)Instructions burned: 130 (million)
% 2.91/1.76 % (734)------------------------------
% 2.91/1.76 % (734)------------------------------
% 2.91/1.77 % (736)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_578 for (2998ds/3Mi)
% 2.91/1.77 % (736)Instruction limit reached!
% 2.91/1.77 % (736)------------------------------
% 2.91/1.77 % (736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.77 % (736)Termination reason: Unknown
% 2.91/1.77 % (736)Termination phase: shuffling
% 2.91/1.77
% 2.91/1.77 % (736)Memory used [KB]: 1407
% 2.91/1.77 % (736)Time elapsed: 0.002 s
% 2.91/1.77 % (736)Instructions burned: 3 (million)
% 2.91/1.77 % (736)------------------------------
% 2.91/1.77 % (736)------------------------------
% 2.91/1.77 % (735)Instruction limit reached!
% 2.91/1.77 % (735)------------------------------
% 2.91/1.77 % (735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.77 % (735)Termination reason: Unknown
% 2.91/1.77 % (735)Termination phase: Property scanning
% 2.91/1.77
% 2.91/1.77 % (735)Memory used [KB]: 2302
% 2.91/1.77 % (735)Time elapsed: 0.030 s
% 2.91/1.77 % (735)Instructions burned: 100 (million)
% 2.91/1.77 % (735)------------------------------
% 2.91/1.77 % (735)------------------------------
% 2.91/1.78 % (737)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_578 for (2997ds/20Mi)
% 2.91/1.78 % (738)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_578 for (2997ds/86Mi)
% 2.91/1.79 % (737)Instruction limit reached!
% 2.91/1.79 % (737)------------------------------
% 2.91/1.79 % (737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.79 % (737)Termination reason: Unknown
% 2.91/1.79 % (737)Termination phase: Property scanning
% 2.91/1.79
% 2.91/1.79 % (737)Memory used [KB]: 1918
% 2.91/1.79 % (737)Time elapsed: 0.008 s
% 2.91/1.79 % (737)Instructions burned: 22 (million)
% 2.91/1.79 % (737)------------------------------
% 2.91/1.79 % (737)------------------------------
% 2.91/1.80 % (739)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_578 for (2997ds/107Mi)
% 2.91/1.80 % (726)Instruction limit reached!
% 2.91/1.80 % (726)------------------------------
% 2.91/1.80 % (726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.80 % (726)Termination reason: Unknown
% 2.91/1.80 % (726)Termination phase: Saturation
% 2.91/1.80
% 2.91/1.80 % (726)Memory used [KB]: 8315
% 2.91/1.80 % (726)Time elapsed: 0.152 s
% 2.91/1.80 % (726)Instructions burned: 377 (million)
% 2.91/1.80 % (726)------------------------------
% 2.91/1.80 % (726)------------------------------
% 2.91/1.81 % (738)Instruction limit reached!
% 2.91/1.81 % (738)------------------------------
% 2.91/1.81 % (738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.81 % (738)Termination reason: Unknown
% 2.91/1.81 % (738)Termination phase: Saturation
% 2.91/1.81
% 2.91/1.81 % (738)Memory used [KB]: 6908
% 2.91/1.81 % (738)Time elapsed: 0.029 s
% 2.91/1.81 % (738)Instructions burned: 86 (million)
% 2.91/1.81 % (738)------------------------------
% 2.91/1.81 % (738)------------------------------
% 2.91/1.81 % (740)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_578 for (2997ds/39Mi)
% 2.91/1.82 % (741)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_578 for (2997ds/448Mi)
% 2.91/1.83 % (740)Instruction limit reached!
% 2.91/1.83 % (740)------------------------------
% 2.91/1.83 % (740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.83 % (740)Termination reason: Unknown
% 2.91/1.83 % (740)Termination phase: Property scanning
% 2.91/1.83
% 2.91/1.83 % (740)Memory used [KB]: 2174
% 2.91/1.83 % (740)Time elapsed: 0.013 s
% 2.91/1.83 % (740)Instructions burned: 41 (million)
% 2.91/1.83 % (740)------------------------------
% 2.91/1.83 % (740)------------------------------
% 2.91/1.83 % (739)Instruction limit reached!
% 2.91/1.83 % (739)------------------------------
% 2.91/1.83 % (739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.83 % (739)Termination reason: Unknown
% 2.91/1.83 % (739)Termination phase: Saturation
% 2.91/1.83
% 2.91/1.83 % (739)Memory used [KB]: 6908
% 2.91/1.83 % (739)Time elapsed: 0.033 s
% 2.91/1.83 % (739)Instructions burned: 107 (million)
% 2.91/1.83 % (739)------------------------------
% 2.91/1.83 % (739)------------------------------
% 2.91/1.84 % (742)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_578 for (2997ds/46Mi)
% 2.91/1.84 % (745)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_578 for (2997ds/98Mi)
% 2.91/1.85 % (742)Instruction limit reached!
% 2.91/1.85 % (742)------------------------------
% 2.91/1.85 % (742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.85 % (742)Termination reason: Unknown
% 2.91/1.85 % (742)Termination phase: Property scanning
% 2.91/1.85
% 2.91/1.85 % (742)Memory used [KB]: 2174
% 2.91/1.85 % (742)Time elapsed: 0.018 s
% 2.91/1.85 % (742)Instructions burned: 48 (million)
% 2.91/1.85 % (742)------------------------------
% 2.91/1.85 % (742)------------------------------
% 2.91/1.86 % (746)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_578 for (2997ds/507Mi)
% 2.91/1.86 % (745)Instruction limit reached!
% 2.91/1.86 % (745)------------------------------
% 2.91/1.86 % (745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.86 % (745)Termination reason: Unknown
% 2.91/1.86 % (745)Termination phase: Property scanning
% 2.91/1.86
% 2.91/1.86 % (745)Memory used [KB]: 2302
% 2.91/1.86 % (745)Time elapsed: 0.027 s
% 2.91/1.86 % (745)Instructions burned: 98 (million)
% 2.91/1.86 % (745)------------------------------
% 2.91/1.86 % (745)------------------------------
% 2.91/1.87 % (720)Instruction limit reached!
% 2.91/1.87 % (720)------------------------------
% 2.91/1.87 % (720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.87 % (720)Termination reason: Unknown
% 2.91/1.87 % (720)Termination phase: Saturation
% 2.91/1.87
% 2.91/1.87 % (720)Memory used [KB]: 8315
% 2.91/1.87 % (720)Time elapsed: 0.222 s
% 2.91/1.87 % (720)Instructions burned: 710 (million)
% 2.91/1.87 % (720)------------------------------
% 2.91/1.87 % (720)------------------------------
% 2.91/1.87 % (747)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_578 for (2997ds/149Mi)
% 2.91/1.88 % (748)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_578 for (2997ds/39Mi)
% 2.91/1.89 % (748)Instruction limit reached!
% 2.91/1.89 % (748)------------------------------
% 2.91/1.89 % (748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.89 % (748)Termination reason: Unknown
% 2.91/1.89 % (748)Termination phase: Preprocessing 3
% 2.91/1.89
% 2.91/1.89 % (748)Memory used [KB]: 2174
% 2.91/1.89 % (748)Time elapsed: 0.014 s
% 2.91/1.89 % (748)Instructions burned: 41 (million)
% 2.91/1.89 % (748)------------------------------
% 2.91/1.89 % (748)------------------------------
% 2.91/1.90 % (749)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_578 for (2996ds/6Mi)
% 2.91/1.90 % (749)Instruction limit reached!
% 2.91/1.90 % (749)------------------------------
% 2.91/1.90 % (749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.90 % (749)Termination reason: Unknown
% 2.91/1.90 % (749)Termination phase: shuffling
% 2.91/1.90
% 2.91/1.90 % (749)Memory used [KB]: 1535
% 2.91/1.90 % (749)Time elapsed: 0.003 s
% 2.91/1.90 % (749)Instructions burned: 6 (million)
% 2.91/1.90 % (749)------------------------------
% 2.91/1.90 % (749)------------------------------
% 2.91/1.90 % (746)Refutation not found, incomplete strategy
% 2.91/1.90 % (746)------------------------------
% 2.91/1.90 % (746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.90 % (746)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.90
% 2.91/1.90
% 2.91/1.90 % (746)Memory used [KB]: 7547
% 2.91/1.90 % (746)Time elapsed: 0.039 s
% 2.91/1.90 % (746)Instructions burned: 117 (million)
% 2.91/1.90 % (746)------------------------------
% 2.91/1.90 % (746)------------------------------
% 2.91/1.91 % (751)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_578 for (2996ds/1087Mi)
% 2.91/1.91 % (752)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_578 for (2996ds/47Mi)
% 2.91/1.92 % (747)Instruction limit reached!
% 2.91/1.92 % (747)------------------------------
% 2.91/1.92 % (747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.92 % (747)Termination reason: Unknown
% 2.91/1.92 % (747)Termination phase: Saturation
% 2.91/1.92
% 2.91/1.92 % (747)Memory used [KB]: 7291
% 2.91/1.92 % (747)Time elapsed: 0.047 s
% 2.91/1.92 % (747)Instructions burned: 149 (million)
% 2.91/1.92 % (747)------------------------------
% 2.91/1.92 % (747)------------------------------
% 2.91/1.92 % (727)Instruction limit reached!
% 2.91/1.92 % (727)------------------------------
% 2.91/1.92 % (727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.92 % (727)Termination reason: Unknown
% 2.91/1.92 % (727)Termination phase: Saturation
% 2.91/1.92
% 2.91/1.92 % (727)Memory used [KB]: 8315
% 2.91/1.92 % (727)Time elapsed: 0.272 s
% 2.91/1.92 % (727)Instructions burned: 779 (million)
% 2.91/1.92 % (727)------------------------------
% 2.91/1.92 % (727)------------------------------
% 2.91/1.93 % (708)Instruction limit reached!
% 2.91/1.93 % (708)------------------------------
% 2.91/1.93 % (708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.93 % (708)Termination reason: Unknown
% 2.91/1.93 % (708)Termination phase: Saturation
% 2.91/1.93
% 2.91/1.93 % (708)Memory used [KB]: 9083
% 2.91/1.93 % (708)Time elapsed: 0.314 s
% 2.91/1.93 % (708)Instructions burned: 1042 (million)
% 2.91/1.93 % (708)------------------------------
% 2.91/1.93 % (708)------------------------------
% 2.91/1.93 % (752)Instruction limit reached!
% 2.91/1.93 % (752)------------------------------
% 2.91/1.93 % (752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.93 % (752)Termination reason: Unknown
% 2.91/1.93 % (752)Termination phase: Property scanning
% 2.91/1.93
% 2.91/1.93 % (752)Memory used [KB]: 2302
% 2.91/1.93 % (752)Time elapsed: 0.018 s
% 2.91/1.93 % (752)Instructions burned: 49 (million)
% 2.91/1.93 % (752)------------------------------
% 2.91/1.93 % (752)------------------------------
% 2.91/1.93 % (753)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_578 for (2996ds/44Mi)
% 2.91/1.93 % (755)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_578 for (2996ds/432Mi)
% 2.91/1.94 % (756)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_578 for (2996ds/62Mi)
% 2.91/1.94 % (757)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_578 for (2996ds/31Mi)
% 2.91/1.94 % (753)Instruction limit reached!
% 2.91/1.94 % (753)------------------------------
% 2.91/1.94 % (753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.94 % (753)Termination reason: Unknown
% 2.91/1.94 % (753)Termination phase: Property scanning
% 2.91/1.94
% 2.91/1.94 % (753)Memory used [KB]: 2174
% 2.91/1.94 % (753)Time elapsed: 0.013 s
% 2.91/1.94 % (753)Instructions burned: 44 (million)
% 2.91/1.94 % (753)------------------------------
% 2.91/1.94 % (753)------------------------------
% 2.91/1.95 % (757)Instruction limit reached!
% 2.91/1.95 % (757)------------------------------
% 2.91/1.95 % (757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.95 % (757)Termination reason: Unknown
% 2.91/1.95 % (757)Termination phase: Preprocessing 1
% 2.91/1.95
% 2.91/1.95 % (757)Memory used [KB]: 1791
% 2.91/1.95 % (757)Time elapsed: 0.012 s
% 2.91/1.95 % (757)Instructions burned: 31 (million)
% 2.91/1.95 % (757)------------------------------
% 2.91/1.95 % (757)------------------------------
% 2.91/1.95 % (758)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_578 for (2996ds/96Mi)
% 2.91/1.95 % (756)Instruction limit reached!
