%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP062^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 08:55:15 AM UTC 2026
% Result : Theorem 167.96s 25.17s
% Output : Refutation 167.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP062^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:16 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.31/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : ITP062^2 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.47 % Domain : Interactive Theorem Proving
% 0.31/0.47 % Problem : Sledgehammer GenClock problem prob_249__3245100_1
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English :
% 0.31/0.47
% 0.31/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Des21]
% 0.31/0.47 % Names : GenClock/prob_249__3245100_1 [Des21]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.33 v9.1.0, 0.00 v8.1.0, 0.25 v7.5.0
% 0.31/0.47 % Syntax : Number of formulae : 411 ( 132 unt; 71 typ; 0 def)
% 0.31/0.47 % Number of atoms : 798 ( 265 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 13 ( 2 avg)
% 0.31/0.47 % Number of connectives : 3648 ( 19 ~; 7 |; 32 &;3264 @)
% 0.31/0.47 % ( 0 <=>; 326 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 17 ( 6 avg)
% 0.31/0.47 % Number of types : 4 ( 3 usr)
% 0.31/0.47 % Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 69 ( 68 usr; 6 con; 0-4 aty)
% 0.31/0.47 % Number of variables : 907 ( 37 ^; 813 !; 5 ?; 907 :)
% 0.31/0.47 % ( 52 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.47 % SPC : TH1_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:15:17.989
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % Could-be-implicit typings (4)
% 0.31/0.47 thf(ty_t_Real_Oreal,type,
% 0.31/0.47 real: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Set_Oset,type,
% 0.31/0.47 set: $tType > $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Num_Onum,type,
% 0.31/0.47 num: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(ty_t_Nat_Onat,type,
% 0.31/0.47 nat: $tType ).
% 0.31/0.47
% 0.31/0.47 % Explicit typings (67)
% 0.31/0.47 thf(sy_cl_HOL_Otype,type,
% 0.31/0.47 type:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Odvd,type,
% 0.31/0.47 dvd:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oone,type,
% 0.31/0.47 one:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Oring,type,
% 0.31/0.47 ring:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Num_Onumeral,type,
% 0.31/0.47 numeral:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ominus,type,
% 0.31/0.47 minus:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Oring__1,type,
% 0.31/0.47 ring_1:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.31/0.47 ord:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Osemiring,type,
% 0.31/0.47 semiring:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Num_Oneg__numeral,type,
% 0.31/0.47 neg_numeral:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.31/0.47 order:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Ocomm__ring,type,
% 0.31/0.47 comm_ring:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.31/0.47 group_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.31/0.47 monoid_mult:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/0.47 linorder:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.31/0.47 preorder:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Oidom__abs__sgn,type,
% 0.31/0.47 idom_abs_sgn:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Oordered__ring,type,
% 0.31/0.47 ordered_ring:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oab__group__add,type,
% 0.31/0.47 ab_group_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.31/0.47 semiring_char_0:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Ocomm__semiring,type,
% 0.31/0.47 comm_semiring:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.31/0.47 semigroup_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Num_Osemiring__numeral,type,
% 0.31/0.47 semiring_numeral:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.31/0.47 semigroup_mult:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.31/0.47 linordered_idom:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.31/0.47 comm_monoid_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.31/0.47 ab_semigroup_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 0.31/0.47 comm_monoid_mult:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.31/0.47 ab_semigroup_mult:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.31/0.47 linordered_semidom:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.31/0.47 cancel_semigroup_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.31/0.47 ordered_ab_group_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Ocomm__semiring__1__cancel,type,
% 0.31/0.47 comm_s1003936772cancel:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.31/0.47 cancel1352612707id_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.31/0.47 cancel146912293up_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oordered__ab__group__add__abs,type,
% 0.31/0.47 ordere142940540dd_abs:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.31/0.47 ordere779506340up_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.31/0.47 linord1659791738miring:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.31/0.47 canoni770627133id_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.31/0.47 ordere236663937imp_le:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__diff,type,
% 0.31/0.47 ordere623563068d_diff:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 0.31/0.47 semiri456707255roduct:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OPC,type,
% 0.31/0.47 genClo1161277105lle_PC: nat > real > real ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060rho_062,type,
% 0.31/0.47 genClo1144207539le_rho: real ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ocorrect,type,
% 0.31/0.47 genClo1015804716orrect: nat > real > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead1,type,
% 0.31/0.47 genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead2,type,
% 0.31/0.47 genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Orho__bound1,type,
% 0.31/0.47 genClo2108747022bound1: ( nat > real > real ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Orho__bound2,type,
% 0.31/0.47 genClo2108747023bound2: ( nat > real > real ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Groups_Oabs__class_Oabs,type,
% 0.31/0.47 abs_abs:
% 0.31/0.47 !>[A: $tType] : ( A > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.31/0.47 minus_minus:
% 0.31/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.31/0.47 one_one:
% 0.31/0.47 !>[A: $tType] : A ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.31/0.47 plus_plus:
% 0.31/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.31/0.47 times_times:
% 0.31/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Num_Oneg__numeral__class_Odbl,type,
% 0.31/0.47 neg_numeral_dbl:
% 0.31/0.47 !>[A: $tType] : ( A > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Num_Onum_OBit0,type,
% 0.31/0.47 bit0: num > num ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Num_Onum_OOne,type,
% 0.31/0.47 one2: num ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 0.31/0.47 numeral_numeral:
% 0.31/0.47 !>[A: $tType] : ( num > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/0.47 ord_less_eq:
% 0.31/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect,type,
% 0.31/0.47 collect:
% 0.31/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member,type,
% 0.31/0.47 member:
% 0.31/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_C,type,
% 0.31/0.47 c: nat > real > real ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_D,type,
% 0.31/0.47 d: nat > real > real ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_p,type,
% 0.31/0.47 p: nat ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_q,type,
% 0.31/0.47 q: nat ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_s,type,
% 0.31/0.47 s: real ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_t,type,
% 0.31/0.47 t: real ).
% 0.31/0.47
% 0.31/0.47 % Relevant facts (253)
% 0.31/0.47 thf(fact_0_rb2,axiom,
% 0.31/0.47 genClo2108747023bound2 @ d ).
% 0.31/0.47
% 0.31/0.47 % rb2
% 0.31/0.47 thf(fact_1_rb1,axiom,
% 0.31/0.47 genClo2108747022bound1 @ c ).
% 0.31/0.47
% 0.31/0.47 % rb1
% 0.31/0.47 thf(fact_2_ie,axiom,
% 0.31/0.47 ord_less_eq @ real @ s @ t ).
% 0.31/0.47
% 0.31/0.47 % ie
% 0.31/0.47 thf(fact_3_Eq1,axiom,
% 0.31/0.47 ( ( abs_abs @ real @ ( minus_minus @ real @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
% 0.31/0.47 = ( minus_minus @ real @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Eq1
% 0.31/0.47 thf(fact_4_Eq4,axiom,
% 0.31/0.47 ( ( minus_minus @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) )
% 0.31/0.47 = ( times_times @ real @ ( times_times @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ genClo1144207539le_rho ) @ ( minus_minus @ real @ t @ s ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Eq4
% 0.31/0.47 thf(fact_5_Eq3,axiom,
% 0.31/0.47 ord_less_eq @ real @ ( minus_minus @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Eq3
% 0.31/0.47 thf(fact_6_corr__q,axiom,
% 0.31/0.47 genClo1015804716orrect @ q @ t ).
% 0.31/0.47
% 0.31/0.47 % corr_q
% 0.31/0.47 thf(fact_7_PC__ie,axiom,
% 0.31/0.47 ord_less_eq @ real @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) ).
% 0.31/0.47
% 0.31/0.47 % PC_ie
% 0.31/0.47 thf(fact_8_corr__p,axiom,
% 0.31/0.47 genClo1015804716orrect @ p @ t ).
% 0.31/0.47
% 0.31/0.47 % corr_p
% 0.31/0.47 thf(fact_9_Eq2,axiom,
% 0.31/0.47 ord_less_eq @ real @ ( minus_minus @ real @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Eq2
% 0.31/0.47 thf(fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062,axiom,
% 0.31/0.47 ord_less_eq @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>(t - s) * (1 - \<rho>) \<le> D q t - D q s\<close>
% 0.31/0.47 thf(fact_11_left__diff__distrib__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ( numeral @ A )
% 0.31/0.47 & ( ring @ A ) )
% 0.31/0.47 => ! [A2: A,B: A,V: num] :
% 0.31/0.47 ( ( times_times @ A @ ( minus_minus @ A @ A2 @ B ) @ ( numeral_numeral @ A @ V ) )
% 0.31/0.47 = ( minus_minus @ A @ ( times_times @ A @ A2 @ ( numeral_numeral @ A @ V ) ) @ ( times_times @ A @ B @ ( numeral_numeral @ A @ V ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % left_diff_distrib_numeral
% 0.31/0.47 thf(fact_12_right__diff__distrib__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ( numeral @ A )
% 0.31/0.47 & ( ring @ A ) )
% 0.31/0.47 => ! [V: num,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( minus_minus @ A @ B @ C ) )
% 0.31/0.47 = ( minus_minus @ A @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ B ) @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % right_diff_distrib_numeral
% 0.31/0.47 thf(fact_13_abs__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [N: num] :
% 0.31/0.47 ( ( abs_abs @ A @ ( numeral_numeral @ A @ N ) )
% 0.31/0.47 = ( numeral_numeral @ A @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_numeral
% 0.31/0.47 thf(fact_14_abs__mult__self__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( times_times @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ A2 ) )
% 0.31/0.47 = ( times_times @ A @ A2 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_mult_self_eq
% 0.31/0.47 thf(fact_15_semiring__norm_I85_J,axiom,
% 0.31/0.47 ! [M: num] :
% 0.31/0.47 ( ( bit0 @ M )
% 0.31/0.47 != one2 ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(85)
% 0.31/0.47 thf(fact_16_semiring__norm_I83_J,axiom,
% 0.31/0.47 ! [N: num] :
% 0.31/0.47 ( one2
% 0.31/0.47 != ( bit0 @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(83)
% 0.31/0.47 thf(fact_17_mult__numeral__left__semiring__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_numeral @ A )
% 0.31/0.47 => ! [V: num,W: num,Z: A] :
% 0.31/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( times_times @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.31/0.47 = ( times_times @ A @ ( numeral_numeral @ A @ ( times_times @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult_numeral_left_semiring_numeral
% 0.31/0.47 thf(fact_18_numeral__times__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_numeral @ A )
% 0.31/0.47 => ! [M: num,N: num] :
% 0.31/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.31/0.47 = ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_times_numeral
% 0.31/0.47 thf(fact_19_numeral__le__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linord1659791738miring @ A )
% 0.31/0.47 => ! [M: num,N: num] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.31/0.47 = ( ord_less_eq @ num @ M @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_le_iff
% 0.31/0.47 thf(fact_20_okRead2__def,axiom,
% 0.31/0.47 ( genClo293725282kRead2
% 0.31/0.47 = ( ^ [F: nat > real,G: nat > real,X: real,Ppred: nat > $o] :
% 0.31/0.47 ! [P: nat] :
% 0.31/0.47 ( ( Ppred @ P )
% 0.31/0.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( F @ P ) @ ( G @ P ) ) ) @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % okRead2_def
% 0.31/0.47 thf(fact_21_abs__triangle__ineq2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_triangle_ineq2
% 0.31/0.47 thf(fact_22_abs__triangle__ineq3,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_triangle_ineq3
% 0.31/0.47 thf(fact_23_numeral__eq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_char_0 @ A )
% 0.31/0.47 => ! [M: num,N: num] :
% 0.31/0.47 ( ( ( numeral_numeral @ A @ M )
% 0.31/0.47 = ( numeral_numeral @ A @ N ) )
% 0.31/0.47 = ( M = N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_eq_iff
% 0.31/0.47 thf(fact_24_add__left__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel_semigroup_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/0.47 = ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_left_cancel
% 0.31/0.47 thf(fact_25_add__right__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel_semigroup_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.31/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/0.47 = ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_right_cancel
% 0.31/0.47 thf(fact_26_semiring__norm_I87_J,axiom,
% 0.31/0.47 ! [M: num,N: num] :
% 0.31/0.47 ( ( ( bit0 @ M )
% 0.31/0.47 = ( bit0 @ N ) )
% 0.31/0.47 = ( M = N ) ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(87)
% 0.31/0.47 thf(fact_27_abs__idempotent,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 0.31/0.47 = ( abs_abs @ A @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_idempotent
% 0.31/0.47 thf(fact_28_abs__abs,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( idom_abs_sgn @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 0.31/0.47 = ( abs_abs @ A @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_abs
% 0.31/0.47 thf(fact_29_add__le__cancel__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_cancel_right
% 0.31/0.47 thf(fact_30_add__le__cancel__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [C: A,A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.31/0.47 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_cancel_left
% 0.31/0.47 thf(fact_31_mult_Oright__neutral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( monoid_mult @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult.right_neutral
% 0.31/0.47 thf(fact_32_mult_Oleft__neutral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( monoid_mult @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult.left_neutral
% 0.31/0.47 thf(fact_33_numeral__plus__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( numeral @ A )
% 0.31/0.47 => ! [M: num,N: num] :
% 0.31/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.31/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ M @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_plus_numeral
% 0.31/0.47 thf(fact_34_add__numeral__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( numeral @ A )
% 0.31/0.47 => ! [V: num,W: num,Z: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.31/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_numeral_left
% 0.31/0.47 thf(fact_35_add__diff__cancel__right_H,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel146912293up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_diff_cancel_right'
% 0.31/0.47 thf(fact_36_add__diff__cancel__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel146912293up_add @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_diff_cancel_right
% 0.31/0.47 thf(fact_37_add__diff__cancel__left_H,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel146912293up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ A2 )
% 0.31/0.47 = B ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_diff_cancel_left'
% 0.31/0.47 thf(fact_38_add__diff__cancel__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel146912293up_add @ A )
% 0.31/0.47 => ! [C: A,A2: A,B: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.31/0.47 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_diff_cancel_left
% 0.31/0.47 thf(fact_39_diff__add__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_add_cancel
% 0.31/0.47 thf(fact_40_add__diff__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_diff_cancel
% 0.31/0.47 thf(fact_41_abs__add__abs,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( abs_abs @ A @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) )
% 0.31/0.47 = ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_add_abs
% 0.31/0.47 thf(fact_42_abs__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( idom_abs_sgn @ A )
% 0.31/0.47 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.31/0.47 = ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_1
% 0.31/0.47 thf(fact_43_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: $tType,A2: A,P2: A > $o] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.31/0.47 = ( P2 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_44_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A: $tType,A3: set @ A] :
% 0.31/0.47 ( ( collect @ A
% 0.31/0.47 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 0.31/0.47 = A3 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_45_Collect__cong,axiom,
% 0.31/0.47 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.31/0.47 ( ! [X2: A] :
% 0.31/0.47 ( ( P2 @ X2 )
% 0.31/0.47 = ( Q @ X2 ) )
% 0.31/0.47 => ( ( collect @ A @ P2 )
% 0.31/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_46_ext,axiom,
% 0.31/0.47 ! [B2: $tType,A: $tType,F2: A > B2,G2: A > B2] :
% 0.31/0.47 ( ! [X2: A] :
% 0.31/0.47 ( ( F2 @ X2 )
% 0.31/0.47 = ( G2 @ X2 ) )
% 0.31/0.47 => ( F2 = G2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % ext
% 0.31/0.47 thf(fact_47_semiring__norm_I13_J,axiom,
% 0.31/0.47 ! [M: num,N: num] :
% 0.31/0.47 ( ( times_times @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.31/0.47 = ( bit0 @ ( bit0 @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(13)
% 0.31/0.47 thf(fact_48_semiring__norm_I11_J,axiom,
% 0.31/0.47 ! [M: num] :
% 0.31/0.47 ( ( times_times @ num @ M @ one2 )
% 0.31/0.47 = M ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(11)
% 0.31/0.47 thf(fact_49_semiring__norm_I12_J,axiom,
% 0.31/0.47 ! [N: num] :
% 0.31/0.47 ( ( times_times @ num @ one2 @ N )
% 0.31/0.47 = N ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(12)
% 0.31/0.47 thf(fact_50_semiring__norm_I71_J,axiom,
% 0.31/0.47 ! [M: num,N: num] :
% 0.31/0.47 ( ( ord_less_eq @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.31/0.47 = ( ord_less_eq @ num @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(71)
% 0.31/0.47 thf(fact_51_semiring__norm_I68_J,axiom,
% 0.31/0.47 ! [N: num] : ( ord_less_eq @ num @ one2 @ N ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(68)
% 0.31/0.47 thf(fact_52_le__add__diff__inverse2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_semidom @ A )
% 0.31/0.47 => ! [B: A,A2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.47 => ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 0.31/0.47 = A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_add_diff_inverse2
% 0.31/0.47 thf(fact_53_le__add__diff__inverse,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_semidom @ A )
% 0.31/0.47 => ! [B: A,A2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.47 => ( ( plus_plus @ A @ B @ ( minus_minus @ A @ A2 @ B ) )
% 0.31/0.47 = A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_add_diff_inverse
% 0.31/0.47 thf(fact_54_distrib__right__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ( numeral @ A )
% 0.31/0.47 & ( semiring @ A ) )
% 0.31/0.47 => ! [A2: A,B: A,V: num] :
% 0.31/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ ( numeral_numeral @ A @ V ) )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ A2 @ ( numeral_numeral @ A @ V ) ) @ ( times_times @ A @ B @ ( numeral_numeral @ A @ V ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % distrib_right_numeral
% 0.31/0.47 thf(fact_55_distrib__left__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ( numeral @ A )
% 0.31/0.47 & ( semiring @ A ) )
% 0.31/0.47 => ! [V: num,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ B ) @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % distrib_left_numeral
% 0.31/0.47 thf(fact_56_one__eq__numeral__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_char_0 @ A )
% 0.31/0.47 => ! [N: num] :
% 0.31/0.47 ( ( ( one_one @ A )
% 0.31/0.47 = ( numeral_numeral @ A @ N ) )
% 0.31/0.47 = ( one2 = N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_eq_numeral_iff
% 0.31/0.47 thf(fact_57_numeral__eq__one__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_char_0 @ A )
% 0.31/0.47 => ! [N: num] :
% 0.31/0.47 ( ( ( numeral_numeral @ A @ N )
% 0.31/0.47 = ( one_one @ A ) )
% 0.31/0.47 = ( N = one2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_eq_one_iff
% 0.31/0.47 thf(fact_58_num__double,axiom,
% 0.31/0.47 ! [N: num] :
% 0.31/0.47 ( ( times_times @ num @ ( bit0 @ one2 ) @ N )
% 0.31/0.47 = ( bit0 @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % num_double
% 0.31/0.47 thf(fact_59_semiring__norm_I69_J,axiom,
% 0.31/0.47 ! [M: num] :
% 0.31/0.47 ~ ( ord_less_eq @ num @ ( bit0 @ M ) @ one2 ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(69)
% 0.31/0.47 thf(fact_60_one__plus__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( numeral @ A )
% 0.31/0.47 => ! [N: num] :
% 0.31/0.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
% 0.31/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_plus_numeral
% 0.31/0.47 thf(fact_61_numeral__plus__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( numeral @ A )
% 0.31/0.47 => ! [N: num] :
% 0.31/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 0.31/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ N @ one2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_plus_one
% 0.31/0.47 thf(fact_62_one__add__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( numeral @ A )
% 0.31/0.47 => ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.31/0.47 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_add_one
% 0.31/0.47 thf(fact_63_numeral__le__one__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linord1659791738miring @ A )
% 0.31/0.47 => ! [N: num] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 0.31/0.47 = ( ord_less_eq @ num @ N @ one2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_le_one_iff
% 0.31/0.47 thf(fact_64_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.31/0.47 thf(fact_65_is__num__normalize_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( neg_numeral @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % is_num_normalize(1)
% 0.31/0.47 thf(fact_66_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( I = J )
% 0.31/0.47 & ( K = L ) )
% 0.31/0.47 => ( ( plus_plus @ A @ I @ K )
% 0.31/0.47 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_semiring(4)
% 0.31/0.47 thf(fact_67_one__reorient,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( one @ A )
% 0.31/0.47 => ! [X3: A] :
% 0.31/0.47 ( ( ( one_one @ A )
% 0.31/0.47 = X3 )
% 0.31/0.47 = ( X3
% 0.31/0.47 = ( one_one @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_reorient
% 0.31/0.47 thf(fact_68_group__cancel_Oadd1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_monoid_add @ A )
% 0.31/0.47 => ! [A3: A,K: A,A2: A,B: A] :
% 0.31/0.47 ( ( A3
% 0.31/0.47 = ( plus_plus @ A @ K @ A2 ) )
% 0.31/0.47 => ( ( plus_plus @ A @ A3 @ B )
% 0.31/0.47 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % group_cancel.add1
% 0.31/0.47 thf(fact_69_group__cancel_Oadd2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_monoid_add @ A )
% 0.31/0.47 => ! [B3: A,K: A,B: A,A2: A] :
% 0.31/0.47 ( ( B3
% 0.31/0.47 = ( plus_plus @ A @ K @ B ) )
% 0.31/0.47 => ( ( plus_plus @ A @ A2 @ B3 )
% 0.31/0.47 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % group_cancel.add2
% 0.31/0.47 thf(fact_70_add_Oassoc,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semigroup_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.assoc
% 0.31/0.47 thf(fact_71_add_Oleft__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/0.47 = ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.left_cancel
% 0.31/0.47 thf(fact_72_add_Oright__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.31/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/0.47 = ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.right_cancel
% 0.31/0.47 thf(fact_73_add_Ocommute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_add @ A )
% 0.31/0.47 => ( ( plus_plus @ A )
% 0.31/0.47 = ( ^ [A4: A,B4: A] : ( plus_plus @ A @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.commute
% 0.31/0.47 thf(fact_74_add_Oleft__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.left_commute
% 0.31/0.47 thf(fact_75_add__left__imp__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel_semigroup_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/0.47 => ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_left_imp_eq
% 0.31/0.47 thf(fact_76_add__right__imp__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel_semigroup_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.31/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/0.47 => ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_right_imp_eq
% 0.31/0.47 thf(fact_77_le__num__One__iff,axiom,
% 0.31/0.47 ! [X3: num] :
% 0.31/0.47 ( ( ord_less_eq @ num @ X3 @ one2 )
% 0.31/0.47 = ( X3 = one2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_num_One_iff
% 0.31/0.47 thf(fact_78_one__plus__numeral__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( numeral @ A )
% 0.31/0.47 => ! [X3: num] :
% 0.31/0.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X3 ) )
% 0.31/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ X3 ) @ ( one_one @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_plus_numeral_commute
% 0.31/0.47 thf(fact_79_correct__closed,axiom,
% 0.31/0.47 ! [P3: nat,S: real,T: real] :
% 0.31/0.47 ( ( ( ord_less_eq @ real @ S @ T )
% 0.31/0.47 & ( genClo1015804716orrect @ P3 @ T ) )
% 0.31/0.47 => ( genClo1015804716orrect @ P3 @ S ) ) ).
% 0.31/0.47
% 0.31/0.47 % correct_closed
% 0.31/0.47 thf(fact_80_add__le__imp__le__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_imp_le_right
% 0.31/0.47 thf(fact_81_add__le__imp__le__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [C: A,A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_imp_le_left
% 0.31/0.47 thf(fact_82_le__iff__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( canoni770627133id_add @ A )
% 0.31/0.47 => ( ( ord_less_eq @ A )
% 0.31/0.47 = ( ^ [A4: A,B4: A] :
% 0.31/0.47 ? [C2: A] :
% 0.31/0.47 ( B4
% 0.31/0.47 = ( plus_plus @ A @ A4 @ C2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_iff_add
% 0.31/0.47 thf(fact_83_add__right__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_right_mono
% 0.31/0.47 thf(fact_84_less__eqE,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( canoni770627133id_add @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ~ ! [C3: A] :
% 0.31/0.47 ( B
% 0.31/0.47 != ( plus_plus @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_eqE
% 0.31/0.47 thf(fact_85_add__left__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_left_mono
% 0.31/0.47 thf(fact_86_add__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ C @ D )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono
% 0.31/0.47 thf(fact_87_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/0.47 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_semiring(1)
% 0.31/0.47 thf(fact_88_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( I = J )
% 0.31/0.47 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_semiring(2)
% 0.31/0.47 thf(fact_89_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/0.47 & ( K = L ) )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_semiring(3)
% 0.31/0.47 thf(fact_90_combine__common__factor,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring @ A )
% 0.31/0.47 => ! [A2: A,E: A,B: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ C ) )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ E ) @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % combine_common_factor
% 0.31/0.47 thf(fact_91_distrib__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % distrib_right
% 0.31/0.47 thf(fact_92_distrib__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ A2 @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ A2 @ B ) @ ( times_times @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % distrib_left
% 0.31/0.47 thf(fact_93_comm__semiring__class_Odistrib,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_semiring @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % comm_semiring_class.distrib
% 0.31/0.47 thf(fact_94_ring__class_Oring__distribs_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ A2 @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ A2 @ B ) @ ( times_times @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ring_class.ring_distribs(1)
% 0.31/0.47 thf(fact_95_ring__class_Oring__distribs_I2_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ring_class.ring_distribs(2)
% 0.31/0.47 thf(fact_96_le__numeral__extra_I4_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linord1659791738miring @ A )
% 0.31/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_numeral_extra(4)
% 0.31/0.47 thf(fact_97_add__implies__diff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel1352612707id_add @ A )
% 0.31/0.47 => ! [C: A,B: A,A2: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ C @ B )
% 0.31/0.47 = A2 )
% 0.31/0.47 => ( C
% 0.31/0.47 = ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_implies_diff
% 0.31/0.47 thf(fact_98_diff__diff__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel146912293up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_diff_add
% 0.31/0.47 thf(fact_99_diff__add__eq__diff__diff__swap,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_add_eq_diff_diff_swap
% 0.31/0.47 thf(fact_100_diff__add__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_add_eq
% 0.31/0.47 thf(fact_101_diff__diff__eq2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( minus_minus @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.31/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_diff_eq2
% 0.31/0.47 thf(fact_102_add__diff__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.31/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_diff_eq
% 0.31/0.47 thf(fact_103_eq__diff__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( minus_minus @ A @ C @ B ) )
% 0.31/0.47 = ( ( plus_plus @ A @ A2 @ B )
% 0.31/0.47 = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_diff_eq
% 0.31/0.47 thf(fact_104_diff__eq__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ( minus_minus @ A @ A2 @ B )
% 0.31/0.47 = C )
% 0.31/0.47 = ( A2
% 0.31/0.47 = ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_eq_eq
% 0.31/0.47 thf(fact_105_group__cancel_Osub1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_group_add @ A )
% 0.31/0.47 => ! [A3: A,K: A,A2: A,B: A] :
% 0.31/0.47 ( ( A3
% 0.31/0.47 = ( plus_plus @ A @ K @ A2 ) )
% 0.31/0.47 => ( ( minus_minus @ A @ A3 @ B )
% 0.31/0.47 = ( plus_plus @ A @ K @ ( minus_minus @ A @ A2 @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % group_cancel.sub1
% 0.31/0.47 thf(fact_106_mult_Ocomm__neutral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_monoid_mult @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult.comm_neutral
% 0.31/0.47 thf(fact_107_comm__monoid__mult__class_Omult__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_monoid_mult @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % comm_monoid_mult_class.mult_1
% 0.31/0.47 thf(fact_108_abs__one,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.31/0.47 = ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_one
% 0.31/0.47 thf(fact_109_square__diff__one__factored,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring_1 @ A )
% 0.31/0.47 => ! [X3: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( times_times @ A @ X3 @ X3 ) @ ( one_one @ A ) )
% 0.31/0.47 = ( times_times @ A @ ( plus_plus @ A @ X3 @ ( one_one @ A ) ) @ ( minus_minus @ A @ X3 @ ( one_one @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % square_diff_one_factored
% 0.31/0.47 thf(fact_110_rho__bound1__def,axiom,
% 0.31/0.47 ( genClo2108747022bound1
% 0.31/0.47 = ( ^ [C4: nat > real > real] :
% 0.31/0.47 ! [P: nat,S2: real,T2: real] :
% 0.31/0.47 ( ( ( genClo1015804716orrect @ P @ T2 )
% 0.31/0.47 & ( ord_less_eq @ real @ S2 @ T2 ) )
% 0.31/0.47 => ( ord_less_eq @ real @ ( minus_minus @ real @ ( C4 @ P @ T2 ) @ ( C4 @ P @ S2 ) ) @ ( times_times @ real @ ( minus_minus @ real @ T2 @ S2 ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rho_bound1_def
% 0.31/0.47 thf(fact_111_mult_Oleft__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_mult @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ B @ ( times_times @ A @ A2 @ C ) )
% 0.31/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult.left_commute
% 0.31/0.47 thf(fact_112_mult_Ocommute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_mult @ A )
% 0.31/0.47 => ( ( times_times @ A )
% 0.31/0.47 = ( ^ [A4: A,B4: A] : ( times_times @ A @ B4 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult.commute
% 0.31/0.47 thf(fact_113_mult_Oassoc,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semigroup_mult @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ ( times_times @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult.assoc
% 0.31/0.47 thf(fact_114_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_mult @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ ( times_times @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ab_semigroup_mult_class.mult_ac(1)
% 0.31/0.47 thf(fact_115_diff__right__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel146912293up_add @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B )
% 0.31/0.47 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_right_commute
% 0.31/0.47 thf(fact_116_diff__eq__diff__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.31/0.47 ( ( ( minus_minus @ A @ A2 @ B )
% 0.31/0.47 = ( minus_minus @ A @ C @ D ) )
% 0.31/0.47 => ( ( A2 = B )
% 0.31/0.47 = ( C = D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_eq_diff_eq
% 0.31/0.47 thf(fact_117_rho__bound2__def,axiom,
% 0.31/0.47 ( genClo2108747023bound2
% 0.31/0.47 = ( ^ [C4: nat > real > real] :
% 0.31/0.47 ! [P: nat,S2: real,T2: real] :
% 0.31/0.47 ( ( ( genClo1015804716orrect @ P @ T2 )
% 0.31/0.47 & ( ord_less_eq @ real @ S2 @ T2 ) )
% 0.31/0.47 => ( ord_less_eq @ real @ ( times_times @ real @ ( minus_minus @ real @ T2 @ S2 ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( C4 @ P @ T2 ) @ ( C4 @ P @ S2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rho_bound2_def
% 0.31/0.47 thf(fact_118_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ( minus_minus @ A @ B @ A2 )
% 0.31/0.47 = C )
% 0.31/0.47 = ( B
% 0.31/0.47 = ( plus_plus @ A @ C @ A2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.31/0.47 thf(fact_119_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ A2 ) )
% 0.31/0.47 = B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.31/0.47 thf(fact_120_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( minus_minus @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.31/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ C @ A2 ) @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.31/0.47 thf(fact_121_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 )
% 0.31/0.47 = ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.31/0.47 thf(fact_122_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C )
% 0.31/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.31/0.47 thf(fact_123_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( minus_minus @ A @ ( plus_plus @ A @ C @ B ) @ A2 )
% 0.31/0.47 = ( plus_plus @ A @ C @ ( minus_minus @ A @ B @ A2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.31/0.47 thf(fact_124_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( plus_plus @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.31/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ C @ B ) @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.31/0.47 thf(fact_125_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.31/0.47 = ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.31/0.47 thf(fact_126_le__add__diff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ C @ ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_add_diff
% 0.31/0.47 thf(fact_127_add__le__add__imp__diff__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_semidom @ A )
% 0.31/0.47 => ! [I: A,K: A,N: A,J: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.31/0.47 => ( ( ord_less_eq @ A @ N @ ( plus_plus @ A @ J @ K ) )
% 0.31/0.47 => ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.31/0.47 => ( ( ord_less_eq @ A @ N @ ( plus_plus @ A @ J @ K ) )
% 0.31/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ N @ K ) @ J ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_add_imp_diff_le
% 0.31/0.47 thf(fact_128_diff__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere623563068d_diff @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ A2 )
% 0.31/0.47 = B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_add
% 0.31/0.47 thf(fact_129_add__le__imp__le__diff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_semidom @ A )
% 0.31/0.47 => ! [I: A,K: A,N: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.31/0.47 => ( ord_less_eq @ A @ I @ ( minus_minus @ A @ N @ K ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_imp_le_diff
% 0.31/0.47 thf(fact_130_le__diff__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ ( minus_minus @ A @ C @ B ) )
% 0.31/0.47 = ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_diff_eq
% 0.31/0.47 thf(fact_131_diff__le__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_le_eq
% 0.31/0.47 thf(fact_132_square__diff__square__factored,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_ring @ A )
% 0.31/0.47 => ! [X3: A,Y: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( times_times @ A @ X3 @ X3 ) @ ( times_times @ A @ Y @ Y ) )
% 0.31/0.47 = ( times_times @ A @ ( plus_plus @ A @ X3 @ Y ) @ ( minus_minus @ A @ X3 @ Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % square_diff_square_factored
% 0.31/0.47 thf(fact_133_eq__add__iff2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring @ A )
% 0.31/0.47 => ! [A2: A,E: A,C: A,B: A,D: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ D ) )
% 0.31/0.47 = ( C
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ ( minus_minus @ A @ B @ A2 ) @ E ) @ D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_add_iff2
% 0.31/0.47 thf(fact_134_eq__add__iff1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring @ A )
% 0.31/0.47 => ! [A2: A,E: A,C: A,B: A,D: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ D ) )
% 0.31/0.47 = ( ( plus_plus @ A @ ( times_times @ A @ ( minus_minus @ A @ A2 @ B ) @ E ) @ C )
% 0.31/0.47 = D ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_add_iff1
% 0.31/0.47 thf(fact_135_numeral__Bit0,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( numeral @ A )
% 0.31/0.47 => ! [N: num] :
% 0.31/0.47 ( ( numeral_numeral @ A @ ( bit0 @ N ) )
% 0.31/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_Bit0
% 0.31/0.47 thf(fact_136_one__le__numeral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linord1659791738miring @ A )
% 0.31/0.47 => ! [N: num] : ( ord_less_eq @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % one_le_numeral
% 0.31/0.47 thf(fact_137_abs__triangle__ineq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( plus_plus @ A @ A2 @ B ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_triangle_ineq
% 0.31/0.47 thf(fact_138_numeral__One,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( numeral @ A )
% 0.31/0.47 => ( ( numeral_numeral @ A @ one2 )
% 0.31/0.47 = ( one_one @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % numeral_One
% 0.31/0.47 thf(fact_139_ordered__ring__class_Ole__add__iff2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ring @ A )
% 0.31/0.47 => ! [A2: A,E: A,C: A,B: A,D: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ C ) @ ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ D ) )
% 0.31/0.47 = ( ord_less_eq @ A @ C @ ( plus_plus @ A @ ( times_times @ A @ ( minus_minus @ A @ B @ A2 ) @ E ) @ D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_ring_class.le_add_iff2
% 0.31/0.47 thf(fact_140_ordered__ring__class_Ole__add__iff1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ring @ A )
% 0.31/0.47 => ! [A2: A,E: A,C: A,B: A,D: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ C ) @ ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ D ) )
% 0.31/0.47 = ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ ( minus_minus @ A @ A2 @ B ) @ E ) @ C ) @ D ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ordered_ring_class.le_add_iff1
% 0.31/0.47 thf(fact_141_abs__diff__triangle__ineq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A,D: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ ( plus_plus @ A @ C @ D ) ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ C ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_diff_triangle_ineq
% 0.31/0.47 thf(fact_142_abs__triangle__ineq4,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_triangle_ineq4
% 0.31/0.47 thf(fact_143_abs__diff__le__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ! [X3: A,A2: A,R: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ X3 @ A2 ) ) @ R )
% 0.31/0.47 = ( ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ R ) @ X3 )
% 0.31/0.47 & ( ord_less_eq @ A @ X3 @ ( plus_plus @ A @ A2 @ R ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_diff_le_iff
% 0.31/0.47 thf(fact_144_diff__eq__diff__less__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.31/0.47 ( ( ( minus_minus @ A @ A2 @ B )
% 0.31/0.47 = ( minus_minus @ A @ C @ D ) )
% 0.31/0.47 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_eq_diff_less_eq
% 0.31/0.47 thf(fact_145_diff__right__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_right_mono
% 0.31/0.47 thf(fact_146_diff__left__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_left_mono
% 0.31/0.47 thf(fact_147_diff__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordered_ab_group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,D: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ D @ C )
% 0.31/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % diff_mono
% 0.31/0.47 thf(fact_148_right__diff__distrib_H,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_s1003936772cancel @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.31/0.47 = ( minus_minus @ A @ ( times_times @ A @ A2 @ B ) @ ( times_times @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % right_diff_distrib'
% 0.31/0.47 thf(fact_149_left__diff__distrib_H,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_s1003936772cancel @ A )
% 0.31/0.47 => ! [B: A,C: A,A2: A] :
% 0.31/0.47 ( ( times_times @ A @ ( minus_minus @ A @ B @ C ) @ A2 )
% 0.31/0.47 = ( minus_minus @ A @ ( times_times @ A @ B @ A2 ) @ ( times_times @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % left_diff_distrib'
% 0.31/0.47 thf(fact_150_right__diff__distrib,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.31/0.47 = ( minus_minus @ A @ ( times_times @ A @ A2 @ B ) @ ( times_times @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % right_diff_distrib
% 0.31/0.47 thf(fact_151_left__diff__distrib,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( times_times @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( minus_minus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % left_diff_distrib
% 0.31/0.47 thf(fact_152_abs__ge__self,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( abs_abs @ A @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_ge_self
% 0.31/0.47 thf(fact_153_abs__le__D1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_le_D1
% 0.31/0.47 thf(fact_154_abs__mult,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( idom_abs_sgn @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( abs_abs @ A @ ( times_times @ A @ A2 @ B ) )
% 0.31/0.47 = ( times_times @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_mult
% 0.31/0.47 thf(fact_155_abs__minus__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) )
% 0.31/0.47 = ( abs_abs @ A @ ( minus_minus @ A @ B @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_minus_commute
% 0.31/0.47 thf(fact_156_left__add__twice,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_numeral @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) @ A2 ) @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % left_add_twice
% 0.31/0.47 thf(fact_157_mult__2__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_numeral @ A )
% 0.31/0.47 => ! [Z: A] :
% 0.31/0.47 ( ( times_times @ A @ Z @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) )
% 0.31/0.47 = ( plus_plus @ A @ Z @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult_2_right
% 0.31/0.47 thf(fact_158_mult__2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_numeral @ A )
% 0.31/0.47 => ! [Z: A] :
% 0.31/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) @ Z )
% 0.31/0.47 = ( plus_plus @ A @ Z @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult_2
% 0.31/0.47 thf(fact_159_mult__numeral__1__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_numeral @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( times_times @ A @ A2 @ ( numeral_numeral @ A @ one2 ) )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult_numeral_1_right
% 0.31/0.47 thf(fact_160_mult__numeral__1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semiring_numeral @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ one2 ) @ A2 )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult_numeral_1
% 0.31/0.47 thf(fact_161_abs__triangle__ineq2__sym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere142940540dd_abs @ A )
% 0.31/0.47 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % abs_triangle_ineq2_sym
% 0.31/0.47 thf(fact_162_sin__bound__lemma,axiom,
% 0.31/0.47 ! [X3: real,Y: real,U: real,V: real] :
% 0.31/0.47 ( ( X3 = Y )
% 0.31/0.47 => ( ( ord_less_eq @ real @ ( abs_abs @ real @ U ) @ V )
% 0.31/0.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( plus_plus @ real @ X3 @ U ) @ Y ) ) @ V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sin_bound_lemma
% 0.31/0.47 thf(fact_163_rate__1,axiom,
% 0.31/0.47 ! [P3: nat,S: real,T: real] :
% 0.31/0.47 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.31/0.47 & ( ord_less_eq @ real @ S @ T ) )
% 0.31/0.47 => ( ord_less_eq @ real @ ( minus_minus @ real @ ( genClo1161277105lle_PC @ P3 @ T ) @ ( genClo1161277105lle_PC @ P3 @ S ) ) @ ( times_times @ real @ ( minus_minus @ real @ T @ S ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rate_1
% 0.31/0.47 thf(fact_164_rate__2,axiom,
% 0.31/0.47 ! [P3: nat,S: real,T: real] :
% 0.31/0.47 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.31/0.47 & ( ord_less_eq @ real @ S @ T ) )
% 0.31/0.47 => ( ord_less_eq @ real @ ( times_times @ real @ ( minus_minus @ real @ T @ S ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( genClo1161277105lle_PC @ P3 @ T ) @ ( genClo1161277105lle_PC @ P3 @ S ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rate_2
% 0.31/0.47 thf(fact_165_dbl__simps_I3_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( neg_numeral @ A )
% 0.31/0.47 => ( ( neg_numeral_dbl @ A @ ( one_one @ A ) )
% 0.31/0.47 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dbl_simps(3)
% 0.31/0.47 thf(fact_166_mult__diff__mult,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ring @ A )
% 0.31/0.47 => ! [X3: A,Y: A,A2: A,B: A] :
% 0.31/0.47 ( ( minus_minus @ A @ ( times_times @ A @ X3 @ Y ) @ ( times_times @ A @ A2 @ B ) )
% 0.31/0.47 = ( plus_plus @ A @ ( times_times @ A @ X3 @ ( minus_minus @ A @ Y @ B ) ) @ ( times_times @ A @ ( minus_minus @ A @ X3 @ A2 ) @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mult_diff_mult
% 0.31/0.47 thf(fact_167_verit__eq__simplify_I8_J,axiom,
% 0.31/0.47 ! [X22: num,Y2: num] :
% 0.31/0.47 ( ( ( bit0 @ X22 )
% 0.31/0.47 = ( bit0 @ Y2 ) )
% 0.31/0.47 = ( X22 = Y2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % verit_eq_simplify(8)
% 0.31/0.47 thf(fact_168_minus__apply,axiom,
% 0.31/0.47 ! [B2: $tType,A: $tType] :
% 0.31/0.47 ( ( minus @ B2 )
% 0.31/0.47 => ( ( minus_minus @ ( A > B2 ) )
% 0.31/0.47 = ( ^ [A5: A > B2,B5: A > B2,X: A] : ( minus_minus @ B2 @ ( A5 @ X ) @ ( B5 @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % minus_apply
% 0.31/0.47 thf(fact_169_okRead1__def,axiom,
% 0.31/0.47 ( genClo293725281kRead1
% 0.31/0.47 = ( ^ [F: nat > real,X: real,Ppred: nat > $o] :
% 0.31/0.47 ! [L2: nat,M2: nat] :
% 0.31/0.47 ( ( ( Ppred @ L2 )
% 0.31/0.47 & ( Ppred @ M2 ) )
% 0.31/0.47 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( F @ L2 ) @ ( F @ M2 ) ) ) @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % okRead1_def
% 0.31/0.47 thf(fact_170_order__refl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_refl
% 0.31/0.47 thf(fact_171_eq__diff__eq_H,axiom,
% 0.31/0.47 ! [X3: real,Y: real,Z: real] :
% 0.31/0.47 ( ( X3
% 0.31/0.47 = ( minus_minus @ real @ Y @ Z ) )
% 0.31/0.47 = ( Y
% 0.31/0.47 = ( plus_plus @ real @ X3 @ Z ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_diff_eq'
% 0.31/0.47 thf(fact_172_semiring__norm_I6_J,axiom,
% 0.31/0.47 ! [M: num,N: num] :
% 0.31/0.47 ( ( plus_plus @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.31/0.47 = ( bit0 @ ( plus_plus @ num @ M @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(6)
% 0.31/0.47 thf(fact_173_semiring__norm_I2_J,axiom,
% 0.31/0.47 ( ( plus_plus @ num @ one2 @ one2 )
% 0.31/0.47 = ( bit0 @ one2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % semiring_norm(2)
% 0.31/0.47 thf(fact_174_dbl__simps_I5_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( neg_numeral @ A )
% 0.31/0.47 => ! [K: num] :
% 0.31/0.47 ( ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) )
% 0.31/0.47 = ( numeral_numeral @ A @ ( bit0 @ K ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dbl_simps(5)
% 0.31/0.47 thf(fact_175_nat__1__add__1,axiom,
% 0.31/0.47 ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
% 0.31/0.47 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_1_add_1
% 0.31/0.47 thf(fact_176_add__One__commute,axiom,
% 0.31/0.47 ! [N: num] :
% 0.31/0.47 ( ( plus_plus @ num @ one2 @ N )
% 0.31/0.47 = ( plus_plus @ num @ N @ one2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_One_commute
% 0.31/0.47 thf(fact_177_numerals_I1_J,axiom,
% 0.31/0.47 ( ( numeral_numeral @ nat @ one2 )
% 0.31/0.47 = ( one_one @ nat ) ) ).
% 0.31/0.47
% 0.31/0.47 % numerals(1)
% 0.31/0.47 thf(fact_178_dbl__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( neg_numeral @ A )
% 0.31/0.47 => ( ( neg_numeral_dbl @ A )
% 0.31/0.47 = ( ^ [X: A] : ( plus_plus @ A @ X @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dbl_def
% 0.31/0.47 thf(fact_179_le__funD,axiom,
% 0.31/0.47 ! [B2: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B2 )
% 0.31/0.47 => ! [F2: A > B2,G2: A > B2,X3: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( A > B2 ) @ F2 @ G2 )
% 0.31/0.47 => ( ord_less_eq @ B2 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funD
% 0.31/0.47 thf(fact_180_le__funE,axiom,
% 0.31/0.47 ! [B2: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B2 )
% 0.31/0.47 => ! [F2: A > B2,G2: A > B2,X3: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( A > B2 ) @ F2 @ G2 )
% 0.31/0.47 => ( ord_less_eq @ B2 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funE
% 0.31/0.47 thf(fact_181_le__funI,axiom,
% 0.31/0.47 ! [B2: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B2 )
% 0.31/0.47 => ! [F2: A > B2,G2: A > B2] :
% 0.31/0.47 ( ! [X2: A] : ( ord_less_eq @ B2 @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
% 0.31/0.47 => ( ord_less_eq @ ( A > B2 ) @ F2 @ G2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funI
% 0.31/0.47 thf(fact_182_le__fun__def,axiom,
% 0.31/0.47 ! [B2: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B2 )
% 0.31/0.47 => ( ( ord_less_eq @ ( A > B2 ) )
% 0.31/0.47 = ( ^ [F: A > B2,G: A > B2] :
% 0.31/0.47 ! [X: A] : ( ord_less_eq @ B2 @ ( F @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_fun_def
% 0.31/0.47 thf(fact_183_order__subst1,axiom,
% 0.31/0.47 ! [A: $tType,B2: $tType] :
% 0.31/0.47 ( ( ( order @ B2 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,F2: B2 > A,B: B2,C: B2] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B ) )
% 0.31/0.47 => ( ( ord_less_eq @ B2 @ B @ C )
% 0.31/0.47 => ( ! [X2: B2,Y3: B2] :
% 0.31/0.47 ( ( ord_less_eq @ B2 @ X2 @ Y3 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ ( F2 @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst1
% 0.31/0.47 thf(fact_184_order__subst2,axiom,
% 0.31/0.47 ! [A: $tType,C5: $tType] :
% 0.31/0.47 ( ( ( order @ C5 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,B: A,F2: A > C5,C: C5] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ C5 @ ( F2 @ B ) @ C )
% 0.31/0.47 => ( ! [X2: A,Y3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/0.47 => ( ord_less_eq @ C5 @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/0.47 => ( ord_less_eq @ C5 @ ( F2 @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst2
% 0.31/0.47 thf(fact_185_verit__la__disequality,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( A2 = B )
% 0.31/0.47 | ~ ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 | ~ ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % verit_la_disequality
% 0.31/0.47 thf(fact_186_ord__eq__le__subst,axiom,
% 0.31/0.47 ! [A: $tType,B2: $tType] :
% 0.31/0.48 ( ( ( ord @ B2 )
% 0.31/0.48 & ( ord @ A ) )
% 0.31/0.48 => ! [A2: A,F2: B2 > A,B: B2,C: B2] :
% 0.31/0.48 ( ( A2
% 0.31/0.48 = ( F2 @ B ) )
% 0.31/0.48 => ( ( ord_less_eq @ B2 @ B @ C )
% 0.31/0.48 => ( ! [X2: B2,Y3: B2] :
% 0.31/0.48 ( ( ord_less_eq @ B2 @ X2 @ Y3 )
% 0.31/0.48 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/0.48 => ( ord_less_eq @ A @ A2 @ ( F2 @ C ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_le_subst
% 0.31/0.48 thf(fact_187_ord__le__eq__subst,axiom,
% 0.31/0.48 ! [A: $tType,B2: $tType] :
% 0.31/0.48 ( ( ( ord @ B2 )
% 0.31/0.48 & ( ord @ A ) )
% 0.31/0.48 => ! [A2: A,B: A,F2: A > B2,C: B2] :
% 0.31/0.48 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.48 => ( ( ( F2 @ B )
% 0.31/0.48 = C )
% 0.31/0.48 => ( ! [X2: A,Y3: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/0.48 => ( ord_less_eq @ B2 @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/0.48 => ( ord_less_eq @ B2 @ ( F2 @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_le_eq_subst
% 0.31/0.48 thf(fact_188_eq__iff,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.31/0.48 = ( ^ [X: A,Y5: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ X @ Y5 )
% 0.31/0.48 & ( ord_less_eq @ A @ Y5 @ X ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_iff
% 0.31/0.48 thf(fact_189_antisym,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ! [X3: A,Y: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.31/0.48 => ( ( ord_less_eq @ A @ Y @ X3 )
% 0.31/0.48 => ( X3 = Y ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % antisym
% 0.31/0.48 thf(fact_190_linear,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( linorder @ A )
% 0.31/0.48 => ! [X3: A,Y: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.31/0.48 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % linear
% 0.31/0.48 thf(fact_191_eq__refl,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( preorder @ A )
% 0.31/0.48 => ! [X3: A,Y: A] :
% 0.31/0.48 ( ( X3 = Y )
% 0.31/0.48 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_refl
% 0.31/0.48 thf(fact_192_le__cases,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( linorder @ A )
% 0.31/0.48 => ! [X3: A,Y: A] :
% 0.31/0.48 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 0.31/0.48 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % le_cases
% 0.31/0.48 thf(fact_193_order_Otrans,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ! [A2: A,B: A,C: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.48 => ( ( ord_less_eq @ A @ B @ C )
% 0.31/0.48 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order.trans
% 0.31/0.48 thf(fact_194_le__cases3,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( linorder @ A )
% 0.31/0.48 => ! [X3: A,Y: A,Z: A] :
% 0.31/0.48 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 0.31/0.48 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.31/0.48 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 0.31/0.48 => ~ ( ord_less_eq @ A @ X3 @ Z ) )
% 0.31/0.48 => ( ( ( ord_less_eq @ A @ X3 @ Z )
% 0.31/0.48 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.31/0.48 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.31/0.48 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 0.31/0.48 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.31/0.48 => ~ ( ord_less_eq @ A @ Z @ X3 ) )
% 0.31/0.48 => ~ ( ( ord_less_eq @ A @ Z @ X3 )
% 0.31/0.48 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % le_cases3
% 0.31/0.48 thf(fact_195_antisym__conv,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ! [Y: A,X3: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ Y @ X3 )
% 0.31/0.48 => ( ( ord_less_eq @ A @ X3 @ Y )
% 0.31/0.48 = ( X3 = Y ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % antisym_conv
% 0.31/0.48 thf(fact_196_order__class_Oorder_Oeq__iff,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.31/0.48 = ( ^ [A4: A,B4: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/0.48 & ( ord_less_eq @ A @ B4 @ A4 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_class.order.eq_iff
% 0.31/0.48 thf(fact_197_ord__eq__le__trans,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( ord @ A )
% 0.31/0.48 => ! [A2: A,B: A,C: A] :
% 0.31/0.48 ( ( A2 = B )
% 0.31/0.48 => ( ( ord_less_eq @ A @ B @ C )
% 0.31/0.48 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_eq_le_trans
% 0.31/0.48 thf(fact_198_ord__le__eq__trans,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( ord @ A )
% 0.31/0.48 => ! [A2: A,B: A,C: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.48 => ( ( B = C )
% 0.31/0.48 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % ord_le_eq_trans
% 0.31/0.48 thf(fact_199_order__class_Oorder_Oantisym,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ! [A2: A,B: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.48 => ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.48 => ( A2 = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_class.order.antisym
% 0.31/0.48 thf(fact_200_order__trans,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( preorder @ A )
% 0.31/0.48 => ! [X3: A,Y: A,Z: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.31/0.48 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.31/0.48 => ( ord_less_eq @ A @ X3 @ Z ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % order_trans
% 0.31/0.48 thf(fact_201_dual__order_Orefl,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % dual_order.refl
% 0.31/0.48 thf(fact_202_linorder__wlog,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( linorder @ A )
% 0.31/0.48 => ! [P2: A > A > $o,A2: A,B: A] :
% 0.31/0.48 ( ! [A6: A,B6: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.31/0.48 => ( P2 @ A6 @ B6 ) )
% 0.31/0.48 => ( ! [A6: A,B6: A] :
% 0.31/0.48 ( ( P2 @ B6 @ A6 )
% 0.31/0.48 => ( P2 @ A6 @ B6 ) )
% 0.31/0.48 => ( P2 @ A2 @ B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % linorder_wlog
% 0.31/0.48 thf(fact_203_dual__order_Otrans,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ! [B: A,A2: A,C: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.48 => ( ( ord_less_eq @ A @ C @ B )
% 0.31/0.48 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % dual_order.trans
% 0.31/0.48 thf(fact_204_dual__order_Oeq__iff,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.31/0.48 = ( ^ [A4: A,B4: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.31/0.48 & ( ord_less_eq @ A @ A4 @ B4 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % dual_order.eq_iff
% 0.31/0.48 thf(fact_205_dual__order_Oantisym,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( order @ A )
% 0.31/0.48 => ! [B: A,A2: A] :
% 0.31/0.48 ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.48 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.48 => ( A2 = B ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % dual_order.antisym
% 0.31/0.48 thf(fact_206_fun__diff__def,axiom,
% 0.31/0.48 ! [B2: $tType,A: $tType] :
% 0.31/0.48 ( ( minus @ B2 )
% 0.31/0.48 => ( ( minus_minus @ ( A > B2 ) )
% 0.31/0.48 = ( ^ [A5: A > B2,B5: A > B2,X: A] : ( minus_minus @ B2 @ ( A5 @ X ) @ ( B5 @ X ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % fun_diff_def
% 0.31/0.48 thf(fact_207_complete__real,axiom,
% 0.31/0.48 ! [S3: set @ real] :
% 0.31/0.48 ( ? [X4: real] : ( member @ real @ X4 @ S3 )
% 0.31/0.48 => ( ? [Z3: real] :
% 0.31/0.48 ! [X2: real] :
% 0.31/0.48 ( ( member @ real @ X2 @ S3 )
% 0.31/0.48 => ( ord_less_eq @ real @ X2 @ Z3 ) )
% 0.31/0.48 => ? [Y3: real] :
% 0.31/0.48 ( ! [X4: real] :
% 0.31/0.48 ( ( member @ real @ X4 @ S3 )
% 0.31/0.48 => ( ord_less_eq @ real @ X4 @ Y3 ) )
% 0.31/0.48 & ! [Z3: real] :
% 0.31/0.48 ( ! [X2: real] :
% 0.31/0.48 ( ( member @ real @ X2 @ S3 )
% 0.31/0.48 => ( ord_less_eq @ real @ X2 @ Z3 ) )
% 0.31/0.48 => ( ord_less_eq @ real @ Y3 @ Z3 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % complete_real
% 0.31/0.48 thf(fact_208_PC__monotone,axiom,
% 0.31/0.48 ! [P3: nat,S: real,T: real] :
% 0.31/0.48 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.31/0.48 & ( ord_less_eq @ real @ S @ T ) )
% 0.31/0.48 => ( ord_less_eq @ real @ ( genClo1161277105lle_PC @ P3 @ S ) @ ( genClo1161277105lle_PC @ P3 @ T ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % PC_monotone
% 0.31/0.48 thf(fact_209_add__diff__add,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( ab_group_add @ A )
% 0.31/0.48 => ! [A2: A,C: A,B: A,D: A] :
% 0.31/0.48 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) )
% 0.31/0.48 = ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ ( minus_minus @ A @ C @ D ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % add_diff_add
% 0.31/0.48 thf(fact_210_verit__eq__simplify_I10_J,axiom,
% 0.31/0.48 ! [X22: num] :
% 0.31/0.48 ( one2
% 0.31/0.48 != ( bit0 @ X22 ) ) ).
