%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP156^2 : 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 : n018.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 08:56:00 AM UTC 2026
% Result : Theorem 35.63s 6.37s
% Output : Refutation 35.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP156^2 : 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 : n018.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 08:28:01 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : ITP156^2 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.46 % Domain : Interactive Theorem Proving
% 0.28/0.46 % Problem : Sledgehammer Preferences problem prob_474__6256716_1
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Des21]
% 0.28/0.46 % Names : Preferences/prob_474__6256716_1 [Des21]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.33 v8.1.0, 0.50 v7.5.0
% 0.28/0.46 % Syntax : Number of formulae : 399 ( 70 unt; 58 typ; 0 def)
% 0.28/0.46 % Number of atoms : 1015 ( 235 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.28/0.46 % Number of connectives : 4501 ( 54 ~; 13 |; 81 &;3881 @)
% 0.28/0.46 % ( 0 <=>; 472 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 28 ( 8 avg)
% 0.28/0.46 % Number of types : 3 ( 2 usr)
% 0.28/0.46 % Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 57 ( 56 usr; 5 con; 0-5 aty)
% 0.28/0.46 % Number of variables : 1126 ( 33 ^;1034 !; 7 ?;1126 :)
% 0.28/0.46 % ( 52 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.46 % SPC : TH1_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:31:20.776
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % Could-be-implicit typings (4)
% 0.28/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.28/0.46 product_prod: $tType > $tType > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_Real_Oreal,type,
% 0.28/0.46 real: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_Set_Oset,type,
% 0.28/0.46 set: $tType > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_tf_a,type,
% 0.28/0.46 a: $tType ).
% 0.28/0.46
% 0.28/0.46 % Explicit typings (54)
% 0.28/0.46 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space,type,
% 0.28/0.46 ordere890947078_space:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_HOL_Otype,type,
% 0.28/0.46 type:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oone,type,
% 0.28/0.46 one:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oplus,type,
% 0.28/0.46 plus:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.28/0.46 zero:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.28/0.46 ord:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Num_Oneg__numeral,type,
% 0.28/0.46 neg_numeral:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.28/0.46 order:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.28/0.46 group_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Omonoid__add,type,
% 0.28/0.46 monoid_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.28/0.46 linorder:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.28/0.46 preorder:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.28/0.46 zero_neq_one:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Rings_Ozero__less__one,type,
% 0.28/0.46 zero_less_one:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.28/0.46 semigroup_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.28/0.46 linordered_idom:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.28/0.46 comm_monoid_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Fields_Olinordered__field,type,
% 0.28/0.46 linordered_field:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.28/0.46 ab_semigroup_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.28/0.46 linordered_semidom:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.28/0.46 cancel_semigroup_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.28/0.46 cancel1352612707id_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.28/0.46 linord219039673up_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.28/0.46 ordere216010020id_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Real__Vector__Spaces_Oreal__vector,type,
% 0.28/0.46 real_V1076094709vector:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.28/0.46 ordere779506340up_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.28/0.46 linord1659791738miring:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.28/0.46 canoni770627133id_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add,type,
% 0.28/0.46 ordere1818651114id_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add,type,
% 0.28/0.46 strict797366125id_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 0.28/0.46 real_V55928688vector:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.28/0.46 ordere236663937imp_le:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.28/0.46 ordere223160158up_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.28/0.46 strict2144017051up_add:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Real__Vector__Spaces_Oordered__real__vector,type,
% 0.28/0.46 real_V1587248058vector:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 0.28/0.46 unique1598680935umeral:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.28/0.46 ordere516151231imp_le:
% 0.28/0.46 !>[A: $tType] : $o ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux,type,
% 0.28/0.46 unique455577585es_aux:
% 0.28/0.46 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.28/0.46 one_one:
% 0.28/0.46 !>[A: $tType] : A ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.28/0.46 plus_plus:
% 0.28/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.28/0.46 zero_zero:
% 0.28/0.46 !>[A: $tType] : A ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.28/0.46 ord_less:
% 0.28/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.28/0.46 ord_less_eq:
% 0.28/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Preferences__Mirabelle__stygcjuplb_Oweak__convex__pref,type,
% 0.28/0.46 prefer1289595409x_pref:
% 0.28/0.46 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Product__Type_OPair,type,
% 0.28/0.46 product_Pair:
% 0.28/0.46 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.28/0.46 product_rec_prod:
% 0.28/0.46 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR,type,
% 0.28/0.46 real_V1908273582scaleR:
% 0.28/0.46 !>[A: $tType] : ( real > A > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Set_OCollect,type,
% 0.28/0.46 collect:
% 0.28/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member,type,
% 0.28/0.46 member:
% 0.28/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_relation,type,
% 0.28/0.46 relation: set @ ( product_prod @ a @ a ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_u,type,
% 0.28/0.46 u: real ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_v,type,
% 0.28/0.46 v: real ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_x,type,
% 0.28/0.46 x: a ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_y,type,
% 0.28/0.46 y: a ).
% 0.28/0.46
% 0.28/0.46 % Relevant facts (254)
% 0.28/0.46 thf(fact_0_assms_I1_J,axiom,
% 0.28/0.46 prefer1289595409x_pref @ a @ relation ).
% 0.28/0.46
% 0.28/0.46 % assms(1)
% 0.28/0.46 thf(fact_1_indifferent__imp__weak__pref_I2_J,axiom,
% 0.28/0.46 ! [X: a,Y: a] :
% 0.28/0.46 ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation )
% 0.28/0.46 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) )
% 0.28/0.46 => ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) ) ).
% 0.28/0.46
% 0.28/0.46 % indifferent_imp_weak_pref(2)
% 0.28/0.46 thf(fact_2_indifferent__imp__weak__pref_I1_J,axiom,
% 0.28/0.46 ! [X: a,Y: a] :
% 0.28/0.46 ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation )
% 0.28/0.46 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) )
% 0.28/0.46 => ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation ) ) ).
% 0.28/0.46
% 0.28/0.46 % indifferent_imp_weak_pref(1)
% 0.28/0.46 thf(fact_3_indiff__trans,axiom,
% 0.28/0.46 ! [X: a,Y: a,Z: a] :
% 0.28/0.46 ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation )
% 0.28/0.46 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) )
% 0.28/0.46 => ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ Z ) @ relation )
% 0.28/0.46 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Z @ Y ) @ relation ) )
% 0.28/0.46 => ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Z ) @ relation )
% 0.28/0.46 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Z @ X ) @ relation ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % indiff_trans
% 0.28/0.46 thf(fact_4_strict__trans,axiom,
% 0.28/0.46 ! [X: a,Y: a,Z: a] :
% 0.28/0.46 ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation )
% 0.28/0.46 & ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) )
% 0.28/0.46 => ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ Z ) @ relation )
% 0.28/0.46 & ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Z @ Y ) @ relation ) )
% 0.28/0.46 => ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Z ) @ relation )
% 0.28/0.46 & ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Z @ X ) @ relation ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % strict_trans
% 0.28/0.46 thf(fact_5_assms_I2_J,axiom,
% 0.28/0.46 member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ x @ y ) @ relation ).
% 0.28/0.46
% 0.28/0.46 % assms(2)
% 0.28/0.46 thf(fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,axiom,
% 0.28/0.46 ( ( ( u
% 0.28/0.46 != ( zero_zero @ real ) )
% 0.28/0.46 & ( u
% 0.28/0.46 != ( one_one @ real ) ) )
% 0.28/0.46 => ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ ( plus_plus @ a @ ( real_V1908273582scaleR @ a @ u @ x ) @ ( real_V1908273582scaleR @ a @ v @ y ) ) @ y ) @ relation ) ) ).
% 0.28/0.46
% 0.28/0.46 % \<open>u \<noteq> 0 \<and> u \<noteq> 1 \<longrightarrow> u *\<^sub>R x + v *\<^sub>R y \<succeq> y\<close>
% 0.28/0.46 thf(fact_7_u__0,axiom,
% 0.28/0.46 ( ( u
% 0.28/0.46 = ( zero_zero @ real ) )
% 0.28/0.46 => ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ ( plus_plus @ a @ ( real_V1908273582scaleR @ a @ u @ x ) @ ( real_V1908273582scaleR @ a @ v @ y ) ) @ y ) @ relation ) ) ).
% 0.28/0.46
% 0.28/0.46 % u_0
% 0.28/0.46 thf(fact_8_assms_I4_J,axiom,
% 0.28/0.46 ord_less_eq @ real @ ( zero_zero @ real ) @ v ).
% 0.28/0.46
% 0.28/0.46 % assms(4)
% 0.28/0.46 thf(fact_9_assms_I5_J,axiom,
% 0.28/0.46 ( ( plus_plus @ real @ u @ v )
% 0.28/0.46 = ( one_one @ real ) ) ).
% 0.28/0.46
% 0.28/0.46 % assms(5)
% 0.28/0.46 thf(fact_10_assms_I3_J,axiom,
% 0.28/0.46 ord_less_eq @ real @ ( zero_zero @ real ) @ u ).
% 0.28/0.46
% 0.28/0.46 % assms(3)
% 0.28/0.46 thf(fact_11_scaleR__Pair,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType] :
% 0.28/0.46 ( ( ( real_V1076094709vector @ B )
% 0.28/0.46 & ( real_V1076094709vector @ A ) )
% 0.28/0.46 => ! [R: real,A2: A,B2: B] :
% 0.28/0.46 ( ( real_V1908273582scaleR @ ( product_prod @ A @ B ) @ R @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.28/0.46 = ( product_Pair @ A @ B @ ( real_V1908273582scaleR @ A @ R @ A2 ) @ ( real_V1908273582scaleR @ B @ R @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % scaleR_Pair
% 0.28/0.46 thf(fact_12_scale__prod,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType] :
% 0.28/0.46 ( ( ( real_V1076094709vector @ B )
% 0.28/0.46 & ( real_V1076094709vector @ A ) )
% 0.28/0.46 => ! [X: real,A2: A,B2: B] :
% 0.28/0.46 ( ( real_V1908273582scaleR @ ( product_prod @ A @ B ) @ X @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.28/0.46 = ( product_Pair @ A @ B @ ( real_V1908273582scaleR @ A @ X @ A2 ) @ ( real_V1908273582scaleR @ B @ X @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % scale_prod
% 0.28/0.46 thf(fact_13_add__Pair,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType] :
% 0.28/0.46 ( ( ( plus @ B )
% 0.28/0.46 & ( plus @ A ) )
% 0.28/0.46 => ! [A2: A,B2: B,C: A,D: B] :
% 0.28/0.46 ( ( plus_plus @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ C @ D ) )
% 0.28/0.46 = ( product_Pair @ A @ B @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ B @ B2 @ D ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_Pair
% 0.28/0.46 thf(fact_14_prod_Oinject,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.28/0.46 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.28/0.46 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.28/0.46 = ( ( X1 = Y1 )
% 0.28/0.46 & ( X2 = Y2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % prod.inject
% 0.28/0.46 thf(fact_15_old_Oprod_Oinject,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.28/0.46 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.28/0.46 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.28/0.46 = ( ( A2 = A3 )
% 0.28/0.46 & ( B2 = B3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % old.prod.inject
% 0.28/0.46 thf(fact_16_set__plus__intro,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( plus @ A )
% 0.28/0.46 => ! [A2: A,C2: set @ A,B2: A,D2: set @ A] :
% 0.28/0.46 ( ( member @ A @ A2 @ C2 )
% 0.28/0.46 => ( ( member @ A @ B2 @ D2 )
% 0.28/0.46 => ( member @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( plus_plus @ ( set @ A ) @ C2 @ D2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % set_plus_intro
% 0.28/0.46 thf(fact_17_add__left__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel_semigroup_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A,C: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.28/0.46 = ( plus_plus @ A @ A2 @ C ) )
% 0.28/0.46 = ( B2 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_left_cancel
% 0.28/0.46 thf(fact_18_add__right__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel_semigroup_add @ A )
% 0.28/0.46 => ! [B2: A,A2: A,C: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.28/0.46 = ( plus_plus @ A @ C @ A2 ) )
% 0.28/0.46 = ( B2 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_right_cancel
% 0.28/0.46 thf(fact_19_pth__9_I3_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( real_V55928688vector @ A )
% 0.28/0.46 => ! [C: real,X: A,W: A,D: real,Z: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ W ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ X ) @ Z ) )
% 0.28/0.46 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ C @ D ) @ X ) @ ( plus_plus @ A @ W @ Z ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % pth_9(3)
% 0.28/0.46 thf(fact_20_le__zero__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A )
% 0.28/0.46 => ! [N: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.28/0.46 = ( N
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_zero_eq
% 0.28/0.46 thf(fact_21_add__le__cancel__right,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere236663937imp_le @ A )
% 0.28/0.46 => ! [A2: A,C: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.28/0.46 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_le_cancel_right
% 0.28/0.46 thf(fact_22_add__le__cancel__left,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere236663937imp_le @ A )
% 0.28/0.46 => ! [C: A,A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.28/0.46 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_le_cancel_left
% 0.28/0.46 thf(fact_23_zero__eq__add__iff__both__eq__0,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A )
% 0.28/0.46 => ! [X: A,Y: A] :
% 0.28/0.46 ( ( ( zero_zero @ A )
% 0.28/0.46 = ( plus_plus @ A @ X @ Y ) )
% 0.28/0.46 = ( ( X
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 & ( Y
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % zero_eq_add_iff_both_eq_0
% 0.28/0.46 thf(fact_24_add__eq__0__iff__both__eq__0,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A )
% 0.28/0.46 => ! [X: A,Y: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ X @ Y )
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 = ( ( X
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 & ( Y
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_eq_0_iff_both_eq_0
% 0.28/0.46 thf(fact_25_add__cancel__right__right,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( plus_plus @ A @ A2 @ B2 ) )
% 0.28/0.46 = ( B2
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_cancel_right_right
% 0.28/0.46 thf(fact_26_add__cancel__right__left,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( A2
% 0.28/0.46 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.28/0.46 = ( B2
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_cancel_right_left
% 0.28/0.46 thf(fact_27_add__cancel__left__right,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.28/0.46 = A2 )
% 0.28/0.46 = ( B2
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_cancel_left_right
% 0.28/0.46 thf(fact_28_add__cancel__left__left,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A )
% 0.28/0.46 => ! [B2: A,A2: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.28/0.46 = A2 )
% 0.28/0.46 = ( B2
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_cancel_left_left
% 0.28/0.46 thf(fact_29_double__zero__sym,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linord219039673up_add @ A )
% 0.28/0.46 => ! [A2: A] :
% 0.28/0.46 ( ( ( zero_zero @ A )
% 0.28/0.46 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.28/0.46 = ( A2
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % double_zero_sym
% 0.28/0.46 thf(fact_30_double__zero,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linord219039673up_add @ A )
% 0.28/0.46 => ! [A2: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 = ( A2
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % double_zero
% 0.28/0.46 thf(fact_31_add_Oright__neutral,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( monoid_add @ A )
% 0.28/0.46 => ! [A2: A] :
% 0.28/0.46 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.46 = A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.right_neutral
% 0.28/0.46 thf(fact_32_add_Oleft__neutral,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( monoid_add @ A )
% 0.28/0.46 => ! [A2: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.46 = A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.left_neutral
% 0.28/0.46 thf(fact_33_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linord219039673up_add @ A )
% 0.28/0.46 => ! [A2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.28/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % zero_le_double_add_iff_zero_le_single_add
% 0.28/0.46 thf(fact_34_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linord219039673up_add @ A )
% 0.28/0.46 => ! [A2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.28/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % double_add_le_zero_iff_single_add_le_zero
% 0.28/0.46 thf(fact_35_le__add__same__cancel2,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere516151231imp_le @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.28/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_add_same_cancel2
% 0.28/0.46 thf(fact_36_le__add__same__cancel1,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere516151231imp_le @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.28/0.46 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_add_same_cancel1
% 0.28/0.46 thf(fact_37_add__le__same__cancel2,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere516151231imp_le @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.28/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_le_same_cancel2
% 0.28/0.46 thf(fact_38_add__le__same__cancel1,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere516151231imp_le @ A )
% 0.28/0.46 => ! [B2: A,A2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.28/0.46 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_le_same_cancel1
% 0.28/0.46 thf(fact_39_one__reorient,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( one @ A )
% 0.28/0.46 => ! [X: A] :
% 0.28/0.46 ( ( ( one_one @ A )
% 0.28/0.46 = X )
% 0.28/0.46 = ( X
% 0.28/0.46 = ( one_one @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % one_reorient
% 0.28/0.46 thf(fact_40_zero__reorient,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( zero @ A )
% 0.28/0.46 => ! [X: A] :
% 0.28/0.46 ( ( ( zero_zero @ A )
% 0.28/0.46 = X )
% 0.28/0.46 = ( X
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % zero_reorient
% 0.28/0.46 thf(fact_41_zero__le,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A )
% 0.28/0.46 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.28/0.46
% 0.28/0.46 % zero_le
% 0.28/0.46 thf(fact_42_add__nonpos__eq__0__iff,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere216010020id_add @ A )
% 0.28/0.46 => ! [X: A,Y: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 0.28/0.46 => ( ( ord_less_eq @ A @ Y @ ( zero_zero @ A ) )
% 0.28/0.46 => ( ( ( plus_plus @ A @ X @ Y )
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 = ( ( X
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 & ( Y
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_nonpos_eq_0_iff
% 0.28/0.46 thf(fact_43_mem__Collect__eq,axiom,
% 0.28/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.28/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.28/0.46 = ( P @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % mem_Collect_eq
% 0.28/0.46 thf(fact_44_Collect__mem__eq,axiom,
% 0.28/0.46 ! [A: $tType,A4: set @ A] :
% 0.28/0.46 ( ( collect @ A
% 0.28/0.46 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.28/0.46 = A4 ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_mem_eq
% 0.28/0.46 thf(fact_45_Collect__cong,axiom,
% 0.28/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.46 ( ! [X4: A] :
% 0.28/0.46 ( ( P @ X4 )
% 0.28/0.46 = ( Q @ X4 ) )
% 0.28/0.46 => ( ( collect @ A @ P )
% 0.28/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_cong
% 0.28/0.46 thf(fact_46_add__nonneg__eq__0__iff,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere216010020id_add @ A )
% 0.28/0.46 => ! [X: A,Y: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.28/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.28/0.46 => ( ( ( plus_plus @ A @ X @ Y )
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 = ( ( X
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 & ( Y
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_nonneg_eq_0_iff
% 0.28/0.46 thf(fact_47_add__nonpos__nonpos,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere216010020id_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.46 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.28/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_nonpos_nonpos
% 0.28/0.46 thf(fact_48_add__nonneg__nonneg,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere216010020id_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.46 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.28/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_nonneg_nonneg
% 0.28/0.46 thf(fact_49_add__increasing2,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere216010020id_add @ A )
% 0.28/0.46 => ! [C: A,B2: A,A2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.28/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.46 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_increasing2
% 0.28/0.46 thf(fact_50_add__decreasing2,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere216010020id_add @ A )
% 0.28/0.46 => ! [C: A,A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.28/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_decreasing2
% 0.28/0.46 thf(fact_51_add__increasing,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere216010020id_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A,C: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.46 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.28/0.46 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_increasing
% 0.28/0.46 thf(fact_52_add__decreasing,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere216010020id_add @ A )
% 0.28/0.46 => ! [A2: A,C: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.46 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.28/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_decreasing
% 0.28/0.46 thf(fact_53_zero__prod__def,axiom,
% 0.28/0.46 ! [A: $tType,B: $tType] :
% 0.28/0.46 ( ( ( zero @ B )
% 0.28/0.46 & ( zero @ A ) )
% 0.28/0.46 => ( ( zero_zero @ ( product_prod @ A @ B ) )
% 0.28/0.46 = ( product_Pair @ A @ B @ ( zero_zero @ A ) @ ( zero_zero @ B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % zero_prod_def
% 0.28/0.46 thf(fact_54_add__le__imp__le__right,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere236663937imp_le @ A )
% 0.28/0.46 => ! [A2: A,C: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.28/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_le_imp_le_right
% 0.28/0.46 thf(fact_55_add__le__imp__le__left,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere236663937imp_le @ A )
% 0.28/0.46 => ! [C: A,A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.28/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_le_imp_le_left
% 0.28/0.46 thf(fact_56_le__iff__add,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A )
% 0.28/0.46 => ( ( ord_less_eq @ A )
% 0.28/0.46 = ( ^ [A5: A,B4: A] :
% 0.28/0.46 ? [C3: A] :
% 0.28/0.46 ( B4
% 0.28/0.46 = ( plus_plus @ A @ A5 @ C3 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % le_iff_add
% 0.28/0.46 thf(fact_57_add__right__mono,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere779506340up_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A,C: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_right_mono
% 0.28/0.46 thf(fact_58_less__eqE,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.46 => ~ ! [C4: A] :
% 0.28/0.46 ( B2
% 0.28/0.46 != ( plus_plus @ A @ A2 @ C4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % less_eqE
% 0.28/0.46 thf(fact_59_add__left__mono,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere779506340up_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A,C: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_left_mono
% 0.28/0.46 thf(fact_60_add__mono,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere779506340up_add @ A )
% 0.28/0.46 => ! [A2: A,B2: A,C: A,D: A] :
% 0.28/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.46 => ( ( ord_less_eq @ A @ C @ D )
% 0.28/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_mono
% 0.28/0.46 thf(fact_61_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere779506340up_add @ A )
% 0.28/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.28/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.28/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_semiring(1)
% 0.28/0.47 thf(fact_62_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere779506340up_add @ A )
% 0.28/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.47 ( ( ( I = J )
% 0.28/0.47 & ( ord_less_eq @ A @ K @ L ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_semiring(2)
% 0.28/0.47 thf(fact_63_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere779506340up_add @ A )
% 0.28/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.47 ( ( ( ord_less_eq @ A @ I @ J )
% 0.28/0.47 & ( K = L ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_semiring(3)
% 0.28/0.47 thf(fact_64_pth__4_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [X: A] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ ( zero_zero @ real ) @ X )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_4(1)
% 0.28/0.47 thf(fact_65_convex__ge__imp__conved,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [Pr: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ! [X4: A,Y3: A] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y3 ) @ Pr )
% 0.28/0.47 => ! [Alpha: real,Beta: real] :
% 0.28/0.47 ( ( ( ( plus_plus @ real @ Alpha @ Beta )
% 0.28/0.47 = ( one_one @ real ) )
% 0.28/0.47 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Alpha )
% 0.28/0.47 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Beta ) )
% 0.28/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ Alpha @ X4 ) @ ( real_V1908273582scaleR @ A @ Beta @ Y3 ) ) @ Y3 ) @ Pr ) ) )
% 0.28/0.47 => ( prefer1289595409x_pref @ A @ Pr ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % convex_ge_imp_conved
% 0.28/0.47 thf(fact_66_add_Ogroup__left__neutral,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( group_add @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % add.group_left_neutral
% 0.28/0.47 thf(fact_67_add_Ocomm__neutral,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( comm_monoid_add @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % add.comm_neutral
% 0.28/0.47 thf(fact_68_comm__monoid__add__class_Oadd__0,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( comm_monoid_add @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 = A2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % comm_monoid_add_class.add_0
% 0.28/0.47 thf(fact_69_pth__d,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [X: A] :
% 0.28/0.47 ( ( plus_plus @ A @ X @ ( zero_zero @ A ) )
% 0.28/0.47 = X ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_d
% 0.28/0.47 thf(fact_70_pth__7_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [X: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( zero_zero @ A ) @ X )
% 0.28/0.47 = X ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_7(1)
% 0.28/0.47 thf(fact_71_pth__1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [X: A] :
% 0.28/0.47 ( X
% 0.28/0.47 = ( real_V1908273582scaleR @ A @ ( one_one @ real ) @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_1
% 0.28/0.47 thf(fact_72_pth__4_I2_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ C @ ( zero_zero @ A ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_4(2)
% 0.28/0.47 thf(fact_73_add__right__imp__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( cancel_semigroup_add @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C: A] :
% 0.28/0.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.28/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.28/0.47 => ( B2 = C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_right_imp_eq
% 0.28/0.47 thf(fact_74_add__left__imp__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( cancel_semigroup_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.28/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.28/0.47 => ( B2 = C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_left_imp_eq
% 0.28/0.47 thf(fact_75_add_Oleft__commute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ab_semigroup_add @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C: A] :
% 0.28/0.47 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) )
% 0.28/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add.left_commute
% 0.28/0.47 thf(fact_76_add_Ocommute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ab_semigroup_add @ A )
% 0.28/0.47 => ( ( plus_plus @ A )
% 0.28/0.47 = ( ^ [A5: A,B4: A] : ( plus_plus @ A @ B4 @ A5 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add.commute
% 0.28/0.47 thf(fact_77_add_Oright__cancel,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( group_add @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C: A] :
% 0.28/0.47 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.28/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.28/0.47 = ( B2 = C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add.right_cancel
% 0.28/0.47 thf(fact_78_add_Oleft__cancel,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( group_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.28/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.28/0.47 = ( B2 = C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add.left_cancel
% 0.28/0.47 thf(fact_79_add_Oassoc,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( semigroup_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 0.28/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add.assoc
% 0.28/0.47 thf(fact_80_set__plus__elim,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( plus @ A )
% 0.28/0.47 => ! [X: A,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( member @ A @ X @ ( plus_plus @ ( set @ A ) @ A4 @ B5 ) )
% 0.28/0.47 => ~ ! [A6: A,B6: A] :
% 0.28/0.47 ( ( X
% 0.28/0.47 = ( plus_plus @ A @ A6 @ B6 ) )
% 0.28/0.47 => ( ( member @ A @ A6 @ A4 )
% 0.28/0.47 => ~ ( member @ A @ B6 @ B5 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_plus_elim
% 0.28/0.47 thf(fact_81_group__cancel_Oadd2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( comm_monoid_add @ A )
% 0.28/0.47 => ! [B5: A,K: A,B2: A,A2: A] :
% 0.28/0.47 ( ( B5
% 0.28/0.47 = ( plus_plus @ A @ K @ B2 ) )
% 0.28/0.47 => ( ( plus_plus @ A @ A2 @ B5 )
% 0.28/0.47 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % group_cancel.add2
% 0.28/0.47 thf(fact_82_group__cancel_Oadd1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( comm_monoid_add @ A )
% 0.28/0.47 => ! [A4: A,K: A,A2: A,B2: A] :
% 0.28/0.47 ( ( A4
% 0.28/0.47 = ( plus_plus @ A @ K @ A2 ) )
% 0.28/0.47 => ( ( plus_plus @ A @ A4 @ B2 )
% 0.28/0.47 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % group_cancel.add1
% 0.28/0.47 thf(fact_83_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere779506340up_add @ A )
% 0.28/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.47 ( ( ( I = J )
% 0.28/0.47 & ( K = L ) )
% 0.28/0.47 => ( ( plus_plus @ A @ I @ K )
% 0.28/0.47 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_semiring(4)
% 0.28/0.47 thf(fact_84_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ab_semigroup_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 0.28/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.28/0.47 thf(fact_85_old_Oprod_Oinducts,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.28/0.47 ( ! [A6: A,B6: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B6 ) )
% 0.28/0.47 => ( P @ Prod ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.inducts
% 0.28/0.47 thf(fact_86_old_Oprod_Oexhaust,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.28/0.47 ~ ! [A6: A,B6: B] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ B @ A6 @ B6 ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.exhaust
% 0.28/0.47 thf(fact_87_prod__induct7,axiom,
% 0.28/0.47 ! [G: $tType,F: $tType,E: $tType,D3: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.28/0.47 ( ! [A6: A,B6: B,C4: C5,D4: D3,E2: E,F2: F,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C4 @ ( product_Pair @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D4 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 0.28/0.47 => ( P @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct7
% 0.28/0.47 thf(fact_88_prod__induct6,axiom,
% 0.28/0.47 ! [F: $tType,E: $tType,D3: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) )] :
% 0.28/0.47 ( ! [A6: A,B6: B,C4: C5,D4: D3,E2: E,F2: F] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) @ C4 @ ( product_Pair @ D3 @ ( product_prod @ E @ F ) @ D4 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 0.28/0.47 => ( P @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct6
% 0.28/0.47 thf(fact_89_prod__induct5,axiom,
% 0.28/0.47 ! [E: $tType,D3: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) )] :
% 0.28/0.47 ( ! [A6: A,B6: B,C4: C5,D4: D3,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ E ) @ C4 @ ( product_Pair @ D3 @ E @ D4 @ E2 ) ) ) ) )
% 0.28/0.47 => ( P @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct5
% 0.28/0.47 thf(fact_90_prod__induct4,axiom,
% 0.28/0.47 ! [D3: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) )] :
% 0.28/0.47 ( ! [A6: A,B6: B,C4: C5,D4: D3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ D3 ) @ B6 @ ( product_Pair @ C5 @ D3 @ C4 @ D4 ) ) ) )
% 0.28/0.47 => ( P @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct4
% 0.28/0.47 thf(fact_91_prod__induct3,axiom,
% 0.28/0.47 ! [C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C5 ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C5 )] :
% 0.28/0.47 ( ! [A6: A,B6: B,C4: C5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C5 ) @ A6 @ ( product_Pair @ B @ C5 @ B6 @ C4 ) ) )
% 0.28/0.47 => ( P @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_induct3
% 0.28/0.47 thf(fact_92_prod__cases7,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C5: $tType,D3: $tType,E: $tType,F: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.28/0.47 ~ ! [A6: A,B6: B,C4: C5,D4: D3,E2: E,F2: F,G2: G] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C4 @ ( product_Pair @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D4 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases7
% 0.28/0.47 thf(fact_93_prod__cases6,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C5: $tType,D3: $tType,E: $tType,F: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) )] :
% 0.28/0.47 ~ ! [A6: A,B6: B,C4: C5,D4: D3,E2: E,F2: F] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) @ C4 @ ( product_Pair @ D3 @ ( product_prod @ E @ F ) @ D4 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases6
% 0.28/0.47 thf(fact_94_prod__cases5,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C5: $tType,D3: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) )] :
% 0.28/0.47 ~ ! [A6: A,B6: B,C4: C5,D4: D3,E2: E] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ E ) @ C4 @ ( product_Pair @ D3 @ E @ D4 @ E2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases5
% 0.28/0.47 thf(fact_95_prod__cases4,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C5: $tType,D3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) )] :
% 0.28/0.47 ~ ! [A6: A,B6: B,C4: C5,D4: D3] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ D3 ) @ B6 @ ( product_Pair @ C5 @ D3 @ C4 @ D4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases4
% 0.28/0.47 thf(fact_96_prod__cases3,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,C5: $tType,Y: product_prod @ A @ ( product_prod @ B @ C5 )] :
% 0.28/0.47 ~ ! [A6: A,B6: B,C4: C5] :
% 0.28/0.47 ( Y
% 0.28/0.47 != ( product_Pair @ A @ ( product_prod @ B @ C5 ) @ A6 @ ( product_Pair @ B @ C5 @ B6 @ C4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases3
% 0.28/0.47 thf(fact_97_Pair__inject,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.28/0.47 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.28/0.47 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.28/0.47 => ~ ( ( A2 = A3 )
% 0.28/0.47 => ( B2 != B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Pair_inject
% 0.28/0.47 thf(fact_98_prod__cases,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.28/0.47 ( ! [A6: A,B6: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B6 ) )
% 0.28/0.47 => ( P @ P2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % prod_cases
% 0.28/0.47 thf(fact_99_surj__pair,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.28/0.47 ? [X4: A,Y3: B] :
% 0.28/0.47 ( P2
% 0.28/0.47 = ( product_Pair @ A @ B @ X4 @ Y3 ) ) ).