% 2.91/1.95 % (756)------------------------------
% 2.91/1.95 % (756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.95 % (756)Termination reason: Unknown
% 2.91/1.95 % (756)Termination phase: Unused predicate definition removal
% 2.91/1.95
% 2.91/1.95 % (756)Memory used [KB]: 2302
% 2.91/1.95 % (756)Time elapsed: 0.018 s
% 2.91/1.95 % (756)Instructions burned: 64 (million)
% 2.91/1.95 % (756)------------------------------
% 2.91/1.95 % (756)------------------------------
% 2.91/1.96 % (759)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_578 for (2996ds/453Mi)
% 2.91/1.96 % (760)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_578 for (2996ds/71Mi)
% 2.91/1.97 % (741)Instruction limit reached!
% 2.91/1.97 % (741)------------------------------
% 2.91/1.97 % (741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.97 % (741)Termination reason: Unknown
% 2.91/1.97 % (741)Termination phase: Saturation
% 2.91/1.97
% 2.91/1.97 % (741)Memory used [KB]: 8315
% 2.91/1.97 % (741)Time elapsed: 0.150 s
% 2.91/1.97 % (741)Instructions burned: 448 (million)
% 2.91/1.97 % (741)------------------------------
% 2.91/1.97 % (741)------------------------------
% 2.91/1.98 % (758)Instruction limit reached!
% 2.91/1.98 % (758)------------------------------
% 2.91/1.98 % (758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.98 % (758)Termination reason: Unknown
% 2.91/1.98 % (758)Termination phase: Saturation
% 2.91/1.98
% 2.91/1.98 % (758)Memory used [KB]: 6908
% 2.91/1.98 % (758)Time elapsed: 0.029 s
% 2.91/1.98 % (758)Instructions burned: 97 (million)
% 2.91/1.98 % (758)------------------------------
% 2.91/1.98 % (758)------------------------------
% 2.91/1.98 % (729)Instruction limit reached!
% 2.91/1.98 % (729)------------------------------
% 2.91/1.98 % (729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.98 % (729)Termination reason: Unknown
% 2.91/1.98 % (729)Termination phase: Saturation
% 2.91/1.98
% 2.91/1.98 % (729)Memory used [KB]: 8955
% 2.91/1.98 % (729)Time elapsed: 0.313 s
% 2.91/1.98 % (729)Instructions burned: 880 (million)
% 2.91/1.98 % (729)------------------------------
% 2.91/1.98 % (729)------------------------------
% 2.91/1.98 % (761)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_578 for (2996ds/83Mi)
% 2.91/1.98 % (760)Instruction limit reached!
% 2.91/1.98 % (760)------------------------------
% 2.91/1.98 % (760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.98 % (760)Termination reason: Unknown
% 2.91/1.98 % (760)Termination phase: Property scanning
% 2.91/1.98
% 2.91/1.98 % (760)Memory used [KB]: 2302
% 2.91/1.98 % (760)Time elapsed: 0.022 s
% 2.91/1.98 % (760)Instructions burned: 72 (million)
% 2.91/1.98 % (760)------------------------------
% 2.91/1.98 % (760)------------------------------
% 2.91/1.99 % (762)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_578 for (2996ds/11Mi)
% 2.91/1.99 % (765)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_578 for (2995ds/41Mi)
% 2.91/1.99 % (762)Instruction limit reached!
% 2.91/1.99 % (762)------------------------------
% 2.91/1.99 % (762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/1.99 % (762)Termination reason: Unknown
% 2.91/1.99 % (762)Termination phase: shuffling
% 2.91/1.99
% 2.91/1.99 % (762)Memory used [KB]: 1663
% 2.91/1.99 % (762)Time elapsed: 0.004 s
% 2.91/1.99 % (762)Instructions burned: 11 (million)
% 2.91/1.99 % (762)------------------------------
% 2.91/1.99 % (762)------------------------------
% 2.91/1.99 % (766)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_578 for (2995ds/6Mi)
% 2.91/2.00 % (766)Instruction limit reached!
% 2.91/2.00 % (766)------------------------------
% 2.91/2.00 % (766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/2.00 % (766)Termination reason: Unknown
% 2.91/2.00 % (766)Termination phase: shuffling
% 2.91/2.00
% 2.91/2.00 % (766)Memory used [KB]: 1535
% 2.91/2.00 % (766)Time elapsed: 0.003 s
% 2.91/2.00 % (766)Instructions burned: 6 (million)
% 2.91/2.00 % (766)------------------------------
% 2.91/2.00 % (766)------------------------------
% 2.91/2.00 % (767)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_578 for (2995ds/150Mi)
% 2.91/2.00 % (765)Instruction limit reached!
% 2.91/2.00 % (765)------------------------------
% 2.91/2.00 % (765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/2.00 % (765)Termination reason: Unknown
% 2.91/2.00 % (765)Termination phase: Property scanning
% 2.91/2.00
% 2.91/2.00 % (765)Memory used [KB]: 2174
% 2.91/2.00 % (765)Time elapsed: 0.012 s
% 2.91/2.00 % (765)Instructions burned: 41 (million)
% 2.91/2.00 % (765)------------------------------
% 2.91/2.00 % (765)------------------------------
% 2.91/2.00 % (768)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_578 for (2995ds/343Mi)
% 2.91/2.01 % (761)Instruction limit reached!
% 2.91/2.01 % (761)------------------------------
% 2.91/2.01 % (761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.91/2.01 % (761)Termination reason: Unknown
% 2.91/2.01 % (761)Termination phase: Saturation
% 2.91/2.01
% 2.91/2.01 % (761)Memory used [KB]: 6780
% 2.91/2.01 % (761)Time elapsed: 0.029 s
% 2.91/2.01 % (761)Instructions burned: 83 (million)
% 2.91/2.01 % (761)------------------------------
% 2.91/2.01 % (761)------------------------------
% 5.81/2.02 % (770)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_578 for (2995ds/253Mi)
% 5.81/2.02 % (769)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_578 for (2995ds/109Mi)
% 5.81/2.05 % (767)Instruction limit reached!
% 5.81/2.05 % (767)------------------------------
% 5.81/2.05 % (767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.05 % (767)Termination reason: Unknown
% 5.81/2.05 % (767)Termination phase: Saturation
% 5.81/2.05
% 5.81/2.05 % (767)Memory used [KB]: 7291
% 5.81/2.05 % (767)Time elapsed: 0.048 s
% 5.81/2.05 % (767)Instructions burned: 150 (million)
% 5.81/2.05 % (767)------------------------------
% 5.81/2.05 % (767)------------------------------
% 5.81/2.05 % (769)Instruction limit reached!
% 5.81/2.05 % (769)------------------------------
% 5.81/2.05 % (769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.05 % (769)Termination reason: Unknown
% 5.81/2.05 % (769)Termination phase: Saturation
% 5.81/2.05
% 5.81/2.05 % (769)Memory used [KB]: 7036
% 5.81/2.05 % (769)Time elapsed: 0.034 s
% 5.81/2.05 % (769)Instructions burned: 111 (million)
% 5.81/2.05 % (769)------------------------------
% 5.81/2.05 % (769)------------------------------
% 5.81/2.06 % (771)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_578 for (2995ds/140Mi)
% 5.81/2.06 % (772)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_578 for (2995ds/614Mi)
% 5.81/2.07 % (755)Instruction limit reached!
% 5.81/2.07 % (755)------------------------------
% 5.81/2.07 % (755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.07 % (755)Termination reason: Unknown
% 5.81/2.07 % (755)Termination phase: Saturation
% 5.81/2.07
% 5.81/2.07 % (755)Memory used [KB]: 3965
% 5.81/2.07 % (755)Time elapsed: 0.134 s
% 5.81/2.07 % (755)Instructions burned: 434 (million)
% 5.81/2.07 % (755)------------------------------
% 5.81/2.07 % (755)------------------------------
% 5.81/2.08 % (773)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_578 for (2995ds/202Mi)
% 5.81/2.09 % (759)Instruction limit reached!
% 5.81/2.09 % (759)------------------------------
% 5.81/2.09 % (759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.09 % (759)Termination reason: Unknown
% 5.81/2.09 % (759)Termination phase: Saturation
% 5.81/2.09
% 5.81/2.09 % (759)Memory used [KB]: 7803
% 5.81/2.09 % (759)Time elapsed: 0.133 s
% 5.81/2.09 % (759)Instructions burned: 455 (million)
% 5.81/2.09 % (759)------------------------------
% 5.81/2.09 % (759)------------------------------
% 5.81/2.10 % (774)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_578 for (2994ds/339Mi)
% 5.81/2.10 % (771)Instruction limit reached!
% 5.81/2.10 % (771)------------------------------
% 5.81/2.10 % (771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.10 % (771)Termination reason: Unknown
% 5.81/2.10 % (771)Termination phase: Saturation
% 5.81/2.10
% 5.81/2.10 % (771)Memory used [KB]: 7164
% 5.81/2.10 % (771)Time elapsed: 0.046 s
% 5.81/2.10 % (771)Instructions burned: 140 (million)
% 5.81/2.10 % (771)------------------------------
% 5.81/2.10 % (771)------------------------------
% 5.81/2.10 % (770)Instruction limit reached!
% 5.81/2.10 % (770)------------------------------
% 5.81/2.10 % (770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.10 % (770)Termination reason: Unknown
% 5.81/2.10 % (770)Termination phase: Saturation
% 5.81/2.10
% 5.81/2.10 % (770)Memory used [KB]: 7803
% 5.81/2.10 % (770)Time elapsed: 0.085 s
% 5.81/2.10 % (770)Instructions burned: 254 (million)
% 5.81/2.10 % (770)------------------------------
% 5.81/2.10 % (770)------------------------------
% 5.81/2.10 % (773)Refutation not found, incomplete strategy
% 5.81/2.10 % (773)------------------------------
% 5.81/2.10 % (773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.10 % (773)Termination reason: Refutation not found, incomplete strategy
% 5.81/2.10
% 5.81/2.10
% 5.81/2.10 % (773)Memory used [KB]: 7036
% 5.81/2.10 % (773)Time elapsed: 0.047 s
% 5.81/2.10 % (773)Instructions burned: 75 (million)
% 5.81/2.10 % (773)------------------------------
% 5.81/2.10 % (773)------------------------------
% 5.81/2.11 % (775)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_578 for (2994ds/283Mi)
% 6.46/2.11 % (768)Instruction limit reached!
% 6.46/2.11 % (768)------------------------------
% 6.46/2.11 % (768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.11 % (768)Termination reason: Unknown
% 6.46/2.11 % (768)Termination phase: Saturation
% 6.46/2.11
% 6.46/2.11 % (768)Memory used [KB]: 7803
% 6.46/2.11 % (768)Time elapsed: 0.109 s
% 6.46/2.11 % (768)Instructions burned: 343 (million)
% 6.46/2.11 % (768)------------------------------
% 6.46/2.11 % (768)------------------------------
% 6.46/2.11 % (776)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_578 for (2994ds/134Mi)
% 6.46/2.11 % (777)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_578 for (2994ds/298Mi)
% 6.46/2.12 % (778)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_578 for (2994ds/192Mi)
% 6.46/2.15 % (776)Instruction limit reached!
% 6.46/2.15 % (776)------------------------------
% 6.46/2.15 % (776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.15 % (776)Termination reason: Unknown
% 6.46/2.15 % (776)Termination phase: Saturation
% 6.46/2.15
% 6.46/2.15 % (776)Memory used [KB]: 7164
% 6.46/2.15 % (776)Time elapsed: 0.066 s
% 6.46/2.15 % (776)Instructions burned: 135 (million)
% 6.46/2.15 % (776)------------------------------
% 6.46/2.15 % (776)------------------------------
% 6.46/2.16 % (779)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_578 for (2994ds/258Mi)
% 6.46/2.18 % (778)Instruction limit reached!