% 0.31/0.48
% 0.31/0.48 % verit_eq_simplify(10)
% 0.31/0.48 thf(fact_211_inf__period_I2_J,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( ( comm_ring @ A )
% 0.31/0.48 & ( dvd @ A ) )
% 0.31/0.48 => ! [P2: A > $o,D2: A,Q: A > $o] :
% 0.31/0.48 ( ! [X2: A,K2: A] :
% 0.31/0.48 ( ( P2 @ X2 )
% 0.31/0.48 = ( P2 @ ( minus_minus @ A @ X2 @ ( times_times @ A @ K2 @ D2 ) ) ) )
% 0.31/0.48 => ( ! [X2: A,K2: A] :
% 0.31/0.48 ( ( Q @ X2 )
% 0.31/0.48 = ( Q @ ( minus_minus @ A @ X2 @ ( times_times @ A @ K2 @ D2 ) ) ) )
% 0.31/0.48 => ! [X4: A,K3: A] :
% 0.31/0.48 ( ( ( P2 @ X4 )
% 0.31/0.48 | ( Q @ X4 ) )
% 0.31/0.48 = ( ( P2 @ ( minus_minus @ A @ X4 @ ( times_times @ A @ K3 @ D2 ) ) )
% 0.31/0.48 | ( Q @ ( minus_minus @ A @ X4 @ ( times_times @ A @ K3 @ D2 ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inf_period(2)
% 0.31/0.48 thf(fact_212_inf__period_I1_J,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( ( comm_ring @ A )
% 0.31/0.48 & ( dvd @ A ) )
% 0.31/0.48 => ! [P2: A > $o,D2: A,Q: A > $o] :
% 0.31/0.48 ( ! [X2: A,K2: A] :
% 0.31/0.48 ( ( P2 @ X2 )
% 0.31/0.48 = ( P2 @ ( minus_minus @ A @ X2 @ ( times_times @ A @ K2 @ D2 ) ) ) )
% 0.31/0.48 => ( ! [X2: A,K2: A] :
% 0.31/0.48 ( ( Q @ X2 )
% 0.31/0.48 = ( Q @ ( minus_minus @ A @ X2 @ ( times_times @ A @ K2 @ D2 ) ) ) )
% 0.31/0.48 => ! [X4: A,K3: A] :
% 0.31/0.48 ( ( ( P2 @ X4 )
% 0.31/0.48 & ( Q @ X4 ) )
% 0.31/0.48 = ( ( P2 @ ( minus_minus @ A @ X4 @ ( times_times @ A @ K3 @ D2 ) ) )
% 0.31/0.48 & ( Q @ ( minus_minus @ A @ X4 @ ( times_times @ A @ K3 @ D2 ) ) ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % inf_period(1)
% 0.31/0.48 thf(fact_213_crossproduct__eq,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( semiri456707255roduct @ A )
% 0.31/0.48 => ! [W: A,Y: A,X3: A,Z: A] :
% 0.31/0.48 ( ( ( plus_plus @ A @ ( times_times @ A @ W @ Y ) @ ( times_times @ A @ X3 @ Z ) )
% 0.31/0.48 = ( plus_plus @ A @ ( times_times @ A @ W @ Z ) @ ( times_times @ A @ X3 @ Y ) ) )
% 0.31/0.48 = ( ( W = X3 )
% 0.31/0.48 | ( Y = Z ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % crossproduct_eq
% 0.31/0.48 thf(fact_214_nat__eq__add__iff1,axiom,
% 0.31/0.48 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ J @ I )
% 0.31/0.48 => ( ( ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M )
% 0.31/0.48 = ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.31/0.48 = ( ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ I @ J ) @ U ) @ M )
% 0.31/0.48 = N ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_eq_add_iff1
% 0.31/0.48 thf(fact_215_nat__eq__add__iff2,axiom,
% 0.31/0.48 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.48 => ( ( ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M )
% 0.31/0.48 = ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.31/0.48 = ( M
% 0.31/0.48 = ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_eq_add_iff2
% 0.31/0.48 thf(fact_216_nat__le__add__iff1,axiom,
% 0.31/0.48 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ J @ I )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.31/0.48 = ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_le_add_iff1
% 0.31/0.48 thf(fact_217_nat__le__add__iff2,axiom,
% 0.31/0.48 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.31/0.48 = ( ord_less_eq @ nat @ M @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_le_add_iff2
% 0.31/0.48 thf(fact_218_nat__diff__add__eq1,axiom,
% 0.31/0.48 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ J @ I )
% 0.31/0.48 => ( ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.31/0.48 = ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_diff_add_eq1
% 0.31/0.48 thf(fact_219_nat__diff__add__eq2,axiom,
% 0.31/0.48 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.48 => ( ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.31/0.48 = ( minus_minus @ nat @ M @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_diff_add_eq2
% 0.31/0.48 thf(fact_220_left__add__mult__distrib,axiom,
% 0.31/0.48 ! [I: nat,U: nat,J: nat,K: nat] :
% 0.31/0.48 ( ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ K ) )
% 0.31/0.48 = ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ I @ J ) @ U ) @ K ) ) ).
% 0.31/0.48
% 0.31/0.48 % left_add_mult_distrib
% 0.31/0.48 thf(fact_221_crossproduct__noteq,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( semiri456707255roduct @ A )
% 0.31/0.48 => ! [A2: A,B: A,C: A,D: A] :
% 0.31/0.48 ( ( ( A2 != B )
% 0.31/0.48 & ( C != D ) )
% 0.31/0.48 = ( ( plus_plus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ D ) )
% 0.31/0.48 != ( plus_plus @ A @ ( times_times @ A @ A2 @ D ) @ ( times_times @ A @ B @ C ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % crossproduct_noteq
% 0.31/0.48 thf(fact_222_nat__1__eq__mult__iff,axiom,
% 0.31/0.48 ! [M: nat,N: nat] :
% 0.31/0.48 ( ( ( one_one @ nat )
% 0.31/0.48 = ( times_times @ nat @ M @ N ) )
% 0.31/0.48 = ( ( M
% 0.31/0.48 = ( one_one @ nat ) )
% 0.31/0.48 & ( N
% 0.31/0.48 = ( one_one @ nat ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_1_eq_mult_iff
% 0.31/0.48 thf(fact_223_nat__mult__eq__1__iff,axiom,
% 0.31/0.48 ! [M: nat,N: nat] :
% 0.31/0.48 ( ( ( times_times @ nat @ M @ N )
% 0.31/0.48 = ( one_one @ nat ) )
% 0.31/0.48 = ( ( M
% 0.31/0.48 = ( one_one @ nat ) )
% 0.31/0.48 & ( N
% 0.31/0.48 = ( one_one @ nat ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_mult_eq_1_iff
% 0.31/0.48 thf(fact_224_nat__add__left__cancel__le,axiom,
% 0.31/0.48 ! [K: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.31/0.48 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_add_left_cancel_le
% 0.31/0.48 thf(fact_225_diff__diff__cancel,axiom,
% 0.31/0.48 ! [I: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ N )
% 0.31/0.48 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I ) )
% 0.31/0.48 = I ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_diff_cancel
% 0.31/0.48 thf(fact_226_diff__diff__left,axiom,
% 0.31/0.48 ! [I: nat,J: nat,K: nat] :
% 0.31/0.48 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.31/0.48 = ( minus_minus @ nat @ I @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_diff_left
% 0.31/0.48 thf(fact_227_Nat_Odiff__diff__right,axiom,
% 0.31/0.48 ! [K: nat,J: nat,I: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ K @ J )
% 0.31/0.48 => ( ( minus_minus @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 0.31/0.48 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ K ) @ J ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Nat.diff_diff_right
% 0.31/0.48 thf(fact_228_Nat_Oadd__diff__assoc2,axiom,
% 0.31/0.48 ! [K: nat,J: nat,I: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ K @ J )
% 0.31/0.48 => ( ( plus_plus @ nat @ ( minus_minus @ nat @ J @ K ) @ I )
% 0.31/0.48 = ( minus_minus @ nat @ ( plus_plus @ nat @ J @ I ) @ K ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Nat.add_diff_assoc2
% 0.31/0.48 thf(fact_229_Nat_Oadd__diff__assoc,axiom,
% 0.31/0.48 ! [K: nat,J: nat,I: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ K @ J )
% 0.31/0.48 => ( ( plus_plus @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 0.31/0.48 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ J ) @ K ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Nat.add_diff_assoc
% 0.31/0.48 thf(fact_230_eq__diff__iff,axiom,
% 0.31/0.48 ! [K: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ K @ M )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ K @ N )
% 0.31/0.48 => ( ( ( minus_minus @ nat @ M @ K )
% 0.31/0.48 = ( minus_minus @ nat @ N @ K ) )
% 0.31/0.48 = ( M = N ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_diff_iff
% 0.31/0.48 thf(fact_231_le__diff__iff,axiom,
% 0.31/0.48 ! [K: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ K @ M )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ K @ N )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.31/0.48 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % le_diff_iff
% 0.31/0.48 thf(fact_232_Nat_Odiff__diff__eq,axiom,
% 0.31/0.48 ! [K: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ K @ M )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ K @ N )
% 0.31/0.48 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.31/0.48 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Nat.diff_diff_eq
% 0.31/0.48 thf(fact_233_diff__le__mono,axiom,
% 0.31/0.48 ! [M: nat,N: nat,L: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/0.48 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_le_mono
% 0.31/0.48 thf(fact_234_diff__le__self,axiom,
% 0.31/0.48 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 0.31/0.48
% 0.31/0.48 % diff_le_self
% 0.31/0.48 thf(fact_235_le__diff__iff_H,axiom,
% 0.31/0.48 ! [A2: nat,C: nat,B: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ A2 @ C )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ B @ C )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A2 ) @ ( minus_minus @ nat @ C @ B ) )
% 0.31/0.48 = ( ord_less_eq @ nat @ B @ A2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % le_diff_iff'
% 0.31/0.48 thf(fact_236_diff__le__mono2,axiom,
% 0.31/0.48 ! [M: nat,N: nat,L: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/0.48 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_le_mono2
% 0.31/0.48 thf(fact_237_Nat_Oex__has__greatest__nat,axiom,
% 0.31/0.48 ! [P2: nat > $o,K: nat,B: nat] :
% 0.31/0.48 ( ( P2 @ K )
% 0.31/0.48 => ( ! [Y3: nat] :
% 0.31/0.48 ( ( P2 @ Y3 )
% 0.31/0.48 => ( ord_less_eq @ nat @ Y3 @ B ) )
% 0.31/0.48 => ? [X2: nat] :
% 0.31/0.48 ( ( P2 @ X2 )
% 0.31/0.48 & ! [Y6: nat] :
% 0.31/0.48 ( ( P2 @ Y6 )
% 0.31/0.48 => ( ord_less_eq @ nat @ Y6 @ X2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Nat.ex_has_greatest_nat
% 0.31/0.48 thf(fact_238_nat__le__linear,axiom,
% 0.31/0.48 ! [M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/0.48 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.31/0.48
% 0.31/0.48 % nat_le_linear
% 0.31/0.48 thf(fact_239_mult__le__mono2,axiom,
% 0.31/0.48 ! [I: nat,J: nat,K: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.48 => ( ord_less_eq @ nat @ ( times_times @ nat @ K @ I ) @ ( times_times @ nat @ K @ J ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mult_le_mono2
% 0.31/0.48 thf(fact_240_mult__le__mono1,axiom,
% 0.31/0.48 ! [I: nat,J: nat,K: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.48 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ K ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mult_le_mono1
% 0.31/0.48 thf(fact_241_mult__le__mono,axiom,
% 0.31/0.48 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ K @ L )
% 0.31/0.48 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ L ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % mult_le_mono
% 0.31/0.48 thf(fact_242_le__antisym,axiom,
% 0.31/0.48 ! [M: nat,N: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ N @ M )
% 0.31/0.48 => ( M = N ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % le_antisym
% 0.31/0.48 thf(fact_243_le__square,axiom,
% 0.31/0.48 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ M ) ) ).
% 0.31/0.48
% 0.31/0.48 % le_square
% 0.31/0.48 thf(fact_244_eq__imp__le,axiom,
% 0.31/0.48 ! [M: nat,N: nat] :
% 0.31/0.48 ( ( M = N )
% 0.31/0.48 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_imp_le
% 0.31/0.48 thf(fact_245_le__trans,axiom,
% 0.31/0.48 ! [I: nat,J: nat,K: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.48 => ( ( ord_less_eq @ nat @ J @ K )
% 0.31/0.48 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % le_trans
% 0.31/0.48 thf(fact_246_le__refl,axiom,
% 0.31/0.48 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.31/0.48
% 0.31/0.48 % le_refl
% 0.31/0.48 thf(fact_247_le__cube,axiom,
% 0.31/0.48 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ ( times_times @ nat @ M @ M ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % le_cube
% 0.31/0.48 thf(fact_248_diff__mult__distrib2,axiom,
% 0.31/0.48 ! [K: nat,M: nat,N: nat] :
% 0.31/0.48 ( ( times_times @ nat @ K @ ( minus_minus @ nat @ M @ N ) )
% 0.31/0.48 = ( minus_minus @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_mult_distrib2
% 0.31/0.48 thf(fact_249_diff__mult__distrib,axiom,
% 0.31/0.48 ! [M: nat,N: nat,K: nat] :
% 0.31/0.48 ( ( times_times @ nat @ ( minus_minus @ nat @ M @ N ) @ K )
% 0.31/0.48 = ( minus_minus @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_mult_distrib
% 0.31/0.48 thf(fact_250_diff__commute,axiom,
% 0.31/0.48 ! [I: nat,J: nat,K: nat] :
% 0.31/0.48 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.31/0.48 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 0.31/0.48
% 0.31/0.48 % diff_commute
% 0.31/0.48 thf(fact_251_Nat_Ole__imp__diff__is__add,axiom,
% 0.31/0.48 ! [I: nat,J: nat,K: nat] :
% 0.31/0.48 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.48 => ( ( ( minus_minus @ nat @ J @ I )
% 0.31/0.48 = K )
% 0.31/0.48 = ( J
% 0.31/0.48 = ( plus_plus @ nat @ K @ I ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % Nat.le_imp_diff_is_add
% 0.31/0.48 thf(fact_252_diff__add__inverse2,axiom,
% 0.31/0.48 ! [M: nat,N: nat] :
% 0.31/0.48 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ N ) @ N )
% 0.31/0.48 = M ) ).
% 0.31/0.48
% 0.31/0.48 % diff_add_inverse2
% 0.31/0.48
% 0.31/0.48 % Type constructors (86)
% 0.31/0.48 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/0.48 ! [A7: $tType,A8: $tType] :
% 0.31/0.48 ( ( preorder @ A8 )
% 0.31/0.48 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/0.48 ! [A7: $tType,A8: $tType] :
% 0.31/0.48 ( ( order @ A8 )
% 0.31/0.48 => ( order @ ( A7 > A8 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/0.48 ! [A7: $tType,A8: $tType] :
% 0.31/0.48 ( ( ord @ A8 )
% 0.31/0.48 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_fun___Groups_Ominus,axiom,
% 0.31/0.48 ! [A7: $tType,A8: $tType] :
% 0.31/0.48 ( ( minus @ A8 )
% 0.31/0.48 => ( minus @ ( A7 > A8 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 0.31/0.48 semiri456707255roduct @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff,axiom,
% 0.31/0.48 ordere623563068d_diff @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.31/0.48 ordere236663937imp_le @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.31/0.48 canoni770627133id_add @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.31/0.48 linord1659791738miring @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.31/0.48 ordere779506340up_add @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.31/0.48 cancel146912293up_add @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.31/0.48 cancel1352612707id_add @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1__cancel,axiom,
% 0.31/0.48 comm_s1003936772cancel @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.31/0.48 cancel_semigroup_add @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.31/0.48 linordered_semidom @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.31/0.48 ab_semigroup_mult @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 0.31/0.48 comm_monoid_mult @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.31/0.48 ab_semigroup_add @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.31/0.48 comm_monoid_add @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.31/0.48 semigroup_mult @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Num_Osemiring__numeral,axiom,
% 0.31/0.48 semiring_numeral @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.31/0.48 semigroup_add @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Rings_Ocomm__semiring,axiom,
% 0.31/0.48 comm_semiring @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 0.31/0.48 semiring_char_0 @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.31/0.48 preorder @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.31/0.48 linorder @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.31/0.48 monoid_mult @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.31/0.48 order @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Rings_Osemiring,axiom,
% 0.31/0.48 semiring @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.31/0.48 ord @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Ominus_4,axiom,
% 0.31/0.48 minus @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 0.31/0.48 numeral @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.31/0.48 one @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Nat_Onat___Rings_Odvd,axiom,
% 0.31/0.48 dvd @ nat ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Num_Onum___Orderings_Opreorder_5,axiom,
% 0.31/0.48 preorder @ num ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Num_Onum___Orderings_Olinorder_6,axiom,
% 0.31/0.48 linorder @ num ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Num_Onum___Orderings_Oorder_7,axiom,
% 0.31/0.48 order @ num ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Num_Onum___Orderings_Oord_8,axiom,
% 0.31/0.48 ord @ num ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Set_Oset___Orderings_Opreorder_9,axiom,
% 0.31/0.48 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Set_Oset___Orderings_Oorder_10,axiom,
% 0.31/0.48 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Set_Oset___Orderings_Oord_11,axiom,
% 0.31/0.48 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Set_Oset___Groups_Ominus_12,axiom,
% 0.31/0.48 ! [A7: $tType] : ( minus @ ( set @ A7 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 0.31/0.48 preorder @ $o ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 0.31/0.48 linorder @ $o ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 0.31/0.48 order @ $o ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 0.31/0.48 ord @ $o ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_HOL_Obool___Groups_Ominus_17,axiom,
% 0.31/0.48 minus @ $o ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_18,axiom,
% 0.31/0.48 semiri456707255roduct @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_19,axiom,
% 0.31/0.48 ordere236663937imp_le @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_20,axiom,
% 0.31/0.48 linord1659791738miring @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_21,axiom,
% 0.31/0.48 ordere779506340up_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs,axiom,
% 0.31/0.48 ordere142940540dd_abs @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_22,axiom,
% 0.31/0.48 cancel146912293up_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_23,axiom,
% 0.31/0.48 cancel1352612707id_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1__cancel_24,axiom,
% 0.31/0.48 comm_s1003936772cancel @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
% 0.31/0.48 ordered_ab_group_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_25,axiom,
% 0.31/0.48 cancel_semigroup_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_26,axiom,
% 0.31/0.48 linordered_semidom @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Oab__semigroup__mult_27,axiom,
% 0.31/0.48 ab_semigroup_mult @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__mult_28,axiom,
% 0.31/0.48 comm_monoid_mult @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_29,axiom,
% 0.31/0.48 ab_semigroup_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_30,axiom,
% 0.31/0.48 comm_monoid_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 0.31/0.48 linordered_idom @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Osemigroup__mult_31,axiom,
% 0.31/0.48 semigroup_mult @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Num_Osemiring__numeral_32,axiom,
% 0.31/0.48 semiring_numeral @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Osemigroup__add_33,axiom,
% 0.31/0.48 semigroup_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Ocomm__semiring_34,axiom,
% 0.31/0.48 comm_semiring @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Nat_Osemiring__char__0_35,axiom,
% 0.31/0.48 semiring_char_0 @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Oab__group__add,axiom,
% 0.31/0.48 ab_group_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Oordered__ring,axiom,
% 0.31/0.48 ordered_ring @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Oidom__abs__sgn,axiom,
% 0.31/0.48 idom_abs_sgn @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Orderings_Opreorder_36,axiom,
% 0.31/0.48 preorder @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Orderings_Olinorder_37,axiom,
% 0.31/0.48 linorder @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Omonoid__mult_38,axiom,
% 0.31/0.48 monoid_mult @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.31/0.48 group_add @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Ocomm__ring,axiom,
% 0.31/0.48 comm_ring @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Orderings_Oorder_39,axiom,
% 0.31/0.48 order @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 0.31/0.48 neg_numeral @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Osemiring_40,axiom,
% 0.31/0.48 semiring @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Orderings_Oord_41,axiom,
% 0.31/0.48 ord @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Oring__1,axiom,
% 0.31/0.48 ring_1 @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Ominus_42,axiom,
% 0.31/0.48 minus @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Num_Onumeral_43,axiom,
% 0.31/0.48 numeral @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Oring,axiom,
% 0.31/0.48 ring @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Groups_Oone_44,axiom,
% 0.31/0.48 one @ real ).
% 0.31/0.48
% 0.31/0.48 thf(tcon_Real_Oreal___Rings_Odvd_45,axiom,
% 0.31/0.48 dvd @ real ).
% 0.31/0.48
% 0.31/0.48 % Conjectures (1)
% 0.31/0.48 thf(conj_0,conjecture,
% 0.31/0.48 ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ genClo1144207539le_rho ) @ ( minus_minus @ real @ t @ s ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 0.33/1.50 ---- Embedded in THF ---
% 0.33/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.33/1.50 %%% Generated on Tue Feb 24 08:25:17 EST 2026
% 0.33/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.33/1.50 %%% Logic specification used:
% 0.33/1.50 %%% thf(spec, logic, $$dhol).
% 0.33/1.50
% 0.33/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2DTF19870.p
% 0.33/1.50 thf(ty_t_Real_Oreal, type, real: $tType).
% 0.33/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.33/1.50 thf(ty_t_Num_Onum, type, num: $tType).
% 0.33/1.50 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.33/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Odvd, type, dvd: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Oring, type, ring: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Num_Onumeral, type, numeral: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Oring__1, type, ring_1: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Osemiring, type, semiring: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Ocomm__ring, type, comm_ring: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Omonoid__mult, type, monoid_mult: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Oidom__abs__sgn, type, idom_abs_sgn: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Oordered__ring, type, ordered_ring: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oab__group__add, type, ab_group_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Nat_Osemiring__char__0, type, semiring_char_0: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Ocomm__semiring, type, comm_semiring: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Num_Osemiring__numeral, type, semiring_numeral: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Osemigroup__mult, type, semigroup_mult: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Ocomm__monoid__mult, type, comm_monoid_mult: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oab__semigroup__mult, type, ab_semigroup_mult: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Ocomm__semiring__1__cancel, type, comm_s1003936772cancel: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oordered__ab__group__add__abs, type, ordere142940540dd_abs: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__diff, type, ordere623563068d_diff: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, type, semiri456707255roduct: (!> [A:$tType]: ($o))).
% 0.33/1.50 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OPC, type, genClo1161277105lle_PC: (nat > (real > real))).
% 0.33/1.50 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060rho_062, type, genClo1144207539le_rho: real).
% 0.33/1.50 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ocorrect, type, genClo1015804716orrect: (nat > (real > $o))).
% 0.33/1.50 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead1, type, genClo293725281kRead1: ((nat > real) > (real > ((nat > $o) > $o)))).
% 0.33/1.50 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead2, type, genClo293725282kRead2: ((nat > real) > ((nat > real) > (real > ((nat > $o) > $o))))).
% 0.33/1.50 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Orho__bound1, type, genClo2108747022bound1: ((nat > (real > real)) > $o)).
% 0.33/1.50 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Orho__bound2, type, genClo2108747023bound2: ((nat > (real > real)) > $o)).
% 0.33/1.50 thf(sy_c_Groups_Oabs__class_Oabs, type, abs_abs: (!> [A:$tType]: ((A > A)))).
% 0.33/1.50 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 0.33/1.50 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 0.33/1.50 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 0.33/1.50 thf(sy_c_Groups_Otimes__class_Otimes, type, times_times: (!> [A:$tType]: ((A > (A > A))))).
% 0.33/1.50 thf(sy_c_Num_Oneg__numeral__class_Odbl, type, neg_numeral_dbl: (!> [A:$tType]: ((A > A)))).
% 0.33/1.50 thf(sy_c_Num_Onum_OBit0, type, bit0: (num > num)).
% 0.33/1.50 thf(sy_c_Num_Onum_OOne, type, one2: num).
% 0.33/1.50 thf(sy_c_Num_Onumeral__class_Onumeral, type, numeral_numeral: (!> [A:$tType]: ((num > A)))).
% 0.33/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.33/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.33/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.33/1.50 thf(sy_v_C, type, c: (nat > (real > real))).
% 0.33/1.50 thf(sy_v_D, type, d: (nat > (real > real))).
% 0.33/1.50 thf(sy_v_p, type, p: nat).
% 0.33/1.50 thf(sy_v_q, type, q: nat).
% 0.33/1.50 thf(sy_v_s, type, s: real).
% 0.33/1.50 thf(sy_v_t, type, t: real).
% 0.33/1.50 thf(fact_0_rb2, axiom, (genClo2108747023bound2 @ d)).
% 0.33/1.50 thf(fact_1_rb1, axiom, (genClo2108747022bound1 @ c)).
% 0.33/1.50 thf(fact_2_ie, axiom, (((ord_less_eq @ real) @ s) @ t)).
% 0.33/1.50 thf(fact_3_Eq1, axiom, (((abs_abs @ real) @ (((minus_minus @ real) @ (((minus_minus @ real) @ ((c @ p) @ t)) @ ((c @ p) @ s))) @ (((minus_minus @ real) @ ((d @ q) @ t)) @ ((d @ q) @ s)))) = (((minus_minus @ real) @ (((minus_minus @ real) @ ((c @ p) @ t)) @ ((c @ p) @ s))) @ (((minus_minus @ real) @ ((d @ q) @ t)) @ ((d @ q) @ s))))).
% 0.33/1.50 thf(fact_4_Eq4, axiom, ((((minus_minus @ real) @ (((times_times @ real) @ (((minus_minus @ real) @ t) @ s)) @ (((plus_plus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))) @ (((times_times @ real) @ (((minus_minus @ real) @ t) @ s)) @ (((minus_minus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))) = (((times_times @ real) @ (((times_times @ real) @ ((numeral_numeral @ real) @ (bit0 @ one2))) @ genClo1144207539le_rho)) @ (((minus_minus @ real) @ t) @ s)))).
% 0.33/1.50 thf(fact_5_Eq3, axiom, (((ord_less_eq @ real) @ (((minus_minus @ real) @ (((times_times @ real) @ (((minus_minus @ real) @ t) @ s)) @ (((plus_plus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))) @ (((minus_minus @ real) @ ((d @ q) @ t)) @ ((d @ q) @ s)))) @ (((minus_minus @ real) @ (((times_times @ real) @ (((minus_minus @ real) @ t) @ s)) @ (((plus_plus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))) @ (((times_times @ real) @ (((minus_minus @ real) @ t) @ s)) @ (((minus_minus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))))).
% 0.33/1.50 thf(fact_6_corr__q, axiom, ((genClo1015804716orrect @ q) @ t)).
% 0.33/1.50 thf(fact_7_PC__ie, axiom, (((ord_less_eq @ real) @ (((minus_minus @ real) @ ((d @ q) @ t)) @ ((d @ q) @ s))) @ (((minus_minus @ real) @ ((c @ p) @ t)) @ ((c @ p) @ s)))).
% 0.33/1.50 thf(fact_8_corr__p, axiom, ((genClo1015804716orrect @ p) @ t)).
% 0.33/1.50 thf(fact_9_Eq2, axiom, (((ord_less_eq @ real) @ (((minus_minus @ real) @ (((minus_minus @ real) @ ((c @ p) @ t)) @ ((c @ p) @ s))) @ (((minus_minus @ real) @ ((d @ q) @ t)) @ ((d @ q) @ s)))) @ (((minus_minus @ real) @ (((times_times @ real) @ (((minus_minus @ real) @ t) @ s)) @ (((plus_plus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))) @ (((minus_minus @ real) @ ((d @ q) @ t)) @ ((d @ q) @ s))))).
% 0.33/1.50 thf(fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062, axiom, (((ord_less_eq @ real) @ (((times_times @ real) @ (((minus_minus @ real) @ t) @ s)) @ (((minus_minus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))) @ (((minus_minus @ real) @ ((d @ q) @ t)) @ ((d @ q) @ s)))).
% 0.33/1.50 thf(fact_11_left__diff__distrib__numeral, axiom, (! [A:$tType]: ((((numeral @ A) & (ring @ A)) => (! [A2:A,B:A,V:num]: (((((times_times @ A) @ (((minus_minus @ A) @ A2) @ B)) @ ((numeral_numeral @ A) @ V)) = (((minus_minus @ A) @ (((times_times @ A) @ A2) @ ((numeral_numeral @ A) @ V))) @ (((times_times @ A) @ B) @ ((numeral_numeral @ A) @ V)))))))))).
% 0.33/1.50 thf(fact_12_right__diff__distrib__numeral, axiom, (! [A:$tType]: ((((numeral @ A) & (ring @ A)) => (! [V:num,B:A,C:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ (((minus_minus @ A) @ B) @ C)) = (((minus_minus @ A) @ (((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ B)) @ (((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ C))))))))).
% 0.33/1.50 thf(fact_13_abs__numeral, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [N:num]: ((((abs_abs @ A) @ ((numeral_numeral @ A) @ N)) = ((numeral_numeral @ A) @ N)))))))).
% 0.33/1.50 thf(fact_14_abs__mult__self__eq, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [A2:A]: (((((times_times @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ A2)) = (((times_times @ A) @ A2) @ A2)))))))).
% 0.33/1.50 thf(fact_15_semiring__norm_I85_J, axiom, (! [M:num]: (((bit0 @ M) != one2)))).
% 0.33/1.50 thf(fact_16_semiring__norm_I83_J, axiom, (! [N:num]: ((one2 != (bit0 @ N))))).
% 0.33/1.50 thf(fact_17_mult__numeral__left__semiring__numeral, axiom, (! [A:$tType]: (((semiring_numeral @ A) => (! [V:num,W:num,Z:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ (((times_times @ A) @ ((numeral_numeral @ A) @ W)) @ Z)) = (((times_times @ A) @ ((numeral_numeral @ A) @ (((times_times @ num) @ V) @ W))) @ Z)))))))).
% 0.33/1.50 thf(fact_18_numeral__times__numeral, axiom, (! [A:$tType]: (((semiring_numeral @ A) => (! [M:num,N:num]: (((((times_times @ A) @ ((numeral_numeral @ A) @ M)) @ ((numeral_numeral @ A) @ N)) = ((numeral_numeral @ A) @ (((times_times @ num) @ M) @ N))))))))).
% 0.33/1.50 thf(fact_19_numeral__le__iff, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [M:num,N:num]: (((((ord_less_eq @ A) @ ((numeral_numeral @ A) @ M)) @ ((numeral_numeral @ A) @ N)) = (((ord_less_eq @ num) @ M) @ N)))))))).
% 0.33/1.50 thf(fact_20_okRead2__def, axiom, (genClo293725282kRead2 = (^ [F:(nat > real),G:(nat > real),X:real,Ppred:(nat > $o)]: ((! [P:nat]: (((Ppred @ P) => (((ord_less_eq @ real) @ ((abs_abs @ real) @ (((minus_minus @ real) @ (F @ P)) @ (G @ P)))) @ X)))))))).
% 0.33/1.50 thf(fact_21_abs__triangle__ineq2, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A]: ((((ord_less_eq @ A) @ (((minus_minus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B))) @ ((abs_abs @ A) @ (((minus_minus @ A) @ A2) @ B))))))))).
% 0.33/1.50 thf(fact_22_abs__triangle__ineq3, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A]: ((((ord_less_eq @ A) @ ((abs_abs @ A) @ (((minus_minus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B)))) @ ((abs_abs @ A) @ (((minus_minus @ A) @ A2) @ B))))))))).
% 0.33/1.50 thf(fact_23_numeral__eq__iff, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [M:num,N:num]: (((((numeral_numeral @ A) @ M) = ((numeral_numeral @ A) @ N)) = (M = N)))))))).
% 0.33/1.50 thf(fact_24_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) = (B = C)))))))).
% 0.33/1.50 thf(fact_25_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B = C)))))))).
% 0.33/1.50 thf(fact_26_semiring__norm_I87_J, axiom, (! [M:num,N:num]: ((((bit0 @ M) = (bit0 @ N)) = (M = N))))).
% 0.33/1.50 thf(fact_27_abs__idempotent, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A]: ((((abs_abs @ A) @ ((abs_abs @ A) @ A2)) = ((abs_abs @ A) @ A2)))))))).
% 0.33/1.50 thf(fact_28_abs__abs, axiom, (! [A:$tType]: (((idom_abs_sgn @ A) => (! [A2:A]: ((((abs_abs @ A) @ ((abs_abs @ A) @ A2)) = ((abs_abs @ A) @ A2)))))))).
% 0.33/1.50 thf(fact_29_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) = (((ord_less_eq @ A) @ A2) @ B)))))))).
% 0.33/1.50 thf(fact_30_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) = (((ord_less_eq @ A) @ A2) @ B)))))))).
% 0.33/1.50 thf(fact_31_mult_Oright__neutral, axiom, (! [A:$tType]: (((monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 0.33/1.50 thf(fact_32_mult_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 0.33/1.50 thf(fact_33_numeral__plus__numeral, axiom, (! [A:$tType]: (((numeral @ A) => (! [M:num,N:num]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ M)) @ ((numeral_numeral @ A) @ N)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ M) @ N))))))))).
% 0.33/1.50 thf(fact_34_add__numeral__left, axiom, (! [A:$tType]: (((numeral @ A) => (! [V:num,W:num,Z:A]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ V)) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ W)) @ Z)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ (((plus_plus @ num) @ V) @ W))) @ Z)))))))).
% 0.33/1.50 thf(fact_35_add__diff__cancel__right_H, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ B) = A2))))))).
% 0.33/1.50 thf(fact_36_add__diff__cancel__right, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,C:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) = (((minus_minus @ A) @ A2) @ B)))))))).
% 0.33/1.50 thf(fact_37_add__diff__cancel__left_H, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ A2) = B))))))).
% 0.33/1.50 thf(fact_38_add__diff__cancel__left, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [C:A,A2:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) = (((minus_minus @ A) @ A2) @ B)))))))).
% 0.33/1.50 thf(fact_39_diff__add__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ B) = A2))))))).
% 0.33/1.50 thf(fact_40_add__diff__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ B) = A2))))))).
% 0.33/1.50 thf(fact_41_abs__add__abs, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A]: ((((abs_abs @ A) @ (((plus_plus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B))) = (((plus_plus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B))))))))).
% 0.33/1.50 thf(fact_42_abs__1, axiom, (! [A:$tType]: (((idom_abs_sgn @ A) => (((abs_abs @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 0.33/1.50 thf(fact_43_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 0.33/1.50 thf(fact_44_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A3)))) = A3)))).
% 0.33/1.50 thf(fact_45_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P2 @ X2) = (Q @ X2)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 0.33/1.50 thf(fact_46_ext, axiom, (! [B2:$tType,A:$tType,F2:(A > B2),G2:(A > B2)]: (((! [X2:A]: (((F2 @ X2) = (G2 @ X2)))) => (F2 = G2))))).
% 0.33/1.50 thf(fact_47_semiring__norm_I13_J, axiom, (! [M:num,N:num]: (((((times_times @ num) @ (bit0 @ M)) @ (bit0 @ N)) = (bit0 @ (bit0 @ (((times_times @ num) @ M) @ N))))))).
% 0.33/1.50 thf(fact_48_semiring__norm_I11_J, axiom, (! [M:num]: (((((times_times @ num) @ M) @ one2) = M)))).
% 0.33/1.50 thf(fact_49_semiring__norm_I12_J, axiom, (! [N:num]: (((((times_times @ num) @ one2) @ N) = N)))).
% 0.33/1.50 thf(fact_50_semiring__norm_I71_J, axiom, (! [M:num,N:num]: (((((ord_less_eq @ num) @ (bit0 @ M)) @ (bit0 @ N)) = (((ord_less_eq @ num) @ M) @ N))))).
% 0.33/1.50 thf(fact_51_semiring__norm_I68_J, axiom, (! [N:num]: ((((ord_less_eq @ num) @ one2) @ N)))).
% 0.33/1.50 thf(fact_52_le__add__diff__inverse2, axiom, (! [A:$tType]: (((linordered_semidom @ A) => (! [B:A,A2:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ B) = A2)))))))).
% 0.33/1.50 thf(fact_53_le__add__diff__inverse, axiom, (! [A:$tType]: (((linordered_semidom @ A) => (! [B:A,A2:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((plus_plus @ A) @ B) @ (((minus_minus @ A) @ A2) @ B)) = A2)))))))).
% 0.33/1.50 thf(fact_54_distrib__right__numeral, axiom, (! [A:$tType]: ((((numeral @ A) & (semiring @ A)) => (! [A2:A,B:A,V:num]: (((((times_times @ A) @ (((plus_plus @ A) @ A2) @ B)) @ ((numeral_numeral @ A) @ V)) = (((plus_plus @ A) @ (((times_times @ A) @ A2) @ ((numeral_numeral @ A) @ V))) @ (((times_times @ A) @ B) @ ((numeral_numeral @ A) @ V)))))))))).
% 0.33/1.50 thf(fact_55_distrib__left__numeral, axiom, (! [A:$tType]: ((((numeral @ A) & (semiring @ A)) => (! [V:num,B:A,C:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ (((plus_plus @ A) @ B) @ C)) = (((plus_plus @ A) @ (((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ B)) @ (((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ C))))))))).
% 0.33/1.50 thf(fact_56_one__eq__numeral__iff, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [N:num]: ((((one_one @ A) = ((numeral_numeral @ A) @ N)) = (one2 = N)))))))).
% 0.33/1.50 thf(fact_57_numeral__eq__one__iff, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [N:num]: (((((numeral_numeral @ A) @ N) = (one_one @ A)) = (N = one2)))))))).
% 0.33/1.50 thf(fact_58_num__double, axiom, (! [N:num]: (((((times_times @ num) @ (bit0 @ one2)) @ N) = (bit0 @ N))))).
% 0.33/1.50 thf(fact_59_semiring__norm_I69_J, axiom, (! [M:num]: ((~ ((((ord_less_eq @ num) @ (bit0 @ M)) @ one2)))))).
% 0.33/1.50 thf(fact_60_one__plus__numeral, axiom, (! [A:$tType]: (((numeral @ A) => (! [N:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ N)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ one2) @ N))))))))).
% 0.33/1.50 thf(fact_61_numeral__plus__one, axiom, (! [A:$tType]: (((numeral @ A) => (! [N:num]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ N)) @ (one_one @ A)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ N) @ one2))))))))).
% 0.33/1.50 thf(fact_62_one__add__one, axiom, (! [A:$tType]: (((numeral @ A) => ((((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 0.33/1.50 thf(fact_63_numeral__le__one__iff, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [N:num]: (((((ord_less_eq @ A) @ ((numeral_numeral @ A) @ N)) @ (one_one @ A)) = (((ord_less_eq @ num) @ N) @ one2)))))))).
% 0.33/1.50 thf(fact_64_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_65_is__num__normalize_I1_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_66_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 0.33/1.50 thf(fact_67_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X3:A]: ((((one_one @ A) = X3) = (X3 = (one_one @ A))))))))).
% 0.33/1.50 thf(fact_68_group__cancel_Oadd1, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A3:A,K:A,A2:A,B:A]: (((A3 = (((plus_plus @ A) @ K) @ A2)) => ((((plus_plus @ A) @ A3) @ B) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B)))))))))).
% 0.33/1.50 thf(fact_69_group__cancel_Oadd2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [B3:A,K:A,B:A,A2:A]: (((B3 = (((plus_plus @ A) @ K) @ B)) => ((((plus_plus @ A) @ A2) @ B3) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B)))))))))).
% 0.33/1.50 thf(fact_70_add_Oassoc, axiom, (! [A:$tType]: (((semigroup_add @ A) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_71_add_Oleft__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) = (B = C)))))))).
% 0.33/1.50 thf(fact_72_add_Oright__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B = C)))))))).
% 0.33/1.50 thf(fact_73_add_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => ((plus_plus @ A) = (^ [A4:A,B4:A]: ((((plus_plus @ A) @ B4) @ A4)))))))).
% 0.33/1.50 thf(fact_74_add_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [B:A,A2:A,C:A]: (((((plus_plus @ A) @ B) @ (((plus_plus @ A) @ A2) @ C)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_75_add__left__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) => (B = C)))))))).
% 0.33/1.50 thf(fact_76_add__right__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) => (B = C)))))))).
% 0.33/1.50 thf(fact_77_le__num__One__iff, axiom, (! [X3:num]: (((((ord_less_eq @ num) @ X3) @ one2) = (X3 = one2))))).
% 0.33/1.50 thf(fact_78_one__plus__numeral__commute, axiom, (! [A:$tType]: (((numeral @ A) => (! [X3:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ X3)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ X3)) @ (one_one @ A))))))))).
% 0.33/1.50 thf(fact_79_correct__closed, axiom, (! [P3:nat,S:real,T:real]: ((((((ord_less_eq @ real) @ S) @ T) & ((genClo1015804716orrect @ P3) @ T)) => ((genClo1015804716orrect @ P3) @ S))))).
% 0.33/1.50 thf(fact_80_add__le__imp__le__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 0.33/1.50 thf(fact_81_add__le__imp__le__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 0.33/1.50 thf(fact_82_le__iff__add, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => ((ord_less_eq @ A) = (^ [A4:A,B4:A]: ((? [C2:A]: ((B4 = (((plus_plus @ A) @ A4) @ C2))))))))))).
% 0.33/1.50 thf(fact_83_add__right__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_84_less__eqE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => (~ ((! [C3:A]: ((B != (((plus_plus @ A) @ A2) @ C3))))))))))))).
% 0.33/1.50 thf(fact_85_add__left__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B))))))))).
% 0.33/1.50 thf(fact_86_add__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ C) @ D) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 0.33/1.50 thf(fact_87_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.33/1.50 thf(fact_88_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.33/1.50 thf(fact_89_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (K = L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.33/1.50 thf(fact_90_combine__common__factor, axiom, (! [A:$tType]: (((semiring @ A) => (! [A2:A,E:A,B:A,C:A]: (((((plus_plus @ A) @ (((times_times @ A) @ A2) @ E)) @ (((plus_plus @ A) @ (((times_times @ A) @ B) @ E)) @ C)) = (((plus_plus @ A) @ (((times_times @ A) @ (((plus_plus @ A) @ A2) @ B)) @ E)) @ C)))))))).
% 0.33/1.50 thf(fact_91_distrib__right, axiom, (! [A:$tType]: (((semiring @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_92_distrib__left, axiom, (! [A:$tType]: (((semiring @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ A2) @ (((plus_plus @ A) @ B) @ C)) = (((plus_plus @ A) @ (((times_times @ A) @ A2) @ B)) @ (((times_times @ A) @ A2) @ C))))))))).
% 0.33/1.50 thf(fact_93_comm__semiring__class_Odistrib, axiom, (! [A:$tType]: (((comm_semiring @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_94_ring__class_Oring__distribs_I1_J, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ A2) @ (((plus_plus @ A) @ B) @ C)) = (((plus_plus @ A) @ (((times_times @ A) @ A2) @ B)) @ (((times_times @ A) @ A2) @ C))))))))).
% 0.33/1.50 thf(fact_95_ring__class_Oring__distribs_I2_J, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_96_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 0.33/1.50 thf(fact_97_add__implies__diff, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [C:A,B:A,A2:A]: ((((((plus_plus @ A) @ C) @ B) = A2) => (C = (((minus_minus @ A) @ A2) @ B))))))))).
% 0.33/1.50 thf(fact_98_diff__diff__add, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,B:A,C:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ C) = (((minus_minus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_99_diff__add__eq__diff__diff__swap, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A,C:A]: (((((minus_minus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C)) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C)) @ B)))))))).
% 0.33/1.50 thf(fact_100_diff__add__eq, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ C) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ B)))))))).
% 0.33/1.50 thf(fact_101_diff__diff__eq2, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A,C:A]: (((((minus_minus @ A) @ A2) @ (((minus_minus @ A) @ B) @ C)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ B)))))))).
% 0.33/1.50 thf(fact_102_add__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ A2) @ (((minus_minus @ A) @ B) @ C)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C)))))))).
% 0.33/1.50 thf(fact_103_eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,C:A,B:A]: (((A2 = (((minus_minus @ A) @ C) @ B)) = ((((plus_plus @ A) @ A2) @ B) = C)))))))).
% 0.33/1.50 thf(fact_104_diff__eq__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A,C:A]: ((((((minus_minus @ A) @ A2) @ B) = C) = (A2 = (((plus_plus @ A) @ C) @ B))))))))).
% 0.33/1.50 thf(fact_105_group__cancel_Osub1, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A3:A,K:A,A2:A,B:A]: (((A3 = (((plus_plus @ A) @ K) @ A2)) => ((((minus_minus @ A) @ A3) @ B) = (((plus_plus @ A) @ K) @ (((minus_minus @ A) @ A2) @ B)))))))))).
% 0.33/1.50 thf(fact_106_mult_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 0.33/1.50 thf(fact_107_comm__monoid__mult__class_Omult__1, axiom, (! [A:$tType]: (((comm_monoid_mult @ A) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 0.33/1.50 thf(fact_108_abs__one, axiom, (! [A:$tType]: (((linordered_idom @ A) => (((abs_abs @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 0.33/1.50 thf(fact_109_square__diff__one__factored, axiom, (! [A:$tType]: (((ring_1 @ A) => (! [X3:A]: (((((minus_minus @ A) @ (((times_times @ A) @ X3) @ X3)) @ (one_one @ A)) = (((times_times @ A) @ (((plus_plus @ A) @ X3) @ (one_one @ A))) @ (((minus_minus @ A) @ X3) @ (one_one @ A)))))))))).
% 0.33/1.50 thf(fact_110_rho__bound1__def, axiom, (genClo2108747022bound1 = (^ [C4:(nat > (real > real))]: ((! [P:nat,S2:real,T2:real]: (((((genClo1015804716orrect @ P) @ T2) & (((ord_less_eq @ real) @ S2) @ T2)) => (((ord_less_eq @ real) @ (((minus_minus @ real) @ ((C4 @ P) @ T2)) @ ((C4 @ P) @ S2))) @ (((times_times @ real) @ (((minus_minus @ real) @ T2) @ S2)) @ (((plus_plus @ real) @ (one_one @ real)) @ genClo1144207539le_rho)))))))))).
% 0.33/1.50 thf(fact_111_mult_Oleft__commute, axiom, (! [A:$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))))))))).
% 0.33/1.50 thf(fact_112_mult_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => ((times_times @ A) = (^ [A4:A,B4:A]: ((((times_times @ A) @ B4) @ A4)))))))).
% 0.33/1.50 thf(fact_113_mult_Oassoc, axiom, (! [A:$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))))))))).
% 0.33/1.50 thf(fact_114_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_mult @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_115_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,C:A,B:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C)) @ B) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ C)))))))).
% 0.33/1.50 thf(fact_116_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B) = (((minus_minus @ A) @ C) @ D)) => ((A2 = B) = (C = D))))))))).
% 0.33/1.50 thf(fact_117_rho__bound2__def, axiom, (genClo2108747023bound2 = (^ [C4:(nat > (real > real))]: ((! [P:nat,S2:real,T2:real]: (((((genClo1015804716orrect @ P) @ T2) & (((ord_less_eq @ real) @ S2) @ T2)) => (((ord_less_eq @ real) @ (((times_times @ real) @ (((minus_minus @ real) @ T2) @ S2)) @ (((minus_minus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))) @ (((minus_minus @ real) @ ((C4 @ P) @ T2)) @ ((C4 @ P) @ S2)))))))))).
% 0.33/1.50 thf(fact_118_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ A2) @ B) => (((((minus_minus @ A) @ B) @ A2) = C) = (B = (((plus_plus @ A) @ C) @ A2))))))))))).
% 0.33/1.50 thf(fact_119_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((plus_plus @ A) @ A2) @ (((minus_minus @ A) @ B) @ A2)) = B)))))))).
% 0.33/1.50 thf(fact_120_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((minus_minus @ A) @ C) @ (((minus_minus @ A) @ B) @ A2)) = (((minus_minus @ A) @ (((plus_plus @ A) @ C) @ A2)) @ B))))))))).
% 0.33/1.50 thf(fact_121_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((minus_minus @ A) @ (((plus_plus @ A) @ B) @ C)) @ A2) = (((plus_plus @ A) @ (((minus_minus @ A) @ B) @ A2)) @ C))))))))).
% 0.33/1.50 thf(fact_122_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((plus_plus @ A) @ (((minus_minus @ A) @ B) @ A2)) @ C) = (((minus_minus @ A) @ (((plus_plus @ A) @ B) @ C)) @ A2))))))))).
% 0.33/1.50 thf(fact_123_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((minus_minus @ A) @ (((plus_plus @ A) @ C) @ B)) @ A2) = (((plus_plus @ A) @ C) @ (((minus_minus @ A) @ B) @ A2)))))))))).
% 0.33/1.50 thf(fact_124_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((plus_plus @ A) @ C) @ (((minus_minus @ A) @ B) @ A2)) = (((minus_minus @ A) @ (((plus_plus @ A) @ C) @ B)) @ A2))))))))).
% 0.33/1.50 thf(fact_125_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ C) @ (((minus_minus @ A) @ B) @ A2)) = (((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ B))))))))).
% 0.33/1.50 thf(fact_126_le__add__diff, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ C) @ (((minus_minus @ A) @ (((plus_plus @ A) @ B) @ C)) @ A2))))))))).
% 0.33/1.50 thf(fact_127_add__le__add__imp__diff__le, axiom, (! [A:$tType]: (((linordered_semidom @ A) => (! [I:A,K:A,N:A,J:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ N) => ((((ord_less_eq @ A) @ N) @ (((plus_plus @ A) @ J) @ K)) => ((((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ N) => ((((ord_less_eq @ A) @ N) @ (((plus_plus @ A) @ J) @ K)) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ N) @ K)) @ J))))))))))).
% 0.33/1.50 thf(fact_128_diff__add, axiom, (! [A:$tType]: (((ordere623563068d_diff @ A) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((plus_plus @ A) @ (((minus_minus @ A) @ B) @ A2)) @ A2) = B)))))))).
% 0.33/1.50 thf(fact_129_add__le__imp__le__diff, axiom, (! [A:$tType]: (((linordered_semidom @ A) => (! [I:A,K:A,N:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ N) => (((ord_less_eq @ A) @ I) @ (((minus_minus @ A) @ N) @ K))))))))).
% 0.33/1.50 thf(fact_130_le__diff__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,C:A,B:A]: (((((ord_less_eq @ A) @ A2) @ (((minus_minus @ A) @ C) @ B)) = (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C)))))))).
% 0.33/1.50 thf(fact_131_diff__le__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ B)) @ C) = (((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ C) @ B))))))))).
% 0.33/1.50 thf(fact_132_square__diff__square__factored, axiom, (! [A:$tType]: (((comm_ring @ A) => (! [X3:A,Y:A]: (((((minus_minus @ A) @ (((times_times @ A) @ X3) @ X3)) @ (((times_times @ A) @ Y) @ Y)) = (((times_times @ A) @ (((plus_plus @ A) @ X3) @ Y)) @ (((minus_minus @ A) @ X3) @ Y))))))))).
% 0.33/1.50 thf(fact_133_eq__add__iff2, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,E:A,C:A,B:A,D:A]: ((((((plus_plus @ A) @ (((times_times @ A) @ A2) @ E)) @ C) = (((plus_plus @ A) @ (((times_times @ A) @ B) @ E)) @ D)) = (C = (((plus_plus @ A) @ (((times_times @ A) @ (((minus_minus @ A) @ B) @ A2)) @ E)) @ D))))))))).
% 0.33/1.50 thf(fact_134_eq__add__iff1, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,E:A,C:A,B:A,D:A]: ((((((plus_plus @ A) @ (((times_times @ A) @ A2) @ E)) @ C) = (((plus_plus @ A) @ (((times_times @ A) @ B) @ E)) @ D)) = ((((plus_plus @ A) @ (((times_times @ A) @ (((minus_minus @ A) @ A2) @ B)) @ E)) @ C) = D)))))))).
% 0.33/1.50 thf(fact_135_numeral__Bit0, axiom, (! [A:$tType]: (((numeral @ A) => (! [N:num]: ((((numeral_numeral @ A) @ (bit0 @ N)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ N)) @ ((numeral_numeral @ A) @ N))))))))).
% 0.33/1.50 thf(fact_136_one__le__numeral, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [N:num]: ((((ord_less_eq @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ N)))))))).
% 0.33/1.50 thf(fact_137_abs__triangle__ineq, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A]: ((((ord_less_eq @ A) @ ((abs_abs @ A) @ (((plus_plus @ A) @ A2) @ B))) @ (((plus_plus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B))))))))).
% 0.33/1.50 thf(fact_138_numeral__One, axiom, (! [A:$tType]: (((numeral @ A) => (((numeral_numeral @ A) @ one2) = (one_one @ A)))))).