% 0.28/0.47
% 0.28/0.47 % surj_pair
% 0.28/0.47 thf(fact_100_pth__a,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [X: A,Y: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ ( zero_zero @ real ) @ X ) @ Y )
% 0.28/0.47 = Y ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_a
% 0.28/0.47 thf(fact_101_pth__8,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,D: real] :
% 0.28/0.47 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ D @ X ) )
% 0.28/0.47 = ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ C @ D ) @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_8
% 0.28/0.47 thf(fact_102_pth__6,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,Y: A] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ C @ ( plus_plus @ A @ X @ Y ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ C @ Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_6
% 0.28/0.47 thf(fact_103_pth__c_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,D: real,Y: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ D @ Y ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ ( real_V1908273582scaleR @ A @ C @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_c(1)
% 0.28/0.47 thf(fact_104_pth__c_I2_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,Z: A,D: real,Y: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) @ ( real_V1908273582scaleR @ A @ D @ Y ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_c(2)
% 0.28/0.47 thf(fact_105_pth__c_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,D: real,Y: A,Z: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_c(3)
% 0.28/0.47 thf(fact_106_pth__c_I4_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,W: A,D: real,Y: A,Z: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ W ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ W ) @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_c(4)
% 0.28/0.47 thf(fact_107_pth__b_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,D: real,Y: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ D @ Y ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ D @ Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_b(1)
% 0.28/0.47 thf(fact_108_pth__b_I2_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,Z: A,D: real,Y: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) @ ( real_V1908273582scaleR @ A @ D @ Y ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ Z @ ( real_V1908273582scaleR @ A @ D @ Y ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_b(2)
% 0.28/0.47 thf(fact_109_pth__b_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,D: real,Y: A,Z: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_b(3)
% 0.28/0.47 thf(fact_110_pth__b_I4_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,W: A,D: real,Y: A,Z: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ W ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ W @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_b(4)
% 0.28/0.47 thf(fact_111_pth__9_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,Z: A,D: real] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) @ ( real_V1908273582scaleR @ A @ D @ X ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ C @ D ) @ X ) @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_9(1)
% 0.28/0.47 thf(fact_112_pth__9_I2_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V55928688vector @ A )
% 0.28/0.47 => ! [C: real,X: A,D: real,Z: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ X ) @ Z ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ C @ D ) @ X ) @ Z ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pth_9(2)
% 0.28/0.47 thf(fact_113_scaleR__eq__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [B2: A,U: real,A2: A] :
% 0.28/0.47 ( ( ( plus_plus @ A @ B2 @ ( real_V1908273582scaleR @ A @ U @ A2 ) )
% 0.28/0.47 = ( plus_plus @ A @ A2 @ ( real_V1908273582scaleR @ A @ U @ B2 ) ) )
% 0.28/0.47 = ( ( A2 = B2 )
% 0.28/0.47 | ( U
% 0.28/0.47 = ( one_one @ real ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_eq_iff
% 0.28/0.47 thf(fact_114_scale__zero__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [X: A] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ ( zero_zero @ real ) @ X )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_zero_left
% 0.28/0.47 thf(fact_115_scale__eq__0__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [A2: real,X: A] :
% 0.28/0.47 ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.28/0.47 = ( zero_zero @ A ) )
% 0.28/0.47 = ( ( A2
% 0.28/0.47 = ( zero_zero @ real ) )
% 0.28/0.47 | ( X
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_eq_0_iff
% 0.28/0.47 thf(fact_116_scaleR__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [X: A] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ ( one_one @ real ) @ X )
% 0.28/0.47 = X ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_one
% 0.28/0.47 thf(fact_117_scale__cancel__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [A2: real,X: A,Y: A] :
% 0.28/0.47 ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.28/0.47 = ( real_V1908273582scaleR @ A @ A2 @ Y ) )
% 0.28/0.47 = ( ( X = Y )
% 0.28/0.47 | ( A2
% 0.28/0.47 = ( zero_zero @ real ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_cancel_left
% 0.28/0.47 thf(fact_118_scaleR__left__le__one__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [X: A,A2: real] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.28/0.47 => ( ( ord_less_eq @ real @ A2 @ ( one_one @ real ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left_le_one_le
% 0.28/0.47 thf(fact_119_scale__cancel__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [A2: real,X: A,B2: real] :
% 0.28/0.47 ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.28/0.47 = ( real_V1908273582scaleR @ A @ B2 @ X ) )
% 0.28/0.47 = ( ( A2 = B2 )
% 0.28/0.47 | ( X
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_cancel_right
% 0.28/0.47 thf(fact_120_scale__zero__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [A2: real] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 = ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_zero_right
% 0.28/0.47 thf(fact_121_split__scaleR__neg__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,X: A] :
% 0.28/0.47 ( ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ X @ ( zero_zero @ A ) ) )
% 0.28/0.47 | ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.28/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_scaleR_neg_le
% 0.28/0.47 thf(fact_122_split__scaleR__pos__le,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,B2: A] :
% 0.28/0.47 ( ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.28/0.47 | ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.28/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( real_V1908273582scaleR @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % split_scaleR_pos_le
% 0.28/0.47 thf(fact_123_set__plus__mono2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( plus @ A )
% 0.28/0.47 => ! [C2: set @ A,D2: set @ A,E3: set @ A,F3: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ C2 @ D2 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ E3 @ F3 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ ( plus_plus @ ( set @ A ) @ C2 @ E3 ) @ ( plus_plus @ ( set @ A ) @ D2 @ F3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_plus_mono2
% 0.28/0.47 thf(fact_124_set__plus__mono2__b,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( plus @ A )
% 0.28/0.47 => ! [C2: set @ A,D2: set @ A,E3: set @ A,F3: set @ A,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ C2 @ D2 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ E3 @ F3 )
% 0.28/0.47 => ( ( member @ A @ X @ ( plus_plus @ ( set @ A ) @ C2 @ E3 ) )
% 0.28/0.47 => ( member @ A @ X @ ( plus_plus @ ( set @ A ) @ D2 @ F3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_plus_mono2_b
% 0.28/0.47 thf(fact_125_set__zero__plus2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( comm_monoid_add @ A )
% 0.28/0.47 => ! [A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( member @ A @ ( zero_zero @ A ) @ A4 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ B5 @ ( plus_plus @ ( set @ A ) @ A4 @ B5 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_zero_plus2
% 0.28/0.47 thf(fact_126_scale__left__commute,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [A2: real,B2: real,X: A] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ A2 @ ( real_V1908273582scaleR @ A @ B2 @ X ) )
% 0.28/0.47 = ( real_V1908273582scaleR @ A @ B2 @ ( real_V1908273582scaleR @ A @ A2 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_left_commute
% 0.28/0.47 thf(fact_127_scale__right__imp__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [X: A,A2: real,B2: real] :
% 0.28/0.47 ( ( X
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.28/0.47 = ( real_V1908273582scaleR @ A @ B2 @ X ) )
% 0.28/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_right_imp_eq
% 0.28/0.47 thf(fact_128_scaleR__add__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [A2: real,X: A,Y: A] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ A2 @ ( plus_plus @ A @ X @ Y ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ A2 @ Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_add_right
% 0.28/0.47 thf(fact_129_scale__left__imp__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [A2: real,X: A,Y: A] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 != ( zero_zero @ real ) )
% 0.28/0.47 => ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.28/0.47 = ( real_V1908273582scaleR @ A @ A2 @ Y ) )
% 0.28/0.47 => ( X = Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scale_left_imp_eq
% 0.28/0.47 thf(fact_130_scaleR__left_Oadd,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [X: real,Y: real,Xa: A] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ X @ Y ) @ Xa )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ X @ Xa ) @ ( real_V1908273582scaleR @ A @ Y @ Xa ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left.add
% 0.28/0.47 thf(fact_131_scaleR__add__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [A2: real,B2: real,X: A] :
% 0.28/0.47 ( ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ A2 @ B2 ) @ X )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ B2 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_add_left
% 0.28/0.47 thf(fact_132_scaleR__right__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,B2: real,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ B2 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_right_mono
% 0.28/0.47 thf(fact_133_scaleR__right__mono__neg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [B2: real,A2: real,C: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ C ) @ ( real_V1908273582scaleR @ A @ B2 @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_right_mono_neg
% 0.28/0.47 thf(fact_134_scaleR__left__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [X: A,Y: A,A2: real] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.28/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ A2 @ Y ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left_mono
% 0.28/0.47 thf(fact_135_scaleR__left__mono__neg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [B2: A,A2: A,C: real] :
% 0.28/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ real @ C @ ( zero_zero @ real ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ C @ A2 ) @ ( real_V1908273582scaleR @ A @ C @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_left_mono_neg
% 0.28/0.47 thf(fact_136_scaleR__mono_H,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,B2: real,C: A,D: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C @ D )
% 0.28/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ C ) @ ( real_V1908273582scaleR @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_mono'
% 0.28/0.47 thf(fact_137_scaleR__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,B2: real,X: A,Y: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ X @ Y )
% 0.28/0.47 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ B2 @ Y ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_mono
% 0.28/0.47 thf(fact_138_scaleR__nonpos__nonpos,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( real_V1908273582scaleR @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_nonpos_nonpos
% 0.28/0.47 thf(fact_139_scaleR__nonpos__nonneg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_nonpos_nonneg
% 0.28/0.47 thf(fact_140_scaleR__nonneg__nonpos,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_nonneg_nonpos
% 0.28/0.47 thf(fact_141_scaleR__nonneg__nonneg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( real_V1908273582scaleR @ A @ A2 @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_nonneg_nonneg
% 0.28/0.47 thf(fact_142_Pair__le,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType] :
% 0.28/0.47 ( ( ( ord @ B )
% 0.28/0.47 & ( ord @ A ) )
% 0.28/0.47 => ! [A2: A,B2: B,C: A,D: B] :
% 0.28/0.47 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ C @ D ) )
% 0.28/0.47 = ( ( ord_less_eq @ A @ A2 @ C )
% 0.28/0.47 & ( ord_less_eq @ B @ B2 @ D ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Pair_le
% 0.28/0.47 thf(fact_143_old_Oprod_Orec,axiom,
% 0.28/0.47 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.28/0.47 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.28/0.47 = ( F1 @ A2 @ B2 ) ) ).
% 0.28/0.47
% 0.28/0.47 % old.prod.rec
% 0.28/0.47 thf(fact_144_not__one__le__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_one_le_zero
% 0.28/0.47 thf(fact_145_zero__le__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_le_one
% 0.28/0.47 thf(fact_146_zero__neq__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( zero_neq_one @ A )
% 0.28/0.47 => ( ( zero_zero @ A )
% 0.28/0.47 != ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_neq_one
% 0.28/0.47 thf(fact_147_Pair__mono,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType] :
% 0.28/0.47 ( ( ( ord @ B )
% 0.28/0.47 & ( ord @ A ) )
% 0.28/0.47 => ! [X: A,X5: A,Y: B,Y4: B] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X @ X5 )
% 0.28/0.47 => ( ( ord_less_eq @ B @ Y @ Y4 )
% 0.28/0.47 => ( ord_less_eq @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( product_Pair @ A @ B @ X5 @ Y4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Pair_mono
% 0.28/0.47 thf(fact_148_weak__convexI,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [Pr: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ( ! [X4: A,Y3: A,Alpha: real,Beta: real] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y3 ) @ Pr )
% 0.28/0.47 => ( ( ( plus_plus @ real @ Alpha @ Beta )
% 0.28/0.47 = ( one_one @ real ) )
% 0.28/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Alpha )
% 0.28/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Beta )
% 0.28/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ Alpha @ X4 ) @ ( real_V1908273582scaleR @ A @ Beta @ Y3 ) ) @ Y3 ) @ Pr ) ) ) ) )
% 0.28/0.47 => ( prefer1289595409x_pref @ A @ Pr ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % weak_convexI
% 0.28/0.47 thf(fact_149_subsetI,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ! [X4: A] :
% 0.28/0.47 ( ( member @ A @ X4 @ A4 )
% 0.28/0.47 => ( member @ A @ X4 @ B5 ) )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetI
% 0.28/0.47 thf(fact_150_subset__antisym,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.28/0.47 => ( A4 = B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_antisym
% 0.28/0.47 thf(fact_151_not__gr__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A )
% 0.28/0.47 => ! [N: A] :
% 0.28/0.47 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.28/0.47 = ( N
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_gr_zero
% 0.28/0.47 thf(fact_152_add__less__cancel__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere236663937imp_le @ A )
% 0.28/0.47 => ! [A2: A,C: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.28/0.47 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_less_cancel_right
% 0.28/0.47 thf(fact_153_add__less__cancel__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere236663937imp_le @ A )
% 0.28/0.47 => ! [C: A,A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.28/0.47 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_less_cancel_left
% 0.28/0.47 thf(fact_154_add__less__same__cancel1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere516151231imp_le @ A )
% 0.28/0.47 => ! [B2: A,A2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.28/0.47 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_less_same_cancel1
% 0.28/0.47 thf(fact_155_add__less__same__cancel2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere516151231imp_le @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.28/0.47 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_less_same_cancel2
% 0.28/0.47 thf(fact_156_less__add__same__cancel1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere516151231imp_le @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.28/0.47 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_add_same_cancel1
% 0.28/0.47 thf(fact_157_less__add__same__cancel2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere516151231imp_le @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.28/0.47 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_add_same_cancel2
% 0.28/0.47 thf(fact_158_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord219039673up_add @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.28/0.47 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % double_add_less_zero_iff_single_add_less_zero
% 0.28/0.47 thf(fact_159_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord219039673up_add @ A )
% 0.28/0.47 => ! [A2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.28/0.47 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_less_double_add_iff_zero_less_single_add
% 0.28/0.47 thf(fact_160_linorder__neqE__linordered__idom,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_idom @ A )
% 0.28/0.47 => ! [X: A,Y: A] :
% 0.28/0.47 ( ( X != Y )
% 0.28/0.47 => ( ~ ( ord_less @ A @ X @ Y )
% 0.28/0.47 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linorder_neqE_linordered_idom
% 0.28/0.47 thf(fact_161_add__less__imp__less__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere236663937imp_le @ A )
% 0.28/0.47 => ! [A2: A,C: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.28/0.47 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_less_imp_less_right
% 0.28/0.47 thf(fact_162_add__less__imp__less__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere236663937imp_le @ A )
% 0.28/0.47 => ! [C: A,A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.28/0.47 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_less_imp_less_left
% 0.28/0.47 thf(fact_163_add__strict__right__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_strict_right_mono
% 0.28/0.47 thf(fact_164_add__strict__left__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_strict_left_mono
% 0.28/0.47 thf(fact_165_add__strict__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( strict2144017051up_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A,D: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less @ A @ C @ D )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_strict_mono
% 0.28/0.47 thf(fact_166_add__mono__thms__linordered__field_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.47 ( ( ( ord_less @ A @ I @ J )
% 0.28/0.47 & ( K = L ) )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_field(1)
% 0.28/0.47 thf(fact_167_add__mono__thms__linordered__field_I2_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.47 ( ( ( I = J )
% 0.28/0.47 & ( ord_less @ A @ K @ L ) )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_field(2)
% 0.28/0.47 thf(fact_168_add__mono__thms__linordered__field_I5_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.47 ( ( ( ord_less @ A @ I @ J )
% 0.28/0.47 & ( ord_less @ A @ K @ L ) )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_field(5)
% 0.28/0.47 thf(fact_169_gr__zeroI,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A )
% 0.28/0.47 => ! [N: A] :
% 0.28/0.47 ( ( N
% 0.28/0.47 != ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % gr_zeroI
% 0.28/0.47 thf(fact_170_not__less__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A )
% 0.28/0.47 => ! [N: A] :
% 0.28/0.47 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_less_zero
% 0.28/0.47 thf(fact_171_gr__implies__not__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A )
% 0.28/0.47 => ! [M: A,N: A] :
% 0.28/0.47 ( ( ord_less @ A @ M @ N )
% 0.28/0.47 => ( N
% 0.28/0.47 != ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % gr_implies_not_zero
% 0.28/0.47 thf(fact_172_zero__less__iff__neq__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A )
% 0.28/0.47 => ! [N: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.28/0.47 = ( N
% 0.28/0.47 != ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_less_iff_neq_zero
% 0.28/0.47 thf(fact_173_add__less__le__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A,D: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ C @ D )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_less_le_mono
% 0.28/0.47 thf(fact_174_add__le__less__mono,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A,D: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less @ A @ C @ D )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_le_less_mono
% 0.28/0.47 thf(fact_175_add__mono__thms__linordered__field_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.47 ( ( ( ord_less @ A @ I @ J )
% 0.28/0.47 & ( ord_less_eq @ A @ K @ L ) )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_field(3)
% 0.28/0.47 thf(fact_176_add__mono__thms__linordered__field_I4_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere223160158up_add @ A )
% 0.28/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.47 ( ( ( ord_less_eq @ A @ I @ J )
% 0.28/0.47 & ( ord_less @ A @ K @ L ) )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono_thms_linordered_field(4)
% 0.28/0.47 thf(fact_177_add__neg__neg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere216010020id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_neg_neg
% 0.28/0.47 thf(fact_178_add__pos__pos,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere216010020id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.28/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_pos_pos
% 0.28/0.47 thf(fact_179_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.47 => ~ ! [C4: A] :
% 0.28/0.47 ( ( B2
% 0.28/0.47 = ( plus_plus @ A @ A2 @ C4 ) )
% 0.28/0.47 => ( C4
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % canonically_ordered_monoid_add_class.lessE
% 0.28/0.47 thf(fact_180_pos__add__strict,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( strict797366125id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less @ A @ B2 @ C )
% 0.28/0.47 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % pos_add_strict
% 0.28/0.47 thf(fact_181_add__less__zeroD,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_idom @ A )
% 0.28/0.47 => ! [X: A,Y: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ X @ Y ) @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ord_less @ A @ X @ ( zero_zero @ A ) )
% 0.28/0.47 | ( ord_less @ A @ Y @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_less_zeroD
% 0.28/0.47 thf(fact_182_zero__less__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( zero_less_one @ A )
% 0.28/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_less_one
% 0.28/0.47 thf(fact_183_not__one__less__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % not_one_less_zero
% 0.28/0.47 thf(fact_184_add__mono1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ B2 )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) @ ( plus_plus @ A @ B2 @ ( one_one @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_mono1
% 0.28/0.47 thf(fact_185_less__add__one,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_semidom @ A )
% 0.28/0.47 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_add_one
% 0.28/0.47 thf(fact_186_add__strict__increasing2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere1818651114id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less @ A @ B2 @ C )
% 0.28/0.47 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_strict_increasing2
% 0.28/0.47 thf(fact_187_add__strict__increasing,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere1818651114id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.28/0.47 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_strict_increasing
% 0.28/0.47 thf(fact_188_add__pos__nonneg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere216010020id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.28/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_pos_nonneg
% 0.28/0.47 thf(fact_189_add__nonpos__neg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere216010020id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_nonpos_neg
% 0.28/0.47 thf(fact_190_add__nonneg__pos,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere216010020id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.28/0.47 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.28/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_nonneg_pos
% 0.28/0.47 thf(fact_191_add__neg__nonpos,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere216010020id_add @ A )
% 0.28/0.47 => ! [A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.28/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_neg_nonpos
% 0.28/0.47 thf(fact_192_zero__less__two,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_less_two
% 0.28/0.47 thf(fact_193_scaleR__le__cancel__left__pos,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [C: real,A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ C )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ C @ A2 ) @ ( real_V1908273582scaleR @ A @ C @ B2 ) )
% 0.28/0.47 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_le_cancel_left_pos
% 0.28/0.47 thf(fact_194_scaleR__le__cancel__left__neg,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [C: real,A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less @ real @ C @ ( zero_zero @ real ) )
% 0.28/0.47 => ( ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ C @ A2 ) @ ( real_V1908273582scaleR @ A @ C @ B2 ) )
% 0.28/0.47 = ( ord_less_eq @ A @ B2 @ A2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_le_cancel_left_neg
% 0.28/0.47 thf(fact_195_scaleR__le__cancel__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [C: real,A2: A,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ C @ A2 ) @ ( real_V1908273582scaleR @ A @ C @ B2 ) )
% 0.28/0.47 = ( ( ( ord_less @ real @ ( zero_zero @ real ) @ C )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ B2 ) )
% 0.28/0.47 & ( ( ord_less @ real @ C @ ( zero_zero @ real ) )
% 0.28/0.47 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_le_cancel_left
% 0.28/0.47 thf(fact_196_Collect__mono__iff,axiom,
% 0.28/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.28/0.47 = ( ! [X3: A] :
% 0.28/0.47 ( ( P @ X3 )
% 0.28/0.47 => ( Q @ X3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono_iff
% 0.28/0.47 thf(fact_197_set__eq__subset,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ^ [Y5: set @ A,Z2: set @ A] : ( Y5 = Z2 ) )
% 0.28/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.28/0.47 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % set_eq_subset
% 0.28/0.47 thf(fact_198_subset__trans,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C2: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C2 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_trans
% 0.28/0.47 thf(fact_199_Collect__mono,axiom,
% 0.28/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.47 ( ! [X4: A] :
% 0.28/0.47 ( ( P @ X4 )
% 0.28/0.47 => ( Q @ X4 ) )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Collect_mono
% 0.28/0.47 thf(fact_200_subset__refl,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.28/0.47
% 0.28/0.47 % subset_refl
% 0.28/0.47 thf(fact_201_subset__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.28/0.47 ! [T2: A] :
% 0.28/0.47 ( ( member @ A @ T2 @ A7 )
% 0.28/0.47 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff
% 0.28/0.47 thf(fact_202_equalityD2,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( A4 = B5 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD2
% 0.28/0.47 thf(fact_203_equalityD1,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( A4 = B5 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityD1
% 0.28/0.47 thf(fact_204_subset__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.28/0.47 ! [X3: A] :
% 0.28/0.47 ( ( member @ A @ X3 @ A7 )
% 0.28/0.47 => ( member @ A @ X3 @ B7 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_eq
% 0.28/0.47 thf(fact_205_equalityE,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( A4 = B5 )
% 0.28/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % equalityE
% 0.28/0.47 thf(fact_206_subsetD,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( member @ A @ C @ A4 )
% 0.28/0.47 => ( member @ A @ C @ B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subsetD
% 0.28/0.47 thf(fact_207_in__mono,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( member @ A @ X @ A4 )
% 0.28/0.47 => ( member @ A @ X @ B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % in_mono
% 0.28/0.47 thf(fact_208_zero__le__scaleR__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( real_V1908273582scaleR @ A @ A2 @ B2 ) )
% 0.28/0.47 = ( ( ( ord_less @ real @ ( zero_zero @ real ) @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.28/0.47 | ( ( ord_less @ real @ A2 @ ( zero_zero @ real ) )
% 0.28/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.28/0.47 | ( A2
% 0.28/0.47 = ( zero_zero @ real ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_le_scaleR_iff
% 0.28/0.47 thf(fact_209_scaleR__le__0__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1587248058vector @ A )
% 0.28/0.47 => ! [A2: real,B2: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 0.28/0.47 = ( ( ( ord_less @ real @ ( zero_zero @ real ) @ A2 )
% 0.28/0.47 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.28/0.47 | ( ( ord_less @ real @ A2 @ ( zero_zero @ real ) )
% 0.28/0.47 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.28/0.47 | ( A2
% 0.28/0.47 = ( zero_zero @ real ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % scaleR_le_0_iff
% 0.28/0.47 thf(fact_210_weak__convexD,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [Pr: set @ ( product_prod @ A @ A ),X: A,Y: A,U: real,V: real] :
% 0.28/0.47 ( ( prefer1289595409x_pref @ A @ Pr )
% 0.28/0.47 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ Pr )
% 0.28/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ U )
% 0.28/0.47 => ( ( ord_less @ real @ ( zero_zero @ real ) @ V )
% 0.28/0.47 => ( ( ( plus_plus @ real @ U @ V )
% 0.28/0.47 = ( one_one @ real ) )
% 0.28/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ U @ X ) @ ( real_V1908273582scaleR @ A @ V @ Y ) ) @ Y ) @ Pr ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % weak_convexD
% 0.28/0.47 thf(fact_211_weak__convex__pref__def,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( ( prefer1289595409x_pref @ A )
% 0.28/0.47 = ( ^ [Pr2: set @ ( product_prod @ A @ A )] :
% 0.28/0.47 ! [X3: A,Y6: A] :
% 0.28/0.47 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y6 ) @ Pr2 )
% 0.28/0.47 => ! [Alpha2: real,Beta2: real] :
% 0.28/0.47 ( ( ( ( plus_plus @ real @ Alpha2 @ Beta2 )
% 0.28/0.47 = ( one_one @ real ) )
% 0.28/0.47 & ( ord_less @ real @ ( zero_zero @ real ) @ Alpha2 )
% 0.28/0.47 & ( ord_less @ real @ ( zero_zero @ real ) @ Beta2 ) )
% 0.28/0.47 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ Alpha2 @ X3 ) @ ( real_V1908273582scaleR @ A @ Beta2 @ Y6 ) ) @ Y6 ) @ Pr2 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % weak_convex_pref_def
% 0.28/0.47 thf(fact_212_discrete,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( unique1598680935umeral @ A )
% 0.28/0.47 => ( ( ord_less @ A )
% 0.28/0.47 = ( ^ [A5: A] : ( ord_less_eq @ A @ ( plus_plus @ A @ A5 @ ( one_one @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % discrete
% 0.28/0.47 thf(fact_213_field__le__epsilon,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A )
% 0.28/0.47 => ! [X: A,Y: A] :
% 0.28/0.47 ( ! [E2: A] :
% 0.28/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ E2 )
% 0.28/0.47 => ( ord_less_eq @ A @ X @ ( plus_plus @ A @ Y @ E2 ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % field_le_epsilon
% 0.28/0.47 thf(fact_214_approachable__lt__le2,axiom,
% 0.28/0.47 ! [A: $tType,Q: A > $o,F4: A > real,P: A > $o] :
% 0.28/0.47 ( ( ? [D5: real] :
% 0.28/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ D5 )
% 0.28/0.47 & ! [X3: A] :
% 0.28/0.47 ( ( Q @ X3 )
% 0.28/0.47 => ( ( ord_less @ real @ ( F4 @ X3 ) @ D5 )
% 0.28/0.47 => ( P @ X3 ) ) ) ) )
% 0.28/0.47 = ( ? [D5: real] :
% 0.28/0.47 ( ( ord_less @ real @ ( zero_zero @ real ) @ D5 )
% 0.28/0.47 & ! [X3: A] :
% 0.28/0.47 ( ( ord_less_eq @ real @ ( F4 @ X3 ) @ D5 )
% 0.28/0.47 => ( ( Q @ X3 )
% 0.28/0.47 => ( P @ X3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % approachable_lt_le2
% 0.28/0.47 thf(fact_215_psubsetI,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( A4 != B5 )
% 0.28/0.47 => ( ord_less @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % psubsetI
% 0.28/0.47 thf(fact_216_psubsetE,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % psubsetE
% 0.28/0.47 thf(fact_217_psubset__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.28/0.47 & ( A7 != B7 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % psubset_eq
% 0.28/0.47 thf(fact_218_psubset__imp__subset,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.28/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.28/0.47
% 0.28/0.47 % psubset_imp_subset
% 0.28/0.47 thf(fact_219_psubset__subset__trans,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C2: set @ A] :
% 0.28/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C2 )
% 0.28/0.47 => ( ord_less @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % psubset_subset_trans
% 0.28/0.47 thf(fact_220_subset__not__subset__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.28/0.47 & ~ ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_not_subset_eq
% 0.28/0.47 thf(fact_221_subset__psubset__trans,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C2: set @ A] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( ord_less @ ( set @ A ) @ B5 @ C2 )
% 0.28/0.47 => ( ord_less @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_psubset_trans
% 0.28/0.47 thf(fact_222_subset__iff__psubset__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.28/0.47 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.28/0.47 ( ( ord_less @ ( set @ A ) @ A7 @ B7 )
% 0.28/0.47 | ( A7 = B7 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % subset_iff_psubset_eq
% 0.28/0.47 thf(fact_223_less__prod__def,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ( ord @ A )
% 0.28/0.47 & ( ord @ B ) )
% 0.28/0.47 => ( ( ord_less @ ( product_prod @ A @ B ) )
% 0.28/0.47 = ( ^ [X3: product_prod @ A @ B,Y6: product_prod @ A @ B] :
% 0.28/0.47 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ X3 @ Y6 )
% 0.28/0.47 & ~ ( ord_less_eq @ ( product_prod @ A @ B ) @ Y6 @ X3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_prod_def
% 0.28/0.47 thf(fact_224_linordered__field__no__lb,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A )
% 0.28/0.47 => ! [X6: A] :
% 0.28/0.47 ? [Y3: A] : ( ord_less @ A @ Y3 @ X6 ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_no_lb
% 0.28/0.47 thf(fact_225_linordered__field__no__ub,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A )
% 0.28/0.47 => ! [X6: A] :
% 0.28/0.47 ? [X_1: A] : ( ord_less @ A @ X6 @ X_1 ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_no_ub
% 0.28/0.47 thf(fact_226_divides__aux__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( unique1598680935umeral @ A )
% 0.28/0.47 => ! [Q2: A,R: A] :
% 0.28/0.47 ( ( unique455577585es_aux @ A @ ( product_Pair @ A @ A @ Q2 @ R ) )
% 0.28/0.47 = ( R
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % divides_aux_eq
% 0.28/0.47 thf(fact_227_less__numeral__extra_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_numeral_extra(1)
% 0.28/0.47 thf(fact_228_psubset__trans,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C2: set @ A] :
% 0.28/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( ord_less @ ( set @ A ) @ B5 @ C2 )
% 0.28/0.47 => ( ord_less @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % psubset_trans
% 0.28/0.47 thf(fact_229_psubsetD,axiom,
% 0.28/0.47 ! [A: $tType,A4: set @ A,B5: set @ A,C: A] :
% 0.28/0.47 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.28/0.47 => ( ( member @ A @ C @ A4 )
% 0.28/0.47 => ( member @ A @ C @ B5 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % psubsetD
% 0.28/0.47 thf(fact_230_is__num__normalize_I1_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( neg_numeral @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 0.28/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % is_num_normalize(1)
% 0.28/0.47 thf(fact_231_le__numeral__extra_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_numeral_extra(3)
% 0.28/0.47 thf(fact_232_less__numeral__extra_I3_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_numeral_extra(3)
% 0.28/0.47 thf(fact_233_le__numeral__extra_I4_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_numeral_extra(4)
% 0.28/0.47 thf(fact_234_less__numeral__extra_I4_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord1659791738miring @ A )
% 0.28/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % less_numeral_extra(4)
% 0.28/0.47 thf(fact_235_order__refl,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_refl
% 0.28/0.47 thf(fact_236_add__scaleR__degen,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ! [U: real,B2: A,V: real,A2: A] :
% 0.28/0.47 ( ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ U @ B2 ) @ ( real_V1908273582scaleR @ A @ V @ A2 ) )
% 0.28/0.47 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ U @ A2 ) @ ( real_V1908273582scaleR @ A @ V @ B2 ) ) )
% 0.28/0.47 => ( ( U != V )
% 0.28/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_scaleR_degen
% 0.28/0.47 thf(fact_237_le__funD,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ord @ B )
% 0.28/0.47 => ! [F4: A > B,G3: A > B,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( A > B ) @ F4 @ G3 )
% 0.28/0.47 => ( ord_less_eq @ B @ ( F4 @ X ) @ ( G3 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_funD
% 0.28/0.47 thf(fact_238_le__funE,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ord @ B )
% 0.28/0.47 => ! [F4: A > B,G3: A > B,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ ( A > B ) @ F4 @ G3 )
% 0.28/0.47 => ( ord_less_eq @ B @ ( F4 @ X ) @ ( G3 @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_funE
% 0.28/0.47 thf(fact_239_le__funI,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ord @ B )
% 0.28/0.47 => ! [F4: A > B,G3: A > B] :
% 0.28/0.47 ( ! [X4: A] : ( ord_less_eq @ B @ ( F4 @ X4 ) @ ( G3 @ X4 ) )
% 0.28/0.47 => ( ord_less_eq @ ( A > B ) @ F4 @ G3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_funI
% 0.28/0.47 thf(fact_240_le__fun__def,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType] :
% 0.28/0.47 ( ( ord @ B )
% 0.28/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.28/0.47 = ( ^ [F5: A > B,G4: A > B] :
% 0.28/0.47 ! [X3: A] : ( ord_less_eq @ B @ ( F5 @ X3 ) @ ( G4 @ X3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_fun_def
% 0.28/0.47 thf(fact_241_order__subst1,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType] :
% 0.28/0.47 ( ( ( order @ B )
% 0.28/0.47 & ( order @ A ) )
% 0.28/0.47 => ! [A2: A,F4: B > A,B2: B,C: B] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ ( F4 @ B2 ) )
% 0.28/0.47 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.28/0.47 => ( ! [X4: B,Y3: B] :
% 0.28/0.47 ( ( ord_less_eq @ B @ X4 @ Y3 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( F4 @ X4 ) @ ( F4 @ Y3 ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ ( F4 @ C ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst1
% 0.28/0.47 thf(fact_242_order__subst2,axiom,
% 0.28/0.47 ! [A: $tType,C5: $tType] :
% 0.28/0.47 ( ( ( order @ C5 )
% 0.28/0.47 & ( order @ A ) )
% 0.28/0.47 => ! [A2: A,B2: A,F4: A > C5,C: C5] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ C5 @ ( F4 @ B2 ) @ C )
% 0.28/0.47 => ( ! [X4: A,Y3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.28/0.47 => ( ord_less_eq @ C5 @ ( F4 @ X4 ) @ ( F4 @ Y3 ) ) )
% 0.28/0.47 => ( ord_less_eq @ C5 @ ( F4 @ A2 ) @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_subst2
% 0.28/0.47 thf(fact_243_ord__eq__le__subst,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType] :
% 0.28/0.47 ( ( ( ord @ B )
% 0.28/0.47 & ( ord @ A ) )
% 0.28/0.47 => ! [A2: A,F4: B > A,B2: B,C: B] :
% 0.28/0.47 ( ( A2
% 0.28/0.47 = ( F4 @ B2 ) )
% 0.28/0.47 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.28/0.47 => ( ! [X4: B,Y3: B] :
% 0.28/0.47 ( ( ord_less_eq @ B @ X4 @ Y3 )
% 0.28/0.47 => ( ord_less_eq @ A @ ( F4 @ X4 ) @ ( F4 @ Y3 ) ) )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ ( F4 @ C ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_eq_le_subst
% 0.28/0.47 thf(fact_244_ord__le__eq__subst,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType] :
% 0.28/0.47 ( ( ( ord @ B )
% 0.28/0.47 & ( ord @ A ) )
% 0.28/0.47 => ! [A2: A,B2: A,F4: A > B,C: B] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ( F4 @ B2 )
% 0.28/0.47 = C )
% 0.28/0.47 => ( ! [X4: A,Y3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.28/0.47 => ( ord_less_eq @ B @ ( F4 @ X4 ) @ ( F4 @ Y3 ) ) )
% 0.28/0.47 => ( ord_less_eq @ B @ ( F4 @ A2 ) @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % ord_le_eq_subst
% 0.28/0.47 thf(fact_245_eq__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.28/0.47 = ( ^ [X3: A,Y6: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X3 @ Y6 )
% 0.28/0.47 & ( ord_less_eq @ A @ Y6 @ X3 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_iff
% 0.28/0.47 thf(fact_246_antisym,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [X: A,Y: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.28/0.47 => ( ( ord_less_eq @ A @ Y @ X )
% 0.28/0.47 => ( X = Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym
% 0.28/0.47 thf(fact_247_linear,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ! [X: A,Y: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.28/0.47 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linear
% 0.28/0.47 thf(fact_248_eq__refl,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A )
% 0.28/0.47 => ! [X: A,Y: A] :
% 0.28/0.47 ( ( X = Y )
% 0.28/0.47 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % eq_refl
% 0.28/0.47 thf(fact_249_le__cases,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ! [X: A,Y: A] :
% 0.28/0.47 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.28/0.47 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_cases
% 0.28/0.47 thf(fact_250_order_Otrans,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [A2: A,B2: A,C: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.28/0.47 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.28/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order.trans
% 0.28/0.47 thf(fact_251_le__cases3,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linorder @ A )
% 0.28/0.47 => ! [X: A,Y: A,Z: A] :
% 0.28/0.47 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.28/0.47 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.28/0.47 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.28/0.47 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.28/0.47 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.28/0.47 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.28/0.47 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_cases3
% 0.28/0.47 thf(fact_252_antisym__conv,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ! [Y: A,X: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ Y @ X )
% 0.28/0.47 => ( ( ord_less_eq @ A @ X @ Y )
% 0.28/0.47 = ( X = Y ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % antisym_conv
% 0.28/0.47 thf(fact_253_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( order @ A )
% 0.28/0.47 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.28/0.47 = ( ^ [A5: A,B4: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.28/0.47 & ( ord_less_eq @ A @ B4 @ A5 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_class.order.eq_iff
% 0.28/0.47
% 0.28/0.47 % Subclasses (10)
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___HOL_Otype,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( type @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Oplus,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( plus @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ozero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( zero @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ogroup__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( group_add @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Omonoid__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( monoid_add @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Osemigroup__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( semigroup_add @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocomm__monoid__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( comm_monoid_add @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Oab__semigroup__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( ab_semigroup_add @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocancel__semigroup__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( cancel_semigroup_add @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocancel__comm__monoid__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( real_V1076094709vector @ A )
% 0.28/0.47 => ( cancel1352612707id_add @ A ) ) ).