% 6.46/2.18 % (778)------------------------------
% 6.46/2.18 % (778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.46/2.18 % (778)Termination reason: Unknown
% 6.46/2.18 % (778)Termination phase: Saturation
% 6.46/2.18
% 6.46/2.18 % (778)Memory used [KB]: 8059
% 6.46/2.18 % (778)Time elapsed: 0.060 s
% 6.46/2.18 % (778)Instructions burned: 193 (million)
% 6.46/2.18 % (778)------------------------------
% 6.46/2.18 % (778)------------------------------
% 6.46/2.19 % (781)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_578 for (2993ds/90Mi)
% 6.68/2.20 % (774)Instruction limit reached!
% 6.68/2.20 % (774)------------------------------
% 6.68/2.20 % (774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.20 % (774)Termination reason: Unknown
% 6.68/2.20 % (774)Termination phase: Saturation
% 6.68/2.20
% 6.68/2.20 % (774)Memory used [KB]: 7803
% 6.68/2.20 % (774)Time elapsed: 0.098 s
% 6.68/2.20 % (774)Instructions burned: 339 (million)
% 6.68/2.20 % (774)------------------------------
% 6.68/2.20 % (774)------------------------------
% 6.68/2.20 % (775)Instruction limit reached!
% 6.68/2.20 % (775)------------------------------
% 6.68/2.20 % (775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.20 % (775)Termination reason: Unknown
% 6.68/2.20 % (775)Termination phase: Saturation
% 6.68/2.20
% 6.68/2.20 % (775)Memory used [KB]: 7547
% 6.68/2.20 % (775)Time elapsed: 0.111 s
% 6.68/2.20 % (775)Instructions burned: 283 (million)
% 6.68/2.20 % (775)------------------------------
% 6.68/2.20 % (775)------------------------------
% 6.68/2.20 % (777)Instruction limit reached!
% 6.68/2.20 % (777)------------------------------
% 6.68/2.20 % (777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.20 % (777)Termination reason: Unknown
% 6.68/2.20 % (777)Termination phase: Saturation
% 6.68/2.20
% 6.68/2.20 % (777)Memory used [KB]: 8059
% 6.68/2.20 % (777)Time elapsed: 0.085 s
% 6.68/2.20 % (777)Instructions burned: 300 (million)
% 6.68/2.20 % (777)------------------------------
% 6.68/2.20 % (777)------------------------------
% 6.68/2.21 % (782)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_578 for (2993ds/231Mi)
% 6.68/2.21 % (783)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_578 for (2993ds/458Mi)
% 6.68/2.21 % (784)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_578 for (2993ds/31Mi)
% 6.68/2.22 % (781)Instruction limit reached!
% 6.68/2.22 % (781)------------------------------
% 6.68/2.22 % (781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.22 % (781)Termination reason: Unknown
% 6.68/2.22 % (781)Termination phase: Saturation
% 6.68/2.22
% 6.68/2.22 % (784)Instruction limit reached!
% 6.68/2.22 % (784)------------------------------
% 6.68/2.22 % (784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.22 % (781)Memory used [KB]: 6908
% 6.68/2.22 % (781)Time elapsed: 0.028 s
% 6.68/2.22 % (781)Instructions burned: 92 (million)
% 6.68/2.22 % (781)------------------------------
% 6.68/2.22 % (781)------------------------------
% 6.68/2.22 % (784)Termination reason: Unknown
% 6.68/2.22 % (784)Termination phase: shuffling
% 6.68/2.22
% 6.68/2.22 % (784)Memory used [KB]: 1918
% 6.68/2.22 % (784)Time elapsed: 0.011 s
% 6.68/2.22 % (784)Instructions burned: 33 (million)
% 6.68/2.22 % (784)------------------------------
% 6.68/2.22 % (784)------------------------------
% 6.68/2.23 % (785)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_578 for (2993ds/297Mi)
% 6.68/2.23 % (786)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_578 for (2993ds/987Mi)
% 6.68/2.24 % (779)Instruction limit reached!
% 6.68/2.24 % (779)------------------------------
% 6.68/2.24 % (779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.24 % (779)Termination reason: Unknown
% 6.68/2.24 % (779)Termination phase: Saturation
% 6.68/2.24
% 6.68/2.24 % (779)Memory used [KB]: 7547
% 6.68/2.24 % (779)Time elapsed: 0.078 s
% 6.68/2.24 % (779)Instructions burned: 260 (million)
% 6.68/2.24 % (779)------------------------------
% 6.68/2.24 % (779)------------------------------
% 6.68/2.25 % (751)Instruction limit reached!
% 6.68/2.25 % (751)------------------------------
% 6.68/2.25 % (751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.25 % (751)Termination reason: Unknown
% 6.68/2.25 % (751)Termination phase: Saturation
% 6.68/2.25
% 6.68/2.25 % (751)Memory used [KB]: 8827
% 6.68/2.25 % (751)Time elapsed: 0.342 s
% 6.68/2.25 % (751)Instructions burned: 1088 (million)
% 6.68/2.25 % (751)------------------------------
% 6.68/2.25 % (751)------------------------------
% 6.68/2.25 % (787)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_578 for (2993ds/182Mi)
% 6.68/2.26 % (772)Instruction limit reached!
% 6.68/2.26 % (772)------------------------------
% 6.68/2.26 % (772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.26 % (772)Termination reason: Unknown
% 6.68/2.26 % (772)Termination phase: Saturation
% 6.68/2.26
% 6.68/2.26 % (772)Memory used [KB]: 8827
% 6.68/2.26 % (772)Time elapsed: 0.215 s
% 6.68/2.26 % (772)Instructions burned: 614 (million)
% 6.68/2.26 % (772)------------------------------
% 6.68/2.26 % (772)------------------------------
% 6.68/2.26 % (788)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_578 for (2993ds/182Mi)
% 6.68/2.27 % (782)Instruction limit reached!
% 6.68/2.27 % (782)------------------------------
% 6.68/2.27 % (782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.27 % (782)Termination reason: Unknown
% 6.68/2.27 % (782)Termination phase: Saturation
% 6.68/2.27
% 6.68/2.27 % (782)Memory used [KB]: 7291
% 6.68/2.27 % (782)Time elapsed: 0.063 s
% 6.68/2.27 % (782)Instructions burned: 233 (million)
% 6.68/2.27 % (782)------------------------------
% 6.68/2.27 % (782)------------------------------
% 6.68/2.27 % (789)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_578 for (2993ds/154Mi)
% 6.68/2.28 % (790)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_578 for (2993ds/79Mi)
% 7.45/2.30 % (790)Instruction limit reached!
% 7.45/2.30 % (790)------------------------------
% 7.45/2.30 % (790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.30 % (790)Termination reason: Unknown
% 7.45/2.30 % (790)Termination phase: Saturation
% 7.45/2.30
% 7.45/2.30 % (790)Memory used [KB]: 6908
% 7.45/2.30 % (790)Time elapsed: 0.025 s
% 7.45/2.30 % (790)Instructions burned: 81 (million)
% 7.45/2.30 % (790)------------------------------
% 7.45/2.30 % (790)------------------------------
% 7.45/2.31 % (787)Instruction limit reached!
% 7.45/2.31 % (787)------------------------------
% 7.45/2.31 % (787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.31 % (787)Termination reason: Unknown
% 7.45/2.31 % (787)Termination phase: Saturation
% 7.45/2.31
% 7.45/2.31 % (787)Memory used [KB]: 7291
% 7.45/2.31 % (787)Time elapsed: 0.056 s
% 7.45/2.31 % (787)Instructions burned: 182 (million)
% 7.45/2.31 % (787)------------------------------
% 7.45/2.31 % (787)------------------------------
% 7.45/2.31 % (791)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_578 for (2992ds/216Mi)
% 7.45/2.31 % (789)Instruction limit reached!
% 7.45/2.31 % (789)------------------------------
% 7.45/2.31 % (789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.31 % (789)Termination reason: Unknown
% 7.45/2.31 % (789)Termination phase: Saturation
% 7.45/2.31
% 7.45/2.31 % (789)Memory used [KB]: 2686
% 7.45/2.31 % (789)Time elapsed: 0.043 s
% 7.45/2.31 % (789)Instructions burned: 155 (million)
% 7.45/2.31 % (789)------------------------------
% 7.45/2.31 % (789)------------------------------
% 7.45/2.31 % (792)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_578 for (2992ds/114Mi)
% 7.45/2.32 % (785)Instruction limit reached!
% 7.45/2.32 % (785)------------------------------
% 7.45/2.32 % (785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.32 % (785)Termination reason: Unknown
% 7.45/2.32 % (785)Termination phase: Saturation
% 7.45/2.32
% 7.45/2.32 % (785)Memory used [KB]: 7675
% 7.45/2.32 % (785)Time elapsed: 0.089 s
% 7.45/2.32 % (785)Instructions burned: 299 (million)
% 7.45/2.32 % (785)------------------------------
% 7.45/2.32 % (785)------------------------------
% 7.45/2.32 % (788)Instruction limit reached!
% 7.45/2.32 % (788)------------------------------
% 7.45/2.32 % (788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.32 % (788)Termination reason: Unknown
% 7.45/2.32 % (788)Termination phase: Saturation
% 7.45/2.32
% 7.45/2.32 % (788)Memory used [KB]: 7419
% 7.45/2.32 % (788)Time elapsed: 0.059 s
% 7.45/2.32 % (788)Instructions burned: 184 (million)
% 7.45/2.32 % (788)------------------------------
% 7.45/2.32 % (788)------------------------------
% 7.45/2.32 % (793)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_578 for (2992ds/922Mi)
% 7.45/2.33 % (794)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_578 for (2992ds/182Mi)
% 7.45/2.33 % (795)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_578 for (2992ds/164Mi)
% 7.45/2.35 % (792)Instruction limit reached!
% 7.45/2.35 % (792)------------------------------
% 7.45/2.35 % (792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.35 % (792)Termination reason: Unknown
% 7.45/2.35 % (792)Termination phase: Saturation
% 7.45/2.35
% 7.45/2.35 % (792)Memory used [KB]: 7164
% 7.45/2.35 % (792)Time elapsed: 0.035 s
% 7.45/2.35 % (792)Instructions burned: 116 (million)
% 7.45/2.35 % (792)------------------------------
% 7.45/2.35 % (792)------------------------------
% 7.45/2.35 % (783)Refutation not found, non-redundant clauses discarded% (783)------------------------------
% 7.45/2.35 % (783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.35 % (783)Termination reason: Refutation not found, non-redundant clauses discarded
% 7.45/2.35
% 7.45/2.35 % (783)Memory used [KB]: 8059
% 7.45/2.35 % (783)Time elapsed: 0.145 s
% 7.45/2.35 % (783)Instructions burned: 456 (million)
% 7.45/2.35 % (783)------------------------------
% 7.45/2.35 % (783)------------------------------
% 7.45/2.36 % (796)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_578 for (2992ds/50Mi)
% 7.45/2.36 % (797)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_578 for (2992ds/368Mi)
% 7.45/2.37 % (791)Instruction limit reached!
% 7.45/2.37 % (791)------------------------------
% 7.45/2.37 % (791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.37 % (791)Termination reason: Unknown
% 7.45/2.37 % (791)Termination phase: Saturation
% 7.45/2.37
% 7.45/2.37 % (791)Memory used [KB]: 7547
% 7.45/2.37 % (791)Time elapsed: 0.062 s
% 7.45/2.37 % (791)Instructions burned: 216 (million)
% 7.45/2.37 % (791)------------------------------
% 7.45/2.37 % (791)------------------------------
% 7.45/2.37 % (796)Instruction limit reached!
% 7.45/2.37 % (796)------------------------------
% 7.45/2.37 % (796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.37 % (796)Termination reason: Unknown
% 7.45/2.37 % (796)Termination phase: Property scanning
% 7.45/2.37
% 7.45/2.37 % (796)Memory used [KB]: 2174
% 7.45/2.37 % (796)Time elapsed: 0.015 s
% 7.45/2.37 % (796)Instructions burned: 52 (million)
% 7.45/2.37 % (796)------------------------------
% 7.45/2.37 % (796)------------------------------
% 7.45/2.37 % (795)Instruction limit reached!
% 7.45/2.37 % (795)------------------------------
% 7.45/2.37 % (795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.37 % (795)Termination reason: Unknown
% 7.45/2.37 % (795)Termination phase: Saturation
% 7.45/2.37
% 7.45/2.37 % (795)Memory used [KB]: 2558
% 7.45/2.37 % (795)Time elapsed: 0.046 s
% 7.45/2.37 % (795)Instructions burned: 164 (million)
% 7.45/2.37 % (795)------------------------------
% 7.45/2.37 % (795)------------------------------
% 7.45/2.37 % (794)Instruction limit reached!