% 0.33/1.50 thf(fact_139_ordered__ring__class_Ole__add__iff2, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [A2:A,E:A,C:A,B:A,D:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ (((times_times @ A) @ A2) @ E)) @ C)) @ (((plus_plus @ A) @ (((times_times @ A) @ B) @ E)) @ D)) = (((ord_less_eq @ A) @ C) @ (((plus_plus @ A) @ (((times_times @ A) @ (((minus_minus @ A) @ B) @ A2)) @ E)) @ D))))))))).
% 0.33/1.50 thf(fact_140_ordered__ring__class_Ole__add__iff1, axiom, (! [A:$tType]: (((ordered_ring @ A) => (! [A2:A,E:A,C:A,B:A,D:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ (((times_times @ A) @ A2) @ E)) @ C)) @ (((plus_plus @ A) @ (((times_times @ A) @ B) @ E)) @ D)) = (((ord_less_eq @ A) @ (((plus_plus @ A) @ (((times_times @ A) @ (((minus_minus @ A) @ A2) @ B)) @ E)) @ C)) @ D)))))))).
% 0.33/1.50 thf(fact_141_abs__diff__triangle__ineq, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A,C:A,D:A]: ((((ord_less_eq @ A) @ ((abs_abs @ A) @ (((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ (((plus_plus @ A) @ C) @ D)))) @ (((plus_plus @ A) @ ((abs_abs @ A) @ (((minus_minus @ A) @ A2) @ C))) @ ((abs_abs @ A) @ (((minus_minus @ A) @ B) @ D)))))))))).
% 0.33/1.50 thf(fact_142_abs__triangle__ineq4, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A]: ((((ord_less_eq @ A) @ ((abs_abs @ A) @ (((minus_minus @ A) @ A2) @ B))) @ (((plus_plus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B))))))))).
% 0.33/1.50 thf(fact_143_abs__diff__le__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X3:A,A2:A,R:A]: (((((ord_less_eq @ A) @ ((abs_abs @ A) @ (((minus_minus @ A) @ X3) @ A2))) @ R) = ((((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ R)) @ X3) & (((ord_less_eq @ A) @ X3) @ (((plus_plus @ A) @ A2) @ R)))))))))).
% 0.33/1.50 thf(fact_144_diff__eq__diff__less__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less_eq @ A) @ A2) @ B) = (((ord_less_eq @ A) @ C) @ D))))))))).
% 0.33/1.50 thf(fact_145_diff__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_146_diff__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B) @ A2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C) @ A2)) @ (((minus_minus @ A) @ C) @ B))))))))).
% 0.33/1.50 thf(fact_147_diff__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B:A,D:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ D) @ C) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B) @ D)))))))))).
% 0.33/1.50 thf(fact_148_right__diff__distrib_H, axiom, (! [A:$tType]: (((comm_s1003936772cancel @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ A2) @ (((minus_minus @ A) @ B) @ C)) = (((minus_minus @ A) @ (((times_times @ A) @ A2) @ B)) @ (((times_times @ A) @ A2) @ C))))))))).
% 0.33/1.50 thf(fact_149_left__diff__distrib_H, axiom, (! [A:$tType]: (((comm_s1003936772cancel @ A) => (! [B:A,C:A,A2:A]: (((((times_times @ A) @ (((minus_minus @ A) @ B) @ C)) @ A2) = (((minus_minus @ A) @ (((times_times @ A) @ B) @ A2)) @ (((times_times @ A) @ C) @ A2))))))))).
% 0.33/1.50 thf(fact_150_right__diff__distrib, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ A2) @ (((minus_minus @ A) @ B) @ C)) = (((minus_minus @ A) @ (((times_times @ A) @ A2) @ B)) @ (((times_times @ A) @ A2) @ C))))))))).
% 0.33/1.50 thf(fact_151_left__diff__distrib, axiom, (! [A:$tType]: (((ring @ A) => (! [A2:A,B:A,C:A]: (((((times_times @ A) @ (((minus_minus @ A) @ A2) @ B)) @ C) = (((minus_minus @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B) @ C))))))))).
% 0.33/1.50 thf(fact_152_abs__ge__self, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ ((abs_abs @ A) @ A2)))))))).
% 0.33/1.50 thf(fact_153_abs__le__D1, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ ((abs_abs @ A) @ A2)) @ B) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 0.33/1.50 thf(fact_154_abs__mult, axiom, (! [A:$tType]: (((idom_abs_sgn @ A) => (! [A2:A,B:A]: ((((abs_abs @ A) @ (((times_times @ A) @ A2) @ B)) = (((times_times @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B))))))))).
% 0.33/1.50 thf(fact_155_abs__minus__commute, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A]: ((((abs_abs @ A) @ (((minus_minus @ A) @ A2) @ B)) = ((abs_abs @ A) @ (((minus_minus @ A) @ B) @ A2))))))))).
% 0.33/1.50 thf(fact_156_left__add__twice, axiom, (! [A:$tType]: (((semiring_numeral @ A) => (! [A2:A,B:A]: (((((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B)) = (((plus_plus @ A) @ (((times_times @ A) @ ((numeral_numeral @ A) @ (bit0 @ one2))) @ A2)) @ B)))))))).
% 0.33/1.50 thf(fact_157_mult__2__right, axiom, (! [A:$tType]: (((semiring_numeral @ A) => (! [Z:A]: (((((times_times @ A) @ Z) @ ((numeral_numeral @ A) @ (bit0 @ one2))) = (((plus_plus @ A) @ Z) @ Z)))))))).
% 0.33/1.50 thf(fact_158_mult__2, axiom, (! [A:$tType]: (((semiring_numeral @ A) => (! [Z:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ (bit0 @ one2))) @ Z) = (((plus_plus @ A) @ Z) @ Z)))))))).
% 0.33/1.50 thf(fact_159_mult__numeral__1__right, axiom, (! [A:$tType]: (((semiring_numeral @ A) => (! [A2:A]: (((((times_times @ A) @ A2) @ ((numeral_numeral @ A) @ one2)) = A2))))))).
% 0.33/1.50 thf(fact_160_mult__numeral__1, axiom, (! [A:$tType]: (((semiring_numeral @ A) => (! [A2:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ one2)) @ A2) = A2))))))).
% 0.33/1.50 thf(fact_161_abs__triangle__ineq2__sym, axiom, (! [A:$tType]: (((ordere142940540dd_abs @ A) => (! [A2:A,B:A]: ((((ord_less_eq @ A) @ (((minus_minus @ A) @ ((abs_abs @ A) @ A2)) @ ((abs_abs @ A) @ B))) @ ((abs_abs @ A) @ (((minus_minus @ A) @ B) @ A2))))))))).
% 0.33/1.50 thf(fact_162_sin__bound__lemma, axiom, (! [X3:real,Y:real,U:real,V:real]: (((X3 = Y) => ((((ord_less_eq @ real) @ ((abs_abs @ real) @ U)) @ V) => (((ord_less_eq @ real) @ ((abs_abs @ real) @ (((minus_minus @ real) @ (((plus_plus @ real) @ X3) @ U)) @ Y))) @ V)))))).
% 0.33/1.50 thf(fact_163_rate__1, axiom, (! [P3:nat,S:real,T:real]: (((((genClo1015804716orrect @ P3) @ T) & (((ord_less_eq @ real) @ S) @ T)) => (((ord_less_eq @ real) @ (((minus_minus @ real) @ ((genClo1161277105lle_PC @ P3) @ T)) @ ((genClo1161277105lle_PC @ P3) @ S))) @ (((times_times @ real) @ (((minus_minus @ real) @ T) @ S)) @ (((plus_plus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))))))).
% 0.33/1.50 thf(fact_164_rate__2, axiom, (! [P3:nat,S:real,T:real]: (((((genClo1015804716orrect @ P3) @ T) & (((ord_less_eq @ real) @ S) @ T)) => (((ord_less_eq @ real) @ (((times_times @ real) @ (((minus_minus @ real) @ T) @ S)) @ (((minus_minus @ real) @ (one_one @ real)) @ genClo1144207539le_rho))) @ (((minus_minus @ real) @ ((genClo1161277105lle_PC @ P3) @ T)) @ ((genClo1161277105lle_PC @ P3) @ S))))))).
% 0.33/1.50 thf(fact_165_dbl__simps_I3_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (((neg_numeral_dbl @ A) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 0.33/1.50 thf(fact_166_mult__diff__mult, axiom, (! [A:$tType]: (((ring @ A) => (! [X3:A,Y:A,A2:A,B:A]: (((((minus_minus @ A) @ (((times_times @ A) @ X3) @ Y)) @ (((times_times @ A) @ A2) @ B)) = (((plus_plus @ A) @ (((times_times @ A) @ X3) @ (((minus_minus @ A) @ Y) @ B))) @ (((times_times @ A) @ (((minus_minus @ A) @ X3) @ A2)) @ B))))))))).
% 0.33/1.50 thf(fact_167_verit__eq__simplify_I8_J, axiom, (! [X22:num,Y2:num]: ((((bit0 @ X22) = (bit0 @ Y2)) = (X22 = Y2))))).
% 0.33/1.50 thf(fact_168_minus__apply, axiom, (! [B2:$tType,A:$tType]: (((minus @ B2) => ((minus_minus @ (A > B2)) = (^ [A5:(A > B2),B5:(A > B2),X:A]: ((((minus_minus @ B2) @ (A5 @ X)) @ (B5 @ X))))))))).
% 0.33/1.50 thf(fact_169_okRead1__def, axiom, (genClo293725281kRead1 = (^ [F:(nat > real),X:real,Ppred:(nat > $o)]: ((! [L2:nat,M2:nat]: ((((Ppred @ L2) & (Ppred @ M2)) => (((ord_less_eq @ real) @ ((abs_abs @ real) @ (((minus_minus @ real) @ (F @ L2)) @ (F @ M2)))) @ X)))))))).
% 0.33/1.50 thf(fact_170_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 0.33/1.50 thf(fact_171_eq__diff__eq_H, axiom, (! [X3:real,Y:real,Z:real]: (((X3 = (((minus_minus @ real) @ Y) @ Z)) = (Y = (((plus_plus @ real) @ X3) @ Z)))))).
% 0.33/1.50 thf(fact_172_semiring__norm_I6_J, axiom, (! [M:num,N:num]: (((((plus_plus @ num) @ (bit0 @ M)) @ (bit0 @ N)) = (bit0 @ (((plus_plus @ num) @ M) @ N)))))).
% 0.33/1.50 thf(fact_173_semiring__norm_I2_J, axiom, ((((plus_plus @ num) @ one2) @ one2) = (bit0 @ one2))).
% 0.33/1.50 thf(fact_174_dbl__simps_I5_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (! [K:num]: ((((neg_numeral_dbl @ A) @ ((numeral_numeral @ A) @ K)) = ((numeral_numeral @ A) @ (bit0 @ K))))))))).
% 0.33/1.50 thf(fact_175_nat__1__add__1, axiom, ((((plus_plus @ nat) @ (one_one @ nat)) @ (one_one @ nat)) = ((numeral_numeral @ nat) @ (bit0 @ one2)))).
% 0.33/1.50 thf(fact_176_add__One__commute, axiom, (! [N:num]: (((((plus_plus @ num) @ one2) @ N) = (((plus_plus @ num) @ N) @ one2))))).
% 0.33/1.50 thf(fact_177_numerals_I1_J, axiom, (((numeral_numeral @ nat) @ one2) = (one_one @ nat))).
% 0.33/1.50 thf(fact_178_dbl__def, axiom, (! [A:$tType]: (((neg_numeral @ A) => ((neg_numeral_dbl @ A) = (^ [X:A]: ((((plus_plus @ A) @ X) @ X)))))))).
% 0.33/1.50 thf(fact_179_le__funD, axiom, (! [B2:$tType,A:$tType]: (((ord @ B2) => (! [F2:(A > B2),G2:(A > B2),X3:A]: (((((ord_less_eq @ (A > B2)) @ F2) @ G2) => (((ord_less_eq @ B2) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 0.33/1.50 thf(fact_180_le__funE, axiom, (! [B2:$tType,A:$tType]: (((ord @ B2) => (! [F2:(A > B2),G2:(A > B2),X3:A]: (((((ord_less_eq @ (A > B2)) @ F2) @ G2) => (((ord_less_eq @ B2) @ (F2 @ X3)) @ (G2 @ X3))))))))).
% 0.33/1.50 thf(fact_181_le__funI, axiom, (! [B2:$tType,A:$tType]: (((ord @ B2) => (! [F2:(A > B2),G2:(A > B2)]: (((! [X2:A]: ((((ord_less_eq @ B2) @ (F2 @ X2)) @ (G2 @ X2)))) => (((ord_less_eq @ (A > B2)) @ F2) @ G2)))))))).
% 0.33/1.50 thf(fact_182_le__fun__def, axiom, (! [B2:$tType,A:$tType]: (((ord @ B2) => ((ord_less_eq @ (A > B2)) = (^ [F:(A > B2),G:(A > B2)]: ((! [X:A]: ((((ord_less_eq @ B2) @ (F @ X)) @ (G @ X))))))))))).
% 0.33/1.50 thf(fact_183_order__subst1, axiom, (! [A:$tType,B2:$tType]: ((((order @ B2) & (order @ A)) => (! [A2:A,F2:(B2 > A),B:B2,C:B2]: (((((ord_less_eq @ A) @ A2) @ (F2 @ B)) => ((((ord_less_eq @ B2) @ B) @ C) => ((! [X2:B2,Y3:B2]: (((((ord_less_eq @ B2) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C))))))))))).
% 0.33/1.50 thf(fact_184_order__subst2, axiom, (! [A:$tType,C5:$tType]: ((((order @ C5) & (order @ A)) => (! [A2:A,B:A,F2:(A > C5),C:C5]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ C5) @ (F2 @ B)) @ C) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ C5) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less_eq @ C5) @ (F2 @ A2)) @ C)))))))))).
% 0.33/1.50 thf(fact_185_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,B:A]: (((A2 = B) | ((~ ((((ord_less_eq @ A) @ A2) @ B))) | (~ ((((ord_less_eq @ A) @ B) @ A2))))))))))).
% 0.33/1.50 thf(fact_186_ord__eq__le__subst, axiom, (! [A:$tType,B2:$tType]: ((((ord @ B2) & (ord @ A)) => (! [A2:A,F2:(B2 > A),B:B2,C:B2]: (((A2 = (F2 @ B)) => ((((ord_less_eq @ B2) @ B) @ C) => ((! [X2:B2,Y3:B2]: (((((ord_less_eq @ B2) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C))))))))))).
% 0.33/1.50 thf(fact_187_ord__le__eq__subst, axiom, (! [A:$tType,B2:$tType]: ((((ord @ B2) & (ord @ A)) => (! [A2:A,B:A,F2:(A > B2),C:B2]: (((((ord_less_eq @ A) @ A2) @ B) => (((F2 @ B) = C) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ B2) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less_eq @ B2) @ (F2 @ A2)) @ C)))))))))).
% 0.33/1.50 thf(fact_188_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z2:A]: ((Y4 = Z2))) = (^ [X:A,Y5:A]: (((((ord_less_eq @ A) @ X) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X))))))))).
% 0.33/1.50 thf(fact_189_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ X3) => (X3 = Y))))))))).
% 0.33/1.50 thf(fact_190_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((((ord_less_eq @ A) @ X3) @ Y) | (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 0.33/1.50 thf(fact_191_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A]: (((X3 = Y) => (((ord_less_eq @ A) @ X3) @ Y)))))))).
% 0.33/1.50 thf(fact_192_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y))) => (((ord_less_eq @ A) @ Y) @ X3)))))))).
% 0.33/1.50 thf(fact_193_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ B) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.33/1.50 thf(fact_194_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X3) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z)))) => (((((ord_less_eq @ A) @ X3) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X3)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y))))))))))))))))).
% 0.33/1.50 thf(fact_195_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X3:A]: (((((ord_less_eq @ A) @ Y) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y) = (X3 = Y))))))))).
% 0.33/1.50 thf(fact_196_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z2:A]: ((Y4 = Z2))) = (^ [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) & (((ord_less_eq @ A) @ B4) @ A4))))))))).
% 0.33/1.50 thf(fact_197_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B:A,C:A]: (((A2 = B) => ((((ord_less_eq @ A) @ B) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.33/1.50 thf(fact_198_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((B = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.33/1.50 thf(fact_199_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ B) @ A2) => (A2 = B))))))))).
% 0.33/1.50 thf(fact_200_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X3) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X3) @ Z))))))))).
% 0.33/1.50 thf(fact_201_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 0.33/1.50 thf(fact_202_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:(A > (A > $o)),A2:A,B:A]: (((! [A6:A,B6:A]: (((((ord_less_eq @ A) @ A6) @ B6) => ((P2 @ A6) @ B6)))) => ((! [A6:A,B6:A]: ((((P2 @ B6) @ A6) => ((P2 @ A6) @ B6)))) => ((P2 @ A2) @ B))))))))).
% 0.33/1.50 thf(fact_203_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((ord_less_eq @ A) @ C) @ B) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 0.33/1.50 thf(fact_204_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z2:A]: ((Y4 = Z2))) = (^ [A4:A,B4:A]: (((((ord_less_eq @ A) @ B4) @ A4) & (((ord_less_eq @ A) @ A4) @ B4))))))))).
% 0.33/1.50 thf(fact_205_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B:A,A2:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((ord_less_eq @ A) @ A2) @ B) => (A2 = B))))))))).
% 0.33/1.50 thf(fact_206_fun__diff__def, axiom, (! [B2:$tType,A:$tType]: (((minus @ B2) => ((minus_minus @ (A > B2)) = (^ [A5:(A > B2),B5:(A > B2),X:A]: ((((minus_minus @ B2) @ (A5 @ X)) @ (B5 @ X))))))))).
% 0.33/1.50 thf(fact_207_complete__real, axiom, (! [S3:(set @ real)]: (((? [X4:real]: ((((member @ real) @ X4) @ S3))) => ((? [Z3:real]: ((! [X2:real]: (((((member @ real) @ X2) @ S3) => (((ord_less_eq @ real) @ X2) @ Z3)))))) => (? [Y3:real]: (((! [X4:real]: (((((member @ real) @ X4) @ S3) => (((ord_less_eq @ real) @ X4) @ Y3)))) & (! [Z3:real]: (((! [X2:real]: (((((member @ real) @ X2) @ S3) => (((ord_less_eq @ real) @ X2) @ Z3)))) => (((ord_less_eq @ real) @ Y3) @ Z3)))))))))))).
% 0.33/1.50 thf(fact_208_PC__monotone, axiom, (! [P3:nat,S:real,T:real]: (((((genClo1015804716orrect @ P3) @ T) & (((ord_less_eq @ real) @ S) @ T)) => (((ord_less_eq @ real) @ ((genClo1161277105lle_PC @ P3) @ S)) @ ((genClo1161277105lle_PC @ P3) @ T)))))).
% 0.33/1.50 thf(fact_209_add__diff__add, axiom, (! [A:$tType]: (((ab_group_add @ A) => (! [A2:A,C:A,B:A,D:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)) = (((plus_plus @ A) @ (((minus_minus @ A) @ A2) @ B)) @ (((minus_minus @ A) @ C) @ D))))))))).
% 0.33/1.50 thf(fact_210_verit__eq__simplify_I10_J, axiom, (! [X22:num]: ((one2 != (bit0 @ X22))))).
% 0.33/1.50 thf(fact_211_inf__period_I2_J, axiom, (! [A:$tType]: ((((comm_ring @ A) & (dvd @ A)) => (! [P2:(A > $o),D2:A,Q:(A > $o)]: (((! [X2:A,K2:A]: (((P2 @ X2) = (P2 @ (((minus_minus @ A) @ X2) @ (((times_times @ A) @ K2) @ D2)))))) => ((! [X2:A,K2:A]: (((Q @ X2) = (Q @ (((minus_minus @ A) @ X2) @ (((times_times @ A) @ K2) @ D2)))))) => (! [X4:A,K3:A]: ((((P2 @ X4) | (Q @ X4)) = ((P2 @ (((minus_minus @ A) @ X4) @ (((times_times @ A) @ K3) @ D2))) | (Q @ (((minus_minus @ A) @ X4) @ (((times_times @ A) @ K3) @ D2))))))))))))))).
% 0.33/1.50 thf(fact_212_inf__period_I1_J, axiom, (! [A:$tType]: ((((comm_ring @ A) & (dvd @ A)) => (! [P2:(A > $o),D2:A,Q:(A > $o)]: (((! [X2:A,K2:A]: (((P2 @ X2) = (P2 @ (((minus_minus @ A) @ X2) @ (((times_times @ A) @ K2) @ D2)))))) => ((! [X2:A,K2:A]: (((Q @ X2) = (Q @ (((minus_minus @ A) @ X2) @ (((times_times @ A) @ K2) @ D2)))))) => (! [X4:A,K3:A]: ((((P2 @ X4) & (Q @ X4)) = ((P2 @ (((minus_minus @ A) @ X4) @ (((times_times @ A) @ K3) @ D2))) & (Q @ (((minus_minus @ A) @ X4) @ (((times_times @ A) @ K3) @ D2))))))))))))))).
% 0.33/1.50 thf(fact_213_crossproduct__eq, axiom, (! [A:$tType]: (((semiri456707255roduct @ A) => (! [W:A,Y:A,X3:A,Z:A]: ((((((plus_plus @ A) @ (((times_times @ A) @ W) @ Y)) @ (((times_times @ A) @ X3) @ Z)) = (((plus_plus @ A) @ (((times_times @ A) @ W) @ Z)) @ (((times_times @ A) @ X3) @ Y))) = ((W = X3) | (Y = Z))))))))).
% 0.33/1.50 thf(fact_214_nat__eq__add__iff1, axiom, (! [J:nat,I:nat,U:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ J) @ I) => (((((plus_plus @ nat) @ (((times_times @ nat) @ I) @ U)) @ M) = (((plus_plus @ nat) @ (((times_times @ nat) @ J) @ U)) @ N)) = ((((plus_plus @ nat) @ (((times_times @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ U)) @ M) = N)))))).
% 0.33/1.50 thf(fact_215_nat__eq__add__iff2, axiom, (! [I:nat,J:nat,U:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((((plus_plus @ nat) @ (((times_times @ nat) @ I) @ U)) @ M) = (((plus_plus @ nat) @ (((times_times @ nat) @ J) @ U)) @ N)) = (M = (((plus_plus @ nat) @ (((times_times @ nat) @ (((minus_minus @ nat) @ J) @ I)) @ U)) @ N))))))).
% 0.33/1.50 thf(fact_216_nat__le__add__iff1, axiom, (! [J:nat,I:nat,U:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ J) @ I) => ((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (((times_times @ nat) @ I) @ U)) @ M)) @ (((plus_plus @ nat) @ (((times_times @ nat) @ J) @ U)) @ N)) = (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (((times_times @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ U)) @ M)) @ N)))))).
% 0.33/1.50 thf(fact_217_nat__le__add__iff2, axiom, (! [I:nat,J:nat,U:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (((times_times @ nat) @ I) @ U)) @ M)) @ (((plus_plus @ nat) @ (((times_times @ nat) @ J) @ U)) @ N)) = (((ord_less_eq @ nat) @ M) @ (((plus_plus @ nat) @ (((times_times @ nat) @ (((minus_minus @ nat) @ J) @ I)) @ U)) @ N))))))).
% 0.33/1.50 thf(fact_218_nat__diff__add__eq1, axiom, (! [J:nat,I:nat,U:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ J) @ I) => ((((minus_minus @ nat) @ (((plus_plus @ nat) @ (((times_times @ nat) @ I) @ U)) @ M)) @ (((plus_plus @ nat) @ (((times_times @ nat) @ J) @ U)) @ N)) = (((minus_minus @ nat) @ (((plus_plus @ nat) @ (((times_times @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ U)) @ M)) @ N)))))).
% 0.33/1.50 thf(fact_219_nat__diff__add__eq2, axiom, (! [I:nat,J:nat,U:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((minus_minus @ nat) @ (((plus_plus @ nat) @ (((times_times @ nat) @ I) @ U)) @ M)) @ (((plus_plus @ nat) @ (((times_times @ nat) @ J) @ U)) @ N)) = (((minus_minus @ nat) @ M) @ (((plus_plus @ nat) @ (((times_times @ nat) @ (((minus_minus @ nat) @ J) @ I)) @ U)) @ N))))))).
% 0.33/1.50 thf(fact_220_left__add__mult__distrib, axiom, (! [I:nat,U:nat,J:nat,K:nat]: (((((plus_plus @ nat) @ (((times_times @ nat) @ I) @ U)) @ (((plus_plus @ nat) @ (((times_times @ nat) @ J) @ U)) @ K)) = (((plus_plus @ nat) @ (((times_times @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ U)) @ K))))).
% 0.33/1.50 thf(fact_221_crossproduct__noteq, axiom, (! [A:$tType]: (((semiri456707255roduct @ A) => (! [A2:A,B:A,C:A,D:A]: ((((A2 != B) & (C != D)) = ((((plus_plus @ A) @ (((times_times @ A) @ A2) @ C)) @ (((times_times @ A) @ B) @ D)) != (((plus_plus @ A) @ (((times_times @ A) @ A2) @ D)) @ (((times_times @ A) @ B) @ C)))))))))).
% 0.33/1.50 thf(fact_222_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))))))).
% 0.33/1.50 thf(fact_223_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))))))).
% 0.33/1.50 thf(fact_224_nat__add__left__cancel__le, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 0.33/1.50 thf(fact_225_diff__diff__cancel, axiom, (! [I:nat,N:nat]: (((((ord_less_eq @ nat) @ I) @ N) => ((((minus_minus @ nat) @ N) @ (((minus_minus @ nat) @ N) @ I)) = I))))).
% 0.33/1.50 thf(fact_226_diff__diff__left, axiom, (! [I:nat,J:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ K) = (((minus_minus @ nat) @ I) @ (((plus_plus @ nat) @ J) @ K)))))).
% 0.33/1.50 thf(fact_227_Nat_Odiff__diff__right, axiom, (! [K:nat,J:nat,I:nat]: (((((ord_less_eq @ nat) @ K) @ J) => ((((minus_minus @ nat) @ I) @ (((minus_minus @ nat) @ J) @ K)) = (((minus_minus @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ J)))))).
% 0.33/1.50 thf(fact_228_Nat_Oadd__diff__assoc2, axiom, (! [K:nat,J:nat,I:nat]: (((((ord_less_eq @ nat) @ K) @ J) => ((((plus_plus @ nat) @ (((minus_minus @ nat) @ J) @ K)) @ I) = (((minus_minus @ nat) @ (((plus_plus @ nat) @ J) @ I)) @ K)))))).
% 0.33/1.50 thf(fact_229_Nat_Oadd__diff__assoc, axiom, (! [K:nat,J:nat,I:nat]: (((((ord_less_eq @ nat) @ K) @ J) => ((((plus_plus @ nat) @ I) @ (((minus_minus @ nat) @ J) @ K)) = (((minus_minus @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ K)))))).
% 0.33/1.50 thf(fact_230_eq__diff__iff, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => (((((minus_minus @ nat) @ M) @ K) = (((minus_minus @ nat) @ N) @ K)) = (M = N))))))).
% 0.33/1.50 thf(fact_231_le__diff__iff, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N) @ K)) = (((ord_less_eq @ nat) @ M) @ N))))))).
% 0.33/1.50 thf(fact_232_Nat_Odiff__diff__eq, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => ((((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N) @ K)) = (((minus_minus @ nat) @ M) @ N))))))).
% 0.33/1.50 thf(fact_233_diff__le__mono, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ L)) @ (((minus_minus @ nat) @ N) @ L)))))).
% 0.33/1.50 thf(fact_234_diff__le__self, axiom, (! [M:nat,N:nat]: ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ M)))).
% 0.33/1.50 thf(fact_235_le__diff__iff_H, axiom, (! [A2:nat,C:nat,B:nat]: (((((ord_less_eq @ nat) @ A2) @ C) => ((((ord_less_eq @ nat) @ B) @ C) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ C) @ A2)) @ (((minus_minus @ nat) @ C) @ B)) = (((ord_less_eq @ nat) @ B) @ A2))))))).
% 0.33/1.50 thf(fact_236_diff__le__mono2, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ L) @ N)) @ (((minus_minus @ nat) @ L) @ M)))))).
% 0.33/1.50 thf(fact_237_Nat_Oex__has__greatest__nat, axiom, (! [P2:(nat > $o),K:nat,B:nat]: (((P2 @ K) => ((! [Y3:nat]: (((P2 @ Y3) => (((ord_less_eq @ nat) @ Y3) @ B)))) => (? [X2:nat]: (((P2 @ X2) & (! [Y6:nat]: (((P2 @ Y6) => (((ord_less_eq @ nat) @ Y6) @ X2)))))))))))).
% 0.33/1.50 thf(fact_238_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 0.33/1.50 thf(fact_239_mult__le__mono2, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ K) @ I)) @ (((times_times @ nat) @ K) @ J)))))).
% 0.33/1.50 thf(fact_240_mult__le__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ I) @ K)) @ (((times_times @ nat) @ J) @ K)))))).
% 0.33/1.50 thf(fact_241_mult__le__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ K) @ L) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ I) @ K)) @ (((times_times @ nat) @ J) @ L))))))).
% 0.33/1.50 thf(fact_242_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 0.33/1.50 thf(fact_243_le__square, axiom, (! [M:nat]: ((((ord_less_eq @ nat) @ M) @ (((times_times @ nat) @ M) @ M))))).
% 0.33/1.50 thf(fact_244_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.33/1.50 thf(fact_245_le__trans, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I) @ K)))))).
% 0.33/1.50 thf(fact_246_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 0.33/1.50 thf(fact_247_le__cube, axiom, (! [M:nat]: ((((ord_less_eq @ nat) @ M) @ (((times_times @ nat) @ M) @ (((times_times @ nat) @ M) @ M)))))).
% 0.33/1.50 thf(fact_248_diff__mult__distrib2, axiom, (! [K:nat,M:nat,N:nat]: (((((times_times @ nat) @ K) @ (((minus_minus @ nat) @ M) @ N)) = (((minus_minus @ nat) @ (((times_times @ nat) @ K) @ M)) @ (((times_times @ nat) @ K) @ N)))))).
% 0.33/1.50 thf(fact_249_diff__mult__distrib, axiom, (! [M:nat,N:nat,K:nat]: (((((times_times @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ K) = (((minus_minus @ nat) @ (((times_times @ nat) @ M) @ K)) @ (((times_times @ nat) @ N) @ K)))))).
% 0.33/1.50 thf(fact_250_diff__commute, axiom, (! [I:nat,J:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ K) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ K)) @ J))))).
% 0.33/1.50 thf(fact_251_Nat_Ole__imp__diff__is__add, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((((minus_minus @ nat) @ J) @ I) = K) = (J = (((plus_plus @ nat) @ K) @ I))))))).
% 0.33/1.50 thf(fact_252_diff__add__inverse2, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ (((plus_plus @ nat) @ M) @ N)) @ N) = M)))).
% 0.33/1.50 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 0.33/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 0.33/1.50 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 0.33/1.50 thf(tcon_fun___Groups_Ominus, axiom, (! [A7:$tType,A8:$tType]: (((minus @ A8) => (minus @ (A7 > A8)))))).
% 0.33/1.50 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, (semiri456707255roduct @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff, axiom, (ordere623563068d_diff @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, (ordere236663937imp_le @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, (ordere779506340up_add @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1__cancel, axiom, (comm_s1003936772cancel @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, (cancel_semigroup_add @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, (linordered_semidom @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult, axiom, (ab_semigroup_mult @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult, axiom, (comm_monoid_mult @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, (ab_semigroup_add @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Osemigroup__mult, axiom, (semigroup_mult @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Num_Osemiring__numeral, axiom, (semiring_numeral @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, (semigroup_add @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Rings_Ocomm__semiring, axiom, (comm_semiring @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Nat_Osemiring__char__0, axiom, (semiring_char_0 @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, (preorder @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Omonoid__mult, axiom, (monoid_mult @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, (order @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Rings_Osemiring, axiom, (semiring @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, (ord @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Ominus_4, axiom, (minus @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Num_Onumeral, axiom, (numeral @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 0.33/1.50 thf(tcon_Nat_Onat___Rings_Odvd, axiom, (dvd @ nat)).
% 0.33/1.50 thf(tcon_Num_Onum___Orderings_Opreorder_5, axiom, (preorder @ num)).
% 0.33/1.50 thf(tcon_Num_Onum___Orderings_Olinorder_6, axiom, (linorder @ num)).
% 0.33/1.50 thf(tcon_Num_Onum___Orderings_Oorder_7, axiom, (order @ num)).
% 0.33/1.50 thf(tcon_Num_Onum___Orderings_Oord_8, axiom, (ord @ num)).
% 0.33/1.50 thf(tcon_Set_Oset___Orderings_Opreorder_9, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 0.33/1.50 thf(tcon_Set_Oset___Orderings_Oorder_10, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 0.33/1.50 thf(tcon_Set_Oset___Orderings_Oord_11, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 0.33/1.50 thf(tcon_Set_Oset___Groups_Ominus_12, axiom, (! [A7:$tType]: ((minus @ (set @ A7))))).
% 0.33/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_13, axiom, (preorder @ $o)).
% 0.33/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder_14, axiom, (linorder @ $o)).
% 0.33/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_15, axiom, (order @ $o)).
% 0.33/1.50 thf(tcon_HOL_Obool___Orderings_Oord_16, axiom, (ord @ $o)).
% 0.33/1.50 thf(tcon_HOL_Obool___Groups_Ominus_17, axiom, (minus @ $o)).
% 0.33/1.50 thf(tcon_Real_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_18, axiom, (semiri456707255roduct @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_19, axiom, (ordere236663937imp_le @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_20, axiom, (linord1659791738miring @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_21, axiom, (ordere779506340up_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs, axiom, (ordere142940540dd_abs @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_22, axiom, (cancel146912293up_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_23, axiom, (cancel1352612707id_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1__cancel_24, axiom, (comm_s1003936772cancel @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add, axiom, (ordered_ab_group_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_25, axiom, (cancel_semigroup_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_26, axiom, (linordered_semidom @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Oab__semigroup__mult_27, axiom, (ab_semigroup_mult @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__mult_28, axiom, (comm_monoid_mult @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_29, axiom, (ab_semigroup_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_30, axiom, (comm_monoid_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Olinordered__idom, axiom, (linordered_idom @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Osemigroup__mult_31, axiom, (semigroup_mult @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Num_Osemiring__numeral_32, axiom, (semiring_numeral @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Osemigroup__add_33, axiom, (semigroup_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Ocomm__semiring_34, axiom, (comm_semiring @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Nat_Osemiring__char__0_35, axiom, (semiring_char_0 @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Oab__group__add, axiom, (ab_group_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Oordered__ring, axiom, (ordered_ring @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Oidom__abs__sgn, axiom, (idom_abs_sgn @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Orderings_Opreorder_36, axiom, (preorder @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Orderings_Olinorder_37, axiom, (linorder @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Omonoid__mult_38, axiom, (monoid_mult @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Ogroup__add, axiom, (group_add @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Ocomm__ring, axiom, (comm_ring @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Orderings_Oorder_39, axiom, (order @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Num_Oneg__numeral, axiom, (neg_numeral @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Osemiring_40, axiom, (semiring @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Orderings_Oord_41, axiom, (ord @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Oring__1, axiom, (ring_1 @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Ominus_42, axiom, (minus @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Num_Onumeral_43, axiom, (numeral @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Oring, axiom, (ring @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Groups_Oone_44, axiom, (one @ real)).
% 0.33/1.50 thf(tcon_Real_Oreal___Rings_Odvd_45, axiom, (dvd @ real)).
% 0.33/1.50 thf(conj_0, conjecture, (((ord_less_eq @ real) @ ((abs_abs @ real) @ (((minus_minus @ real) @ (((minus_minus @ real) @ ((c @ p) @ t)) @ ((c @ p) @ s))) @ (((minus_minus @ real) @ ((d @ q) @ t)) @ ((d @ q) @ s))))) @ (((times_times @ real) @ (((times_times @ real) @ ((numeral_numeral @ real) @ (bit0 @ one2))) @ genClo1144207539le_rho)) @ (((minus_minus @ real) @ t) @ s)))).
% 0.33/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2DTF19870.p
% 0.33/1.50 ------------------------
% 0.33/1.53 ---- Cleaned THF ---
% 0.33/1.53 thf(ty_t_Real_Oreal,type,
% 0.33/1.53 real: $tType ).
% 0.33/1.53
% 0.33/1.53 thf(ty_t_Set_Oset,type,
% 0.33/1.53 set: $tType > $tType ).
% 0.33/1.53
% 0.33/1.53 thf(ty_t_Num_Onum,type,
% 0.33/1.53 num: $tType ).
% 0.33/1.53
% 0.33/1.53 thf(ty_t_Nat_Onat,type,
% 0.33/1.53 nat: $tType ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_HOL_Otype,type,
% 0.33/1.53 type:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Odvd,type,
% 0.33/1.53 dvd:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oone,type,
% 0.33/1.53 one:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Oring,type,
% 0.33/1.53 ring:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Num_Onumeral,type,
% 0.33/1.53 numeral:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Ominus,type,
% 0.33/1.53 minus:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Oring__1,type,
% 0.33/1.53 ring_1:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Orderings_Oord,type,
% 0.33/1.53 ord:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Osemiring,type,
% 0.33/1.53 semiring:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Num_Oneg__numeral,type,
% 0.33/1.53 neg_numeral:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Orderings_Oorder,type,
% 0.33/1.53 order:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Ocomm__ring,type,
% 0.33/1.53 comm_ring:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Ogroup__add,type,
% 0.33/1.53 group_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.33/1.53 monoid_mult:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Orderings_Olinorder,type,
% 0.33/1.53 linorder:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Orderings_Opreorder,type,
% 0.33/1.53 preorder:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Oidom__abs__sgn,type,
% 0.33/1.53 idom_abs_sgn:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Oordered__ring,type,
% 0.33/1.53 ordered_ring:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oab__group__add,type,
% 0.33/1.53 ab_group_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.33/1.53 semiring_char_0:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Ocomm__semiring,type,
% 0.33/1.53 comm_semiring:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.33/1.53 semigroup_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Num_Osemiring__numeral,type,
% 0.33/1.53 semiring_numeral:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.33/1.53 semigroup_mult:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.33/1.53 linordered_idom:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.33/1.53 comm_monoid_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.33/1.53 ab_semigroup_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 0.33/1.53 comm_monoid_mult:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.33/1.53 ab_semigroup_mult:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.33/1.53 linordered_semidom:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.33/1.53 cancel_semigroup_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.33/1.53 ordered_ab_group_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Ocomm__semiring__1__cancel,type,
% 0.33/1.53 comm_s1003936772cancel:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.33/1.53 cancel1352612707id_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.33/1.53 cancel146912293up_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oordered__ab__group__add__abs,type,
% 0.33/1.53 ordere142940540dd_abs:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.33/1.53 ordere779506340up_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.33/1.53 linord1659791738miring:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.33/1.53 canoni770627133id_add:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.33/1.53 ordere236663937imp_le:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__diff,type,
% 0.33/1.53 ordere623563068d_diff:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 0.33/1.53 semiri456707255roduct:
% 0.33/1.53 !>[A: $tType] : $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OPC,type,
% 0.33/1.53 genClo1161277105lle_PC: nat > real > real ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_GenClock__Mirabelle__pukziqipvs_O_092_060rho_062,type,
% 0.33/1.53 genClo1144207539le_rho: real ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Ocorrect,type,
% 0.33/1.53 genClo1015804716orrect: nat > real > $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead1,type,
% 0.33/1.53 genClo293725281kRead1: ( nat > real ) > real > ( nat > $o ) > $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_GenClock__Mirabelle__pukziqipvs_OokRead2,type,
% 0.33/1.53 genClo293725282kRead2: ( nat > real ) > ( nat > real ) > real > ( nat > $o ) > $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Orho__bound1,type,
% 0.33/1.53 genClo2108747022bound1: ( nat > real > real ) > $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_GenClock__Mirabelle__pukziqipvs_Orho__bound2,type,
% 0.33/1.53 genClo2108747023bound2: ( nat > real > real ) > $o ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Groups_Oabs__class_Oabs,type,
% 0.33/1.53 abs_abs:
% 0.33/1.53 !>[A: $tType] : ( A > A ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.33/1.53 minus_minus:
% 0.33/1.53 !>[A: $tType] : ( A > A > A ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.33/1.53 one_one:
% 0.33/1.53 !>[A: $tType] : A ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.33/1.53 plus_plus:
% 0.33/1.53 !>[A: $tType] : ( A > A > A ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.33/1.53 times_times:
% 0.33/1.53 !>[A: $tType] : ( A > A > A ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Num_Oneg__numeral__class_Odbl,type,
% 0.33/1.53 neg_numeral_dbl:
% 0.33/1.53 !>[A: $tType] : ( A > A ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Num_Onum_OBit0,type,
% 0.33/1.53 bit0: num > num ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Num_Onum_OOne,type,
% 0.33/1.53 one2: num ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 0.33/1.53 numeral_numeral:
% 0.33/1.53 !>[A: $tType] : ( num > A ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.33/1.53 ord_less_eq:
% 0.33/1.53 !>[A: $tType] : ( A > A > $o ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_Set_OCollect,type,
% 0.33/1.53 collect:
% 0.33/1.53 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_c_member,type,
% 0.33/1.53 member:
% 0.33/1.53 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.33/1.53
% 0.33/1.53 thf(sy_v_C,type,
% 0.33/1.53 c: nat > real > real ).
% 0.33/1.53
% 0.33/1.53 thf(sy_v_D,type,
% 0.33/1.53 d: nat > real > real ).
% 0.33/1.53
% 0.33/1.53 thf(sy_v_p,type,
% 0.33/1.53 p: nat ).
% 0.33/1.53
% 0.33/1.53 thf(sy_v_q,type,
% 0.33/1.53 q: nat ).
% 0.33/1.53
% 0.33/1.53 thf(sy_v_s,type,
% 0.33/1.53 s: real ).
% 0.33/1.53
% 0.33/1.53 thf(sy_v_t,type,
% 0.33/1.53 t: real ).
% 0.33/1.53
% 0.33/1.53 thf(fact_0_rb2,axiom,
% 0.33/1.53 genClo2108747023bound2 @ d ).
% 0.33/1.53
% 0.33/1.53 thf(fact_1_rb1,axiom,
% 0.33/1.53 genClo2108747022bound1 @ c ).
% 0.33/1.53
% 0.33/1.53 thf(fact_2_ie,axiom,
% 0.33/1.53 ord_less_eq @ real @ s @ t ).
% 0.33/1.53
% 0.33/1.53 thf(fact_3_Eq1,axiom,
% 0.33/1.53 ( ( abs_abs @ real @ ( minus_minus @ real @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) )
% 0.33/1.53 = ( minus_minus @ real @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_4_Eq4,axiom,
% 0.33/1.53 ( ( minus_minus @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) )
% 0.33/1.53 = ( times_times @ real @ ( times_times @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ genClo1144207539le_rho ) @ ( minus_minus @ real @ t @ s ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_5_Eq3,axiom,
% 0.33/1.53 ord_less_eq @ real @ ( minus_minus @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_6_corr__q,axiom,
% 0.33/1.53 genClo1015804716orrect @ q @ t ).
% 0.33/1.53
% 0.33/1.53 thf(fact_7_PC__ie,axiom,
% 0.33/1.53 ord_less_eq @ real @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_8_corr__p,axiom,
% 0.33/1.53 genClo1015804716orrect @ p @ t ).