% 0.28/0.47
% 0.28/0.47 % Type constructors (75)
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( ordere890947078_space @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1,axiom,
% 0.28/0.47 ordere890947078_space @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( preorder @ A9 )
% 0.28/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( order @ A9 )
% 0.28/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ord @ A9 )
% 0.28/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Oab__semigroup__add,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( ab_semigroup_add @ A8 )
% 0.28/0.47 => ( ab_semigroup_add @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( comm_monoid_add @ A8 )
% 0.28/0.47 => ( comm_monoid_add @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Osemigroup__add,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( semigroup_add @ A8 )
% 0.28/0.47 => ( semigroup_add @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.28/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Omonoid__add,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( monoid_add @ A8 )
% 0.28/0.47 => ( monoid_add @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 0.28/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Oord_4,axiom,
% 0.28/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Ozero,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( zero @ A8 )
% 0.28/0.47 => ( zero @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Oplus,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( plus @ A8 )
% 0.28/0.47 => ( plus @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Groups_Oone,axiom,
% 0.28/0.47 ! [A8: $tType] :
% 0.28/0.47 ( ( one @ A8 )
% 0.28/0.47 => ( one @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_5,axiom,
% 0.28/0.47 preorder @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.28/0.47 linorder @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_6,axiom,
% 0.28/0.47 order @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 0.28/0.47 ord @ $o ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.28/0.47 ordere516151231imp_le @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oordered__real__vector,axiom,
% 0.28/0.47 real_V1587248058vector @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.28/0.47 strict2144017051up_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.28/0.47 ordere223160158up_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.28/0.47 ordere236663937imp_le @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 0.28/0.47 real_V55928688vector @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add,axiom,
% 0.28/0.47 strict797366125id_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add,axiom,
% 0.28/0.47 ordere1818651114id_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring,axiom,
% 0.28/0.47 linord1659791738miring @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add,axiom,
% 0.28/0.47 ordere779506340up_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector,axiom,
% 0.28/0.47 real_V1076094709vector @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add,axiom,
% 0.28/0.47 ordere216010020id_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 0.28/0.47 linord219039673up_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add,axiom,
% 0.28/0.47 cancel1352612707id_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add,axiom,
% 0.28/0.47 cancel_semigroup_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__semidom,axiom,
% 0.28/0.47 linordered_semidom @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_8,axiom,
% 0.28/0.47 ab_semigroup_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Fields_Olinordered__field,axiom,
% 0.28/0.47 linordered_field @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_9,axiom,
% 0.28/0.47 comm_monoid_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 0.28/0.47 linordered_idom @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Osemigroup__add_10,axiom,
% 0.28/0.47 semigroup_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Ozero__less__one,axiom,
% 0.28/0.47 zero_less_one @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Rings_Ozero__neq__one,axiom,
% 0.28/0.47 zero_neq_one @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Orderings_Opreorder_11,axiom,
% 0.28/0.47 preorder @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Orderings_Olinorder_12,axiom,
% 0.28/0.47 linorder @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Omonoid__add_13,axiom,
% 0.28/0.47 monoid_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.28/0.47 group_add @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Orderings_Oorder_14,axiom,
% 0.28/0.47 order @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 0.28/0.47 neg_numeral @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Orderings_Oord_15,axiom,
% 0.28/0.47 ord @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Ozero_16,axiom,
% 0.28/0.47 zero @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oplus_17,axiom,
% 0.28/0.47 plus @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Real_Oreal___Groups_Oone_18,axiom,
% 0.28/0.47 one @ real ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__monoid__add__imp__le_19,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( ordere516151231imp_le @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oordered__real__vector_20,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( real_V1587248058vector @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Ostrict__ordered__ab__semigroup__add_21,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( strict2144017051up_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Oordered__cancel__ab__semigroup__add_22,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( ordere223160158up_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__add__imp__le_23,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( ordere236663937imp_le @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_24,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( real_V55928688vector @ A8 )
% 0.28/0.47 & ( real_V55928688vector @ A9 ) )
% 0.28/0.47 => ( real_V55928688vector @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Ostrict__ordered__comm__monoid__add_25,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( strict797366125id_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Oordered__cancel__comm__monoid__add_26,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( ordere1818651114id_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__add_27,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( ordere779506340up_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__vector_28,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( real_V1076094709vector @ A8 )
% 0.28/0.47 & ( real_V1076094709vector @ A9 ) )
% 0.28/0.47 => ( real_V1076094709vector @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Oordered__comm__monoid__add_29,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ordere890947078_space @ A8 )
% 0.28/0.47 & ( ordere890947078_space @ A9 ) )
% 0.28/0.47 => ( ordere216010020id_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Ocancel__comm__monoid__add_30,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( cancel1352612707id_add @ A8 )
% 0.28/0.47 & ( cancel1352612707id_add @ A9 ) )
% 0.28/0.47 => ( cancel1352612707id_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Ocancel__semigroup__add_31,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( cancel_semigroup_add @ A8 )
% 0.28/0.47 & ( cancel_semigroup_add @ A9 ) )
% 0.28/0.47 => ( cancel_semigroup_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Oab__semigroup__add_32,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ab_semigroup_add @ A8 )
% 0.28/0.47 & ( ab_semigroup_add @ A9 ) )
% 0.28/0.47 => ( ab_semigroup_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Ocomm__monoid__add_33,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( comm_monoid_add @ A8 )
% 0.28/0.47 & ( comm_monoid_add @ A9 ) )
% 0.28/0.47 => ( comm_monoid_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Osemigroup__add_34,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( semigroup_add @ A8 )
% 0.28/0.47 & ( semigroup_add @ A9 ) )
% 0.28/0.47 => ( semigroup_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_35,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( preorder @ A8 )
% 0.28/0.47 & ( preorder @ A9 ) )
% 0.28/0.47 => ( preorder @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Omonoid__add_36,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( monoid_add @ A8 )
% 0.28/0.47 & ( monoid_add @ A9 ) )
% 0.28/0.47 => ( monoid_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Ogroup__add_37,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( group_add @ A8 )
% 0.28/0.47 & ( group_add @ A9 ) )
% 0.28/0.47 => ( group_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Orderings_Oorder_38,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( order @ A8 )
% 0.28/0.47 & ( order @ A9 ) )
% 0.28/0.47 => ( order @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Orderings_Oord_39,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( ord @ A8 )
% 0.28/0.47 & ( ord @ A9 ) )
% 0.28/0.47 => ( ord @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Ozero_40,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( zero @ A8 )
% 0.28/0.47 & ( zero @ A9 ) )
% 0.28/0.47 => ( zero @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Product__Type_Oprod___Groups_Oplus_41,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( ( plus @ A8 )
% 0.28/0.47 & ( plus @ A9 ) )
% 0.28/0.47 => ( plus @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % Free types (1)
% 0.28/0.47 thf(tfree_0,hypothesis,
% 0.28/0.47 real_V1076094709vector @ a ).
% 0.28/0.47
% 0.28/0.47 % Conjectures (1)
% 0.28/0.47 thf(conj_0,conjecture,
% 0.28/0.47 member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ ( plus_plus @ a @ ( real_V1908273582scaleR @ a @ u @ x ) @ ( real_V1908273582scaleR @ a @ v @ y ) ) @ y ) @ relation ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 0.31/1.50 ---- Embedded in THF ---
% 0.31/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.50 %%% Generated on Tue Feb 24 08:28:02 EST 2026
% 0.31/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.50 %%% Logic specification used:
% 0.31/1.50 %%% thf(spec, logic, $$dhol).
% 0.31/1.50
% 0.31/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2DTF11849.p
% 0.31/1.50 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.31/1.50 thf(ty_t_Real_Oreal, type, real: $tType).
% 0.31/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.31/1.50 thf(ty_tf_a, type, a: $tType).
% 0.31/1.50 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space, type, ordere890947078_space: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oplus, type, plus: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Rings_Ozero__neq__one, type, zero_neq_one: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Rings_Ozero__less__one, type, zero_less_one: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__comm__monoid__add, type, ordere216010020id_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Real__Vector__Spaces_Oreal__vector, type, real_V1076094709vector: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add, type, ordere1818651114id_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add, type, strict797366125id_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector, type, real_V55928688vector: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Real__Vector__Spaces_Oordered__real__vector, type, real_V1587248058vector: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral, type, unique1598680935umeral: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux, type, unique455577585es_aux: (!> [A:$tType]: ((((product_prod @ A) @ A) > $o)))).
% 0.31/1.50 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 0.31/1.50 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 0.31/1.50 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Preferences__Mirabelle__stygcjuplb_Oweak__convex__pref, type, prefer1289595409x_pref: (!> [A:$tType]: (((set @ ((product_prod @ A) @ A)) > $o)))).
% 0.31/1.50 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 0.31/1.50 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 0.31/1.50 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR, type, real_V1908273582scaleR: (!> [A:$tType]: ((real > (A > A))))).
% 0.31/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.31/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.31/1.50 thf(sy_v_relation, type, relation: (set @ ((product_prod @ a) @ a))).
% 0.31/1.50 thf(sy_v_u, type, u: real).
% 0.31/1.50 thf(sy_v_v, type, v: real).
% 0.31/1.50 thf(sy_v_x, type, x: a).
% 0.31/1.50 thf(sy_v_y, type, y: a).
% 0.31/1.50 thf(fact_0_assms_I1_J, axiom, ((prefer1289595409x_pref @ a) @ relation)).
% 0.31/1.50 thf(fact_1_indifferent__imp__weak__pref_I2_J, axiom, (! [X:a,Y:a]: ((((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ X) @ Y)) @ relation) & (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Y) @ X)) @ relation)) => (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Y) @ X)) @ relation))))).
% 0.31/1.50 thf(fact_2_indifferent__imp__weak__pref_I1_J, axiom, (! [X:a,Y:a]: ((((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ X) @ Y)) @ relation) & (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Y) @ X)) @ relation)) => (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ X) @ Y)) @ relation))))).
% 0.31/1.50 thf(fact_3_indiff__trans, axiom, (! [X:a,Y:a,Z:a]: ((((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ X) @ Y)) @ relation) & (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Y) @ X)) @ relation)) => (((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Y) @ Z)) @ relation) & (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Z) @ Y)) @ relation)) => ((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ X) @ Z)) @ relation) & (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Z) @ X)) @ relation))))))).
% 0.31/1.50 thf(fact_4_strict__trans, axiom, (! [X:a,Y:a,Z:a]: ((((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ X) @ Y)) @ relation) & (~ ((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Y) @ X)) @ relation)))) => (((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Y) @ Z)) @ relation) & (~ ((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Z) @ Y)) @ relation)))) => ((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ X) @ Z)) @ relation) & (~ ((((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ Z) @ X)) @ relation))))))))).
% 0.31/1.50 thf(fact_5_assms_I2_J, axiom, (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ x) @ y)) @ relation)).
% 0.31/1.50 thf(fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062, axiom, (((u != (zero_zero @ real)) & (u != (one_one @ real))) => (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ (((plus_plus @ a) @ (((real_V1908273582scaleR @ a) @ u) @ x)) @ (((real_V1908273582scaleR @ a) @ v) @ y))) @ y)) @ relation))).
% 0.31/1.50 thf(fact_7_u__0, axiom, ((u = (zero_zero @ real)) => (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ (((plus_plus @ a) @ (((real_V1908273582scaleR @ a) @ u) @ x)) @ (((real_V1908273582scaleR @ a) @ v) @ y))) @ y)) @ relation))).
% 0.31/1.50 thf(fact_8_assms_I4_J, axiom, (((ord_less_eq @ real) @ (zero_zero @ real)) @ v)).
% 0.31/1.50 thf(fact_9_assms_I5_J, axiom, ((((plus_plus @ real) @ u) @ v) = (one_one @ real))).
% 0.31/1.50 thf(fact_10_assms_I3_J, axiom, (((ord_less_eq @ real) @ (zero_zero @ real)) @ u)).
% 0.31/1.50 thf(fact_11_scaleR__Pair, axiom, (! [A:$tType,B:$tType]: ((((real_V1076094709vector @ B) & (real_V1076094709vector @ A)) => (! [R:real,A2:A,B2:B]: (((((real_V1908273582scaleR @ ((product_prod @ A) @ B)) @ R) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((((product_Pair @ A) @ B) @ (((real_V1908273582scaleR @ A) @ R) @ A2)) @ (((real_V1908273582scaleR @ B) @ R) @ B2))))))))).
% 0.31/1.50 thf(fact_12_scale__prod, axiom, (! [A:$tType,B:$tType]: ((((real_V1076094709vector @ B) & (real_V1076094709vector @ A)) => (! [X:real,A2:A,B2:B]: (((((real_V1908273582scaleR @ ((product_prod @ A) @ B)) @ X) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((((product_Pair @ A) @ B) @ (((real_V1908273582scaleR @ A) @ X) @ A2)) @ (((real_V1908273582scaleR @ B) @ X) @ B2))))))))).
% 0.31/1.50 thf(fact_13_add__Pair, axiom, (! [A:$tType,B:$tType]: ((((plus @ B) & (plus @ A)) => (! [A2:A,B2:B,C:A,D:B]: (((((plus_plus @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ ((((product_Pair @ A) @ B) @ C) @ D)) = ((((product_Pair @ A) @ B) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ B) @ B2) @ D))))))))).
% 0.31/1.50 thf(fact_14_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X2:B,Y1:A,Y2:B]: (((((((product_Pair @ A) @ B) @ X1) @ X2) = ((((product_Pair @ A) @ B) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 0.31/1.50 thf(fact_15_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((A2 = A3) & (B2 = B3)))))).
% 0.31/1.50 thf(fact_16_set__plus__intro, axiom, (! [A:$tType]: (((plus @ A) => (! [A2:A,C2:(set @ A),B2:A,D2:(set @ A)]: (((((member @ A) @ A2) @ C2) => ((((member @ A) @ B2) @ D2) => (((member @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (((plus_plus @ (set @ A)) @ C2) @ D2)))))))))).
% 0.31/1.50 thf(fact_17_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C)) = (B2 = C)))))))).
% 0.31/1.50 thf(fact_18_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B2 = C)))))))).
% 0.31/1.50 thf(fact_19_pth__9_I3_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,W:A,D:real,Z:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ W)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ X)) @ Z)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ (((plus_plus @ real) @ C) @ D)) @ X)) @ (((plus_plus @ A) @ W) @ Z))))))))).
% 0.31/1.50 thf(fact_20_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_21_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_22_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_23_zero__eq__add__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A,Y:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ X) @ Y)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_24_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A,Y:A]: ((((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_25_add__cancel__right__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ A2) @ B2)) = (B2 = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_26_add__cancel__right__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: (((A2 = (((plus_plus @ A) @ B2) @ A2)) = (B2 = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_27_add__cancel__left__right, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A,B2:A]: ((((((plus_plus @ A) @ A2) @ B2) = A2) = (B2 = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_28_add__cancel__left__left, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [B2:A,A2:A]: ((((((plus_plus @ A) @ B2) @ A2) = A2) = (B2 = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_29_double__zero__sym, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A2) @ A2)) = (A2 = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_30_double__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: ((((((plus_plus @ A) @ A2) @ A2) = (zero_zero @ A)) = (A2 = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_31_add_Oright__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 0.31/1.50 thf(fact_32_add_Oleft__neutral, axiom, (! [A:$tType]: (((monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 0.31/1.50 thf(fact_33_zero__le__double__add__iff__zero__le__single__add, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ A2)))))))).
% 0.31/1.50 thf(fact_34_double__add__le__zero__iff__single__add__le__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_35_le__add__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ B2) @ A2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 0.31/1.50 thf(fact_36_le__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)))))))).
% 0.31/1.50 thf(fact_37_add__le__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_38_add__le__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less_eq @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_39_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 0.31/1.50 thf(fact_40_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_41_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 0.31/1.50 thf(fact_42_add__nonpos__eq__0__iff, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ Y) @ (zero_zero @ A)) => (((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))))).
% 0.31/1.50 thf(fact_43_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 0.31/1.50 thf(fact_44_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A4)))) = A4)))).
% 0.31/1.50 thf(fact_45_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.31/1.50 thf(fact_46_add__nonneg__eq__0__iff, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ Y) => (((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))))).
% 0.31/1.50 thf(fact_47_add__nonpos__nonpos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_48_add__nonneg__nonneg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_49_add__increasing2, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [C:A,B2:A,A2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => ((((ord_less_eq @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C)))))))))).
% 0.31/1.50 thf(fact_50_add__decreasing2, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ C) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ B2))))))))).
% 0.31/1.50 thf(fact_51_add__increasing, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C)))))))))).
% 0.31/1.50 thf(fact_52_add__decreasing, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ B2))))))))).
% 0.31/1.50 thf(fact_53_zero__prod__def, axiom, (! [A:$tType,B:$tType]: ((((zero @ B) & (zero @ A)) => ((zero_zero @ ((product_prod @ A) @ B)) = ((((product_Pair @ A) @ B) @ (zero_zero @ A)) @ (zero_zero @ B))))))).
% 0.31/1.50 thf(fact_54_add__le__imp__le__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_55_add__le__imp__le__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_56_le__iff__add, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => ((ord_less_eq @ A) = (^ [A5:A,B4:A]: ((? [C3:A]: ((B4 = (((plus_plus @ A) @ A5) @ C3))))))))))).
% 0.31/1.50 thf(fact_57_add__right__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 0.31/1.50 thf(fact_58_less__eqE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((! [C4:A]: ((B2 != (((plus_plus @ A) @ A2) @ C4))))))))))))).
% 0.31/1.50 thf(fact_59_add__left__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2))))))))).
% 0.31/1.50 thf(fact_60_add__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 0.31/1.50 thf(fact_61_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$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))))))))).
% 0.31/1.50 thf(fact_62_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_63_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$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))))))))).
% 0.31/1.50 thf(fact_64_pth__4_I1_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [X:A]: (((((real_V1908273582scaleR @ A) @ (zero_zero @ real)) @ X) = (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_65_convex__ge__imp__conved, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [Pr:(set @ ((product_prod @ A) @ A))]: (((! [X4:A,Y3:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Y3)) @ Pr) => (! [Alpha:real,Beta:real]: (((((((plus_plus @ real) @ Alpha) @ Beta) = (one_one @ real)) & ((((ord_less_eq @ real) @ (zero_zero @ real)) @ Alpha) & (((ord_less_eq @ real) @ (zero_zero @ real)) @ Beta))) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ Alpha) @ X4)) @ (((real_V1908273582scaleR @ A) @ Beta) @ Y3))) @ Y3)) @ Pr))))))) => ((prefer1289595409x_pref @ A) @ Pr)))))))).
% 0.31/1.50 thf(fact_66_add_Ogroup__left__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 0.31/1.50 thf(fact_67_add_Ocomm__neutral, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 0.31/1.50 thf(fact_68_comm__monoid__add__class_Oadd__0, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A2:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A2) = A2))))))).
% 0.31/1.50 thf(fact_69_pth__d, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [X:A]: (((((plus_plus @ A) @ X) @ (zero_zero @ A)) = X))))))).
% 0.31/1.50 thf(fact_70_pth__7_I1_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [X:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ X) = X))))))).
% 0.31/1.50 thf(fact_71_pth__1, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [X:A]: ((X = (((real_V1908273582scaleR @ A) @ (one_one @ real)) @ X)))))))).
% 0.31/1.50 thf(fact_72_pth__4_I2_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real]: (((((real_V1908273582scaleR @ A) @ C) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_73_add__right__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C) @ A2)) => (B2 = C)))))))).
% 0.31/1.50 thf(fact_74_add__left__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C)) => (B2 = C)))))))).
% 0.31/1.50 thf(fact_75_add_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [B2:A,A2:A,C:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 0.31/1.50 thf(fact_76_add_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => ((plus_plus @ A) = (^ [A5:A,B4:A]: ((((plus_plus @ A) @ B4) @ A5)))))))).
% 0.31/1.50 thf(fact_77_add_Oright__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [B2:A,A2:A,C:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B2 = C)))))))).
% 0.31/1.50 thf(fact_78_add_Oleft__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C)) = (B2 = C)))))))).
% 0.31/1.50 thf(fact_79_add_Oassoc, axiom, (! [A:$tType]: (((semigroup_add @ A) => (! [A2:A,B2:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 0.31/1.50 thf(fact_80_set__plus__elim, axiom, (! [A:$tType]: (((plus @ A) => (! [X:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ X) @ (((plus_plus @ (set @ A)) @ A4) @ B5)) => (~ ((! [A6:A,B6:A]: (((X = (((plus_plus @ A) @ A6) @ B6)) => ((((member @ A) @ A6) @ A4) => (~ ((((member @ A) @ B6) @ B5)))))))))))))))).
% 0.31/1.50 thf(fact_81_group__cancel_Oadd2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [B5:A,K:A,B2:A,A2:A]: (((B5 = (((plus_plus @ A) @ K) @ B2)) => ((((plus_plus @ A) @ A2) @ B5) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_82_group__cancel_Oadd1, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A4:A,K:A,A2:A,B2:A]: (((A4 = (((plus_plus @ A) @ K) @ A2)) => ((((plus_plus @ A) @ A4) @ B2) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_83_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$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))))))))).
% 0.31/1.50 thf(fact_84_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [A2:A,B2:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 0.31/1.50 thf(fact_85_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A6:A,B6:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B6)))) => (P @ Prod))))).
% 0.31/1.50 thf(fact_86_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A6:A,B6:B]: ((Y != ((((product_Pair @ A) @ B) @ A6) @ B6))))))))).
% 0.31/1.50 thf(fact_87_prod__induct7, axiom, (! [G:$tType,F:$tType,E:$tType,D3:$tType,C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: (((! [A6:A,B6:B,C4:C5,D4:D3,E2:E,F2:F,G2:G]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B6) @ ((((product_Pair @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C4) @ ((((product_Pair @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D4) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2))))))))) => (P @ X))))).
% 0.31/1.50 thf(fact_88_prod__induct6, axiom, (! [F:$tType,E:$tType,D3:$tType,C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F)))))]: (((! [A6:A,B6:B,C4:C5,D4:D3,E2:E,F2:F]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F)))) @ B6) @ ((((product_Pair @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F))) @ C4) @ ((((product_Pair @ D3) @ ((product_prod @ E) @ F)) @ D4) @ ((((product_Pair @ E) @ F) @ E2) @ F2)))))))) => (P @ X))))).
% 0.31/1.50 thf(fact_89_prod__induct5, axiom, (! [E:$tType,D3:$tType,C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ E))))]: (((! [A6:A,B6:B,C4:C5,D4:D3,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ E))) @ B6) @ ((((product_Pair @ C5) @ ((product_prod @ D3) @ E)) @ C4) @ ((((product_Pair @ D3) @ E) @ D4) @ E2))))))) => (P @ X))))).
% 0.31/1.50 thf(fact_90_prod__induct4, axiom, (! [D3:$tType,C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D3))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D3)))]: (((! [A6:A,B6:B,C4:C5,D4:D3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D3))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ D3)) @ B6) @ ((((product_Pair @ C5) @ D3) @ C4) @ D4)))))) => (P @ X))))).
% 0.31/1.50 thf(fact_91_prod__induct3, axiom, (! [C5:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C5)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C5))]: (((! [A6:A,B6:B,C4:C5]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C5)) @ A6) @ ((((product_Pair @ B) @ C5) @ B6) @ C4))))) => (P @ X))))).
% 0.31/1.50 thf(fact_92_prod__cases7, axiom, (! [A:$tType,B:$tType,C5:$tType,D3:$tType,E:$tType,F:$tType,G:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))))]: ((~ ((! [A6:A,B6:B,C4:C5,D4:D3,E2:E,F2:F,G2:G]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G))))) @ B6) @ ((((product_Pair @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G)))) @ C4) @ ((((product_Pair @ D3) @ ((product_prod @ E) @ ((product_prod @ F) @ G))) @ D4) @ ((((product_Pair @ E) @ ((product_prod @ F) @ G)) @ E2) @ ((((product_Pair @ F) @ G) @ F2) @ G2)))))))))))))).
% 0.31/1.50 thf(fact_93_prod__cases6, axiom, (! [A:$tType,B:$tType,C5:$tType,D3:$tType,E:$tType,F:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F)))))]: ((~ ((! [A6:A,B6:B,C4:C5,D4:D3,E2:E,F2:F]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F))))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F)))) @ B6) @ ((((product_Pair @ C5) @ ((product_prod @ D3) @ ((product_prod @ E) @ F))) @ C4) @ ((((product_Pair @ D3) @ ((product_prod @ E) @ F)) @ D4) @ ((((product_Pair @ E) @ F) @ E2) @ F2))))))))))))).
% 0.31/1.50 thf(fact_94_prod__cases5, axiom, (! [A:$tType,B:$tType,C5:$tType,D3:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ E))))]: ((~ ((! [A6:A,B6:B,C4:C5,D4:D3,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ E)))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ ((product_prod @ D3) @ E))) @ B6) @ ((((product_Pair @ C5) @ ((product_prod @ D3) @ E)) @ C4) @ ((((product_Pair @ D3) @ E) @ D4) @ E2)))))))))))).
% 0.31/1.50 thf(fact_95_prod__cases4, axiom, (! [A:$tType,B:$tType,C5:$tType,D3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D3)))]: ((~ ((! [A6:A,B6:B,C4:C5,D4:D3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C5) @ D3))) @ A6) @ ((((product_Pair @ B) @ ((product_prod @ C5) @ D3)) @ B6) @ ((((product_Pair @ C5) @ D3) @ C4) @ D4))))))))))).
% 0.31/1.50 thf(fact_96_prod__cases3, axiom, (! [A:$tType,B:$tType,C5:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C5))]: ((~ ((! [A6:A,B6:B,C4:C5]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C5)) @ A6) @ ((((product_Pair @ B) @ C5) @ B6) @ C4)))))))))).
% 0.31/1.50 thf(fact_97_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A3:A,B3:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A3) @ B3)) => (~ (((A2 = A3) => (B2 != B3)))))))).
% 0.31/1.50 thf(fact_98_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A6:A,B6:B]: ((P @ ((((product_Pair @ A) @ B) @ A6) @ B6)))) => (P @ P2))))).
% 0.31/1.50 thf(fact_99_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X4:A,Y3:B]: ((P2 = ((((product_Pair @ A) @ B) @ X4) @ Y3))))))).
% 0.31/1.50 thf(fact_100_pth__a, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [X:A,Y:A]: (((((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ (zero_zero @ real)) @ X)) @ Y) = Y))))))).
% 0.31/1.50 thf(fact_101_pth__8, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,D:real]: (((((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((real_V1908273582scaleR @ A) @ D) @ X)) = (((real_V1908273582scaleR @ A) @ (((plus_plus @ real) @ C) @ D)) @ X)))))))).
% 0.31/1.50 thf(fact_102_pth__6, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,Y:A]: (((((real_V1908273582scaleR @ A) @ C) @ (((plus_plus @ A) @ X) @ Y)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((real_V1908273582scaleR @ A) @ C) @ Y))))))))).
% 0.31/1.50 thf(fact_103_pth__c_I1_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,D:real,Y:A]: (((((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ (((real_V1908273582scaleR @ A) @ C) @ X))))))))).
% 0.31/1.50 thf(fact_104_pth__c_I2_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,Z:A,D:real,Y:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ Z)) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ Z))))))))).
% 0.31/1.50 thf(fact_105_pth__c_I3_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,D:real,Y:A,Z:A]: (((((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ Z)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ Z))))))))).
% 0.31/1.50 thf(fact_106_pth__c_I4_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,W:A,D:real,Y:A,Z:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ W)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ Z)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ (((plus_plus @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ W)) @ Z))))))))).
% 0.31/1.50 thf(fact_107_pth__b_I1_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,D:real,Y:A]: (((((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((real_V1908273582scaleR @ A) @ D) @ Y))))))))).
% 0.31/1.50 thf(fact_108_pth__b_I2_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,Z:A,D:real,Y:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ Z)) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((plus_plus @ A) @ Z) @ (((real_V1908273582scaleR @ A) @ D) @ Y)))))))))).
% 0.31/1.50 thf(fact_109_pth__b_I3_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,D:real,Y:A,Z:A]: (((((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ Z)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ Z))))))))).
% 0.31/1.50 thf(fact_110_pth__b_I4_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,W:A,D:real,Y:A,Z:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ W)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ Z)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((plus_plus @ A) @ W) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ Y)) @ Z)))))))))).
% 0.31/1.50 thf(fact_111_pth__9_I1_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,Z:A,D:real]: (((((plus_plus @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ Z)) @ (((real_V1908273582scaleR @ A) @ D) @ X)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ (((plus_plus @ real) @ C) @ D)) @ X)) @ Z)))))))).
% 0.31/1.50 thf(fact_112_pth__9_I2_J, axiom, (! [A:$tType]: (((real_V55928688vector @ A) => (! [C:real,X:A,D:real,Z:A]: (((((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ C) @ X)) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ D) @ X)) @ Z)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ (((plus_plus @ real) @ C) @ D)) @ X)) @ Z)))))))).
% 0.31/1.50 thf(fact_113_scaleR__eq__iff, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [B2:A,U:real,A2:A]: ((((((plus_plus @ A) @ B2) @ (((real_V1908273582scaleR @ A) @ U) @ A2)) = (((plus_plus @ A) @ A2) @ (((real_V1908273582scaleR @ A) @ U) @ B2))) = ((A2 = B2) | (U = (one_one @ real)))))))))).
% 0.31/1.50 thf(fact_114_scale__zero__left, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [X:A]: (((((real_V1908273582scaleR @ A) @ (zero_zero @ real)) @ X) = (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_115_scale__eq__0__iff, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:real,X:A]: ((((((real_V1908273582scaleR @ A) @ A2) @ X) = (zero_zero @ A)) = ((A2 = (zero_zero @ real)) | (X = (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_116_scaleR__one, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [X:A]: (((((real_V1908273582scaleR @ A) @ (one_one @ real)) @ X) = X))))))).
% 0.31/1.50 thf(fact_117_scale__cancel__left, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:real,X:A,Y:A]: ((((((real_V1908273582scaleR @ A) @ A2) @ X) = (((real_V1908273582scaleR @ A) @ A2) @ Y)) = ((X = Y) | (A2 = (zero_zero @ real)))))))))).
% 0.31/1.50 thf(fact_118_scaleR__left__le__one__le, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [X:A,A2:real]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => ((((ord_less_eq @ real) @ A2) @ (one_one @ real)) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ X))))))))).