% 7.45/2.37 % (794)------------------------------
% 7.45/2.37 % (794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.37 % (794)Termination reason: Unknown
% 7.45/2.37 % (794)Termination phase: Saturation
% 7.45/2.37
% 7.45/2.37 % (794)Memory used [KB]: 7036
% 7.45/2.37 % (794)Time elapsed: 0.050 s
% 7.45/2.37 % (794)Instructions burned: 183 (million)
% 7.45/2.37 % (794)------------------------------
% 7.45/2.37 % (794)------------------------------
% 7.45/2.38 % (798)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_578 for (2992ds/1021Mi)
% 7.45/2.38 % (799)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_578 for (2992ds/267Mi)
% 7.45/2.38 % (800)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_578 for (2992ds/204Mi)
% 7.45/2.38 % (801)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_578 for (2992ds/26Mi)
% 7.45/2.39 % (801)Instruction limit reached!
% 7.45/2.39 % (801)------------------------------
% 7.45/2.39 % (801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.45/2.39 % (801)Termination reason: Unknown
% 7.45/2.39 % (801)Termination phase: shuffling
% 7.45/2.39
% 7.45/2.39 % (801)Memory used [KB]: 2046
% 7.45/2.39 % (801)Time elapsed: 0.009 s
% 7.45/2.39 % (801)Instructions burned: 28 (million)
% 7.45/2.39 % (801)------------------------------
% 7.45/2.39 % (801)------------------------------
% 8.19/2.40 % (802)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_578 for (2991ds/53Mi)
% 8.19/2.42 % (802)Instruction limit reached!
% 8.19/2.42 % (802)------------------------------
% 8.19/2.42 % (802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.19/2.42 % (802)Termination reason: Unknown
% 8.19/2.42 % (802)Termination phase: Property scanning
% 8.19/2.42
% 8.19/2.42 % (802)Memory used [KB]: 2174
% 8.19/2.42 % (802)Time elapsed: 0.016 s
% 8.19/2.42 % (802)Instructions burned: 56 (million)
% 8.19/2.42 % (802)------------------------------
% 8.19/2.42 % (802)------------------------------
% 8.19/2.43 % (803)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_578 for (2991ds/4436Mi)
% 8.19/2.45 % (800)Instruction limit reached!
% 8.19/2.45 % (800)------------------------------
% 8.19/2.45 % (800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.19/2.45 % (800)Termination reason: Unknown
% 8.19/2.45 % (800)Termination phase: Saturation
% 8.19/2.45
% 8.19/2.45 % (800)Memory used [KB]: 7419
% 8.19/2.45 % (800)Time elapsed: 0.065 s
% 8.19/2.45 % (800)Instructions burned: 204 (million)
% 8.19/2.45 % (800)------------------------------
% 8.19/2.45 % (800)------------------------------
% 8.19/2.46 % (804)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_578 for (2991ds/1539Mi)
% 8.19/2.46 % (799)Instruction limit reached!
% 8.19/2.46 % (799)------------------------------
% 8.19/2.46 % (799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.19/2.46 % (799)Termination reason: Unknown
% 8.19/2.46 % (799)Termination phase: Saturation
% 8.19/2.46
% 8.19/2.46 % (799)Memory used [KB]: 7547
% 8.19/2.46 % (799)Time elapsed: 0.081 s
% 8.19/2.46 % (799)Instructions burned: 267 (million)
% 8.19/2.46 % (799)------------------------------
% 8.19/2.46 % (799)------------------------------
% 8.19/2.47 % (805)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_578 for (2991ds/408Mi)
% 8.19/2.48 % (797)Instruction limit reached!
% 8.19/2.48 % (797)------------------------------
% 8.19/2.48 % (797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.19/2.48 % (797)Termination reason: Unknown
% 8.19/2.48 % (797)Termination phase: Saturation
% 8.19/2.48
% 8.19/2.48 % (797)Memory used [KB]: 9722
% 8.19/2.48 % (797)Time elapsed: 0.121 s
% 8.19/2.48 % (797)Instructions burned: 368 (million)
% 8.19/2.48 % (797)------------------------------
% 8.19/2.48 % (797)------------------------------
% 8.19/2.49 % (806)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_578 for (2990ds/5205Mi)
% 8.51/2.52 % (786)Instruction limit reached!
% 8.51/2.52 % (786)------------------------------
% 8.51/2.52 % (786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.51/2.52 % (786)Termination reason: Unknown
% 8.51/2.52 % (786)Termination phase: Saturation
% 8.51/2.52
% 8.51/2.52 % (786)Memory used [KB]: 8699
% 8.51/2.52 % (786)Time elapsed: 0.298 s
% 8.51/2.52 % (786)Instructions burned: 988 (million)
% 8.51/2.52 % (786)------------------------------
% 8.51/2.52 % (786)------------------------------
% 8.51/2.53 % (807)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_578 for (2990ds/1913Mi)
% 8.51/2.59 % (805)Instruction limit reached!
% 8.51/2.59 % (805)------------------------------
% 8.51/2.59 % (805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.51/2.59 % (805)Termination reason: Unknown
% 8.51/2.59 % (805)Termination phase: Saturation
% 8.51/2.59
% 8.51/2.59 % (805)Memory used [KB]: 8443
% 8.51/2.59 % (805)Time elapsed: 0.121 s
% 8.51/2.59 % (805)Instructions burned: 409 (million)
% 8.51/2.59 % (805)------------------------------
% 8.51/2.59 % (805)------------------------------
% 8.95/2.60 % (808)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_578 for (2989ds/4350Mi)
% 8.95/2.61 % (793)Instruction limit reached!
% 8.95/2.61 % (793)------------------------------
% 8.95/2.61 % (793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.61 % (793)Termination reason: Unknown
% 8.95/2.61 % (793)Termination phase: Saturation
% 8.95/2.61
% 8.95/2.61 % (793)Memory used [KB]: 8443
% 8.95/2.61 % (793)Time elapsed: 0.288 s
% 8.95/2.61 % (793)Instructions burned: 922 (million)
% 8.95/2.61 % (793)------------------------------
% 8.95/2.61 % (793)------------------------------
% 8.95/2.62 % (809)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_578 for (2989ds/68Mi)
% 8.95/2.64 % (809)Instruction limit reached!
% 8.95/2.64 % (809)------------------------------
% 8.95/2.64 % (809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.95/2.64 % (809)Termination reason: Unknown
% 8.95/2.64 % (809)Termination phase: Property scanning
% 8.95/2.64
% 8.95/2.64 % (809)Memory used [KB]: 2302
% 8.95/2.64 % (809)Time elapsed: 0.022 s
% 8.95/2.64 % (809)Instructions burned: 70 (million)
% 8.95/2.64 % (809)------------------------------
% 8.95/2.64 % (809)------------------------------
% 8.95/2.65 % (810)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_578 for (2989ds/358Mi)
% 9.27/2.71 % (798)Instruction limit reached!
% 9.27/2.71 % (798)------------------------------
% 9.27/2.71 % (798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.71 % (798)Termination reason: Unknown
% 9.27/2.71 % (798)Termination phase: Saturation
% 9.27/2.71
% 9.27/2.71 % (798)Memory used [KB]: 9466
% 9.27/2.71 % (798)Time elapsed: 0.325 s
% 9.27/2.71 % (798)Instructions burned: 1022 (million)
% 9.27/2.71 % (798)------------------------------
% 9.27/2.71 % (798)------------------------------
% 9.27/2.72 % (811)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_578 for (2988ds/31Mi)
% 9.27/2.73 % (811)Instruction limit reached!
% 9.27/2.73 % (811)------------------------------
% 9.27/2.73 % (811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.73 % (811)Termination reason: Unknown
% 9.27/2.73 % (811)Termination phase: Preprocessing 1
% 9.27/2.73
% 9.27/2.73 % (811)Memory used [KB]: 1791
% 9.27/2.73 % (811)Time elapsed: 0.011 s
% 9.27/2.73 % (811)Instructions burned: 32 (million)
% 9.27/2.73 % (811)------------------------------
% 9.27/2.73 % (811)------------------------------
% 9.27/2.74 % (812)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_578 for (2988ds/279Mi)
% 9.27/2.76 % (810)Instruction limit reached!
% 9.27/2.76 % (810)------------------------------
% 9.27/2.76 % (810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.76 % (810)Termination reason: Unknown
% 9.27/2.76 % (810)Termination phase: Saturation
% 9.27/2.76
% 9.27/2.76 % (810)Memory used [KB]: 7547
% 9.27/2.76 % (810)Time elapsed: 0.117 s
% 9.27/2.76 % (810)Instructions burned: 360 (million)
% 9.27/2.76 % (810)------------------------------
% 9.27/2.76 % (810)------------------------------
% 9.27/2.77 % (813)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_578 for (2988ds/258Mi)
% 9.75/2.82 % (812)Instruction limit reached!
% 9.75/2.82 % (812)------------------------------
% 9.75/2.82 % (812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.82 % (812)Termination reason: Unknown
% 9.75/2.82 % (812)Termination phase: Saturation
% 9.75/2.82
% 9.75/2.82 % (812)Memory used [KB]: 7803
% 9.75/2.82 % (812)Time elapsed: 0.082 s
% 9.75/2.82 % (812)Instructions burned: 281 (million)
% 9.75/2.82 % (812)------------------------------
% 9.75/2.82 % (812)------------------------------
% 9.75/2.83 % (814)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_578 for (2987ds/26Mi)
% 9.75/2.83 % (814)Instruction limit reached!
% 9.75/2.83 % (814)------------------------------
% 9.75/2.83 % (814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.83 % (814)Termination reason: Unknown
% 9.75/2.83 % (814)Termination phase: shuffling
% 9.75/2.83
% 9.75/2.83 % (814)Memory used [KB]: 1918
% 9.75/2.83 % (814)Time elapsed: 0.009 s
% 9.75/2.83 % (814)Instructions burned: 27 (million)
% 9.75/2.83 % (814)------------------------------
% 9.75/2.83 % (814)------------------------------
% 9.75/2.84 % (815)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_578 for (2987ds/995Mi)
% 9.75/2.85 % (813)Instruction limit reached!
% 9.75/2.85 % (813)------------------------------
% 9.75/2.85 % (813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.85 % (813)Termination reason: Unknown
% 9.75/2.85 % (813)Termination phase: Saturation
% 9.75/2.85
% 9.75/2.85 % (813)Memory used [KB]: 7803
% 9.75/2.85 % (813)Time elapsed: 0.081 s
% 9.75/2.85 % (813)Instructions burned: 258 (million)
% 9.75/2.85 % (813)------------------------------
% 9.75/2.85 % (813)------------------------------
% 9.75/2.86 % (816)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_578 for (2987ds/373Mi)
% 9.94/2.93 % (804)Instruction limit reached!
% 9.94/2.93 % (804)------------------------------
% 9.94/2.93 % (804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.94/2.93 % (804)Termination reason: Unknown
% 9.94/2.93 % (804)Termination phase: Saturation
% 9.94/2.93
% 9.94/2.93 % (804)Memory used [KB]: 11385
% 9.94/2.93 % (804)Time elapsed: 0.480 s
% 9.94/2.93 % (804)Instructions burned: 1539 (million)
% 9.94/2.93 % (804)------------------------------
% 9.94/2.93 % (804)------------------------------
% 9.94/2.95 % (817)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_578 for (2986ds/253Mi)
% 9.94/2.99 % (816)Instruction limit reached!
% 9.94/2.99 % (816)------------------------------
% 9.94/2.99 % (816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.94/2.99 % (816)Termination reason: Unknown
% 9.94/2.99 % (816)Termination phase: Saturation
% 9.94/2.99
% 9.94/2.99 % (816)Memory used [KB]: 8443
% 9.94/2.99 % (816)Time elapsed: 0.125 s
% 9.94/2.99 % (816)Instructions burned: 373 (million)
% 9.94/2.99 % (816)------------------------------
% 9.94/2.99 % (816)------------------------------
% 9.94/3.01 % (818)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_578 for (2985ds/832Mi)
% 12.76/3.02 % (817)Instruction limit reached!