% 0.33/1.53
% 0.33/1.53 thf(fact_9_Eq2,axiom,
% 0.33/1.53 ord_less_eq @ real @ ( minus_minus @ real @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) @ ( minus_minus @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_10__092_060open_062_It_A_N_As_J_A_K_A_I1_A_N_A_092_060rho_062_J_A_092_060le_062_AD_Aq_At_A_N_AD_Aq_As_092_060close_062,axiom,
% 0.33/1.53 ord_less_eq @ real @ ( times_times @ real @ ( minus_minus @ real @ t @ s ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_11_left__diff__distrib__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ( numeral @ A )
% 0.33/1.53 & ( ring @ A ) )
% 0.33/1.53 => ! [A2: A,B: A,V: num] :
% 0.33/1.53 ( ( times_times @ A @ ( minus_minus @ A @ A2 @ B ) @ ( numeral_numeral @ A @ V ) )
% 0.33/1.53 = ( minus_minus @ A @ ( times_times @ A @ A2 @ ( numeral_numeral @ A @ V ) ) @ ( times_times @ A @ B @ ( numeral_numeral @ A @ V ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_12_right__diff__distrib__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ( numeral @ A )
% 0.33/1.53 & ( ring @ A ) )
% 0.33/1.53 => ! [V: num,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( minus_minus @ A @ B @ C ) )
% 0.33/1.53 = ( minus_minus @ A @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ B ) @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_13_abs__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linordered_idom @ A )
% 0.33/1.53 => ! [N: num] :
% 0.33/1.53 ( ( abs_abs @ A @ ( numeral_numeral @ A @ N ) )
% 0.33/1.53 = ( numeral_numeral @ A @ N ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_14_abs__mult__self__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linordered_idom @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( times_times @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ A2 ) )
% 0.33/1.53 = ( times_times @ A @ A2 @ A2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_15_semiring__norm_I85_J,axiom,
% 0.33/1.53 ! [M: num] :
% 0.33/1.53 ( ( bit0 @ M )
% 0.33/1.53 != one2 ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_16_semiring__norm_I83_J,axiom,
% 0.33/1.53 ! [N: num] :
% 0.33/1.53 ( one2
% 0.33/1.53 != ( bit0 @ N ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_17_mult__numeral__left__semiring__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_numeral @ A )
% 0.33/1.53 => ! [V: num,W: num,Z: A] :
% 0.33/1.53 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( times_times @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.33/1.53 = ( times_times @ A @ ( numeral_numeral @ A @ ( times_times @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_18_numeral__times__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_numeral @ A )
% 0.33/1.53 => ! [M: num,N: num] :
% 0.33/1.53 ( ( times_times @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.33/1.53 = ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_19_numeral__le__iff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linord1659791738miring @ A )
% 0.33/1.53 => ! [M: num,N: num] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.33/1.53 = ( ord_less_eq @ num @ M @ N ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_20_okRead2__def,axiom,
% 0.33/1.53 ( genClo293725282kRead2
% 0.33/1.53 = ( ^ [F: nat > real,G: nat > real,X: real,Ppred: nat > $o] :
% 0.33/1.53 ! [P: nat] :
% 0.33/1.53 ( ( Ppred @ P )
% 0.33/1.53 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( F @ P ) @ ( G @ P ) ) ) @ X ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_21_abs__triangle__ineq2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_22_abs__triangle__ineq3,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_23_numeral__eq__iff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_char_0 @ A )
% 0.33/1.53 => ! [M: num,N: num] :
% 0.33/1.53 ( ( ( numeral_numeral @ A @ M )
% 0.33/1.53 = ( numeral_numeral @ A @ N ) )
% 0.33/1.53 = ( M = N ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_24_add__left__cancel,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel_semigroup_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ A2 @ B )
% 0.33/1.53 = ( plus_plus @ A @ A2 @ C ) )
% 0.33/1.53 = ( B = C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_25_add__right__cancel,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel_semigroup_add @ A )
% 0.33/1.53 => ! [B: A,A2: A,C: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ B @ A2 )
% 0.33/1.53 = ( plus_plus @ A @ C @ A2 ) )
% 0.33/1.53 = ( B = C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_26_semiring__norm_I87_J,axiom,
% 0.33/1.53 ! [M: num,N: num] :
% 0.33/1.53 ( ( ( bit0 @ M )
% 0.33/1.53 = ( bit0 @ N ) )
% 0.33/1.53 = ( M = N ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_27_abs__idempotent,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 0.33/1.53 = ( abs_abs @ A @ A2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_28_abs__abs,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( idom_abs_sgn @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( abs_abs @ A @ ( abs_abs @ A @ A2 ) )
% 0.33/1.53 = ( abs_abs @ A @ A2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_29_add__le__cancel__right,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere236663937imp_le @ A )
% 0.33/1.53 => ! [A2: A,C: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.33/1.53 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_30_add__le__cancel__left,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere236663937imp_le @ A )
% 0.33/1.53 => ! [C: A,A2: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.33/1.53 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_31_mult_Oright__neutral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( monoid_mult @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_32_mult_Oleft__neutral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( monoid_mult @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_33_numeral__plus__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( numeral @ A )
% 0.33/1.53 => ! [M: num,N: num] :
% 0.33/1.53 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.33/1.53 = ( numeral_numeral @ A @ ( plus_plus @ num @ M @ N ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_34_add__numeral__left,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( numeral @ A )
% 0.33/1.53 => ! [V: num,W: num,Z: A] :
% 0.33/1.53 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.33/1.53 = ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_35_add__diff__cancel__right_H,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel146912293up_add @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_36_add__diff__cancel__right,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel146912293up_add @ A )
% 0.33/1.53 => ! [A2: A,C: A,B: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.33/1.53 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_37_add__diff__cancel__left_H,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel146912293up_add @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ A2 )
% 0.33/1.53 = B ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_38_add__diff__cancel__left,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel146912293up_add @ A )
% 0.33/1.53 => ! [C: A,A2: A,B: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.33/1.53 = ( minus_minus @ A @ A2 @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_39_diff__add__cancel,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_40_add__diff__cancel,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ B )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_41_abs__add__abs,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( abs_abs @ A @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) )
% 0.33/1.53 = ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_42_abs__1,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( idom_abs_sgn @ A )
% 0.33/1.53 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.33/1.53 = ( one_one @ A ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_43_mem__Collect__eq,axiom,
% 0.33/1.53 ! [A: $tType,A2: A,P2: A > $o] :
% 0.33/1.53 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.33/1.53 = ( P2 @ A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_44_Collect__mem__eq,axiom,
% 0.33/1.53 ! [A: $tType,A3: set @ A] :
% 0.33/1.53 ( ( collect @ A
% 0.33/1.53 @ ^ [X: A] : ( member @ A @ X @ A3 ) )
% 0.33/1.53 = A3 ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_45_Collect__cong,axiom,
% 0.33/1.53 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.33/1.53 ( ! [X2: A] :
% 0.33/1.53 ( ( P2 @ X2 )
% 0.33/1.53 = ( Q @ X2 ) )
% 0.33/1.53 => ( ( collect @ A @ P2 )
% 0.33/1.53 = ( collect @ A @ Q ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_46_ext,axiom,
% 0.33/1.53 ! [B2: $tType,A: $tType,F2: A > B2,G2: A > B2] :
% 0.33/1.53 ( ! [X2: A] :
% 0.33/1.53 ( ( F2 @ X2 )
% 0.33/1.53 = ( G2 @ X2 ) )
% 0.33/1.53 => ( F2 = G2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_47_semiring__norm_I13_J,axiom,
% 0.33/1.53 ! [M: num,N: num] :
% 0.33/1.53 ( ( times_times @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.33/1.53 = ( bit0 @ ( bit0 @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_48_semiring__norm_I11_J,axiom,
% 0.33/1.53 ! [M: num] :
% 0.33/1.53 ( ( times_times @ num @ M @ one2 )
% 0.33/1.53 = M ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_49_semiring__norm_I12_J,axiom,
% 0.33/1.53 ! [N: num] :
% 0.33/1.53 ( ( times_times @ num @ one2 @ N )
% 0.33/1.53 = N ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_50_semiring__norm_I71_J,axiom,
% 0.33/1.53 ! [M: num,N: num] :
% 0.33/1.53 ( ( ord_less_eq @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.33/1.53 = ( ord_less_eq @ num @ M @ N ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_51_semiring__norm_I68_J,axiom,
% 0.33/1.53 ! [N: num] : ( ord_less_eq @ num @ one2 @ N ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_52_le__add__diff__inverse2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linordered_semidom @ A )
% 0.33/1.53 => ! [B: A,A2: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ B @ A2 )
% 0.33/1.53 => ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ B )
% 0.33/1.53 = A2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_53_le__add__diff__inverse,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linordered_semidom @ A )
% 0.33/1.53 => ! [B: A,A2: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ B @ A2 )
% 0.33/1.53 => ( ( plus_plus @ A @ B @ ( minus_minus @ A @ A2 @ B ) )
% 0.33/1.53 = A2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_54_distrib__right__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ( numeral @ A )
% 0.33/1.53 & ( semiring @ A ) )
% 0.33/1.53 => ! [A2: A,B: A,V: num] :
% 0.33/1.53 ( ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ ( numeral_numeral @ A @ V ) )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ A2 @ ( numeral_numeral @ A @ V ) ) @ ( times_times @ A @ B @ ( numeral_numeral @ A @ V ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_55_distrib__left__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ( numeral @ A )
% 0.33/1.53 & ( semiring @ A ) )
% 0.33/1.53 => ! [V: num,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ B @ C ) )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ B ) @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_56_one__eq__numeral__iff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_char_0 @ A )
% 0.33/1.53 => ! [N: num] :
% 0.33/1.53 ( ( ( one_one @ A )
% 0.33/1.53 = ( numeral_numeral @ A @ N ) )
% 0.33/1.53 = ( one2 = N ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_57_numeral__eq__one__iff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_char_0 @ A )
% 0.33/1.53 => ! [N: num] :
% 0.33/1.53 ( ( ( numeral_numeral @ A @ N )
% 0.33/1.53 = ( one_one @ A ) )
% 0.33/1.53 = ( N = one2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_58_num__double,axiom,
% 0.33/1.53 ! [N: num] :
% 0.33/1.53 ( ( times_times @ num @ ( bit0 @ one2 ) @ N )
% 0.33/1.53 = ( bit0 @ N ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_59_semiring__norm_I69_J,axiom,
% 0.33/1.53 ! [M: num] :
% 0.33/1.53 ~ ( ord_less_eq @ num @ ( bit0 @ M ) @ one2 ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_60_one__plus__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( numeral @ A )
% 0.33/1.53 => ! [N: num] :
% 0.33/1.53 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) )
% 0.33/1.53 = ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_61_numeral__plus__one,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( numeral @ A )
% 0.33/1.53 => ! [N: num] :
% 0.33/1.53 ( ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 0.33/1.53 = ( numeral_numeral @ A @ ( plus_plus @ num @ N @ one2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_62_one__add__one,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( numeral @ A )
% 0.33/1.53 => ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.33/1.53 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_63_numeral__le__one__iff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linord1659791738miring @ A )
% 0.33/1.53 => ! [N: num] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 0.33/1.53 = ( ord_less_eq @ num @ N @ one2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_64_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ab_semigroup_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_65_is__num__normalize_I1_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( neg_numeral @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_66_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere779506340up_add @ A )
% 0.33/1.53 => ! [I: A,J: A,K: A,L: A] :
% 0.33/1.53 ( ( ( I = J )
% 0.33/1.53 & ( K = L ) )
% 0.33/1.53 => ( ( plus_plus @ A @ I @ K )
% 0.33/1.53 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_67_one__reorient,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( one @ A )
% 0.33/1.53 => ! [X3: A] :
% 0.33/1.53 ( ( ( one_one @ A )
% 0.33/1.53 = X3 )
% 0.33/1.53 = ( X3
% 0.33/1.53 = ( one_one @ A ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_68_group__cancel_Oadd1,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( comm_monoid_add @ A )
% 0.33/1.53 => ! [A3: A,K: A,A2: A,B: A] :
% 0.33/1.53 ( ( A3
% 0.33/1.53 = ( plus_plus @ A @ K @ A2 ) )
% 0.33/1.53 => ( ( plus_plus @ A @ A3 @ B )
% 0.33/1.53 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_69_group__cancel_Oadd2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( comm_monoid_add @ A )
% 0.33/1.53 => ! [B3: A,K: A,B: A,A2: A] :
% 0.33/1.53 ( ( B3
% 0.33/1.53 = ( plus_plus @ A @ K @ B ) )
% 0.33/1.53 => ( ( plus_plus @ A @ A2 @ B3 )
% 0.33/1.53 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_70_add_Oassoc,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semigroup_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_71_add_Oleft__cancel,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ A2 @ B )
% 0.33/1.53 = ( plus_plus @ A @ A2 @ C ) )
% 0.33/1.53 = ( B = C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_72_add_Oright__cancel,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [B: A,A2: A,C: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ B @ A2 )
% 0.33/1.53 = ( plus_plus @ A @ C @ A2 ) )
% 0.33/1.53 = ( B = C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_73_add_Ocommute,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ab_semigroup_add @ A )
% 0.33/1.53 => ( ( plus_plus @ A )
% 0.33/1.53 = ( ^ [A4: A,B4: A] : ( plus_plus @ A @ B4 @ A4 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_74_add_Oleft__commute,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ab_semigroup_add @ A )
% 0.33/1.53 => ! [B: A,A2: A,C: A] :
% 0.33/1.53 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 0.33/1.53 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_75_add__left__imp__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel_semigroup_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ A2 @ B )
% 0.33/1.53 = ( plus_plus @ A @ A2 @ C ) )
% 0.33/1.53 => ( B = C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_76_add__right__imp__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel_semigroup_add @ A )
% 0.33/1.53 => ! [B: A,A2: A,C: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ B @ A2 )
% 0.33/1.53 = ( plus_plus @ A @ C @ A2 ) )
% 0.33/1.53 => ( B = C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_77_le__num__One__iff,axiom,
% 0.33/1.53 ! [X3: num] :
% 0.33/1.53 ( ( ord_less_eq @ num @ X3 @ one2 )
% 0.33/1.53 = ( X3 = one2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_78_one__plus__numeral__commute,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( numeral @ A )
% 0.33/1.53 => ! [X3: num] :
% 0.33/1.53 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X3 ) )
% 0.33/1.53 = ( plus_plus @ A @ ( numeral_numeral @ A @ X3 ) @ ( one_one @ A ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_79_correct__closed,axiom,
% 0.33/1.53 ! [P3: nat,S: real,T: real] :
% 0.33/1.53 ( ( ( ord_less_eq @ real @ S @ T )
% 0.33/1.53 & ( genClo1015804716orrect @ P3 @ T ) )
% 0.33/1.53 => ( genClo1015804716orrect @ P3 @ S ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_80_add__le__imp__le__right,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere236663937imp_le @ A )
% 0.33/1.53 => ! [A2: A,C: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.33/1.53 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_81_add__le__imp__le__left,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere236663937imp_le @ A )
% 0.33/1.53 => ! [C: A,A2: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.33/1.53 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_82_le__iff__add,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( canoni770627133id_add @ A )
% 0.33/1.53 => ( ( ord_less_eq @ A )
% 0.33/1.53 = ( ^ [A4: A,B4: A] :
% 0.33/1.53 ? [C2: A] :
% 0.33/1.53 ( B4
% 0.33/1.53 = ( plus_plus @ A @ A4 @ C2 ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_83_add__right__mono,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere779506340up_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_84_less__eqE,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( canoni770627133id_add @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ~ ! [C3: A] :
% 0.33/1.53 ( B
% 0.33/1.53 != ( plus_plus @ A @ A2 @ C3 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_85_add__left__mono,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere779506340up_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_86_add__mono,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere779506340up_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A,D: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( ord_less_eq @ A @ C @ D )
% 0.33/1.53 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_87_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere779506340up_add @ A )
% 0.33/1.53 => ! [I: A,J: A,K: A,L: A] :
% 0.33/1.53 ( ( ( ord_less_eq @ A @ I @ J )
% 0.33/1.53 & ( ord_less_eq @ A @ K @ L ) )
% 0.33/1.53 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_88_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere779506340up_add @ A )
% 0.33/1.53 => ! [I: A,J: A,K: A,L: A] :
% 0.33/1.53 ( ( ( I = J )
% 0.33/1.53 & ( ord_less_eq @ A @ K @ L ) )
% 0.33/1.53 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_89_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere779506340up_add @ A )
% 0.33/1.53 => ! [I: A,J: A,K: A,L: A] :
% 0.33/1.53 ( ( ( ord_less_eq @ A @ I @ J )
% 0.33/1.53 & ( K = L ) )
% 0.33/1.53 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_90_combine__common__factor,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring @ A )
% 0.33/1.53 => ! [A2: A,E: A,B: A,C: A] :
% 0.33/1.53 ( ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ C ) )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ E ) @ C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_91_distrib__right,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_92_distrib__left,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ A2 @ ( plus_plus @ A @ B @ C ) )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ A2 @ B ) @ ( times_times @ A @ A2 @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_93_comm__semiring__class_Odistrib,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( comm_semiring @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_94_ring__class_Oring__distribs_I1_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ring @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ A2 @ ( plus_plus @ A @ B @ C ) )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ A2 @ B ) @ ( times_times @ A @ A2 @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_95_ring__class_Oring__distribs_I2_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ring @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_96_le__numeral__extra_I4_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linord1659791738miring @ A )
% 0.33/1.53 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_97_add__implies__diff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel1352612707id_add @ A )
% 0.33/1.53 => ! [C: A,B: A,A2: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ C @ B )
% 0.33/1.53 = A2 )
% 0.33/1.53 => ( C
% 0.33/1.53 = ( minus_minus @ A @ A2 @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_98_diff__diff__add,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel146912293up_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_99_diff__add__eq__diff__diff__swap,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( minus_minus @ A @ A2 @ ( plus_plus @ A @ B @ C ) )
% 0.33/1.53 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_100_diff__add__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ab_group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_101_diff__diff__eq2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( minus_minus @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.33/1.53 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_102_add__diff__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.33/1.53 = ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_103_eq__diff__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,C: A,B: A] :
% 0.33/1.53 ( ( A2
% 0.33/1.53 = ( minus_minus @ A @ C @ B ) )
% 0.33/1.53 = ( ( plus_plus @ A @ A2 @ B )
% 0.33/1.53 = C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_104_diff__eq__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ( minus_minus @ A @ A2 @ B )
% 0.33/1.53 = C )
% 0.33/1.53 = ( A2
% 0.33/1.53 = ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_105_group__cancel_Osub1,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ab_group_add @ A )
% 0.33/1.53 => ! [A3: A,K: A,A2: A,B: A] :
% 0.33/1.53 ( ( A3
% 0.33/1.53 = ( plus_plus @ A @ K @ A2 ) )
% 0.33/1.53 => ( ( minus_minus @ A @ A3 @ B )
% 0.33/1.53 = ( plus_plus @ A @ K @ ( minus_minus @ A @ A2 @ B ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_106_mult_Ocomm__neutral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( comm_monoid_mult @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_107_comm__monoid__mult__class_Omult__1,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( comm_monoid_mult @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_108_abs__one,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linordered_idom @ A )
% 0.33/1.53 => ( ( abs_abs @ A @ ( one_one @ A ) )
% 0.33/1.53 = ( one_one @ A ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_109_square__diff__one__factored,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ring_1 @ A )
% 0.33/1.53 => ! [X3: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( times_times @ A @ X3 @ X3 ) @ ( one_one @ A ) )
% 0.33/1.53 = ( times_times @ A @ ( plus_plus @ A @ X3 @ ( one_one @ A ) ) @ ( minus_minus @ A @ X3 @ ( one_one @ A ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_110_rho__bound1__def,axiom,
% 0.33/1.53 ( genClo2108747022bound1
% 0.33/1.53 = ( ^ [C4: nat > real > real] :
% 0.33/1.53 ! [P: nat,S2: real,T2: real] :
% 0.33/1.53 ( ( ( genClo1015804716orrect @ P @ T2 )
% 0.33/1.53 & ( ord_less_eq @ real @ S2 @ T2 ) )
% 0.33/1.53 => ( ord_less_eq @ real @ ( minus_minus @ real @ ( C4 @ P @ T2 ) @ ( C4 @ P @ S2 ) ) @ ( times_times @ real @ ( minus_minus @ real @ T2 @ S2 ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_111_mult_Oleft__commute,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ab_semigroup_mult @ A )
% 0.33/1.53 => ! [B: A,A2: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ B @ ( times_times @ A @ A2 @ C ) )
% 0.33/1.53 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_112_mult_Ocommute,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ab_semigroup_mult @ A )
% 0.33/1.53 => ( ( times_times @ A )
% 0.33/1.53 = ( ^ [A4: A,B4: A] : ( times_times @ A @ B4 @ A4 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_113_mult_Oassoc,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semigroup_mult @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ ( times_times @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_114_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ab_semigroup_mult @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ ( times_times @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( times_times @ A @ A2 @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_115_diff__right__commute,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( cancel146912293up_add @ A )
% 0.33/1.53 => ! [A2: A,C: A,B: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B )
% 0.33/1.53 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_116_diff__eq__diff__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A,D: A] :
% 0.33/1.53 ( ( ( minus_minus @ A @ A2 @ B )
% 0.33/1.53 = ( minus_minus @ A @ C @ D ) )
% 0.33/1.53 => ( ( A2 = B )
% 0.33/1.53 = ( C = D ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_117_rho__bound2__def,axiom,
% 0.33/1.53 ( genClo2108747023bound2
% 0.33/1.53 = ( ^ [C4: nat > real > real] :
% 0.33/1.53 ! [P: nat,S2: real,T2: real] :
% 0.33/1.53 ( ( ( genClo1015804716orrect @ P @ T2 )
% 0.33/1.53 & ( ord_less_eq @ real @ S2 @ T2 ) )
% 0.33/1.53 => ( ord_less_eq @ real @ ( times_times @ real @ ( minus_minus @ real @ T2 @ S2 ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( C4 @ P @ T2 ) @ ( C4 @ P @ S2 ) ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_118_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( ( minus_minus @ A @ B @ A2 )
% 0.33/1.53 = C )
% 0.33/1.53 = ( B
% 0.33/1.53 = ( plus_plus @ A @ C @ A2 ) ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_119_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( plus_plus @ A @ A2 @ ( minus_minus @ A @ B @ A2 ) )
% 0.33/1.53 = B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_120_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( minus_minus @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.33/1.53 = ( minus_minus @ A @ ( plus_plus @ A @ C @ A2 ) @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_121_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 )
% 0.33/1.53 = ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_122_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ C )
% 0.33/1.53 = ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_123_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( minus_minus @ A @ ( plus_plus @ A @ C @ B ) @ A2 )
% 0.33/1.53 = ( plus_plus @ A @ C @ ( minus_minus @ A @ B @ A2 ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_124_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( plus_plus @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.33/1.53 = ( minus_minus @ A @ ( plus_plus @ A @ C @ B ) @ A2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_125_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( ord_less_eq @ A @ C @ ( minus_minus @ A @ B @ A2 ) )
% 0.33/1.53 = ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_126_le__add__diff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ord_less_eq @ A @ C @ ( minus_minus @ A @ ( plus_plus @ A @ B @ C ) @ A2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_127_add__le__add__imp__diff__le,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linordered_semidom @ A )
% 0.33/1.53 => ! [I: A,K: A,N: A,J: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.33/1.53 => ( ( ord_less_eq @ A @ N @ ( plus_plus @ A @ J @ K ) )
% 0.33/1.53 => ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.33/1.53 => ( ( ord_less_eq @ A @ N @ ( plus_plus @ A @ J @ K ) )
% 0.33/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ N @ K ) @ J ) ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_128_diff__add,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere623563068d_diff @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( plus_plus @ A @ ( minus_minus @ A @ B @ A2 ) @ A2 )
% 0.33/1.53 = B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_129_add__le__imp__le__diff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linordered_semidom @ A )
% 0.33/1.53 => ! [I: A,K: A,N: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ N )
% 0.33/1.53 => ( ord_less_eq @ A @ I @ ( minus_minus @ A @ N @ K ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_130_le__diff__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordered_ab_group_add @ A )
% 0.33/1.53 => ! [A2: A,C: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ ( minus_minus @ A @ C @ B ) )
% 0.33/1.53 = ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B ) @ C ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_131_diff__le__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordered_ab_group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_132_square__diff__square__factored,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( comm_ring @ A )
% 0.33/1.53 => ! [X3: A,Y: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( times_times @ A @ X3 @ X3 ) @ ( times_times @ A @ Y @ Y ) )
% 0.33/1.53 = ( times_times @ A @ ( plus_plus @ A @ X3 @ Y ) @ ( minus_minus @ A @ X3 @ Y ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_133_eq__add__iff2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ring @ A )
% 0.33/1.53 => ! [A2: A,E: A,C: A,B: A,D: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ C )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ D ) )
% 0.33/1.53 = ( C
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ ( minus_minus @ A @ B @ A2 ) @ E ) @ D ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_134_eq__add__iff1,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ring @ A )
% 0.33/1.53 => ! [A2: A,E: A,C: A,B: A,D: A] :
% 0.33/1.53 ( ( ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ C )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ D ) )
% 0.33/1.53 = ( ( plus_plus @ A @ ( times_times @ A @ ( minus_minus @ A @ A2 @ B ) @ E ) @ C )
% 0.33/1.53 = D ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_135_numeral__Bit0,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( numeral @ A )
% 0.33/1.53 => ! [N: num] :
% 0.33/1.53 ( ( numeral_numeral @ A @ ( bit0 @ N ) )
% 0.33/1.53 = ( plus_plus @ A @ ( numeral_numeral @ A @ N ) @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_136_one__le__numeral,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linord1659791738miring @ A )
% 0.33/1.53 => ! [N: num] : ( ord_less_eq @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_137_abs__triangle__ineq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( plus_plus @ A @ A2 @ B ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_138_numeral__One,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( numeral @ A )
% 0.33/1.53 => ( ( numeral_numeral @ A @ one2 )
% 0.33/1.53 = ( one_one @ A ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_139_ordered__ring__class_Ole__add__iff2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordered_ring @ A )
% 0.33/1.53 => ! [A2: A,E: A,C: A,B: A,D: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ C ) @ ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ D ) )
% 0.33/1.53 = ( ord_less_eq @ A @ C @ ( plus_plus @ A @ ( times_times @ A @ ( minus_minus @ A @ B @ A2 ) @ E ) @ D ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_140_ordered__ring__class_Ole__add__iff1,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordered_ring @ A )
% 0.33/1.53 => ! [A2: A,E: A,C: A,B: A,D: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ A2 @ E ) @ C ) @ ( plus_plus @ A @ ( times_times @ A @ B @ E ) @ D ) )
% 0.33/1.53 = ( ord_less_eq @ A @ ( plus_plus @ A @ ( times_times @ A @ ( minus_minus @ A @ A2 @ B ) @ E ) @ C ) @ D ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_141_abs__diff__triangle__ineq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A,D: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ ( plus_plus @ A @ A2 @ B ) @ ( plus_plus @ A @ C @ D ) ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ C ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_142_abs__triangle__ineq4,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) ) @ ( plus_plus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_143_abs__diff__le__iff,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linordered_idom @ A )
% 0.33/1.53 => ! [X3: A,A2: A,R: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( abs_abs @ A @ ( minus_minus @ A @ X3 @ A2 ) ) @ R )
% 0.33/1.53 = ( ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ R ) @ X3 )
% 0.33/1.53 & ( ord_less_eq @ A @ X3 @ ( plus_plus @ A @ A2 @ R ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_144_diff__eq__diff__less__eq,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordered_ab_group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A,D: A] :
% 0.33/1.53 ( ( ( minus_minus @ A @ A2 @ B )
% 0.33/1.53 = ( minus_minus @ A @ C @ D ) )
% 0.33/1.53 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_145_diff__right__mono,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordered_ab_group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_146_diff__left__mono,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordered_ab_group_add @ A )
% 0.33/1.53 => ! [B: A,A2: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ B @ A2 )
% 0.33/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_147_diff__mono,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordered_ab_group_add @ A )
% 0.33/1.53 => ! [A2: A,B: A,D: A,C: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( ord_less_eq @ A @ D @ C )
% 0.33/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_148_right__diff__distrib_H,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( comm_s1003936772cancel @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.33/1.53 = ( minus_minus @ A @ ( times_times @ A @ A2 @ B ) @ ( times_times @ A @ A2 @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_149_left__diff__distrib_H,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( comm_s1003936772cancel @ A )
% 0.33/1.53 => ! [B: A,C: A,A2: A] :
% 0.33/1.53 ( ( times_times @ A @ ( minus_minus @ A @ B @ C ) @ A2 )
% 0.33/1.53 = ( minus_minus @ A @ ( times_times @ A @ B @ A2 ) @ ( times_times @ A @ C @ A2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_150_right__diff__distrib,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ring @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ A2 @ ( minus_minus @ A @ B @ C ) )
% 0.33/1.53 = ( minus_minus @ A @ ( times_times @ A @ A2 @ B ) @ ( times_times @ A @ A2 @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_151_left__diff__distrib,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ring @ A )
% 0.33/1.53 => ! [A2: A,B: A,C: A] :
% 0.33/1.53 ( ( times_times @ A @ ( minus_minus @ A @ A2 @ B ) @ C )
% 0.33/1.53 = ( minus_minus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ C ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_152_abs__ge__self,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ ( abs_abs @ A @ A2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_153_abs__le__D1,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ ( abs_abs @ A @ A2 ) @ B )
% 0.33/1.53 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_154_abs__mult,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( idom_abs_sgn @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( abs_abs @ A @ ( times_times @ A @ A2 @ B ) )
% 0.33/1.53 = ( times_times @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_155_abs__minus__commute,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( abs_abs @ A @ ( minus_minus @ A @ A2 @ B ) )
% 0.33/1.53 = ( abs_abs @ A @ ( minus_minus @ A @ B @ A2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_156_left__add__twice,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_numeral @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( plus_plus @ A @ A2 @ ( plus_plus @ A @ A2 @ B ) )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) @ A2 ) @ B ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_157_mult__2__right,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_numeral @ A )
% 0.33/1.53 => ! [Z: A] :
% 0.33/1.53 ( ( times_times @ A @ Z @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) )
% 0.33/1.53 = ( plus_plus @ A @ Z @ Z ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_158_mult__2,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_numeral @ A )
% 0.33/1.53 => ! [Z: A] :
% 0.33/1.53 ( ( times_times @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) @ Z )
% 0.33/1.53 = ( plus_plus @ A @ Z @ Z ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_159_mult__numeral__1__right,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_numeral @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( times_times @ A @ A2 @ ( numeral_numeral @ A @ one2 ) )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_160_mult__numeral__1,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( semiring_numeral @ A )
% 0.33/1.53 => ! [A2: A] :
% 0.33/1.53 ( ( times_times @ A @ ( numeral_numeral @ A @ one2 ) @ A2 )
% 0.33/1.53 = A2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_161_abs__triangle__ineq2__sym,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ordere142940540dd_abs @ A )
% 0.33/1.53 => ! [A2: A,B: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ ( abs_abs @ A @ A2 ) @ ( abs_abs @ A @ B ) ) @ ( abs_abs @ A @ ( minus_minus @ A @ B @ A2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_162_sin__bound__lemma,axiom,
% 0.33/1.53 ! [X3: real,Y: real,U: real,V: real] :
% 0.33/1.53 ( ( X3 = Y )
% 0.33/1.53 => ( ( ord_less_eq @ real @ ( abs_abs @ real @ U ) @ V )
% 0.33/1.53 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( plus_plus @ real @ X3 @ U ) @ Y ) ) @ V ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_163_rate__1,axiom,
% 0.33/1.53 ! [P3: nat,S: real,T: real] :
% 0.33/1.53 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.33/1.53 & ( ord_less_eq @ real @ S @ T ) )
% 0.33/1.53 => ( ord_less_eq @ real @ ( minus_minus @ real @ ( genClo1161277105lle_PC @ P3 @ T ) @ ( genClo1161277105lle_PC @ P3 @ S ) ) @ ( times_times @ real @ ( minus_minus @ real @ T @ S ) @ ( plus_plus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_164_rate__2,axiom,
% 0.33/1.53 ! [P3: nat,S: real,T: real] :
% 0.33/1.53 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.33/1.53 & ( ord_less_eq @ real @ S @ T ) )
% 0.33/1.53 => ( ord_less_eq @ real @ ( times_times @ real @ ( minus_minus @ real @ T @ S ) @ ( minus_minus @ real @ ( one_one @ real ) @ genClo1144207539le_rho ) ) @ ( minus_minus @ real @ ( genClo1161277105lle_PC @ P3 @ T ) @ ( genClo1161277105lle_PC @ P3 @ S ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_165_dbl__simps_I3_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( neg_numeral @ A )
% 0.33/1.53 => ( ( neg_numeral_dbl @ A @ ( one_one @ A ) )
% 0.33/1.53 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_166_mult__diff__mult,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( ring @ A )
% 0.33/1.53 => ! [X3: A,Y: A,A2: A,B: A] :
% 0.33/1.53 ( ( minus_minus @ A @ ( times_times @ A @ X3 @ Y ) @ ( times_times @ A @ A2 @ B ) )
% 0.33/1.53 = ( plus_plus @ A @ ( times_times @ A @ X3 @ ( minus_minus @ A @ Y @ B ) ) @ ( times_times @ A @ ( minus_minus @ A @ X3 @ A2 ) @ B ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_167_verit__eq__simplify_I8_J,axiom,
% 0.33/1.53 ! [X22: num,Y2: num] :
% 0.33/1.53 ( ( ( bit0 @ X22 )
% 0.33/1.53 = ( bit0 @ Y2 ) )
% 0.33/1.53 = ( X22 = Y2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_168_minus__apply,axiom,
% 0.33/1.53 ! [B2: $tType,A: $tType] :
% 0.33/1.53 ( ( minus @ B2 )
% 0.33/1.53 => ( ( minus_minus @ ( A > B2 ) )
% 0.33/1.53 = ( ^ [A5: A > B2,B5: A > B2,X: A] : ( minus_minus @ B2 @ ( A5 @ X ) @ ( B5 @ X ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_169_okRead1__def,axiom,
% 0.33/1.53 ( genClo293725281kRead1
% 0.33/1.53 = ( ^ [F: nat > real,X: real,Ppred: nat > $o] :
% 0.33/1.53 ! [L2: nat,M2: nat] :
% 0.33/1.53 ( ( ( Ppred @ L2 )
% 0.33/1.53 & ( Ppred @ M2 ) )
% 0.33/1.53 => ( ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( F @ L2 ) @ ( F @ M2 ) ) ) @ X ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_170_order__refl,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( preorder @ A )
% 0.33/1.53 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_171_eq__diff__eq_H,axiom,
% 0.33/1.53 ! [X3: real,Y: real,Z: real] :
% 0.33/1.53 ( ( X3
% 0.33/1.53 = ( minus_minus @ real @ Y @ Z ) )
% 0.33/1.53 = ( Y
% 0.33/1.53 = ( plus_plus @ real @ X3 @ Z ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_172_semiring__norm_I6_J,axiom,
% 0.33/1.53 ! [M: num,N: num] :
% 0.33/1.53 ( ( plus_plus @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.33/1.53 = ( bit0 @ ( plus_plus @ num @ M @ N ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_173_semiring__norm_I2_J,axiom,
% 0.33/1.53 ( ( plus_plus @ num @ one2 @ one2 )
% 0.33/1.53 = ( bit0 @ one2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_174_dbl__simps_I5_J,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( neg_numeral @ A )
% 0.33/1.53 => ! [K: num] :
% 0.33/1.53 ( ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) )
% 0.33/1.53 = ( numeral_numeral @ A @ ( bit0 @ K ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_175_nat__1__add__1,axiom,
% 0.33/1.53 ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
% 0.33/1.53 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_176_add__One__commute,axiom,
% 0.33/1.53 ! [N: num] :
% 0.33/1.53 ( ( plus_plus @ num @ one2 @ N )
% 0.33/1.53 = ( plus_plus @ num @ N @ one2 ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_177_numerals_I1_J,axiom,
% 0.33/1.53 ( ( numeral_numeral @ nat @ one2 )
% 0.33/1.53 = ( one_one @ nat ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_178_dbl__def,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( neg_numeral @ A )
% 0.33/1.53 => ( ( neg_numeral_dbl @ A )
% 0.33/1.53 = ( ^ [X: A] : ( plus_plus @ A @ X @ X ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_179_le__funD,axiom,
% 0.33/1.53 ! [B2: $tType,A: $tType] :
% 0.33/1.53 ( ( ord @ B2 )
% 0.33/1.53 => ! [F2: A > B2,G2: A > B2,X3: A] :
% 0.33/1.53 ( ( ord_less_eq @ ( A > B2 ) @ F2 @ G2 )
% 0.33/1.53 => ( ord_less_eq @ B2 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_180_le__funE,axiom,
% 0.33/1.53 ! [B2: $tType,A: $tType] :
% 0.33/1.53 ( ( ord @ B2 )
% 0.33/1.53 => ! [F2: A > B2,G2: A > B2,X3: A] :
% 0.33/1.53 ( ( ord_less_eq @ ( A > B2 ) @ F2 @ G2 )
% 0.33/1.53 => ( ord_less_eq @ B2 @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_181_le__funI,axiom,
% 0.33/1.53 ! [B2: $tType,A: $tType] :
% 0.33/1.53 ( ( ord @ B2 )
% 0.33/1.53 => ! [F2: A > B2,G2: A > B2] :
% 0.33/1.53 ( ! [X2: A] : ( ord_less_eq @ B2 @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
% 0.33/1.53 => ( ord_less_eq @ ( A > B2 ) @ F2 @ G2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_182_le__fun__def,axiom,
% 0.33/1.53 ! [B2: $tType,A: $tType] :
% 0.33/1.53 ( ( ord @ B2 )
% 0.33/1.53 => ( ( ord_less_eq @ ( A > B2 ) )
% 0.33/1.53 = ( ^ [F: A > B2,G: A > B2] :
% 0.33/1.53 ! [X: A] : ( ord_less_eq @ B2 @ ( F @ X ) @ ( G @ X ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_183_order__subst1,axiom,
% 0.33/1.53 ! [A: $tType,B2: $tType] :
% 0.33/1.53 ( ( ( order @ B2 )
% 0.33/1.53 & ( order @ A ) )
% 0.33/1.53 => ! [A2: A,F2: B2 > A,B: B2,C: B2] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B ) )
% 0.33/1.53 => ( ( ord_less_eq @ B2 @ B @ C )
% 0.33/1.53 => ( ! [X2: B2,Y3: B2] :
% 0.33/1.53 ( ( ord_less_eq @ B2 @ X2 @ Y3 )
% 0.33/1.53 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.33/1.53 => ( ord_less_eq @ A @ A2 @ ( F2 @ C ) ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_184_order__subst2,axiom,
% 0.33/1.53 ! [A: $tType,C5: $tType] :
% 0.33/1.53 ( ( ( order @ C5 )
% 0.33/1.53 & ( order @ A ) )
% 0.33/1.53 => ! [A2: A,B: A,F2: A > C5,C: C5] :
% 0.33/1.53 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 => ( ( ord_less_eq @ C5 @ ( F2 @ B ) @ C )
% 0.33/1.53 => ( ! [X2: A,Y3: A] :
% 0.33/1.53 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.33/1.53 => ( ord_less_eq @ C5 @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.33/1.53 => ( ord_less_eq @ C5 @ ( F2 @ A2 ) @ C ) ) ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_185_verit__la__disequality,axiom,
% 0.33/1.53 ! [A: $tType] :
% 0.33/1.53 ( ( linorder @ A )
% 0.33/1.53 => ! [A2: A,B: A] :
% 0.33/1.53 ( ( A2 = B )
% 0.33/1.53 | ~ ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.53 | ~ ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 0.33/1.53
% 0.33/1.53 thf(fact_186_ord__eq__le__subst,axiom,
% 0.33/1.53 ! [A: $tType,B2: $tType] :
% 0.33/1.53 ( ( ( ord @ B2 )
% 0.33/1.53 & ( ord @ A ) )
% 0.33/1.53 => ! [A2: A,F2: B2 > A,B: B2,C: B2] :
% 0.33/1.53 ( ( A2
% 0.33/1.53 = ( F2 @ B ) )
% 0.33/1.53 => ( ( ord_less_eq @ B2 @ B @ C )
% 0.33/1.53 => ( ! [X2: B2,Y3: B2] :
% 0.33/1.53 ( ( ord_less_eq @ B2 @ X2 @ Y3 )
% 0.33/1.54 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.33/1.54 => ( ord_less_eq @ A @ A2 @ ( F2 @ C ) ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_187_ord__le__eq__subst,axiom,
% 0.33/1.54 ! [A: $tType,B2: $tType] :
% 0.33/1.54 ( ( ( ord @ B2 )
% 0.33/1.54 & ( ord @ A ) )
% 0.33/1.54 => ! [A2: A,B: A,F2: A > B2,C: B2] :
% 0.33/1.54 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.54 => ( ( ( F2 @ B )
% 0.33/1.54 = C )
% 0.33/1.54 => ( ! [X2: A,Y3: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.33/1.54 => ( ord_less_eq @ B2 @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.33/1.54 => ( ord_less_eq @ B2 @ ( F2 @ A2 ) @ C ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_188_eq__iff,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.33/1.54 = ( ^ [X: A,Y5: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ X @ Y5 )
% 0.33/1.54 & ( ord_less_eq @ A @ Y5 @ X ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_189_antisym,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ! [X3: A,Y: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/1.54 => ( ( ord_less_eq @ A @ Y @ X3 )
% 0.33/1.54 => ( X3 = Y ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_190_linear,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( linorder @ A )
% 0.33/1.54 => ! [X3: A,Y: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/1.54 | ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_191_eq__refl,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( preorder @ A )
% 0.33/1.54 => ! [X3: A,Y: A] :
% 0.33/1.54 ( ( X3 = Y )
% 0.33/1.54 => ( ord_less_eq @ A @ X3 @ Y ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_192_le__cases,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( linorder @ A )
% 0.33/1.54 => ! [X3: A,Y: A] :
% 0.33/1.54 ( ~ ( ord_less_eq @ A @ X3 @ Y )
% 0.33/1.54 => ( ord_less_eq @ A @ Y @ X3 ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_193_order_Otrans,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ! [A2: A,B: A,C: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.54 => ( ( ord_less_eq @ A @ B @ C )
% 0.33/1.54 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_194_le__cases3,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( linorder @ A )
% 0.33/1.54 => ! [X3: A,Y: A,Z: A] :
% 0.33/1.54 ( ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/1.54 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.33/1.54 => ( ( ( ord_less_eq @ A @ Y @ X3 )
% 0.33/1.54 => ~ ( ord_less_eq @ A @ X3 @ Z ) )
% 0.33/1.54 => ( ( ( ord_less_eq @ A @ X3 @ Z )
% 0.33/1.54 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.33/1.54 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.33/1.54 => ~ ( ord_less_eq @ A @ Y @ X3 ) )
% 0.33/1.54 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.33/1.54 => ~ ( ord_less_eq @ A @ Z @ X3 ) )
% 0.33/1.54 => ~ ( ( ord_less_eq @ A @ Z @ X3 )
% 0.33/1.54 => ~ ( ord_less_eq @ A @ X3 @ Y ) ) ) ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_195_antisym__conv,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ! [Y: A,X3: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ Y @ X3 )
% 0.33/1.54 => ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/1.54 = ( X3 = Y ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_196_order__class_Oorder_Oeq__iff,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.33/1.54 = ( ^ [A4: A,B4: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.33/1.54 & ( ord_less_eq @ A @ B4 @ A4 ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_197_ord__eq__le__trans,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( ord @ A )
% 0.33/1.54 => ! [A2: A,B: A,C: A] :
% 0.33/1.54 ( ( A2 = B )
% 0.33/1.54 => ( ( ord_less_eq @ A @ B @ C )
% 0.33/1.54 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_198_ord__le__eq__trans,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( ord @ A )
% 0.33/1.54 => ! [A2: A,B: A,C: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.54 => ( ( B = C )
% 0.33/1.54 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_199_order__class_Oorder_Oantisym,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ! [A2: A,B: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.54 => ( ( ord_less_eq @ A @ B @ A2 )
% 0.33/1.54 => ( A2 = B ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_200_order__trans,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( preorder @ A )
% 0.33/1.54 => ! [X3: A,Y: A,Z: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ X3 @ Y )
% 0.33/1.54 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.33/1.54 => ( ord_less_eq @ A @ X3 @ Z ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_201_dual__order_Orefl,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_202_linorder__wlog,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( linorder @ A )
% 0.33/1.54 => ! [P2: A > A > $o,A2: A,B: A] :
% 0.33/1.54 ( ! [A6: A,B6: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ A6 @ B6 )
% 0.33/1.54 => ( P2 @ A6 @ B6 ) )
% 0.33/1.54 => ( ! [A6: A,B6: A] :
% 0.33/1.54 ( ( P2 @ B6 @ A6 )
% 0.33/1.54 => ( P2 @ A6 @ B6 ) )
% 0.33/1.54 => ( P2 @ A2 @ B ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_203_dual__order_Otrans,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ! [B: A,A2: A,C: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ B @ A2 )
% 0.33/1.54 => ( ( ord_less_eq @ A @ C @ B )
% 0.33/1.54 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_204_dual__order_Oeq__iff,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.33/1.54 = ( ^ [A4: A,B4: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ B4 @ A4 )
% 0.33/1.54 & ( ord_less_eq @ A @ A4 @ B4 ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_205_dual__order_Oantisym,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( order @ A )
% 0.33/1.54 => ! [B: A,A2: A] :
% 0.33/1.54 ( ( ord_less_eq @ A @ B @ A2 )
% 0.33/1.54 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.33/1.54 => ( A2 = B ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_206_fun__diff__def,axiom,
% 0.33/1.54 ! [B2: $tType,A: $tType] :
% 0.33/1.54 ( ( minus @ B2 )
% 0.33/1.54 => ( ( minus_minus @ ( A > B2 ) )
% 0.33/1.54 = ( ^ [A5: A > B2,B5: A > B2,X: A] : ( minus_minus @ B2 @ ( A5 @ X ) @ ( B5 @ X ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_207_complete__real,axiom,
% 0.33/1.54 ! [S3: set @ real] :
% 0.33/1.54 ( ? [X4: real] : ( member @ real @ X4 @ S3 )
% 0.33/1.54 => ( ? [Z3: real] :
% 0.33/1.54 ! [X2: real] :
% 0.33/1.54 ( ( member @ real @ X2 @ S3 )
% 0.33/1.54 => ( ord_less_eq @ real @ X2 @ Z3 ) )
% 0.33/1.54 => ? [Y3: real] :
% 0.33/1.54 ( ! [X4: real] :
% 0.33/1.54 ( ( member @ real @ X4 @ S3 )
% 0.33/1.54 => ( ord_less_eq @ real @ X4 @ Y3 ) )
% 0.33/1.54 & ! [Z3: real] :
% 0.33/1.54 ( ! [X2: real] :
% 0.33/1.54 ( ( member @ real @ X2 @ S3 )
% 0.33/1.54 => ( ord_less_eq @ real @ X2 @ Z3 ) )
% 0.33/1.54 => ( ord_less_eq @ real @ Y3 @ Z3 ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_208_PC__monotone,axiom,
% 0.33/1.54 ! [P3: nat,S: real,T: real] :
% 0.33/1.54 ( ( ( genClo1015804716orrect @ P3 @ T )
% 0.33/1.54 & ( ord_less_eq @ real @ S @ T ) )
% 0.33/1.54 => ( ord_less_eq @ real @ ( genClo1161277105lle_PC @ P3 @ S ) @ ( genClo1161277105lle_PC @ P3 @ T ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_209_add__diff__add,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( ab_group_add @ A )
% 0.33/1.54 => ! [A2: A,C: A,B: A,D: A] :
% 0.33/1.54 ( ( minus_minus @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) )
% 0.33/1.54 = ( plus_plus @ A @ ( minus_minus @ A @ A2 @ B ) @ ( minus_minus @ A @ C @ D ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_210_verit__eq__simplify_I10_J,axiom,
% 0.33/1.54 ! [X22: num] :
% 0.33/1.54 ( one2
% 0.33/1.54 != ( bit0 @ X22 ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_211_inf__period_I2_J,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( ( comm_ring @ A )
% 0.33/1.54 & ( dvd @ A ) )
% 0.33/1.54 => ! [P2: A > $o,D2: A,Q: A > $o] :
% 0.33/1.54 ( ! [X2: A,K2: A] :
% 0.33/1.54 ( ( P2 @ X2 )
% 0.33/1.54 = ( P2 @ ( minus_minus @ A @ X2 @ ( times_times @ A @ K2 @ D2 ) ) ) )
% 0.33/1.54 => ( ! [X2: A,K2: A] :
% 0.33/1.54 ( ( Q @ X2 )
% 0.33/1.54 = ( Q @ ( minus_minus @ A @ X2 @ ( times_times @ A @ K2 @ D2 ) ) ) )
% 0.33/1.54 => ! [X4: A,K3: A] :
% 0.33/1.54 ( ( ( P2 @ X4 )
% 0.33/1.54 | ( Q @ X4 ) )
% 0.33/1.54 = ( ( P2 @ ( minus_minus @ A @ X4 @ ( times_times @ A @ K3 @ D2 ) ) )
% 0.33/1.54 | ( Q @ ( minus_minus @ A @ X4 @ ( times_times @ A @ K3 @ D2 ) ) ) ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_212_inf__period_I1_J,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( ( comm_ring @ A )
% 0.33/1.54 & ( dvd @ A ) )
% 0.33/1.54 => ! [P2: A > $o,D2: A,Q: A > $o] :
% 0.33/1.54 ( ! [X2: A,K2: A] :
% 0.33/1.54 ( ( P2 @ X2 )
% 0.33/1.54 = ( P2 @ ( minus_minus @ A @ X2 @ ( times_times @ A @ K2 @ D2 ) ) ) )
% 0.33/1.54 => ( ! [X2: A,K2: A] :
% 0.33/1.54 ( ( Q @ X2 )
% 0.33/1.54 = ( Q @ ( minus_minus @ A @ X2 @ ( times_times @ A @ K2 @ D2 ) ) ) )
% 0.33/1.54 => ! [X4: A,K3: A] :
% 0.33/1.54 ( ( ( P2 @ X4 )
% 0.33/1.54 & ( Q @ X4 ) )
% 0.33/1.54 = ( ( P2 @ ( minus_minus @ A @ X4 @ ( times_times @ A @ K3 @ D2 ) ) )
% 0.33/1.54 & ( Q @ ( minus_minus @ A @ X4 @ ( times_times @ A @ K3 @ D2 ) ) ) ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_213_crossproduct__eq,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( semiri456707255roduct @ A )
% 0.33/1.54 => ! [W: A,Y: A,X3: A,Z: A] :
% 0.33/1.54 ( ( ( plus_plus @ A @ ( times_times @ A @ W @ Y ) @ ( times_times @ A @ X3 @ Z ) )
% 0.33/1.54 = ( plus_plus @ A @ ( times_times @ A @ W @ Z ) @ ( times_times @ A @ X3 @ Y ) ) )
% 0.33/1.54 = ( ( W = X3 )
% 0.33/1.54 | ( Y = Z ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_214_nat__eq__add__iff1,axiom,
% 0.33/1.54 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ J @ I )
% 0.33/1.54 => ( ( ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M )
% 0.33/1.54 = ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.33/1.54 = ( ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ I @ J ) @ U ) @ M )
% 0.33/1.54 = N ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_215_nat__eq__add__iff2,axiom,
% 0.33/1.54 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.33/1.54 => ( ( ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M )
% 0.33/1.54 = ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.33/1.54 = ( M
% 0.33/1.54 = ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_216_nat__le__add__iff1,axiom,
% 0.33/1.54 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ J @ I )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.33/1.54 = ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_217_nat__le__add__iff2,axiom,
% 0.33/1.54 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.33/1.54 = ( ord_less_eq @ nat @ M @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_218_nat__diff__add__eq1,axiom,
% 0.33/1.54 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ J @ I )
% 0.33/1.54 => ( ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.33/1.54 = ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_219_nat__diff__add__eq2,axiom,
% 0.33/1.54 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.33/1.54 => ( ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ M ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ N ) )
% 0.33/1.54 = ( minus_minus @ nat @ M @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_220_left__add__mult__distrib,axiom,
% 0.33/1.54 ! [I: nat,U: nat,J: nat,K: nat] :
% 0.33/1.54 ( ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ K ) )
% 0.33/1.54 = ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ I @ J ) @ U ) @ K ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_221_crossproduct__noteq,axiom,
% 0.33/1.54 ! [A: $tType] :
% 0.33/1.54 ( ( semiri456707255roduct @ A )
% 0.33/1.54 => ! [A2: A,B: A,C: A,D: A] :
% 0.33/1.54 ( ( ( A2 != B )
% 0.33/1.54 & ( C != D ) )
% 0.33/1.54 = ( ( plus_plus @ A @ ( times_times @ A @ A2 @ C ) @ ( times_times @ A @ B @ D ) )
% 0.33/1.54 != ( plus_plus @ A @ ( times_times @ A @ A2 @ D ) @ ( times_times @ A @ B @ C ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_222_nat__1__eq__mult__iff,axiom,
% 0.33/1.54 ! [M: nat,N: nat] :
% 0.33/1.54 ( ( ( one_one @ nat )
% 0.33/1.54 = ( times_times @ nat @ M @ N ) )
% 0.33/1.54 = ( ( M
% 0.33/1.54 = ( one_one @ nat ) )
% 0.33/1.54 & ( N
% 0.33/1.54 = ( one_one @ nat ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_223_nat__mult__eq__1__iff,axiom,
% 0.33/1.54 ! [M: nat,N: nat] :
% 0.33/1.54 ( ( ( times_times @ nat @ M @ N )
% 0.33/1.54 = ( one_one @ nat ) )
% 0.33/1.54 = ( ( M
% 0.33/1.54 = ( one_one @ nat ) )
% 0.33/1.54 & ( N
% 0.33/1.54 = ( one_one @ nat ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_224_nat__add__left__cancel__le,axiom,
% 0.33/1.54 ! [K: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.33/1.54 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_225_diff__diff__cancel,axiom,
% 0.33/1.54 ! [I: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ N )
% 0.33/1.54 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I ) )
% 0.33/1.54 = I ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_226_diff__diff__left,axiom,
% 0.33/1.54 ! [I: nat,J: nat,K: nat] :
% 0.33/1.54 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.33/1.54 = ( minus_minus @ nat @ I @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_227_Nat_Odiff__diff__right,axiom,
% 0.33/1.54 ! [K: nat,J: nat,I: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ K @ J )
% 0.33/1.54 => ( ( minus_minus @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 0.33/1.54 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ K ) @ J ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_228_Nat_Oadd__diff__assoc2,axiom,
% 0.33/1.54 ! [K: nat,J: nat,I: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ K @ J )
% 0.33/1.54 => ( ( plus_plus @ nat @ ( minus_minus @ nat @ J @ K ) @ I )
% 0.33/1.54 = ( minus_minus @ nat @ ( plus_plus @ nat @ J @ I ) @ K ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_229_Nat_Oadd__diff__assoc,axiom,
% 0.33/1.54 ! [K: nat,J: nat,I: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ K @ J )
% 0.33/1.54 => ( ( plus_plus @ nat @ I @ ( minus_minus @ nat @ J @ K ) )
% 0.33/1.54 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ J ) @ K ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_230_eq__diff__iff,axiom,
% 0.33/1.54 ! [K: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ K @ M )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ K @ N )
% 0.33/1.54 => ( ( ( minus_minus @ nat @ M @ K )
% 0.33/1.54 = ( minus_minus @ nat @ N @ K ) )
% 0.33/1.54 = ( M = N ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_231_le__diff__iff,axiom,
% 0.33/1.54 ! [K: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ K @ M )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ K @ N )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.33/1.54 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_232_Nat_Odiff__diff__eq,axiom,
% 0.33/1.54 ! [K: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ K @ M )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ K @ N )
% 0.33/1.54 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.33/1.54 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_233_diff__le__mono,axiom,
% 0.33/1.54 ! [M: nat,N: nat,L: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ M @ N )
% 0.33/1.54 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_234_diff__le__self,axiom,
% 0.33/1.54 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_235_le__diff__iff_H,axiom,
% 0.33/1.54 ! [A2: nat,C: nat,B: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ A2 @ C )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ B @ C )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A2 ) @ ( minus_minus @ nat @ C @ B ) )
% 0.33/1.54 = ( ord_less_eq @ nat @ B @ A2 ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_236_diff__le__mono2,axiom,
% 0.33/1.54 ! [M: nat,N: nat,L: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ M @ N )
% 0.33/1.54 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_237_Nat_Oex__has__greatest__nat,axiom,
% 0.33/1.54 ! [P2: nat > $o,K: nat,B: nat] :
% 0.33/1.54 ( ( P2 @ K )
% 0.33/1.54 => ( ! [Y3: nat] :
% 0.33/1.54 ( ( P2 @ Y3 )
% 0.33/1.54 => ( ord_less_eq @ nat @ Y3 @ B ) )
% 0.33/1.54 => ? [X2: nat] :
% 0.33/1.54 ( ( P2 @ X2 )
% 0.33/1.54 & ! [Y6: nat] :
% 0.33/1.54 ( ( P2 @ Y6 )
% 0.33/1.54 => ( ord_less_eq @ nat @ Y6 @ X2 ) ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_238_nat__le__linear,axiom,
% 0.33/1.54 ! [M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ M @ N )
% 0.33/1.54 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_239_mult__le__mono2,axiom,
% 0.33/1.54 ! [I: nat,J: nat,K: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.33/1.54 => ( ord_less_eq @ nat @ ( times_times @ nat @ K @ I ) @ ( times_times @ nat @ K @ J ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_240_mult__le__mono1,axiom,
% 0.33/1.54 ! [I: nat,J: nat,K: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.33/1.54 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ K ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_241_mult__le__mono,axiom,
% 0.33/1.54 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ K @ L )
% 0.33/1.54 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K ) @ ( times_times @ nat @ J @ L ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_242_le__antisym,axiom,
% 0.33/1.54 ! [M: nat,N: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ M @ N )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ N @ M )
% 0.33/1.54 => ( M = N ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_243_le__square,axiom,
% 0.33/1.54 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ M ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_244_eq__imp__le,axiom,
% 0.33/1.54 ! [M: nat,N: nat] :
% 0.33/1.54 ( ( M = N )
% 0.33/1.54 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_245_le__trans,axiom,
% 0.33/1.54 ! [I: nat,J: nat,K: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.33/1.54 => ( ( ord_less_eq @ nat @ J @ K )
% 0.33/1.54 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_246_le__refl,axiom,
% 0.33/1.54 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_247_le__cube,axiom,
% 0.33/1.54 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ ( times_times @ nat @ M @ M ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_248_diff__mult__distrib2,axiom,
% 0.33/1.54 ! [K: nat,M: nat,N: nat] :
% 0.33/1.54 ( ( times_times @ nat @ K @ ( minus_minus @ nat @ M @ N ) )
% 0.33/1.54 = ( minus_minus @ nat @ ( times_times @ nat @ K @ M ) @ ( times_times @ nat @ K @ N ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_249_diff__mult__distrib,axiom,
% 0.33/1.54 ! [M: nat,N: nat,K: nat] :
% 0.33/1.54 ( ( times_times @ nat @ ( minus_minus @ nat @ M @ N ) @ K )
% 0.33/1.54 = ( minus_minus @ nat @ ( times_times @ nat @ M @ K ) @ ( times_times @ nat @ N @ K ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_250_diff__commute,axiom,
% 0.33/1.54 ! [I: nat,J: nat,K: nat] :
% 0.33/1.54 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.33/1.54 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_251_Nat_Ole__imp__diff__is__add,axiom,
% 0.33/1.54 ! [I: nat,J: nat,K: nat] :
% 0.33/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.33/1.54 => ( ( ( minus_minus @ nat @ J @ I )
% 0.33/1.54 = K )
% 0.33/1.54 = ( J
% 0.33/1.54 = ( plus_plus @ nat @ K @ I ) ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(fact_252_diff__add__inverse2,axiom,
% 0.33/1.54 ! [M: nat,N: nat] :
% 0.33/1.54 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ N ) @ N )
% 0.33/1.54 = M ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.33/1.54 ! [A7: $tType,A8: $tType] :
% 0.33/1.54 ( ( preorder @ A8 )
% 0.33/1.54 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.33/1.54 ! [A7: $tType,A8: $tType] :
% 0.33/1.54 ( ( order @ A8 )
% 0.33/1.54 => ( order @ ( A7 > A8 ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_fun___Orderings_Oord,axiom,
% 0.33/1.54 ! [A7: $tType,A8: $tType] :
% 0.33/1.54 ( ( ord @ A8 )
% 0.33/1.54 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_fun___Groups_Ominus,axiom,
% 0.33/1.54 ! [A7: $tType,A8: $tType] :
% 0.33/1.54 ( ( minus @ A8 )
% 0.33/1.54 => ( minus @ ( A7 > A8 ) ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 0.33/1.54 semiri456707255roduct @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff,axiom,
% 0.33/1.54 ordere623563068d_diff @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.33/1.54 ordere236663937imp_le @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.33/1.54 canoni770627133id_add @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.33/1.54 linord1659791738miring @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.33/1.54 ordere779506340up_add @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.33/1.54 cancel146912293up_add @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.33/1.54 cancel1352612707id_add @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1__cancel,axiom,
% 0.33/1.54 comm_s1003936772cancel @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.33/1.54 cancel_semigroup_add @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.33/1.54 linordered_semidom @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.33/1.54 ab_semigroup_mult @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 0.33/1.54 comm_monoid_mult @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.33/1.54 ab_semigroup_add @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.33/1.54 comm_monoid_add @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.33/1.54 semigroup_mult @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Num_Osemiring__numeral,axiom,
% 0.33/1.54 semiring_numeral @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.33/1.54 semigroup_add @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Rings_Ocomm__semiring,axiom,
% 0.33/1.54 comm_semiring @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 0.33/1.54 semiring_char_0 @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.33/1.54 preorder @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.33/1.54 linorder @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.33/1.54 monoid_mult @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.33/1.54 order @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Rings_Osemiring,axiom,
% 0.33/1.54 semiring @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.33/1.54 ord @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Ominus_4,axiom,
% 0.33/1.54 minus @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 0.33/1.54 numeral @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.33/1.54 one @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Nat_Onat___Rings_Odvd,axiom,
% 0.33/1.54 dvd @ nat ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Num_Onum___Orderings_Opreorder_5,axiom,
% 0.33/1.54 preorder @ num ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Num_Onum___Orderings_Olinorder_6,axiom,
% 0.33/1.54 linorder @ num ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Num_Onum___Orderings_Oorder_7,axiom,
% 0.33/1.54 order @ num ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Num_Onum___Orderings_Oord_8,axiom,
% 0.33/1.54 ord @ num ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Set_Oset___Orderings_Opreorder_9,axiom,
% 0.33/1.54 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Set_Oset___Orderings_Oorder_10,axiom,
% 0.33/1.54 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Set_Oset___Orderings_Oord_11,axiom,
% 0.33/1.54 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Set_Oset___Groups_Ominus_12,axiom,
% 0.33/1.54 ! [A7: $tType] : ( minus @ ( set @ A7 ) ) ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 0.33/1.54 preorder @ $o ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 0.33/1.54 linorder @ $o ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 0.33/1.54 order @ $o ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 0.33/1.54 ord @ $o ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_HOL_Obool___Groups_Ominus_17,axiom,
% 0.33/1.54 minus @ $o ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_18,axiom,
% 0.33/1.54 semiri456707255roduct @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le_19,axiom,
% 0.33/1.54 ordere236663937imp_le @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_20,axiom,
% 0.33/1.54 linord1659791738miring @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add_21,axiom,
% 0.33/1.54 ordere779506340up_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs,axiom,
% 0.33/1.54 ordere142940540dd_abs @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_22,axiom,
% 0.33/1.54 cancel146912293up_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_23,axiom,
% 0.33/1.54 cancel1352612707id_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Ocomm__semiring__1__cancel_24,axiom,
% 0.33/1.54 comm_s1003936772cancel @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
% 0.33/1.54 ordered_ab_group_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add_25,axiom,
% 0.33/1.54 cancel_semigroup_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Olinordered__semidom_26,axiom,
% 0.33/1.54 linordered_semidom @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Oab__semigroup__mult_27,axiom,
% 0.33/1.54 ab_semigroup_mult @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__mult_28,axiom,
% 0.33/1.54 comm_monoid_mult @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_29,axiom,
% 0.33/1.54 ab_semigroup_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_30,axiom,
% 0.33/1.54 comm_monoid_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 0.33/1.54 linordered_idom @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Osemigroup__mult_31,axiom,
% 0.33/1.54 semigroup_mult @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Num_Osemiring__numeral_32,axiom,
% 0.33/1.54 semiring_numeral @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Osemigroup__add_33,axiom,
% 0.33/1.54 semigroup_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Ocomm__semiring_34,axiom,
% 0.33/1.54 comm_semiring @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Nat_Osemiring__char__0_35,axiom,
% 0.33/1.54 semiring_char_0 @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Oab__group__add,axiom,
% 0.33/1.54 ab_group_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Oordered__ring,axiom,
% 0.33/1.54 ordered_ring @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Oidom__abs__sgn,axiom,
% 0.33/1.54 idom_abs_sgn @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Orderings_Opreorder_36,axiom,
% 0.33/1.54 preorder @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Orderings_Olinorder_37,axiom,
% 0.33/1.54 linorder @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Omonoid__mult_38,axiom,
% 0.33/1.54 monoid_mult @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.33/1.54 group_add @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Ocomm__ring,axiom,
% 0.33/1.54 comm_ring @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Orderings_Oorder_39,axiom,
% 0.33/1.54 order @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 0.33/1.54 neg_numeral @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Osemiring_40,axiom,
% 0.33/1.54 semiring @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Orderings_Oord_41,axiom,
% 0.33/1.54 ord @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Oring__1,axiom,
% 0.33/1.54 ring_1 @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Ominus_42,axiom,
% 0.33/1.54 minus @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Num_Onumeral_43,axiom,
% 0.33/1.54 numeral @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Oring,axiom,
% 0.33/1.54 ring @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Groups_Oone_44,axiom,
% 0.33/1.54 one @ real ).