% 0.31/1.50 thf(fact_119_scale__cancel__right, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:real,X:A,B2:real]: ((((((real_V1908273582scaleR @ A) @ A2) @ X) = (((real_V1908273582scaleR @ A) @ B2) @ X)) = ((A2 = B2) | (X = (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_120_scale__zero__right, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:real]: (((((real_V1908273582scaleR @ A) @ A2) @ (zero_zero @ A)) = (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_121_split__scaleR__neg__le, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,X:A]: (((((((ord_less_eq @ real) @ (zero_zero @ real)) @ A2) & (((ord_less_eq @ A) @ X) @ (zero_zero @ A))) | ((((ord_less_eq @ real) @ A2) @ (zero_zero @ real)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ X))) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_122_split__scaleR__pos__le, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,B2:A]: (((((((ord_less_eq @ real) @ (zero_zero @ real)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | ((((ord_less_eq @ real) @ A2) @ (zero_zero @ real)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A)))) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((real_V1908273582scaleR @ A) @ A2) @ B2))))))))).
% 0.31/1.50 thf(fact_123_set__plus__mono2, axiom, (! [A:$tType]: (((plus @ A) => (! [C2:(set @ A),D2:(set @ A),E3:(set @ A),F3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C2) @ D2) => ((((ord_less_eq @ (set @ A)) @ E3) @ F3) => (((ord_less_eq @ (set @ A)) @ (((plus_plus @ (set @ A)) @ C2) @ E3)) @ (((plus_plus @ (set @ A)) @ D2) @ F3)))))))))).
% 0.31/1.50 thf(fact_124_set__plus__mono2__b, axiom, (! [A:$tType]: (((plus @ A) => (! [C2:(set @ A),D2:(set @ A),E3:(set @ A),F3:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ C2) @ D2) => ((((ord_less_eq @ (set @ A)) @ E3) @ F3) => ((((member @ A) @ X) @ (((plus_plus @ (set @ A)) @ C2) @ E3)) => (((member @ A) @ X) @ (((plus_plus @ (set @ A)) @ D2) @ F3))))))))))).
% 0.31/1.50 thf(fact_125_set__zero__plus2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ (zero_zero @ A)) @ A4) => (((ord_less_eq @ (set @ A)) @ B5) @ (((plus_plus @ (set @ A)) @ A4) @ B5))))))))).
% 0.31/1.50 thf(fact_126_scale__left__commute, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:real,B2:real,X:A]: (((((real_V1908273582scaleR @ A) @ A2) @ (((real_V1908273582scaleR @ A) @ B2) @ X)) = (((real_V1908273582scaleR @ A) @ B2) @ (((real_V1908273582scaleR @ A) @ A2) @ X))))))))).
% 0.31/1.50 thf(fact_127_scale__right__imp__eq, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [X:A,A2:real,B2:real]: (((X != (zero_zero @ A)) => (((((real_V1908273582scaleR @ A) @ A2) @ X) = (((real_V1908273582scaleR @ A) @ B2) @ X)) => (A2 = B2))))))))).
% 0.31/1.50 thf(fact_128_scaleR__add__right, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:real,X:A,Y:A]: (((((real_V1908273582scaleR @ A) @ A2) @ (((plus_plus @ A) @ X) @ Y)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ (((real_V1908273582scaleR @ A) @ A2) @ Y))))))))).
% 0.31/1.50 thf(fact_129_scale__left__imp__eq, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:real,X:A,Y:A]: (((A2 != (zero_zero @ real)) => (((((real_V1908273582scaleR @ A) @ A2) @ X) = (((real_V1908273582scaleR @ A) @ A2) @ Y)) => (X = Y))))))))).
% 0.31/1.50 thf(fact_130_scaleR__left_Oadd, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [X:real,Y:real,Xa:A]: (((((real_V1908273582scaleR @ A) @ (((plus_plus @ real) @ X) @ Y)) @ Xa) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ X) @ Xa)) @ (((real_V1908273582scaleR @ A) @ Y) @ Xa))))))))).
% 0.31/1.50 thf(fact_131_scaleR__add__left, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [A2:real,B2:real,X:A]: (((((real_V1908273582scaleR @ A) @ (((plus_plus @ real) @ A2) @ B2)) @ X) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ (((real_V1908273582scaleR @ A) @ B2) @ X))))))))).
% 0.31/1.50 thf(fact_132_scaleR__right__mono, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,B2:real,X:A]: (((((ord_less_eq @ real) @ A2) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ (((real_V1908273582scaleR @ A) @ B2) @ X)))))))))).
% 0.31/1.50 thf(fact_133_scaleR__right__mono__neg, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [B2:real,A2:real,C:A]: (((((ord_less_eq @ real) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ C)) @ (((real_V1908273582scaleR @ A) @ B2) @ C)))))))))).
% 0.31/1.50 thf(fact_134_scaleR__left__mono, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [X:A,Y:A,A2:real]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ A2) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ (((real_V1908273582scaleR @ A) @ A2) @ Y)))))))))).
% 0.31/1.50 thf(fact_135_scaleR__left__mono__neg, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [B2:A,A2:A,C:real]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ real) @ C) @ (zero_zero @ real)) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ C) @ A2)) @ (((real_V1908273582scaleR @ A) @ C) @ B2)))))))))).
% 0.31/1.50 thf(fact_136_scaleR__mono_H, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,B2:real,C:A,D:A]: (((((ord_less_eq @ real) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ C) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ C)) @ (((real_V1908273582scaleR @ A) @ B2) @ D)))))))))))).
% 0.31/1.50 thf(fact_137_scaleR__mono, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,B2:real,X:A,Y:A]: (((((ord_less_eq @ real) @ A2) @ B2) => ((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ real) @ (zero_zero @ real)) @ B2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ (((real_V1908273582scaleR @ A) @ B2) @ Y)))))))))))).
% 0.31/1.50 thf(fact_138_scaleR__nonpos__nonpos, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,B2:A]: (((((ord_less_eq @ real) @ A2) @ (zero_zero @ real)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((real_V1908273582scaleR @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_139_scaleR__nonpos__nonneg, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,X:A]: (((((ord_less_eq @ real) @ A2) @ (zero_zero @ real)) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_140_scaleR__nonneg__nonpos, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,X:A]: (((((ord_less_eq @ real) @ (zero_zero @ real)) @ A2) => ((((ord_less_eq @ A) @ X) @ (zero_zero @ A)) => (((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ X)) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_141_scaleR__nonneg__nonneg, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,X:A]: (((((ord_less_eq @ real) @ (zero_zero @ real)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (((real_V1908273582scaleR @ A) @ A2) @ X)))))))))).
% 0.31/1.50 thf(fact_142_Pair__le, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:B,C:A,D:B]: (((((ord_less_eq @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) @ ((((product_Pair @ A) @ B) @ C) @ D)) = ((((ord_less_eq @ A) @ A2) @ C) & (((ord_less_eq @ B) @ B2) @ D))))))))).
% 0.31/1.50 thf(fact_143_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 0.31/1.50 thf(fact_144_not__one__le__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less_eq @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_145_zero__le__one, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 0.31/1.50 thf(fact_146_zero__neq__one, axiom, (! [A:$tType]: (((zero_neq_one @ A) => ((zero_zero @ A) != (one_one @ A)))))).
% 0.31/1.50 thf(fact_147_Pair__mono, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [X:A,X5:A,Y:B,Y4:B]: (((((ord_less_eq @ A) @ X) @ X5) => ((((ord_less_eq @ B) @ Y) @ Y4) => (((ord_less_eq @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X) @ Y)) @ ((((product_Pair @ A) @ B) @ X5) @ Y4)))))))))).
% 0.31/1.50 thf(fact_148_weak__convexI, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [Pr:(set @ ((product_prod @ A) @ A))]: (((! [X4:A,Y3:A,Alpha:real,Beta:real]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X4) @ Y3)) @ Pr) => (((((plus_plus @ real) @ Alpha) @ Beta) = (one_one @ real)) => ((((ord_less @ real) @ (zero_zero @ real)) @ Alpha) => ((((ord_less @ real) @ (zero_zero @ real)) @ Beta) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ Alpha) @ X4)) @ (((real_V1908273582scaleR @ A) @ Beta) @ Y3))) @ Y3)) @ Pr))))))) => ((prefer1289595409x_pref @ A) @ Pr)))))))).
% 0.31/1.50 thf(fact_149_subsetI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A4) => (((member @ A) @ X4) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 0.31/1.50 thf(fact_150_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A4) => (A4 = B5)))))).
% 0.31/1.50 thf(fact_151_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_152_add__less__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_153_add__less__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_154_add__less__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ B2) @ A2)) @ B2) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_155_add__less__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ B2) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_156_less__add__same__cancel1, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ B2)) = (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))).
% 0.31/1.50 thf(fact_157_less__add__same__cancel2, axiom, (! [A:$tType]: (((ordere516151231imp_le @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ B2) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ B2)))))))).
% 0.31/1.50 thf(fact_158_double__add__less__zero__iff__single__add__less__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ A2)) @ (zero_zero @ A)) = (((ord_less @ A) @ A2) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_159_zero__less__double__add__iff__zero__less__single__add, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ A2)) = (((ord_less @ A) @ (zero_zero @ A)) @ A2)))))))).
% 0.31/1.50 thf(fact_160_linorder__neqE__linordered__idom, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 0.31/1.50 thf(fact_161_add__less__imp__less__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_162_add__less__imp__less__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_163_add__strict__right__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 0.31/1.50 thf(fact_164_add__strict__left__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2))))))))).
% 0.31/1.50 thf(fact_165_add__strict__mono, axiom, (! [A:$tType]: (((strict2144017051up_add @ A) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 0.31/1.50 thf(fact_166_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_167_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_168_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_169_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 0.31/1.50 thf(fact_170_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_171_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_172_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_173_add__less__le__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 0.31/1.50 thf(fact_174_add__le__less__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 0.31/1.50 thf(fact_175_add__mono__thms__linordered__field_I3_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_176_add__mono__thms__linordered__field_I4_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_177_add__neg__neg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_178_add__pos__pos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_179_canonically__ordered__monoid__add__class_OlessE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((! [C4:A]: (((B2 = (((plus_plus @ A) @ A2) @ C4)) => (C4 = (zero_zero @ A)))))))))))))).
% 0.31/1.50 thf(fact_180_pos__add__strict, axiom, (! [A:$tType]: (((strict797366125id_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C)))))))))).
% 0.31/1.50 thf(fact_181_add__less__zeroD, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ X) @ Y)) @ (zero_zero @ A)) => ((((ord_less @ A) @ X) @ (zero_zero @ A)) | (((ord_less @ A) @ Y) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_182_zero__less__one, axiom, (! [A:$tType]: (((zero_less_one @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 0.31/1.50 thf(fact_183_not__one__less__zero, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_184_add__mono1, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ (one_one @ A))) @ (((plus_plus @ A) @ B2) @ (one_one @ A)))))))))).
% 0.31/1.50 thf(fact_185_less__add__one, axiom, (! [A:$tType]: (((linordered_semidom @ A) => (! [A2:A]: ((((ord_less @ A) @ A2) @ (((plus_plus @ A) @ A2) @ (one_one @ A))))))))).
% 0.31/1.50 thf(fact_186_add__strict__increasing2, axiom, (! [A:$tType]: (((ordere1818651114id_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C)))))))))).
% 0.31/1.50 thf(fact_187_add__strict__increasing, axiom, (! [A:$tType]: (((ordere1818651114id_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C)))))))))).
% 0.31/1.50 thf(fact_188_add__pos__nonneg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less_eq @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_189_add__nonpos__neg, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_190_add__nonneg__pos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ A2) => ((((ord_less @ A) @ (zero_zero @ A)) @ B2) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_191_add__neg__nonpos, axiom, (! [A:$tType]: (((ordere216010020id_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ (zero_zero @ A)) => ((((ord_less_eq @ A) @ B2) @ (zero_zero @ A)) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_192_zero__less__two, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A))))))).
% 0.31/1.50 thf(fact_193_scaleR__le__cancel__left__pos, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [C:real,A2:A,B2:A]: (((((ord_less @ real) @ (zero_zero @ real)) @ C) => ((((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ C) @ A2)) @ (((real_V1908273582scaleR @ A) @ C) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2))))))))).
% 0.31/1.50 thf(fact_194_scaleR__le__cancel__left__neg, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [C:real,A2:A,B2:A]: (((((ord_less @ real) @ C) @ (zero_zero @ real)) => ((((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ C) @ A2)) @ (((real_V1908273582scaleR @ A) @ C) @ B2)) = (((ord_less_eq @ A) @ B2) @ A2))))))))).
% 0.31/1.50 thf(fact_195_scaleR__le__cancel__left, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [C:real,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ C) @ A2)) @ (((real_V1908273582scaleR @ A) @ C) @ B2)) = (((((ord_less @ real) @ (zero_zero @ real)) @ C) => (((ord_less_eq @ A) @ A2) @ B2)) & ((((ord_less @ real) @ C) @ (zero_zero @ real)) => (((ord_less_eq @ A) @ B2) @ A2)))))))))).
% 0.31/1.50 thf(fact_196_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X3:A]: (((P @ X3) => (Q @ X3)))))))).
% 0.31/1.50 thf(fact_197_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y5:(set @ A),Z2:(set @ A)]: ((Y5 = Z2))) = (^ [A7:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B7) & (((ord_less_eq @ (set @ A)) @ B7) @ A7)))))))).
% 0.31/1.50 thf(fact_198_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C2) => (((ord_less_eq @ (set @ A)) @ A4) @ C2)))))).
% 0.31/1.50 thf(fact_199_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) => (Q @ X4)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 0.31/1.50 thf(fact_200_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 0.31/1.50 thf(fact_201_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A7) => (((member @ A) @ T2) @ B7)))))))))).
% 0.31/1.50 thf(fact_202_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A4))))).
% 0.31/1.50 thf(fact_203_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 0.31/1.50 thf(fact_204_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: ((! [X3:A]: (((((member @ A) @ X3) @ A7) => (((member @ A) @ X3) @ B7)))))))))).
% 0.31/1.50 thf(fact_205_equalityE, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))))).
% 0.31/1.50 thf(fact_206_subsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C) @ A4) => (((member @ A) @ C) @ B5)))))).
% 0.31/1.50 thf(fact_207_in__mono, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B5)))))).
% 0.31/1.50 thf(fact_208_zero__le__scaleR__iff, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((real_V1908273582scaleR @ A) @ A2) @ B2)) = (((((ord_less @ real) @ (zero_zero @ real)) @ A2) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | (((((ord_less @ real) @ A2) @ (zero_zero @ real)) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | (A2 = (zero_zero @ real))))))))))).
% 0.31/1.50 thf(fact_209_scaleR__le__0__iff, axiom, (! [A:$tType]: (((real_V1587248058vector @ A) => (! [A2:real,B2:A]: (((((ord_less_eq @ A) @ (((real_V1908273582scaleR @ A) @ A2) @ B2)) @ (zero_zero @ A)) = (((((ord_less @ real) @ (zero_zero @ real)) @ A2) & (((ord_less_eq @ A) @ B2) @ (zero_zero @ A))) | (((((ord_less @ real) @ A2) @ (zero_zero @ real)) & (((ord_less_eq @ A) @ (zero_zero @ A)) @ B2)) | (A2 = (zero_zero @ real))))))))))).
% 0.31/1.50 thf(fact_210_weak__convexD, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [Pr:(set @ ((product_prod @ A) @ A)),X:A,Y:A,U:real,V:real]: ((((prefer1289595409x_pref @ A) @ Pr) => ((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X) @ Y)) @ Pr) => ((((ord_less @ real) @ (zero_zero @ real)) @ U) => ((((ord_less @ real) @ (zero_zero @ real)) @ V) => (((((plus_plus @ real) @ U) @ V) = (one_one @ real)) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ U) @ X)) @ (((real_V1908273582scaleR @ A) @ V) @ Y))) @ Y)) @ Pr)))))))))))).
% 0.31/1.50 thf(fact_211_weak__convex__pref__def, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => ((prefer1289595409x_pref @ A) = (^ [Pr2:(set @ ((product_prod @ A) @ A))]: ((! [X3:A,Y6:A]: (((((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ X3) @ Y6)) @ Pr2) => (! [Alpha2:real,Beta2:real]: (((((((plus_plus @ real) @ Alpha2) @ Beta2) = (one_one @ real)) & ((((ord_less @ real) @ (zero_zero @ real)) @ Alpha2) & (((ord_less @ real) @ (zero_zero @ real)) @ Beta2))) => (((member @ ((product_prod @ A) @ A)) @ ((((product_Pair @ A) @ A) @ (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ Alpha2) @ X3)) @ (((real_V1908273582scaleR @ A) @ Beta2) @ Y6))) @ Y6)) @ Pr2)))))))))))))).
% 0.31/1.50 thf(fact_212_discrete, axiom, (! [A:$tType]: (((unique1598680935umeral @ A) => ((ord_less @ A) = (^ [A5:A]: (((ord_less_eq @ A) @ (((plus_plus @ A) @ A5) @ (one_one @ A)))))))))).
% 0.31/1.50 thf(fact_213_field__le__epsilon, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X:A,Y:A]: (((! [E2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ E2) => (((ord_less_eq @ A) @ X) @ (((plus_plus @ A) @ Y) @ E2))))) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.31/1.50 thf(fact_214_approachable__lt__le2, axiom, (! [A:$tType,Q:(A > $o),F4:(A > real),P:(A > $o)]: (((? [D5:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ D5) & (! [X3:A]: (((Q @ X3) => ((((ord_less @ real) @ (F4 @ X3)) @ D5) => (P @ X3)))))))) = (? [D5:real]: (((((ord_less @ real) @ (zero_zero @ real)) @ D5) & (! [X3:A]: (((((ord_less_eq @ real) @ (F4 @ X3)) @ D5) => ((Q @ X3) => (P @ X3)))))))))))).
% 0.31/1.50 thf(fact_215_psubsetI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((A4 != B5) => (((ord_less @ (set @ A)) @ A4) @ B5)))))).
% 0.31/1.50 thf(fact_216_psubsetE, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B5) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))).
% 0.31/1.50 thf(fact_217_psubset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B7) & (A7 != B7)))))))).
% 0.31/1.50 thf(fact_218_psubset__imp__subset, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B5) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 0.31/1.50 thf(fact_219_psubset__subset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C2:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C2) => (((ord_less @ (set @ A)) @ A4) @ C2)))))).
% 0.31/1.50 thf(fact_220_subset__not__subset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B7) & (~ ((((ord_less_eq @ (set @ A)) @ B7) @ A7)))))))))).
% 0.31/1.50 thf(fact_221_subset__psubset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less @ (set @ A)) @ B5) @ C2) => (((ord_less @ (set @ A)) @ A4) @ C2)))))).
% 0.31/1.50 thf(fact_222_subset__iff__psubset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B7:(set @ A)]: (((((ord_less @ (set @ A)) @ A7) @ B7) | (A7 = B7)))))))).
% 0.31/1.50 thf(fact_223_less__prod__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ A) & (ord @ B)) => ((ord_less @ ((product_prod @ A) @ B)) = (^ [X3:((product_prod @ A) @ B),Y6:((product_prod @ A) @ B)]: (((((ord_less_eq @ ((product_prod @ A) @ B)) @ X3) @ Y6) & (~ ((((ord_less_eq @ ((product_prod @ A) @ B)) @ Y6) @ X3))))))))))).
% 0.31/1.50 thf(fact_224_linordered__field__no__lb, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X6:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X6))))))))).
% 0.31/1.50 thf(fact_225_linordered__field__no__ub, axiom, (! [A:$tType]: (((linordered_field @ A) => (! [X6:A]: ((? [X_1:A]: ((((ord_less @ A) @ X6) @ X_1))))))))).
% 0.31/1.50 thf(fact_226_divides__aux__eq, axiom, (! [A:$tType]: (((unique1598680935umeral @ A) => (! [Q2:A,R:A]: ((((unique455577585es_aux @ A) @ ((((product_Pair @ A) @ A) @ Q2) @ R)) = (R = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_227_less__numeral__extra_I1_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 0.31/1.50 thf(fact_228_psubset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C2:(set @ A)]: (((((ord_less @ (set @ A)) @ A4) @ B5) => ((((ord_less @ (set @ A)) @ B5) @ C2) => (((ord_less @ (set @ A)) @ A4) @ C2)))))).
% 0.31/1.50 thf(fact_229_psubsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C:A]: (((((ord_less @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C) @ A4) => (((member @ A) @ C) @ B5)))))).
% 0.31/1.50 thf(fact_230_is__num__normalize_I1_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => (! [A2:A,B2:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 0.31/1.50 thf(fact_231_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 0.31/1.50 thf(fact_232_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_233_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 0.31/1.50 thf(fact_234_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 0.31/1.50 thf(fact_235_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 0.31/1.50 thf(fact_236_add__scaleR__degen, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (! [U:real,B2:A,V:real,A2:A]: ((((((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ U) @ B2)) @ (((real_V1908273582scaleR @ A) @ V) @ A2)) = (((plus_plus @ A) @ (((real_V1908273582scaleR @ A) @ U) @ A2)) @ (((real_V1908273582scaleR @ A) @ V) @ B2))) => ((U != V) => (A2 = B2))))))))).
% 0.31/1.50 thf(fact_237_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F4:(A > B),G3:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F4) @ G3) => (((ord_less_eq @ B) @ (F4 @ X)) @ (G3 @ X))))))))).
% 0.31/1.50 thf(fact_238_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F4:(A > B),G3:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F4) @ G3) => (((ord_less_eq @ B) @ (F4 @ X)) @ (G3 @ X))))))))).
% 0.31/1.50 thf(fact_239_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F4:(A > B),G3:(A > B)]: (((! [X4:A]: ((((ord_less_eq @ B) @ (F4 @ X4)) @ (G3 @ X4)))) => (((ord_less_eq @ (A > B)) @ F4) @ G3)))))))).
% 0.31/1.50 thf(fact_240_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F5:(A > B),G4:(A > B)]: ((! [X3:A]: ((((ord_less_eq @ B) @ (F5 @ X3)) @ (G4 @ X3))))))))))).
% 0.31/1.50 thf(fact_241_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F4:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F4 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X4:B,Y3:B]: (((((ord_less_eq @ B) @ X4) @ Y3) => (((ord_less_eq @ A) @ (F4 @ X4)) @ (F4 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F4 @ C))))))))))).
% 0.31/1.50 thf(fact_242_order__subst2, axiom, (! [A:$tType,C5:$tType]: ((((order @ C5) & (order @ A)) => (! [A2:A,B2:A,F4:(A > C5),C:C5]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C5) @ (F4 @ B2)) @ C) => ((! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => (((ord_less_eq @ C5) @ (F4 @ X4)) @ (F4 @ Y3))))) => (((ord_less_eq @ C5) @ (F4 @ A2)) @ C)))))))))).
% 0.31/1.50 thf(fact_243_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F4:(B > A),B2:B,C:B]: (((A2 = (F4 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X4:B,Y3:B]: (((((ord_less_eq @ B) @ X4) @ Y3) => (((ord_less_eq @ A) @ (F4 @ X4)) @ (F4 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F4 @ C))))))))))).
% 0.31/1.50 thf(fact_244_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F4:(A > B),C:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F4 @ B2) = C) => ((! [X4:A,Y3:A]: (((((ord_less_eq @ A) @ X4) @ Y3) => (((ord_less_eq @ B) @ (F4 @ X4)) @ (F4 @ Y3))))) => (((ord_less_eq @ B) @ (F4 @ A2)) @ C)))))))))).
% 0.31/1.50 thf(fact_245_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z2:A]: ((Y5 = Z2))) = (^ [X3:A,Y6:A]: (((((ord_less_eq @ A) @ X3) @ Y6) & (((ord_less_eq @ A) @ Y6) @ X3))))))))).
% 0.31/1.50 thf(fact_246_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 0.31/1.50 thf(fact_247_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.31/1.50 thf(fact_248_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.31/1.50 thf(fact_249_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.31/1.50 thf(fact_250_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.31/1.50 thf(fact_251_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z)))) => (((((ord_less_eq @ A) @ X) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X)))) => (~ (((((ord_less_eq @ A) @ Z) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 0.31/1.50 thf(fact_252_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 0.31/1.50 thf(fact_253_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z2:A]: ((Y5 = Z2))) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ A5) @ B4) & (((ord_less_eq @ A) @ B4) @ A5))))))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___HOL_Otype, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (type @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Oplus, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (plus @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ozero, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (zero @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ogroup__add, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (group_add @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Omonoid__add, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (monoid_add @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Osemigroup__add, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (semigroup_add @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocomm__monoid__add, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (comm_monoid_add @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Oab__semigroup__add, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (ab_semigroup_add @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocancel__semigroup__add, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (cancel_semigroup_add @ A))))).
% 0.31/1.50 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocancel__comm__monoid__add, axiom, (! [A:$tType]: (((real_V1076094709vector @ A) => (cancel1352612707id_add @ A))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (ordere890947078_space @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1, axiom, (ordere890947078_space @ real)).
% 0.31/1.50 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 0.31/1.50 thf(tcon_Set_Oset___Groups_Oab__semigroup__add, axiom, (! [A8:$tType]: (((ab_semigroup_add @ A8) => (ab_semigroup_add @ (set @ A8)))))).
% 0.31/1.50 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add, axiom, (! [A8:$tType]: (((comm_monoid_add @ A8) => (comm_monoid_add @ (set @ A8)))))).
% 0.31/1.50 thf(tcon_Set_Oset___Groups_Osemigroup__add, axiom, (! [A8:$tType]: (((semigroup_add @ A8) => (semigroup_add @ (set @ A8)))))).
% 0.31/1.50 thf(tcon_Set_Oset___Orderings_Opreorder_2, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 0.31/1.50 thf(tcon_Set_Oset___Groups_Omonoid__add, axiom, (! [A8:$tType]: (((monoid_add @ A8) => (monoid_add @ (set @ A8)))))).
% 0.31/1.50 thf(tcon_Set_Oset___Orderings_Oorder_3, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 0.31/1.50 thf(tcon_Set_Oset___Orderings_Oord_4, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 0.31/1.50 thf(tcon_Set_Oset___Groups_Ozero, axiom, (! [A8:$tType]: (((zero @ A8) => (zero @ (set @ A8)))))).
% 0.31/1.50 thf(tcon_Set_Oset___Groups_Oplus, axiom, (! [A8:$tType]: (((plus @ A8) => (plus @ (set @ A8)))))).
% 0.31/1.50 thf(tcon_Set_Oset___Groups_Oone, axiom, (! [A8:$tType]: (((one @ A8) => (one @ (set @ A8)))))).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_5, axiom, (preorder @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_6, axiom, (order @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Oord_7, axiom, (ord @ $o)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le, axiom, (ordere516151231imp_le @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oordered__real__vector, axiom, (real_V1587248058vector @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add, axiom, (strict2144017051up_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add, axiom, (ordere223160158up_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le, axiom, (ordere236663937imp_le @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector, axiom, (real_V55928688vector @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add, axiom, (strict797366125id_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add, axiom, (ordere1818651114id_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add, axiom, (ordere779506340up_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector, axiom, (real_V1076094709vector @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add, axiom, (ordere216010020id_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add, axiom, (linord219039673up_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add, axiom, (cancel_semigroup_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Rings_Olinordered__semidom, axiom, (linordered_semidom @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_8, axiom, (ab_semigroup_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Fields_Olinordered__field, axiom, (linordered_field @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_9, axiom, (comm_monoid_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Rings_Olinordered__idom, axiom, (linordered_idom @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Osemigroup__add_10, axiom, (semigroup_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Rings_Ozero__less__one, axiom, (zero_less_one @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Rings_Ozero__neq__one, axiom, (zero_neq_one @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Orderings_Opreorder_11, axiom, (preorder @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Orderings_Olinorder_12, axiom, (linorder @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Omonoid__add_13, axiom, (monoid_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Ogroup__add, axiom, (group_add @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Orderings_Oorder_14, axiom, (order @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Num_Oneg__numeral, axiom, (neg_numeral @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Orderings_Oord_15, axiom, (ord @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Ozero_16, axiom, (zero @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oplus_17, axiom, (plus @ real)).
% 0.31/1.50 thf(tcon_Real_Oreal___Groups_Oone_18, axiom, (one @ real)).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__monoid__add__imp__le_19, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (ordere516151231imp_le @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oordered__real__vector_20, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (real_V1587248058vector @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Ostrict__ordered__ab__semigroup__add_21, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (strict2144017051up_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Oordered__cancel__ab__semigroup__add_22, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (ordere223160158up_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__add__imp__le_23, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (ordere236663937imp_le @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_24, axiom, (! [A8:$tType,A9:$tType]: ((((real_V55928688vector @ A8) & (real_V55928688vector @ A9)) => (real_V55928688vector @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Ostrict__ordered__comm__monoid__add_25, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (strict797366125id_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Oordered__cancel__comm__monoid__add_26, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (ordere1818651114id_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__add_27, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (ordere779506340up_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__vector_28, axiom, (! [A8:$tType,A9:$tType]: ((((real_V1076094709vector @ A8) & (real_V1076094709vector @ A9)) => (real_V1076094709vector @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Oordered__comm__monoid__add_29, axiom, (! [A8:$tType,A9:$tType]: ((((ordere890947078_space @ A8) & (ordere890947078_space @ A9)) => (ordere216010020id_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Ocancel__comm__monoid__add_30, axiom, (! [A8:$tType,A9:$tType]: ((((cancel1352612707id_add @ A8) & (cancel1352612707id_add @ A9)) => (cancel1352612707id_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Ocancel__semigroup__add_31, axiom, (! [A8:$tType,A9:$tType]: ((((cancel_semigroup_add @ A8) & (cancel_semigroup_add @ A9)) => (cancel_semigroup_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Oab__semigroup__add_32, axiom, (! [A8:$tType,A9:$tType]: ((((ab_semigroup_add @ A8) & (ab_semigroup_add @ A9)) => (ab_semigroup_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Ocomm__monoid__add_33, axiom, (! [A8:$tType,A9:$tType]: ((((comm_monoid_add @ A8) & (comm_monoid_add @ A9)) => (comm_monoid_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Osemigroup__add_34, axiom, (! [A8:$tType,A9:$tType]: ((((semigroup_add @ A8) & (semigroup_add @ A9)) => (semigroup_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_35, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A8) & (preorder @ A9)) => (preorder @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Omonoid__add_36, axiom, (! [A8:$tType,A9:$tType]: ((((monoid_add @ A8) & (monoid_add @ A9)) => (monoid_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Ogroup__add_37, axiom, (! [A8:$tType,A9:$tType]: ((((group_add @ A8) & (group_add @ A9)) => (group_add @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Orderings_Oorder_38, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A8) & (order @ A9)) => (order @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Orderings_Oord_39, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A8) & (ord @ A9)) => (ord @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Ozero_40, axiom, (! [A8:$tType,A9:$tType]: ((((zero @ A8) & (zero @ A9)) => (zero @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Groups_Oplus_41, axiom, (! [A8:$tType,A9:$tType]: ((((plus @ A8) & (plus @ A9)) => (plus @ ((product_prod @ A8) @ A9)))))).
% 0.31/1.50 thf(tfree_0, hypothesis, (real_V1076094709vector @ a)).
% 0.31/1.50 thf(conj_0, conjecture, (((member @ ((product_prod @ a) @ a)) @ ((((product_Pair @ a) @ a) @ (((plus_plus @ a) @ (((real_V1908273582scaleR @ a) @ u) @ x)) @ (((real_V1908273582scaleR @ a) @ v) @ y))) @ y)) @ relation)).