% 12.76/3.02 % (817)------------------------------
% 12.76/3.02 % (817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.76/3.02 % (817)Termination reason: Unknown
% 12.76/3.02 % (817)Termination phase: Saturation
% 12.76/3.02
% 12.76/3.02 % (817)Memory used [KB]: 7547
% 12.76/3.02 % (817)Time elapsed: 0.074 s
% 12.76/3.02 % (817)Instructions burned: 253 (million)
% 12.76/3.02 % (817)------------------------------
% 12.76/3.02 % (817)------------------------------
% 12.76/3.03 % (819)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_578 for (2985ds/668Mi)
% 12.76/3.04 % (818)Refutation not found, incomplete strategy
% 12.76/3.04 % (818)------------------------------
% 12.76/3.04 % (818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.76/3.04 % (818)Termination reason: Refutation not found, incomplete strategy
% 12.76/3.04
% 12.76/3.04
% 12.76/3.04 % (818)Memory used [KB]: 7675
% 12.76/3.04 % (818)Time elapsed: 0.039 s
% 12.76/3.04 % (818)Instructions burned: 121 (million)
% 12.76/3.04 % (818)------------------------------
% 12.76/3.04 % (818)------------------------------
% 12.76/3.05 % (820)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_578 for (2985ds/40Mi)
% 12.76/3.07 % (820)Instruction limit reached!
% 12.76/3.07 % (820)------------------------------
% 12.76/3.07 % (820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.76/3.07 % (820)Termination reason: Unknown
% 12.76/3.07 % (820)Termination phase: Property scanning
% 12.76/3.07
% 12.76/3.07 % (820)Memory used [KB]: 2174
% 12.76/3.07 % (820)Time elapsed: 0.013 s
% 12.76/3.07 % (820)Instructions burned: 43 (million)
% 12.76/3.07 % (820)------------------------------
% 12.76/3.07 % (820)------------------------------
% 12.76/3.08 % (821)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_578 for (2985ds/294Mi)
% 13.37/3.13 % (807)Instruction limit reached!
% 13.37/3.13 % (807)------------------------------
% 13.37/3.13 % (807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/3.13 % (807)Termination reason: Unknown
% 13.37/3.13 % (807)Termination phase: Saturation
% 13.37/3.13
% 13.37/3.13 % (807)Memory used [KB]: 6012
% 13.37/3.13 % (807)Time elapsed: 0.592 s
% 13.37/3.13 % (807)Instructions burned: 1913 (million)
% 13.37/3.13 % (807)------------------------------
% 13.37/3.13 % (807)------------------------------
% 13.37/3.14 % (822)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_578 for (2984ds/187Mi)
% 13.37/3.14 % (815)Instruction limit reached!
% 13.37/3.14 % (815)------------------------------
% 13.37/3.14 % (815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/3.14 % (815)Termination reason: Unknown
% 13.37/3.14 % (815)Termination phase: Saturation
% 13.37/3.14
% 13.37/3.14 % (815)Memory used [KB]: 9722
% 13.37/3.14 % (815)Time elapsed: 0.317 s
% 13.37/3.14 % (815)Instructions burned: 997 (million)
% 13.37/3.14 % (815)------------------------------
% 13.37/3.14 % (815)------------------------------
% 13.37/3.15 % (823)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_578 for (2984ds/371Mi)
% 13.37/3.16 % (821)Instruction limit reached!
% 13.37/3.16 % (821)------------------------------
% 13.37/3.16 % (821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/3.16 % (821)Termination reason: Unknown
% 13.37/3.16 % (821)Termination phase: Saturation
% 13.37/3.16
% 13.37/3.16 % (821)Memory used [KB]: 7675
% 13.37/3.16 % (821)Time elapsed: 0.085 s
% 13.37/3.16 % (821)Instructions burned: 297 (million)
% 13.37/3.16 % (821)------------------------------
% 13.37/3.16 % (821)------------------------------
% 13.37/3.17 % (824)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_578 for (2984ds/1827Mi)
% 13.37/3.20 % (822)Instruction limit reached!
% 13.37/3.20 % (822)------------------------------
% 13.37/3.20 % (822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/3.20 % (822)Termination reason: Unknown
% 13.37/3.20 % (822)Termination phase: Saturation
% 13.37/3.20
% 13.37/3.20 % (822)Memory used [KB]: 7675
% 13.37/3.20 % (822)Time elapsed: 0.061 s
% 13.37/3.20 % (822)Instructions burned: 190 (million)
% 13.37/3.20 % (822)------------------------------
% 13.37/3.20 % (822)------------------------------
% 13.85/3.21 % (825)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_578 for (2983ds/70Mi)
% 13.85/3.22 % (825)Instruction limit reached!
% 13.85/3.22 % (825)------------------------------
% 13.85/3.22 % (825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.85/3.22 % (825)Termination reason: Unknown
% 13.85/3.23 % (825)Termination phase: Property scanning
% 13.85/3.23
% 13.85/3.23 % (825)Memory used [KB]: 2302
% 13.85/3.23 % (825)Time elapsed: 0.021 s
% 13.85/3.23 % (825)Instructions burned: 72 (million)
% 13.85/3.23 % (825)------------------------------
% 13.85/3.23 % (825)------------------------------
% 13.85/3.23 % (819)Instruction limit reached!
% 13.85/3.23 % (819)------------------------------
% 13.85/3.23 % (819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.85/3.23 % (819)Termination reason: Unknown
% 13.85/3.23 % (819)Termination phase: Saturation
% 13.85/3.23
% 13.85/3.23 % (819)Memory used [KB]: 14072
% 13.85/3.23 % (819)Time elapsed: 0.199 s
% 13.85/3.23 % (819)Instructions burned: 670 (million)
% 13.85/3.23 % (819)------------------------------
% 13.85/3.23 % (819)------------------------------
% 13.85/3.23 % (826)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_578 for (2983ds/316Mi)
% 13.85/3.24 % (827)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_578 for (2983ds/932Mi)
% 13.85/3.26 % (823)Instruction limit reached!
% 13.85/3.26 % (823)------------------------------
% 13.85/3.26 % (823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.85/3.26 % (823)Termination reason: Unknown
% 13.85/3.26 % (823)Termination phase: Saturation
% 13.85/3.26
% 13.85/3.26 % (823)Memory used [KB]: 8699
% 13.85/3.26 % (823)Time elapsed: 0.119 s
% 13.85/3.26 % (823)Instructions burned: 372 (million)
% 13.85/3.26 % (823)------------------------------
% 13.85/3.26 % (823)------------------------------
% 13.85/3.27 % (828)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_578 for (2983ds/4714Mi)
% 14.52/3.32 % (826)Instruction limit reached!
% 14.52/3.32 % (826)------------------------------
% 14.52/3.32 % (826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.52/3.32 % (826)Termination reason: Unknown
% 14.52/3.32 % (826)Termination phase: Saturation
% 14.52/3.32
% 14.52/3.32 % (826)Memory used [KB]: 8187
% 14.52/3.32 % (826)Time elapsed: 0.090 s
% 14.52/3.32 % (826)Instructions burned: 317 (million)
% 14.52/3.32 % (826)------------------------------
% 14.52/3.32 % (826)------------------------------
% 14.52/3.33 % (829)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_578 for (2982ds/8250Mi)
% 15.23/3.54 % (827)Instruction limit reached!
% 15.23/3.54 % (827)------------------------------
% 15.23/3.54 % (827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.23/3.54 % (827)Termination reason: Unknown
% 15.23/3.54 % (827)Termination phase: Saturation
% 15.23/3.54
% 15.23/3.54 % (827)Memory used [KB]: 11257
% 15.23/3.54 % (827)Time elapsed: 0.293 s
% 15.23/3.54 % (827)Instructions burned: 933 (million)
% 15.23/3.54 % (827)------------------------------
% 15.23/3.54 % (827)------------------------------
% 15.23/3.55 % (830)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_578 for (2980ds/770Mi)
% 15.23/3.56 % (830)Refutation not found, incomplete strategy
% 15.23/3.56 % (830)------------------------------
% 15.23/3.56 % (830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.23/3.56 % (830)Termination reason: Refutation not found, incomplete strategy
% 15.23/3.56
% 15.23/3.56
% 15.23/3.56 % (830)Memory used [KB]: 6652
% 15.23/3.56 % (830)Time elapsed: 0.016 s
% 15.23/3.56 % (830)Instructions burned: 46 (million)
% 15.23/3.56 % (830)------------------------------
% 15.23/3.56 % (830)------------------------------
% 15.23/3.57 % (831)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_578 for (2980ds/794Mi)
% 16.15/3.75 % (824)Instruction limit reached!
% 16.15/3.75 % (824)------------------------------
% 16.15/3.75 % (824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.15/3.75 % (824)Termination reason: Unknown
% 16.15/3.75 % (824)Termination phase: Saturation
% 16.15/3.75
% 16.15/3.75 % (824)Memory used [KB]: 11513
% 16.15/3.75 % (824)Time elapsed: 0.585 s
% 16.15/3.75 % (824)Instructions burned: 1829 (million)
% 16.15/3.75 % (824)------------------------------
% 16.15/3.75 % (824)------------------------------
% 16.15/3.76 % (832)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_578 for (2978ds/464Mi)
% 17.06/3.81 % (803)Instruction limit reached!
% 17.06/3.81 % (803)------------------------------
% 17.06/3.81 % (803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.06/3.81 % (803)Termination reason: Unknown
% 17.06/3.81 % (803)Termination phase: Saturation
% 17.06/3.81
% 17.06/3.81 % (803)Memory used [KB]: 11129
% 17.06/3.81 % (803)Time elapsed: 1.388 s
% 17.06/3.81 % (803)Instructions burned: 4437 (million)
% 17.06/3.81 % (803)------------------------------
% 17.06/3.81 % (803)------------------------------
% 17.06/3.82 % (831)Instruction limit reached!
% 17.06/3.82 % (831)------------------------------
% 17.06/3.82 % (831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.06/3.82 % (831)Termination reason: Unknown
% 17.06/3.82 % (831)Termination phase: Saturation
% 17.06/3.82
% 17.06/3.82 % (831)Memory used [KB]: 6268
% 17.06/3.82 % (831)Time elapsed: 0.248 s
% 17.06/3.82 % (831)Instructions burned: 794 (million)
% 17.06/3.82 % (831)------------------------------
% 17.06/3.82 % (831)------------------------------
% 17.06/3.82 % (833)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_578 for (2977ds/1376Mi)
% 17.06/3.83 % (834)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_578 for (2977ds/906Mi)
% 17.54/3.91 % (832)Instruction limit reached!
% 17.54/3.91 % (832)------------------------------
% 17.54/3.91 % (832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.54/3.91 % (832)Termination reason: Unknown
% 17.54/3.91 % (832)Termination phase: Saturation
% 17.54/3.91
% 17.54/3.91 % (832)Memory used [KB]: 7803
% 17.54/3.91 % (832)Time elapsed: 0.146 s
% 17.54/3.91 % (832)Instructions burned: 464 (million)
% 17.54/3.91 % (832)------------------------------
% 17.54/3.91 % (832)------------------------------
% 17.54/3.92 % (835)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_578 for (2976ds/434Mi)
% 17.54/3.93 % (808)Instruction limit reached!
% 17.54/3.93 % (808)------------------------------
% 17.54/3.93 % (808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.54/3.93 % (808)Termination reason: Unknown
% 17.54/3.93 % (808)Termination phase: Saturation
% 17.54/3.93
% 17.54/3.93 % (808)Memory used [KB]: 11513
% 17.54/3.93 % (808)Time elapsed: 1.325 s
% 17.54/3.93 % (808)Instructions burned: 4350 (million)
% 17.54/3.93 % (808)------------------------------
% 17.54/3.93 % (808)------------------------------
% 17.54/3.94 % (836)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_578 for (2976ds/865Mi)
% 19.75/4.04 % (806)Instruction limit reached!
% 19.75/4.04 % (806)------------------------------
% 19.75/4.04 % (806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.75/4.04 % (806)Termination reason: Unknown
% 19.75/4.04 % (806)Termination phase: Saturation
% 19.75/4.04
% 19.75/4.04 % (806)Memory used [KB]: 17014
% 19.75/4.04 % (806)Time elapsed: 1.547 s
% 19.75/4.04 % (806)Instructions burned: 5205 (million)
% 19.75/4.04 % (806)------------------------------
% 19.75/4.04 % (806)------------------------------
% 19.75/4.05 % (837)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_578 for (2975ds/593Mi)
% 19.75/4.06 % (835)Instruction limit reached!