% 0.33/1.54
% 0.33/1.54 thf(tcon_Real_Oreal___Rings_Odvd_45,axiom,
% 0.33/1.54 dvd @ real ).
% 0.33/1.54
% 0.33/1.54 thf(conj_0,conjecture,
% 0.33/1.54 ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ ( minus_minus @ real @ ( c @ p @ t ) @ ( c @ p @ s ) ) @ ( minus_minus @ real @ ( d @ q @ t ) @ ( d @ q @ s ) ) ) ) @ ( times_times @ real @ ( times_times @ real @ ( numeral_numeral @ real @ ( bit0 @ one2 ) ) @ genClo1144207539le_rho ) @ ( minus_minus @ real @ t @ s ) ) ).
% 0.33/1.54 ------------------------
% 0.33/1.57 % (19973)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_19870 for (2999ds/27Mi)
% 0.33/1.57 % (19976)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_19870 for (2999ds/275Mi)
% 0.33/1.57 % (19975)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_19870 for (2999ds/2Mi)
% 0.33/1.57 % (19971)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/183Mi)
% 0.33/1.57 % (19975)Instruction limit reached!
% 0.33/1.57 % (19975)------------------------------
% 0.33/1.57 % (19975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.57 % (19975)Termination reason: Unknown
% 0.33/1.57 % (19975)Termination phase: shuffling
% 0.33/1.57
% 0.33/1.57 % (19975)Memory used [KB]: 1407
% 0.33/1.57 % (19975)Time elapsed: 0.002 s
% 0.33/1.57 % (19975)Instructions burned: 3 (million)
% 0.33/1.57 % (19975)------------------------------
% 0.33/1.57 % (19975)------------------------------
% 0.33/1.57 % (19974)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/2Mi)
% 0.33/1.57 % (19974)Instruction limit reached!
% 0.33/1.57 % (19974)------------------------------
% 0.33/1.57 % (19974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.57 % (19974)Termination reason: Unknown
% 0.33/1.57 % (19974)Termination phase: shuffling
% 0.33/1.57
% 0.33/1.57 % (19974)Memory used [KB]: 1407
% 0.33/1.57 % (19974)Time elapsed: 0.003 s
% 0.33/1.57 % (19974)Instructions burned: 2 (million)
% 0.33/1.57 % (19974)------------------------------
% 0.33/1.57 % (19974)------------------------------
% 0.33/1.58 % (19972)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_19870 for (2999ds/4Mi)
% 0.33/1.58 % (19977)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/18Mi)
% 0.33/1.58 % (19973)Instruction limit reached!
% 0.33/1.58 % (19973)------------------------------
% 0.33/1.58 % (19973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.58 % (19973)Termination reason: Unknown
% 0.33/1.58 % (19973)Termination phase: Property scanning
% 0.33/1.58
% 0.33/1.58 % (19973)Memory used [KB]: 1791
% 0.33/1.58 % (19973)Time elapsed: 0.010 s
% 0.33/1.58 % (19973)Instructions burned: 27 (million)
% 0.33/1.58 % (19973)------------------------------
% 0.33/1.58 % (19973)------------------------------
% 0.33/1.58 % (19972)Instruction limit reached!
% 0.33/1.58 % (19972)------------------------------
% 0.33/1.58 % (19972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.58 % (19972)Termination reason: Unknown
% 0.33/1.58 % (19972)Termination phase: shuffling
% 0.33/1.58
% 0.33/1.58 % (19972)Memory used [KB]: 1407
% 0.33/1.58 % (19972)Time elapsed: 0.005 s
% 0.33/1.58 % (19972)Instructions burned: 5 (million)
% 0.33/1.58 % (19972)------------------------------
% 0.33/1.58 % (19972)------------------------------
% 0.33/1.58 % (19978)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/3Mi)
% 0.33/1.58 % (19978)Instruction limit reached!
% 0.33/1.58 % (19978)------------------------------
% 0.33/1.58 % (19978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.58 % (19978)Termination reason: Unknown
% 0.33/1.58 % (19978)Termination phase: shuffling
% 0.33/1.58
% 0.33/1.58 % (19978)Memory used [KB]: 1407
% 0.33/1.58 % (19978)Time elapsed: 0.003 s
% 0.33/1.58 % (19978)Instructions burned: 3 (million)
% 0.33/1.58 % (19978)------------------------------
% 0.33/1.58 % (19978)------------------------------
% 0.33/1.59 % (19976)Refutation not found, incomplete strategy
% 0.33/1.59 % (19976)------------------------------
% 0.33/1.59 % (19976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.59 % (19976)Termination reason: Refutation not found, incomplete strategy
% 0.33/1.59
% 0.33/1.59
% 0.33/1.59 % (19976)Memory used [KB]: 6524
% 0.33/1.59 % (19976)Time elapsed: 0.018 s
% 0.33/1.59 % (19976)Instructions burned: 56 (million)
% 0.33/1.59 % (19976)------------------------------
% 0.33/1.59 % (19976)------------------------------
% 0.33/1.59 % (19980)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_19870 for (2999ds/15Mi)
% 0.33/1.59 % (19979)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_19870 for (2999ds/37Mi)
% 0.33/1.59 % (19977)Instruction limit reached!
% 0.33/1.59 % (19977)------------------------------
% 0.33/1.59 % (19977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.59 % (19977)Termination reason: Unknown
% 0.33/1.59 % (19977)Termination phase: shuffling
% 0.33/1.59
% 0.33/1.59 % (19977)Memory used [KB]: 1663
% 0.33/1.59 % (19977)Time elapsed: 0.013 s
% 0.33/1.59 % (19977)Instructions burned: 18 (million)
% 0.33/1.59 % (19977)------------------------------
% 0.33/1.59 % (19977)------------------------------
% 0.33/1.59 % (19980)Instruction limit reached!
% 0.33/1.59 % (19980)------------------------------
% 0.33/1.59 % (19980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.33/1.59 % (19980)Termination reason: Unknown
% 0.33/1.59 % (19980)Termination phase: shuffling
% 0.33/1.59
% 0.33/1.59 % (19980)Memory used [KB]: 1663
% 0.33/1.59 % (19980)Time elapsed: 0.006 s
% 0.33/1.59 % (19980)Instructions burned: 16 (million)
% 0.33/1.59 % (19980)------------------------------
% 0.33/1.59 % (19980)------------------------------
% 0.33/1.59 % (19982)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_19870 for (2999ds/1041Mi)
% 0.33/1.59 % (19983)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/7Mi)
% 0.33/1.60 % (19981)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_19870 for (2999ds/3Mi)
% 2.95/1.60 % (19981)Instruction limit reached!
% 2.95/1.60 % (19981)------------------------------
% 2.95/1.60 % (19981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (19981)Termination reason: Unknown
% 2.95/1.60 % (19981)Termination phase: shuffling
% 2.95/1.60
% 2.95/1.60 % (19981)Memory used [KB]: 1407
% 2.95/1.60 % (19981)Time elapsed: 0.004 s
% 2.95/1.60 % (19981)Instructions burned: 3 (million)
% 2.95/1.60 % (19981)------------------------------
% 2.95/1.60 % (19981)------------------------------
% 2.95/1.60 % (19983)Instruction limit reached!
% 2.95/1.60 % (19983)------------------------------
% 2.95/1.60 % (19983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (19983)Termination reason: Unknown
% 2.95/1.60 % (19983)Termination phase: shuffling
% 2.95/1.60
% 2.95/1.60 % (19983)Memory used [KB]: 1535
% 2.95/1.60 % (19983)Time elapsed: 0.004 s
% 2.95/1.60 % (19983)Instructions burned: 10 (million)
% 2.95/1.60 % (19983)------------------------------
% 2.95/1.60 % (19983)------------------------------
% 2.95/1.60 % (19985)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_19870 for (2999ds/3Mi)
% 2.95/1.60 % (19985)Instruction limit reached!
% 2.95/1.60 % (19985)------------------------------
% 2.95/1.60 % (19985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (19985)Termination reason: Unknown
% 2.95/1.60 % (19985)Termination phase: shuffling
% 2.95/1.60
% 2.95/1.60 % (19985)Memory used [KB]: 1407
% 2.95/1.60 % (19985)Time elapsed: 0.002 s
% 2.95/1.60 % (19985)Instructions burned: 3 (million)
% 2.95/1.60 % (19985)------------------------------
% 2.95/1.60 % (19985)------------------------------
% 2.95/1.60 % (19979)Instruction limit reached!
% 2.95/1.60 % (19979)------------------------------
% 2.95/1.60 % (19979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (19979)Termination reason: Unknown
% 2.95/1.60 % (19979)Termination phase: Property scanning
% 2.95/1.60
% 2.95/1.60 % (19979)Memory used [KB]: 2174
% 2.95/1.60 % (19979)Time elapsed: 0.017 s
% 2.95/1.60 % (19979)Instructions burned: 40 (million)
% 2.95/1.60 % (19979)------------------------------
% 2.95/1.60 % (19979)------------------------------
% 2.95/1.60 % (19984)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/16Mi)
% 2.95/1.61 % (19987)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/7Mi)
% 2.95/1.61 % (19988)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/3Mi)
% 2.95/1.61 % (19987)Instruction limit reached!
% 2.95/1.61 % (19987)------------------------------
% 2.95/1.61 % (19987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19987)Termination reason: Unknown
% 2.95/1.61 % (19987)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19987)Memory used [KB]: 1535
% 2.95/1.61 % (19987)Time elapsed: 0.004 s
% 2.95/1.61 % (19987)Instructions burned: 10 (million)
% 2.95/1.61 % (19987)------------------------------
% 2.95/1.61 % (19987)------------------------------
% 2.95/1.61 % (19989)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/4Mi)
% 2.95/1.61 % (19988)Instruction limit reached!
% 2.95/1.61 % (19988)------------------------------
% 2.95/1.61 % (19988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19988)Termination reason: Unknown
% 2.95/1.61 % (19988)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19988)Memory used [KB]: 1407
% 2.95/1.61 % (19988)Time elapsed: 0.002 s
% 2.95/1.61 % (19988)Instructions burned: 4 (million)
% 2.95/1.61 % (19988)------------------------------
% 2.95/1.61 % (19988)------------------------------
% 2.95/1.61 % (19989)Instruction limit reached!
% 2.95/1.61 % (19989)------------------------------
% 2.95/1.61 % (19989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19989)Termination reason: Unknown
% 2.95/1.61 % (19989)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19989)Memory used [KB]: 1407
% 2.95/1.61 % (19989)Time elapsed: 0.003 s
% 2.95/1.61 % (19989)Instructions burned: 6 (million)
% 2.95/1.61 % (19989)------------------------------
% 2.95/1.61 % (19989)------------------------------
% 2.95/1.61 % (19984)Instruction limit reached!
% 2.95/1.61 % (19984)------------------------------
% 2.95/1.61 % (19984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (19984)Termination reason: Unknown
% 2.95/1.61 % (19984)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (19984)Memory used [KB]: 1663
% 2.95/1.61 % (19984)Time elapsed: 0.012 s
% 2.95/1.61 % (19984)Instructions burned: 16 (million)
% 2.95/1.61 % (19984)------------------------------
% 2.95/1.61 % (19984)------------------------------
% 2.95/1.62 % (19986)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_19870 for (2999ds/3Mi)
% 2.95/1.62 % (19986)Instruction limit reached!
% 2.95/1.62 % (19986)------------------------------
% 2.95/1.62 % (19986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (19986)Termination reason: Unknown
% 2.95/1.62 % (19986)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (19986)Memory used [KB]: 1407
% 2.95/1.62 % (19986)Time elapsed: 0.004 s
% 2.95/1.62 % (19986)Instructions burned: 4 (million)
% 2.95/1.62 % (19986)------------------------------
% 2.95/1.62 % (19986)------------------------------
% 2.95/1.62 % (19990)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/18Mi)
% 2.95/1.62 % (19991)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/710Mi)
% 2.95/1.62 % (19992)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/6Mi)
% 2.95/1.62 % (19992)Instruction limit reached!
% 2.95/1.62 % (19992)------------------------------
% 2.95/1.62 % (19992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (19992)Termination reason: Unknown
% 2.95/1.62 % (19992)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (19992)Memory used [KB]: 1407
% 2.95/1.62 % (19992)Time elapsed: 0.003 s
% 2.95/1.62 % (19992)Instructions burned: 7 (million)
% 2.95/1.62 % (19992)------------------------------
% 2.95/1.62 % (19992)------------------------------
% 2.95/1.63 % (19990)Instruction limit reached!
% 2.95/1.63 % (19990)------------------------------
% 2.95/1.63 % (19990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (19990)Termination reason: Unknown
% 2.95/1.63 % (19990)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (19990)Memory used [KB]: 1663
% 2.95/1.63 % (19990)Time elapsed: 0.007 s
% 2.95/1.63 % (19990)Instructions burned: 19 (million)
% 2.95/1.63 % (19990)------------------------------
% 2.95/1.63 % (19990)------------------------------
% 2.95/1.63 % (19971)Instruction limit reached!
% 2.95/1.63 % (19971)------------------------------
% 2.95/1.63 % (19971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (19971)Termination reason: Unknown
% 2.95/1.63 % (19971)Termination phase: Saturation
% 2.95/1.63
% 2.95/1.63 % (19971)Memory used [KB]: 6908
% 2.95/1.63 % (19971)Time elapsed: 0.061 s
% 2.95/1.63 % (19971)Instructions burned: 184 (million)
% 2.95/1.63 % (19971)------------------------------
% 2.95/1.63 % (19971)------------------------------
% 2.95/1.63 % (19993)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_19870 for (2999ds/902Mi)
% 2.95/1.63 % (19995)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/5Mi)
% 2.95/1.63 % (19994)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_19870 for (2999ds/21Mi)
% 2.95/1.63 % (19996)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_19870 for (2999ds/6Mi)
% 2.95/1.64 % (19995)Instruction limit reached!
% 2.95/1.64 % (19995)------------------------------
% 2.95/1.64 % (19995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (19995)Termination reason: Unknown
% 2.95/1.64 % (19995)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (19995)Memory used [KB]: 1535
% 2.95/1.64 % (19995)Time elapsed: 0.003 s
% 2.95/1.64 % (19995)Instructions burned: 8 (million)
% 2.95/1.64 % (19995)------------------------------
% 2.95/1.64 % (19995)------------------------------
% 2.95/1.64 % (19996)Instruction limit reached!
% 2.95/1.64 % (19996)------------------------------
% 2.95/1.64 % (19996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (19996)Termination reason: Unknown
% 2.95/1.64 % (19996)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (19996)Memory used [KB]: 1535
% 2.95/1.64 % (19996)Time elapsed: 0.003 s
% 2.95/1.64 % (19996)Instructions burned: 7 (million)
% 2.95/1.64 % (19996)------------------------------
% 2.95/1.64 % (19996)------------------------------
% 2.95/1.64 % (19997)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/377Mi)
% 2.95/1.65 % (19998)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_19870 for (2999ds/779Mi)
% 2.95/1.65 % (19999)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_19870 for (2999ds/19Mi)
% 2.95/1.65 % (19994)Instruction limit reached!
% 2.95/1.65 % (19994)------------------------------
% 2.95/1.65 % (19994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (19994)Termination reason: Unknown
% 2.95/1.65 % (19994)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (19994)Memory used [KB]: 1791
% 2.95/1.65 % (19994)Time elapsed: 0.015 s
% 2.95/1.65 % (19994)Instructions burned: 21 (million)
% 2.95/1.65 % (19994)------------------------------
% 2.95/1.65 % (19994)------------------------------
% 2.95/1.65 % (19999)Instruction limit reached!
% 2.95/1.65 % (19999)------------------------------
% 2.95/1.65 % (19999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (19999)Termination reason: Unknown
% 2.95/1.65 % (19999)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (19999)Memory used [KB]: 1791
% 2.95/1.65 % (19999)Time elapsed: 0.007 s
% 2.95/1.65 % (19999)Instructions burned: 22 (million)
% 2.95/1.65 % (19999)------------------------------
% 2.95/1.65 % (19999)------------------------------
% 2.95/1.66 % (20001)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/17Mi)
% 2.95/1.67 % (20000)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/879Mi)
% 2.95/1.67 % (20001)Instruction limit reached!
% 2.95/1.67 % (20001)------------------------------
% 2.95/1.67 % (20001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.67 % (20001)Termination reason: Unknown
% 2.95/1.67 % (20001)Termination phase: shuffling
% 2.95/1.67
% 2.95/1.67 % (20001)Memory used [KB]: 1663
% 2.95/1.67 % (20001)Time elapsed: 0.007 s
% 2.95/1.67 % (20001)Instructions burned: 18 (million)
% 2.95/1.67 % (20001)------------------------------
% 2.95/1.67 % (20001)------------------------------
% 2.95/1.68 % (20002)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/3Mi)
% 2.95/1.68 % (20002)Instruction limit reached!
% 2.95/1.68 % (20002)------------------------------
% 2.95/1.68 % (20002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.68 % (20002)Termination reason: Unknown
% 2.95/1.68 % (20002)Termination phase: shuffling
% 2.95/1.68
% 2.95/1.68 % (20002)Memory used [KB]: 1407
% 2.95/1.68 % (20002)Time elapsed: 0.003 s
% 2.95/1.68 % (20002)Instructions burned: 5 (million)
% 2.95/1.68 % (20002)------------------------------
% 2.95/1.68 % (20002)------------------------------
% 2.95/1.69 % (20003)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/30Mi)
% 2.95/1.70 % (20003)Instruction limit reached!
% 2.95/1.70 % (20003)------------------------------
% 2.95/1.70 % (20003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.70 % (20003)Termination reason: Unknown
% 2.95/1.70 % (20003)Termination phase: Property scanning
% 2.95/1.70
% 2.95/1.70 % (20003)Memory used [KB]: 1791
% 2.95/1.70 % (20003)Time elapsed: 0.011 s
% 2.95/1.70 % (20003)Instructions burned: 31 (million)
% 2.95/1.70 % (20003)------------------------------
% 2.95/1.70 % (20003)------------------------------
% 2.95/1.71 % (20004)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/127Mi)
% 2.95/1.75 % (20004)Instruction limit reached!
% 2.95/1.75 % (20004)------------------------------
% 2.95/1.75 % (20004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.75 % (20004)Termination reason: Unknown
% 2.95/1.75 % (20004)Termination phase: Saturation
% 2.95/1.75
% 2.95/1.75 % (20004)Memory used [KB]: 6780
% 2.95/1.75 % (20004)Time elapsed: 0.040 s
% 2.95/1.75 % (20004)Instructions burned: 129 (million)
% 2.95/1.75 % (20004)------------------------------
% 2.95/1.75 % (20004)------------------------------
% 2.95/1.76 % (19997)Instruction limit reached!
% 2.95/1.76 % (19997)------------------------------
% 2.95/1.76 % (19997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.76 % (19997)Termination reason: Unknown
% 2.95/1.76 % (19997)Termination phase: Saturation
% 2.95/1.76
% 2.95/1.76 % (19997)Memory used [KB]: 7547
% 2.95/1.76 % (19997)Time elapsed: 0.118 s
% 2.95/1.76 % (19997)Instructions burned: 378 (million)
% 2.95/1.76 % (19997)------------------------------
% 2.95/1.76 % (19997)------------------------------
% 2.95/1.76 % (20005)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19870 for (2997ds/100Mi)
% 2.95/1.77 % (20006)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_19870 for (2997ds/3Mi)
% 2.95/1.77 % (20006)Instruction limit reached!
% 2.95/1.77 % (20006)------------------------------
% 2.95/1.77 % (20006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.77 % (20006)Termination reason: Unknown
% 2.95/1.77 % (20006)Termination phase: shuffling
% 2.95/1.77
% 2.95/1.77 % (20006)Memory used [KB]: 1407
% 2.95/1.77 % (20006)Time elapsed: 0.003 s
% 2.95/1.77 % (20006)Instructions burned: 6 (million)
% 2.95/1.77 % (20006)------------------------------
% 2.95/1.77 % (20006)------------------------------
% 2.95/1.78 % (20007)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_19870 for (2997ds/20Mi)
% 2.95/1.78 % (20007)Instruction limit reached!
% 2.95/1.78 % (20007)------------------------------
% 2.95/1.78 % (20007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.78 % (20007)Termination reason: Unknown
% 2.95/1.78 % (20007)Termination phase: shuffling
% 2.95/1.78
% 2.95/1.78 % (20007)Memory used [KB]: 1663
% 2.95/1.78 % (20007)Time elapsed: 0.008 s
% 2.95/1.78 % (20007)Instructions burned: 21 (million)
% 2.95/1.78 % (20007)------------------------------
% 2.95/1.78 % (20007)------------------------------
% 2.95/1.78 % (20005)Instruction limit reached!
% 2.95/1.78 % (20005)------------------------------
% 2.95/1.78 % (20005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.78 % (20005)Termination reason: Unknown
% 2.95/1.78 % (20005)Termination phase: Property scanning
% 2.95/1.78
% 2.95/1.78 % (20005)Memory used [KB]: 2174
% 2.95/1.78 % (20005)Time elapsed: 0.028 s
% 2.95/1.78 % (20005)Instructions burned: 102 (million)
% 2.95/1.78 % (20005)------------------------------
% 2.95/1.78 % (20005)------------------------------
% 2.95/1.79 % (20008)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_19870 for (2997ds/86Mi)
% 2.95/1.79 % (20009)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_19870 for (2997ds/107Mi)
% 2.95/1.82 % (20008)Instruction limit reached!
% 2.95/1.82 % (20008)------------------------------
% 2.95/1.82 % (20008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.82 % (20008)Termination reason: Unknown
% 2.95/1.82 % (20008)Termination phase: Saturation
% 2.95/1.82
% 2.95/1.82 % (20008)Memory used [KB]: 6524
% 2.95/1.82 % (20008)Time elapsed: 0.026 s
% 2.95/1.82 % (20008)Instructions burned: 87 (million)
% 2.95/1.82 % (20008)------------------------------
% 2.95/1.82 % (20008)------------------------------
% 2.95/1.83 % (20009)Instruction limit reached!
% 2.95/1.83 % (20009)------------------------------
% 2.95/1.83 % (20009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.83 % (20009)Termination reason: Unknown
% 2.95/1.83 % (20009)Termination phase: Saturation
% 2.95/1.83
% 2.95/1.83 % (20009)Memory used [KB]: 6652
% 2.95/1.83 % (20009)Time elapsed: 0.033 s
% 2.95/1.83 % (20009)Instructions burned: 107 (million)
% 2.95/1.83 % (20009)------------------------------
% 2.95/1.83 % (20009)------------------------------
% 2.95/1.83 % (20010)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_19870 for (2997ds/39Mi)
% 2.95/1.84 % (20011)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_19870 for (2997ds/448Mi)
% 2.95/1.84 % (20010)Instruction limit reached!
% 2.95/1.84 % (20010)------------------------------
% 2.95/1.84 % (20010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.84 % (19991)Instruction limit reached!
% 2.95/1.84 % (19991)------------------------------
% 2.95/1.84 % (19991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.84 % (19991)Termination reason: Unknown
% 2.95/1.84 % (19991)Termination phase: Saturation
% 2.95/1.84
% 2.95/1.84 % (19991)Memory used [KB]: 8059
% 2.95/1.84 % (19991)Time elapsed: 0.219 s
% 2.95/1.84 % (19991)Instructions burned: 713 (million)
% 2.95/1.84 % (19991)------------------------------
% 2.95/1.84 % (19991)------------------------------
% 2.95/1.84 % (20010)Termination reason: Unknown
% 2.95/1.84 % (20010)Termination phase: Property scanning
% 2.95/1.84
% 2.95/1.84 % (20010)Memory used [KB]: 2174
% 2.95/1.84 % (20010)Time elapsed: 0.012 s
% 2.95/1.84 % (20010)Instructions burned: 39 (million)
% 2.95/1.84 % (20010)------------------------------
% 2.95/1.84 % (20010)------------------------------
% 2.95/1.85 % (20012)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_19870 for (2997ds/46Mi)
% 2.95/1.85 % (20013)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_19870 for (2997ds/98Mi)
% 2.95/1.86 % (20012)Instruction limit reached!
% 2.95/1.86 % (20012)------------------------------
% 2.95/1.86 % (20012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.86 % (20012)Termination reason: Unknown
% 2.95/1.86 % (20012)Termination phase: Preprocessing 3
% 2.95/1.86
% 2.95/1.86 % (20012)Memory used [KB]: 1918
% 2.95/1.86 % (20012)Time elapsed: 0.015 s
% 2.95/1.86 % (20012)Instructions burned: 46 (million)
% 2.95/1.86 % (20012)------------------------------
% 2.95/1.86 % (20012)------------------------------
% 2.95/1.87 % (20014)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_19870 for (2996ds/507Mi)
% 2.95/1.87 % (20013)Instruction limit reached!
% 2.95/1.87 % (20013)------------------------------
% 2.95/1.87 % (20013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.87 % (20013)Termination reason: Unknown
% 2.95/1.87 % (20013)Termination phase: Property scanning
% 2.95/1.87
% 2.95/1.87 % (20013)Memory used [KB]: 2174
% 2.95/1.87 % (20013)Time elapsed: 0.027 s
% 2.95/1.87 % (20013)Instructions burned: 99 (million)
% 2.95/1.87 % (20013)------------------------------
% 2.95/1.87 % (20013)------------------------------
% 2.95/1.88 % (19998)Instruction limit reached!
% 2.95/1.88 % (19998)------------------------------
% 2.95/1.88 % (19998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.88 % (19998)Termination reason: Unknown
% 2.95/1.88 % (19998)Termination phase: Saturation
% 2.95/1.88
% 2.95/1.88 % (19998)Memory used [KB]: 7803
% 2.95/1.88 % (19998)Time elapsed: 0.239 s
% 2.95/1.88 % (19998)Instructions burned: 780 (million)
% 2.95/1.88 % (19998)------------------------------
% 2.95/1.88 % (19998)------------------------------
% 2.95/1.88 % (20015)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_19870 for (2996ds/149Mi)
% 2.95/1.89 % (20016)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_19870 for (2996ds/39Mi)
% 2.95/1.91 % (20016)Instruction limit reached!
% 2.95/1.91 % (20016)------------------------------
% 2.95/1.91 % (20016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.91 % (20016)Termination reason: Unknown
% 2.95/1.91 % (20016)Termination phase: Preprocessing 3
% 2.95/1.91
% 2.95/1.91 % (20016)Memory used [KB]: 1918
% 2.95/1.91 % (20016)Time elapsed: 0.014 s
% 2.95/1.91 % (20016)Instructions burned: 42 (million)
% 2.95/1.91 % (20016)------------------------------
% 2.95/1.91 % (20016)------------------------------
% 2.95/1.91 % (19982)Instruction limit reached!
% 2.95/1.91 % (19982)------------------------------
% 2.95/1.91 % (19982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.91 % (19982)Termination reason: Unknown
% 2.95/1.91 % (19982)Termination phase: Saturation
% 2.95/1.91
% 2.95/1.91 % (19982)Memory used [KB]: 9722
% 2.95/1.91 % (19982)Time elapsed: 0.338 s
% 2.95/1.91 % (19982)Instructions burned: 1043 (million)
% 2.95/1.91 % (19982)------------------------------
% 2.95/1.91 % (19982)------------------------------
% 2.95/1.91 % (19993)Instruction limit reached!
% 2.95/1.91 % (19993)------------------------------
% 2.95/1.91 % (19993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.91 % (19993)Termination reason: Unknown
% 2.95/1.91 % (19993)Termination phase: Saturation
% 2.95/1.91
% 2.95/1.91 % (19993)Memory used [KB]: 7291
% 2.95/1.91 % (19993)Time elapsed: 0.283 s
% 2.95/1.91 % (19993)Instructions burned: 902 (million)
% 2.95/1.91 % (19993)------------------------------
% 2.95/1.91 % (19993)------------------------------
% 2.95/1.92 % (20017)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_19870 for (2996ds/6Mi)
% 2.95/1.92 % (20018)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_19870 for (2996ds/1087Mi)
% 2.95/1.92 % (20017)Instruction limit reached!
% 2.95/1.92 % (20017)------------------------------
% 2.95/1.92 % (20017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.92 % (20017)Termination reason: Unknown
% 2.95/1.92 % (20017)Termination phase: shuffling
% 2.95/1.92
% 2.95/1.92 % (20017)Memory used [KB]: 1407
% 2.95/1.92 % (20017)Time elapsed: 0.003 s
% 2.95/1.92 % (20017)Instructions burned: 6 (million)
% 2.95/1.92 % (20017)------------------------------
% 2.95/1.92 % (20017)------------------------------
% 2.95/1.92 % (20019)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_19870 for (2996ds/47Mi)
% 2.95/1.93 % (20020)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_19870 for (2996ds/44Mi)
% 2.95/1.93 % (20015)Instruction limit reached!
% 2.95/1.93 % (20015)------------------------------
% 2.95/1.93 % (20015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.93 % (20015)Termination reason: Unknown
% 2.95/1.93 % (20015)Termination phase: Saturation
% 2.95/1.93
% 2.95/1.93 % (20015)Memory used [KB]: 6908
% 2.95/1.93 % (20015)Time elapsed: 0.046 s
% 2.95/1.93 % (20015)Instructions burned: 150 (million)
% 2.95/1.93 % (20015)------------------------------
% 2.95/1.93 % (20015)------------------------------
% 2.95/1.94 % (20021)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_19870 for (2996ds/432Mi)
% 2.95/1.94 % (20020)Instruction limit reached!
% 2.95/1.94 % (20020)------------------------------
% 2.95/1.94 % (20020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.94 % (20020)Termination reason: Unknown
% 2.95/1.94 % (20020)Termination phase: Property scanning
% 2.95/1.94
% 2.95/1.94 % (20020)Memory used [KB]: 2174
% 2.95/1.94 % (20020)Time elapsed: 0.013 s
% 2.95/1.94 % (20020)Instructions burned: 45 (million)
% 2.95/1.94 % (20020)------------------------------
% 2.95/1.94 % (20020)------------------------------
% 2.95/1.94 % (20019)Instruction limit reached!
% 2.95/1.94 % (20019)------------------------------
% 2.95/1.94 % (20019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.94 % (20019)Termination reason: Unknown
% 2.95/1.94 % (20019)Termination phase: Property scanning
% 2.95/1.94
% 2.95/1.94 % (20019)Memory used [KB]: 2046
% 2.95/1.94 % (20019)Time elapsed: 0.017 s
% 2.95/1.94 % (20019)Instructions burned: 49 (million)
% 2.95/1.94 % (20019)------------------------------
% 2.95/1.94 % (20019)------------------------------
% 2.95/1.95 % (20022)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_19870 for (2996ds/62Mi)
% 2.95/1.95 % (20023)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_19870 for (2996ds/31Mi)
% 2.95/1.96 % (20023)Instruction limit reached!
% 2.95/1.96 % (20023)------------------------------
% 2.95/1.96 % (20023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.96 % (20023)Termination reason: Unknown
% 2.95/1.96 % (20023)Termination phase: Property scanning
% 2.95/1.96
% 2.95/1.96 % (20023)Memory used [KB]: 1791
% 2.95/1.96 % (20023)Time elapsed: 0.012 s
% 2.95/1.96 % (20023)Instructions burned: 33 (million)
% 2.95/1.96 % (20023)------------------------------
% 2.95/1.96 % (20023)------------------------------
% 2.95/1.96 % (20022)Instruction limit reached!
% 2.95/1.96 % (20022)------------------------------
% 2.95/1.96 % (20022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.96 % (20022)Termination reason: Unknown
% 2.95/1.96 % (20022)Termination phase: Property scanning
% 2.95/1.96
% 2.95/1.96 % (20022)Memory used [KB]: 2174
% 2.95/1.96 % (20022)Time elapsed: 0.017 s
% 2.95/1.96 % (20022)Instructions burned: 62 (million)
% 2.95/1.96 % (20022)------------------------------
% 2.95/1.96 % (20022)------------------------------
% 2.95/1.97 % (20011)Instruction limit reached!
% 2.95/1.97 % (20011)------------------------------
% 2.95/1.97 % (20011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.97 % (20011)Termination reason: Unknown
% 2.95/1.97 % (20011)Termination phase: Saturation
% 2.95/1.97
% 2.95/1.97 % (20011)Memory used [KB]: 7803
% 2.95/1.97 % (20011)Time elapsed: 0.136 s
% 2.95/1.97 % (20011)Instructions burned: 448 (million)
% 2.95/1.97 % (20011)------------------------------
% 2.95/1.97 % (20011)------------------------------
% 2.95/1.97 % (20024)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/96Mi)
% 2.95/1.97 % (20000)Instruction limit reached!
% 2.95/1.97 % (20000)------------------------------
% 2.95/1.97 % (20000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.97 % (20000)Termination reason: Unknown
% 2.95/1.97 % (20000)Termination phase: Saturation
% 2.95/1.97
% 2.95/1.97 % (20025)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_19870 for (2995ds/453Mi)
% 2.95/1.97 % (20000)Memory used [KB]: 7547
% 2.95/1.97 % (20000)Time elapsed: 0.310 s
% 2.95/1.97 % (20000)Instructions burned: 880 (million)
% 2.95/1.97 % (20000)------------------------------
% 2.95/1.97 % (20000)------------------------------
% 2.95/1.98 % (20026)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_19870 for (2995ds/71Mi)
% 2.95/1.98 % (20027)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/83Mi)
% 2.95/2.00 % (20026)Instruction limit reached!
% 2.95/2.00 % (20026)------------------------------
% 2.95/2.00 % (20026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.00 % (20026)Termination reason: Unknown
% 2.95/2.00 % (20026)Termination phase: Property scanning
% 2.95/2.00
% 2.95/2.00 % (20026)Memory used [KB]: 2046
% 2.95/2.00 % (20026)Time elapsed: 0.021 s
% 2.95/2.00 % (20026)Instructions burned: 71 (million)
% 2.95/2.00 % (20026)------------------------------
% 2.95/2.00 % (20026)------------------------------
% 2.95/2.01 % (20028)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/11Mi)
% 2.95/2.01 % (20027)Instruction limit reached!
% 2.95/2.01 % (20027)------------------------------
% 2.95/2.01 % (20027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.01 % (20027)Termination reason: Unknown
% 2.95/2.01 % (20027)Termination phase: Saturation
% 2.95/2.01
% 2.95/2.01 % (20027)Memory used [KB]: 6396
% 2.95/2.01 % (20027)Time elapsed: 0.051 s
% 2.95/2.01 % (20027)Instructions burned: 83 (million)
% 2.95/2.01 % (20027)------------------------------
% 2.95/2.01 % (20027)------------------------------
% 2.95/2.01 % (20028)Instruction limit reached!
% 2.95/2.01 % (20028)------------------------------
% 2.95/2.01 % (20028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.01 % (20028)Termination reason: Unknown
% 2.95/2.01 % (20028)Termination phase: shuffling
% 2.95/2.01
% 2.95/2.01 % (20028)Memory used [KB]: 1663
% 2.95/2.01 % (20028)Time elapsed: 0.005 s
% 2.95/2.01 % (20028)Instructions burned: 12 (million)
% 2.95/2.01 % (20028)------------------------------
% 2.95/2.01 % (20028)------------------------------
% 2.95/2.02 % (20014)Instruction limit reached!
% 2.95/2.02 % (20014)------------------------------
% 2.95/2.02 % (20014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.02 % (20014)Termination reason: Unknown
% 2.95/2.02 % (20014)Termination phase: Saturation
% 2.95/2.02
% 2.95/2.02 % (20014)Memory used [KB]: 7291
% 2.95/2.02 % (20014)Time elapsed: 0.146 s
% 2.95/2.02 % (20014)Instructions burned: 509 (million)
% 2.95/2.02 % (20014)------------------------------
% 2.95/2.02 % (20014)------------------------------
% 2.95/2.02 % (20024)Instruction limit reached!
% 2.95/2.02 % (20024)------------------------------
% 2.95/2.02 % (20024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.02 % (20024)Termination reason: Unknown
% 2.95/2.02 % (20024)Termination phase: Saturation
% 2.95/2.02
% 2.95/2.02 % (20024)Memory used [KB]: 6652
% 2.95/2.02 % (20024)Time elapsed: 0.034 s
% 2.95/2.02 % (20024)Instructions burned: 98 (million)
% 2.95/2.02 % (20024)------------------------------
% 2.95/2.02 % (20024)------------------------------
% 6.12/2.02 % (20030)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/6Mi)
% 6.12/2.02 % (20029)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_19870 for (2995ds/41Mi)
% 6.12/2.02 % (20030)Instruction limit reached!
% 6.12/2.02 % (20030)------------------------------
% 6.12/2.02 % (20030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.02 % (20030)Termination reason: Unknown
% 6.12/2.02 % (20030)Termination phase: shuffling
% 6.12/2.02
% 6.12/2.02 % (20030)Memory used [KB]: 1407
% 6.12/2.02 % (20030)Time elapsed: 0.003 s
% 6.12/2.02 % (20030)Instructions burned: 6 (million)
% 6.12/2.02 % (20030)------------------------------
% 6.12/2.02 % (20030)------------------------------
% 6.12/2.03 % (20031)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/150Mi)
% 6.12/2.03 % (20032)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/343Mi)
% 6.12/2.03 % (20033)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_19870 for (2995ds/109Mi)
% 6.12/2.03 % (20029)Instruction limit reached!
% 6.12/2.03 % (20029)------------------------------
% 6.12/2.03 % (20029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.03 % (20029)Termination reason: Unknown
% 6.12/2.03 % (20029)Termination phase: Property scanning
% 6.12/2.03
% 6.12/2.03 % (20029)Memory used [KB]: 2046
% 6.12/2.03 % (20029)Time elapsed: 0.013 s
% 6.12/2.03 % (20029)Instructions burned: 41 (million)
% 6.12/2.03 % (20029)------------------------------
% 6.12/2.03 % (20029)------------------------------
% 6.12/2.05 % (20034)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_19870 for (2994ds/253Mi)
% 6.12/2.07 % (20033)Instruction limit reached!
% 6.12/2.07 % (20033)------------------------------
% 6.12/2.07 % (20033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.07 % (20033)Termination reason: Unknown
% 6.12/2.07 % (20033)Termination phase: Saturation
% 6.12/2.07
% 6.12/2.07 % (20033)Memory used [KB]: 6652
% 6.12/2.07 % (20033)Time elapsed: 0.033 s
% 6.12/2.07 % (20033)Instructions burned: 110 (million)
% 6.12/2.07 % (20033)------------------------------
% 6.12/2.07 % (20033)------------------------------
% 6.12/2.07 % (20021)Instruction limit reached!
% 6.12/2.07 % (20021)------------------------------
% 6.12/2.07 % (20021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.07 % (20021)Termination reason: Unknown
% 6.12/2.07 % (20021)Termination phase: Saturation
% 6.12/2.07
% 6.12/2.07 % (20021)Memory used [KB]: 3709
% 6.12/2.07 % (20021)Time elapsed: 0.133 s
% 6.12/2.07 % (20021)Instructions burned: 433 (million)
% 6.12/2.07 % (20021)------------------------------
% 6.12/2.07 % (20021)------------------------------
% 6.12/2.07 % (20031)Instruction limit reached!
% 6.12/2.07 % (20031)------------------------------
% 6.12/2.07 % (20031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.07 % (20031)Termination reason: Unknown
% 6.12/2.07 % (20031)Termination phase: Saturation
% 6.12/2.07
% 6.12/2.07 % (20031)Memory used [KB]: 6908
% 6.12/2.07 % (20031)Time elapsed: 0.048 s
% 6.12/2.07 % (20031)Instructions burned: 151 (million)
% 6.12/2.07 % (20031)------------------------------
% 6.12/2.07 % (20031)------------------------------
% 6.12/2.08 % (20035)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/140Mi)
% 6.12/2.08 % (20036)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_19870 for (2994ds/614Mi)
% 6.12/2.08 % (20037)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_19870 for (2994ds/202Mi)
% 6.12/2.10 % (20037)Refutation not found, incomplete strategy
% 6.12/2.10 % (20037)------------------------------
% 6.12/2.10 % (20037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.10 % (20037)Termination reason: Refutation not found, incomplete strategy
% 6.12/2.10
% 6.12/2.10
% 6.12/2.10 % (20037)Memory used [KB]: 6652
% 6.12/2.10 % (20037)Time elapsed: 0.021 s
% 6.12/2.10 % (20037)Instructions burned: 66 (million)
% 6.12/2.10 % (20037)------------------------------
% 6.12/2.10 % (20037)------------------------------
% 6.12/2.11 % (20025)Instruction limit reached!
% 6.12/2.11 % (20025)------------------------------
% 6.12/2.11 % (20025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.11 % (20025)Termination reason: Unknown
% 6.12/2.11 % (20025)Termination phase: Saturation
% 6.12/2.11
% 6.12/2.11 % (20025)Memory used [KB]: 7803
% 6.12/2.11 % (20025)Time elapsed: 0.154 s
% 6.12/2.11 % (20025)Instructions burned: 454 (million)
% 6.12/2.11 % (20025)------------------------------
% 6.12/2.11 % (20025)------------------------------
% 6.12/2.11 % (20038)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_19870 for (2994ds/339Mi)
% 6.12/2.12 % (20039)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_19870 for (2994ds/283Mi)
% 6.12/2.12 % (20035)Instruction limit reached!
% 6.12/2.12 % (20035)------------------------------
% 6.12/2.12 % (20035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.12/2.12 % (20035)Termination reason: Unknown
% 6.12/2.12 % (20035)Termination phase: Saturation
% 6.12/2.12
% 6.12/2.12 % (20035)Memory used [KB]: 6780
% 6.12/2.12 % (20035)Time elapsed: 0.045 s
% 6.12/2.12 % (20035)Instructions burned: 141 (million)
% 6.12/2.12 % (20035)------------------------------
% 6.12/2.12 % (20035)------------------------------
% 6.60/2.12 % (20034)Instruction limit reached!
% 6.60/2.12 % (20034)------------------------------
% 6.60/2.12 % (20034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.12 % (20034)Termination reason: Unknown
% 6.60/2.12 % (20034)Termination phase: Saturation
% 6.60/2.12
% 6.60/2.12 % (20034)Memory used [KB]: 6908
% 6.60/2.12 % (20034)Time elapsed: 0.078 s
% 6.60/2.12 % (20034)Instructions burned: 253 (million)
% 6.60/2.12 % (20034)------------------------------
% 6.60/2.12 % (20034)------------------------------
% 6.60/2.13 % (20040)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/134Mi)
% 6.60/2.13 % (20041)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/298Mi)
% 6.60/2.14 % (20032)Instruction limit reached!
% 6.60/2.14 % (20032)------------------------------
% 6.60/2.14 % (20032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.14 % (20032)Termination reason: Unknown
% 6.60/2.14 % (20032)Termination phase: Saturation
% 6.60/2.14
% 6.60/2.14 % (20032)Memory used [KB]: 7036
% 6.60/2.14 % (20032)Time elapsed: 0.112 s
% 6.60/2.14 % (20032)Instructions burned: 344 (million)
% 6.60/2.14 % (20032)------------------------------
% 6.60/2.14 % (20032)------------------------------
% 6.60/2.15 % (20042)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/192Mi)
% 6.60/2.17 % (20040)Instruction limit reached!
% 6.60/2.17 % (20040)------------------------------
% 6.60/2.17 % (20040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.17 % (20040)Termination reason: Unknown
% 6.60/2.17 % (20040)Termination phase: Saturation
% 6.60/2.17
% 6.60/2.17 % (20040)Memory used [KB]: 6780
% 6.60/2.17 % (20040)Time elapsed: 0.041 s
% 6.60/2.17 % (20040)Instructions burned: 134 (million)
% 6.60/2.17 % (20040)------------------------------
% 6.60/2.17 % (20040)------------------------------
% 6.60/2.18 % (20043)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_19870 for (2993ds/258Mi)
% 6.92/2.20 % (20039)Instruction limit reached!
% 6.92/2.20 % (20039)------------------------------
% 6.92/2.20 % (20039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.20 % (20039)Termination reason: Unknown
% 6.92/2.20 % (20039)Termination phase: Saturation
% 6.92/2.20
% 6.92/2.20 % (20039)Memory used [KB]: 7547
% 6.92/2.20 % (20039)Time elapsed: 0.087 s
% 6.92/2.20 % (20039)Instructions burned: 284 (million)
% 6.92/2.20 % (20039)------------------------------
% 6.92/2.20 % (20039)------------------------------
% 6.92/2.21 % (20044)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_19870 for (2993ds/90Mi)
% 6.92/2.22 % (20038)Instruction limit reached!
% 6.92/2.22 % (20038)------------------------------
% 6.92/2.22 % (20038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.22 % (20038)Termination reason: Unknown
% 6.92/2.22 % (20038)Termination phase: Saturation
% 6.92/2.22
% 6.92/2.22 % (20038)Memory used [KB]: 7036
% 6.92/2.22 % (20038)Time elapsed: 0.103 s
% 6.92/2.22 % (20038)Instructions burned: 341 (million)
% 6.92/2.22 % (20038)------------------------------
% 6.92/2.22 % (20038)------------------------------
% 6.92/2.22 % (20041)Instruction limit reached!
% 6.92/2.22 % (20041)------------------------------
% 6.92/2.22 % (20041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.22 % (20041)Termination reason: Unknown
% 6.92/2.22 % (20041)Termination phase: Saturation
% 6.92/2.22
% 6.92/2.22 % (20041)Memory used [KB]: 7803
% 6.92/2.22 % (20041)Time elapsed: 0.086 s
% 6.92/2.22 % (20041)Instructions burned: 300 (million)
% 6.92/2.22 % (20041)------------------------------
% 6.92/2.22 % (20041)------------------------------
% 6.92/2.22 % (20042)Instruction limit reached!
% 6.92/2.22 % (20042)------------------------------
% 6.92/2.22 % (20042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.22 % (20042)Termination reason: Unknown
% 6.92/2.22 % (20042)Termination phase: Saturation
% 6.92/2.22
% 6.92/2.22 % (20042)Memory used [KB]: 7547
% 6.92/2.22 % (20042)Time elapsed: 0.067 s
% 6.92/2.22 % (20042)Instructions burned: 194 (million)
% 6.92/2.22 % (20042)------------------------------
% 6.92/2.22 % (20042)------------------------------
% 6.92/2.23 % (20045)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_19870 for (2993ds/231Mi)
% 6.92/2.23 % (20046)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_19870 for (2993ds/458Mi)
% 6.92/2.23 % (20047)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_19870 for (2993ds/31Mi)
% 6.92/2.24 % (20044)Instruction limit reached!
% 6.92/2.24 % (20044)------------------------------
% 6.92/2.24 % (20044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.24 % (20044)Termination reason: Unknown
% 6.92/2.24 % (20044)Termination phase: Saturation
% 6.92/2.24
% 6.92/2.24 % (20044)Memory used [KB]: 6524
% 6.92/2.24 % (20044)Time elapsed: 0.027 s
% 6.92/2.24 % (20044)Instructions burned: 90 (million)
% 6.92/2.24 % (20044)------------------------------
% 6.92/2.24 % (20044)------------------------------
% 6.92/2.24 % (20047)Instruction limit reached!
% 6.92/2.24 % (20047)------------------------------
% 6.92/2.24 % (20047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.24 % (20047)Termination reason: Unknown
% 6.92/2.24 % (20047)Termination phase: Property scanning
% 6.92/2.24
% 6.92/2.24 % (20047)Memory used [KB]: 1791
% 6.92/2.24 % (20047)Time elapsed: 0.011 s
% 6.92/2.24 % (20047)Instructions burned: 34 (million)
% 6.92/2.24 % (20047)------------------------------
% 6.92/2.24 % (20047)------------------------------
% 6.92/2.25 % (20048)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_19870 for (2993ds/297Mi)
% 6.92/2.25 % (20049)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_19870 for (2993ds/987Mi)
% 6.92/2.25 % (20018)Instruction limit reached!
% 6.92/2.25 % (20018)------------------------------
% 6.92/2.25 % (20018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.25 % (20018)Termination reason: Unknown
% 6.92/2.25 % (20018)Termination phase: Saturation
% 6.92/2.25
% 6.92/2.25 % (20018)Memory used [KB]: 8187
% 6.92/2.25 % (20018)Time elapsed: 0.333 s
% 6.92/2.25 % (20018)Instructions burned: 1087 (million)
% 6.92/2.25 % (20018)------------------------------
% 6.92/2.25 % (20018)------------------------------
% 6.92/2.25 % (20043)Instruction limit reached!
% 6.92/2.25 % (20043)------------------------------
% 6.92/2.25 % (20043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.25 % (20043)Termination reason: Unknown
% 6.92/2.25 % (20043)Termination phase: Saturation
% 6.92/2.25
% 6.92/2.25 % (20043)Memory used [KB]: 6780
% 6.92/2.25 % (20043)Time elapsed: 0.077 s
% 6.92/2.25 % (20043)Instructions burned: 258 (million)
% 6.92/2.25 % (20043)------------------------------
% 6.92/2.25 % (20043)------------------------------
% 6.92/2.26 % (20050)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_19870 for (2992ds/182Mi)
% 6.92/2.26 % (20036)Instruction limit reached!
% 6.92/2.26 % (20036)------------------------------
% 6.92/2.26 % (20036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.26 % (20036)Termination reason: Unknown
% 6.92/2.26 % (20036)Termination phase: Saturation
% 6.92/2.26
% 6.92/2.26 % (20036)Memory used [KB]: 8059
% 6.92/2.26 % (20036)Time elapsed: 0.181 s
% 6.92/2.26 % (20036)Instructions burned: 616 (million)
% 6.92/2.26 % (20036)------------------------------
% 6.92/2.26 % (20036)------------------------------
% 6.92/2.26 % (20051)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_19870 for (2992ds/182Mi)
% 6.92/2.27 % (20052)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_19870 for (2992ds/154Mi)
% 6.92/2.29 % (20045)Instruction limit reached!
% 6.92/2.29 % (20045)------------------------------
% 6.92/2.29 % (20045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.92/2.29 % (20045)Termination reason: Unknown
% 6.92/2.29 % (20045)Termination phase: Saturation
% 6.92/2.29
% 6.92/2.29 % (20045)Memory used [KB]: 6908
% 6.92/2.29 % (20045)Time elapsed: 0.062 s
% 6.92/2.29 % (20045)Instructions burned: 234 (million)
% 6.92/2.29 % (20045)------------------------------
% 6.92/2.29 % (20045)------------------------------
% 7.77/2.30 % (20053)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_19870 for (2992ds/79Mi)
% 7.77/2.31 % (20052)Instruction limit reached!
% 7.77/2.31 % (20052)------------------------------
% 7.77/2.31 % (20052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.31 % (20052)Termination reason: Unknown
% 7.77/2.31 % (20052)Termination phase: Saturation
% 7.77/2.31
% 7.77/2.31 % (20052)Memory used [KB]: 2558
% 7.77/2.31 % (20052)Time elapsed: 0.042 s
% 7.77/2.31 % (20052)Instructions burned: 154 (million)
% 7.77/2.31 % (20052)------------------------------
% 7.77/2.31 % (20052)------------------------------
% 7.77/2.31 % (20050)Instruction limit reached!
% 7.77/2.31 % (20050)------------------------------
% 7.77/2.31 % (20050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.31 % (20050)Termination reason: Unknown
% 7.77/2.31 % (20050)Termination phase: Saturation
% 7.77/2.31
% 7.77/2.31 % (20050)Memory used [KB]: 6908
% 7.77/2.31 % (20050)Time elapsed: 0.055 s
% 7.77/2.31 % (20050)Instructions burned: 182 (million)
% 7.77/2.31 % (20050)------------------------------
% 7.77/2.31 % (20050)------------------------------
% 7.77/2.32 % (20053)Instruction limit reached!
% 7.77/2.32 % (20053)------------------------------
% 7.77/2.32 % (20053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.32 % (20053)Termination reason: Unknown
% 7.77/2.32 % (20053)Termination phase: Saturation
% 7.77/2.32
% 7.77/2.32 % (20053)Memory used [KB]: 6652
% 7.77/2.32 % (20053)Time elapsed: 0.025 s
% 7.77/2.32 % (20053)Instructions burned: 81 (million)
% 7.77/2.32 % (20053)------------------------------
% 7.77/2.32 % (20053)------------------------------
% 7.77/2.32 % (20051)Instruction limit reached!
% 7.77/2.32 % (20051)------------------------------
% 7.77/2.32 % (20051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.32 % (20051)Termination reason: Unknown
% 7.77/2.32 % (20051)Termination phase: Saturation
% 7.77/2.32
% 7.77/2.32 % (20051)Memory used [KB]: 6908
% 7.77/2.32 % (20051)Time elapsed: 0.057 s
% 7.77/2.32 % (20051)Instructions burned: 183 (million)
% 7.77/2.32 % (20051)------------------------------
% 7.77/2.32 % (20051)------------------------------
% 7.77/2.32 % (20054)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_19870 for (2992ds/216Mi)
% 7.77/2.32 % (20055)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_19870 for (2992ds/114Mi)
% 7.77/2.33 % (20056)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_19870 for (2992ds/922Mi)
% 7.77/2.33 % (20057)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_19870 for (2992ds/182Mi)
% 7.77/2.34 % (20048)Instruction limit reached!
% 7.77/2.34 % (20048)------------------------------
% 7.77/2.34 % (20048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.34 % (20048)Termination reason: Unknown
% 7.77/2.34 % (20048)Termination phase: Saturation
% 7.77/2.34
% 7.77/2.34 % (20048)Memory used [KB]: 7164
% 7.77/2.34 % (20048)Time elapsed: 0.091 s
% 7.77/2.34 % (20048)Instructions burned: 298 (million)
% 7.77/2.34 % (20048)------------------------------
% 7.77/2.34 % (20048)------------------------------
% 7.77/2.35 % (20058)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_19870 for (2992ds/164Mi)
% 7.77/2.35 % (20055)Instruction limit reached!