% 0.31/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2DTF11849.p
% 0.31/1.50 ------------------------
% 0.31/1.55 ---- Cleaned THF ---
% 0.31/1.55 thf(ty_t_Product__Type_Oprod,type,
% 0.31/1.55 product_prod: $tType > $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Real_Oreal,type,
% 0.31/1.55 real: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Set_Oset,type,
% 0.31/1.55 set: $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_tf_a,type,
% 0.31/1.55 a: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Ordered__Euclidean__Space_Oordered__euclidean__space,type,
% 0.31/1.55 ordere890947078_space:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_HOL_Otype,type,
% 0.31/1.55 type:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oone,type,
% 0.31/1.55 one:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oplus,type,
% 0.31/1.55 plus:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ozero,type,
% 0.31/1.55 zero:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Oord,type,
% 0.31/1.55 ord:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Num_Oneg__numeral,type,
% 0.31/1.55 neg_numeral:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Oorder,type,
% 0.31/1.55 order:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ogroup__add,type,
% 0.31/1.55 group_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Omonoid__add,type,
% 0.31/1.55 monoid_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/1.55 linorder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Opreorder,type,
% 0.31/1.55 preorder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Rings_Ozero__neq__one,type,
% 0.31/1.55 zero_neq_one:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Rings_Ozero__less__one,type,
% 0.31/1.55 zero_less_one:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.31/1.55 semigroup_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.31/1.55 linordered_idom:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.31/1.55 comm_monoid_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Fields_Olinordered__field,type,
% 0.31/1.55 linordered_field:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.31/1.55 ab_semigroup_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.31/1.55 linordered_semidom:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.31/1.55 cancel_semigroup_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.31/1.55 cancel1352612707id_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.31/1.55 linord219039673up_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__comm__monoid__add,type,
% 0.31/1.55 ordere216010020id_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Real__Vector__Spaces_Oreal__vector,type,
% 0.31/1.55 real_V1076094709vector:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.31/1.55 ordere779506340up_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.31/1.55 linord1659791738miring:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.31/1.55 canoni770627133id_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__cancel__comm__monoid__add,type,
% 0.31/1.55 ordere1818651114id_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ostrict__ordered__comm__monoid__add,type,
% 0.31/1.55 strict797366125id_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Real__Vector__Spaces_Oreal__normed__vector,type,
% 0.31/1.55 real_V55928688vector:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.31/1.55 ordere236663937imp_le:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.31/1.55 ordere223160158up_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.31/1.55 strict2144017051up_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Real__Vector__Spaces_Oordered__real__vector,type,
% 0.31/1.55 real_V1587248058vector:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 0.31/1.55 unique1598680935umeral:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.31/1.55 ordere516151231imp_le:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux,type,
% 0.31/1.55 unique455577585es_aux:
% 0.31/1.55 !>[A: $tType] : ( ( product_prod @ A @ A ) > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.31/1.55 one_one:
% 0.31/1.55 !>[A: $tType] : A ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.31/1.55 plus_plus:
% 0.31/1.55 !>[A: $tType] : ( A > A > A ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.31/1.55 zero_zero:
% 0.31/1.55 !>[A: $tType] : A ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.31/1.55 ord_less:
% 0.31/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/1.55 ord_less_eq:
% 0.31/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Preferences__Mirabelle__stygcjuplb_Oweak__convex__pref,type,
% 0.31/1.55 prefer1289595409x_pref:
% 0.31/1.55 !>[A: $tType] : ( ( set @ ( product_prod @ A @ A ) ) > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Product__Type_OPair,type,
% 0.31/1.55 product_Pair:
% 0.31/1.55 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.31/1.55 product_rec_prod:
% 0.31/1.55 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR,type,
% 0.31/1.55 real_V1908273582scaleR:
% 0.31/1.55 !>[A: $tType] : ( real > A > A ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Set_OCollect,type,
% 0.31/1.55 collect:
% 0.31/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_member,type,
% 0.31/1.55 member:
% 0.31/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_relation,type,
% 0.31/1.55 relation: set @ ( product_prod @ a @ a ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_u,type,
% 0.31/1.55 u: real ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_v,type,
% 0.31/1.55 v: real ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_x,type,
% 0.31/1.55 x: a ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_y,type,
% 0.31/1.55 y: a ).
% 0.31/1.55
% 0.31/1.55 thf(fact_0_assms_I1_J,axiom,
% 0.31/1.55 prefer1289595409x_pref @ a @ relation ).
% 0.31/1.55
% 0.31/1.55 thf(fact_1_indifferent__imp__weak__pref_I2_J,axiom,
% 0.31/1.55 ! [X: a,Y: a] :
% 0.31/1.55 ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation )
% 0.31/1.55 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) )
% 0.31/1.55 => ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_2_indifferent__imp__weak__pref_I1_J,axiom,
% 0.31/1.55 ! [X: a,Y: a] :
% 0.31/1.55 ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation )
% 0.31/1.55 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) )
% 0.31/1.55 => ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_3_indiff__trans,axiom,
% 0.31/1.55 ! [X: a,Y: a,Z: a] :
% 0.31/1.55 ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation )
% 0.31/1.55 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) )
% 0.31/1.55 => ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ Z ) @ relation )
% 0.31/1.55 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Z @ Y ) @ relation ) )
% 0.31/1.55 => ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Z ) @ relation )
% 0.31/1.55 & ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Z @ X ) @ relation ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_4_strict__trans,axiom,
% 0.31/1.55 ! [X: a,Y: a,Z: a] :
% 0.31/1.55 ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Y ) @ relation )
% 0.31/1.55 & ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ X ) @ relation ) )
% 0.31/1.55 => ( ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Y @ Z ) @ relation )
% 0.31/1.55 & ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Z @ Y ) @ relation ) )
% 0.31/1.55 => ( ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ X @ Z ) @ relation )
% 0.31/1.55 & ~ ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ Z @ X ) @ relation ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_5_assms_I2_J,axiom,
% 0.31/1.55 member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ x @ y ) @ relation ).
% 0.31/1.55
% 0.31/1.55 thf(fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062,axiom,
% 0.31/1.55 ( ( ( u
% 0.31/1.55 != ( zero_zero @ real ) )
% 0.31/1.55 & ( u
% 0.31/1.55 != ( one_one @ real ) ) )
% 0.31/1.55 => ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ ( plus_plus @ a @ ( real_V1908273582scaleR @ a @ u @ x ) @ ( real_V1908273582scaleR @ a @ v @ y ) ) @ y ) @ relation ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_7_u__0,axiom,
% 0.31/1.55 ( ( u
% 0.31/1.55 = ( zero_zero @ real ) )
% 0.31/1.55 => ( member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ ( plus_plus @ a @ ( real_V1908273582scaleR @ a @ u @ x ) @ ( real_V1908273582scaleR @ a @ v @ y ) ) @ y ) @ relation ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_8_assms_I4_J,axiom,
% 0.31/1.55 ord_less_eq @ real @ ( zero_zero @ real ) @ v ).
% 0.31/1.55
% 0.31/1.55 thf(fact_9_assms_I5_J,axiom,
% 0.31/1.55 ( ( plus_plus @ real @ u @ v )
% 0.31/1.55 = ( one_one @ real ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_10_assms_I3_J,axiom,
% 0.31/1.55 ord_less_eq @ real @ ( zero_zero @ real ) @ u ).
% 0.31/1.55
% 0.31/1.55 thf(fact_11_scaleR__Pair,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( real_V1076094709vector @ B )
% 0.31/1.55 & ( real_V1076094709vector @ A ) )
% 0.31/1.55 => ! [R: real,A2: A,B2: B] :
% 0.31/1.55 ( ( real_V1908273582scaleR @ ( product_prod @ A @ B ) @ R @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.31/1.55 = ( product_Pair @ A @ B @ ( real_V1908273582scaleR @ A @ R @ A2 ) @ ( real_V1908273582scaleR @ B @ R @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_12_scale__prod,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( real_V1076094709vector @ B )
% 0.31/1.55 & ( real_V1076094709vector @ A ) )
% 0.31/1.55 => ! [X: real,A2: A,B2: B] :
% 0.31/1.55 ( ( real_V1908273582scaleR @ ( product_prod @ A @ B ) @ X @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.31/1.55 = ( product_Pair @ A @ B @ ( real_V1908273582scaleR @ A @ X @ A2 ) @ ( real_V1908273582scaleR @ B @ X @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_13_add__Pair,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( plus @ B )
% 0.31/1.55 & ( plus @ A ) )
% 0.31/1.55 => ! [A2: A,B2: B,C: A,D: B] :
% 0.31/1.55 ( ( plus_plus @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ C @ D ) )
% 0.31/1.55 = ( product_Pair @ A @ B @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ B @ B2 @ D ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_14_prod_Oinject,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,X1: A,X2: B,Y1: A,Y2: B] :
% 0.31/1.55 ( ( ( product_Pair @ A @ B @ X1 @ X2 )
% 0.31/1.55 = ( product_Pair @ A @ B @ Y1 @ Y2 ) )
% 0.31/1.55 = ( ( X1 = Y1 )
% 0.31/1.55 & ( X2 = Y2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_15_old_Oprod_Oinject,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.31/1.55 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/1.55 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.31/1.55 = ( ( A2 = A3 )
% 0.31/1.55 & ( B2 = B3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_16_set__plus__intro,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( plus @ A )
% 0.31/1.55 => ! [A2: A,C2: set @ A,B2: A,D2: set @ A] :
% 0.31/1.55 ( ( member @ A @ A2 @ C2 )
% 0.31/1.55 => ( ( member @ A @ B2 @ D2 )
% 0.31/1.55 => ( member @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( plus_plus @ ( set @ A ) @ C2 @ D2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_17_add__left__cancel,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel_semigroup_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.31/1.55 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/1.55 = ( B2 = C ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_18_add__right__cancel,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel_semigroup_add @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.31/1.55 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/1.55 = ( B2 = C ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_19_pth__9_I3_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( real_V55928688vector @ A )
% 0.31/1.55 => ! [C: real,X: A,W: A,D: real,Z: A] :
% 0.31/1.55 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ W ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ X ) @ Z ) )
% 0.31/1.55 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ C @ D ) @ X ) @ ( plus_plus @ A @ W @ Z ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_20_le__zero__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( canoni770627133id_add @ A )
% 0.31/1.55 => ! [N: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.31/1.55 = ( N
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_21_add__le__cancel__right,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [A2: A,C: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.31/1.55 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_22_add__le__cancel__left,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [C: A,A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.31/1.55 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_23_zero__eq__add__iff__both__eq__0,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( canoni770627133id_add @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ( zero_zero @ A )
% 0.31/1.55 = ( plus_plus @ A @ X @ Y ) )
% 0.31/1.55 = ( ( X
% 0.31/1.55 = ( zero_zero @ A ) )
% 0.31/1.55 & ( Y
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_24_add__eq__0__iff__both__eq__0,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( canoni770627133id_add @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ X @ Y )
% 0.31/1.55 = ( zero_zero @ A ) )
% 0.31/1.55 = ( ( X
% 0.31/1.55 = ( zero_zero @ A ) )
% 0.31/1.55 & ( Y
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_25_add__cancel__right__right,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel1352612707id_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( A2
% 0.31/1.55 = ( plus_plus @ A @ A2 @ B2 ) )
% 0.31/1.55 = ( B2
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_26_add__cancel__right__left,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel1352612707id_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( A2
% 0.31/1.55 = ( plus_plus @ A @ B2 @ A2 ) )
% 0.31/1.55 = ( B2
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_27_add__cancel__left__right,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel1352612707id_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.31/1.55 = A2 )
% 0.31/1.55 = ( B2
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_28_add__cancel__left__left,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel1352612707id_add @ A )
% 0.31/1.55 => ! [B2: A,A2: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.31/1.55 = A2 )
% 0.31/1.55 = ( B2
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_29_double__zero__sym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linord219039673up_add @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ( ( ( zero_zero @ A )
% 0.31/1.55 = ( plus_plus @ A @ A2 @ A2 ) )
% 0.31/1.55 = ( A2
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_30_double__zero,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linord219039673up_add @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ A2 @ A2 )
% 0.31/1.55 = ( zero_zero @ A ) )
% 0.31/1.55 = ( A2
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_31_add_Oright__neutral,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( monoid_add @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.31/1.55 = A2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_32_add_Oleft__neutral,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( monoid_add @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.55 = A2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_33_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linord219039673up_add @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.31/1.55 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_34_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linord219039673up_add @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.31/1.55 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_35_le__add__same__cancel2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere516151231imp_le @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.31/1.55 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_36_le__add__same__cancel1,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere516151231imp_le @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.31/1.55 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_37_add__le__same__cancel2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere516151231imp_le @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.31/1.55 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_38_add__le__same__cancel1,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere516151231imp_le @ A )
% 0.31/1.55 => ! [B2: A,A2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.31/1.55 = ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_39_one__reorient,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( one @ A )
% 0.31/1.55 => ! [X: A] :
% 0.31/1.55 ( ( ( one_one @ A )
% 0.31/1.55 = X )
% 0.31/1.55 = ( X
% 0.31/1.55 = ( one_one @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_40_zero__reorient,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( zero @ A )
% 0.31/1.55 => ! [X: A] :
% 0.31/1.55 ( ( ( zero_zero @ A )
% 0.31/1.55 = X )
% 0.31/1.55 = ( X
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_41_zero__le,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( canoni770627133id_add @ A )
% 0.31/1.55 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_42_add__nonpos__eq__0__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere216010020id_add @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 0.31/1.55 => ( ( ord_less_eq @ A @ Y @ ( zero_zero @ A ) )
% 0.31/1.55 => ( ( ( plus_plus @ A @ X @ Y )
% 0.31/1.55 = ( zero_zero @ A ) )
% 0.31/1.55 = ( ( X
% 0.31/1.55 = ( zero_zero @ A ) )
% 0.31/1.55 & ( Y
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_43_mem__Collect__eq,axiom,
% 0.31/1.55 ! [A: $tType,A2: A,P: A > $o] :
% 0.31/1.55 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.31/1.55 = ( P @ A2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_44_Collect__mem__eq,axiom,
% 0.31/1.55 ! [A: $tType,A4: set @ A] :
% 0.31/1.55 ( ( collect @ A
% 0.31/1.55 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.31/1.55 = A4 ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_45_Collect__cong,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.55 ( ! [X4: A] :
% 0.31/1.55 ( ( P @ X4 )
% 0.31/1.55 = ( Q @ X4 ) )
% 0.31/1.55 => ( ( collect @ A @ P )
% 0.31/1.55 = ( collect @ A @ Q ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_46_add__nonneg__eq__0__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere216010020id_add @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.31/1.55 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ Y )
% 0.31/1.55 => ( ( ( plus_plus @ A @ X @ Y )
% 0.31/1.55 = ( zero_zero @ A ) )
% 0.31/1.55 = ( ( X
% 0.31/1.55 = ( zero_zero @ A ) )
% 0.31/1.55 & ( Y
% 0.31/1.55 = ( zero_zero @ A ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_47_add__nonpos__nonpos,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere216010020id_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_48_add__nonneg__nonneg,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere216010020id_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_49_add__increasing2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere216010020id_add @ A )
% 0.31/1.55 => ! [C: A,B2: A,A2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.55 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_50_add__decreasing2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere216010020id_add @ A )
% 0.31/1.55 => ! [C: A,A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.31/1.55 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_51_add__increasing,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere216010020id_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.31/1.55 => ( ord_less_eq @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_52_add__decreasing,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere216010020id_add @ A )
% 0.31/1.55 => ! [A2: A,C: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.31/1.55 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_53_zero__prod__def,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( zero @ B )
% 0.31/1.55 & ( zero @ A ) )
% 0.31/1.55 => ( ( zero_zero @ ( product_prod @ A @ B ) )
% 0.31/1.55 = ( product_Pair @ A @ B @ ( zero_zero @ A ) @ ( zero_zero @ B ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_54_add__le__imp__le__right,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [A2: A,C: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_55_add__le__imp__le__left,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [C: A,A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_56_le__iff__add,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( canoni770627133id_add @ A )
% 0.31/1.55 => ( ( ord_less_eq @ A )
% 0.31/1.55 = ( ^ [A5: A,B4: A] :
% 0.31/1.55 ? [C3: A] :
% 0.31/1.55 ( B4
% 0.31/1.55 = ( plus_plus @ A @ A5 @ C3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_57_add__right__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_58_less__eqE,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( canoni770627133id_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ~ ! [C4: A] :
% 0.31/1.55 ( B2
% 0.31/1.55 != ( plus_plus @ A @ A2 @ C4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_59_add__left__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_60_add__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C: A,D: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ C @ D )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_61_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.56 ( ( ordere779506340up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/1.56 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_62_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere779506340up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( I = J )
% 0.31/1.56 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_63_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere779506340up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/1.56 & ( K = L ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_64_pth__4_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [X: A] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ ( zero_zero @ real ) @ X )
% 0.31/1.56 = ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_65_convex__ge__imp__conved,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [Pr: set @ ( product_prod @ A @ A )] :
% 0.31/1.56 ( ! [X4: A,Y3: A] :
% 0.31/1.56 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y3 ) @ Pr )
% 0.31/1.56 => ! [Alpha: real,Beta: real] :
% 0.31/1.56 ( ( ( ( plus_plus @ real @ Alpha @ Beta )
% 0.31/1.56 = ( one_one @ real ) )
% 0.31/1.56 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Alpha )
% 0.31/1.56 & ( ord_less_eq @ real @ ( zero_zero @ real ) @ Beta ) )
% 0.31/1.56 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ Alpha @ X4 ) @ ( real_V1908273582scaleR @ A @ Beta @ Y3 ) ) @ Y3 ) @ Pr ) ) )
% 0.31/1.56 => ( prefer1289595409x_pref @ A @ Pr ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_66_add_Ogroup__left__neutral,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( group_add @ A )
% 0.31/1.56 => ! [A2: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.56 = A2 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_67_add_Ocomm__neutral,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( comm_monoid_add @ A )
% 0.31/1.56 => ! [A2: A] :
% 0.31/1.56 ( ( plus_plus @ A @ A2 @ ( zero_zero @ A ) )
% 0.31/1.56 = A2 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_68_comm__monoid__add__class_Oadd__0,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( comm_monoid_add @ A )
% 0.31/1.56 => ! [A2: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.56 = A2 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_69_pth__d,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [X: A] :
% 0.31/1.56 ( ( plus_plus @ A @ X @ ( zero_zero @ A ) )
% 0.31/1.56 = X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_70_pth__7_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [X: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( zero_zero @ A ) @ X )
% 0.31/1.56 = X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_71_pth__1,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [X: A] :
% 0.31/1.56 ( X
% 0.31/1.56 = ( real_V1908273582scaleR @ A @ ( one_one @ real ) @ X ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_72_pth__4_I2_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ C @ ( zero_zero @ A ) )
% 0.31/1.56 = ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_73_add__right__imp__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( cancel_semigroup_add @ A )
% 0.31/1.56 => ! [B2: A,A2: A,C: A] :
% 0.31/1.56 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.31/1.56 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/1.56 => ( B2 = C ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_74_add__left__imp__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( cancel_semigroup_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.31/1.56 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/1.56 => ( B2 = C ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_75_add_Oleft__commute,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ab_semigroup_add @ A )
% 0.31/1.56 => ! [B2: A,A2: A,C: A] :
% 0.31/1.56 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) )
% 0.31/1.56 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_76_add_Ocommute,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ab_semigroup_add @ A )
% 0.31/1.56 => ( ( plus_plus @ A )
% 0.31/1.56 = ( ^ [A5: A,B4: A] : ( plus_plus @ A @ B4 @ A5 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_77_add_Oright__cancel,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( group_add @ A )
% 0.31/1.56 => ! [B2: A,A2: A,C: A] :
% 0.31/1.56 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.31/1.56 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/1.56 = ( B2 = C ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_78_add_Oleft__cancel,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( group_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.31/1.56 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/1.56 = ( B2 = C ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_79_add_Oassoc,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( semigroup_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 0.31/1.56 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_80_set__plus__elim,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( plus @ A )
% 0.31/1.56 => ! [X: A,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( member @ A @ X @ ( plus_plus @ ( set @ A ) @ A4 @ B5 ) )
% 0.31/1.56 => ~ ! [A6: A,B6: A] :
% 0.31/1.56 ( ( X
% 0.31/1.56 = ( plus_plus @ A @ A6 @ B6 ) )
% 0.31/1.56 => ( ( member @ A @ A6 @ A4 )
% 0.31/1.56 => ~ ( member @ A @ B6 @ B5 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_81_group__cancel_Oadd2,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( comm_monoid_add @ A )
% 0.31/1.56 => ! [B5: A,K: A,B2: A,A2: A] :
% 0.31/1.56 ( ( B5
% 0.31/1.56 = ( plus_plus @ A @ K @ B2 ) )
% 0.31/1.56 => ( ( plus_plus @ A @ A2 @ B5 )
% 0.31/1.56 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_82_group__cancel_Oadd1,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( comm_monoid_add @ A )
% 0.31/1.56 => ! [A4: A,K: A,A2: A,B2: A] :
% 0.31/1.56 ( ( A4
% 0.31/1.56 = ( plus_plus @ A @ K @ A2 ) )
% 0.31/1.56 => ( ( plus_plus @ A @ A4 @ B2 )
% 0.31/1.56 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_83_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere779506340up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( I = J )
% 0.31/1.56 & ( K = L ) )
% 0.31/1.56 => ( ( plus_plus @ A @ I @ K )
% 0.31/1.56 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_84_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ab_semigroup_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 0.31/1.56 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_85_old_Oprod_Oinducts,axiom,
% 0.31/1.56 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.31/1.56 ( ! [A6: A,B6: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B6 ) )
% 0.31/1.56 => ( P @ Prod ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_86_old_Oprod_Oexhaust,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.31/1.56 ~ ! [A6: A,B6: B] :
% 0.31/1.56 ( Y
% 0.31/1.56 != ( product_Pair @ A @ B @ A6 @ B6 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_87_prod__induct7,axiom,
% 0.31/1.56 ! [G: $tType,F: $tType,E: $tType,D3: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.31/1.56 ( ! [A6: A,B6: B,C4: C5,D4: D3,E2: E,F2: F,G2: G] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C4 @ ( product_Pair @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D4 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) )
% 0.31/1.56 => ( P @ X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_88_prod__induct6,axiom,
% 0.31/1.56 ! [F: $tType,E: $tType,D3: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) )] :
% 0.31/1.56 ( ! [A6: A,B6: B,C4: C5,D4: D3,E2: E,F2: F] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) @ C4 @ ( product_Pair @ D3 @ ( product_prod @ E @ F ) @ D4 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) )
% 0.31/1.56 => ( P @ X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_89_prod__induct5,axiom,
% 0.31/1.56 ! [E: $tType,D3: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) )] :
% 0.31/1.56 ( ! [A6: A,B6: B,C4: C5,D4: D3,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ E ) @ C4 @ ( product_Pair @ D3 @ E @ D4 @ E2 ) ) ) ) )
% 0.31/1.56 => ( P @ X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_90_prod__induct4,axiom,
% 0.31/1.56 ! [D3: $tType,C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) )] :
% 0.31/1.56 ( ! [A6: A,B6: B,C4: C5,D4: D3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ D3 ) @ B6 @ ( product_Pair @ C5 @ D3 @ C4 @ D4 ) ) ) )
% 0.31/1.56 => ( P @ X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_91_prod__induct3,axiom,
% 0.31/1.56 ! [C5: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C5 ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C5 )] :
% 0.31/1.56 ( ! [A6: A,B6: B,C4: C5] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C5 ) @ A6 @ ( product_Pair @ B @ C5 @ B6 @ C4 ) ) )
% 0.31/1.56 => ( P @ X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_92_prod__cases7,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType,C5: $tType,D3: $tType,E: $tType,F: $tType,G: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) )] :
% 0.31/1.56 ~ ! [A6: A,B6: B,C4: C5,D4: D3,E2: E,F2: F,G2: G] :
% 0.31/1.56 ( Y
% 0.31/1.56 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) ) @ C4 @ ( product_Pair @ D3 @ ( product_prod @ E @ ( product_prod @ F @ G ) ) @ D4 @ ( product_Pair @ E @ ( product_prod @ F @ G ) @ E2 @ ( product_Pair @ F @ G @ F2 @ G2 ) ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_93_prod__cases6,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType,C5: $tType,D3: $tType,E: $tType,F: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) )] :
% 0.31/1.56 ~ ! [A6: A,B6: B,C4: C5,D4: D3,E2: E,F2: F] :
% 0.31/1.56 ( Y
% 0.31/1.56 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ ( product_prod @ E @ F ) ) @ C4 @ ( product_Pair @ D3 @ ( product_prod @ E @ F ) @ D4 @ ( product_Pair @ E @ F @ E2 @ F2 ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_94_prod__cases5,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType,C5: $tType,D3: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) )] :
% 0.31/1.56 ~ ! [A6: A,B6: B,C4: C5,D4: D3,E2: E] :
% 0.31/1.56 ( Y
% 0.31/1.56 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ ( product_prod @ D3 @ E ) ) @ B6 @ ( product_Pair @ C5 @ ( product_prod @ D3 @ E ) @ C4 @ ( product_Pair @ D3 @ E @ D4 @ E2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_95_prod__cases4,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType,C5: $tType,D3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) )] :
% 0.31/1.56 ~ ! [A6: A,B6: B,C4: C5,D4: D3] :
% 0.31/1.56 ( Y
% 0.31/1.56 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C5 @ D3 ) ) @ A6 @ ( product_Pair @ B @ ( product_prod @ C5 @ D3 ) @ B6 @ ( product_Pair @ C5 @ D3 @ C4 @ D4 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_96_prod__cases3,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType,C5: $tType,Y: product_prod @ A @ ( product_prod @ B @ C5 )] :
% 0.31/1.56 ~ ! [A6: A,B6: B,C4: C5] :
% 0.31/1.56 ( Y
% 0.31/1.56 != ( product_Pair @ A @ ( product_prod @ B @ C5 ) @ A6 @ ( product_Pair @ B @ C5 @ B6 @ C4 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_97_Pair__inject,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType,A2: A,B2: B,A3: A,B3: B] :
% 0.31/1.56 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.31/1.56 = ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.31/1.56 => ~ ( ( A2 = A3 )
% 0.31/1.56 => ( B2 != B3 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_98_prod__cases,axiom,
% 0.31/1.56 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.31/1.56 ( ! [A6: A,B6: B] : ( P @ ( product_Pair @ A @ B @ A6 @ B6 ) )
% 0.31/1.56 => ( P @ P2 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_99_surj__pair,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.31/1.56 ? [X4: A,Y3: B] :
% 0.31/1.56 ( P2
% 0.31/1.56 = ( product_Pair @ A @ B @ X4 @ Y3 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_100_pth__a,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [X: A,Y: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ ( zero_zero @ real ) @ X ) @ Y )
% 0.31/1.56 = Y ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_101_pth__8,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,D: real] :
% 0.31/1.56 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ D @ X ) )
% 0.31/1.56 = ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ C @ D ) @ X ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_102_pth__6,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,Y: A] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ C @ ( plus_plus @ A @ X @ Y ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ C @ Y ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_103_pth__c_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,D: real,Y: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ D @ Y ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ ( real_V1908273582scaleR @ A @ C @ X ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_104_pth__c_I2_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,Z: A,D: real,Y: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) @ ( real_V1908273582scaleR @ A @ D @ Y ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_105_pth__c_I3_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,D: real,Y: A,Z: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_106_pth__c_I4_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,W: A,D: real,Y: A,Z: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ W ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ W ) @ Z ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_107_pth__b_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,D: real,Y: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ D @ Y ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( real_V1908273582scaleR @ A @ D @ Y ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_108_pth__b_I2_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,Z: A,D: real,Y: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) @ ( real_V1908273582scaleR @ A @ D @ Y ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ Z @ ( real_V1908273582scaleR @ A @ D @ Y ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_109_pth__b_I3_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,D: real,Y: A,Z: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_110_pth__b_I4_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,W: A,D: real,Y: A,Z: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ W ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ W @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ Y ) @ Z ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_111_pth__9_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,Z: A,D: real] :
% 0.31/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ Z ) @ ( real_V1908273582scaleR @ A @ D @ X ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ C @ D ) @ X ) @ Z ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_112_pth__9_I2_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V55928688vector @ A )
% 0.31/1.56 => ! [C: real,X: A,D: real,Z: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ C @ X ) @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ D @ X ) @ Z ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ C @ D ) @ X ) @ Z ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_113_scaleR__eq__iff,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [B2: A,U: real,A2: A] :
% 0.31/1.56 ( ( ( plus_plus @ A @ B2 @ ( real_V1908273582scaleR @ A @ U @ A2 ) )
% 0.31/1.56 = ( plus_plus @ A @ A2 @ ( real_V1908273582scaleR @ A @ U @ B2 ) ) )
% 0.31/1.56 = ( ( A2 = B2 )
% 0.31/1.56 | ( U
% 0.31/1.56 = ( one_one @ real ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_114_scale__zero__left,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [X: A] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ ( zero_zero @ real ) @ X )
% 0.31/1.56 = ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_115_scale__eq__0__iff,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [A2: real,X: A] :
% 0.31/1.56 ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.31/1.56 = ( zero_zero @ A ) )
% 0.31/1.56 = ( ( A2
% 0.31/1.56 = ( zero_zero @ real ) )
% 0.31/1.56 | ( X
% 0.31/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_116_scaleR__one,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [X: A] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ ( one_one @ real ) @ X )
% 0.31/1.56 = X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_117_scale__cancel__left,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [A2: real,X: A,Y: A] :
% 0.31/1.56 ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.31/1.56 = ( real_V1908273582scaleR @ A @ A2 @ Y ) )
% 0.31/1.56 = ( ( X = Y )
% 0.31/1.56 | ( A2
% 0.31/1.56 = ( zero_zero @ real ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_118_scaleR__left__le__one__le,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [X: A,A2: real] :
% 0.31/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.31/1.56 => ( ( ord_less_eq @ real @ A2 @ ( one_one @ real ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ X ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_119_scale__cancel__right,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [A2: real,X: A,B2: real] :
% 0.31/1.56 ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.31/1.56 = ( real_V1908273582scaleR @ A @ B2 @ X ) )
% 0.31/1.56 = ( ( A2 = B2 )
% 0.31/1.56 | ( X
% 0.31/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_120_scale__zero__right,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [A2: real] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ A2 @ ( zero_zero @ A ) )
% 0.31/1.56 = ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_121_split__scaleR__neg__le,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,X: A] :
% 0.31/1.56 ( ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.31/1.56 & ( ord_less_eq @ A @ X @ ( zero_zero @ A ) ) )
% 0.31/1.56 | ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.31/1.56 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( zero_zero @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_122_split__scaleR__pos__le,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,B2: A] :
% 0.31/1.56 ( ( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.31/1.56 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.31/1.56 | ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.31/1.56 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( real_V1908273582scaleR @ A @ A2 @ B2 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_123_set__plus__mono2,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( plus @ A )
% 0.31/1.56 => ! [C2: set @ A,D2: set @ A,E3: set @ A,F3: set @ A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ C2 @ D2 )
% 0.31/1.56 => ( ( ord_less_eq @ ( set @ A ) @ E3 @ F3 )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ ( plus_plus @ ( set @ A ) @ C2 @ E3 ) @ ( plus_plus @ ( set @ A ) @ D2 @ F3 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_124_set__plus__mono2__b,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( plus @ A )
% 0.31/1.56 => ! [C2: set @ A,D2: set @ A,E3: set @ A,F3: set @ A,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ C2 @ D2 )
% 0.31/1.56 => ( ( ord_less_eq @ ( set @ A ) @ E3 @ F3 )
% 0.31/1.56 => ( ( member @ A @ X @ ( plus_plus @ ( set @ A ) @ C2 @ E3 ) )
% 0.31/1.56 => ( member @ A @ X @ ( plus_plus @ ( set @ A ) @ D2 @ F3 ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_125_set__zero__plus2,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( comm_monoid_add @ A )
% 0.31/1.56 => ! [A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( member @ A @ ( zero_zero @ A ) @ A4 )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ B5 @ ( plus_plus @ ( set @ A ) @ A4 @ B5 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_126_scale__left__commute,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [A2: real,B2: real,X: A] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ A2 @ ( real_V1908273582scaleR @ A @ B2 @ X ) )
% 0.31/1.56 = ( real_V1908273582scaleR @ A @ B2 @ ( real_V1908273582scaleR @ A @ A2 @ X ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_127_scale__right__imp__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [X: A,A2: real,B2: real] :
% 0.31/1.56 ( ( X
% 0.31/1.56 != ( zero_zero @ A ) )
% 0.31/1.56 => ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.31/1.56 = ( real_V1908273582scaleR @ A @ B2 @ X ) )
% 0.31/1.56 => ( A2 = B2 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_128_scaleR__add__right,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [A2: real,X: A,Y: A] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ A2 @ ( plus_plus @ A @ X @ Y ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ A2 @ Y ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_129_scale__left__imp__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [A2: real,X: A,Y: A] :
% 0.31/1.56 ( ( A2
% 0.31/1.56 != ( zero_zero @ real ) )
% 0.31/1.56 => ( ( ( real_V1908273582scaleR @ A @ A2 @ X )
% 0.31/1.56 = ( real_V1908273582scaleR @ A @ A2 @ Y ) )
% 0.31/1.56 => ( X = Y ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_130_scaleR__left_Oadd,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [X: real,Y: real,Xa: A] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ X @ Y ) @ Xa )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ X @ Xa ) @ ( real_V1908273582scaleR @ A @ Y @ Xa ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_131_scaleR__add__left,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [A2: real,B2: real,X: A] :
% 0.31/1.56 ( ( real_V1908273582scaleR @ A @ ( plus_plus @ real @ A2 @ B2 ) @ X )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ B2 @ X ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_132_scaleR__right__mono,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,B2: real,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ B2 @ X ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_133_scaleR__right__mono__neg,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [B2: real,A2: real,C: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ B2 @ A2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ C @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ C ) @ ( real_V1908273582scaleR @ A @ B2 @ C ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_134_scaleR__left__mono,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [X: A,Y: A,A2: real] :
% 0.31/1.56 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.56 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ A2 @ Y ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_135_scaleR__left__mono__neg,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [B2: A,A2: A,C: real] :