% 19.75/4.06 % (835)------------------------------
% 19.75/4.06 % (835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.75/4.06 % (835)Termination reason: Unknown
% 19.75/4.06 % (835)Termination phase: Saturation
% 19.75/4.06
% 19.75/4.06 % (835)Memory used [KB]: 8059
% 19.75/4.06 % (835)Time elapsed: 0.153 s
% 19.75/4.06 % (835)Instructions burned: 437 (million)
% 19.75/4.06 % (835)------------------------------
% 19.75/4.06 % (835)------------------------------
% 19.75/4.07 % (838)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_578 for (2975ds/443Mi)
% 20.40/4.15 % (834)Instruction limit reached!
% 20.40/4.15 % (834)------------------------------
% 20.40/4.15 % (834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.40/4.15 % (834)Termination reason: Unknown
% 20.40/4.15 % (834)Termination phase: Saturation
% 20.40/4.15
% 20.40/4.15 % (834)Memory used [KB]: 11129
% 20.40/4.15 % (834)Time elapsed: 0.320 s
% 20.40/4.15 % (834)Instructions burned: 908 (million)
% 20.40/4.15 % (834)------------------------------
% 20.40/4.15 % (834)------------------------------
% 20.40/4.16 % (839)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_578 for (2974ds/594Mi)
% 20.40/4.19 % (836)Instruction limit reached!
% 20.40/4.19 % (836)------------------------------
% 20.40/4.19 % (836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.40/4.19 % (836)Termination reason: Unknown
% 20.40/4.19 % (836)Termination phase: Saturation
% 20.40/4.19
% 20.40/4.19 % (836)Memory used [KB]: 9466
% 20.40/4.19 % (836)Time elapsed: 0.259 s
% 20.40/4.19 % (836)Instructions burned: 865 (million)
% 20.40/4.19 % (836)------------------------------
% 20.40/4.19 % (836)------------------------------
% 20.76/4.20 % (840)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_578 for (2973ds/327Mi)
% 20.76/4.21 % (838)Instruction limit reached!
% 20.76/4.21 % (838)------------------------------
% 20.76/4.21 % (838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.76/4.21 % (838)Termination reason: Unknown
% 20.76/4.21 % (838)Termination phase: Saturation
% 20.76/4.21
% 20.76/4.21 % (838)Memory used [KB]: 8699
% 20.76/4.21 % (838)Time elapsed: 0.145 s
% 20.76/4.21 % (838)Instructions burned: 443 (million)
% 20.76/4.21 % (838)------------------------------
% 20.76/4.21 % (838)------------------------------
% 20.76/4.22 % (841)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_578 for (2973ds/5411Mi)
% 20.76/4.22 % (837)Instruction limit reached!
% 20.76/4.22 % (837)------------------------------
% 20.76/4.22 % (837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.76/4.22 % (837)Termination reason: Unknown
% 20.76/4.22 % (837)Termination phase: Saturation
% 20.76/4.22
% 20.76/4.22 % (837)Memory used [KB]: 8443
% 20.76/4.22 % (837)Time elapsed: 0.177 s
% 20.76/4.22 % (837)Instructions burned: 596 (million)
% 20.76/4.22 % (837)------------------------------
% 20.76/4.22 % (837)------------------------------
% 20.76/4.23 % (842)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_578 for (2973ds/1762Mi)
% 20.76/4.25 % (833)Instruction limit reached!
% 20.76/4.25 % (833)------------------------------
% 20.76/4.25 % (833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.76/4.25 % (833)Termination reason: Unknown
% 20.76/4.25 % (833)Termination phase: Saturation
% 20.76/4.25
% 20.76/4.25 % (833)Memory used [KB]: 13048
% 20.76/4.25 % (833)Time elapsed: 0.425 s
% 20.76/4.25 % (833)Instructions burned: 1376 (million)
% 20.76/4.25 % (833)------------------------------
% 20.76/4.25 % (833)------------------------------
% 20.76/4.26 % (841)Refutation not found, incomplete strategy
% 20.76/4.26 % (841)------------------------------
% 20.76/4.26 % (841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.76/4.26 % (841)Termination reason: Refutation not found, incomplete strategy
% 20.76/4.26
% 20.76/4.26
% 20.76/4.26 % (841)Memory used [KB]: 6908
% 20.76/4.26 % (841)Time elapsed: 0.032 s
% 20.76/4.26 % (841)Instructions burned: 78 (million)
% 20.76/4.26 % (841)------------------------------
% 20.76/4.26 % (841)------------------------------
% 20.76/4.26 % (843)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_578 for (2973ds/96Mi)
% 20.76/4.27 % (844)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_578 for (2973ds/503Mi)
% 20.76/4.28 % (843)Instruction limit reached!
% 20.76/4.28 % (843)------------------------------
% 20.76/4.28 % (843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.76/4.28 % (843)Termination reason: Unknown
% 20.76/4.28 % (843)Termination phase: Function definition elimination
% 20.76/4.28
% 20.76/4.28 % (843)Memory used [KB]: 2430
% 20.76/4.28 % (843)Time elapsed: 0.027 s
% 20.76/4.28 % (843)Instructions burned: 98 (million)
% 20.76/4.28 % (843)------------------------------
% 20.76/4.28 % (843)------------------------------
% 20.76/4.29 % (845)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_578 for (2973ds/90Mi)
% 21.44/4.31 % (840)Instruction limit reached!
% 21.44/4.31 % (840)------------------------------
% 21.44/4.31 % (840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.44/4.31 % (840)Termination reason: Unknown
% 21.44/4.31 % (840)Termination phase: Saturation
% 21.44/4.31
% 21.44/4.31 % (840)Memory used [KB]: 8187
% 21.44/4.31 % (840)Time elapsed: 0.127 s
% 21.44/4.31 % (840)Instructions burned: 329 (million)
% 21.44/4.31 % (840)------------------------------
% 21.44/4.31 % (840)------------------------------
% 21.44/4.32 % (846)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_578 for (2972ds/593Mi)
% 21.44/4.32 % (845)Instruction limit reached!
% 21.44/4.32 % (845)------------------------------
% 21.44/4.32 % (845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.44/4.32 % (845)Termination reason: Unknown
% 21.44/4.32 % (845)Termination phase: Saturation
% 21.44/4.32
% 21.44/4.32 % (845)Memory used [KB]: 6908
% 21.44/4.32 % (845)Time elapsed: 0.028 s
% 21.44/4.32 % (845)Instructions burned: 92 (million)
% 21.44/4.32 % (845)------------------------------
% 21.44/4.32 % (845)------------------------------
% 21.44/4.33 % (847)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_578 for (2972ds/1512Mi)
% 21.44/4.34 % (839)Instruction limit reached!
% 21.44/4.34 % (839)------------------------------
% 21.44/4.34 % (839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.44/4.34 % (839)Termination reason: Unknown
% 21.44/4.34 % (839)Termination phase: Saturation
% 21.44/4.34
% 21.44/4.34 % (839)Memory used [KB]: 8571
% 21.44/4.34 % (839)Time elapsed: 0.184 s
% 21.44/4.34 % (839)Instructions burned: 597 (million)
% 21.44/4.34 % (839)------------------------------
% 21.44/4.34 % (839)------------------------------
% 21.44/4.35 % (848)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_578 for (2972ds/569Mi)
% 21.44/4.37 % (847)Refutation not found, incomplete strategy
% 21.44/4.37 % (847)------------------------------
% 21.44/4.37 % (847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.44/4.37 % (847)Termination reason: Refutation not found, incomplete strategy
% 21.44/4.37
% 21.44/4.37
% 21.44/4.37 % (847)Memory used [KB]: 7675
% 21.44/4.37 % (847)Time elapsed: 0.062 s
% 21.44/4.37 % (847)Instructions burned: 122 (million)
% 21.44/4.37 % (847)------------------------------
% 21.44/4.37 % (847)------------------------------
% 21.44/4.38 % (849)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_578 for (2972ds/501Mi)
% 22.03/4.41 % (844)Instruction limit reached!
% 22.03/4.41 % (844)------------------------------
% 22.03/4.41 % (844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.03/4.41 % (844)Termination reason: Unknown
% 22.03/4.41 % (844)Termination phase: Saturation
% 22.03/4.41
% 22.03/4.41 % (844)Memory used [KB]: 8187
% 22.03/4.41 % (844)Time elapsed: 0.144 s
% 22.03/4.41 % (844)Instructions burned: 505 (million)
% 22.03/4.41 % (844)------------------------------
% 22.03/4.41 % (844)------------------------------
% 22.03/4.42 % (850)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_578 for (2971ds/562Mi)
% 22.38/4.51 % (846)Instruction limit reached!
% 22.38/4.51 % (846)------------------------------
% 22.38/4.51 % (846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.38/4.51 % (846)Termination reason: Unknown
% 22.38/4.51 % (846)Termination phase: Saturation
% 22.38/4.51
% 22.38/4.51 % (846)Memory used [KB]: 8827
% 22.38/4.51 % (846)Time elapsed: 0.211 s
% 22.38/4.51 % (846)Instructions burned: 593 (million)
% 22.38/4.51 % (846)------------------------------
% 22.38/4.51 % (846)------------------------------
% 22.38/4.52 % (848)Instruction limit reached!
% 22.38/4.52 % (848)------------------------------
% 22.38/4.52 % (848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.38/4.52 % (848)Termination reason: Unknown
% 22.38/4.52 % (848)Termination phase: Saturation
% 22.38/4.52
% 22.38/4.52 % (848)Memory used [KB]: 8187
% 22.38/4.52 % (848)Time elapsed: 0.165 s
% 22.38/4.52 % (848)Instructions burned: 569 (million)
% 22.38/4.52 % (848)------------------------------
% 22.38/4.52 % (848)------------------------------
% 22.38/4.52 % (851)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_578 for (2970ds/406Mi)
% 22.38/4.53 % (852)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_578 for (2970ds/582Mi)
% 22.38/4.53 % (849)Instruction limit reached!
% 22.38/4.53 % (849)------------------------------
% 22.38/4.53 % (849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.38/4.53 % (849)Termination reason: Unknown
% 22.38/4.53 % (849)Termination phase: Saturation
% 22.38/4.53
% 22.38/4.53 % (849)Memory used [KB]: 9083
% 22.38/4.53 % (849)Time elapsed: 0.155 s
% 22.38/4.53 % (849)Instructions burned: 501 (million)
% 22.38/4.53 % (849)------------------------------
% 22.38/4.53 % (849)------------------------------
% 22.38/4.54 % (854)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_578 for (2970ds/456Mi)
% 22.38/4.60 % (850)Instruction limit reached!
% 22.38/4.60 % (850)------------------------------
% 22.38/4.60 % (850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.38/4.60 % (850)Termination reason: Unknown
% 22.38/4.60 % (850)Termination phase: Saturation
% 22.38/4.60
% 22.38/4.60 % (850)Memory used [KB]: 8059
% 22.38/4.60 % (850)Time elapsed: 0.174 s
% 22.38/4.60 % (850)Instructions burned: 562 (million)
% 22.38/4.60 % (850)------------------------------
% 22.38/4.60 % (850)------------------------------
% 23.12/4.61 % (855)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_578 for (2969ds/393Mi)
% 23.12/4.63 % (851)Refutation not found, non-redundant clauses discarded% (851)------------------------------
% 23.12/4.63 % (851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.12/4.63 % (851)Termination reason: Refutation not found, non-redundant clauses discarded
% 23.12/4.63
% 23.12/4.63 % (851)Memory used [KB]: 7931
% 23.12/4.63 % (851)Time elapsed: 0.113 s
% 23.12/4.63 % (851)Instructions burned: 362 (million)
% 23.12/4.63 % (851)------------------------------
% 23.12/4.63 % (851)------------------------------
% 23.12/4.63 % (854)First to succeed.
% 23.12/4.63 % (854)Refutation found. Thanks to Tanya!
% 23.12/4.63 % SZS status Theorem for DTF2THF_578
% 23.12/4.63 % SZS output start Proof for DTF2THF_578
% 23.12/4.63 thf(type_def_5, type, list: ($tType) > $tType).