% 7.77/2.35 % (20055)------------------------------
% 7.77/2.35 % (20055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.35 % (20055)Termination reason: Unknown
% 7.77/2.35 % (20055)Termination phase: Saturation
% 7.77/2.35
% 7.77/2.35 % (20055)Memory used [KB]: 6780
% 7.77/2.35 % (20055)Time elapsed: 0.034 s
% 7.77/2.35 % (20055)Instructions burned: 114 (million)
% 7.77/2.35 % (20055)------------------------------
% 7.77/2.35 % (20055)------------------------------
% 7.77/2.36 % (20059)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_19870 for (2991ds/50Mi)
% 7.77/2.37 % (20046)Instruction limit reached!
% 7.77/2.37 % (20046)------------------------------
% 7.77/2.37 % (20046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.37 % (20046)Termination reason: Unknown
% 7.77/2.37 % (20046)Termination phase: Saturation
% 7.77/2.37
% 7.77/2.37 % (20046)Memory used [KB]: 7547
% 7.77/2.37 % (20046)Time elapsed: 0.143 s
% 7.77/2.37 % (20046)Instructions burned: 458 (million)
% 7.77/2.37 % (20046)------------------------------
% 7.77/2.37 % (20046)------------------------------
% 7.77/2.38 % (20057)Instruction limit reached!
% 7.77/2.38 % (20057)------------------------------
% 7.77/2.38 % (20057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.38 % (20060)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_19870 for (2991ds/368Mi)
% 7.77/2.38 % (20057)Termination reason: Unknown
% 7.77/2.38 % (20057)Termination phase: Saturation
% 7.77/2.38
% 7.77/2.38 % (20057)Memory used [KB]: 6908
% 7.77/2.38 % (20057)Time elapsed: 0.050 s
% 7.77/2.38 % (20057)Instructions burned: 182 (million)
% 7.77/2.38 % (20057)------------------------------
% 7.77/2.38 % (20057)------------------------------
% 7.77/2.38 % (20059)Instruction limit reached!
% 7.77/2.38 % (20059)------------------------------
% 7.77/2.38 % (20059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.38 % (20059)Termination reason: Unknown
% 7.77/2.38 % (20059)Termination phase: Property scanning
% 7.77/2.38
% 7.77/2.38 % (20059)Memory used [KB]: 2174
% 7.77/2.38 % (20059)Time elapsed: 0.016 s
% 7.77/2.38 % (20059)Instructions burned: 53 (million)
% 7.77/2.38 % (20059)------------------------------
% 7.77/2.38 % (20059)------------------------------
% 7.77/2.38 % (20054)Instruction limit reached!
% 7.77/2.38 % (20054)------------------------------
% 7.77/2.38 % (20054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.38 % (20054)Termination reason: Unknown
% 7.77/2.38 % (20054)Termination phase: Saturation
% 7.77/2.38
% 7.77/2.38 % (20054)Memory used [KB]: 7291
% 7.77/2.38 % (20054)Time elapsed: 0.064 s
% 7.77/2.38 % (20054)Instructions burned: 217 (million)
% 7.77/2.38 % (20054)------------------------------
% 7.77/2.38 % (20054)------------------------------
% 7.77/2.39 % (20061)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_19870 for (2991ds/1021Mi)
% 7.77/2.39 % (20062)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_19870 for (2991ds/267Mi)
% 7.77/2.39 % (20063)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_19870 for (2991ds/204Mi)
% 7.77/2.39 % (20058)Instruction limit reached!
% 7.77/2.39 % (20058)------------------------------
% 7.77/2.39 % (20058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.39 % (20058)Termination reason: Unknown
% 7.77/2.39 % (20058)Termination phase: Saturation
% 7.77/2.39
% 7.77/2.39 % (20058)Memory used [KB]: 2558
% 7.77/2.39 % (20058)Time elapsed: 0.049 s
% 7.77/2.39 % (20058)Instructions burned: 167 (million)
% 7.77/2.39 % (20058)------------------------------
% 7.77/2.39 % (20058)------------------------------
% 8.48/2.40 % (20064)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_19870 for (2991ds/26Mi)
% 8.48/2.41 % (20064)Instruction limit reached!
% 8.48/2.41 % (20064)------------------------------
% 8.48/2.41 % (20064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.41 % (20064)Termination reason: Unknown
% 8.48/2.41 % (20064)Termination phase: shuffling
% 8.48/2.41
% 8.48/2.41 % (20064)Memory used [KB]: 1918
% 8.48/2.41 % (20064)Time elapsed: 0.009 s
% 8.48/2.41 % (20064)Instructions burned: 28 (million)
% 8.48/2.41 % (20064)------------------------------
% 8.48/2.41 % (20064)------------------------------
% 8.48/2.42 % (20065)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_19870 for (2991ds/53Mi)
% 8.48/2.44 % (20065)Instruction limit reached!
% 8.48/2.44 % (20065)------------------------------
% 8.48/2.44 % (20065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.44 % (20065)Termination reason: Unknown
% 8.48/2.44 % (20065)Termination phase: Property scanning
% 8.48/2.44
% 8.48/2.44 % (20065)Memory used [KB]: 2174
% 8.48/2.44 % (20065)Time elapsed: 0.016 s
% 8.48/2.44 % (20065)Instructions burned: 54 (million)
% 8.48/2.44 % (20065)------------------------------
% 8.48/2.44 % (20065)------------------------------
% 8.48/2.45 % (20066)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_19870 for (2991ds/4436Mi)
% 8.48/2.46 % (20063)Instruction limit reached!
% 8.48/2.46 % (20063)------------------------------
% 8.48/2.46 % (20063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.46 % (20063)Termination reason: Unknown
% 8.48/2.46 % (20063)Termination phase: Saturation
% 8.48/2.46
% 8.48/2.46 % (20063)Memory used [KB]: 6780
% 8.48/2.46 % (20063)Time elapsed: 0.064 s
% 8.48/2.46 % (20063)Instructions burned: 205 (million)
% 8.48/2.46 % (20063)------------------------------
% 8.48/2.46 % (20063)------------------------------
% 8.48/2.47 % (20067)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_19870 for (2990ds/1539Mi)
% 8.48/2.47 % (20062)Instruction limit reached!
% 8.48/2.47 % (20062)------------------------------
% 8.48/2.47 % (20062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.47 % (20062)Termination reason: Unknown
% 8.48/2.47 % (20062)Termination phase: Saturation
% 8.48/2.47
% 8.48/2.47 % (20062)Memory used [KB]: 7547
% 8.48/2.47 % (20062)Time elapsed: 0.082 s
% 8.48/2.47 % (20062)Instructions burned: 269 (million)
% 8.48/2.47 % (20062)------------------------------
% 8.48/2.47 % (20062)------------------------------
% 8.48/2.48 % (20068)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_19870 for (2990ds/408Mi)
% 8.48/2.49 % (20060)Instruction limit reached!
% 8.48/2.49 % (20060)------------------------------
% 8.48/2.49 % (20060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.48/2.49 % (20060)Termination reason: Unknown
% 8.48/2.49 % (20060)Termination phase: Saturation
% 8.48/2.49
% 8.48/2.49 % (20060)Memory used [KB]: 8187
% 8.48/2.49 % (20060)Time elapsed: 0.115 s
% 8.48/2.49 % (20060)Instructions burned: 368 (million)
% 8.48/2.49 % (20060)------------------------------
% 8.48/2.49 % (20060)------------------------------
% 8.81/2.50 % (20069)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_19870 for (2990ds/5205Mi)
% 8.81/2.55 % (20049)Instruction limit reached!
% 8.81/2.55 % (20049)------------------------------
% 8.81/2.55 % (20049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.81/2.55 % (20049)Termination reason: Unknown
% 8.81/2.55 % (20049)Termination phase: Saturation
% 8.81/2.55
% 8.81/2.55 % (20049)Memory used [KB]: 8827
% 8.81/2.55 % (20049)Time elapsed: 0.305 s
% 8.81/2.55 % (20049)Instructions burned: 988 (million)
% 8.81/2.55 % (20049)------------------------------
% 8.81/2.55 % (20049)------------------------------
% 8.81/2.56 % (20070)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_19870 for (2989ds/1913Mi)
% 9.13/2.60 % (20068)Instruction limit reached!
% 9.13/2.60 % (20068)------------------------------
% 9.13/2.60 % (20068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.13/2.60 % (20068)Termination reason: Unknown
% 9.13/2.60 % (20068)Termination phase: Saturation
% 9.13/2.60
% 9.13/2.60 % (20068)Memory used [KB]: 7803
% 9.13/2.60 % (20068)Time elapsed: 0.118 s
% 9.13/2.60 % (20068)Instructions burned: 410 (million)
% 9.13/2.60 % (20068)------------------------------
% 9.13/2.60 % (20068)------------------------------
% 9.13/2.61 % (20071)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_19870 for (2989ds/4350Mi)
% 9.13/2.62 % (20056)Instruction limit reached!
% 9.13/2.62 % (20056)------------------------------
% 9.13/2.62 % (20056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.13/2.62 % (20056)Termination reason: Unknown
% 9.13/2.62 % (20056)Termination phase: Saturation
% 9.13/2.62
% 9.13/2.62 % (20056)Memory used [KB]: 8315
% 9.13/2.62 % (20056)Time elapsed: 0.292 s
% 9.13/2.62 % (20056)Instructions burned: 923 (million)
% 9.13/2.62 % (20056)------------------------------
% 9.13/2.62 % (20056)------------------------------
% 9.13/2.63 % (20072)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_19870 for (2989ds/68Mi)
% 9.13/2.65 % (20072)Instruction limit reached!
% 9.13/2.65 % (20072)------------------------------
% 9.13/2.65 % (20072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.13/2.65 % (20072)Termination reason: Unknown
% 9.13/2.65 % (20072)Termination phase: Property scanning
% 9.13/2.65
% 9.13/2.65 % (20072)Memory used [KB]: 1918
% 9.13/2.65 % (20072)Time elapsed: 0.022 s
% 9.13/2.65 % (20072)Instructions burned: 69 (million)
% 9.13/2.65 % (20072)------------------------------
% 9.13/2.65 % (20072)------------------------------
% 9.13/2.66 % (20073)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_19870 for (2988ds/358Mi)
% 9.59/2.70 % (20061)Instruction limit reached!
% 9.59/2.70 % (20061)------------------------------
% 9.59/2.70 % (20061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.70 % (20061)Termination reason: Unknown
% 9.59/2.70 % (20061)Termination phase: Saturation
% 9.59/2.70
% 9.59/2.70 % (20061)Memory used [KB]: 8571
% 9.59/2.70 % (20061)Time elapsed: 0.315 s
% 9.59/2.70 % (20061)Instructions burned: 1023 (million)
% 9.59/2.70 % (20061)------------------------------
% 9.59/2.70 % (20061)------------------------------
% 9.59/2.71 % (20074)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_19870 for (2988ds/31Mi)
% 9.59/2.72 % (20074)Instruction limit reached!
% 9.59/2.72 % (20074)------------------------------
% 9.59/2.72 % (20074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.72 % (20074)Termination reason: Unknown
% 9.59/2.72 % (20074)Termination phase: Preprocessing 1
% 9.59/2.72
% 9.59/2.72 % (20074)Memory used [KB]: 1791
% 9.59/2.72 % (20074)Time elapsed: 0.012 s
% 9.59/2.72 % (20074)Instructions burned: 34 (million)
% 9.59/2.72 % (20074)------------------------------
% 9.59/2.72 % (20074)------------------------------
% 9.59/2.73 % (20075)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_19870 for (2988ds/279Mi)
% 9.59/2.76 % (20075)Refutation not found, incomplete strategy
% 9.59/2.76 % (20075)------------------------------
% 9.59/2.76 % (20075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.76 % (20075)Termination reason: Refutation not found, incomplete strategy
% 9.59/2.76
% 9.59/2.76
% 9.59/2.76 % (20075)Memory used [KB]: 6780
% 9.59/2.76 % (20075)Time elapsed: 0.026 s
% 9.59/2.76 % (20075)Instructions burned: 89 (million)
% 9.59/2.76 % (20075)------------------------------
% 9.59/2.76 % (20075)------------------------------
% 9.59/2.77 % (20076)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_19870 for (2987ds/258Mi)
% 9.59/2.78 % (20073)Instruction limit reached!
% 9.59/2.78 % (20073)------------------------------
% 9.59/2.78 % (20073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.78 % (20073)Termination reason: Unknown
% 9.59/2.78 % (20073)Termination phase: Saturation
% 9.59/2.78
% 9.59/2.78 % (20073)Memory used [KB]: 7419
% 9.59/2.78 % (20073)Time elapsed: 0.117 s
% 9.59/2.78 % (20073)Instructions burned: 359 (million)
% 9.59/2.78 % (20073)------------------------------
% 9.59/2.78 % (20073)------------------------------
% 9.59/2.79 % (20077)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_19870 for (2987ds/26Mi)
% 9.59/2.79 % (20077)Instruction limit reached!
% 9.59/2.79 % (20077)------------------------------
% 9.59/2.79 % (20077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.59/2.79 % (20077)Termination reason: Unknown
% 9.59/2.79 % (20077)Termination phase: shuffling
% 9.59/2.79
% 9.59/2.79 % (20077)Memory used [KB]: 1918
% 9.59/2.79 % (20077)Time elapsed: 0.009 s
% 9.59/2.79 % (20077)Instructions burned: 26 (million)
% 9.59/2.79 % (20077)------------------------------
% 9.59/2.79 % (20077)------------------------------
% 10.12/2.80 % (20078)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_19870 for (2987ds/995Mi)
% 10.12/2.85 % (20076)Instruction limit reached!
% 10.12/2.85 % (20076)------------------------------
% 10.12/2.85 % (20076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.85 % (20076)Termination reason: Unknown
% 10.12/2.85 % (20076)Termination phase: Saturation
% 10.12/2.85
% 10.12/2.85 % (20076)Memory used [KB]: 7291
% 10.12/2.85 % (20076)Time elapsed: 0.081 s
% 10.12/2.85 % (20076)Instructions burned: 260 (million)
% 10.12/2.85 % (20076)------------------------------
% 10.12/2.85 % (20076)------------------------------
% 10.12/2.86 % (20079)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_19870 for (2986ds/373Mi)
% 10.20/2.94 % (20067)Instruction limit reached!
% 10.20/2.94 % (20067)------------------------------
% 10.20/2.94 % (20067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.94 % (20067)Termination reason: Unknown
% 10.20/2.94 % (20067)Termination phase: Saturation
% 10.20/2.94
% 10.20/2.94 % (20067)Memory used [KB]: 10490
% 10.20/2.94 % (20067)Time elapsed: 0.495 s
% 10.20/2.94 % (20067)Instructions burned: 1541 (million)
% 10.20/2.94 % (20067)------------------------------
% 10.20/2.94 % (20067)------------------------------
% 10.20/2.94 % (20070)Instruction limit reached!
% 10.20/2.94 % (20070)------------------------------
% 10.20/2.94 % (20070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.94 % (20070)Termination reason: Unknown
% 10.20/2.94 % (20070)Termination phase: Saturation
% 10.20/2.94
% 10.20/2.94 % (20070)Memory used [KB]: 2558
% 10.20/2.94 % (20070)Time elapsed: 0.384 s
% 10.20/2.94 % (20070)Instructions burned: 1914 (million)
% 10.20/2.94 % (20070)------------------------------
% 10.20/2.94 % (20070)------------------------------
% 10.20/2.95 % (20080)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_19870 for (2986ds/253Mi)
% 10.20/2.95 % (20081)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_19870 for (2985ds/832Mi)
% 10.20/2.97 % (20079)Instruction limit reached!
% 10.20/2.97 % (20079)------------------------------
% 10.20/2.97 % (20079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.20/2.97 % (20079)Termination reason: Unknown
% 10.20/2.97 % (20079)Termination phase: Saturation
% 10.20/2.97
% 10.20/2.97 % (20079)Memory used [KB]: 8059
% 10.20/2.97 % (20079)Time elapsed: 0.118 s
% 10.20/2.97 % (20079)Instructions burned: 374 (million)
% 10.20/2.97 % (20079)------------------------------
% 10.20/2.97 % (20079)------------------------------
% 10.20/2.98 % (20082)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_19870 for (2985ds/668Mi)
% 13.03/3.02 % (20080)Instruction limit reached!
% 13.03/3.02 % (20080)------------------------------
% 13.03/3.02 % (20080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.02 % (20080)Termination reason: Unknown
% 13.03/3.02 % (20080)Termination phase: Saturation
% 13.03/3.02
% 13.03/3.02 % (20080)Memory used [KB]: 7547
% 13.03/3.02 % (20080)Time elapsed: 0.072 s
% 13.03/3.02 % (20080)Instructions burned: 254 (million)
% 13.03/3.02 % (20080)------------------------------
% 13.03/3.02 % (20080)------------------------------
% 13.03/3.03 % (20083)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_19870 for (2985ds/40Mi)
% 13.03/3.04 % (20083)Instruction limit reached!
% 13.03/3.04 % (20083)------------------------------
% 13.03/3.04 % (20083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.04 % (20083)Termination reason: Unknown
% 13.03/3.04 % (20083)Termination phase: Property scanning
% 13.03/3.04
% 13.03/3.04 % (20083)Memory used [KB]: 2174
% 13.03/3.04 % (20083)Time elapsed: 0.013 s
% 13.03/3.04 % (20083)Instructions burned: 42 (million)
% 13.03/3.04 % (20083)------------------------------
% 13.03/3.04 % (20083)------------------------------
% 13.03/3.05 % (20084)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_19870 for (2984ds/294Mi)
% 13.03/3.08 % (20084)Refutation not found, incomplete strategy
% 13.03/3.08 % (20084)------------------------------
% 13.03/3.08 % (20084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.08 % (20084)Termination reason: Refutation not found, incomplete strategy
% 13.03/3.08
% 13.03/3.08
% 13.03/3.08 % (20084)Memory used [KB]: 6908
% 13.03/3.08 % (20084)Time elapsed: 0.033 s
% 13.03/3.08 % (20084)Instructions burned: 115 (million)
% 13.03/3.08 % (20084)------------------------------
% 13.03/3.08 % (20084)------------------------------
% 13.03/3.09 % (20085)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_19870 for (2984ds/187Mi)
% 13.03/3.11 % (20078)Instruction limit reached!
% 13.03/3.11 % (20078)------------------------------
% 13.03/3.11 % (20078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.03/3.11 % (20078)Termination reason: Unknown
% 13.03/3.11 % (20078)Termination phase: Saturation
% 13.03/3.11
% 13.03/3.11 % (20078)Memory used [KB]: 9594
% 13.03/3.11 % (20078)Time elapsed: 0.304 s
% 13.03/3.11 % (20078)Instructions burned: 996 (million)
% 13.03/3.11 % (20078)------------------------------
% 13.03/3.11 % (20078)------------------------------
% 13.72/3.12 % (20086)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_19870 for (2984ds/371Mi)
% 13.72/3.15 % (20085)Instruction limit reached!
% 13.72/3.15 % (20085)------------------------------
% 13.72/3.15 % (20085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.15 % (20085)Termination reason: Unknown
% 13.72/3.15 % (20085)Termination phase: Saturation
% 13.72/3.15
% 13.72/3.15 % (20085)Memory used [KB]: 7164
% 13.72/3.15 % (20085)Time elapsed: 0.062 s
% 13.72/3.15 % (20085)Instructions burned: 188 (million)
% 13.72/3.15 % (20085)------------------------------
% 13.72/3.15 % (20085)------------------------------
% 13.72/3.16 % (20087)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_19870 for (2983ds/1827Mi)
% 13.72/3.18 % (20082)Instruction limit reached!
% 13.72/3.18 % (20082)------------------------------
% 13.72/3.18 % (20082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.72/3.18 % (20082)Termination reason: Unknown
% 13.72/3.18 % (20082)Termination phase: Saturation
% 13.72/3.18
% 13.72/3.18 % (20082)Memory used [KB]: 14072
% 13.72/3.18 % (20082)Time elapsed: 0.200 s
% 13.72/3.18 % (20082)Instructions burned: 670 (million)
% 13.72/3.18 % (20082)------------------------------
% 13.72/3.18 % (20082)------------------------------
% 13.72/3.19 % (20088)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_19870 for (2983ds/70Mi)
% 14.20/3.20 % (20081)Instruction limit reached!
% 14.20/3.20 % (20081)------------------------------
% 14.20/3.20 % (20081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.20 % (20081)Termination reason: Unknown
% 14.20/3.20 % (20081)Termination phase: Saturation
% 14.20/3.20
% 14.20/3.20 % (20081)Memory used [KB]: 7419
% 14.20/3.20 % (20081)Time elapsed: 0.249 s
% 14.20/3.20 % (20081)Instructions burned: 833 (million)
% 14.20/3.20 % (20081)------------------------------
% 14.20/3.20 % (20081)------------------------------
% 14.20/3.21 % (20086)Refutation not found, non-redundant clauses discarded% (20086)------------------------------
% 14.20/3.21 % (20086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.21 % (20086)Termination reason: Refutation not found, non-redundant clauses discarded
% 14.20/3.21
% 14.20/3.21 % (20086)Memory used [KB]: 6908
% 14.20/3.21 % (20086)Time elapsed: 0.092 s
% 14.20/3.21 % (20086)Instructions burned: 279 (million)
% 14.20/3.21 % (20086)------------------------------
% 14.20/3.21 % (20086)------------------------------
% 14.20/3.21 % (20088)Instruction limit reached!
% 14.20/3.21 % (20088)------------------------------
% 14.20/3.21 % (20088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.21 % (20088)Termination reason: Unknown
% 14.20/3.21 % (20088)Termination phase: Property scanning
% 14.20/3.21
% 14.20/3.21 % (20088)Memory used [KB]: 2174
% 14.20/3.21 % (20088)Time elapsed: 0.020 s
% 14.20/3.21 % (20088)Instructions burned: 70 (million)
% 14.20/3.21 % (20088)------------------------------
% 14.20/3.21 % (20088)------------------------------
% 14.20/3.21 % (20089)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_19870 for (2983ds/316Mi)
% 14.20/3.22 % (20090)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_19870 for (2983ds/932Mi)
% 14.20/3.22 % (20091)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_19870 for (2983ds/4714Mi)
% 14.20/3.26 % (20089)Refutation not found, incomplete strategy
% 14.20/3.26 % (20089)------------------------------
% 14.20/3.26 % (20089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.26 % (20089)Termination reason: Refutation not found, incomplete strategy
% 14.20/3.26
% 14.20/3.26
% 14.20/3.26 % (20089)Memory used [KB]: 7547
% 14.20/3.26 % (20089)Time elapsed: 0.050 s
% 14.20/3.26 % (20089)Instructions burned: 185 (million)
% 14.20/3.26 % (20089)------------------------------
% 14.20/3.26 % (20089)------------------------------
% 14.20/3.27 % (20092)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_19870 for (2982ds/8250Mi)
% 14.20/3.28 % (20091)Refutation not found, incomplete strategy
% 14.20/3.28 % (20091)------------------------------
% 14.20/3.28 % (20091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.28 % (20091)Termination reason: Refutation not found, incomplete strategy
% 14.20/3.28
% 14.20/3.28
% 14.20/3.28 % (20091)Memory used [KB]: 7675
% 14.20/3.28 % (20091)Time elapsed: 0.057 s
% 14.20/3.28 % (20091)Instructions burned: 203 (million)
% 14.20/3.28 % (20091)------------------------------
% 14.20/3.28 % (20091)------------------------------
% 14.20/3.29 % (20093)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_19870 for (2982ds/770Mi)
% 14.77/3.31 % (20093)Refutation not found, incomplete strategy
% 14.77/3.31 % (20093)------------------------------
% 14.77/3.31 % (20093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.77/3.31 % (20093)Termination reason: Refutation not found, incomplete strategy
% 14.77/3.31
% 14.77/3.31
% 14.77/3.31 % (20093)Memory used [KB]: 6524
% 14.77/3.31 % (20093)Time elapsed: 0.019 s
% 14.77/3.31 % (20093)Instructions burned: 58 (million)
% 14.77/3.31 % (20093)------------------------------
% 14.77/3.31 % (20093)------------------------------
% 14.77/3.32 % (20094)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_19870 for (2982ds/794Mi)
% 15.39/3.50 % (20090)Instruction limit reached!
% 15.39/3.50 % (20090)------------------------------
% 15.39/3.50 % (20090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.50 % (20090)Termination reason: Unknown
% 15.39/3.50 % (20090)Termination phase: Saturation
% 15.39/3.50
% 15.39/3.50 % (20090)Memory used [KB]: 10106
% 15.39/3.50 % (20090)Time elapsed: 0.283 s
% 15.39/3.50 % (20090)Instructions burned: 934 (million)
% 15.39/3.50 % (20090)------------------------------
% 15.39/3.50 % (20090)------------------------------
% 15.39/3.51 % (20095)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_19870 for (2980ds/464Mi)
% 15.39/3.57 % (20094)Instruction limit reached!
% 15.39/3.57 % (20094)------------------------------
% 15.39/3.57 % (20094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.39/3.57 % (20094)Termination reason: Unknown
% 15.39/3.57 % (20094)Termination phase: Saturation
% 15.39/3.57
% 15.39/3.57 % (20094)Memory used [KB]: 5117
% 15.39/3.57 % (20094)Time elapsed: 0.255 s
% 15.39/3.57 % (20094)Instructions burned: 795 (million)
% 15.39/3.57 % (20094)------------------------------
% 15.39/3.57 % (20094)------------------------------
% 15.39/3.58 % (20096)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_19870 for (2979ds/1376Mi)
% 16.25/3.66 % (20095)Instruction limit reached!
% 16.25/3.66 % (20095)------------------------------
% 16.25/3.66 % (20095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.25/3.66 % (20095)Termination reason: Unknown
% 16.25/3.66 % (20095)Termination phase: Saturation
% 16.25/3.66
% 16.25/3.66 % (20095)Memory used [KB]: 7547
% 16.25/3.66 % (20095)Time elapsed: 0.147 s
% 16.25/3.66 % (20095)Instructions burned: 464 (million)
% 16.25/3.66 % (20095)------------------------------
% 16.25/3.66 % (20095)------------------------------
% 16.25/3.67 % (20097)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_19870 for (2978ds/906Mi)
% 16.70/3.70 % (20087)Instruction limit reached!
% 16.70/3.70 % (20087)------------------------------
% 16.70/3.70 % (20087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.70/3.70 % (20087)Termination reason: Unknown
% 16.70/3.70 % (20087)Termination phase: Saturation
% 16.70/3.70
% 16.70/3.70 % (20087)Memory used [KB]: 10234
% 16.70/3.70 % (20087)Time elapsed: 0.542 s
% 16.70/3.70 % (20087)Instructions burned: 1832 (million)
% 16.70/3.70 % (20087)------------------------------
% 16.70/3.70 % (20087)------------------------------
% 16.70/3.71 % (20098)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_19870 for (2978ds/434Mi)
% 17.56/3.80 % (20066)Instruction limit reached!
% 17.56/3.80 % (20066)------------------------------
% 17.56/3.80 % (20066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.56/3.80 % (20066)Termination reason: Unknown
% 17.56/3.80 % (20066)Termination phase: Saturation
% 17.56/3.80
% 17.56/3.80 % (20066)Memory used [KB]: 10874
% 17.56/3.80 % (20066)Time elapsed: 1.378 s
% 17.56/3.80 % (20066)Instructions burned: 4438 (million)
% 17.56/3.80 % (20066)------------------------------
% 17.56/3.80 % (20066)------------------------------
% 17.56/3.81 % (20099)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_19870 for (2977ds/865Mi)
% 17.56/3.83 % (20071)Instruction limit reached!
% 17.56/3.83 % (20071)------------------------------
% 17.56/3.83 % (20071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.56/3.83 % (20071)Termination reason: Unknown
% 17.56/3.83 % (20071)Termination phase: Saturation
% 17.56/3.83
% 17.56/3.83 % (20071)Memory used [KB]: 12025
% 17.56/3.83 % (20071)Time elapsed: 1.227 s
% 17.56/3.83 % (20071)Instructions burned: 4352 (million)
% 17.56/3.83 % (20071)------------------------------
% 17.56/3.83 % (20071)------------------------------
% 17.56/3.84 % (20098)Instruction limit reached!
% 17.56/3.84 % (20098)------------------------------
% 17.56/3.84 % (20098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.56/3.84 % (20098)Termination reason: Unknown
% 17.56/3.84 % (20098)Termination phase: Saturation
% 17.56/3.84
% 17.56/3.84 % (20098)Memory used [KB]: 7547
% 17.56/3.84 % (20098)Time elapsed: 0.129 s
% 17.56/3.84 % (20098)Instructions burned: 435 (million)
% 17.56/3.84 % (20098)------------------------------
% 17.56/3.84 % (20098)------------------------------
% 17.56/3.84 % (20100)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_19870 for (2977ds/593Mi)
% 17.56/3.85 % (20101)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_19870 for (2977ds/443Mi)
% 17.85/3.97 % (20097)Instruction limit reached!
% 17.85/3.97 % (20097)------------------------------
% 17.85/3.97 % (20097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.85/3.97 % (20097)Termination reason: Unknown
% 17.85/3.97 % (20097)Termination phase: Saturation
% 17.85/3.97
% 17.85/3.97 % (20097)Memory used [KB]: 10618
% 17.85/3.97 % (20097)Time elapsed: 0.308 s
% 17.85/3.97 % (20097)Instructions burned: 906 (million)
% 17.85/3.97 % (20097)------------------------------
% 17.85/3.97 % (20097)------------------------------
% 17.85/3.98 % (20102)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_19870 for (2975ds/594Mi)
% 17.85/3.99 % (20101)Instruction limit reached!
% 17.85/3.99 % (20101)------------------------------
% 17.85/3.99 % (20101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.85/3.99 % (20101)Termination reason: Unknown
% 17.85/3.99 % (20101)Termination phase: Saturation
% 17.85/3.99
% 17.85/3.99 % (20101)Memory used [KB]: 7547
% 17.85/3.99 % (20101)Time elapsed: 0.142 s
% 17.85/3.99 % (20101)Instructions burned: 445 (million)
% 17.85/3.99 % (20101)------------------------------
% 17.85/3.99 % (20101)------------------------------
% 17.85/3.99 % (20096)Instruction limit reached!
% 17.85/3.99 % (20096)------------------------------
% 17.85/3.99 % (20096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.85/3.99 % (20096)Termination reason: Unknown
% 17.85/3.99 % (20096)Termination phase: Saturation
% 17.85/3.99
% 17.85/3.99 % (20096)Memory used [KB]: 14328
% 17.85/3.99 % (20096)Time elapsed: 0.414 s
% 17.85/3.99 % (20096)Instructions burned: 1379 (million)
% 17.85/3.99 % (20096)------------------------------
% 17.85/3.99 % (20096)------------------------------
% 17.85/4.00 % (20103)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_19870 for (2975ds/327Mi)
% 17.85/4.00 % (20104)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_19870 for (2975ds/5411Mi)
% 19.99/4.01 % (20069)Instruction limit reached!
% 19.99/4.01 % (20069)------------------------------
% 19.99/4.01 % (20069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.99/4.01 % (20069)Termination reason: Unknown
% 19.99/4.01 % (20069)Termination phase: Saturation
% 19.99/4.01
% 19.99/4.01 % (20069)Memory used [KB]: 15095
% 19.99/4.01 % (20069)Time elapsed: 1.503 s
% 19.99/4.01 % (20069)Instructions burned: 5207 (million)
% 19.99/4.01 % (20069)------------------------------
% 19.99/4.01 % (20069)------------------------------
% 19.99/4.02 % (20100)Instruction limit reached!
% 19.99/4.02 % (20100)------------------------------
% 19.99/4.02 % (20100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.99/4.02 % (20100)Termination reason: Unknown
% 19.99/4.02 % (20100)Termination phase: Saturation
% 19.99/4.02
% 19.99/4.02 % (20100)Memory used [KB]: 8443
% 19.99/4.02 % (20100)Time elapsed: 0.178 s
% 19.99/4.02 % (20100)Instructions burned: 593 (million)
% 19.99/4.02 % (20100)------------------------------
% 19.99/4.02 % (20100)------------------------------
% 19.99/4.02 % (20104)Refutation not found, incomplete strategy
% 19.99/4.02 % (20104)------------------------------
% 19.99/4.02 % (20104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.99/4.02 % (20104)Termination reason: Refutation not found, incomplete strategy
% 19.99/4.02
% 19.99/4.02
% 19.99/4.02 % (20104)Memory used [KB]: 6524
% 19.99/4.02 % (20104)Time elapsed: 0.018 s
% 19.99/4.02 % (20104)Instructions burned: 57 (million)
% 19.99/4.02 % (20104)------------------------------
% 19.99/4.02 % (20104)------------------------------
% 19.99/4.03 % (20105)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_19870 for (2975ds/1762Mi)
% 19.99/4.03 % (20106)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_19870 for (2975ds/96Mi)
% 19.99/4.03 % (20107)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_19870 for (2975ds/503Mi)
% 19.99/4.05 % (20107)Refutation not found, incomplete strategy
% 19.99/4.05 % (20107)------------------------------
% 19.99/4.05 % (20107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.99/4.05 % (20107)Termination reason: Refutation not found, incomplete strategy
% 19.99/4.05
% 19.99/4.05
% 19.99/4.05 % (20107)Memory used [KB]: 6524
% 19.99/4.05 % (20107)Time elapsed: 0.019 s
% 19.99/4.05 % (20107)Instructions burned: 60 (million)
% 19.99/4.05 % (20107)------------------------------
% 19.99/4.05 % (20107)------------------------------
% 19.99/4.05 % (20106)Instruction limit reached!
% 19.99/4.05 % (20106)------------------------------
% 19.99/4.05 % (20106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.99/4.05 % (20106)Termination reason: Unknown
% 19.99/4.05 % (20106)Termination phase: Function definition elimination
% 19.99/4.05
% 19.99/4.05 % (20106)Memory used [KB]: 2174
% 19.99/4.05 % (20106)Time elapsed: 0.026 s
% 19.99/4.05 % (20106)Instructions burned: 96 (million)
% 19.99/4.05 % (20106)------------------------------
% 19.99/4.05 % (20106)------------------------------
% 19.99/4.06 % (20108)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_19870 for (2974ds/90Mi)
% 19.99/4.06 % (20109)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_19870 for (2974ds/593Mi)
% 19.99/4.07 % (20099)Instruction limit reached!
% 19.99/4.07 % (20099)------------------------------
% 19.99/4.07 % (20099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.99/4.07 % (20099)Termination reason: Unknown
% 19.99/4.07 % (20099)Termination phase: Saturation
% 19.99/4.07
% 19.99/4.07 % (20099)Memory used [KB]: 8187
% 19.99/4.07 % (20099)Time elapsed: 0.257 s
% 19.99/4.07 % (20099)Instructions burned: 869 (million)
% 19.99/4.07 % (20099)------------------------------
% 19.99/4.07 % (20099)------------------------------
% 19.99/4.08 % (20110)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_19870 for (2974ds/1512Mi)
% 19.99/4.09 % (20108)Instruction limit reached!
% 19.99/4.09 % (20108)------------------------------
% 19.99/4.09 % (20108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.99/4.09 % (20108)Termination reason: Unknown
% 19.99/4.09 % (20108)Termination phase: Saturation
% 19.99/4.09
% 19.99/4.09 % (20108)Memory used [KB]: 6524
% 19.99/4.09 % (20108)Time elapsed: 0.027 s
% 19.99/4.09 % (20108)Instructions burned: 90 (million)
% 19.99/4.09 % (20108)------------------------------
% 19.99/4.09 % (20108)------------------------------
% 19.99/4.10 % (20111)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_19870 for (2974ds/569Mi)
% 20.50/4.11 % (20103)Instruction limit reached!
% 20.50/4.11 % (20103)------------------------------
% 20.50/4.11 % (20103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.50/4.11 % (20103)Termination reason: Unknown
% 20.50/4.11 % (20103)Termination phase: Saturation
% 20.50/4.11
% 20.50/4.11 % (20103)Memory used [KB]: 7547
% 20.50/4.11 % (20103)Time elapsed: 0.128 s
% 20.50/4.11 % (20103)Instructions burned: 329 (million)
% 20.50/4.11 % (20103)------------------------------
% 20.50/4.11 % (20103)------------------------------
% 20.50/4.12 % (20112)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_19870 for (2974ds/501Mi)
% 20.50/4.17 % (20102)Instruction limit reached!
% 20.50/4.17 % (20102)------------------------------
% 20.50/4.17 % (20102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.50/4.17 % (20102)Termination reason: Unknown
% 20.50/4.17 % (20102)Termination phase: Saturation
% 20.50/4.17
% 20.50/4.17 % (20102)Memory used [KB]: 7803
% 20.50/4.17 % (20102)Time elapsed: 0.187 s
% 20.50/4.17 % (20102)Instructions burned: 596 (million)
% 20.50/4.17 % (20102)------------------------------
% 20.50/4.17 % (20102)------------------------------
% 20.50/4.18 % (20113)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_19870 for (2973ds/562Mi)
% 20.68/4.24 % (20109)Instruction limit reached!
% 20.68/4.24 % (20109)------------------------------
% 20.68/4.24 % (20109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.68/4.24 % (20109)Termination reason: Unknown
% 20.68/4.24 % (20109)Termination phase: Saturation
% 20.68/4.24
% 20.68/4.24 % (20109)Memory used [KB]: 7803
% 20.68/4.24 % (20109)Time elapsed: 0.173 s
% 20.68/4.24 % (20109)Instructions burned: 595 (million)
% 20.68/4.24 % (20109)------------------------------
% 20.68/4.24 % (20109)------------------------------
% 20.68/4.25 % (20114)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_19870 for (2973ds/406Mi)
% 20.68/4.26 % (20111)Instruction limit reached!
% 20.68/4.26 % (20111)------------------------------
% 20.68/4.26 % (20111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.68/4.26 % (20111)Termination reason: Unknown
% 20.68/4.26 % (20111)Termination phase: Saturation
% 20.68/4.26
% 20.68/4.26 % (20111)Memory used [KB]: 7931
% 20.68/4.26 % (20111)Time elapsed: 0.166 s
% 20.68/4.26 % (20111)Instructions burned: 569 (million)
% 20.68/4.26 % (20111)------------------------------
% 20.68/4.26 % (20111)------------------------------
% 20.68/4.27 % (20115)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_19870 for (2972ds/582Mi)
% 20.68/4.29 % (20112)Instruction limit reached!
% 20.68/4.29 % (20112)------------------------------
% 20.68/4.29 % (20112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.68/4.29 % (20112)Termination reason: Unknown
% 20.68/4.29 % (20112)Termination phase: Saturation
% 20.68/4.29
% 20.68/4.29 % (20112)Memory used [KB]: 7675
% 20.68/4.29 % (20112)Time elapsed: 0.164 s
% 20.68/4.29 % (20112)Instructions burned: 501 (million)
% 20.68/4.29 % (20112)------------------------------
% 20.68/4.29 % (20112)------------------------------
% 21.30/4.30 % (20116)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_19870 for (2972ds/456Mi)
% 21.30/4.34 % (20116)Refutation not found, incomplete strategy
% 21.30/4.34 % (20116)------------------------------
% 21.30/4.34 % (20116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.30/4.34 % (20116)Termination reason: Refutation not found, incomplete strategy
% 21.30/4.34
% 21.30/4.34
% 21.30/4.34 % (20116)Memory used [KB]: 6908
% 21.30/4.34 % (20116)Time elapsed: 0.040 s
% 21.30/4.34 % (20116)Instructions burned: 131 (million)
% 21.30/4.34 % (20116)------------------------------
% 21.30/4.34 % (20116)------------------------------
% 21.30/4.35 % (20117)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_19870 for (2972ds/393Mi)
% 21.30/4.36 % (20113)Instruction limit reached!
% 21.30/4.36 % (20113)------------------------------
% 21.30/4.36 % (20113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.30/4.36 % (20113)Termination reason: Unknown
% 21.30/4.36 % (20113)Termination phase: Saturation
% 21.30/4.36
% 21.30/4.36 % (20113)Memory used [KB]: 7291
% 21.30/4.36 % (20113)Time elapsed: 0.179 s
% 21.30/4.36 % (20113)Instructions burned: 563 (million)
% 21.30/4.36 % (20113)------------------------------
% 21.30/4.36 % (20113)------------------------------
% 21.30/4.36 % (20114)Refutation not found, non-redundant clauses discarded% (20114)------------------------------
% 21.30/4.36 % (20114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.30/4.36 % (20114)Termination reason: Refutation not found, non-redundant clauses discarded
% 21.30/4.36
% 21.30/4.36 % (20114)Memory used [KB]: 7675
% 21.30/4.36 % (20114)Time elapsed: 0.120 s
% 21.30/4.36 % (20114)Instructions burned: 368 (million)
% 21.30/4.37 % (20114)------------------------------
% 21.30/4.37 % (20114)------------------------------
% 21.30/4.37 % (20118)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_19870 for (2971ds/1335Mi)
% 21.30/4.38 % (20119)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_19870 for (2971ds/3373Mi)
% 21.77/4.45 % (20115)Instruction limit reached!
% 21.77/4.45 % (20115)------------------------------
% 21.77/4.45 % (20115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.77/4.45 % (20115)Termination reason: Unknown
% 21.77/4.45 % (20115)Termination phase: Saturation
% 21.77/4.45
% 21.77/4.45 % (20115)Memory used [KB]: 8187
% 21.77/4.45 % (20115)Time elapsed: 0.185 s
% 21.77/4.45 % (20115)Instructions burned: 583 (million)
% 21.77/4.45 % (20115)------------------------------
% 21.77/4.45 % (20115)------------------------------
% 21.77/4.46 % (20117)Instruction limit reached!
% 21.77/4.46 % (20117)------------------------------
% 21.77/4.46 % (20117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.77/4.46 % (20117)Termination reason: Unknown
% 21.77/4.46 % (20117)Termination phase: Saturation
% 21.77/4.46
% 21.77/4.46 % (20117)Memory used [KB]: 7675
% 21.77/4.46 % (20117)Time elapsed: 0.116 s
% 21.77/4.46 % (20117)Instructions burned: 395 (million)
% 21.77/4.46 % (20117)------------------------------
% 21.77/4.46 % (20117)------------------------------
% 21.77/4.46 % (20120)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_19870 for (2970ds/474Mi)
% 21.77/4.47 % (20121)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_19870 for (2970ds/157Mi)
% 22.19/4.51 % (20121)Instruction limit reached!
% 22.19/4.51 % (20121)------------------------------
% 22.19/4.51 % (20121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.51 % (20121)Termination reason: Unknown
% 22.19/4.51 % (20121)Termination phase: Saturation
% 22.19/4.51
% 22.19/4.51 % (20121)Memory used [KB]: 6780
% 22.19/4.51 % (20121)Time elapsed: 0.044 s
% 22.19/4.51 % (20121)Instructions burned: 158 (million)
% 22.19/4.51 % (20121)------------------------------
% 22.19/4.51 % (20121)------------------------------
% 22.19/4.52 % (20110)Instruction limit reached!
% 22.19/4.52 % (20110)------------------------------
% 22.19/4.52 % (20110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.52 % (20110)Termination reason: Unknown
% 22.19/4.52 % (20110)Termination phase: Saturation
% 22.19/4.52
% 22.19/4.52 % (20110)Memory used [KB]: 7803
% 22.19/4.52 % (20110)Time elapsed: 0.448 s
% 22.19/4.52 % (20110)Instructions burned: 1515 (million)
% 22.19/4.52 % (20110)------------------------------
% 22.19/4.52 % (20110)------------------------------
% 22.19/4.52 % (20122)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_19870 for (2970ds/590Mi)
% 22.19/4.53 % (20105)Instruction limit reached!
% 22.19/4.53 % (20105)------------------------------
% 22.19/4.53 % (20105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.53 % (20105)Termination reason: Unknown
% 22.19/4.53 % (20105)Termination phase: Saturation
% 22.19/4.53
% 22.19/4.53 % (20105)Memory used [KB]: 9850
% 22.19/4.53 % (20105)Time elapsed: 0.524 s
% 22.19/4.53 % (20105)Instructions burned: 1762 (million)
% 22.19/4.53 % (20105)------------------------------
% 22.19/4.53 % (20105)------------------------------
% 22.19/4.53 % (20123)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_19870 for (2970ds/104Mi)
% 22.19/4.54 % (20124)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_19870 for (2970ds/414Mi)
% 22.19/4.57 % (20123)Instruction limit reached!
% 22.19/4.57 % (20123)------------------------------
% 22.19/4.57 % (20123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.19/4.57 % (20123)Termination reason: Unknown
% 22.19/4.57 % (20123)Termination phase: Saturation
% 22.19/4.57
% 22.19/4.57 % (20123)Memory used [KB]: 2558
% 22.19/4.57 % (20123)Time elapsed: 0.032 s
% 22.19/4.57 % (20123)Instructions burned: 107 (million)
% 22.19/4.57 % (20123)------------------------------
% 22.19/4.57 % (20123)------------------------------
% 22.19/4.58 % (20125)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_19870 for (2969ds/715Mi)
% 23.35/4.61 % (20120)Instruction limit reached!
% 23.35/4.61 % (20120)------------------------------
% 23.35/4.61 % (20120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.35/4.61 % (20120)Termination reason: Unknown
% 23.35/4.61 % (20120)Termination phase: Saturation
% 23.35/4.61
% 23.35/4.61 % (20120)Memory used [KB]: 8059
% 23.35/4.61 % (20120)Time elapsed: 0.143 s
% 23.35/4.61 % (20120)Instructions burned: 475 (million)
% 23.35/4.61 % (20120)------------------------------
% 23.35/4.61 % (20120)------------------------------
% 23.35/4.62 % (20126)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_19870 for (2969ds/961Mi)
% 23.35/4.65 % (20124)Instruction limit reached!
% 23.35/4.65 % (20124)------------------------------
% 23.35/4.65 % (20124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.35/4.65 % (20124)Termination reason: Unknown
% 23.35/4.66 % (20124)Termination phase: Saturation
% 23.35/4.66
% 23.35/4.66 % (20124)Memory used [KB]: 7547
% 23.35/4.66 % (20124)Time elapsed: 0.120 s
% 23.35/4.66 % (20124)Instructions burned: 414 (million)
% 23.35/4.66 % (20124)------------------------------
% 23.35/4.66 % (20124)------------------------------
% 23.35/4.66 % (20118)Instruction limit reached!
% 23.35/4.66 % (20118)------------------------------
% 23.35/4.66 % (20118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.35/4.66 % (20118)Termination reason: Unknown
% 23.35/4.66 % (20118)Termination phase: Saturation
% 23.35/4.66
% 23.35/4.66 % (20118)Memory used [KB]: 7675
% 23.35/4.66 % (20118)Time elapsed: 0.299 s
% 23.35/4.66 % (20118)Instructions burned: 1339 (million)
% 23.35/4.66 % (20118)------------------------------
% 23.35/4.66 % (20118)------------------------------
% 23.35/4.67 % (20127)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_19870 for (2968ds/1213Mi)
% 23.35/4.67 % (20128)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_19870 for (2968ds/1979Mi)
% 24.03/4.70 % (20122)Instruction limit reached!
% 24.03/4.70 % (20122)------------------------------
% 24.03/4.70 % (20122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.03/4.70 % (20122)Termination reason: Unknown
% 24.03/4.70 % (20122)Termination phase: Saturation
% 24.03/4.70
% 24.03/4.70 % (20122)Memory used [KB]: 7419
% 24.03/4.70 % (20122)Time elapsed: 0.174 s
% 24.03/4.70 % (20122)Instructions burned: 591 (million)
% 24.03/4.70 % (20122)------------------------------
% 24.03/4.70 % (20122)------------------------------
% 24.03/4.71 % (20129)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_19870 for (2968ds/481Mi)
% 24.31/4.80 % (20125)Instruction limit reached!
% 24.31/4.80 % (20125)------------------------------
% 24.31/4.80 % (20125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.31/4.80 % (20125)Termination reason: Unknown
% 24.31/4.80 % (20125)Termination phase: Saturation
% 24.31/4.80
% 24.31/4.80 % (20125)Memory used [KB]: 4221
% 24.31/4.80 % (20125)Time elapsed: 0.231 s
% 24.31/4.80 % (20125)Instructions burned: 718 (million)
% 24.31/4.80 % (20125)------------------------------
% 24.31/4.80 % (20125)------------------------------
% 24.31/4.82 % (20130)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_19870 for (2967ds/783Mi)
% 24.31/4.86 % (20129)Instruction limit reached!
% 24.31/4.86 % (20129)------------------------------
% 24.31/4.86 % (20129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.31/4.86 % (20129)Termination reason: Unknown
% 24.31/4.86 % (20129)Termination phase: Saturation
% 24.31/4.86
% 24.31/4.86 % (20129)Memory used [KB]: 7675
% 24.31/4.86 % (20129)Time elapsed: 0.152 s
% 24.31/4.86 % (20129)Instructions burned: 483 (million)
% 24.31/4.86 % (20129)------------------------------
% 24.31/4.86 % (20129)------------------------------
% 24.31/4.87 % (20131)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_19870 for (2966ds/432Mi)
% 24.81/4.91 % (20126)Instruction limit reached!
% 24.81/4.91 % (20126)------------------------------
% 24.81/4.91 % (20126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.81/4.91 % (20126)Termination reason: Unknown
% 24.81/4.91 % (20126)Termination phase: Saturation
% 24.81/4.91
% 24.81/4.91 % (20126)Memory used [KB]: 7419
% 24.81/4.91 % (20126)Time elapsed: 0.299 s
% 24.81/4.91 % (20126)Instructions burned: 963 (million)
% 24.81/4.91 % (20126)------------------------------
% 24.81/4.91 % (20126)------------------------------
% 24.81/4.92 % (20132)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_19870 for (2966ds/1670Mi)
% 24.81/5.01 % (20131)Instruction limit reached!
% 24.81/5.01 % (20131)------------------------------
% 24.81/5.01 % (20131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.81/5.01 % (20131)Termination reason: Unknown
% 24.81/5.01 % (20131)Termination phase: Saturation
% 24.81/5.01
% 24.81/5.01 % (20131)Memory used [KB]: 7164
% 24.81/5.01 % (20131)Time elapsed: 0.140 s
% 24.81/5.01 % (20131)Instructions burned: 434 (million)
% 24.81/5.01 % (20131)------------------------------
% 24.81/5.01 % (20131)------------------------------
% 24.81/5.02 % (20133)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_19870 for (2965ds/90Mi)
% 27.01/5.04 % (20133)Instruction limit reached!
% 27.01/5.04 % (20133)------------------------------
% 27.01/5.04 % (20133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.01/5.04 % (20133)Termination reason: Unknown
% 27.01/5.04 % (20133)Termination phase: Saturation
% 27.01/5.04
% 27.01/5.04 % (20133)Memory used [KB]: 6652
% 27.01/5.04 % (20133)Time elapsed: 0.028 s
% 27.01/5.04 % (20133)Instructions burned: 92 (million)
% 27.01/5.04 % (20133)------------------------------
% 27.01/5.04 % (20133)------------------------------
% 27.01/5.05 % (20127)Instruction limit reached!
% 27.01/5.05 % (20127)------------------------------
% 27.01/5.05 % (20127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.01/5.05 % (20127)Termination reason: Unknown
% 27.01/5.05 % (20127)Termination phase: Saturation
% 27.01/5.05
% 27.01/5.05 % (20127)Memory used [KB]: 9210
% 27.01/5.05 % (20127)Time elapsed: 0.387 s
% 27.01/5.05 % (20127)Instructions burned: 1215 (million)
% 27.01/5.05 % (20127)------------------------------
% 27.01/5.05 % (20127)------------------------------
% 27.01/5.05 % (20134)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_19870 for (2965ds/346Mi)
% 27.01/5.06 % (20135)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_19870 for (2964ds/401Mi)
% 27.01/5.07 % (20130)Instruction limit reached!
% 27.01/5.07 % (20130)------------------------------
% 27.01/5.07 % (20130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.01/5.07 % (20130)Termination reason: Unknown
% 27.01/5.07 % (20130)Termination phase: Saturation
% 27.01/5.07
% 27.01/5.07 % (20130)Memory used [KB]: 7931
% 27.01/5.07 % (20130)Time elapsed: 0.272 s
% 27.01/5.07 % (20130)Instructions burned: 783 (million)
% 27.01/5.07 % (20130)------------------------------
% 27.01/5.07 % (20130)------------------------------
% 27.01/5.08 % (20136)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_19870 for (2964ds/6454Mi)
% 27.55/5.16 % (20134)Instruction limit reached!
% 27.55/5.16 % (20134)------------------------------
% 27.55/5.16 % (20134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.55/5.16 % (20134)Termination reason: Unknown
% 27.55/5.16 % (20134)Termination phase: Saturation
% 27.55/5.16
% 27.55/5.16 % (20134)Memory used [KB]: 7675
% 27.55/5.16 % (20134)Time elapsed: 0.127 s
% 27.55/5.16 % (20134)Instructions burned: 346 (million)
% 27.55/5.16 % (20134)------------------------------
% 27.55/5.16 % (20134)------------------------------
% 27.55/5.17 % (20137)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_19870 for (2963ds/283Mi)
% 27.55/5.18 % (20135)Instruction limit reached!
% 27.55/5.18 % (20135)------------------------------
% 27.55/5.18 % (20135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.55/5.18 % (20135)Termination reason: Unknown
% 27.55/5.18 % (20135)Termination phase: Saturation
% 27.55/5.18
% 27.55/5.18 % (20135)Memory used [KB]: 8059
% 27.55/5.18 % (20135)Time elapsed: 0.138 s
% 27.55/5.18 % (20135)Instructions burned: 401 (million)
% 27.55/5.18 % (20135)------------------------------
% 27.55/5.18 % (20135)------------------------------
% 27.55/5.19 % (20138)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_19870 for (2963ds/865Mi)
% 28.11/5.26 % (20137)Instruction limit reached!
% 28.11/5.26 % (20137)------------------------------
% 28.11/5.26 % (20137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.11/5.26 % (20137)Termination reason: Unknown
% 28.11/5.26 % (20137)Termination phase: Saturation
% 28.11/5.26
% 28.11/5.26 % (20137)Memory used [KB]: 7803
% 28.11/5.26 % (20137)Time elapsed: 0.114 s
% 28.11/5.26 % (20137)Instructions burned: 285 (million)
% 28.11/5.26 % (20137)------------------------------
% 28.11/5.26 % (20137)------------------------------
% 28.11/5.27 % (20139)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_19870 for (2962ds/4528Mi)
% 28.11/5.28 % (20128)Instruction limit reached!