% 0.31/1.56 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.56 => ( ( ord_less_eq @ real @ C @ ( zero_zero @ real ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ C @ A2 ) @ ( real_V1908273582scaleR @ A @ C @ B2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_136_scaleR__mono_H,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,B2: real,C: A,D: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ C @ D )
% 0.31/1.56 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ C )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ C ) @ ( real_V1908273582scaleR @ A @ B2 @ D ) ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_137_scaleR__mono,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,B2: real,X: A,Y: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ A2 @ B2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.56 => ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ B2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( real_V1908273582scaleR @ A @ B2 @ Y ) ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_138_scaleR__nonpos__nonpos,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,B2: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.31/1.56 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( real_V1908273582scaleR @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_139_scaleR__nonpos__nonneg,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ A2 @ ( zero_zero @ real ) )
% 0.31/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_140_scaleR__nonneg__nonpos,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ X @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ X ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_141_scaleR__nonneg__nonneg,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ X )
% 0.31/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( real_V1908273582scaleR @ A @ A2 @ X ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_142_Pair__le,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType] :
% 0.31/1.56 ( ( ( ord @ B )
% 0.31/1.56 & ( ord @ A ) )
% 0.31/1.56 => ! [A2: A,B2: B,C: A,D: B] :
% 0.31/1.56 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ A2 @ B2 ) @ ( product_Pair @ A @ B @ C @ D ) )
% 0.31/1.56 = ( ( ord_less_eq @ A @ A2 @ C )
% 0.31/1.56 & ( ord_less_eq @ B @ B2 @ D ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_143_old_Oprod_Orec,axiom,
% 0.31/1.56 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.31/1.56 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.31/1.56 = ( F1 @ A2 @ B2 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_144_not__one__le__zero,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_145_zero__le__one,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_146_zero__neq__one,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( zero_neq_one @ A )
% 0.31/1.56 => ( ( zero_zero @ A )
% 0.31/1.56 != ( one_one @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_147_Pair__mono,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType] :
% 0.31/1.56 ( ( ( ord @ B )
% 0.31/1.56 & ( ord @ A ) )
% 0.31/1.56 => ! [X: A,X5: A,Y: B,Y4: B] :
% 0.31/1.56 ( ( ord_less_eq @ A @ X @ X5 )
% 0.31/1.56 => ( ( ord_less_eq @ B @ Y @ Y4 )
% 0.31/1.56 => ( ord_less_eq @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X @ Y ) @ ( product_Pair @ A @ B @ X5 @ Y4 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_148_weak__convexI,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [Pr: set @ ( product_prod @ A @ A )] :
% 0.31/1.56 ( ! [X4: A,Y3: A,Alpha: real,Beta: real] :
% 0.31/1.56 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X4 @ Y3 ) @ Pr )
% 0.31/1.56 => ( ( ( plus_plus @ real @ Alpha @ Beta )
% 0.31/1.56 = ( one_one @ real ) )
% 0.31/1.56 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Alpha )
% 0.31/1.56 => ( ( ord_less @ real @ ( zero_zero @ real ) @ Beta )
% 0.31/1.56 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ Alpha @ X4 ) @ ( real_V1908273582scaleR @ A @ Beta @ Y3 ) ) @ Y3 ) @ Pr ) ) ) ) )
% 0.31/1.56 => ( prefer1289595409x_pref @ A @ Pr ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_149_subsetI,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ! [X4: A] :
% 0.31/1.56 ( ( member @ A @ X4 @ A4 )
% 0.31/1.56 => ( member @ A @ X4 @ B5 ) )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_150_subset__antisym,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.31/1.56 => ( A4 = B5 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_151_not__gr__zero,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( canoni770627133id_add @ A )
% 0.31/1.56 => ! [N: A] :
% 0.31/1.56 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.31/1.56 = ( N
% 0.31/1.56 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_152_add__less__cancel__right,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere236663937imp_le @ A )
% 0.31/1.56 => ! [A2: A,C: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.31/1.56 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_153_add__less__cancel__left,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere236663937imp_le @ A )
% 0.31/1.56 => ! [C: A,A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.31/1.56 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_154_add__less__same__cancel1,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere516151231imp_le @ A )
% 0.31/1.56 => ! [B2: A,A2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ B2 @ A2 ) @ B2 )
% 0.31/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_155_add__less__same__cancel2,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere516151231imp_le @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ B2 )
% 0.31/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_156_less__add__same__cancel1,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere516151231imp_le @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ B2 ) )
% 0.31/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_157_less__add__same__cancel2,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere516151231imp_le @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ ( plus_plus @ A @ B2 @ A2 ) )
% 0.31/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ B2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_158_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord219039673up_add @ A )
% 0.31/1.56 => ! [A2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ A2 ) @ ( zero_zero @ A ) )
% 0.31/1.56 = ( ord_less @ A @ A2 @ ( zero_zero @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_159_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord219039673up_add @ A )
% 0.31/1.56 => ! [A2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ A2 ) )
% 0.31/1.56 = ( ord_less @ A @ ( zero_zero @ A ) @ A2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_160_linorder__neqE__linordered__idom,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linordered_idom @ A )
% 0.31/1.56 => ! [X: A,Y: A] :
% 0.31/1.56 ( ( X != Y )
% 0.31/1.56 => ( ~ ( ord_less @ A @ X @ Y )
% 0.31/1.56 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_161_add__less__imp__less__right,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere236663937imp_le @ A )
% 0.31/1.56 => ! [A2: A,C: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.31/1.56 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_162_add__less__imp__less__left,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere236663937imp_le @ A )
% 0.31/1.56 => ! [C: A,A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.31/1.56 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_163_add__strict__right__mono,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_164_add__strict__left__mono,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_165_add__strict__mono,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( strict2144017051up_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A,D: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.56 => ( ( ord_less @ A @ C @ D )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_166_add__mono__thms__linordered__field_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( ord_less @ A @ I @ J )
% 0.31/1.56 & ( K = L ) )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_167_add__mono__thms__linordered__field_I2_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( I = J )
% 0.31/1.56 & ( ord_less @ A @ K @ L ) )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_168_add__mono__thms__linordered__field_I5_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( ord_less @ A @ I @ J )
% 0.31/1.56 & ( ord_less @ A @ K @ L ) )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_169_gr__zeroI,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( canoni770627133id_add @ A )
% 0.31/1.56 => ! [N: A] :
% 0.31/1.56 ( ( N
% 0.31/1.56 != ( zero_zero @ A ) )
% 0.31/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_170_not__less__zero,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( canoni770627133id_add @ A )
% 0.31/1.56 => ! [N: A] :
% 0.31/1.56 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_171_gr__implies__not__zero,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( canoni770627133id_add @ A )
% 0.31/1.56 => ! [M: A,N: A] :
% 0.31/1.56 ( ( ord_less @ A @ M @ N )
% 0.31/1.56 => ( N
% 0.31/1.56 != ( zero_zero @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_172_zero__less__iff__neq__zero,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( canoni770627133id_add @ A )
% 0.31/1.56 => ! [N: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.31/1.56 = ( N
% 0.31/1.56 != ( zero_zero @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_173_add__less__le__mono,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A,D: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ C @ D )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_174_add__le__less__mono,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A,D: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.56 => ( ( ord_less @ A @ C @ D )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_175_add__mono__thms__linordered__field_I3_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( ord_less @ A @ I @ J )
% 0.31/1.56 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_176_add__mono__thms__linordered__field_I4_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere223160158up_add @ A )
% 0.31/1.56 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.56 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/1.56 & ( ord_less @ A @ K @ L ) )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_177_add__neg__neg,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere216010020id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_178_add__pos__pos,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere216010020id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.31/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_179_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( canoni770627133id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.56 => ~ ! [C4: A] :
% 0.31/1.56 ( ( B2
% 0.31/1.56 = ( plus_plus @ A @ A2 @ C4 ) )
% 0.31/1.56 => ( C4
% 0.31/1.56 = ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_180_pos__add__strict,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( strict797366125id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.56 => ( ( ord_less @ A @ B2 @ C )
% 0.31/1.56 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_181_add__less__zeroD,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linordered_idom @ A )
% 0.31/1.56 => ! [X: A,Y: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( plus_plus @ A @ X @ Y ) @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ( ord_less @ A @ X @ ( zero_zero @ A ) )
% 0.31/1.56 | ( ord_less @ A @ Y @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_182_zero__less__one,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( zero_less_one @ A )
% 0.31/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_183_not__one__less__zero,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_184_add__mono1,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) @ ( plus_plus @ A @ B2 @ ( one_one @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_185_less__add__one,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linordered_semidom @ A )
% 0.31/1.56 => ! [A2: A] : ( ord_less @ A @ A2 @ ( plus_plus @ A @ A2 @ ( one_one @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_186_add__strict__increasing2,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere1818651114id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.56 => ( ( ord_less @ A @ B2 @ C )
% 0.31/1.56 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_187_add__strict__increasing,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere1818651114id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.31/1.56 => ( ord_less @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_188_add__pos__nonneg,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere216010020id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 )
% 0.31/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_189_add__nonpos__neg,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere216010020id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ A2 @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ( ord_less @ A @ B2 @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_190_add__nonneg__pos,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere216010020id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ A2 )
% 0.31/1.56 => ( ( ord_less @ A @ ( zero_zero @ A ) @ B2 )
% 0.31/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_191_add__neg__nonpos,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ordere216010020id_add @ A )
% 0.31/1.56 => ! [A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ A @ A2 @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) )
% 0.31/1.56 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ B2 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_192_zero__less__two,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_193_scaleR__le__cancel__left__pos,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [C: real,A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ real @ ( zero_zero @ real ) @ C )
% 0.31/1.56 => ( ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ C @ A2 ) @ ( real_V1908273582scaleR @ A @ C @ B2 ) )
% 0.31/1.56 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_194_scaleR__le__cancel__left__neg,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [C: real,A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less @ real @ C @ ( zero_zero @ real ) )
% 0.31/1.56 => ( ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ C @ A2 ) @ ( real_V1908273582scaleR @ A @ C @ B2 ) )
% 0.31/1.56 = ( ord_less_eq @ A @ B2 @ A2 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_195_scaleR__le__cancel__left,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [C: real,A2: A,B2: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ C @ A2 ) @ ( real_V1908273582scaleR @ A @ C @ B2 ) )
% 0.31/1.56 = ( ( ( ord_less @ real @ ( zero_zero @ real ) @ C )
% 0.31/1.56 => ( ord_less_eq @ A @ A2 @ B2 ) )
% 0.31/1.56 & ( ( ord_less @ real @ C @ ( zero_zero @ real ) )
% 0.31/1.56 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_196_Collect__mono__iff,axiom,
% 0.31/1.56 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.31/1.56 = ( ! [X3: A] :
% 0.31/1.56 ( ( P @ X3 )
% 0.31/1.56 => ( Q @ X3 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_197_set__eq__subset,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ^ [Y5: set @ A,Z2: set @ A] : ( Y5 = Z2 ) )
% 0.31/1.56 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.31/1.56 & ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_198_subset__trans,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A,C2: set @ A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C2 )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_199_Collect__mono,axiom,
% 0.31/1.56 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/1.56 ( ! [X4: A] :
% 0.31/1.56 ( ( P @ X4 )
% 0.31/1.56 => ( Q @ X4 ) )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_200_subset__refl,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_201_subset__iff,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.56 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.31/1.56 ! [T2: A] :
% 0.31/1.56 ( ( member @ A @ T2 @ A7 )
% 0.31/1.56 => ( member @ A @ T2 @ B7 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_202_equalityD2,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( A4 = B5 )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_203_equalityD1,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( A4 = B5 )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_204_subset__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.56 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.31/1.56 ! [X3: A] :
% 0.31/1.56 ( ( member @ A @ X3 @ A7 )
% 0.31/1.56 => ( member @ A @ X3 @ B7 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_205_equalityE,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( A4 = B5 )
% 0.31/1.56 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_206_subsetD,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A,C: A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( member @ A @ C @ A4 )
% 0.31/1.56 => ( member @ A @ C @ B5 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_207_in__mono,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( member @ A @ X @ A4 )
% 0.31/1.56 => ( member @ A @ X @ B5 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_208_zero__le__scaleR__iff,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,B2: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( real_V1908273582scaleR @ A @ A2 @ B2 ) )
% 0.31/1.56 = ( ( ( ord_less @ real @ ( zero_zero @ real ) @ A2 )
% 0.31/1.56 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.31/1.56 | ( ( ord_less @ real @ A2 @ ( zero_zero @ real ) )
% 0.31/1.56 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.31/1.56 | ( A2
% 0.31/1.56 = ( zero_zero @ real ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_209_scaleR__le__0__iff,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1587248058vector @ A )
% 0.31/1.56 => ! [A2: real,B2: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ ( real_V1908273582scaleR @ A @ A2 @ B2 ) @ ( zero_zero @ A ) )
% 0.31/1.56 = ( ( ( ord_less @ real @ ( zero_zero @ real ) @ A2 )
% 0.31/1.56 & ( ord_less_eq @ A @ B2 @ ( zero_zero @ A ) ) )
% 0.31/1.56 | ( ( ord_less @ real @ A2 @ ( zero_zero @ real ) )
% 0.31/1.56 & ( ord_less_eq @ A @ ( zero_zero @ A ) @ B2 ) )
% 0.31/1.56 | ( A2
% 0.31/1.56 = ( zero_zero @ real ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_210_weak__convexD,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [Pr: set @ ( product_prod @ A @ A ),X: A,Y: A,U: real,V: real] :
% 0.31/1.56 ( ( prefer1289595409x_pref @ A @ Pr )
% 0.31/1.56 => ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X @ Y ) @ Pr )
% 0.31/1.56 => ( ( ord_less @ real @ ( zero_zero @ real ) @ U )
% 0.31/1.56 => ( ( ord_less @ real @ ( zero_zero @ real ) @ V )
% 0.31/1.56 => ( ( ( plus_plus @ real @ U @ V )
% 0.31/1.56 = ( one_one @ real ) )
% 0.31/1.56 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ U @ X ) @ ( real_V1908273582scaleR @ A @ V @ Y ) ) @ Y ) @ Pr ) ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_211_weak__convex__pref__def,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( ( prefer1289595409x_pref @ A )
% 0.31/1.56 = ( ^ [Pr2: set @ ( product_prod @ A @ A )] :
% 0.31/1.56 ! [X3: A,Y6: A] :
% 0.31/1.56 ( ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ X3 @ Y6 ) @ Pr2 )
% 0.31/1.56 => ! [Alpha2: real,Beta2: real] :
% 0.31/1.56 ( ( ( ( plus_plus @ real @ Alpha2 @ Beta2 )
% 0.31/1.56 = ( one_one @ real ) )
% 0.31/1.56 & ( ord_less @ real @ ( zero_zero @ real ) @ Alpha2 )
% 0.31/1.56 & ( ord_less @ real @ ( zero_zero @ real ) @ Beta2 ) )
% 0.31/1.56 => ( member @ ( product_prod @ A @ A ) @ ( product_Pair @ A @ A @ ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ Alpha2 @ X3 ) @ ( real_V1908273582scaleR @ A @ Beta2 @ Y6 ) ) @ Y6 ) @ Pr2 ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_212_discrete,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( unique1598680935umeral @ A )
% 0.31/1.56 => ( ( ord_less @ A )
% 0.31/1.56 = ( ^ [A5: A] : ( ord_less_eq @ A @ ( plus_plus @ A @ A5 @ ( one_one @ A ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_213_field__le__epsilon,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linordered_field @ A )
% 0.31/1.56 => ! [X: A,Y: A] :
% 0.31/1.56 ( ! [E2: A] :
% 0.31/1.56 ( ( ord_less @ A @ ( zero_zero @ A ) @ E2 )
% 0.31/1.56 => ( ord_less_eq @ A @ X @ ( plus_plus @ A @ Y @ E2 ) ) )
% 0.31/1.56 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_214_approachable__lt__le2,axiom,
% 0.31/1.56 ! [A: $tType,Q: A > $o,F4: A > real,P: A > $o] :
% 0.31/1.56 ( ( ? [D5: real] :
% 0.31/1.56 ( ( ord_less @ real @ ( zero_zero @ real ) @ D5 )
% 0.31/1.56 & ! [X3: A] :
% 0.31/1.56 ( ( Q @ X3 )
% 0.31/1.56 => ( ( ord_less @ real @ ( F4 @ X3 ) @ D5 )
% 0.31/1.56 => ( P @ X3 ) ) ) ) )
% 0.31/1.56 = ( ? [D5: real] :
% 0.31/1.56 ( ( ord_less @ real @ ( zero_zero @ real ) @ D5 )
% 0.31/1.56 & ! [X3: A] :
% 0.31/1.56 ( ( ord_less_eq @ real @ ( F4 @ X3 ) @ D5 )
% 0.31/1.56 => ( ( Q @ X3 )
% 0.31/1.56 => ( P @ X3 ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_215_psubsetI,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( A4 != B5 )
% 0.31/1.56 => ( ord_less @ ( set @ A ) @ A4 @ B5 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_216_psubsetE,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_217_psubset__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ord_less @ ( set @ A ) )
% 0.31/1.56 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.31/1.56 & ( A7 != B7 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_218_psubset__imp__subset,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.31/1.56 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_219_psubset__subset__trans,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A,C2: set @ A] :
% 0.31/1.56 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C2 )
% 0.31/1.56 => ( ord_less @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_220_subset__not__subset__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ord_less @ ( set @ A ) )
% 0.31/1.56 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B7 )
% 0.31/1.56 & ~ ( ord_less_eq @ ( set @ A ) @ B7 @ A7 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_221_subset__psubset__trans,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A,C2: set @ A] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( ord_less @ ( set @ A ) @ B5 @ C2 )
% 0.31/1.56 => ( ord_less @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_222_subset__iff__psubset__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/1.56 = ( ^ [A7: set @ A,B7: set @ A] :
% 0.31/1.56 ( ( ord_less @ ( set @ A ) @ A7 @ B7 )
% 0.31/1.56 | ( A7 = B7 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_223_less__prod__def,axiom,
% 0.31/1.56 ! [B: $tType,A: $tType] :
% 0.31/1.56 ( ( ( ord @ A )
% 0.31/1.56 & ( ord @ B ) )
% 0.31/1.56 => ( ( ord_less @ ( product_prod @ A @ B ) )
% 0.31/1.56 = ( ^ [X3: product_prod @ A @ B,Y6: product_prod @ A @ B] :
% 0.31/1.56 ( ( ord_less_eq @ ( product_prod @ A @ B ) @ X3 @ Y6 )
% 0.31/1.56 & ~ ( ord_less_eq @ ( product_prod @ A @ B ) @ Y6 @ X3 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_224_linordered__field__no__lb,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linordered_field @ A )
% 0.31/1.56 => ! [X6: A] :
% 0.31/1.56 ? [Y3: A] : ( ord_less @ A @ Y3 @ X6 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_225_linordered__field__no__ub,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linordered_field @ A )
% 0.31/1.56 => ! [X6: A] :
% 0.31/1.56 ? [X_1: A] : ( ord_less @ A @ X6 @ X_1 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_226_divides__aux__eq,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( unique1598680935umeral @ A )
% 0.31/1.56 => ! [Q2: A,R: A] :
% 0.31/1.56 ( ( unique455577585es_aux @ A @ ( product_Pair @ A @ A @ Q2 @ R ) )
% 0.31/1.56 = ( R
% 0.31/1.56 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_227_less__numeral__extra_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_228_psubset__trans,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A,C2: set @ A] :
% 0.31/1.56 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( ord_less @ ( set @ A ) @ B5 @ C2 )
% 0.31/1.56 => ( ord_less @ ( set @ A ) @ A4 @ C2 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_229_psubsetD,axiom,
% 0.31/1.56 ! [A: $tType,A4: set @ A,B5: set @ A,C: A] :
% 0.31/1.56 ( ( ord_less @ ( set @ A ) @ A4 @ B5 )
% 0.31/1.56 => ( ( member @ A @ C @ A4 )
% 0.31/1.56 => ( member @ A @ C @ B5 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_230_is__num__normalize_I1_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( neg_numeral @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 0.31/1.56 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_231_le__numeral__extra_I3_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_232_less__numeral__extra_I3_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_233_le__numeral__extra_I4_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_234_less__numeral__extra_I4_J,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linord1659791738miring @ A )
% 0.31/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_235_order__refl,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( preorder @ A )
% 0.31/1.56 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_236_add__scaleR__degen,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ! [U: real,B2: A,V: real,A2: A] :
% 0.31/1.56 ( ( ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ U @ B2 ) @ ( real_V1908273582scaleR @ A @ V @ A2 ) )
% 0.31/1.56 = ( plus_plus @ A @ ( real_V1908273582scaleR @ A @ U @ A2 ) @ ( real_V1908273582scaleR @ A @ V @ B2 ) ) )
% 0.31/1.56 => ( ( U != V )
% 0.31/1.56 => ( A2 = B2 ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_237_le__funD,axiom,
% 0.31/1.56 ! [B: $tType,A: $tType] :
% 0.31/1.56 ( ( ord @ B )
% 0.31/1.56 => ! [F4: A > B,G3: A > B,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ ( A > B ) @ F4 @ G3 )
% 0.31/1.56 => ( ord_less_eq @ B @ ( F4 @ X ) @ ( G3 @ X ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_238_le__funE,axiom,
% 0.31/1.56 ! [B: $tType,A: $tType] :
% 0.31/1.56 ( ( ord @ B )
% 0.31/1.56 => ! [F4: A > B,G3: A > B,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ ( A > B ) @ F4 @ G3 )
% 0.31/1.56 => ( ord_less_eq @ B @ ( F4 @ X ) @ ( G3 @ X ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_239_le__funI,axiom,
% 0.31/1.56 ! [B: $tType,A: $tType] :
% 0.31/1.56 ( ( ord @ B )
% 0.31/1.56 => ! [F4: A > B,G3: A > B] :
% 0.31/1.56 ( ! [X4: A] : ( ord_less_eq @ B @ ( F4 @ X4 ) @ ( G3 @ X4 ) )
% 0.31/1.56 => ( ord_less_eq @ ( A > B ) @ F4 @ G3 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_240_le__fun__def,axiom,
% 0.31/1.56 ! [B: $tType,A: $tType] :
% 0.31/1.56 ( ( ord @ B )
% 0.31/1.56 => ( ( ord_less_eq @ ( A > B ) )
% 0.31/1.56 = ( ^ [F5: A > B,G4: A > B] :
% 0.31/1.56 ! [X3: A] : ( ord_less_eq @ B @ ( F5 @ X3 ) @ ( G4 @ X3 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_241_order__subst1,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType] :
% 0.31/1.56 ( ( ( order @ B )
% 0.31/1.56 & ( order @ A ) )
% 0.31/1.56 => ! [A2: A,F4: B > A,B2: B,C: B] :
% 0.31/1.56 ( ( ord_less_eq @ A @ A2 @ ( F4 @ B2 ) )
% 0.31/1.56 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.31/1.56 => ( ! [X4: B,Y3: B] :
% 0.31/1.56 ( ( ord_less_eq @ B @ X4 @ Y3 )
% 0.31/1.56 => ( ord_less_eq @ A @ ( F4 @ X4 ) @ ( F4 @ Y3 ) ) )
% 0.31/1.56 => ( ord_less_eq @ A @ A2 @ ( F4 @ C ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_242_order__subst2,axiom,
% 0.31/1.56 ! [A: $tType,C5: $tType] :
% 0.31/1.56 ( ( ( order @ C5 )
% 0.31/1.56 & ( order @ A ) )
% 0.31/1.56 => ! [A2: A,B2: A,F4: A > C5,C: C5] :
% 0.31/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.56 => ( ( ord_less_eq @ C5 @ ( F4 @ B2 ) @ C )
% 0.31/1.56 => ( ! [X4: A,Y3: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.31/1.56 => ( ord_less_eq @ C5 @ ( F4 @ X4 ) @ ( F4 @ Y3 ) ) )
% 0.31/1.56 => ( ord_less_eq @ C5 @ ( F4 @ A2 ) @ C ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_243_ord__eq__le__subst,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType] :
% 0.31/1.56 ( ( ( ord @ B )
% 0.31/1.56 & ( ord @ A ) )
% 0.31/1.56 => ! [A2: A,F4: B > A,B2: B,C: B] :
% 0.31/1.56 ( ( A2
% 0.31/1.56 = ( F4 @ B2 ) )
% 0.31/1.56 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.31/1.56 => ( ! [X4: B,Y3: B] :
% 0.31/1.56 ( ( ord_less_eq @ B @ X4 @ Y3 )
% 0.31/1.56 => ( ord_less_eq @ A @ ( F4 @ X4 ) @ ( F4 @ Y3 ) ) )
% 0.31/1.56 => ( ord_less_eq @ A @ A2 @ ( F4 @ C ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_244_ord__le__eq__subst,axiom,
% 0.31/1.56 ! [A: $tType,B: $tType] :
% 0.31/1.56 ( ( ( ord @ B )
% 0.31/1.56 & ( ord @ A ) )
% 0.31/1.56 => ! [A2: A,B2: A,F4: A > B,C: B] :
% 0.31/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.56 => ( ( ( F4 @ B2 )
% 0.31/1.56 = C )
% 0.31/1.56 => ( ! [X4: A,Y3: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ X4 @ Y3 )
% 0.31/1.56 => ( ord_less_eq @ B @ ( F4 @ X4 ) @ ( F4 @ Y3 ) ) )
% 0.31/1.56 => ( ord_less_eq @ B @ ( F4 @ A2 ) @ C ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_245_eq__iff,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( order @ A )
% 0.31/1.56 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.31/1.56 = ( ^ [X3: A,Y6: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ X3 @ Y6 )
% 0.31/1.56 & ( ord_less_eq @ A @ Y6 @ X3 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_246_antisym,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( order @ A )
% 0.31/1.56 => ! [X: A,Y: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.56 => ( ( ord_less_eq @ A @ Y @ X )
% 0.31/1.56 => ( X = Y ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_247_linear,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linorder @ A )
% 0.31/1.56 => ! [X: A,Y: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.56 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_248_eq__refl,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( preorder @ A )
% 0.31/1.56 => ! [X: A,Y: A] :
% 0.31/1.56 ( ( X = Y )
% 0.31/1.56 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_249_le__cases,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linorder @ A )
% 0.31/1.56 => ! [X: A,Y: A] :
% 0.31/1.56 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.31/1.56 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_250_order_Otrans,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( order @ A )
% 0.31/1.56 => ! [A2: A,B2: A,C: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.56 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.31/1.56 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_251_le__cases3,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( linorder @ A )
% 0.31/1.56 => ! [X: A,Y: A,Z: A] :
% 0.31/1.56 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.56 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.31/1.56 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.31/1.56 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.31/1.56 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.31/1.56 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.31/1.56 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.31/1.56 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.31/1.56 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.31/1.56 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.31/1.56 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.31/1.56 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_252_antisym__conv,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( order @ A )
% 0.31/1.56 => ! [Y: A,X: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ Y @ X )
% 0.31/1.56 => ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.56 = ( X = Y ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(fact_253_order__class_Oorder_Oeq__iff,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( order @ A )
% 0.31/1.56 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.31/1.56 = ( ^ [A5: A,B4: A] :
% 0.31/1.56 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.31/1.56 & ( ord_less_eq @ A @ B4 @ A5 ) ) ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___HOL_Otype,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( type @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Oplus,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( plus @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ozero,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( zero @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ogroup__add,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( group_add @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Omonoid__add,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( monoid_add @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Osemigroup__add,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( semigroup_add @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocomm__monoid__add,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( comm_monoid_add @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Oab__semigroup__add,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( ab_semigroup_add @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocancel__semigroup__add,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( cancel_semigroup_add @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocancel__comm__monoid__add,axiom,
% 0.31/1.56 ! [A: $tType] :
% 0.31/1.56 ( ( real_V1076094709vector @ A )
% 0.31/1.56 => ( cancel1352612707id_add @ A ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Ordered__Euclidean__Space_Oordered__euclidean__space,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( ordere890947078_space @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Ordered__Euclidean__Space_Oordered__euclidean__space_1,axiom,
% 0.31/1.56 ordere890947078_space @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( preorder @ A9 )
% 0.31/1.56 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( order @ A9 )
% 0.31/1.56 => ( order @ ( A8 > A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ord @ A9 )
% 0.31/1.56 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Groups_Oab__semigroup__add,axiom,
% 0.31/1.56 ! [A8: $tType] :
% 0.31/1.56 ( ( ab_semigroup_add @ A8 )
% 0.31/1.56 => ( ab_semigroup_add @ ( set @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Groups_Ocomm__monoid__add,axiom,
% 0.31/1.56 ! [A8: $tType] :
% 0.31/1.56 ( ( comm_monoid_add @ A8 )
% 0.31/1.56 => ( comm_monoid_add @ ( set @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Groups_Osemigroup__add,axiom,
% 0.31/1.56 ! [A8: $tType] :
% 0.31/1.56 ( ( semigroup_add @ A8 )
% 0.31/1.56 => ( semigroup_add @ ( set @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.31/1.56 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Groups_Omonoid__add,axiom,
% 0.31/1.56 ! [A8: $tType] :
% 0.31/1.56 ( ( monoid_add @ A8 )
% 0.31/1.56 => ( monoid_add @ ( set @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Orderings_Oorder_3,axiom,
% 0.31/1.56 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Orderings_Oord_4,axiom,
% 0.31/1.56 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Groups_Ozero,axiom,
% 0.31/1.56 ! [A8: $tType] :
% 0.31/1.56 ( ( zero @ A8 )
% 0.31/1.56 => ( zero @ ( set @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Groups_Oplus,axiom,
% 0.31/1.56 ! [A8: $tType] :
% 0.31/1.56 ( ( plus @ A8 )
% 0.31/1.56 => ( plus @ ( set @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Set_Oset___Groups_Oone,axiom,
% 0.31/1.56 ! [A8: $tType] :
% 0.31/1.56 ( ( one @ A8 )
% 0.31/1.56 => ( one @ ( set @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_HOL_Obool___Orderings_Opreorder_5,axiom,
% 0.31/1.56 preorder @ $o ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.31/1.56 linorder @ $o ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_6,axiom,
% 0.31/1.56 order @ $o ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 0.31/1.56 ord @ $o ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.31/1.56 ordere516151231imp_le @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oordered__real__vector,axiom,
% 0.31/1.56 real_V1587248058vector @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.31/1.56 strict2144017051up_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.31/1.56 ordere223160158up_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.31/1.56 ordere236663937imp_le @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__normed__vector,axiom,
% 0.31/1.56 real_V55928688vector @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Ostrict__ordered__comm__monoid__add,axiom,
% 0.31/1.56 strict797366125id_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oordered__cancel__comm__monoid__add,axiom,
% 0.31/1.56 ordere1818651114id_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring,axiom,
% 0.31/1.56 linord1659791738miring @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oordered__ab__semigroup__add,axiom,
% 0.31/1.56 ordere779506340up_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Real__Vector__Spaces_Oreal__vector,axiom,
% 0.31/1.56 real_V1076094709vector @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oordered__comm__monoid__add,axiom,
% 0.31/1.56 ordere216010020id_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Olinordered__ab__group__add,axiom,
% 0.31/1.56 linord219039673up_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add,axiom,
% 0.31/1.56 cancel1352612707id_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Ocancel__semigroup__add,axiom,
% 0.31/1.56 cancel_semigroup_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__semidom,axiom,
% 0.31/1.56 linordered_semidom @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oab__semigroup__add_8,axiom,
% 0.31/1.56 ab_semigroup_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Fields_Olinordered__field,axiom,
% 0.31/1.56 linordered_field @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Ocomm__monoid__add_9,axiom,
% 0.31/1.56 comm_monoid_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Rings_Olinordered__idom,axiom,
% 0.31/1.56 linordered_idom @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Osemigroup__add_10,axiom,
% 0.31/1.56 semigroup_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Rings_Ozero__less__one,axiom,
% 0.31/1.56 zero_less_one @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Rings_Ozero__neq__one,axiom,
% 0.31/1.56 zero_neq_one @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Orderings_Opreorder_11,axiom,
% 0.31/1.56 preorder @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Orderings_Olinorder_12,axiom,
% 0.31/1.56 linorder @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Omonoid__add_13,axiom,
% 0.31/1.56 monoid_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.31/1.56 group_add @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Orderings_Oorder_14,axiom,
% 0.31/1.56 order @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Num_Oneg__numeral,axiom,
% 0.31/1.56 neg_numeral @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Orderings_Oord_15,axiom,
% 0.31/1.56 ord @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Ozero_16,axiom,
% 0.31/1.56 zero @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oplus_17,axiom,
% 0.31/1.56 plus @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Real_Oreal___Groups_Oone_18,axiom,
% 0.31/1.56 one @ real ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__monoid__add__imp__le_19,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( ordere516151231imp_le @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oordered__real__vector_20,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( real_V1587248058vector @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Ostrict__ordered__ab__semigroup__add_21,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( strict2144017051up_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Oordered__cancel__ab__semigroup__add_22,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( ordere223160158up_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__add__imp__le_23,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( ordere236663937imp_le @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__normed__vector_24,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( real_V55928688vector @ A8 )
% 0.31/1.56 & ( real_V55928688vector @ A9 ) )
% 0.31/1.56 => ( real_V55928688vector @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Ostrict__ordered__comm__monoid__add_25,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( strict797366125id_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Oordered__cancel__comm__monoid__add_26,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( ordere1818651114id_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Oordered__ab__semigroup__add_27,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( ordere779506340up_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Real__Vector__Spaces_Oreal__vector_28,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( real_V1076094709vector @ A8 )
% 0.31/1.56 & ( real_V1076094709vector @ A9 ) )
% 0.31/1.56 => ( real_V1076094709vector @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Oordered__comm__monoid__add_29,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ordere890947078_space @ A8 )
% 0.31/1.56 & ( ordere890947078_space @ A9 ) )
% 0.31/1.56 => ( ordere216010020id_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Ocancel__comm__monoid__add_30,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( cancel1352612707id_add @ A8 )
% 0.31/1.56 & ( cancel1352612707id_add @ A9 ) )
% 0.31/1.56 => ( cancel1352612707id_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Ocancel__semigroup__add_31,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( cancel_semigroup_add @ A8 )
% 0.31/1.56 & ( cancel_semigroup_add @ A9 ) )
% 0.31/1.56 => ( cancel_semigroup_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Oab__semigroup__add_32,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ab_semigroup_add @ A8 )
% 0.31/1.56 & ( ab_semigroup_add @ A9 ) )
% 0.31/1.56 => ( ab_semigroup_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Ocomm__monoid__add_33,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( comm_monoid_add @ A8 )
% 0.31/1.56 & ( comm_monoid_add @ A9 ) )
% 0.31/1.56 => ( comm_monoid_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Osemigroup__add_34,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( semigroup_add @ A8 )
% 0.31/1.56 & ( semigroup_add @ A9 ) )
% 0.31/1.56 => ( semigroup_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_35,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( preorder @ A8 )
% 0.31/1.56 & ( preorder @ A9 ) )
% 0.31/1.56 => ( preorder @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Omonoid__add_36,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( monoid_add @ A8 )
% 0.31/1.56 & ( monoid_add @ A9 ) )
% 0.31/1.56 => ( monoid_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Ogroup__add_37,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( group_add @ A8 )
% 0.31/1.56 & ( group_add @ A9 ) )
% 0.31/1.56 => ( group_add @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Orderings_Oorder_38,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( order @ A8 )
% 0.31/1.56 & ( order @ A9 ) )
% 0.31/1.56 => ( order @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Orderings_Oord_39,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( ord @ A8 )
% 0.31/1.56 & ( ord @ A9 ) )
% 0.31/1.56 => ( ord @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Ozero_40,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( zero @ A8 )
% 0.31/1.56 & ( zero @ A9 ) )
% 0.31/1.56 => ( zero @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Groups_Oplus_41,axiom,
% 0.31/1.56 ! [A8: $tType,A9: $tType] :
% 0.31/1.56 ( ( ( plus @ A8 )
% 0.31/1.56 & ( plus @ A9 ) )
% 0.31/1.56 => ( plus @ ( product_prod @ A8 @ A9 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tfree_0,hypothesis,
% 0.31/1.56 real_V1076094709vector @ a ).