% 23.12/4.63 thf(type_def_7, type, poly: ($tType) > $tType).
% 23.12/4.63 thf(type_def_8, type, nat: $tType).
% 23.12/4.63 thf(type_def_9, type, a: $tType).
% 23.12/4.63 thf(func_def_0, type, poly: ($tType) > $tType).
% 23.12/4.63 thf(func_def_1, type, list: ($tType) > $tType).
% 23.12/4.63 thf(func_def_2, type, nat: $tType).
% 23.12/4.63 thf(func_def_3, type, a: $tType).
% 23.12/4.63 thf(func_def_4, type, comm_ring_1: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_5, type, type: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_6, type, one: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_7, type, sgn: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_8, type, idom: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_9, type, ring: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_10, type, plus: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_11, type, zero: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_12, type, ring_1: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_13, type, uminus: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_14, type, ord: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_15, type, ring_char_0: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_16, type, neg_numeral: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_17, type, comm_ring: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_18, type, mult_zero: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_19, type, group_add: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_20, type, monoid_add: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_21, type, monoid_mult: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_22, type, linorder: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_23, type, idom_abs_sgn: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_24, type, zero_neq_one: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_25, type, ab_group_add: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_26, type, wellorder: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_27, type, zero_less_one: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_28, type, semigroup_mult: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_29, type, comm_semiring_0: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_30, type, comm_semiring_1: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_31, type, linordered_idom: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_32, type, linordered_ring: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_33, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_34, type, comm_monoid_mult: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_35, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_36, type, boolean_algebra: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_37, type, linordered_semidom: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_38, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_39, type, linord581940658strict: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_40, type, ring_11004092258visors: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_41, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_42, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_43, type, linord20386208strict: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_44, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_45, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_46, type, linord893533164strict: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_47, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 23.12/4.63 thf(func_def_48, type, descar1668888542_psums: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 23.12/4.63 thf(func_def_49, type, descar316357986e_root: !>[X0: $tType]:(X0 > poly @ X0 > poly @ X0)).
% 23.12/4.63 thf(func_def_50, type, descar149487500hanges: !>[X0: $tType]:(list @ X0 > nat)).
% 23.12/4.63 thf(func_def_51, type, one_one: !>[X0: $tType]:(X0)).
% 23.12/4.63 thf(func_def_52, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 23.12/4.63 thf(func_def_53, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 23.12/4.63 thf(func_def_54, type, zero_zero: !>[X0: $tType]:(X0)).
% 23.12/4.63 thf(func_def_55, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 23.12/4.63 thf(func_def_56, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 23.12/4.63 thf(func_def_57, type, nil: !>[X0: $tType]:(list @ X0)).
% 23.12/4.63 thf(func_def_58, type, n_lists: !>[X0: $tType]:(nat > list @ X0 > list @ list @ X0)).
% 23.12/4.63 thf(func_def_59, type, null: !>[X0: $tType]:(list @ X0 > $o)).
% 23.12/4.63 thf(func_def_60, type, neg_numeral_dbl_dec: !>[X0: $tType]:(X0 > X0)).
% 23.12/4.63 thf(func_def_61, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 23.12/4.63 thf(func_def_62, type, poly2: !>[X0: $tType]:(list @ X0 > poly @ X0)).
% 23.12/4.63 thf(func_def_63, type, coeffs: !>[X0: $tType]:(poly @ X0 > list @ X0)).
% 23.12/4.63 thf(func_def_64, type, is_zero: !>[X0: $tType]:(poly @ X0 > $o)).
% 23.12/4.63 thf(func_def_65, type, pCons: !>[X0: $tType]:(X0 > poly @ X0 > poly @ X0)).
% 23.12/4.63 thf(func_def_66, type, poly_cutoff: !>[X0: $tType]:(nat > poly @ X0 > poly @ X0)).
% 23.12/4.63 thf(func_def_67, type, smult: !>[X0: $tType]:(X0 > poly @ X0 > poly @ X0)).
% 23.12/4.63 thf(func_def_68, type, g: poly @ a).
% 23.12/4.63 thf(func_def_69, type, v: poly @ a > nat).
% 23.12/4.63 thf(func_def_70, type, xs: list @ a).
% 23.12/4.63 thf(func_def_71, type, ys: list @ a).
% 23.12/4.63 thf(func_def_83, type, sK0: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 23.12/4.63 thf(func_def_84, type, sK1: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 23.12/4.63 thf(func_def_85, type, sK2: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 23.12/4.63 thf(func_def_86, type, sK3: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 23.12/4.63 thf(func_def_87, type, sK4: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 23.12/4.63 thf(func_def_88, type, sK5: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_89, type, sK6: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 23.12/4.63 thf(func_def_90, type, sK7: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 23.12/4.63 thf(func_def_91, type, sK8: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 23.12/4.63 thf(func_def_92, type, sK9: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_93, type, sK10: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 23.12/4.63 thf(func_def_94, type, sK11: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 23.12/4.63 thf(func_def_95, type, sK12: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 23.12/4.63 thf(func_def_96, type, sK13: !>[X0: $tType]:(list @ X0 > X0)).
% 23.12/4.63 thf(func_def_97, type, sK14: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_98, type, sK15: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_99, type, sK16: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_100, type, sK17: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_101, type, sK18: !>[X0: $tType]:((poly @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_102, type, sK19: !>[X0: $tType]:((poly @ X0 > $o) > poly @ X0)).
% 23.12/4.63 thf(func_def_103, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 23.12/4.63 thf(func_def_104, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 23.12/4.63 thf(func_def_105, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_106, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 23.12/4.63 thf(func_def_107, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 23.12/4.63 thf(func_def_108, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 23.12/4.63 thf(func_def_109, type, sK26: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 23.12/4.63 thf(func_def_110, type, sK27: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 23.12/4.63 thf(func_def_111, type, sK28: !>[X0: $tType]:(poly @ X0 > X0)).
% 23.12/4.63 thf(func_def_112, type, sK29: !>[X0: $tType]:(poly @ X0 > poly @ X0)).
% 23.12/4.63 thf(func_def_113, type, sK30: !>[X0: $tType]:(list @ X0 > X0)).
% 23.12/4.63 thf(func_def_114, type, sK31: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 23.12/4.63 thf(func_def_115, type, sK32: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_116, type, sK33: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_117, type, sK34: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_118, type, sK35: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_119, type, sK36: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_120, type, sK37: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_121, type, sK38: (nat > $o) > nat).
% 23.12/4.63 thf(func_def_122, type, sK39: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_123, type, sK40: !>[X0: $tType, X1: $tType]:((poly @ X0 > poly @ X1 > $o) > X0)).
% 23.12/4.63 thf(func_def_124, type, sK41: !>[X0: $tType, X1: $tType]:((poly @ X0 > poly @ X1 > $o) > poly @ X0)).
% 23.12/4.63 thf(func_def_125, type, sK42: !>[X0: $tType, X1: $tType]:((poly @ X0 > poly @ X1 > $o) > X1)).
% 23.12/4.63 thf(func_def_126, type, sK43: !>[X0: $tType, X1: $tType]:((poly @ X0 > poly @ X1 > $o) > poly @ X1)).
% 23.12/4.63 thf(func_def_127, type, sK44: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 23.12/4.63 thf(func_def_128, type, sK45: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_129, type, sK46: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 23.12/4.63 thf(func_def_130, type, sK47: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 23.12/4.63 thf(func_def_131, type, sK48: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_132, type, sK49: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_133, type, sK50: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_134, type, sK51: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_135, type, sK52: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_136, type, sK53: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 23.12/4.63 thf(func_def_137, type, sK54: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 23.12/4.63 thf(func_def_138, type, sK55: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_139, type, sK56: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_140, type, sK57: (nat > $o) > nat).
% 23.12/4.63 thf(func_def_141, type, sK58: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_142, type, sK59: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_143, type, sK60: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_144, type, sK61: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_145, type, sK62: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_146, type, sK63: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_147, type, sK64: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_148, type, sK65: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_149, type, sK66: !>[X0: $tType]:((poly @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_150, type, sK67: !>[X0: $tType]:((poly @ X0 > $o) > poly @ X0)).
% 23.12/4.63 thf(func_def_151, type, sK68: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_152, type, sK69: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_153, type, sK70: !>[X0: $tType]:(poly @ X0 > X0)).
% 23.12/4.63 thf(func_def_154, type, sK71: !>[X0: $tType]:(poly @ X0 > poly @ X0)).
% 23.12/4.63 thf(func_def_155, type, sK72: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_156, type, sK73: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_157, type, sK74: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_158, type, sK75: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_159, type, sK76: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 23.12/4.63 thf(func_def_160, type, sK77: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 23.12/4.63 thf(func_def_161, type, sK78: !>[X0: $tType]:(list @ X0 > X0)).
% 23.12/4.63 thf(func_def_162, type, sK79: !>[X0: $tType]:(list @ X0 > X0)).
% 23.12/4.63 thf(func_def_163, type, sK80: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 23.12/4.63 thf(func_def_164, type, sK81: !>[X0: $tType]:(list @ X0 > X0)).
% 23.12/4.63 thf(func_def_165, type, sK82: (nat > $o) > nat).
% 23.12/4.63 thf(func_def_166, type, sK83: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 23.12/4.63 thf(func_def_168, type, ph85: !>[X0: $tType]:(X0)).
% 23.12/4.63 thf(f2093,plain,(
% 23.12/4.63 $false),
% 23.12/4.63 inference(subsumption_resolution,[status(thm)],[f1506,f2092])).
% 23.12/4.63 thf(f2092,plain,(
% 23.12/4.63 ( ! [X0 : list @ a] : (((descar149487500hanges @ a @ X0) = (descar149487500hanges @ a @ (append @ a @ X0 @ (cons @ a @ zero_zero @ a @ nil @ a))))) )),
% 23.12/4.63 inference(forward_demodulation,[status(thm)],[f2091,f1546])).
% 23.12/4.63 thf(f1546,plain,(
% 23.12/4.63 ( ! [X0 : list @ a] : (((descar149487500hanges @ a @ (coeffs @ a @ (poly2 @ a @ X0))) = (descar149487500hanges @ a @ X0))) )),
% 23.12/4.63 inference(trivial_inequality_removal,[status(thm)],[f1530])).
% 23.12/4.63 thf(f1530,plain,(
% 23.12/4.63 ( ! [X0 : list @ a] : (((descar149487500hanges @ a @ (coeffs @ a @ (poly2 @ a @ X0))) = (descar149487500hanges @ a @ X0)) | ($true != $true)) )),
% 23.12/4.63 inference(superposition,[status(thm)],[f1502,f1395])).
% 23.12/4.63 thf(f1395,plain,(
% 23.12/4.63 (linordered_idom @ a = $true)),
% 23.12/4.63 inference(cnf_transformation,[status(thm)],[f567])).
% 23.12/4.63 thf(f567,plain,(
% 23.12/4.63 (linordered_idom @ a = $true)),
% 23.12/4.63 inference(fool_elimination,[status(thm)],[f566])).
% 23.12/4.63 thf(f566,plain,(
% 23.12/4.63 linordered_idom @ a),
% 23.12/4.63 inference(rectify,[status(thm)],[f364])).
% 23.12/4.63 thf(f364,axiom,(
% 23.12/4.63 linordered_idom @ a),
% 23.12/4.63 file('/export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2THF_578.p',tfree_0)).
% 23.12/4.63 thf(f1502,plain,(
% 23.12/4.63 ( ! [X0 : $tType,X1 : list @ X0] : ((linordered_idom @ X0 != $true) | ((descar149487500hanges @ X0 @ (coeffs @ X0 @ (poly2 @ X0 @ X1))) = (descar149487500hanges @ X0 @ X1))) )),
% 23.12/4.63 inference(equality_resolution,[status(thm)],[f1485])).
% 23.12/4.63 thf(f1485,plain,(
% 23.12/4.63 ( ! [X0 : $tType,X2 : poly @ X0,X1 : list @ X0] : ((linordered_idom @ X0 != $true) | ((poly2 @ X0 @ X1) != X2) | ((descar149487500hanges @ X0 @ (coeffs @ X0 @ X2)) = (descar149487500hanges @ X0 @ X1))) )),
% 23.12/4.63 inference(cnf_transformation,[status(thm)],[f1083])).