% 28.11/5.28 % (20128)------------------------------
% 28.11/5.28 % (20128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.11/5.28 % (20128)Termination reason: Unknown
% 28.11/5.28 % (20128)Termination phase: Saturation
% 28.11/5.28
% 28.11/5.28 % (20128)Memory used [KB]: 8059
% 28.11/5.28 % (20128)Time elapsed: 0.603 s
% 28.11/5.28 % (20128)Instructions burned: 1980 (million)
% 28.11/5.28 % (20128)------------------------------
% 28.11/5.28 % (20128)------------------------------
% 28.11/5.29 % (20140)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_19870 for (2962ds/1001Mi)
% 28.11/5.29 % (20139)Refutation not found, incomplete strategy
% 28.11/5.29 % (20139)------------------------------
% 28.11/5.29 % (20139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.11/5.29 % (20139)Termination reason: Refutation not found, incomplete strategy
% 28.11/5.29
% 28.11/5.29
% 28.11/5.29 % (20139)Memory used [KB]: 2046
% 28.11/5.29 % (20139)Time elapsed: 0.019 s
% 28.11/5.29 % (20139)Instructions burned: 59 (million)
% 28.11/5.29 % (20139)------------------------------
% 28.11/5.29 % (20139)------------------------------
% 28.63/5.30 % (20141)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_19870 for (2962ds/102Mi)
% 28.63/5.32 % (20141)Instruction limit reached!
% 28.63/5.32 % (20141)------------------------------
% 28.63/5.32 % (20141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.63/5.32 % (20141)Termination reason: Unknown
% 28.63/5.32 % (20141)Termination phase: Property scanning
% 28.63/5.32
% 28.63/5.32 % (20141)Memory used [KB]: 2174
% 28.63/5.32 % (20141)Time elapsed: 0.028 s
% 28.63/5.32 % (20141)Instructions burned: 103 (million)
% 28.63/5.32 % (20141)------------------------------
% 28.63/5.32 % (20141)------------------------------
% 28.63/5.33 % (20142)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_19870 for (2962ds/952Mi)
% 28.63/5.39 % (20119)Instruction limit reached!
% 28.63/5.39 % (20119)------------------------------
% 28.63/5.39 % (20119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.63/5.39 % (20119)Termination reason: Unknown
% 28.63/5.39 % (20119)Termination phase: Saturation
% 28.63/5.39
% 28.63/5.39 % (20119)Memory used [KB]: 11385
% 28.63/5.39 % (20119)Time elapsed: 1.011 s
% 28.63/5.39 % (20119)Instructions burned: 3373 (million)
% 28.63/5.39 % (20119)------------------------------
% 28.63/5.39 % (20119)------------------------------
% 28.63/5.40 % (20143)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_19870 for (2961ds/578Mi)
% 28.97/5.43 % (20132)Instruction limit reached!
% 28.97/5.43 % (20132)------------------------------
% 28.97/5.43 % (20132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.97/5.43 % (20132)Termination reason: Unknown
% 28.97/5.43 % (20132)Termination phase: Saturation
% 28.97/5.43
% 28.97/5.43 % (20132)Memory used [KB]: 9978
% 28.97/5.43 % (20132)Time elapsed: 0.512 s
% 28.97/5.43 % (20132)Instructions burned: 1670 (million)
% 28.97/5.43 % (20132)------------------------------
% 28.97/5.43 % (20132)------------------------------
% 28.97/5.44 % (20144)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_19870 for (2960ds/643Mi)
% 28.97/5.45 % (20138)Instruction limit reached!
% 28.97/5.45 % (20138)------------------------------
% 28.97/5.45 % (20138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.97/5.45 % (20138)Termination reason: Unknown
% 28.97/5.45 % (20138)Termination phase: Saturation
% 28.97/5.45
% 28.97/5.45 % (20138)Memory used [KB]: 8955
% 28.97/5.45 % (20138)Time elapsed: 0.285 s
% 28.97/5.45 % (20138)Instructions burned: 866 (million)
% 28.97/5.45 % (20138)------------------------------
% 28.97/5.45 % (20138)------------------------------
% 28.97/5.46 % (20145)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_19870 for (2960ds/865Mi)
% 29.38/5.50 % (20140)Instruction limit reached!
% 29.38/5.50 % (20140)------------------------------
% 29.38/5.50 % (20140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.38/5.50 % (20140)Termination reason: Unknown
% 29.38/5.50 % (20140)Termination phase: Saturation
% 29.38/5.50
% 29.38/5.50 % (20140)Memory used [KB]: 7036
% 29.38/5.50 % (20140)Time elapsed: 0.213 s
% 29.38/5.50 % (20140)Instructions burned: 1001 (million)
% 29.38/5.50 % (20140)------------------------------
% 29.38/5.50 % (20140)------------------------------
% 29.38/5.51 % (20146)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_19870 for (2960ds/1174Mi)
% 29.38/5.57 % (20143)Instruction limit reached!
% 29.38/5.57 % (20143)------------------------------
% 29.38/5.57 % (20143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.38/5.57 % (20143)Termination reason: Unknown
% 29.38/5.57 % (20143)Termination phase: Saturation
% 29.38/5.57
% 29.38/5.57 % (20143)Memory used [KB]: 8443
% 29.38/5.57 % (20143)Time elapsed: 0.173 s
% 29.38/5.57 % (20143)Instructions burned: 580 (million)
% 29.38/5.57 % (20143)------------------------------
% 29.38/5.57 % (20143)------------------------------
% 29.38/5.58 % (20147)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_19870 for (2959ds/644Mi)
% 29.89/5.63 % (20142)Instruction limit reached!
% 29.89/5.63 % (20142)------------------------------
% 29.89/5.63 % (20142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.89/5.63 % (20142)Termination reason: Unknown
% 29.89/5.63 % (20142)Termination phase: Saturation
% 29.89/5.63
% 29.89/5.63 % (20142)Memory used [KB]: 9210
% 29.89/5.63 % (20142)Time elapsed: 0.302 s
% 29.89/5.63 % (20142)Instructions burned: 952 (million)
% 29.89/5.63 % (20142)------------------------------
% 29.89/5.63 % (20142)------------------------------
% 29.89/5.64 % (20144)Instruction limit reached!
% 29.89/5.64 % (20144)------------------------------
% 29.89/5.64 % (20144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.89/5.64 % (20144)Termination reason: Unknown
% 29.89/5.64 % (20144)Termination phase: Saturation
% 29.89/5.64
% 29.89/5.64 % (20144)Memory used [KB]: 8443
% 29.89/5.64 % (20144)Time elapsed: 0.197 s
% 29.89/5.64 % (20144)Instructions burned: 646 (million)
% 29.89/5.64 % (20144)------------------------------
% 29.89/5.64 % (20144)------------------------------
% 29.89/5.65 % (20148)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_19870 for (2958ds/1201Mi)
% 29.89/5.65 % (20149)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_19870 for (2958ds/1046Mi)
% 30.52/5.72 % (20145)Instruction limit reached!
% 30.52/5.72 % (20145)------------------------------
% 30.52/5.72 % (20145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.52/5.73 % (20145)Termination reason: Unknown
% 30.52/5.73 % (20145)Termination phase: Saturation
% 30.52/5.73
% 30.52/5.73 % (20145)Memory used [KB]: 8443
% 30.52/5.73 % (20145)Time elapsed: 0.268 s
% 30.52/5.73 % (20145)Instructions burned: 868 (million)
% 30.52/5.73 % (20145)------------------------------
% 30.52/5.73 % (20145)------------------------------
% 30.52/5.74 % (20150)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_19870 for (2958ds/222Mi)
% 30.52/5.77 % (20147)Instruction limit reached!
% 30.52/5.77 % (20147)------------------------------
% 30.52/5.77 % (20147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.52/5.77 % (20147)Termination reason: Unknown
% 30.52/5.77 % (20147)Termination phase: Saturation
% 30.52/5.77
% 30.52/5.77 % (20147)Memory used [KB]: 8571
% 30.52/5.77 % (20147)Time elapsed: 0.195 s
% 30.52/5.77 % (20147)Instructions burned: 645 (million)
% 30.52/5.77 % (20147)------------------------------
% 30.52/5.77 % (20147)------------------------------
% 30.52/5.78 % (20151)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_19870 for (2957ds/68Mi)
% 31.09/5.80 % (20150)Instruction limit reached!
% 31.09/5.80 % (20150)------------------------------
% 31.09/5.80 % (20150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.09/5.80 % (20150)Termination reason: Unknown
% 31.09/5.80 % (20150)Termination phase: Saturation
% 31.09/5.80
% 31.09/5.80 % (20150)Memory used [KB]: 7291
% 31.09/5.80 % (20150)Time elapsed: 0.064 s
% 31.09/5.80 % (20150)Instructions burned: 223 (million)
% 31.09/5.80 % (20150)------------------------------
% 31.09/5.80 % (20150)------------------------------
% 31.09/5.80 % (20092)Instruction limit reached!
% 31.09/5.80 % (20092)------------------------------
% 31.09/5.80 % (20092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.09/5.80 % (20092)Termination reason: Unknown
% 31.09/5.80 % (20092)Termination phase: Saturation
% 31.09/5.80
% 31.09/5.80 % (20092)Memory used [KB]: 16119
% 31.09/5.80 % (20092)Time elapsed: 2.542 s
% 31.09/5.80 % (20092)Instructions burned: 8251 (million)
% 31.09/5.80 % (20092)------------------------------
% 31.09/5.80 % (20092)------------------------------
% 31.09/5.80 % (20151)Instruction limit reached!
% 31.09/5.80 % (20151)------------------------------
% 31.09/5.80 % (20151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.09/5.80 % (20151)Termination reason: Unknown
% 31.09/5.80 % (20151)Termination phase: Saturation
% 31.09/5.80
% 31.09/5.80 % (20151)Memory used [KB]: 1918
% 31.09/5.80 % (20151)Time elapsed: 0.022 s
% 31.09/5.80 % (20151)Instructions burned: 70 (million)
% 31.09/5.80 % (20151)------------------------------
% 31.09/5.80 % (20151)------------------------------
% 31.09/5.81 % (20152)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=454:si=on:rtra=on_0 on DTF2THF_19870 for (2957ds/454Mi)
% 31.09/5.81 % (20153)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_19870 for (2957ds/360Mi)
% 31.09/5.81 % (20154)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_19870 for (2957ds/157Mi)
% 31.09/5.85 % (20154)Instruction limit reached!
% 31.09/5.85 % (20154)------------------------------
% 31.09/5.85 % (20154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.09/5.85 % (20154)Termination reason: Unknown
% 31.09/5.85 % (20154)Termination phase: Saturation
% 31.09/5.85
% 31.09/5.85 % (20154)Memory used [KB]: 6780
% 31.09/5.85 % (20154)Time elapsed: 0.043 s
% 31.09/5.85 % (20154)Instructions burned: 158 (million)
% 31.09/5.85 % (20154)------------------------------
% 31.09/5.85 % (20154)------------------------------
% 31.09/5.86 % (20155)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_19870 for (2956ds/5061Mi)
% 31.09/5.87 % (20146)Instruction limit reached!
% 31.09/5.87 % (20146)------------------------------
% 31.09/5.87 % (20146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.09/5.87 % (20146)Termination reason: Unknown
% 31.09/5.87 % (20146)Termination phase: Saturation
% 31.09/5.87
% 31.09/5.87 % (20146)Memory used [KB]: 8699
% 31.09/5.87 % (20146)Time elapsed: 0.361 s
% 31.09/5.87 % (20146)Instructions burned: 1176 (million)
% 31.09/5.87 % (20146)------------------------------
% 31.09/5.87 % (20146)------------------------------
% 31.09/5.88 % (20156)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_19870 for (2956ds/2401Mi)
% 31.63/5.91 % (20153)Instruction limit reached!
% 31.63/5.91 % (20153)------------------------------
% 31.63/5.91 % (20153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.63/5.91 % (20153)Termination reason: Unknown
% 31.63/5.91 % (20153)Termination phase: Saturation
% 31.63/5.91
% 31.63/5.91 % (20153)Memory used [KB]: 7931
% 31.63/5.91 % (20153)Time elapsed: 0.104 s
% 31.63/5.91 % (20153)Instructions burned: 361 (million)
% 31.63/5.91 % (20153)------------------------------
% 31.63/5.91 % (20153)------------------------------
% 31.63/5.92 % (20157)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_19870 for (2956ds/5798Mi)
% 31.63/5.94 % (20152)Instruction limit reached!
% 31.63/5.94 % (20152)------------------------------
% 31.63/5.94 % (20152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.63/5.94 % (20152)Termination reason: Unknown
% 31.63/5.94 % (20152)Termination phase: Saturation
% 31.63/5.94
% 31.63/5.94 % (20152)Memory used [KB]: 12792
% 31.63/5.94 % (20152)Time elapsed: 0.133 s
% 31.63/5.94 % (20152)Instructions burned: 454 (million)
% 31.63/5.94 % (20152)------------------------------
% 31.63/5.94 % (20152)------------------------------
% 31.63/5.95 % (20158)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_19870 for (2956ds/346Mi)
% 31.63/5.96 % (20149)Instruction limit reached!
% 31.63/5.96 % (20149)------------------------------
% 31.63/5.96 % (20149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.63/5.96 % (20149)Termination reason: Unknown
% 31.63/5.96 % (20149)Termination phase: Saturation
% 31.63/5.96
% 31.63/5.96 % (20149)Memory used [KB]: 9083
% 31.63/5.96 % (20149)Time elapsed: 0.311 s
% 31.63/5.96 % (20149)Instructions burned: 1046 (million)
% 31.63/5.96 % (20149)------------------------------
% 31.63/5.96 % (20149)------------------------------
% 31.63/5.97 % (20159)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_19870 for (2955ds/1321Mi)
% 33.97/6.02 % (20148)Instruction limit reached!
% 33.97/6.02 % (20148)------------------------------
% 33.97/6.02 % (20148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.97/6.02 % (20148)Termination reason: Unknown
% 33.97/6.02 % (20148)Termination phase: Saturation
% 33.97/6.02
% 33.97/6.02 % (20148)Memory used [KB]: 9083
% 33.97/6.02 % (20148)Time elapsed: 0.372 s
% 33.97/6.02 % (20148)Instructions burned: 1201 (million)
% 33.97/6.02 % (20148)------------------------------
% 33.97/6.02 % (20148)------------------------------
% 33.97/6.03 % (20160)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_19870 for (2955ds/1312Mi)
% 33.97/6.06 % (20158)Instruction limit reached!
% 33.97/6.06 % (20158)------------------------------
% 33.97/6.06 % (20158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.97/6.06 % (20158)Termination reason: Unknown
% 33.97/6.06 % (20158)Termination phase: Saturation
% 33.97/6.06
% 33.97/6.06 % (20158)Memory used [KB]: 7675
% 33.97/6.06 % (20158)Time elapsed: 0.109 s
% 33.97/6.06 % (20158)Instructions burned: 347 (million)
% 33.97/6.06 % (20158)------------------------------
% 33.97/6.06 % (20158)------------------------------
% 33.97/6.07 % (20161)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_19870 for (2954ds/672Mi)
% 34.96/6.29 % (20161)Instruction limit reached!
% 34.96/6.29 % (20161)------------------------------
% 34.96/6.29 % (20161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.96/6.29 % (20161)Termination reason: Unknown
% 34.96/6.29 % (20161)Termination phase: Saturation
% 34.96/6.29
% 34.96/6.29 % (20161)Memory used [KB]: 8315
% 34.96/6.29 % (20161)Time elapsed: 0.222 s
% 34.96/6.29 % (20161)Instructions burned: 672 (million)
% 34.96/6.29 % (20161)------------------------------
% 34.96/6.29 % (20161)------------------------------
% 35.69/6.31 % (20162)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_19870 for (2952ds/1897Mi)
% 35.69/6.36 % (20159)Instruction limit reached!
% 35.69/6.36 % (20159)------------------------------
% 35.69/6.36 % (20159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.69/6.36 % (20159)Termination reason: Unknown
% 35.69/6.36 % (20159)Termination phase: Saturation
% 35.69/6.36
% 35.69/6.36 % (20159)Memory used [KB]: 3582
% 35.69/6.36 % (20159)Time elapsed: 0.391 s
% 35.69/6.36 % (20159)Instructions burned: 1323 (million)
% 35.69/6.36 % (20159)------------------------------
% 35.69/6.36 % (20159)------------------------------
% 35.69/6.37 % (20163)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_19870 for (2951ds/1202Mi)
% 36.14/6.43 % (20160)Instruction limit reached!
% 36.14/6.43 % (20160)------------------------------
% 36.14/6.43 % (20160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.14/6.43 % (20160)Termination reason: Unknown
% 36.14/6.43 % (20160)Termination phase: Saturation
% 36.14/6.43
% 36.14/6.43 % (20160)Memory used [KB]: 8827
% 36.14/6.43 % (20160)Time elapsed: 0.403 s
% 36.14/6.43 % (20160)Instructions burned: 1314 (million)
% 36.14/6.43 % (20160)------------------------------
% 36.14/6.43 % (20160)------------------------------
% 36.14/6.44 % (20164)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_19870 for (2951ds/1493Mi)
% 36.14/6.46 % (20164)Refutation not found, incomplete strategy
% 36.14/6.46 % (20164)------------------------------
% 36.14/6.46 % (20164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.14/6.46 % (20164)Termination reason: Refutation not found, incomplete strategy
% 36.14/6.46
% 36.14/6.46
% 36.14/6.46 % (20164)Memory used [KB]: 6780
% 36.14/6.46 % (20164)Time elapsed: 0.025 s
% 36.14/6.46 % (20164)Instructions burned: 84 (million)
% 36.14/6.46 % (20164)------------------------------
% 36.14/6.46 % (20164)------------------------------
% 36.14/6.47 % (20165)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_19870 for (2950ds/7679Mi)
% 37.39/6.61 % (20156)Instruction limit reached!
% 37.39/6.61 % (20156)------------------------------
% 37.39/6.61 % (20156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.39/6.61 % (20156)Termination reason: Unknown
% 37.39/6.61 % (20156)Termination phase: Saturation
% 37.39/6.61
% 37.39/6.61 % (20156)Memory used [KB]: 6780
% 37.39/6.61 % (20156)Time elapsed: 0.732 s
% 37.39/6.61 % (20156)Instructions burned: 2402 (million)
% 37.39/6.61 % (20156)------------------------------
% 37.39/6.61 % (20156)------------------------------
% 37.39/6.62 % (20166)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_19870 for (2949ds/340Mi)
% 37.71/6.73 % (20166)Instruction limit reached!
% 37.71/6.73 % (20166)------------------------------
% 37.71/6.73 % (20166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.71/6.73 % (20166)Termination reason: Unknown
% 37.71/6.73 % (20166)Termination phase: Saturation
% 37.71/6.73
% 37.71/6.73 % (20166)Memory used [KB]: 8443
% 37.71/6.73 % (20166)Time elapsed: 0.108 s
% 37.71/6.73 % (20166)Instructions burned: 341 (million)
% 37.71/6.73 % (20166)------------------------------
% 37.71/6.73 % (20166)------------------------------
% 37.71/6.73 % (20163)Instruction limit reached!
% 37.71/6.73 % (20163)------------------------------
% 37.71/6.73 % (20163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.71/6.73 % (20163)Termination reason: Unknown
% 37.71/6.73 % (20163)Termination phase: Saturation
% 37.71/6.73
% 37.71/6.73 % (20163)Memory used [KB]: 4093
% 37.71/6.73 % (20163)Time elapsed: 0.365 s
% 37.71/6.73 % (20163)Instructions burned: 1202 (million)
% 37.71/6.73 % (20163)------------------------------
% 37.71/6.73 % (20163)------------------------------
% 37.71/6.74 % (20172)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_19870 for (2948ds/3672Mi)
% 37.71/6.74 % (20176)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_19870 for (2948ds/1535Mi)
% 38.50/6.86 % (20162)Instruction limit reached!
% 38.50/6.86 % (20162)------------------------------
% 38.50/6.86 % (20162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.50/6.86 % (20162)Termination reason: Unknown
% 38.50/6.86 % (20162)Termination phase: Saturation
% 38.50/6.86
% 38.50/6.86 % (20162)Memory used [KB]: 8059
% 38.50/6.86 % (20162)Time elapsed: 0.557 s
% 38.50/6.86 % (20162)Instructions burned: 1899 (million)
% 38.50/6.86 % (20162)------------------------------
% 38.50/6.86 % (20162)------------------------------
% 38.50/6.87 % (20227)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_19870 for (2946ds/4637Mi)
% 39.37/7.01 % (20136)Refutation not found, non-redundant clauses discarded% (20136)------------------------------
% 39.37/7.01 % (20136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.37/7.01 % (20136)Termination reason: Refutation not found, non-redundant clauses discarded
% 39.37/7.01
% 39.37/7.01 % (20136)Memory used [KB]: 11513
% 39.37/7.01 % (20136)Time elapsed: 1.943 s
% 39.37/7.01 % (20136)Instructions burned: 6222 (million)
% 39.37/7.01 % (20136)------------------------------
% 39.37/7.01 % (20136)------------------------------
% 39.02/7.02 % (20298)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_19870 for (2945ds/3174Mi)
% 41.57/7.20 % (20176)Instruction limit reached!
% 41.57/7.20 % (20176)------------------------------
% 41.57/7.20 % (20176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.57/7.20 % (20176)Termination reason: Unknown
% 41.57/7.20 % (20176)Termination phase: Saturation
% 41.57/7.20
% 41.57/7.20 % (20176)Memory used [KB]: 10874
% 41.57/7.20 % (20176)Time elapsed: 0.453 s
% 41.57/7.20 % (20176)Instructions burned: 1535 (million)
% 41.57/7.20 % (20176)------------------------------
% 41.57/7.20 % (20176)------------------------------
% 42.07/7.21 % (20369)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_19870 for (2943ds/307Mi)
% 42.07/7.29 % (20369)Instruction limit reached!
% 42.07/7.29 % (20369)------------------------------
% 42.07/7.29 % (20369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.07/7.29 % (20369)Termination reason: Unknown
% 42.07/7.29 % (20369)Termination phase: Saturation
% 42.07/7.29
% 42.07/7.29 % (20369)Memory used [KB]: 7291
% 42.07/7.29 % (20369)Time elapsed: 0.088 s
% 42.07/7.29 % (20369)Instructions burned: 309 (million)
% 42.07/7.29 % (20369)------------------------------
% 42.07/7.29 % (20369)------------------------------
% 42.68/7.30 % (20402)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_19870 for (2942ds/3619Mi)
% 42.68/7.35 % (20155)Instruction limit reached!
% 42.68/7.35 % (20155)------------------------------
% 42.68/7.35 % (20155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.68/7.35 % (20155)Termination reason: Unknown
% 42.68/7.35 % (20155)Termination phase: Saturation
% 42.68/7.35
% 42.68/7.35 % (20155)Memory used [KB]: 10618
% 42.68/7.35 % (20155)Time elapsed: 1.487 s
% 42.68/7.35 % (20155)Instructions burned: 5064 (million)
% 42.68/7.35 % (20155)------------------------------
% 42.68/7.35 % (20155)------------------------------
% 42.68/7.36 % (20403)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_19870 for (2942ds/2325Mi)
% 43.93/7.67 % (20157)Instruction limit reached!
% 43.93/7.67 % (20157)------------------------------
% 43.93/7.67 % (20157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.93/7.67 % (20157)Termination reason: Unknown
% 43.93/7.67 % (20157)Termination phase: Saturation
% 43.93/7.67
% 43.93/7.67 % (20157)Memory used [KB]: 10362
% 43.93/7.67 % (20157)Time elapsed: 1.749 s
% 43.93/7.67 % (20157)Instructions burned: 5800 (million)
% 43.93/7.67 % (20157)------------------------------
% 43.93/7.67 % (20157)------------------------------
% 43.93/7.68 % (20404)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_19870 for (2938ds/2341Mi)
% 44.62/7.87 % (20172)Instruction limit reached!
% 44.62/7.87 % (20172)------------------------------
% 44.62/7.87 % (20172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.62/7.87 % (20172)Termination reason: Unknown
% 44.62/7.87 % (20172)Termination phase: Saturation
% 44.62/7.87
% 44.62/7.87 % (20172)Memory used [KB]: 12153
% 44.62/7.87 % (20172)Time elapsed: 1.132 s
% 44.62/7.87 % (20172)Instructions burned: 3673 (million)
% 44.62/7.87 % (20172)------------------------------
% 44.62/7.87 % (20172)------------------------------
% 44.62/7.88 % (20405)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_19870 for (2936ds/7257Mi)
% 44.62/7.89 % (20405)Refutation not found, incomplete strategy
% 44.62/7.89 % (20405)------------------------------
% 44.62/7.89 % (20405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.62/7.89 % (20405)Termination reason: Refutation not found, incomplete strategy
% 44.62/7.89
% 44.62/7.89
% 44.62/7.89 % (20405)Memory used [KB]: 6652
% 44.62/7.89 % (20405)Time elapsed: 0.019 s
% 44.62/7.89 % (20405)Instructions burned: 60 (million)
% 44.62/7.89 % (20405)------------------------------
% 44.62/7.89 % (20405)------------------------------
% 44.94/7.90 % (20406)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_19870 for (2936ds/3710Mi)
% 44.94/7.99 % (20298)Instruction limit reached!
% 44.94/7.99 % (20298)------------------------------
% 44.94/7.99 % (20298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.94/7.99 % (20298)Termination reason: Unknown
% 44.94/7.99 % (20298)Termination phase: Saturation
% 44.94/7.99
% 44.94/7.99 % (20298)Memory used [KB]: 9083
% 44.94/7.99 % (20298)Time elapsed: 0.968 s
% 44.94/7.99 % (20298)Instructions burned: 3175 (million)
% 44.94/7.99 % (20298)------------------------------
% 44.94/7.99 % (20298)------------------------------
% 44.94/8.00 % (20407)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_19870 for (2935ds/326Mi)
% 47.96/8.07 % (20403)Instruction limit reached!
% 47.96/8.07 % (20403)------------------------------
% 47.96/8.07 % (20403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.96/8.07 % (20403)Termination reason: Unknown
% 47.96/8.07 % (20403)Termination phase: Saturation
% 47.96/8.07
% 47.96/8.07 % (20403)Memory used [KB]: 9978
% 47.96/8.07 % (20403)Time elapsed: 0.733 s
% 47.96/8.07 % (20403)Instructions burned: 2327 (million)
% 47.96/8.07 % (20403)------------------------------
% 47.96/8.07 % (20403)------------------------------
% 47.96/8.08 % (20408)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_19870 for (2934ds/1100Mi)
% 47.96/8.10 % (20407)Instruction limit reached!
% 47.96/8.10 % (20407)------------------------------
% 47.96/8.10 % (20407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.96/8.10 % (20407)Termination reason: Unknown
% 47.96/8.10 % (20407)Termination phase: Saturation
% 47.96/8.10
% 47.96/8.10 % (20407)Memory used [KB]: 7036
% 47.96/8.10 % (20407)Time elapsed: 0.130 s
% 47.96/8.10 % (20407)Instructions burned: 326 (million)
% 47.96/8.10 % (20407)------------------------------
% 47.96/8.10 % (20407)------------------------------
% 47.96/8.11 % (20409)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_19870 for (2934ds/406Mi)
% 49.05/8.24 % (20409)Instruction limit reached!
% 49.05/8.24 % (20409)------------------------------
% 49.05/8.24 % (20409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.05/8.24 % (20409)Termination reason: Unknown
% 49.05/8.24 % (20409)Termination phase: Saturation
% 49.05/8.24
% 49.05/8.24 % (20409)Memory used [KB]: 7931
% 49.05/8.24 % (20409)Time elapsed: 0.131 s
% 49.05/8.24 % (20409)Instructions burned: 408 (million)
% 49.05/8.24 % (20409)------------------------------
% 49.05/8.24 % (20409)------------------------------
% 49.05/8.25 % (20410)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_19870 for (2932ds/1871Mi)
% 49.69/8.36 % (20227)Instruction limit reached!
% 49.69/8.36 % (20227)------------------------------
% 49.69/8.36 % (20227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.36 % (20227)Termination reason: Unknown
% 49.69/8.36 % (20227)Termination phase: Saturation
% 49.69/8.36
% 49.69/8.36 % (20227)Memory used [KB]: 13304
% 49.69/8.36 % (20227)Time elapsed: 1.512 s
% 49.69/8.36 % (20227)Instructions burned: 4637 (million)
% 49.69/8.36 % (20227)------------------------------
% 49.69/8.36 % (20227)------------------------------
% 49.69/8.37 % (20402)Instruction limit reached!
% 49.69/8.37 % (20402)------------------------------
% 49.69/8.37 % (20402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.69/8.37 % (20402)Termination reason: Unknown
% 49.69/8.37 % (20402)Termination phase: Saturation
% 49.69/8.37
% 49.69/8.37 % (20402)Memory used [KB]: 8059
% 49.69/8.37 % (20402)Time elapsed: 1.084 s
% 49.69/8.37 % (20402)Instructions burned: 3621 (million)
% 49.69/8.37 % (20402)------------------------------
% 49.69/8.37 % (20402)------------------------------
% 49.69/8.37 % (20411)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_19870 for (2931ds/1194Mi)
% 49.69/8.37 % (20412)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_19870 for (2931ds/474Mi)
% 50.16/8.40 % (20404)Instruction limit reached!
% 50.16/8.40 % (20404)------------------------------
% 50.16/8.40 % (20404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.16/8.40 % (20404)Termination reason: Unknown
% 50.16/8.40 % (20404)Termination phase: Saturation
% 50.16/8.40
% 50.16/8.40 % (20404)Memory used [KB]: 8699
% 50.16/8.40 % (20404)Time elapsed: 0.742 s
% 50.16/8.40 % (20404)Instructions burned: 2341 (million)
% 50.16/8.40 % (20404)------------------------------
% 50.16/8.40 % (20404)------------------------------
% 50.16/8.41 % (20413)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_19870 for (2931ds/3115Mi)
% 50.16/8.42 % (20408)Instruction limit reached!
% 50.16/8.42 % (20408)------------------------------
% 50.16/8.42 % (20408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.16/8.42 % (20408)Termination reason: Unknown
% 50.16/8.42 % (20408)Termination phase: Saturation
% 50.16/8.42
% 50.16/8.42 % (20408)Memory used [KB]: 9850
% 50.16/8.42 % (20408)Time elapsed: 0.345 s
% 50.16/8.42 % (20408)Instructions burned: 1102 (million)
% 50.16/8.42 % (20408)------------------------------
% 50.16/8.42 % (20408)------------------------------
% 50.16/8.43 % (20414)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_19870 for (2931ds/831Mi)
% 50.71/8.52 % (20412)Instruction limit reached!
% 50.71/8.52 % (20412)------------------------------
% 50.71/8.52 % (20412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.71/8.52 % (20412)Termination reason: Unknown
% 50.71/8.52 % (20412)Termination phase: Saturation
% 50.71/8.52
% 50.71/8.52 % (20412)Memory used [KB]: 8059
% 50.71/8.52 % (20412)Time elapsed: 0.146 s
% 50.71/8.52 % (20412)Instructions burned: 476 (million)
% 50.71/8.52 % (20412)------------------------------
% 50.71/8.52 % (20412)------------------------------
% 50.71/8.53 % (20415)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_19870 for (2930ds/1188Mi)
% 51.07/8.69 % (20414)Instruction limit reached!
% 51.07/8.69 % (20414)------------------------------
% 51.07/8.69 % (20414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.07/8.69 % (20414)Termination reason: Unknown
% 51.07/8.69 % (20414)Termination phase: Saturation
% 51.07/8.69
% 51.07/8.69 % (20414)Memory used [KB]: 7931
% 51.07/8.69 % (20414)Time elapsed: 0.258 s
% 51.07/8.69 % (20414)Instructions burned: 831 (million)
% 51.07/8.69 % (20414)------------------------------
% 51.07/8.69 % (20414)------------------------------
% 51.54/8.70 % (20416)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_19870 for (2928ds/2868Mi)
% 51.54/8.74 % (20165)Instruction limit reached!
% 51.54/8.74 % (20165)------------------------------
% 51.54/8.74 % (20165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.54/8.74 % (20165)Termination reason: Unknown
% 51.54/8.74 % (20165)Termination phase: Saturation
% 51.54/8.74
% 51.54/8.74 % (20165)Memory used [KB]: 13560
% 51.54/8.74 % (20165)Time elapsed: 2.271 s
% 51.54/8.74 % (20165)Instructions burned: 7679 (million)
% 51.54/8.74 % (20165)------------------------------
% 51.54/8.74 % (20165)------------------------------
% 51.54/8.75 % (20417)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_19870 for (2927ds/1516Mi)
% 51.54/8.76 % (20411)Instruction limit reached!
% 51.54/8.76 % (20411)------------------------------
% 51.54/8.76 % (20411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.54/8.76 % (20411)Termination reason: Unknown
% 51.54/8.76 % (20411)Termination phase: Saturation
% 51.54/8.76
% 51.54/8.76 % (20411)Memory used [KB]: 8827
% 51.54/8.76 % (20411)Time elapsed: 0.384 s
% 51.54/8.76 % (20411)Instructions burned: 1196 (million)
% 51.54/8.76 % (20411)------------------------------
% 51.54/8.76 % (20411)------------------------------
% 51.54/8.76 % (20416)Refutation not found, incomplete strategy
% 51.54/8.76 % (20416)------------------------------
% 51.54/8.76 % (20416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.54/8.76 % (20416)Termination reason: Refutation not found, incomplete strategy
% 51.54/8.76
% 51.54/8.76
% 51.54/8.76 % (20416)Memory used [KB]: 7675
% 51.54/8.76 % (20416)Time elapsed: 0.059 s
% 51.54/8.76 % (20416)Instructions burned: 210 (million)
% 51.54/8.76 % (20416)------------------------------
% 51.54/8.76 % (20416)------------------------------
% 51.54/8.77 % (20418)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_19870 for (2927ds/2321Mi)
% 51.54/8.77 % (20419)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_19870 for (2927ds/2812Mi)
% 52.17/8.83 % (20418)Refutation not found, incomplete strategy
% 52.17/8.83 % (20418)------------------------------
% 52.17/8.83 % (20418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.17/8.83 % (20418)Termination reason: Refutation not found, incomplete strategy
% 52.17/8.83
% 52.17/8.83
% 52.17/8.83 % (20418)Memory used [KB]: 7547
% 52.17/8.83 % (20418)Time elapsed: 0.059 s
% 52.17/8.83 % (20418)Instructions burned: 214 (million)
% 52.17/8.83 % (20418)------------------------------
% 52.17/8.83 % (20418)------------------------------
% 52.17/8.84 % (20420)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_19870 for (2927ds/4604Mi)
% 52.17/8.84 % (20410)Instruction limit reached!
% 52.17/8.84 % (20410)------------------------------
% 52.17/8.84 % (20410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.17/8.84 % (20410)Termination reason: Unknown
% 52.17/8.84 % (20410)Termination phase: Saturation
% 52.17/8.84
% 52.17/8.84 % (20410)Memory used [KB]: 12537
% 52.17/8.84 % (20410)Time elapsed: 0.595 s
% 52.17/8.84 % (20410)Instructions burned: 1873 (million)
% 52.17/8.84 % (20410)------------------------------
% 52.17/8.84 % (20410)------------------------------
% 52.17/8.85 % (20421)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_19870 for (2926ds/2678Mi)
% 52.94/8.90 % (20415)Instruction limit reached!
% 52.94/8.90 % (20415)------------------------------
% 52.94/8.90 % (20415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.94/8.90 % (20415)Termination reason: Unknown
% 52.94/8.90 % (20415)Termination phase: Saturation
% 52.94/8.90
% 52.94/8.90 % (20415)Memory used [KB]: 9978
% 52.94/8.90 % (20415)Time elapsed: 0.374 s
% 52.94/8.90 % (20415)Instructions burned: 1190 (million)
% 52.94/8.90 % (20415)------------------------------
% 52.94/8.90 % (20415)------------------------------
% 52.94/8.91 % (20422)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_19870 for (2926ds/643Mi)
% 55.06/9.08 % (20406)Instruction limit reached!
% 55.06/9.08 % (20406)------------------------------
% 55.06/9.08 % (20406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.06/9.08 % (20406)Termination reason: Unknown
% 55.06/9.08 % (20406)Termination phase: Saturation
% 55.06/9.08
% 55.06/9.08 % (20406)Memory used [KB]: 15735
% 55.06/9.08 % (20406)Time elapsed: 1.202 s
% 55.06/9.08 % (20406)Instructions burned: 3710 (million)
% 55.06/9.08 % (20406)------------------------------
% 55.06/9.08 % (20406)------------------------------
% 55.06/9.09 % (20423)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_19870 for (2924ds/458Mi)
% 55.06/9.11 % (20422)Instruction limit reached!
% 55.06/9.11 % (20422)------------------------------
% 55.06/9.11 % (20422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.06/9.11 % (20422)Termination reason: Unknown
% 55.06/9.11 % (20422)Termination phase: Saturation
% 55.06/9.11
% 55.06/9.11 % (20422)Memory used [KB]: 8443
% 55.06/9.11 % (20422)Time elapsed: 0.201 s
% 55.06/9.11 % (20422)Instructions burned: 644 (million)
% 55.06/9.11 % (20422)------------------------------
% 55.06/9.11 % (20422)------------------------------
% 55.06/9.12 % (20424)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_19870 for (2924ds/2546Mi)
% 56.12/9.22 % (20417)Instruction limit reached!
% 56.12/9.22 % (20417)------------------------------
% 56.12/9.22 % (20417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.12/9.22 % (20417)Termination reason: Unknown
% 56.12/9.22 % (20417)Termination phase: Saturation
% 56.12/9.22
% 56.12/9.22 % (20417)Memory used [KB]: 9083
% 56.12/9.22 % (20417)Time elapsed: 0.466 s
% 56.12/9.22 % (20417)Instructions burned: 1516 (million)
% 56.12/9.22 % (20417)------------------------------
% 56.12/9.22 % (20417)------------------------------
% 56.12/9.23 % (20423)Instruction limit reached!
% 56.12/9.23 % (20423)------------------------------
% 56.12/9.23 % (20423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.12/9.23 % (20423)Termination reason: Unknown
% 56.12/9.23 % (20423)Termination phase: Saturation
% 56.12/9.23
% 56.12/9.23 % (20423)Memory used [KB]: 7803
% 56.12/9.23 % (20423)Time elapsed: 0.133 s
% 56.12/9.23 % (20423)Instructions burned: 460 (million)
% 56.12/9.23 % (20423)------------------------------
% 56.12/9.23 % (20423)------------------------------
% 56.12/9.23 % (20425)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_19870 for (2923ds/1432Mi)
% 56.12/9.23 % (20426)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_19870 for (2923ds/386Mi)
% 56.67/9.32 % (20413)Instruction limit reached!
% 56.67/9.32 % (20413)------------------------------
% 56.67/9.32 % (20413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.67/9.32 % (20413)Termination reason: Unknown
% 56.67/9.32 % (20413)Termination phase: Saturation
% 56.67/9.32
% 56.67/9.32 % (20413)Memory used [KB]: 12920
% 56.67/9.32 % (20413)Time elapsed: 0.910 s
% 56.67/9.32 % (20413)Instructions burned: 3116 (million)
% 56.67/9.32 % (20413)------------------------------
% 56.67/9.32 % (20413)------------------------------
% 56.67/9.33 % (20427)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_19870 for (2922ds/360Mi)
% 56.67/9.35 % (20426)Instruction limit reached!
% 56.67/9.35 % (20426)------------------------------
% 56.67/9.35 % (20426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.67/9.35 % (20426)Termination reason: Unknown
% 56.67/9.35 % (20426)Termination phase: Saturation
% 56.67/9.35
% 56.67/9.35 % (20426)Memory used [KB]: 7931
% 56.67/9.35 % (20426)Time elapsed: 0.137 s
% 56.67/9.35 % (20426)Instructions burned: 388 (million)
% 56.67/9.35 % (20426)------------------------------
% 56.67/9.35 % (20426)------------------------------
% 56.67/9.36 % (20428)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_19870 for (2921ds/5446Mi)
% 57.13/9.44 % (20427)Instruction limit reached!
% 57.13/9.44 % (20427)------------------------------
% 57.13/9.44 % (20427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.13/9.44 % (20427)Termination reason: Unknown
% 57.13/9.44 % (20427)Termination phase: Saturation
% 57.13/9.44
% 57.13/9.44 % (20427)Memory used [KB]: 7931
% 57.13/9.44 % (20427)Time elapsed: 0.108 s
% 57.13/9.44 % (20427)Instructions burned: 361 (million)
% 57.13/9.44 % (20427)------------------------------
% 57.13/9.44 % (20427)------------------------------
% 57.13/9.45 % (20429)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_19870 for (2920ds/2573Mi)
% 57.54/9.57 % (20425)Instruction limit reached!
% 57.54/9.57 % (20425)------------------------------
% 57.54/9.57 % (20425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.54/9.57 % (20425)Termination reason: Unknown
% 57.54/9.57 % (20425)Termination phase: Saturation
% 57.54/9.57
% 57.54/9.57 % (20425)Memory used [KB]: 9466
% 57.54/9.57 % (20425)Time elapsed: 0.363 s
% 57.54/9.57 % (20425)Instructions burned: 1432 (million)
% 57.54/9.57 % (20425)------------------------------
% 57.54/9.57 % (20425)------------------------------
% 57.54/9.58 % (20430)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=2655:si=on:rtra=on_0 on DTF2THF_19870 for (2919ds/2655Mi)
% 58.21/9.68 % (20419)Instruction limit reached!
% 58.21/9.68 % (20419)------------------------------
% 58.21/9.68 % (20419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.21/9.68 % (20419)Termination reason: Unknown
% 58.21/9.68 % (20419)Termination phase: Saturation
% 58.21/9.68
% 58.21/9.68 % (20419)Memory used [KB]: 11513
% 58.21/9.68 % (20419)Time elapsed: 0.909 s
% 58.21/9.68 % (20419)Instructions burned: 2813 (million)
% 58.21/9.68 % (20419)------------------------------
% 58.21/9.68 % (20419)------------------------------
% 58.21/9.69 % (20431)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_19870 for (2918ds/2781Mi)
% 58.49/9.71 % (20421)Instruction limit reached!
% 58.49/9.71 % (20421)------------------------------
% 58.49/9.71 % (20421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.49/9.71 % (20421)Termination reason: Unknown
% 58.49/9.71 % (20421)Termination phase: Saturation
% 58.49/9.71
% 58.49/9.71 % (20421)Memory used [KB]: 11385
% 58.49/9.71 % (20421)Time elapsed: 0.854 s
% 58.49/9.71 % (20421)Instructions burned: 2680 (million)
% 58.49/9.71 % (20421)------------------------------
% 58.49/9.71 % (20421)------------------------------
% 58.49/9.72 % (20432)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_19870 for (2918ds/307Mi)
% 58.61/9.80 % (20432)Instruction limit reached!
% 58.61/9.80 % (20432)------------------------------
% 58.61/9.80 % (20432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.61/9.80 % (20432)Termination reason: Unknown
% 58.61/9.80 % (20432)Termination phase: Saturation
% 58.61/9.80
% 58.61/9.80 % (20432)Memory used [KB]: 7291
% 58.61/9.80 % (20432)Time elapsed: 0.087 s
% 58.61/9.80 % (20432)Instructions burned: 308 (million)
% 58.61/9.80 % (20432)------------------------------
% 58.61/9.80 % (20432)------------------------------
% 58.61/9.81 % (20433)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_19870 for (2917ds/1548Mi)
% 58.81/9.96 % (20424)Refutation not found, non-redundant clauses discarded% (20424)------------------------------
% 58.81/9.96 % (20424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.81/9.96 % (20424)Termination reason: Refutation not found, non-redundant clauses discarded
% 58.81/9.96
% 58.81/9.96 % (20424)Memory used [KB]: 11001
% 58.81/9.96 % (20424)Time elapsed: 0.862 s
% 58.81/9.96 % (20424)Instructions burned: 2540 (million)
% 58.81/9.96 % (20424)------------------------------
% 58.81/9.96 % (20424)------------------------------
% 58.81/9.97 % (20434)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_19870 for (2915ds/5214Mi)
% 63.30/10.21 % (20429)Instruction limit reached!
% 63.30/10.21 % (20429)------------------------------
% 63.30/10.21 % (20429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.30/10.21 % (20429)Termination reason: Unknown
% 63.30/10.21 % (20429)Termination phase: Saturation
% 63.30/10.21
% 63.30/10.21 % (20429)Memory used [KB]: 12409
% 63.30/10.21 % (20429)Time elapsed: 0.762 s
% 63.30/10.21 % (20429)Instructions burned: 2575 (million)
% 63.30/10.21 % (20429)------------------------------
% 63.30/10.21 % (20429)------------------------------
% 63.30/10.22 % (20435)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_19870 for (2913ds/3201Mi)
% 63.30/10.24 % (20420)Instruction limit reached!
% 63.30/10.24 % (20420)------------------------------
% 63.30/10.24 % (20420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.30/10.24 % (20420)Termination reason: Unknown
% 63.30/10.24 % (20420)Termination phase: Saturation
% 63.30/10.24
% 63.30/10.24 % (20420)Memory used [KB]: 12153
% 63.30/10.24 % (20420)Time elapsed: 1.408 s
% 63.30/10.24 % (20420)Instructions burned: 4604 (million)
% 63.30/10.24 % (20420)------------------------------
% 63.30/10.24 % (20420)------------------------------
% 63.30/10.25 % (20436)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=454:si=on:rtra=on_0 on DTF2THF_19870 for (2912ds/454Mi)
% 63.30/10.29 % (20433)Instruction limit reached!
% 63.30/10.29 % (20433)------------------------------
% 63.30/10.29 % (20433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.30/10.29 % (20433)Termination reason: Unknown
% 63.30/10.29 % (20433)Termination phase: Saturation
% 63.30/10.29
% 63.30/10.29 % (20433)Memory used [KB]: 7675
% 63.30/10.29 % (20433)Time elapsed: 0.476 s
% 63.30/10.29 % (20433)Instructions burned: 1550 (million)
% 63.30/10.29 % (20433)------------------------------
% 63.30/10.29 % (20433)------------------------------
% 63.87/10.30 % (20437)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_19870 for (2912ds/3049Mi)
% 63.87/10.36 % (20430)Instruction limit reached!
% 63.87/10.36 % (20430)------------------------------
% 63.87/10.36 % (20430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.87/10.36 % (20430)Termination reason: Unknown
% 63.87/10.36 % (20430)Termination phase: Saturation
% 63.87/10.36
% 63.87/10.36 % (20430)Memory used [KB]: 12025
% 63.87/10.36 % (20430)Time elapsed: 0.786 s
% 63.87/10.36 % (20430)Instructions burned: 2655 (million)
% 63.87/10.36 % (20430)------------------------------
% 63.87/10.36 % (20430)------------------------------
% 63.87/10.37 % (20438)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_19870 for (2911ds/7311Mi)
% 63.87/10.39 % (20436)Instruction limit reached!
% 63.87/10.39 % (20436)------------------------------
% 63.87/10.39 % (20436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.87/10.39 % (20436)Termination reason: Unknown
% 63.87/10.39 % (20436)Termination phase: Saturation
% 63.87/10.39
% 63.87/10.39 % (20436)Memory used [KB]: 12792
% 63.87/10.39 % (20436)Time elapsed: 0.136 s
% 63.87/10.39 % (20436)Instructions burned: 456 (million)
% 63.87/10.39 % (20436)------------------------------
% 63.87/10.39 % (20436)------------------------------
% 64.39/10.40 % (20439)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_19870 for (2911ds/6804Mi)
% 64.70/10.56 % (20431)Instruction limit reached!
% 64.70/10.56 % (20431)------------------------------
% 64.70/10.56 % (20431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.70/10.56 % (20431)Termination reason: Unknown
% 64.70/10.56 % (20431)Termination phase: Saturation
% 64.70/10.56
% 64.70/10.56 % (20431)Memory used [KB]: 4989
% 64.70/10.56 % (20431)Time elapsed: 0.874 s
% 64.70/10.56 % (20431)Instructions burned: 2783 (million)
% 64.70/10.56 % (20431)------------------------------
% 64.70/10.56 % (20431)------------------------------
% 64.70/10.57 % (20440)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_19870 for (2909ds/1683Mi)
% 69.12/11.07 % (20440)Instruction limit reached!
% 69.12/11.07 % (20440)------------------------------
% 69.12/11.07 % (20440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.12/11.07 % (20440)Termination reason: Unknown
% 69.12/11.07 % (20440)Termination phase: Saturation
% 69.12/11.07
% 69.12/11.07 % (20440)Memory used [KB]: 9978
% 69.12/11.07 % (20440)Time elapsed: 0.497 s
% 69.12/11.07 % (20440)Instructions burned: 1683 (million)
% 69.12/11.07 % (20440)------------------------------
% 69.12/11.07 % (20440)------------------------------
% 69.12/11.08 % (20441)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_19870 for (2904ds/4688Mi)
% 69.78/11.13 % (20428)Instruction limit reached!
% 69.78/11.13 % (20428)------------------------------
% 69.78/11.13 % (20428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.78/11.13 % (20428)Termination reason: Unknown
% 69.78/11.13 % (20428)Termination phase: Saturation
% 69.78/11.13
% 69.78/11.13 % (20428)Memory used [KB]: 17398
% 69.78/11.13 % (20428)Time elapsed: 1.770 s
% 69.78/11.13 % (20428)Instructions burned: 5448 (million)
% 69.78/11.13 % (20428)------------------------------
% 69.78/11.13 % (20428)------------------------------
% 69.78/11.14 % (20442)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_19870 for (2904ds/2207Mi)
% 69.78/11.18 % (20435)Instruction limit reached!
% 69.78/11.18 % (20435)------------------------------
% 69.78/11.18 % (20435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.78/11.18 % (20435)Termination reason: Unknown
% 69.78/11.18 % (20435)Termination phase: Saturation
% 69.78/11.18
% 69.78/11.18 % (20435)Memory used [KB]: 11257
% 69.78/11.18 % (20435)Time elapsed: 0.961 s
% 69.78/11.18 % (20435)Instructions burned: 3203 (million)
% 69.78/11.18 % (20435)------------------------------
% 69.78/11.18 % (20435)------------------------------
% 69.78/11.19 % (20443)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=8216:si=on:rtra=on_0 on DTF2THF_19870 for (2903ds/8216Mi)
% 70.13/11.22 % (20437)Instruction limit reached!
% 70.13/11.22 % (20437)------------------------------
% 70.13/11.22 % (20437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.13/11.22 % (20437)Termination reason: Unknown
% 70.13/11.22 % (20437)Termination phase: Saturation
% 70.13/11.22
% 70.13/11.22 % (20437)Memory used [KB]: 9466
% 70.13/11.22 % (20437)Time elapsed: 0.925 s
% 70.13/11.22 % (20437)Instructions burned: 3051 (million)
% 70.13/11.22 % (20437)------------------------------
% 70.13/11.22 % (20437)------------------------------
% 70.13/11.23 % (20444)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_19870 for (2903ds/430Mi)
% 70.48/11.36 % (20444)Instruction limit reached!
% 70.48/11.36 % (20444)------------------------------
% 70.48/11.36 % (20444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.48/11.36 % (20444)Termination reason: Unknown
% 70.48/11.36 % (20444)Termination phase: Saturation
% 70.48/11.36
% 70.48/11.36 % (20444)Memory used [KB]: 7931
% 70.48/11.36 % (20444)Time elapsed: 0.125 s
% 70.48/11.36 % (20444)Instructions burned: 432 (million)
% 70.48/11.36 % (20444)------------------------------
% 70.48/11.36 % (20444)------------------------------
% 70.48/11.37 % (20445)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_19870 for (2901ds/2012Mi)
% 71.21/11.57 % (20434)Instruction limit reached!
% 71.21/11.57 % (20434)------------------------------
% 71.21/11.57 % (20434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.21/11.57 % (20434)Termination reason: Unknown
% 71.21/11.57 % (20434)Termination phase: Saturation
% 71.21/11.57
% 71.21/11.57 % (20434)Memory used [KB]: 15351
% 71.21/11.57 % (20434)Time elapsed: 1.598 s
% 71.21/11.57 % (20434)Instructions burned: 5216 (million)
% 71.21/11.57 % (20434)------------------------------
% 71.21/11.57 % (20434)------------------------------
% 71.21/11.58 % (20446)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_19870 for (2899ds/631Mi)
% 71.70/11.77 % (20446)Instruction limit reached!
% 71.70/11.77 % (20446)------------------------------
% 71.70/11.77 % (20446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.70/11.77 % (20446)Termination reason: Unknown
% 71.70/11.77 % (20446)Termination phase: Saturation
% 71.70/11.77
% 71.70/11.77 % (20446)Memory used [KB]: 8315
% 71.70/11.77 % (20446)Time elapsed: 0.189 s
% 71.70/11.77 % (20446)Instructions burned: 631 (million)
% 71.70/11.77 % (20446)------------------------------
% 71.70/11.77 % (20446)------------------------------
% 71.70/11.78 % (20447)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_19870 for (2897ds/8785Mi)
% 72.10/11.83 % (20442)Instruction limit reached!
% 72.10/11.83 % (20442)------------------------------
% 72.10/11.83 % (20442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.10/11.83 % (20442)Termination reason: Unknown
% 72.10/11.83 % (20442)Termination phase: Saturation
% 72.10/11.83
% 72.10/11.83 % (20442)Memory used [KB]: 11001
% 72.10/11.83 % (20442)Time elapsed: 0.700 s
% 72.10/11.83 % (20442)Instructions burned: 2207 (million)
% 72.10/11.83 % (20442)------------------------------
% 72.10/11.83 % (20442)------------------------------
% 72.10/11.84 % (20448)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_19870 for (2897ds/739Mi)
% 73.01/11.99 % (20445)Instruction limit reached!
% 73.01/11.99 % (20445)------------------------------
% 73.01/11.99 % (20445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.01/11.99 % (20445)Termination reason: Unknown
% 73.01/11.99 % (20445)Termination phase: Saturation
% 73.01/11.99
% 73.01/11.99 % (20445)Memory used [KB]: 17142
% 73.01/11.99 % (20445)Time elapsed: 0.628 s
% 73.01/11.99 % (20445)Instructions burned: 2012 (million)
% 73.01/11.99 % (20445)------------------------------
% 73.01/11.99 % (20445)------------------------------
% 73.01/12.00 % (20449)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_19870 for (2895ds/5473Mi)
% 76.13/12.08 % (20448)Instruction limit reached!