% 0.31/1.56
% 0.31/1.56 thf(conj_0,conjecture,
% 0.31/1.56 member @ ( product_prod @ a @ a ) @ ( product_Pair @ a @ a @ ( plus_plus @ a @ ( real_V1908273582scaleR @ a @ u @ x ) @ ( real_V1908273582scaleR @ a @ v @ y ) ) @ y ) @ relation ).
% 0.31/1.56 ------------------------
% 0.31/1.59 % (12126)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/2Mi)
% 0.31/1.59 % (12123)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/183Mi)
% 0.31/1.59 % (12126)Instruction limit reached!
% 0.31/1.59 % (12126)------------------------------
% 0.31/1.59 % (12126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (12126)Termination reason: Unknown
% 0.31/1.59 % (12126)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (12126)Memory used [KB]: 1407
% 0.31/1.59 % (12126)Time elapsed: 0.002 s
% 0.31/1.59 % (12126)Instructions burned: 2 (million)
% 0.31/1.59 % (12126)------------------------------
% 0.31/1.59 % (12126)------------------------------
% 0.31/1.59 % (12127)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_11849 for (2999ds/2Mi)
% 0.31/1.59 % (12127)Instruction limit reached!
% 0.31/1.59 % (12127)------------------------------
% 0.31/1.59 % (12127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (12127)Termination reason: Unknown
% 0.31/1.59 % (12127)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (12127)Memory used [KB]: 1407
% 0.31/1.59 % (12127)Time elapsed: 0.002 s
% 0.31/1.59 % (12127)Instructions burned: 3 (million)
% 0.31/1.59 % (12127)------------------------------
% 0.31/1.59 % (12127)------------------------------
% 2.95/1.60 % (12124)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_11849 for (2999ds/4Mi)
% 2.95/1.60 % (12125)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_11849 for (2999ds/27Mi)
% 2.95/1.60 % (12129)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/18Mi)
% 2.95/1.60 % (12128)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_11849 for (2999ds/275Mi)
% 2.95/1.60 % (12130)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/3Mi)
% 2.95/1.60 % (12124)Instruction limit reached!
% 2.95/1.60 % (12124)------------------------------
% 2.95/1.60 % (12124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (12124)Termination reason: Unknown
% 2.95/1.60 % (12124)Termination phase: shuffling
% 2.95/1.60
% 2.95/1.60 % (12124)Memory used [KB]: 1407
% 2.95/1.60 % (12124)Time elapsed: 0.005 s
% 2.95/1.60 % (12124)Instructions burned: 5 (million)
% 2.95/1.60 % (12124)------------------------------
% 2.95/1.60 % (12124)------------------------------
% 2.95/1.60 % (12130)Instruction limit reached!
% 2.95/1.60 % (12130)------------------------------
% 2.95/1.60 % (12130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.60 % (12130)Termination reason: Unknown
% 2.95/1.60 % (12130)Termination phase: shuffling
% 2.95/1.60
% 2.95/1.60 % (12130)Memory used [KB]: 1407
% 2.95/1.60 % (12130)Time elapsed: 0.002 s
% 2.95/1.60 % (12130)Instructions burned: 3 (million)
% 2.95/1.60 % (12130)------------------------------
% 2.95/1.60 % (12130)------------------------------
% 2.95/1.60 % (12131)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_11849 for (2999ds/37Mi)
% 2.95/1.61 % (12129)Instruction limit reached!
% 2.95/1.61 % (12129)------------------------------
% 2.95/1.61 % (12129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (12129)Termination reason: Unknown
% 2.95/1.61 % (12129)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (12129)Memory used [KB]: 1791
% 2.95/1.61 % (12129)Time elapsed: 0.014 s
% 2.95/1.61 % (12129)Instructions burned: 18 (million)
% 2.95/1.61 % (12129)------------------------------
% 2.95/1.61 % (12129)------------------------------
% 2.95/1.61 % (12133)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_11849 for (2999ds/3Mi)
% 2.95/1.61 % (12133)Instruction limit reached!
% 2.95/1.61 % (12133)------------------------------
% 2.95/1.61 % (12133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (12133)Termination reason: Unknown
% 2.95/1.61 % (12133)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (12133)Memory used [KB]: 1535
% 2.95/1.61 % (12133)Time elapsed: 0.003 s
% 2.95/1.61 % (12133)Instructions burned: 5 (million)
% 2.95/1.61 % (12133)------------------------------
% 2.95/1.61 % (12133)------------------------------
% 2.95/1.61 % (12131)Instruction limit reached!
% 2.95/1.61 % (12131)------------------------------
% 2.95/1.61 % (12131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (12131)Termination reason: Unknown
% 2.95/1.61 % (12131)Termination phase: shuffling
% 2.95/1.61
% 2.95/1.61 % (12131)Memory used [KB]: 2174
% 2.95/1.61 % (12131)Time elapsed: 0.013 s
% 2.95/1.61 % (12131)Instructions burned: 37 (million)
% 2.95/1.61 % (12131)------------------------------
% 2.95/1.61 % (12131)------------------------------
% 2.95/1.61 % (12125)Instruction limit reached!
% 2.95/1.61 % (12125)------------------------------
% 2.95/1.61 % (12125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.61 % (12125)Termination reason: Unknown
% 2.95/1.61 % (12125)Termination phase: Property scanning
% 2.95/1.61
% 2.95/1.61 % (12125)Memory used [KB]: 1918
% 2.95/1.61 % (12125)Time elapsed: 0.019 s
% 2.95/1.61 % (12125)Instructions burned: 27 (million)
% 2.95/1.61 % (12125)------------------------------
% 2.95/1.61 % (12125)------------------------------
% 2.95/1.62 % (12132)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_11849 for (2999ds/15Mi)
% 2.95/1.62 % (12135)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/7Mi)
% 2.95/1.62 % (12136)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/16Mi)
% 2.95/1.62 % (12135)Instruction limit reached!
% 2.95/1.62 % (12135)------------------------------
% 2.95/1.62 % (12135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.62 % (12135)Termination reason: Unknown
% 2.95/1.62 % (12135)Termination phase: shuffling
% 2.95/1.62
% 2.95/1.62 % (12135)Memory used [KB]: 1535
% 2.95/1.62 % (12135)Time elapsed: 0.004 s
% 2.95/1.62 % (12135)Instructions burned: 9 (million)
% 2.95/1.62 % (12135)------------------------------
% 2.95/1.62 % (12135)------------------------------
% 2.95/1.63 % (12134)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_11849 for (2999ds/1041Mi)
% 2.95/1.63 % (12132)Instruction limit reached!
% 2.95/1.63 % (12132)------------------------------
% 2.95/1.63 % (12132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (12132)Termination reason: Unknown
% 2.95/1.63 % (12132)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (12132)Memory used [KB]: 1663
% 2.95/1.63 % (12132)Time elapsed: 0.012 s
% 2.95/1.63 % (12132)Instructions burned: 16 (million)
% 2.95/1.63 % (12132)------------------------------
% 2.95/1.63 % (12132)------------------------------
% 2.95/1.63 % (12136)Instruction limit reached!
% 2.95/1.63 % (12136)------------------------------
% 2.95/1.63 % (12136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (12136)Termination reason: Unknown
% 2.95/1.63 % (12136)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (12136)Memory used [KB]: 1663
% 2.95/1.63 % (12136)Time elapsed: 0.007 s
% 2.95/1.63 % (12136)Instructions burned: 17 (million)
% 2.95/1.63 % (12136)------------------------------
% 2.95/1.63 % (12136)------------------------------
% 2.95/1.63 % (12137)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_11849 for (2999ds/3Mi)
% 2.95/1.63 % (12137)Instruction limit reached!
% 2.95/1.63 % (12137)------------------------------
% 2.95/1.63 % (12137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (12137)Termination reason: Unknown
% 2.95/1.63 % (12137)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (12137)Memory used [KB]: 1407
% 2.95/1.63 % (12137)Time elapsed: 0.003 s
% 2.95/1.63 % (12137)Instructions burned: 3 (million)
% 2.95/1.63 % (12137)------------------------------
% 2.95/1.63 % (12137)------------------------------
% 2.95/1.63 % (12138)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_11849 for (2999ds/3Mi)
% 2.95/1.63 % (12138)Instruction limit reached!
% 2.95/1.63 % (12138)------------------------------
% 2.95/1.63 % (12138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.63 % (12138)Termination reason: Unknown
% 2.95/1.63 % (12138)Termination phase: shuffling
% 2.95/1.63
% 2.95/1.63 % (12138)Memory used [KB]: 1407
% 2.95/1.63 % (12138)Time elapsed: 0.002 s
% 2.95/1.63 % (12138)Instructions burned: 3 (million)
% 2.95/1.63 % (12138)------------------------------
% 2.95/1.63 % (12138)------------------------------
% 2.95/1.64 % (12140)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/3Mi)
% 2.95/1.64 % (12140)Instruction limit reached!
% 2.95/1.64 % (12140)------------------------------
% 2.95/1.64 % (12140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.64 % (12140)Termination reason: Unknown
% 2.95/1.64 % (12140)Termination phase: shuffling
% 2.95/1.64
% 2.95/1.64 % (12140)Memory used [KB]: 1407
% 2.95/1.64 % (12140)Time elapsed: 0.002 s
% 2.95/1.64 % (12140)Instructions burned: 3 (million)
% 2.95/1.64 % (12140)------------------------------
% 2.95/1.64 % (12140)------------------------------
% 2.95/1.64 % (12141)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/4Mi)
% 2.95/1.64 % (12142)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/18Mi)
% 2.95/1.65 % (12141)Instruction limit reached!
% 2.95/1.65 % (12141)------------------------------
% 2.95/1.65 % (12141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (12141)Termination reason: Unknown
% 2.95/1.65 % (12141)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (12141)Memory used [KB]: 1407
% 2.95/1.65 % (12141)Time elapsed: 0.003 s
% 2.95/1.65 % (12141)Instructions burned: 4 (million)
% 2.95/1.65 % (12141)------------------------------
% 2.95/1.65 % (12141)------------------------------
% 2.95/1.65 % (12139)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/7Mi)
% 2.95/1.65 % (12143)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/710Mi)
% 2.95/1.65 % (12142)Instruction limit reached!
% 2.95/1.65 % (12142)------------------------------
% 2.95/1.65 % (12142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (12142)Termination reason: Unknown
% 2.95/1.65 % (12142)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (12142)Memory used [KB]: 1791
% 2.95/1.65 % (12142)Time elapsed: 0.007 s
% 2.95/1.65 % (12142)Instructions burned: 18 (million)
% 2.95/1.65 % (12142)------------------------------
% 2.95/1.65 % (12142)------------------------------
% 2.95/1.65 % (12139)Instruction limit reached!
% 2.95/1.65 % (12139)------------------------------
% 2.95/1.65 % (12139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (12139)Termination reason: Unknown
% 2.95/1.65 % (12139)Termination phase: shuffling
% 2.95/1.65
% 2.95/1.65 % (12139)Memory used [KB]: 1535
% 2.95/1.65 % (12139)Time elapsed: 0.007 s
% 2.95/1.65 % (12139)Instructions burned: 8 (million)
% 2.95/1.65 % (12139)------------------------------
% 2.95/1.65 % (12139)------------------------------
% 2.95/1.65 % (12123)Instruction limit reached!
% 2.95/1.65 % (12123)------------------------------
% 2.95/1.65 % (12123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.65 % (12123)Termination reason: Unknown
% 2.95/1.65 % (12123)Termination phase: Saturation
% 2.95/1.65
% 2.95/1.65 % (12123)Memory used [KB]: 7291
% 2.95/1.65 % (12123)Time elapsed: 0.062 s
% 2.95/1.65 % (12123)Instructions burned: 185 (million)
% 2.95/1.65 % (12123)------------------------------
% 2.95/1.65 % (12123)------------------------------
% 2.95/1.66 % (12144)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/6Mi)
% 2.95/1.66 % (12144)Instruction limit reached!
% 2.95/1.66 % (12144)------------------------------
% 2.95/1.66 % (12144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.66 % (12144)Termination reason: Unknown
% 2.95/1.66 % (12144)Termination phase: shuffling
% 2.95/1.66
% 2.95/1.66 % (12144)Memory used [KB]: 1535
% 2.95/1.66 % (12144)Time elapsed: 0.004 s
% 2.95/1.66 % (12144)Instructions burned: 6 (million)
% 2.95/1.66 % (12144)------------------------------
% 2.95/1.66 % (12144)------------------------------
% 2.95/1.66 % (12147)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/5Mi)
% 2.95/1.66 % (12147)Instruction limit reached!
% 2.95/1.66 % (12147)------------------------------
% 2.95/1.66 % (12147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.66 % (12147)Termination reason: Unknown
% 2.95/1.66 % (12147)Termination phase: shuffling
% 2.95/1.66
% 2.95/1.66 % (12147)Memory used [KB]: 1535
% 2.95/1.66 % (12147)Time elapsed: 0.004 s
% 2.95/1.66 % (12147)Instructions burned: 8 (million)
% 2.95/1.66 % (12147)------------------------------
% 2.95/1.66 % (12147)------------------------------
% 2.95/1.67 % (12145)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_11849 for (2999ds/902Mi)
% 2.95/1.67 % (12148)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_11849 for (2999ds/6Mi)
% 2.95/1.67 % (12146)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_11849 for (2999ds/21Mi)
% 2.95/1.67 % (12148)Instruction limit reached!
% 2.95/1.67 % (12148)------------------------------
% 2.95/1.67 % (12148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.67 % (12148)Termination reason: Unknown
% 2.95/1.67 % (12148)Termination phase: shuffling
% 2.95/1.67
% 2.95/1.67 % (12148)Memory used [KB]: 1535
% 2.95/1.67 % (12148)Time elapsed: 0.004 s
% 2.95/1.67 % (12148)Instructions burned: 7 (million)
% 2.95/1.67 % (12148)------------------------------
% 2.95/1.67 % (12148)------------------------------
% 2.95/1.67 % (12149)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_11849 for (2999ds/377Mi)
% 2.95/1.68 % (12146)Instruction limit reached!
% 2.95/1.68 % (12146)------------------------------
% 2.95/1.68 % (12146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.68 % (12146)Termination reason: Unknown
% 2.95/1.68 % (12146)Termination phase: shuffling
% 2.95/1.68
% 2.95/1.68 % (12146)Memory used [KB]: 1791
% 2.95/1.68 % (12146)Time elapsed: 0.014 s
% 2.95/1.68 % (12146)Instructions burned: 22 (million)
% 2.95/1.68 % (12146)------------------------------
% 2.95/1.68 % (12146)------------------------------
% 2.95/1.68 % (12150)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_11849 for (2998ds/779Mi)
% 2.95/1.69 % (12151)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_11849 for (2998ds/19Mi)
% 2.95/1.70 % (12151)Instruction limit reached!
% 2.95/1.70 % (12151)------------------------------
% 2.95/1.70 % (12151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.70 % (12151)Termination reason: Unknown
% 2.95/1.70 % (12151)Termination phase: shuffling
% 2.95/1.70
% 2.95/1.70 % (12151)Memory used [KB]: 1791
% 2.95/1.70 % (12151)Time elapsed: 0.007 s
% 2.95/1.70 % (12151)Instructions burned: 19 (million)
% 2.95/1.70 % (12151)------------------------------
% 2.95/1.70 % (12151)------------------------------
% 2.95/1.71 % (12152)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_11849 for (2998ds/879Mi)
% 2.95/1.73 % (12128)Instruction limit reached!
% 2.95/1.73 % (12128)------------------------------
% 2.95/1.73 % (12128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.73 % (12128)Termination reason: Unknown
% 2.95/1.73 % (12128)Termination phase: Saturation
% 2.95/1.73
% 2.95/1.73 % (12128)Memory used [KB]: 7291
% 2.95/1.73 % (12128)Time elapsed: 0.136 s
% 2.95/1.73 % (12128)Instructions burned: 277 (million)
% 2.95/1.73 % (12128)------------------------------
% 2.95/1.73 % (12128)------------------------------
% 2.95/1.74 % (12153)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_11849 for (2998ds/17Mi)
% 2.95/1.75 % (12153)Instruction limit reached!
% 2.95/1.75 % (12153)------------------------------
% 2.95/1.75 % (12153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.75 % (12153)Termination reason: Unknown
% 2.95/1.75 % (12153)Termination phase: shuffling
% 2.95/1.75
% 2.95/1.75 % (12153)Memory used [KB]: 1791
% 2.95/1.75 % (12153)Time elapsed: 0.008 s
% 2.95/1.75 % (12153)Instructions burned: 17 (million)
% 2.95/1.75 % (12153)------------------------------
% 2.95/1.75 % (12153)------------------------------
% 2.95/1.76 % (12154)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_11849 for (2998ds/3Mi)
% 2.95/1.76 % (12154)Instruction limit reached!
% 2.95/1.76 % (12154)------------------------------
% 2.95/1.76 % (12154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.76 % (12154)Termination reason: Unknown
% 2.95/1.76 % (12154)Termination phase: shuffling
% 2.95/1.76
% 2.95/1.76 % (12154)Memory used [KB]: 1407
% 2.95/1.76 % (12154)Time elapsed: 0.003 s
% 2.95/1.76 % (12154)Instructions burned: 4 (million)
% 2.95/1.76 % (12154)------------------------------
% 2.95/1.76 % (12154)------------------------------
% 2.95/1.77 % (12155)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_11849 for (2997ds/30Mi)
% 2.95/1.78 % (12155)Instruction limit reached!
% 2.95/1.78 % (12155)------------------------------
% 2.95/1.78 % (12155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.78 % (12155)Termination reason: Unknown
% 2.95/1.78 % (12155)Termination phase: Property scanning
% 2.95/1.78
% 2.95/1.78 % (12155)Memory used [KB]: 1918
% 2.95/1.78 % (12155)Time elapsed: 0.013 s
% 2.95/1.78 % (12155)Instructions burned: 33 (million)
% 2.95/1.78 % (12155)------------------------------
% 2.95/1.78 % (12155)------------------------------
% 2.95/1.79 % (12156)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_11849 for (2997ds/127Mi)
% 2.95/1.79 % (12149)Instruction limit reached!
% 2.95/1.79 % (12149)------------------------------
% 2.95/1.79 % (12149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.79 % (12149)Termination reason: Unknown
% 2.95/1.79 % (12149)Termination phase: Saturation
% 2.95/1.79
% 2.95/1.79 % (12149)Memory used [KB]: 8059
% 2.95/1.79 % (12149)Time elapsed: 0.144 s
% 2.95/1.79 % (12149)Instructions burned: 379 (million)
% 2.95/1.79 % (12149)------------------------------
% 2.95/1.79 % (12149)------------------------------
% 2.95/1.80 % (12157)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_11849 for (2997ds/100Mi)
% 2.95/1.83 % (12157)Instruction limit reached!
% 2.95/1.83 % (12157)------------------------------
% 2.95/1.83 % (12157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.83 % (12157)Termination reason: Unknown
% 2.95/1.83 % (12157)Termination phase: Property scanning
% 2.95/1.83
% 2.95/1.83 % (12157)Memory used [KB]: 2302
% 2.95/1.83 % (12157)Time elapsed: 0.028 s
% 2.95/1.83 % (12157)Instructions burned: 102 (million)
% 2.95/1.83 % (12157)------------------------------
% 2.95/1.83 % (12157)------------------------------
% 2.95/1.83 % (12156)Instruction limit reached!
% 2.95/1.83 % (12156)------------------------------
% 2.95/1.83 % (12156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.83 % (12156)Termination reason: Unknown
% 2.95/1.83 % (12156)Termination phase: Saturation
% 2.95/1.83
% 2.95/1.83 % (12156)Memory used [KB]: 7036
% 2.95/1.83 % (12156)Time elapsed: 0.044 s
% 2.95/1.83 % (12156)Instructions burned: 128 (million)
% 2.95/1.83 % (12156)------------------------------
% 2.95/1.83 % (12156)------------------------------
% 2.95/1.84 % (12158)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_11849 for (2997ds/3Mi)
% 2.95/1.84 % (12158)Instruction limit reached!
% 2.95/1.84 % (12158)------------------------------
% 2.95/1.84 % (12158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.84 % (12158)Termination reason: Unknown
% 2.95/1.84 % (12158)Termination phase: shuffling
% 2.95/1.84
% 2.95/1.84 % (12158)Memory used [KB]: 1407
% 2.95/1.84 % (12158)Time elapsed: 0.002 s
% 2.95/1.84 % (12158)Instructions burned: 4 (million)
% 2.95/1.84 % (12158)------------------------------
% 2.95/1.84 % (12158)------------------------------
% 2.95/1.84 % (12159)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_11849 for (2997ds/20Mi)
% 2.95/1.85 % (12160)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_11849 for (2997ds/86Mi)
% 2.95/1.85 % (12159)Instruction limit reached!
% 2.95/1.85 % (12159)------------------------------
% 2.95/1.85 % (12159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.85 % (12159)Termination reason: Unknown
% 2.95/1.85 % (12159)Termination phase: shuffling
% 2.95/1.85
% 2.95/1.85 % (12159)Memory used [KB]: 1791
% 2.95/1.85 % (12159)Time elapsed: 0.009 s
% 2.95/1.85 % (12159)Instructions burned: 20 (million)
% 2.95/1.85 % (12159)------------------------------
% 2.95/1.85 % (12159)------------------------------
% 2.95/1.86 % (12161)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_11849 for (2997ds/107Mi)
% 2.95/1.86 % (12143)Instruction limit reached!
% 2.95/1.86 % (12143)------------------------------
% 2.95/1.86 % (12143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.86 % (12143)Termination reason: Unknown
% 2.95/1.86 % (12143)Termination phase: Saturation
% 2.95/1.86
% 2.95/1.86 % (12143)Memory used [KB]: 9722
% 2.95/1.86 % (12143)Time elapsed: 0.217 s
% 2.95/1.86 % (12143)Instructions burned: 712 (million)
% 2.95/1.86 % (12143)------------------------------
% 2.95/1.86 % (12143)------------------------------
% 2.95/1.87 % (12162)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_11849 for (2996ds/39Mi)
% 2.95/1.88 % (12160)Instruction limit reached!
% 2.95/1.88 % (12160)------------------------------
% 2.95/1.88 % (12160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.88 % (12160)Termination reason: Unknown
% 2.95/1.88 % (12160)Termination phase: Saturation
% 2.95/1.88
% 2.95/1.88 % (12160)Memory used [KB]: 6780
% 2.95/1.88 % (12160)Time elapsed: 0.027 s
% 2.95/1.88 % (12160)Instructions burned: 88 (million)
% 2.95/1.88 % (12160)------------------------------
% 2.95/1.88 % (12160)------------------------------
% 2.95/1.88 % (12162)Instruction limit reached!
% 2.95/1.88 % (12162)------------------------------
% 2.95/1.88 % (12162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.88 % (12162)Termination reason: Unknown
% 2.95/1.88 % (12162)Termination phase: shuffling
% 2.95/1.88
% 2.95/1.88 % (12162)Memory used [KB]: 2174
% 2.95/1.88 % (12162)Time elapsed: 0.012 s
% 2.95/1.88 % (12162)Instructions burned: 41 (million)
% 2.95/1.88 % (12162)------------------------------
% 2.95/1.88 % (12162)------------------------------
% 2.95/1.89 % (12163)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_11849 for (2996ds/448Mi)
% 2.95/1.89 % (12164)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_11849 for (2996ds/46Mi)
% 2.95/1.90 % (12161)Instruction limit reached!
% 2.95/1.90 % (12161)------------------------------
% 2.95/1.90 % (12161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.90 % (12161)Termination reason: Unknown
% 2.95/1.90 % (12161)Termination phase: Saturation
% 2.95/1.90
% 2.95/1.90 % (12161)Memory used [KB]: 6908
% 2.95/1.90 % (12161)Time elapsed: 0.037 s
% 2.95/1.90 % (12161)Instructions burned: 108 (million)
% 2.95/1.90 % (12161)------------------------------
% 2.95/1.90 % (12161)------------------------------
% 2.95/1.91 % (12165)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_11849 for (2996ds/98Mi)
% 2.95/1.91 % (12164)Instruction limit reached!
% 2.95/1.91 % (12164)------------------------------
% 2.95/1.91 % (12164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.91 % (12164)Termination reason: Unknown
% 2.95/1.91 % (12164)Termination phase: shuffling
% 2.95/1.91
% 2.95/1.91 % (12164)Memory used [KB]: 2046
% 2.95/1.91 % (12164)Time elapsed: 0.016 s
% 2.95/1.91 % (12164)Instructions burned: 48 (million)
% 2.95/1.91 % (12164)------------------------------
% 2.95/1.91 % (12164)------------------------------
% 2.95/1.92 % (12166)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_11849 for (2996ds/507Mi)
% 2.95/1.93 % (12150)Instruction limit reached!
% 2.95/1.93 % (12150)------------------------------
% 2.95/1.93 % (12150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.93 % (12150)Termination reason: Unknown
% 2.95/1.93 % (12150)Termination phase: Saturation
% 2.95/1.93
% 2.95/1.93 % (12150)Memory used [KB]: 7803
% 2.95/1.93 % (12150)Time elapsed: 0.254 s
% 2.95/1.93 % (12150)Instructions burned: 780 (million)
% 2.95/1.93 % (12150)------------------------------
% 2.95/1.93 % (12150)------------------------------
% 2.95/1.94 % (12165)Instruction limit reached!
% 2.95/1.94 % (12165)------------------------------
% 2.95/1.94 % (12165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.94 % (12165)Termination reason: Unknown
% 2.95/1.94 % (12165)Termination phase: Property scanning
% 2.95/1.94
% 2.95/1.94 % (12165)Memory used [KB]: 2302
% 2.95/1.94 % (12165)Time elapsed: 0.031 s
% 2.95/1.94 % (12165)Instructions burned: 101 (million)
% 2.95/1.94 % (12165)------------------------------
% 2.95/1.94 % (12165)------------------------------
% 2.95/1.94 % (12167)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_11849 for (2996ds/149Mi)
% 2.95/1.95 % (12168)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_11849 for (2996ds/39Mi)
% 2.95/1.96 % (12168)Instruction limit reached!
% 2.95/1.96 % (12168)------------------------------
% 2.95/1.96 % (12168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.96 % (12168)Termination reason: Unknown
% 2.95/1.96 % (12168)Termination phase: Preprocessing 1
% 2.95/1.96
% 2.95/1.96 % (12168)Memory used [KB]: 1918
% 2.95/1.96 % (12168)Time elapsed: 0.015 s
% 2.95/1.96 % (12168)Instructions burned: 40 (million)
% 2.95/1.96 % (12168)------------------------------
% 2.95/1.96 % (12168)------------------------------
% 2.95/1.96 % (12152)Instruction limit reached!
% 2.95/1.96 % (12152)------------------------------
% 2.95/1.96 % (12152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.96 % (12152)Termination reason: Unknown
% 2.95/1.96 % (12152)Termination phase: Saturation
% 2.95/1.96
% 2.95/1.96 % (12152)Memory used [KB]: 11257
% 2.95/1.96 % (12152)Time elapsed: 0.259 s
% 2.95/1.96 % (12152)Instructions burned: 880 (million)
% 2.95/1.96 % (12152)------------------------------
% 2.95/1.96 % (12152)------------------------------
% 2.95/1.96 % (12145)Instruction limit reached!
% 2.95/1.96 % (12145)------------------------------
% 2.95/1.96 % (12145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.96 % (12145)Termination reason: Unknown
% 2.95/1.96 % (12145)Termination phase: Saturation
% 2.95/1.96
% 2.95/1.96 % (12145)Memory used [KB]: 8443
% 2.95/1.96 % (12145)Time elapsed: 0.299 s
% 2.95/1.96 % (12145)Instructions burned: 903 (million)
% 2.95/1.96 % (12145)------------------------------
% 2.95/1.96 % (12145)------------------------------
% 2.95/1.97 % (12169)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_11849 for (2996ds/6Mi)
% 2.95/1.97 % (12169)Instruction limit reached!
% 2.95/1.97 % (12169)------------------------------
% 2.95/1.97 % (12169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.97 % (12169)Termination reason: Unknown
% 2.95/1.97 % (12169)Termination phase: shuffling
% 2.95/1.97
% 2.95/1.97 % (12169)Memory used [KB]: 1535
% 2.95/1.97 % (12169)Time elapsed: 0.004 s
% 2.95/1.97 % (12169)Instructions burned: 7 (million)
% 2.95/1.97 % (12169)------------------------------
% 2.95/1.97 % (12169)------------------------------
% 2.95/1.97 % (12170)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_11849 for (2995ds/1087Mi)
% 2.95/1.98 % (12171)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_11849 for (2995ds/47Mi)
% 2.95/1.98 % (12172)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_11849 for (2995ds/44Mi)
% 2.95/1.99 % (12134)Instruction limit reached!
% 2.95/1.99 % (12134)------------------------------
% 2.95/1.99 % (12134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.99 % (12134)Termination reason: Unknown
% 2.95/1.99 % (12134)Termination phase: Saturation
% 2.95/1.99
% 2.95/1.99 % (12134)Memory used [KB]: 9594
% 2.95/1.99 % (12134)Time elapsed: 0.362 s
% 2.95/1.99 % (12134)Instructions burned: 1041 (million)
% 2.95/1.99 % (12134)------------------------------
% 2.95/1.99 % (12134)------------------------------
% 2.95/1.99 % (12171)Instruction limit reached!
% 2.95/1.99 % (12171)------------------------------
% 2.95/1.99 % (12171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.99 % (12171)Termination reason: Unknown
% 2.95/1.99 % (12171)Termination phase: Preprocessing 3
% 2.95/1.99
% 2.95/1.99 % (12171)Memory used [KB]: 2174
% 2.95/1.99 % (12171)Time elapsed: 0.017 s
% 2.95/1.99 % (12171)Instructions burned: 48 (million)
% 2.95/1.99 % (12171)------------------------------
% 2.95/1.99 % (12171)------------------------------
% 2.95/1.99 % (12167)Instruction limit reached!
% 2.95/1.99 % (12167)------------------------------
% 2.95/1.99 % (12167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/1.99 % (12167)Termination reason: Unknown
% 2.95/1.99 % (12167)Termination phase: Saturation
% 2.95/1.99
% 2.95/1.99 % (12167)Memory used [KB]: 7036
% 2.95/1.99 % (12167)Time elapsed: 0.051 s
% 2.95/1.99 % (12167)Instructions burned: 149 (million)
% 2.95/1.99 % (12167)------------------------------
% 2.95/1.99 % (12167)------------------------------
% 2.95/2.00 % (12173)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_11849 for (2995ds/432Mi)
% 2.95/2.00 % (12172)Instruction limit reached!
% 2.95/2.00 % (12172)------------------------------
% 2.95/2.00 % (12172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.00 % (12172)Termination reason: Unknown
% 2.95/2.00 % (12172)Termination phase: Property scanning
% 2.95/2.00
% 2.95/2.00 % (12172)Memory used [KB]: 2174
% 2.95/2.00 % (12172)Time elapsed: 0.015 s
% 2.95/2.00 % (12172)Instructions burned: 44 (million)
% 2.95/2.00 % (12172)------------------------------
% 2.95/2.00 % (12172)------------------------------
% 2.95/2.00 % (12175)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_11849 for (2995ds/31Mi)
% 2.95/2.00 % (12174)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_11849 for (2995ds/62Mi)
% 2.95/2.01 % (12175)Instruction limit reached!