% 23.12/4.63 thf(f1083,plain,(
% 23.12/4.63 ! [X0 : $tType] : ((linordered_idom @ X0 != $true) | ! [X1 : list @ X0,X2 : poly @ X0] : (((poly2 @ X0 @ X1) != X2) | ((descar149487500hanges @ X0 @ (coeffs @ X0 @ X2)) = (descar149487500hanges @ X0 @ X1))))),
% 23.12/4.63 inference(ennf_transformation,[status(thm)],[f755])).
% 23.12/4.63 thf(f755,plain,(
% 23.12/4.63 ! [X0 : $tType] : ((linordered_idom @ X0 = $true) => ! [X1 : list @ X0,X2 : poly @ X0] : (((poly2 @ X0 @ X1) = X2) => ((descar149487500hanges @ X0 @ (coeffs @ X0 @ X2)) = (descar149487500hanges @ X0 @ X1))))),
% 23.12/4.63 inference(fool_elimination,[status(thm)],[f754])).
% 23.12/4.63 thf(f754,plain,(
% 23.12/4.63 ! [X0 : $tType] : (linordered_idom @ X0 => ! [X1 : list @ X0,X2 : poly @ X0] : (((poly2 @ X0 @ X1) = X2) => ((descar149487500hanges @ X0 @ (coeffs @ X0 @ X2)) = (descar149487500hanges @ X0 @ X1))))),
% 23.12/4.63 inference(rectify,[status(thm)],[f5])).
% 23.12/4.63 thf(f5,axiom,(
% 23.12/4.63 ! [X0 : $tType] : (linordered_idom @ X0 => ! [X6 : list @ X0,X7 : poly @ X0] : (((poly2 @ X0 @ X6) = X7) => ((descar149487500hanges @ X0 @ X6) = (descar149487500hanges @ X0 @ (coeffs @ X0 @ X7)))))),
% 23.12/4.63 file('/export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2THF_578.p',fact_4_sign__changes__coeff__sign__changes)).
% 23.12/4.63 thf(f2091,plain,(
% 23.12/4.63 ( ! [X0 : list @ a] : (((descar149487500hanges @ a @ (coeffs @ a @ (poly2 @ a @ X0))) = (descar149487500hanges @ a @ (append @ a @ X0 @ (cons @ a @ zero_zero @ a @ nil @ a))))) )),
% 23.12/4.63 inference(subsumption_resolution,[status(thm)],[f2086,f1552])).
% 23.12/4.63 thf(f1552,plain,(
% 23.12/4.63 (zero @ a = $true)),
% 23.12/4.63 inference(trivial_inequality_removal,[status(thm)],[f1527])).
% 23.12/4.63 thf(f1527,plain,(
% 23.12/4.63 (zero @ a = $true) | ($true != $true)),
% 23.12/4.63 inference(superposition,[status(thm)],[f1459,f1395])).
% 23.12/4.63 thf(f1459,plain,(
% 23.12/4.63 ( ! [X0 : $tType] : ((linordered_idom @ X0 != $true) | (zero @ X0 = $true)) )),
% 23.12/4.63 inference(cnf_transformation,[status(thm)],[f1189])).
% 23.12/4.63 thf(f1189,plain,(
% 23.12/4.63 ! [X0 : $tType] : ((zero @ X0 = $true) | (linordered_idom @ X0 != $true))),
% 23.12/4.63 inference(ennf_transformation,[status(thm)],[f1017])).
% 23.12/4.63 thf(f1017,plain,(
% 23.12/4.63 ! [X0 : $tType] : ((linordered_idom @ X0 = $true) => (zero @ X0 = $true))),
% 23.12/4.63 inference(fool_elimination,[status(thm)],[f1016])).
% 23.12/4.63 thf(f1016,plain,(
% 23.12/4.63 ! [X0 : $tType] : (linordered_idom @ X0 => zero @ X0)),
% 23.12/4.63 inference(rectify,[status(thm)],[f260])).
% 23.12/4.63 thf(f260,axiom,(
% 23.12/4.63 ! [X0 : $tType] : (linordered_idom @ X0 => zero @ X0)),
% 23.12/4.63 file('/export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2THF_578.p',subcl_Rings_Olinordered__idom___Groups_Ozero)).
% 23.12/4.63 thf(f2086,plain,(
% 23.12/4.63 ( ! [X0 : list @ a] : (((descar149487500hanges @ a @ (coeffs @ a @ (poly2 @ a @ X0))) = (descar149487500hanges @ a @ (append @ a @ X0 @ (cons @ a @ zero_zero @ a @ nil @ a)))) | (zero @ a != $true)) )),
% 23.12/4.63 inference(superposition,[status(thm)],[f1546,f1384])).
% 23.12/4.63 thf(f1384,plain,(
% 23.12/4.63 ( ! [X0 : $tType,X1 : list @ X0] : ((zero @ X0 != $true) | ((poly2 @ X0 @ X1) = (poly2 @ X0 @ (append @ X0 @ X1 @ (cons @ X0 @ zero_zero @ X0 @ nil @ X0))))) )),
% 23.12/4.63 inference(cnf_transformation,[status(thm)],[f1108])).
% 23.12/4.63 thf(f1108,plain,(
% 23.12/4.63 ! [X0 : $tType] : (! [X1 : list @ X0] : ((poly2 @ X0 @ X1) = (poly2 @ X0 @ (append @ X0 @ X1 @ (cons @ X0 @ zero_zero @ X0 @ nil @ X0)))) | (zero @ X0 != $true))),
% 23.12/4.63 inference(ennf_transformation,[status(thm)],[f915])).
% 23.12/4.63 thf(f915,plain,(
% 23.12/4.63 ! [X0 : $tType] : ((zero @ X0 = $true) => ! [X1 : list @ X0] : ((poly2 @ X0 @ X1) = (poly2 @ X0 @ (append @ X0 @ X1 @ (cons @ X0 @ zero_zero @ X0 @ nil @ X0)))))),
% 23.12/4.63 inference(fool_elimination,[status(thm)],[f914])).
% 23.12/4.63 thf(f914,plain,(
% 23.12/4.63 ! [X0 : $tType] : (zero @ X0 => ! [X1 : list @ X0] : ((poly2 @ X0 @ X1) = (poly2 @ X0 @ (append @ X0 @ X1 @ (cons @ X0 @ zero_zero @ X0 @ nil @ X0)))))),
% 23.12/4.63 inference(rectify,[status(thm)],[f36])).
% 23.12/4.63 thf(f36,axiom,(
% 23.12/4.63 ! [X0 : $tType] : (zero @ X0 => ! [X13 : list @ X0] : ((poly2 @ X0 @ (append @ X0 @ X13 @ (cons @ X0 @ zero_zero @ X0 @ nil @ X0))) = (poly2 @ X0 @ X13)))),
% 23.12/4.63 file('/export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2THF_578.p',fact_35_Poly__snoc__zero)).
% 23.12/4.63 thf(f1506,plain,(
% 23.12/4.63 ((descar149487500hanges @ a @ (coeffs @ a @ g)) != (descar149487500hanges @ a @ (append @ a @ (coeffs @ a @ g) @ (cons @ a @ zero_zero @ a @ nil @ a))))),
% 23.12/4.63 inference(forward_demodulation,[status(thm)],[f1490,f1491])).
% 23.12/4.63 thf(f1491,plain,(
% 23.12/4.63 ((append @ a @ (coeffs @ a @ g) @ (cons @ a @ zero_zero @ a @ nil @ a)) = (descar1668888542_psums @ a @ (coeffs @ a @ (times_times @ poly @ a @ (pCons @ a @ one_one @ a @ (pCons @ a @ (uminus_uminus @ a @ one_one @ a) @ zero_zero @ poly @ a)) @ g))))),
% 23.12/4.63 inference(definition_unfolding,[status(thm)],[f1473,f1488])).
% 23.12/4.63 thf(f1488,plain,(
% 23.12/4.63 (ys = (descar1668888542_psums @ a @ (coeffs @ a @ (times_times @ poly @ a @ (pCons @ a @ one_one @ a @ (pCons @ a @ (uminus_uminus @ a @ one_one @ a) @ zero_zero @ poly @ a)) @ g))))),
% 23.12/4.63 inference(definition_unfolding,[status(thm)],[f1439,f1421])).
% 23.12/4.63 thf(f1421,plain,(
% 23.12/4.63 (xs = (coeffs @ a @ (times_times @ poly @ a @ (pCons @ a @ one_one @ a @ (pCons @ a @ (uminus_uminus @ a @ one_one @ a) @ zero_zero @ poly @ a)) @ g)))),
% 23.12/4.63 inference(cnf_transformation,[status(thm)],[f11])).
% 23.12/4.63 thf(f11,axiom,(
% 23.12/4.63 (xs = (coeffs @ a @ (times_times @ poly @ a @ (pCons @ a @ one_one @ a @ (pCons @ a @ (uminus_uminus @ a @ one_one @ a) @ zero_zero @ poly @ a)) @ g)))),
% 23.12/4.63 file('/export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2THF_578.p',fact_10_xs__def)).
% 23.12/4.63 thf(f1439,plain,(
% 23.12/4.63 (ys = (descar1668888542_psums @ a @ xs))),
% 23.12/4.63 inference(cnf_transformation,[status(thm)],[f4])).
% 23.12/4.63 thf(f4,axiom,(
% 23.12/4.63 (ys = (descar1668888542_psums @ a @ xs))),
% 23.12/4.63 file('/export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2THF_578.p',fact_3_ys)).
% 23.12/4.63 thf(f1473,plain,(
% 23.12/4.63 (ys = (append @ a @ (coeffs @ a @ g) @ (cons @ a @ zero_zero @ a @ nil @ a)))),
% 23.12/4.63 inference(cnf_transformation,[status(thm)],[f6])).
% 23.12/4.63 thf(f6,axiom,(
% 23.12/4.63 (ys = (append @ a @ (coeffs @ a @ g) @ (cons @ a @ zero_zero @ a @ nil @ a)))),
% 23.12/4.63 file('/export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2THF_578.p',fact_5_ys__def)).
% 23.12/4.63 thf(f1490,plain,(
% 23.12/4.63 ((descar149487500hanges @ a @ (coeffs @ a @ g)) != (descar149487500hanges @ a @ (descar1668888542_psums @ a @ (coeffs @ a @ (times_times @ poly @ a @ (pCons @ a @ one_one @ a @ (pCons @ a @ (uminus_uminus @ a @ one_one @ a) @ zero_zero @ poly @ a)) @ g)))))),
% 23.12/4.63 inference(definition_unfolding,[status(thm)],[f1467,f1488])).
% 23.12/4.63 thf(f1467,plain,(
% 23.12/4.63 ((descar149487500hanges @ a @ ys) != (descar149487500hanges @ a @ (coeffs @ a @ g)))),
% 23.12/4.63 inference(cnf_transformation,[status(thm)],[f1036])).
% 23.12/4.63 thf(f1036,plain,(
% 23.12/4.63 ((descar149487500hanges @ a @ ys) != (descar149487500hanges @ a @ (coeffs @ a @ g)))),
% 23.12/4.63 inference(flattening,[status(thm)],[f366])).
% 23.12/4.63 thf(f366,negated_conjecture,(
% 23.12/4.63 ~((descar149487500hanges @ a @ ys) = (descar149487500hanges @ a @ (coeffs @ a @ g)))),
% 23.12/4.63 inference(negated_conjecture,[status(cth)],[f365])).
% 23.12/4.63 thf(f365,conjecture,(
% 23.12/4.63 ((descar149487500hanges @ a @ ys) = (descar149487500hanges @ a @ (coeffs @ a @ g)))),
% 23.12/4.63 file('/export/starexec/sandbox/tmp/tmp.t1D2MPpAeb/DTF2THF_578.p',conj_0)).
% 23.12/4.63 % SZS output end Proof for DTF2THF_578
% 23.12/4.63 % (854)------------------------------
% 23.12/4.63 % (854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.12/4.63 % (854)Termination reason: Refutation
% 23.12/4.63
% 23.12/4.63 % (854)Memory used [KB]: 7803
% 23.12/4.63 % (854)Time elapsed: 0.091 s
% 23.12/4.63 % (854)Instructions burned: 284 (million)
% 23.12/4.63 % (854)------------------------------
% 23.12/4.63 % (854)------------------------------
% 23.12/4.63 % (696)Success in time 3.06 s
%------------------------------------------------------------------------------