% 76.13/12.08 % (20448)------------------------------
% 76.13/12.08 % (20448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.13/12.08 % (20448)Termination reason: Unknown
% 76.13/12.08 % (20448)Termination phase: Saturation
% 76.13/12.08
% 76.13/12.08 % (20448)Memory used [KB]: 8059
% 76.13/12.08 % (20448)Time elapsed: 0.234 s
% 76.13/12.08 % (20448)Instructions burned: 741 (million)
% 76.13/12.08 % (20448)------------------------------
% 76.13/12.08 % (20448)------------------------------
% 76.13/12.09 % (20450)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_19870 for (2894ds/43570Mi)
% 76.13/12.10 % (20450)Refutation not found, incomplete strategy
% 76.13/12.10 % (20450)------------------------------
% 76.13/12.10 % (20450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.13/12.10 % (20450)Termination reason: Refutation not found, incomplete strategy
% 76.13/12.10
% 76.13/12.10
% 76.13/12.10 % (20450)Memory used [KB]: 6524
% 76.13/12.10 % (20450)Time elapsed: 0.018 s
% 76.13/12.10 % (20450)Instructions burned: 57 (million)
% 76.13/12.10 % (20450)------------------------------
% 76.13/12.10 % (20450)------------------------------
% 76.13/12.11 % (20451)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_19870 for (2894ds/8382Mi)
% 77.26/12.28 % (20439)Instruction limit reached!
% 77.26/12.28 % (20439)------------------------------
% 77.26/12.28 % (20439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.26/12.28 % (20439)Termination reason: Unknown
% 77.26/12.28 % (20439)Termination phase: Saturation
% 77.26/12.28
% 77.26/12.28 % (20439)Memory used [KB]: 8443
% 77.26/12.28 % (20439)Time elapsed: 1.888 s
% 77.26/12.28 % (20439)Instructions burned: 6806 (million)
% 77.26/12.28 % (20439)------------------------------
% 77.26/12.28 % (20439)------------------------------
% 77.26/12.29 % (20452)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_19870 for (2892ds/407Mi)
% 78.37/12.42 % (20452)Instruction limit reached!
% 78.37/12.42 % (20452)------------------------------
% 78.37/12.42 % (20452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.37/12.42 % (20452)Termination reason: Unknown
% 78.37/12.42 % (20452)Termination phase: Saturation
% 78.37/12.42
% 78.37/12.42 % (20452)Memory used [KB]: 8187
% 78.37/12.42 % (20452)Time elapsed: 0.127 s
% 78.37/12.42 % (20452)Instructions burned: 410 (million)
% 78.37/12.42 % (20452)------------------------------
% 78.37/12.42 % (20452)------------------------------
% 78.37/12.43 % (20453)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_19870 for (2891ds/2971Mi)
% 78.37/12.49 % (20453)Refutation not found, incomplete strategy
% 78.37/12.49 % (20453)------------------------------
% 78.37/12.49 % (20453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.37/12.49 % (20453)Termination reason: Refutation not found, incomplete strategy
% 78.37/12.49
% 78.37/12.49
% 78.37/12.49 % (20453)Memory used [KB]: 7675
% 78.37/12.49 % (20453)Time elapsed: 0.058 s
% 78.37/12.49 % (20453)Instructions burned: 206 (million)
% 78.37/12.49 % (20453)------------------------------
% 78.37/12.49 % (20453)------------------------------
% 78.37/12.50 % (20454)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_19870 for (2890ds/9822Mi)
% 79.07/12.53 % (20441)Instruction limit reached!
% 79.07/12.53 % (20441)------------------------------
% 79.07/12.53 % (20441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.07/12.53 % (20441)Termination reason: Unknown
% 79.07/12.53 % (20441)Termination phase: Saturation
% 79.07/12.53
% 79.07/12.53 % (20441)Memory used [KB]: 8059
% 79.07/12.53 % (20441)Time elapsed: 1.455 s
% 79.07/12.53 % (20441)Instructions burned: 4690 (million)
% 79.07/12.53 % (20441)------------------------------
% 79.07/12.53 % (20441)------------------------------
% 79.07/12.54 % (20455)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_19870 for (2890ds/8425Mi)
% 79.07/12.57 % (20438)Instruction limit reached!
% 79.07/12.57 % (20438)------------------------------
% 79.07/12.57 % (20438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.07/12.57 % (20438)Termination reason: Unknown
% 79.07/12.57 % (20438)Termination phase: Saturation
% 79.07/12.57
% 79.07/12.57 % (20438)Memory used [KB]: 10490
% 79.07/12.57 % (20438)Time elapsed: 2.199 s
% 79.07/12.57 % (20438)Instructions burned: 7314 (million)
% 79.07/12.57 % (20438)------------------------------
% 79.07/12.57 % (20438)------------------------------
% 79.07/12.58 % (20456)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_19870 for (2889ds/3107Mi)
% 79.50/12.62 % (20456)Refutation not found, incomplete strategy
% 79.50/12.62 % (20456)------------------------------
% 79.50/12.62 % (20456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.50/12.62 % (20456)Termination reason: Refutation not found, incomplete strategy
% 79.50/12.62
% 79.50/12.62
% 79.50/12.62 % (20456)Memory used [KB]: 7164
% 79.50/12.62 % (20456)Time elapsed: 0.038 s
% 79.50/12.62 % (20456)Instructions burned: 118 (million)
% 79.50/12.62 % (20456)------------------------------
% 79.50/12.62 % (20456)------------------------------
% 79.50/12.63 % (20457)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_19870 for (2889ds/7967Mi)
% 79.50/12.68 % (20457)Refutation not found, incomplete strategy
% 79.50/12.68 % (20457)------------------------------
% 79.50/12.68 % (20457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.50/12.68 % (20457)Termination reason: Refutation not found, incomplete strategy
% 79.50/12.68
% 79.50/12.68
% 79.50/12.68 % (20457)Memory used [KB]: 7547
% 79.50/12.68 % (20457)Time elapsed: 0.057 s
% 79.50/12.68 % (20457)Instructions burned: 205 (million)
% 79.50/12.68 % (20457)------------------------------
% 79.50/12.68 % (20457)------------------------------
% 79.50/12.69 % (20458)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_19870 for (2888ds/3629Mi)
% 87.17/13.60 % (20449)Instruction limit reached!
% 87.17/13.60 % (20449)------------------------------
% 87.17/13.60 % (20449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.17/13.60 % (20449)Termination reason: Unknown
% 87.17/13.60 % (20449)Termination phase: Saturation
% 87.17/13.60
% 87.17/13.60 % (20449)Memory used [KB]: 10106
% 87.17/13.60 % (20449)Time elapsed: 1.600 s
% 87.17/13.60 % (20449)Instructions burned: 5474 (million)
% 87.17/13.60 % (20449)------------------------------
% 87.17/13.60 % (20449)------------------------------
% 87.17/13.61 % (20459)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_19870 for (2879ds/939Mi)
% 87.17/13.67 % (20443)Instruction limit reached!
% 87.17/13.67 % (20443)------------------------------
% 87.17/13.67 % (20443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.17/13.67 % (20443)Termination reason: Unknown
% 87.17/13.67 % (20443)Termination phase: Saturation
% 87.17/13.67
% 87.17/13.67 % (20443)Memory used [KB]: 13816
% 87.17/13.67 % (20443)Time elapsed: 2.487 s
% 87.17/13.67 % (20443)Instructions burned: 8217 (million)
% 87.17/13.67 % (20443)------------------------------
% 87.17/13.67 % (20443)------------------------------
% 87.17/13.68 % (20460)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_19870 for (2878ds/1188Mi)
% 87.78/13.79 % (20458)Instruction limit reached!
% 87.78/13.79 % (20458)------------------------------
% 87.78/13.79 % (20458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.78/13.79 % (20458)Termination reason: Unknown
% 87.78/13.79 % (20458)Termination phase: Saturation
% 87.78/13.79
% 87.78/13.79 % (20458)Memory used [KB]: 9850
% 87.78/13.79 % (20458)Time elapsed: 1.099 s
% 87.78/13.79 % (20458)Instructions burned: 3632 (million)
% 87.78/13.79 % (20458)------------------------------
% 87.78/13.79 % (20458)------------------------------
% 88.29/13.80 % (20461)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_19870 for (2877ds/3205Mi)
% 88.29/13.86 % (20459)Instruction limit reached!
% 88.29/13.86 % (20459)------------------------------
% 88.29/13.86 % (20459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.29/13.86 % (20459)Termination reason: Unknown
% 88.29/13.86 % (20459)Termination phase: Saturation
% 88.29/13.86
% 88.29/13.86 % (20459)Memory used [KB]: 7803
% 88.29/13.86 % (20459)Time elapsed: 0.246 s
% 88.29/13.86 % (20459)Instructions burned: 943 (million)
% 88.29/13.86 % (20459)------------------------------
% 88.29/13.86 % (20459)------------------------------
% 88.29/13.87 % (20462)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_19870 for (2876ds/865Mi)
% 90.18/14.05 % (20460)Instruction limit reached!
% 90.18/14.05 % (20460)------------------------------
% 90.18/14.05 % (20460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.18/14.05 % (20460)Termination reason: Unknown
% 90.18/14.05 % (20460)Termination phase: Saturation
% 90.18/14.05
% 90.18/14.05 % (20460)Memory used [KB]: 9978
% 90.18/14.05 % (20460)Time elapsed: 0.372 s
% 90.18/14.05 % (20460)Instructions burned: 1189 (million)
% 90.18/14.05 % (20460)------------------------------
% 90.18/14.05 % (20460)------------------------------
% 90.18/14.06 % (20463)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_19870 for (2874ds/7469Mi)
% 90.82/14.14 % (20462)Instruction limit reached!
% 90.82/14.14 % (20462)------------------------------
% 90.82/14.14 % (20462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.82/14.14 % (20462)Termination reason: Unknown
% 90.82/14.14 % (20462)Termination phase: Saturation
% 90.82/14.14
% 90.82/14.14 % (20462)Memory used [KB]: 8571
% 90.82/14.14 % (20462)Time elapsed: 0.273 s
% 90.82/14.14 % (20462)Instructions burned: 867 (million)
% 90.82/14.14 % (20462)------------------------------
% 90.82/14.14 % (20462)------------------------------
% 90.82/14.15 % (20465)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_19870 for (2874ds/4165Mi)
% 92.19/14.48 % (20447)Instruction limit reached!
% 92.19/14.48 % (20447)------------------------------
% 92.19/14.48 % (20447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.19/14.48 % (20447)Termination reason: Unknown
% 92.19/14.48 % (20447)Termination phase: Saturation
% 92.19/14.48
% 92.19/14.48 % (20447)Memory used [KB]: 15863
% 92.19/14.48 % (20447)Time elapsed: 2.702 s
% 92.19/14.48 % (20447)Instructions burned: 8787 (million)
% 92.19/14.48 % (20447)------------------------------
% 92.19/14.48 % (20447)------------------------------
% 92.19/14.49 % (20565)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_19870 for (2870ds/13468Mi)
% 93.50/14.72 % (20451)Instruction limit reached!
% 93.50/14.72 % (20451)------------------------------
% 93.50/14.72 % (20451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.50/14.72 % (20451)Termination reason: Unknown
% 93.50/14.72 % (20451)Termination phase: Saturation
% 93.50/14.72
% 93.50/14.72 % (20451)Memory used [KB]: 19957
% 93.50/14.72 % (20451)Time elapsed: 2.604 s
% 93.50/14.72 % (20451)Instructions burned: 8383 (million)
% 93.50/14.72 % (20451)------------------------------
% 93.50/14.72 % (20451)------------------------------
% 93.50/14.73 % (20606)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_19870 for (2868ds/2635Mi)
% 93.50/14.79 % (20461)Instruction limit reached!
% 93.50/14.79 % (20461)------------------------------
% 93.50/14.79 % (20461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.50/14.79 % (20461)Termination reason: Unknown
% 93.50/14.79 % (20461)Termination phase: Saturation
% 93.50/14.79
% 93.50/14.79 % (20461)Memory used [KB]: 9850
% 93.50/14.79 % (20461)Time elapsed: 0.990 s
% 93.50/14.79 % (20461)Instructions burned: 3205 (million)
% 93.50/14.79 % (20461)------------------------------
% 93.50/14.79 % (20461)------------------------------
% 93.83/14.80 % (20633)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_19870 for (2867ds/631Mi)
% 94.03/15.00 % (20633)Instruction limit reached!
% 94.03/15.00 % (20633)------------------------------
% 94.03/15.00 % (20633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 94.03/15.00 % (20633)Termination reason: Unknown
% 94.03/15.00 % (20633)Termination phase: Saturation
% 94.03/15.00
% 94.03/15.00 % (20633)Memory used [KB]: 8443
% 94.03/15.00 % (20633)Time elapsed: 0.199 s
% 94.03/15.00 % (20633)Instructions burned: 631 (million)
% 94.03/15.00 % (20633)------------------------------
% 94.03/15.00 % (20633)------------------------------
% 94.03/15.02 % (20710)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_19870 for (2865ds/15557Mi)
% 97.14/15.10 % (20455)Instruction limit reached!
% 97.14/15.10 % (20455)------------------------------
% 97.14/15.10 % (20455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.14/15.10 % (20455)Termination reason: Unknown
% 97.14/15.10 % (20455)Termination phase: Saturation
% 97.14/15.10
% 97.14/15.10 % (20455)Memory used [KB]: 13432
% 97.14/15.10 % (20455)Time elapsed: 2.557 s
% 97.14/15.10 % (20455)Instructions burned: 8425 (million)
% 97.14/15.10 % (20455)------------------------------
% 97.14/15.10 % (20455)------------------------------
% 97.14/15.11 % (20755)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_19870 for (2864ds/2142Mi)
% 98.63/15.36 % (20454)Instruction limit reached!
% 98.63/15.36 % (20454)------------------------------
% 98.63/15.36 % (20454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.63/15.36 % (20454)Termination reason: Unknown
% 98.63/15.36 % (20454)Termination phase: Saturation
% 98.63/15.36
% 98.63/15.36 % (20454)Memory used [KB]: 12792
% 98.63/15.36 % (20454)Time elapsed: 2.862 s
% 98.63/15.36 % (20454)Instructions burned: 9824 (million)
% 98.63/15.36 % (20454)------------------------------
% 98.63/15.36 % (20454)------------------------------
% 98.63/15.37 % (20824)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_19870 for (2861ds/5624Mi)
% 99.50/15.58 % (20465)Instruction limit reached!
% 99.50/15.58 % (20465)------------------------------
% 99.50/15.58 % (20465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.50/15.58 % (20465)Termination reason: Unknown
% 99.50/15.58 % (20465)Termination phase: Saturation
% 99.50/15.58
% 99.50/15.58 % (20465)Memory used [KB]: 14072
% 99.50/15.58 % (20465)Time elapsed: 1.433 s
% 99.50/15.58 % (20465)Instructions burned: 4166 (million)
% 99.50/15.58 % (20465)------------------------------
% 99.50/15.58 % (20465)------------------------------
% 99.89/15.60 % (20832)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_19870 for (2859ds/1665Mi)
% 99.89/15.65 % (20606)Instruction limit reached!
% 99.89/15.65 % (20606)------------------------------
% 99.89/15.65 % (20606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.89/15.65 % (20606)Termination reason: Unknown
% 99.89/15.65 % (20606)Termination phase: Saturation
% 99.89/15.65
% 99.89/15.65 % (20606)Memory used [KB]: 11129
% 99.89/15.65 % (20606)Time elapsed: 0.922 s
% 99.89/15.65 % (20606)Instructions burned: 2635 (million)
% 99.89/15.65 % (20606)------------------------------
% 99.89/15.65 % (20606)------------------------------
% 99.89/15.67 % (20833)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_19870 for (2858ds/64912Mi)
% 100.16/15.70 % (20833)Refutation not found, incomplete strategy
% 100.16/15.70 % (20833)------------------------------
% 100.16/15.70 % (20833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.16/15.70 % (20833)Termination reason: Refutation not found, incomplete strategy
% 100.16/15.70
% 100.16/15.70
% 100.16/15.70 % (20833)Memory used [KB]: 2046
% 100.16/15.70 % (20833)Time elapsed: 0.031 s
% 100.16/15.70 % (20833)Instructions burned: 58 (million)
% 100.16/15.70 % (20833)------------------------------
% 100.16/15.70 % (20833)------------------------------
% 100.16/15.72 % (20834)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_19870 for (2858ds/7801Mi)
% 104.21/16.04 % (20755)Instruction limit reached!
% 104.21/16.04 % (20755)------------------------------
% 104.21/16.04 % (20755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.21/16.04 % (20755)Termination reason: Unknown
% 104.21/16.04 % (20755)Termination phase: Saturation
% 104.21/16.04
% 104.21/16.04 % (20755)Memory used [KB]: 8699
% 104.21/16.04 % (20755)Time elapsed: 0.931 s
% 104.21/16.04 % (20755)Instructions burned: 2142 (million)
% 104.21/16.04 % (20755)------------------------------
% 104.21/16.04 % (20755)------------------------------
% 104.21/16.06 % (20835)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_19870 for (2855ds/15194Mi)
% 106.43/16.44 % (20832)Instruction limit reached!
% 106.43/16.44 % (20832)------------------------------
% 106.43/16.44 % (20832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.43/16.44 % (20832)Termination reason: Unknown
% 106.43/16.44 % (20832)Termination phase: Saturation
% 106.43/16.44
% 106.43/16.44 % (20832)Memory used [KB]: 9850
% 106.43/16.44 % (20832)Time elapsed: 0.844 s
% 106.43/16.44 % (20832)Instructions burned: 1666 (million)
% 106.43/16.44 % (20832)------------------------------
% 106.43/16.44 % (20832)------------------------------
% 106.43/16.46 % (20836)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=6753:si=on:rtra=on_0 on DTF2THF_19870 for (2851ds/6753Mi)
% 108.47/16.85 % (20463)Instruction limit reached!
% 108.47/16.85 % (20463)------------------------------
% 108.47/16.85 % (20463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 108.47/16.85 % (20463)Termination reason: Unknown
% 108.47/16.85 % (20463)Termination phase: Saturation
% 108.47/16.85
% 108.47/16.85 % (20463)Memory used [KB]: 15095
% 108.47/16.85 % (20463)Time elapsed: 2.800 s
% 108.47/16.85 % (20463)Instructions burned: 7470 (million)
% 108.47/16.85 % (20463)------------------------------
% 108.47/16.85 % (20463)------------------------------
% 108.47/16.86 % (20837)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_19870 for (2846ds/1003Mi)
% 112.33/17.20 % (20837)Instruction limit reached!
% 112.33/17.20 % (20837)------------------------------
% 112.33/17.20 % (20837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.33/17.20 % (20837)Termination reason: Unknown
% 112.33/17.20 % (20837)Termination phase: Saturation
% 112.33/17.20
% 112.33/17.20 % (20837)Memory used [KB]: 8699
% 112.33/17.20 % (20837)Time elapsed: 0.335 s
% 112.33/17.20 % (20837)Instructions burned: 1003 (million)
% 112.33/17.20 % (20837)------------------------------
% 112.33/17.20 % (20837)------------------------------
% 112.33/17.21 % (20838)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_19870 for (2843ds/13018Mi)
% 115.95/17.80 % (20824)Instruction limit reached!
% 115.95/17.80 % (20824)------------------------------
% 115.95/17.80 % (20824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.95/17.80 % (20824)Termination reason: Unknown
% 115.95/17.80 % (20824)Termination phase: Saturation
% 115.95/17.80
% 115.95/17.80 % (20824)Memory used [KB]: 12025
% 115.95/17.80 % (20824)Time elapsed: 2.433 s
% 115.95/17.80 % (20824)Instructions burned: 5626 (million)
% 115.95/17.80 % (20824)------------------------------
% 115.95/17.80 % (20824)------------------------------
% 115.95/17.81 % (20839)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_19870 for (2837ds/1267Mi)
% 119.32/18.21 % (20839)Instruction limit reached!
% 119.32/18.21 % (20839)------------------------------
% 119.32/18.21 % (20839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.32/18.21 % (20839)Termination reason: Unknown
% 119.32/18.21 % (20839)Termination phase: Saturation
% 119.32/18.21
% 119.32/18.21 % (20839)Memory used [KB]: 8315
% 119.32/18.21 % (20839)Time elapsed: 0.397 s
% 119.32/18.21 % (20839)Instructions burned: 1268 (million)
% 119.32/18.21 % (20839)------------------------------
% 119.32/18.21 % (20839)------------------------------
% 119.32/18.22 % (20840)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=2570:si=on:rtra=on_0 on DTF2THF_19870 for (2833ds/2570Mi)
% 120.55/18.47 % (20834)Instruction limit reached!
% 120.55/18.47 % (20834)------------------------------
% 120.55/18.47 % (20834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.55/18.47 % (20834)Termination reason: Unknown
% 120.55/18.47 % (20834)Termination phase: Saturation
% 120.55/18.47
% 120.55/18.47 % (20834)Memory used [KB]: 13688
% 120.55/18.47 % (20834)Time elapsed: 2.752 s
% 120.55/18.47 % (20834)Instructions burned: 7802 (million)
% 120.55/18.47 % (20834)------------------------------
% 120.55/18.47 % (20834)------------------------------
% 120.55/18.48 % (20841)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_19870 for (2830ds/13163Mi)
% 122.65/18.82 % (20836)Instruction limit reached!
% 122.65/18.82 % (20836)------------------------------
% 122.65/18.82 % (20836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 122.65/18.82 % (20836)Termination reason: Unknown
% 122.65/18.82 % (20836)Termination phase: Saturation
% 122.65/18.82
% 122.65/18.82 % (20836)Memory used [KB]: 9722
% 122.65/18.82 % (20836)Time elapsed: 2.359 s
% 122.65/18.82 % (20836)Instructions burned: 6754 (million)
% 122.65/18.82 % (20836)------------------------------
% 122.65/18.82 % (20836)------------------------------
% 122.65/18.83 % (20842)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_19870 for (2827ds/5087Mi)
% 123.08/18.94 % (20840)Instruction limit reached!
% 123.08/18.94 % (20840)------------------------------
% 123.08/18.94 % (20840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 123.08/18.94 % (20840)Termination reason: Unknown
% 123.08/18.94 % (20840)Termination phase: Saturation
% 123.08/18.94
% 123.08/18.94 % (20840)Memory used [KB]: 10234
% 123.08/18.94 % (20840)Time elapsed: 0.726 s
% 123.08/18.94 % (20840)Instructions burned: 2571 (million)
% 123.08/18.94 % (20840)------------------------------
% 123.08/18.94 % (20840)------------------------------
% 123.08/18.95 % (20843)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_19870 for (2826ds/10380Mi)
% 127.06/19.33 % (20565)Instruction limit reached!
% 127.06/19.33 % (20565)------------------------------
% 127.06/19.33 % (20565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.06/19.33 % (20565)Termination reason: Unknown
% 127.06/19.33 % (20565)Termination phase: Saturation
% 127.06/19.33
% 127.06/19.33 % (20565)Memory used [KB]: 23666
% 127.06/19.33 % (20565)Time elapsed: 4.843 s
% 127.06/19.33 % (20565)Instructions burned: 13468 (million)
% 127.06/19.33 % (20565)------------------------------
% 127.06/19.33 % (20565)------------------------------
% 127.06/19.34 % (20844)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_19870 for (2822ds/4218Mi)
% 134.06/20.35 % (20710)Instruction limit reached!
% 134.06/20.35 % (20710)------------------------------
% 134.06/20.35 % (20710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 134.06/20.35 % (20710)Termination reason: Unknown
% 134.06/20.35 % (20710)Termination phase: Saturation
% 134.06/20.35
% 134.06/20.35 % (20710)Memory used [KB]: 24562
% 134.06/20.35 % (20710)Time elapsed: 5.336 s
% 134.06/20.35 % (20710)Instructions burned: 15557 (million)
% 134.06/20.35 % (20710)------------------------------
% 134.06/20.35 % (20710)------------------------------
% 134.06/20.36 % (20845)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_19870 for (2811ds/3971Mi)
% 134.73/20.40 % (20842)Instruction limit reached!
% 134.73/20.40 % (20842)------------------------------
% 134.73/20.40 % (20842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 134.73/20.40 % (20842)Termination reason: Unknown
% 134.73/20.40 % (20842)Termination phase: Saturation
% 134.73/20.40
% 134.73/20.40 % (20842)Memory used [KB]: 11513
% 134.73/20.40 % (20842)Time elapsed: 1.594 s
% 134.73/20.40 % (20842)Instructions burned: 5090 (million)
% 134.73/20.40 % (20842)------------------------------
% 134.73/20.40 % (20842)------------------------------
% 134.73/20.41 % (20846)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_19870 for (2811ds/14014Mi)
% 135.25/20.52 % (20844)Instruction limit reached!
% 135.25/20.52 % (20844)------------------------------
% 135.25/20.52 % (20844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 135.25/20.52 % (20844)Termination reason: Unknown
% 135.25/20.52 % (20844)Termination phase: Saturation
% 135.25/20.52
% 135.25/20.52 % (20844)Memory used [KB]: 11897
% 135.25/20.52 % (20844)Time elapsed: 1.200 s
% 135.25/20.52 % (20844)Instructions burned: 4218 (million)
% 135.25/20.52 % (20844)------------------------------
% 135.25/20.52 % (20844)------------------------------
% 135.25/20.53 % (20847)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_19870 for (2810ds/8517Mi)
% 136.89/21.01 % (20835)Instruction limit reached!
% 136.89/21.01 % (20835)------------------------------
% 136.89/21.01 % (20835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 136.89/21.01 % (20835)Termination reason: Unknown
% 136.89/21.01 % (20835)Termination phase: Saturation
% 136.89/21.01
% 136.89/21.01 % (20835)Memory used [KB]: 14583
% 136.89/21.02 % (20835)Time elapsed: 4.976 s
% 136.89/21.02 % (20835)Instructions burned: 15195 (million)
% 136.89/21.02 % (20835)------------------------------
% 136.89/21.02 % (20835)------------------------------
% 136.89/21.03 % (20848)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_19870 for (2805ds/10148Mi)
% 140.20/21.25 % (20838)Instruction limit reached!
% 140.20/21.25 % (20838)------------------------------
% 140.20/21.25 % (20838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 140.20/21.25 % (20838)Termination reason: Unknown
% 140.20/21.25 % (20838)Termination phase: Saturation
% 140.20/21.25
% 140.20/21.25 % (20838)Memory used [KB]: 28656
% 140.20/21.25 % (20838)Time elapsed: 4.042 s
% 140.20/21.25 % (20838)Instructions burned: 13018 (million)
% 140.20/21.25 % (20838)------------------------------
% 140.20/21.25 % (20838)------------------------------
% 140.20/21.26 % (20849)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_19870 for (2802ds/9078Mi)
% 141.78/21.52 % (20845)Instruction limit reached!
% 141.78/21.52 % (20845)------------------------------
% 141.78/21.52 % (20845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 141.78/21.52 % (20845)Termination reason: Unknown
% 141.78/21.52 % (20845)Termination phase: Saturation
% 141.78/21.52
% 141.78/21.52 % (20845)Memory used [KB]: 9978
% 141.78/21.52 % (20845)Time elapsed: 1.177 s
% 141.78/21.52 % (20845)Instructions burned: 3974 (million)
% 141.78/21.52 % (20845)------------------------------
% 141.78/21.52 % (20845)------------------------------
% 141.78/21.53 % (20850)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_19870 for (2800ds/16164Mi)
% 143.40/21.93 % (20843)Instruction limit reached!
% 143.40/21.93 % (20843)------------------------------
% 143.40/21.93 % (20843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 143.40/21.93 % (20843)Termination reason: Unknown
% 143.40/21.93 % (20843)Termination phase: Saturation
% 143.40/21.93
% 143.40/21.93 % (20843)Memory used [KB]: 11001
% 143.40/21.93 % (20843)Time elapsed: 3.005 s
% 143.40/21.93 % (20843)Instructions burned: 10383 (million)
% 143.40/21.93 % (20843)------------------------------
% 143.40/21.93 % (20843)------------------------------
% 143.40/21.94 % (20851)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_19870 for (2796ds/6102Mi)
% 148.77/22.41 % (20841)Instruction limit reached!
% 148.77/22.41 % (20841)------------------------------
% 148.77/22.41 % (20841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.77/22.41 % (20841)Termination reason: Unknown
% 148.77/22.41 % (20841)Termination phase: Saturation
% 148.77/22.41
% 148.77/22.41 % (20841)Memory used [KB]: 13048
% 148.77/22.41 % (20841)Time elapsed: 3.960 s
% 148.77/22.41 % (20841)Instructions burned: 13164 (million)
% 148.77/22.41 % (20841)------------------------------
% 148.77/22.41 % (20841)------------------------------
% 148.77/22.43 % (20852)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on DTF2THF_19870 for (2791ds/10308Mi)
% 153.93/23.14 % (20847)Instruction limit reached!
% 153.93/23.14 % (20847)------------------------------
% 153.93/23.14 % (20847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.93/23.14 % (20847)Termination reason: Unknown
% 153.93/23.14 % (20847)Termination phase: Saturation
% 153.93/23.14
% 153.93/23.14 % (20847)Memory used [KB]: 19957
% 153.93/23.14 % (20847)Time elapsed: 2.607 s
% 153.93/23.14 % (20847)Instructions burned: 8517 (million)
% 153.93/23.14 % (20847)------------------------------
% 153.93/23.14 % (20847)------------------------------
% 153.93/23.15 % (20853)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on DTF2THF_19870 for (2783ds/4041Mi)
% 155.55/23.43 % (20849)Instruction limit reached!
% 155.55/23.43 % (20849)------------------------------
% 155.55/23.43 % (20849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.55/23.43 % (20849)Termination reason: Unknown
% 155.55/23.43 % (20849)Termination phase: Saturation
% 155.55/23.43
% 155.55/23.43 % (20849)Memory used [KB]: 8955
% 155.55/23.43 % (20849)Time elapsed: 2.172 s
% 155.55/23.43 % (20849)Instructions burned: 9079 (million)
% 155.55/23.43 % (20849)------------------------------
% 155.55/23.43 % (20849)------------------------------
% 155.55/23.44 % (20854)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=6901:si=on:rtra=on_0 on DTF2THF_19870 for (2781ds/6901Mi)
% 157.11/23.78 % (20851)Instruction limit reached!
% 157.11/23.78 % (20851)------------------------------
% 157.11/23.78 % (20851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 157.11/23.78 % (20851)Termination reason: Unknown
% 157.11/23.78 % (20851)Termination phase: Saturation
% 157.11/23.78
% 157.11/23.78 % (20851)Memory used [KB]: 14200
% 157.11/23.78 % (20851)Time elapsed: 1.836 s
% 157.11/23.78 % (20851)Instructions burned: 6104 (million)
% 157.11/23.78 % (20851)------------------------------
% 157.11/23.78 % (20851)------------------------------
% 157.11/23.79 % (20855)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_19870 for (2777ds/5576Mi)
% 160.22/24.05 % (20848)Instruction limit reached!
% 160.22/24.05 % (20848)------------------------------
% 160.22/24.05 % (20848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 160.22/24.05 % (20848)Termination reason: Unknown
% 160.22/24.05 % (20848)Termination phase: Saturation
% 160.22/24.05
% 160.22/24.05 % (20848)Memory used [KB]: 15991
% 160.22/24.05 % (20848)Time elapsed: 3.022 s
% 160.22/24.05 % (20848)Instructions burned: 10149 (million)
% 160.22/24.05 % (20848)------------------------------
% 160.22/24.05 % (20848)------------------------------
% 160.22/24.06 % (20856)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_19870 for (2774ds/2014Mi)
% 161.85/24.37 % (20853)Instruction limit reached!
% 161.85/24.37 % (20853)------------------------------
% 161.85/24.37 % (20853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 161.85/24.37 % (20853)Termination reason: Unknown
% 161.85/24.37 % (20853)Termination phase: Saturation
% 161.85/24.37
% 161.85/24.37 % (20853)Memory used [KB]: 12281
% 161.85/24.37 % (20853)Time elapsed: 1.222 s
% 161.85/24.37 % (20853)Instructions burned: 4041 (million)
% 161.85/24.37 % (20853)------------------------------
% 161.85/24.37 % (20853)------------------------------
% 161.85/24.38 % (20857)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=5115:si=on:rtra=on_0 on DTF2THF_19870 for (2771ds/5115Mi)
% 163.46/24.67 % (20856)Instruction limit reached!
% 163.46/24.67 % (20856)------------------------------
% 163.46/24.67 % (20856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.46/24.67 % (20856)Termination reason: Unknown
% 163.46/24.67 % (20856)Termination phase: Saturation
% 163.46/24.67
% 163.46/24.67 % (20856)Memory used [KB]: 10746
% 163.46/24.67 % (20856)Time elapsed: 0.613 s
% 163.46/24.67 % (20856)Instructions burned: 2015 (million)
% 163.46/24.67 % (20856)------------------------------
% 163.46/24.67 % (20856)------------------------------
% 163.46/24.68 % (20858)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on DTF2THF_19870 for (2768ds/13001Mi)
% 164.58/24.70 % (20858)Refutation not found, incomplete strategy
% 164.58/24.70 % (20858)------------------------------
% 164.58/24.70 % (20858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 164.58/24.70 % (20858)Termination reason: Refutation not found, incomplete strategy
% 164.58/24.70
% 164.58/24.70
% 164.58/24.70 % (20858)Memory used [KB]: 6780
% 164.58/24.70 % (20858)Time elapsed: 0.024 s
% 164.58/24.70 % (20858)Instructions burned: 82 (million)
% 164.58/24.70 % (20858)------------------------------
% 164.58/24.70 % (20858)------------------------------
% 164.58/24.71 % (20859)dis+10_1:2_aac=none:acc=on:atotf=0.1:au=on:fde=none:ins=1:ixr=off:nwc=5.0:i=11105:si=on:rtra=on_0 on DTF2THF_19870 for (2768ds/11105Mi)
% 165.12/24.83 % (20846)Instruction limit reached!
% 165.12/24.83 % (20846)------------------------------
% 165.12/24.83 % (20846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 165.12/24.83 % (20846)Termination reason: Unknown
% 165.12/24.83 % (20846)Termination phase: Saturation
% 165.12/24.83
% 165.12/24.83 % (20846)Memory used [KB]: 24562
% 165.12/24.83 % (20846)Time elapsed: 4.437 s
% 165.12/24.83 % (20846)Instructions burned: 14014 (million)
% 165.12/24.83 % (20846)------------------------------
% 165.12/24.83 % (20846)------------------------------
% 165.12/24.84 % (20860)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=13832:si=on:rtra=on_0 on DTF2THF_19870 for (2767ds/13832Mi)
% 167.96/25.16 % (20854)First to succeed.
% 167.96/25.17 % (20854)Refutation found. Thanks to Tanya!
% 167.96/25.17 % SZS status Theorem for DTF2THF_19870
% 167.96/25.17 % SZS output start Proof for DTF2THF_19870
% 167.96/25.17 thf(type_def_5, type, nat: $tType).
% 167.96/25.17 thf(type_def_6, type, real: $tType).
% 167.96/25.17 thf(type_def_8, type, num: $tType).
% 167.96/25.17 thf(type_def_9, type, set: ($tType) > $tType).
% 167.96/25.17 thf(func_def_0, type, real: $tType).
% 167.96/25.17 thf(func_def_1, type, set: ($tType) > $tType).
% 167.96/25.17 thf(func_def_2, type, num: $tType).
% 167.96/25.17 thf(func_def_3, type, nat: $tType).
% 167.96/25.17 thf(func_def_4, type, type: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_5, type, dvd: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_6, type, one: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_7, type, ring: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_8, type, numeral: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_9, type, minus: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_10, type, ring_1: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_11, type, ord: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_12, type, semiring: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_13, type, neg_numeral: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_14, type, order: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_15, type, comm_ring: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_16, type, group_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_17, type, monoid_mult: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_18, type, linorder: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_19, type, preorder: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_20, type, idom_abs_sgn: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_21, type, ordered_ring: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_22, type, ab_group_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_23, type, semiring_char_0: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_24, type, comm_semiring: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_25, type, semigroup_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_26, type, semiring_numeral: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_27, type, semigroup_mult: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_28, type, linordered_idom: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_29, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_30, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_31, type, comm_monoid_mult: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_32, type, ab_semigroup_mult: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_33, type, linordered_semidom: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_34, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_35, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_36, type, comm_s1003936772cancel: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_37, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_38, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_39, type, ordere142940540dd_abs: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_40, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_41, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_42, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_43, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_44, type, ordere623563068d_diff: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_45, type, semiri456707255roduct: !>[X0: $tType]:($o)).
% 167.96/25.17 thf(func_def_46, type, genClo1161277105lle_PC: nat > real > real).
% 167.96/25.17 thf(func_def_47, type, genClo1144207539le_rho: real).
% 167.96/25.17 thf(func_def_48, type, genClo1015804716orrect: nat > real > $o).
% 167.96/25.17 thf(func_def_49, type, genClo293725281kRead1: (nat > real) > real > (nat > $o) > $o).
% 167.96/25.17 thf(func_def_50, type, genClo293725282kRead2: (nat > real) > (nat > real) > real > (nat > $o) > $o).
% 167.96/25.17 thf(func_def_51, type, genClo2108747022bound1: (nat > real > real) > $o).
% 167.96/25.17 thf(func_def_52, type, genClo2108747023bound2: (nat > real > real) > $o).
% 167.96/25.17 thf(func_def_53, type, abs_abs: !>[X0: $tType]:(X0 > X0)).
% 167.96/25.17 thf(func_def_54, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 167.96/25.17 thf(func_def_55, type, one_one: !>[X0: $tType]:(X0)).
% 167.96/25.17 thf(func_def_56, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 167.96/25.17 thf(func_def_57, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 167.96/25.17 thf(func_def_58, type, neg_numeral_dbl: !>[X0: $tType]:(X0 > X0)).
% 167.96/25.17 thf(func_def_59, type, bit0: num > num).
% 167.96/25.17 thf(func_def_60, type, one2: num).
% 167.96/25.17 thf(func_def_61, type, numeral_numeral: !>[X0: $tType]:(num > X0)).
% 167.96/25.17 thf(func_def_62, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 167.96/25.17 thf(func_def_63, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 167.96/25.17 thf(func_def_64, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 167.96/25.17 thf(func_def_65, type, c: nat > real > real).
% 167.96/25.17 thf(func_def_66, type, d: nat > real > real).
% 167.96/25.17 thf(func_def_67, type, p: nat).
% 167.96/25.17 thf(func_def_68, type, q: nat).
% 167.96/25.17 thf(func_def_69, type, s: real).
% 167.96/25.17 thf(func_def_70, type, t: real).
% 167.96/25.17 thf(func_def_87, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 167.96/25.17 thf(func_def_88, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 167.96/25.17 thf(func_def_89, type, sK2: (nat > $o) > nat).
% 167.96/25.17 thf(func_def_90, type, sK3: nat > (nat > $o) > nat).
% 167.96/25.17 thf(func_def_91, type, sK4: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 167.96/25.17 thf(func_def_92, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 167.96/25.17 thf(func_def_93, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 167.96/25.17 thf(func_def_94, type, sK7: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 167.96/25.17 thf(func_def_95, type, sK8: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 167.96/25.17 thf(func_def_96, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 167.96/25.17 thf(func_def_97, type, sK10: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 167.96/25.17 thf(func_def_98, type, sK11: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 167.96/25.17 thf(func_def_100, type, ph13: !>[X0: $tType]:(X0)).
% 167.96/25.17 thf(f11777,plain,(
% 167.96/25.17 $false),
% 167.96/25.17 inference(avatar_sat_refutation,[status(thm)],[f1485,f1500,f1505,f1515,f1555,f1625,f9214,f9270,f11776])).
% 167.96/25.17 thf(f11776,plain,(
% 167.96/25.17 ~spl12_7 | ~spl12_21 | ~spl12_38 | spl12_277),
% 167.96/25.17 inference(avatar_contradiction_clause,[status(thm)],[f11775])).
% 167.96/25.17 thf(f11775,plain,(
% 167.96/25.17 $false | (~spl12_7 | ~spl12_21 | ~spl12_38 | spl12_277)),
% 167.96/25.17 inference(subsumption_resolution,[status(thm)],[f11759,f1639])).
% 167.96/25.17 thf(f1639,plain,(
% 167.96/25.17 ($true = (ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))) | ~spl12_38),
% 167.96/25.17 inference(avatar_component_clause,[status(thm)],[f1637])).
% 167.96/25.17 thf(f1637,definition,(
% 167.96/25.17 spl12_38 <=> ($true = (ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))))),
% 167.96/25.17 introduced(definition,[new_symbols(naming,[spl12_38])],[avatar_definition])).
% 167.96/25.17 thf(f11759,plain,(
% 167.96/25.17 ($true != (ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))) | (~spl12_7 | ~spl12_21 | spl12_277)),
% 167.96/25.17 inference(trivial_inequality_removal,[status(thm)],[f11751])).
% 167.96/25.17 thf(f11751,plain,(
% 167.96/25.17 ($true != (ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))) | ($true != $true) | (~spl12_7 | ~spl12_21 | spl12_277)),
% 167.96/25.17 inference(superposition,[status(thm)],[f9341,f1484])).
% 167.96/25.17 thf(f1484,plain,(
% 167.96/25.17 ((ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) = $true) | ~spl12_7),
% 167.96/25.17 inference(avatar_component_clause,[status(thm)],[f1482])).
% 167.96/25.17 thf(f1482,definition,(
% 167.96/25.17 spl12_7 <=> ((ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) = $true)),
% 167.96/25.17 introduced(definition,[new_symbols(naming,[spl12_7])],[avatar_definition])).
% 167.96/25.17 thf(f9341,plain,(
% 167.96/25.17 ( ! [X0 : real] : (((ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ X0) != $true) | ($true != (ord_less_eq @ real @ X0 @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))))) ) | (~spl12_21 | spl12_277)),
% 167.96/25.17 inference(subsumption_resolution,[status(thm)],[f9340,f1554])).
% 167.96/25.17 thf(f1554,plain,(
% 167.96/25.17 (preorder @ real = $true) | ~spl12_21),
% 167.96/25.17 inference(avatar_component_clause,[status(thm)],[f1552])).
% 167.96/25.17 thf(f1552,definition,(
% 167.96/25.17 spl12_21 <=> (preorder @ real = $true)),
% 167.96/25.17 introduced(definition,[new_symbols(naming,[spl12_21])],[avatar_definition])).
% 167.96/25.17 thf(f9340,plain,(
% 167.96/25.17 ( ! [X0 : real] : ((preorder @ real != $true) | ($true != (ord_less_eq @ real @ X0 @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))) | ((ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ X0) != $true)) ) | spl12_277),
% 167.96/25.17 inference(trivial_inequality_removal,[status(thm)],[f9333])).
% 167.96/25.17 thf(f9333,plain,(
% 167.96/25.17 ( ! [X0 : real] : (((ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ X0) != $true) | ($true != $true) | (preorder @ real != $true) | ($true != (ord_less_eq @ real @ X0 @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))))) ) | spl12_277),
% 167.96/25.17 inference(superposition,[status(thm)],[f9269,f1219])).
% 167.96/25.17 thf(f1219,plain,(
% 167.96/25.17 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = (ord_less_eq @ X0 @ X1 @ X3)) | ((ord_less_eq @ X0 @ X1 @ X2) != $true) | (preorder @ X0 != $true) | ($true != (ord_less_eq @ X0 @ X2 @ X3))) )),
% 167.96/25.17 inference(cnf_transformation,[status(thm)],[f1085])).
% 167.96/25.17 thf(f1085,plain,(
% 167.96/25.17 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = (ord_less_eq @ X0 @ X1 @ X3)) | ($true != (ord_less_eq @ X0 @ X2 @ X3)) | ((ord_less_eq @ X0 @ X1 @ X2) != $true)) | (preorder @ X0 != $true))),
% 167.96/25.17 inference(flattening,[status(thm)],[f1084])).
% 167.96/25.17 thf(f1084,plain,(
% 167.96/25.17 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = (ord_less_eq @ X0 @ X1 @ X3)) | ($true != (ord_less_eq @ X0 @ X2 @ X3))) | ((ord_less_eq @ X0 @ X1 @ X2) != $true)) | (preorder @ X0 != $true))),
% 167.96/25.17 inference(ennf_transformation,[status(thm)],[f504])).
% 167.96/25.17 thf(f504,plain,(
% 167.96/25.17 ! [X0 : $tType] : ((preorder @ X0 = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (((ord_less_eq @ X0 @ X1 @ X2) = $true) => (($true = (ord_less_eq @ X0 @ X2 @ X3)) => ($true = (ord_less_eq @ X0 @ X1 @ X3)))))),
% 167.96/25.17 inference(fool_elimination,[status(thm)],[f503])).
% 167.96/25.17 thf(f503,plain,(
% 167.96/25.17 ! [X0 : $tType] : (preorder @ X0 => ! [X1 : X0,X2 : X0,X3 : X0] : ((ord_less_eq @ X0 @ X1 @ X2) => ((ord_less_eq @ X0 @ X2 @ X3) => (ord_less_eq @ X0 @ X1 @ X3))))),
% 167.96/25.17 inference(rectify,[status(thm)],[f201])).
% 167.96/25.17 thf(f201,axiom,(
% 167.96/25.17 ! [X0 : $tType] : (preorder @ X0 => ! [X25 : X0,X39 : X0,X8 : X0] : ((ord_less_eq @ X0 @ X25 @ X39) => ((ord_less_eq @ X0 @ X39 @ X8) => (ord_less_eq @ X0 @ X25 @ X8))))),
% 167.96/25.17 file('/export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2THF_19870.p',fact_200_order__trans)).
% 167.96/25.17 thf(f9269,plain,(
% 167.96/25.17 ($true != (ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))) | spl12_277),
% 167.96/25.17 inference(avatar_component_clause,[status(thm)],[f9267])).
% 167.96/25.17 thf(f9267,definition,(
% 167.96/25.17 spl12_277 <=> ($true = (ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))))),
% 167.96/25.17 introduced(definition,[new_symbols(naming,[spl12_277])],[avatar_definition])).
% 167.96/25.17 thf(f9270,plain,(
% 167.96/25.17 ~spl12_277 | ~spl12_11 | spl12_35),
% 167.96/25.17 inference(avatar_split_clause,[status(thm)],[f9235,f1622,f1502,f9267])).
% 167.96/25.17 thf(f1502,definition,(
% 167.96/25.17 spl12_11 <=> ((minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) = (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))))),
% 167.96/25.17 introduced(definition,[new_symbols(naming,[spl12_11])],[avatar_definition])).
% 167.96/25.17 thf(f1622,definition,(
% 167.96/25.17 spl12_35 <=> ((ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))) = $true)),
% 167.96/25.17 introduced(definition,[new_symbols(naming,[spl12_35])],[avatar_definition])).
% 167.96/25.17 thf(f9235,plain,(
% 167.96/25.17 ($true != (ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))) | (~spl12_11 | spl12_35)),
% 167.96/25.17 inference(backward_demodulation,[status(thm)],[f1624,f1504])).
% 167.96/25.17 thf(f1504,plain,(
% 167.96/25.17 ((minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) = (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))))) | ~spl12_11),
% 167.96/25.17 inference(avatar_component_clause,[status(thm)],[f1502])).
% 167.96/25.17 thf(f1624,plain,(
% 167.96/25.17 ((ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))) != $true) | spl12_35),
% 167.96/25.17 inference(avatar_component_clause,[status(thm)],[f1622])).
% 167.96/25.17 thf(f9214,plain,(
% 167.96/25.17 ((minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho))) != (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))) | ((ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho)))) != $true) | ($true = (ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))))),
% 167.96/25.17 introduced(definition,[],[theory_tautology_sat_conflict])).
% 167.96/25.17 thf(f1625,plain,(
% 167.96/25.17 ~spl12_35),
% 167.96/25.17 inference(avatar_split_clause,[status(thm)],[f1149,f1622])).
% 167.96/25.17 thf(f1149,plain,(
% 167.96/25.17 ((ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))) != $true)),
% 167.96/25.17 inference(cnf_transformation,[status(thm)],[f973])).
% 167.96/25.17 thf(f973,plain,(
% 167.96/25.17 ((ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))) != $true)),
% 167.96/25.17 inference(flattening,[status(thm)],[f564])).
% 167.96/25.17 thf(f564,plain,(
% 167.96/25.17 ~((ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s))) = $true)),
% 167.96/25.17 inference(fool_elimination,[status(thm)],[f563])).
% 167.96/25.17 thf(f563,plain,(
% 167.96/25.17 ~(ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))),
% 167.96/25.17 inference(rectify,[status(thm)],[f341])).
% 167.96/25.17 thf(f341,negated_conjecture,(
% 167.96/25.17 ~(ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))),
% 167.96/25.17 inference(negated_conjecture,[status(cth)],[f340])).
% 167.96/25.17 thf(f340,conjecture,(
% 167.96/25.17 (ord_less_eq @ real @ (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) @ (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))),
% 167.96/25.17 file('/export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2THF_19870.p',conj_0)).
% 167.96/25.17 thf(f1555,plain,(
% 167.96/25.17 spl12_21),
% 167.96/25.17 inference(avatar_split_clause,[status(thm)],[f1263,f1552])).
% 167.96/25.17 thf(f1263,plain,(
% 167.96/25.17 (preorder @ real = $true)),
% 167.96/25.17 inference(cnf_transformation,[status(thm)],[f870])).
% 167.96/25.17 thf(f870,plain,(
% 167.96/25.17 (preorder @ real = $true)),
% 167.96/25.17 inference(fool_elimination,[status(thm)],[f869])).
% 167.96/25.17 thf(f869,plain,(
% 167.96/25.17 preorder @ real),
% 167.96/25.17 inference(rectify,[status(thm)],[f325])).
% 167.96/25.17 thf(f325,axiom,(
% 167.96/25.17 preorder @ real),
% 167.96/25.17 file('/export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2THF_19870.p',tcon_Real_Oreal___Orderings_Opreorder_36)).
% 167.96/25.17 thf(f1515,plain,(
% 167.96/25.17 spl12_13),
% 167.96/25.17 inference(avatar_split_clause,[status(thm)],[f1178,f1512])).
% 167.96/25.17 thf(f1512,definition,(
% 167.96/25.17 spl12_13 <=> ((minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho))) = (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))),
% 167.96/25.17 introduced(definition,[new_symbols(naming,[spl12_13])],[avatar_definition])).
% 167.96/25.17 thf(f1178,plain,(
% 167.96/25.17 ((minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho))) = (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))),
% 167.96/25.17 inference(cnf_transformation,[status(thm)],[f5])).
% 167.96/25.17 thf(f5,axiom,(
% 167.96/25.17 ((minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho))) = (times_times @ real @ (times_times @ real @ (numeral_numeral @ real @ (bit0 @ one2)) @ genClo1144207539le_rho) @ (minus_minus @ real @ t @ s)))),
% 167.96/25.17 file('/export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2THF_19870.p',fact_4_Eq4)).
% 167.96/25.17 thf(f1505,plain,(
% 167.96/25.17 spl12_11),
% 167.96/25.17 inference(avatar_split_clause,[status(thm)],[f1136,f1502])).
% 167.96/25.17 thf(f1136,plain,(
% 167.96/25.17 ((minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) = (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))))),
% 167.96/25.17 inference(cnf_transformation,[status(thm)],[f4])).
% 167.96/25.17 thf(f4,axiom,(
% 167.96/25.17 ((minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) = (abs_abs @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))))),
% 167.96/25.17 file('/export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2THF_19870.p',fact_3_Eq1)).
% 167.96/25.17 thf(f1500,plain,(
% 167.96/25.17 spl12_10),
% 167.96/25.17 inference(avatar_split_clause,[status(thm)],[f1221,f1497])).
% 167.96/25.17 thf(f1497,definition,(
% 167.96/25.17 spl12_10 <=> ((ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho)))) = $true)),
% 167.96/25.17 introduced(definition,[new_symbols(naming,[spl12_10])],[avatar_definition])).
% 167.96/25.17 thf(f1221,plain,(
% 167.96/25.17 ((ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho)))) = $true)),
% 167.96/25.17 inference(cnf_transformation,[status(thm)],[f510])).
% 167.96/25.17 thf(f510,plain,(
% 167.96/25.17 ((ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho)))) = $true)),
% 167.96/25.17 inference(fool_elimination,[status(thm)],[f509])).
% 167.96/25.17 thf(f509,plain,(
% 167.96/25.17 (ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho))))),
% 167.96/25.17 inference(rectify,[status(thm)],[f6])).
% 167.96/25.17 thf(f6,axiom,(
% 167.96/25.17 (ord_less_eq @ real @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (minus_minus @ real @ one_one @ real @ genClo1144207539le_rho))))),
% 167.96/25.17 file('/export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2THF_19870.p',fact_5_Eq3)).
% 167.96/25.17 thf(f1485,plain,(
% 167.96/25.17 spl12_7),
% 167.96/25.17 inference(avatar_split_clause,[status(thm)],[f1145,f1482])).
% 167.96/25.17 thf(f1145,plain,(
% 167.96/25.17 ((ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) = $true)),
% 167.96/25.17 inference(cnf_transformation,[status(thm)],[f630])).
% 167.96/25.17 thf(f630,plain,(
% 167.96/25.17 ((ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s)))) = $true)),
% 167.96/25.17 inference(fool_elimination,[status(thm)],[f629])).
% 167.96/25.17 thf(f629,plain,(
% 167.96/25.17 (ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))))),
% 167.96/25.17 inference(rectify,[status(thm)],[f10])).
% 167.96/25.17 thf(f10,axiom,(
% 167.96/25.17 (ord_less_eq @ real @ (minus_minus @ real @ (minus_minus @ real @ (c @ p @ t) @ (c @ p @ s)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))) @ (minus_minus @ real @ (times_times @ real @ (minus_minus @ real @ t @ s) @ (plus_plus @ real @ one_one @ real @ genClo1144207539le_rho)) @ (minus_minus @ real @ (d @ q @ t) @ (d @ q @ s))))),
% 167.96/25.17 file('/export/starexec/sandbox2/tmp/tmp.plQEdVXdJs/DTF2THF_19870.p',fact_9_Eq2)).
% 167.96/25.17 % SZS output end Proof for DTF2THF_19870
% 167.96/25.17 % (20854)------------------------------
% 167.96/25.17 % (20854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 167.96/25.17 % (20854)Termination reason: Refutation
% 167.96/25.17
% 167.96/25.17 % (20854)Memory used [KB]: 14967
% 167.96/25.17 % (20854)Time elapsed: 1.724 s
% 167.96/25.17 % (20854)Instructions burned: 5609 (million)
% 167.96/25.17 % (20854)------------------------------
% 167.96/25.17 % (20854)------------------------------
% 167.96/25.17 % (19970)Success in time 23.626 s
%------------------------------------------------------------------------------