% 2.95/2.01 % (12175)------------------------------
% 2.95/2.01 % (12175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.95/2.01 % (12175)Termination reason: Unknown
% 2.95/2.01 % (12175)Termination phase: Property scanning
% 2.95/2.01
% 2.95/2.01 % (12175)Memory used [KB]: 1918
% 2.95/2.01 % (12175)Time elapsed: 0.011 s
% 2.95/2.01 % (12175)Instructions burned: 33 (million)
% 2.95/2.01 % (12175)------------------------------
% 2.95/2.01 % (12175)------------------------------
% 5.92/2.02 % (12176)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_11849 for (2995ds/96Mi)
% 5.92/2.02 % (12163)Instruction limit reached!
% 5.92/2.02 % (12163)------------------------------
% 5.92/2.02 % (12163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.02 % (12163)Termination reason: Unknown
% 5.92/2.02 % (12163)Termination phase: Saturation
% 5.92/2.02
% 5.92/2.02 % (12163)Memory used [KB]: 7803
% 5.92/2.02 % (12163)Time elapsed: 0.133 s
% 5.92/2.02 % (12163)Instructions burned: 450 (million)
% 5.92/2.02 % (12163)------------------------------
% 5.92/2.02 % (12163)------------------------------
% 5.92/2.02 % (12174)Instruction limit reached!
% 5.92/2.02 % (12174)------------------------------
% 5.92/2.02 % (12174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.02 % (12174)Termination reason: Unknown
% 5.92/2.02 % (12174)Termination phase: Property scanning
% 5.92/2.02
% 5.92/2.02 % (12174)Memory used [KB]: 2174
% 5.92/2.02 % (12174)Time elapsed: 0.020 s
% 5.92/2.02 % (12174)Instructions burned: 63 (million)
% 5.92/2.02 % (12174)------------------------------
% 5.92/2.02 % (12174)------------------------------
% 5.92/2.02 % (12177)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_11849 for (2995ds/453Mi)
% 5.92/2.03 % (12178)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_11849 for (2995ds/71Mi)
% 5.92/2.03 % (12179)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_11849 for (2995ds/83Mi)
% 5.92/2.05 % (12178)Instruction limit reached!
% 5.92/2.05 % (12178)------------------------------
% 5.92/2.05 % (12178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.05 % (12178)Termination reason: Unknown
% 5.92/2.05 % (12178)Termination phase: Property scanning
% 5.92/2.05
% 5.92/2.05 % (12178)Memory used [KB]: 2302
% 5.92/2.05 % (12178)Time elapsed: 0.024 s
% 5.92/2.05 % (12178)Instructions burned: 74 (million)
% 5.92/2.05 % (12178)------------------------------
% 5.92/2.05 % (12178)------------------------------
% 5.92/2.06 % (12179)Instruction limit reached!
% 5.92/2.06 % (12179)------------------------------
% 5.92/2.06 % (12179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.06 % (12179)Termination reason: Unknown
% 5.92/2.06 % (12179)Termination phase: Saturation
% 5.92/2.06
% 5.92/2.06 % (12179)Memory used [KB]: 6652
% 5.92/2.06 % (12179)Time elapsed: 0.030 s
% 5.92/2.06 % (12179)Instructions burned: 83 (million)
% 5.92/2.06 % (12179)------------------------------
% 5.92/2.06 % (12179)------------------------------
% 5.92/2.06 % (12180)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_11849 for (2995ds/11Mi)
% 5.92/2.06 % (12180)Instruction limit reached!
% 5.92/2.06 % (12180)------------------------------
% 5.92/2.06 % (12180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.06 % (12180)Termination reason: Unknown
% 5.92/2.06 % (12180)Termination phase: shuffling
% 5.92/2.06
% 5.92/2.06 % (12180)Memory used [KB]: 1663
% 5.92/2.06 % (12180)Time elapsed: 0.004 s
% 5.92/2.06 % (12180)Instructions burned: 11 (million)
% 5.92/2.06 % (12180)------------------------------
% 5.92/2.06 % (12180)------------------------------
% 5.92/2.07 % (12181)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_11849 for (2995ds/41Mi)
% 5.92/2.07 % (12176)Instruction limit reached!
% 5.92/2.07 % (12176)------------------------------
% 5.92/2.07 % (12176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.07 % (12176)Termination reason: Unknown
% 5.92/2.07 % (12176)Termination phase: Saturation
% 5.92/2.07
% 5.92/2.07 % (12176)Memory used [KB]: 6780
% 5.92/2.07 % (12176)Time elapsed: 0.055 s
% 5.92/2.07 % (12176)Instructions burned: 96 (million)
% 5.92/2.07 % (12176)------------------------------
% 5.92/2.07 % (12176)------------------------------
% 5.92/2.07 % (12182)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_11849 for (2995ds/6Mi)
% 5.92/2.07 % (12166)Instruction limit reached!
% 5.92/2.07 % (12166)------------------------------
% 5.92/2.07 % (12166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.07 % (12166)Termination reason: Unknown
% 5.92/2.07 % (12166)Termination phase: Saturation
% 5.92/2.07
% 5.92/2.07 % (12166)Memory used [KB]: 8059
% 5.92/2.07 % (12166)Time elapsed: 0.156 s
% 5.92/2.07 % (12166)Instructions burned: 507 (million)
% 5.92/2.07 % (12166)------------------------------
% 5.92/2.07 % (12166)------------------------------
% 5.92/2.07 % (12182)Instruction limit reached!
% 5.92/2.07 % (12182)------------------------------
% 5.92/2.07 % (12182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.07 % (12182)Termination reason: Unknown
% 5.92/2.07 % (12182)Termination phase: shuffling
% 5.92/2.07
% 5.92/2.07 % (12182)Memory used [KB]: 1535
% 5.92/2.07 % (12182)Time elapsed: 0.003 s
% 5.92/2.07 % (12182)Instructions burned: 6 (million)
% 5.92/2.07 % (12182)------------------------------
% 5.92/2.07 % (12182)------------------------------
% 5.92/2.08 % (12181)Instruction limit reached!
% 5.92/2.08 % (12181)------------------------------
% 5.92/2.08 % (12181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.92/2.08 % (12181)Termination reason: Unknown
% 5.92/2.08 % (12181)Termination phase: Property scanning
% 5.92/2.08
% 5.92/2.08 % (12181)Memory used [KB]: 2174
% 5.92/2.08 % (12181)Time elapsed: 0.013 s
% 5.92/2.08 % (12181)Instructions burned: 42 (million)
% 5.92/2.08 % (12181)------------------------------
% 5.92/2.08 % (12181)------------------------------
% 5.92/2.08 % (12184)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_11849 for (2994ds/343Mi)
% 5.92/2.08 % (12185)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_11849 for (2994ds/109Mi)
% 5.92/2.09 % (12183)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_11849 for (2995ds/150Mi)
% 5.92/2.09 % (12186)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_11849 for (2994ds/253Mi)
% 6.42/2.12 % (12185)Instruction limit reached!
% 6.42/2.12 % (12185)------------------------------
% 6.42/2.12 % (12185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.12 % (12185)Termination reason: Unknown
% 6.42/2.12 % (12185)Termination phase: Saturation
% 6.42/2.12
% 6.42/2.12 % (12185)Memory used [KB]: 6908
% 6.42/2.12 % (12185)Time elapsed: 0.034 s
% 6.42/2.12 % (12185)Instructions burned: 111 (million)
% 6.42/2.12 % (12185)------------------------------
% 6.42/2.12 % (12185)------------------------------
% 6.42/2.13 % (12187)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_11849 for (2994ds/140Mi)
% 6.42/2.13 % (12173)Instruction limit reached!
% 6.42/2.13 % (12173)------------------------------
% 6.42/2.13 % (12173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.13 % (12173)Termination reason: Unknown
% 6.42/2.13 % (12173)Termination phase: Saturation
% 6.42/2.13
% 6.42/2.13 % (12173)Memory used [KB]: 4861
% 6.42/2.13 % (12173)Time elapsed: 0.135 s
% 6.42/2.13 % (12173)Instructions burned: 434 (million)
% 6.42/2.13 % (12173)------------------------------
% 6.42/2.13 % (12173)------------------------------
% 6.42/2.14 % (12188)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_11849 for (2994ds/614Mi)
% 6.42/2.15 % (12183)Instruction limit reached!
% 6.42/2.15 % (12183)------------------------------
% 6.42/2.15 % (12183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.15 % (12183)Termination reason: Unknown
% 6.42/2.15 % (12183)Termination phase: Saturation
% 6.42/2.15
% 6.42/2.15 % (12183)Memory used [KB]: 7164
% 6.42/2.15 % (12183)Time elapsed: 0.084 s
% 6.42/2.15 % (12183)Instructions burned: 150 (million)
% 6.42/2.15 % (12183)------------------------------
% 6.42/2.15 % (12183)------------------------------
% 6.42/2.15 % (12177)Instruction limit reached!
% 6.42/2.15 % (12177)------------------------------
% 6.42/2.15 % (12177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.15 % (12177)Termination reason: Unknown
% 6.42/2.15 % (12177)Termination phase: Saturation
% 6.42/2.15
% 6.42/2.15 % (12177)Memory used [KB]: 7931
% 6.42/2.15 % (12177)Time elapsed: 0.133 s
% 6.42/2.15 % (12177)Instructions burned: 453 (million)
% 6.42/2.15 % (12177)------------------------------
% 6.42/2.15 % (12177)------------------------------
% 6.42/2.16 % (12189)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_11849 for (2994ds/202Mi)
% 6.42/2.16 % (12190)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_11849 for (2994ds/339Mi)
% 6.42/2.17 % (12186)Instruction limit reached!
% 6.42/2.17 % (12186)------------------------------
% 6.42/2.17 % (12186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.17 % (12186)Termination reason: Unknown
% 6.42/2.17 % (12186)Termination phase: Saturation
% 6.42/2.17
% 6.42/2.17 % (12186)Memory used [KB]: 7803
% 6.42/2.17 % (12186)Time elapsed: 0.080 s
% 6.42/2.17 % (12186)Instructions burned: 253 (million)
% 6.42/2.17 % (12186)------------------------------
% 6.42/2.17 % (12186)------------------------------
% 6.42/2.17 % (12187)Instruction limit reached!
% 6.42/2.17 % (12187)------------------------------
% 6.42/2.17 % (12187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.17 % (12187)Termination reason: Unknown
% 6.42/2.17 % (12187)Termination phase: Saturation
% 6.42/2.17
% 6.42/2.17 % (12187)Memory used [KB]: 7547
% 6.42/2.17 % (12187)Time elapsed: 0.047 s
% 6.42/2.17 % (12187)Instructions burned: 142 (million)
% 6.42/2.17 % (12187)------------------------------
% 6.42/2.17 % (12187)------------------------------
% 6.42/2.18 % (12191)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_11849 for (2993ds/283Mi)
% 6.42/2.18 % (12192)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_11849 for (2993ds/134Mi)
% 6.42/2.19 % (12184)Instruction limit reached!
% 6.42/2.19 % (12184)------------------------------
% 6.42/2.19 % (12184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.19 % (12184)Termination reason: Unknown
% 6.42/2.19 % (12184)Termination phase: Saturation
% 6.42/2.19
% 6.42/2.19 % (12184)Memory used [KB]: 8827
% 6.42/2.19 % (12184)Time elapsed: 0.132 s
% 6.42/2.19 % (12184)Instructions burned: 343 (million)
% 6.42/2.19 % (12184)------------------------------
% 6.42/2.19 % (12184)------------------------------
% 7.06/2.20 % (12193)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_11849 for (2993ds/298Mi)
% 7.06/2.22 % (12192)Instruction limit reached!
% 7.06/2.22 % (12192)------------------------------
% 7.06/2.22 % (12192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.22 % (12192)Termination reason: Unknown
% 7.06/2.22 % (12192)Termination phase: Saturation
% 7.06/2.22
% 7.06/2.22 % (12192)Memory used [KB]: 7036
% 7.06/2.22 % (12192)Time elapsed: 0.043 s
% 7.06/2.22 % (12192)Instructions burned: 136 (million)
% 7.06/2.22 % (12192)------------------------------
% 7.06/2.22 % (12192)------------------------------
% 7.06/2.22 % (12189)Instruction limit reached!
% 7.06/2.22 % (12189)------------------------------
% 7.06/2.22 % (12189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.22 % (12189)Termination reason: Unknown
% 7.06/2.22 % (12189)Termination phase: Saturation
% 7.06/2.22
% 7.06/2.22 % (12189)Memory used [KB]: 7803
% 7.06/2.22 % (12189)Time elapsed: 0.069 s
% 7.06/2.22 % (12189)Instructions burned: 204 (million)
% 7.06/2.22 % (12189)------------------------------
% 7.06/2.22 % (12189)------------------------------
% 7.06/2.23 % (12194)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_11849 for (2993ds/192Mi)
% 7.06/2.23 % (12195)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_11849 for (2993ds/258Mi)
% 7.06/2.26 % (12190)Instruction limit reached!
% 7.06/2.26 % (12190)------------------------------
% 7.06/2.26 % (12190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.26 % (12190)Termination reason: Unknown
% 7.06/2.26 % (12190)Termination phase: Saturation
% 7.06/2.26
% 7.06/2.26 % (12190)Memory used [KB]: 7803
% 7.06/2.26 % (12190)Time elapsed: 0.101 s
% 7.06/2.26 % (12190)Instructions burned: 339 (million)
% 7.06/2.26 % (12190)------------------------------
% 7.06/2.26 % (12190)------------------------------
% 7.06/2.27 % (12191)Instruction limit reached!
% 7.06/2.27 % (12191)------------------------------
% 7.06/2.27 % (12191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.27 % (12191)Termination reason: Unknown
% 7.06/2.27 % (12191)Termination phase: Saturation
% 7.06/2.27
% 7.06/2.27 % (12191)Memory used [KB]: 7803
% 7.06/2.27 % (12191)Time elapsed: 0.089 s
% 7.06/2.27 % (12191)Instructions burned: 284 (million)
% 7.06/2.27 % (12191)------------------------------
% 7.06/2.27 % (12191)------------------------------
% 7.06/2.27 % (12196)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_11849 for (2992ds/90Mi)
% 7.06/2.27 % (12197)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_11849 for (2992ds/231Mi)
% 7.06/2.29 % (12193)Instruction limit reached!
% 7.06/2.29 % (12193)------------------------------
% 7.06/2.29 % (12193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.29 % (12193)Termination reason: Unknown
% 7.06/2.29 % (12193)Termination phase: Saturation
% 7.06/2.29
% 7.06/2.29 % (12193)Memory used [KB]: 8699
% 7.06/2.29 % (12193)Time elapsed: 0.085 s
% 7.06/2.29 % (12193)Instructions burned: 298 (million)
% 7.06/2.29 % (12193)------------------------------
% 7.06/2.29 % (12193)------------------------------
% 7.06/2.29 % (12194)Instruction limit reached!
% 7.06/2.29 % (12194)------------------------------
% 7.06/2.29 % (12194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.06/2.29 % (12194)Termination reason: Unknown
% 7.06/2.29 % (12194)Termination phase: Saturation
% 7.06/2.29
% 7.06/2.29 % (12194)Memory used [KB]: 8059
% 7.06/2.29 % (12194)Time elapsed: 0.060 s
% 7.06/2.29 % (12194)Instructions burned: 194 (million)
% 7.06/2.29 % (12194)------------------------------
% 7.06/2.29 % (12194)------------------------------
% 7.65/2.30 % (12198)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_11849 for (2992ds/458Mi)
% 7.65/2.30 % (12196)Instruction limit reached!
% 7.65/2.30 % (12196)------------------------------
% 7.65/2.30 % (12196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.30 % (12196)Termination reason: Unknown
% 7.65/2.30 % (12196)Termination phase: Saturation
% 7.65/2.30
% 7.65/2.30 % (12196)Memory used [KB]: 6780
% 7.65/2.30 % (12196)Time elapsed: 0.028 s
% 7.65/2.30 % (12196)Instructions burned: 92 (million)
% 7.65/2.30 % (12196)------------------------------
% 7.65/2.30 % (12196)------------------------------
% 7.65/2.30 % (12199)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_11849 for (2992ds/31Mi)
% 7.65/2.31 % (12200)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_11849 for (2992ds/297Mi)
% 7.65/2.31 % (12199)Instruction limit reached!
% 7.65/2.31 % (12199)------------------------------
% 7.65/2.31 % (12199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.31 % (12199)Termination reason: Unknown
% 7.65/2.31 % (12199)Termination phase: Property scanning
% 7.65/2.31
% 7.65/2.31 % (12199)Memory used [KB]: 1918
% 7.65/2.31 % (12199)Time elapsed: 0.011 s
% 7.65/2.31 % (12199)Instructions burned: 32 (million)
% 7.65/2.31 % (12199)------------------------------
% 7.65/2.31 % (12199)------------------------------
% 7.65/2.32 % (12195)Instruction limit reached!
% 7.65/2.32 % (12195)------------------------------
% 7.65/2.32 % (12195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.32 % (12195)Termination reason: Unknown
% 7.65/2.32 % (12195)Termination phase: Saturation
% 7.65/2.32
% 7.65/2.32 % (12195)Memory used [KB]: 7675
% 7.65/2.32 % (12195)Time elapsed: 0.086 s
% 7.65/2.32 % (12195)Instructions burned: 259 (million)
% 7.65/2.32 % (12195)------------------------------
% 7.65/2.32 % (12195)------------------------------
% 7.65/2.32 % (12170)Instruction limit reached!
% 7.65/2.32 % (12170)------------------------------
% 7.65/2.32 % (12170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.32 % (12170)Termination reason: Unknown
% 7.65/2.32 % (12170)Termination phase: Saturation
% 7.65/2.32
% 7.65/2.32 % (12170)Memory used [KB]: 8059
% 7.65/2.32 % (12170)Time elapsed: 0.347 s
% 7.65/2.32 % (12170)Instructions burned: 1089 (million)
% 7.65/2.32 % (12170)------------------------------
% 7.65/2.32 % (12170)------------------------------
% 7.65/2.32 % (12201)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_11849 for (2992ds/987Mi)
% 7.65/2.33 % (12202)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_11849 for (2992ds/182Mi)
% 7.65/2.33 % (12203)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_11849 for (2992ds/182Mi)
% 7.65/2.33 % (12188)Instruction limit reached!
% 7.65/2.33 % (12188)------------------------------
% 7.65/2.33 % (12188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.33 % (12188)Termination reason: Unknown
% 7.65/2.33 % (12188)Termination phase: Saturation
% 7.65/2.33
% 7.65/2.33 % (12188)Memory used [KB]: 8315
% 7.65/2.33 % (12188)Time elapsed: 0.193 s
% 7.65/2.33 % (12188)Instructions burned: 616 (million)
% 7.65/2.33 % (12188)------------------------------
% 7.65/2.33 % (12188)------------------------------
% 7.65/2.34 % (12197)Instruction limit reached!
% 7.65/2.34 % (12197)------------------------------
% 7.65/2.34 % (12197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.34 % (12197)Termination reason: Unknown
% 7.65/2.34 % (12197)Termination phase: Saturation
% 7.65/2.34
% 7.65/2.34 % (12197)Memory used [KB]: 7164
% 7.65/2.34 % (12197)Time elapsed: 0.063 s
% 7.65/2.34 % (12197)Instructions burned: 232 (million)
% 7.65/2.34 % (12197)------------------------------
% 7.65/2.34 % (12197)------------------------------
% 7.65/2.34 % (12204)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_11849 for (2992ds/154Mi)
% 7.65/2.35 % (12205)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_11849 for (2992ds/79Mi)
% 7.65/2.37 % (12205)Instruction limit reached!
% 7.65/2.37 % (12205)------------------------------
% 7.65/2.37 % (12205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.37 % (12205)Termination reason: Unknown
% 7.65/2.37 % (12205)Termination phase: Property scanning
% 7.65/2.37
% 7.65/2.37 % (12205)Memory used [KB]: 2302
% 7.65/2.37 % (12205)Time elapsed: 0.025 s
% 7.65/2.37 % (12205)Instructions burned: 79 (million)
% 7.65/2.37 % (12205)------------------------------
% 7.65/2.37 % (12205)------------------------------
% 7.65/2.38 % (12206)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_11849 for (2991ds/216Mi)
% 7.65/2.39 % (12202)Instruction limit reached!
% 7.65/2.39 % (12202)------------------------------
% 7.65/2.39 % (12202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.39 % (12202)Termination reason: Unknown
% 7.65/2.39 % (12202)Termination phase: Saturation
% 7.65/2.39
% 7.65/2.39 % (12202)Memory used [KB]: 7164
% 7.65/2.39 % (12202)Time elapsed: 0.058 s
% 7.65/2.39 % (12202)Instructions burned: 185 (million)
% 7.65/2.39 % (12202)------------------------------
% 7.65/2.39 % (12202)------------------------------
% 7.65/2.39 % (12204)Instruction limit reached!
% 7.65/2.39 % (12204)------------------------------
% 7.65/2.39 % (12204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.39 % (12204)Termination reason: Unknown
% 7.65/2.39 % (12204)Termination phase: Saturation
% 7.65/2.39
% 7.65/2.39 % (12204)Memory used [KB]: 3070
% 7.65/2.39 % (12204)Time elapsed: 0.045 s
% 7.65/2.39 % (12204)Instructions burned: 155 (million)
% 7.65/2.39 % (12204)------------------------------
% 7.65/2.39 % (12204)------------------------------
% 7.65/2.39 % (12203)Instruction limit reached!
% 7.65/2.39 % (12203)------------------------------
% 7.65/2.39 % (12203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.39 % (12203)Termination reason: Unknown
% 7.65/2.39 % (12203)Termination phase: Saturation
% 7.65/2.39
% 7.65/2.39 % (12203)Memory used [KB]: 7164
% 7.65/2.39 % (12203)Time elapsed: 0.060 s
% 7.65/2.39 % (12203)Instructions burned: 184 (million)
% 7.65/2.39 % (12203)------------------------------
% 7.65/2.39 % (12203)------------------------------
% 7.65/2.39 % (12207)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_11849 for (2991ds/114Mi)
% 7.65/2.40 % (12208)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_11849 for (2991ds/922Mi)
% 8.34/2.40 % (12209)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_11849 for (2991ds/182Mi)
% 8.34/2.40 % (12200)Instruction limit reached!
% 8.34/2.40 % (12200)------------------------------
% 8.34/2.40 % (12200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.40 % (12200)Termination reason: Unknown
% 8.34/2.40 % (12200)Termination phase: Saturation
% 8.34/2.40
% 8.34/2.40 % (12200)Memory used [KB]: 7675
% 8.34/2.40 % (12200)Time elapsed: 0.093 s
% 8.34/2.40 % (12200)Instructions burned: 297 (million)
% 8.34/2.40 % (12200)------------------------------
% 8.34/2.40 % (12200)------------------------------
% 8.34/2.41 % (12210)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_11849 for (2991ds/164Mi)
% 8.34/2.43 % (12207)Instruction limit reached!
% 8.34/2.43 % (12207)------------------------------
% 8.34/2.43 % (12207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.43 % (12207)Termination reason: Unknown
% 8.34/2.43 % (12207)Termination phase: Saturation
% 8.34/2.43
% 8.34/2.43 % (12207)Memory used [KB]: 7036
% 8.34/2.43 % (12207)Time elapsed: 0.035 s
% 8.34/2.43 % (12207)Instructions burned: 115 (million)
% 8.34/2.43 % (12207)------------------------------
% 8.34/2.43 % (12207)------------------------------
% 8.34/2.44 % (12211)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_11849 for (2991ds/50Mi)
% 8.34/2.44 % (12198)Instruction limit reached!
% 8.34/2.44 % (12198)------------------------------
% 8.34/2.44 % (12198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.44 % (12198)Termination reason: Unknown
% 8.34/2.44 % (12198)Termination phase: Saturation
% 8.34/2.44
% 8.34/2.44 % (12198)Memory used [KB]: 8187
% 8.34/2.44 % (12198)Time elapsed: 0.147 s
% 8.34/2.44 % (12198)Instructions burned: 460 (million)
% 8.34/2.44 % (12198)------------------------------
% 8.34/2.44 % (12198)------------------------------
% 8.34/2.44 % (12206)Instruction limit reached!
% 8.34/2.44 % (12206)------------------------------
% 8.34/2.44 % (12206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.44 % (12206)Termination reason: Unknown
% 8.34/2.44 % (12206)Termination phase: Saturation
% 8.34/2.44
% 8.34/2.44 % (12206)Memory used [KB]: 7291
% 8.34/2.44 % (12206)Time elapsed: 0.064 s
% 8.34/2.44 % (12206)Instructions burned: 216 (million)
% 8.34/2.44 % (12206)------------------------------
% 8.34/2.44 % (12206)------------------------------
% 8.34/2.45 % (12209)Instruction limit reached!
% 8.34/2.45 % (12209)------------------------------
% 8.34/2.45 % (12209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.45 % (12209)Termination reason: Unknown
% 8.34/2.45 % (12209)Termination phase: Saturation
% 8.34/2.45
% 8.34/2.45 % (12209)Memory used [KB]: 7291
% 8.34/2.45 % (12209)Time elapsed: 0.052 s
% 8.34/2.45 % (12209)Instructions burned: 182 (million)
% 8.34/2.45 % (12209)------------------------------
% 8.34/2.45 % (12209)------------------------------
% 8.34/2.45 % (12211)Instruction limit reached!
% 8.34/2.45 % (12211)------------------------------
% 8.34/2.45 % (12211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.45 % (12211)Termination reason: Unknown
% 8.34/2.45 % (12211)Termination phase: Property scanning
% 8.34/2.45
% 8.34/2.45 % (12211)Memory used [KB]: 2174
% 8.34/2.45 % (12211)Time elapsed: 0.015 s
% 8.34/2.45 % (12211)Instructions burned: 50 (million)
% 8.34/2.45 % (12211)------------------------------
% 8.34/2.45 % (12211)------------------------------
% 8.34/2.45 % (12212)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_11849 for (2991ds/368Mi)
% 8.34/2.45 % (12213)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_11849 for (2991ds/1021Mi)
% 8.34/2.46 % (12210)Instruction limit reached!
% 8.34/2.46 % (12210)------------------------------
% 8.34/2.46 % (12210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.46 % (12210)Termination reason: Unknown
% 8.34/2.46 % (12210)Termination phase: Saturation
% 8.34/2.46
% 8.34/2.46 % (12210)Memory used [KB]: 2558
% 8.34/2.46 % (12210)Time elapsed: 0.048 s
% 8.34/2.46 % (12210)Instructions burned: 165 (million)
% 8.34/2.46 % (12210)------------------------------
% 8.34/2.46 % (12210)------------------------------
% 8.34/2.46 % (12214)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_11849 for (2991ds/267Mi)
% 8.34/2.46 % (12215)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_11849 for (2991ds/204Mi)
% 8.34/2.47 % (12216)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_11849 for (2991ds/26Mi)
% 8.34/2.47 % (12216)Instruction limit reached!
% 8.34/2.47 % (12216)------------------------------
% 8.34/2.47 % (12216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.34/2.47 % (12216)Termination reason: Unknown
% 8.34/2.47 % (12216)Termination phase: shuffling
% 8.34/2.47
% 8.34/2.47 % (12216)Memory used [KB]: 2046
% 8.34/2.47 % (12216)Time elapsed: 0.009 s
% 8.34/2.47 % (12216)Instructions burned: 29 (million)
% 8.34/2.47 % (12216)------------------------------
% 8.34/2.47 % (12216)------------------------------
% 8.34/2.48 % (12217)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_11849 for (2990ds/53Mi)
% 8.87/2.50 % (12217)Instruction limit reached!
% 8.87/2.50 % (12217)------------------------------
% 8.87/2.50 % (12217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.50 % (12217)Termination reason: Unknown
% 8.87/2.50 % (12217)Termination phase: Property scanning
% 8.87/2.50
% 8.87/2.50 % (12217)Memory used [KB]: 2174
% 8.87/2.50 % (12217)Time elapsed: 0.016 s
% 8.87/2.50 % (12217)Instructions burned: 56 (million)
% 8.87/2.50 % (12217)------------------------------
% 8.87/2.50 % (12217)------------------------------
% 8.87/2.51 % (12218)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_11849 for (2990ds/4436Mi)
% 8.87/2.53 % (12215)Instruction limit reached!
% 8.87/2.53 % (12215)------------------------------
% 8.87/2.53 % (12215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.53 % (12215)Termination reason: Unknown
% 8.87/2.53 % (12215)Termination phase: Saturation
% 8.87/2.53
% 8.87/2.53 % (12215)Memory used [KB]: 7036
% 8.87/2.53 % (12215)Time elapsed: 0.065 s
% 8.87/2.53 % (12215)Instructions burned: 204 (million)
% 8.87/2.53 % (12215)------------------------------
% 8.87/2.53 % (12215)------------------------------
% 8.87/2.54 % (12219)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_11849 for (2990ds/1539Mi)
% 8.87/2.54 % (12214)Instruction limit reached!
% 8.87/2.54 % (12214)------------------------------
% 8.87/2.54 % (12214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.54 % (12214)Termination reason: Unknown
% 8.87/2.54 % (12214)Termination phase: Saturation
% 8.87/2.54
% 8.87/2.54 % (12214)Memory used [KB]: 7675
% 8.87/2.54 % (12214)Time elapsed: 0.084 s
% 8.87/2.54 % (12214)Instructions burned: 268 (million)
% 8.87/2.54 % (12214)------------------------------
% 8.87/2.54 % (12214)------------------------------
% 8.87/2.55 % (12220)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_11849 for (2990ds/408Mi)
% 8.87/2.58 % (12212)Instruction limit reached!
% 8.87/2.58 % (12212)------------------------------
% 8.87/2.58 % (12212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.87/2.58 % (12212)Termination reason: Unknown
% 8.87/2.58 % (12212)Termination phase: Saturation
% 8.87/2.58
% 8.87/2.58 % (12212)Memory used [KB]: 8827
% 8.87/2.58 % (12212)Time elapsed: 0.125 s
% 8.87/2.58 % (12212)Instructions burned: 368 (million)
% 8.87/2.58 % (12212)------------------------------
% 8.87/2.58 % (12212)------------------------------
% 8.87/2.59 % (12221)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_11849 for (2989ds/5205Mi)
% 9.19/2.62 % (12201)Instruction limit reached!
% 9.19/2.62 % (12201)------------------------------
% 9.19/2.62 % (12201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.62 % (12201)Termination reason: Unknown
% 9.19/2.62 % (12201)Termination phase: Saturation
% 9.19/2.62
% 9.19/2.62 % (12201)Memory used [KB]: 9594
% 9.19/2.62 % (12201)Time elapsed: 0.305 s
% 9.19/2.62 % (12201)Instructions burned: 989 (million)
% 9.19/2.62 % (12201)------------------------------
% 9.19/2.62 % (12201)------------------------------
% 9.19/2.63 % (12222)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_11849 for (2989ds/1913Mi)
% 9.19/2.68 % (12220)Instruction limit reached!
% 9.19/2.68 % (12220)------------------------------
% 9.19/2.68 % (12220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.68 % (12220)Termination reason: Unknown
% 9.19/2.68 % (12220)Termination phase: Saturation
% 9.19/2.68
% 9.19/2.68 % (12220)Memory used [KB]: 7931
% 9.19/2.68 % (12220)Time elapsed: 0.147 s
% 9.19/2.68 % (12220)Instructions burned: 410 (million)
% 9.19/2.68 % (12220)------------------------------
% 9.19/2.68 % (12220)------------------------------
% 9.19/2.68 % (12208)Instruction limit reached!
% 9.19/2.68 % (12208)------------------------------
% 9.19/2.68 % (12208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.19/2.68 % (12208)Termination reason: Unknown
% 9.19/2.68 % (12208)Termination phase: Saturation
% 9.19/2.68
% 9.19/2.68 % (12208)Memory used [KB]: 8059
% 9.19/2.68 % (12208)Time elapsed: 0.283 s
% 9.19/2.68 % (12208)Instructions burned: 925 (million)
% 9.19/2.68 % (12208)------------------------------
% 9.19/2.68 % (12208)------------------------------
% 9.19/2.69 % (12223)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_11849 for (2988ds/4350Mi)
% 9.19/2.69 % (12224)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_11849 for (2988ds/68Mi)
% 9.93/2.71 % (12224)Instruction limit reached!
% 9.93/2.71 % (12224)------------------------------
% 9.93/2.71 % (12224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.71 % (12224)Termination reason: Unknown
% 9.93/2.71 % (12224)Termination phase: Property scanning
% 9.93/2.71
% 9.93/2.71 % (12224)Memory used [KB]: 2174
% 9.93/2.71 % (12224)Time elapsed: 0.022 s
% 9.93/2.71 % (12224)Instructions burned: 69 (million)
% 9.93/2.71 % (12224)------------------------------
% 9.93/2.71 % (12224)------------------------------
% 9.93/2.72 % (12225)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_11849 for (2988ds/358Mi)
% 9.93/2.76 % (12213)Instruction limit reached!
% 9.93/2.76 % (12213)------------------------------
% 9.93/2.76 % (12213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.76 % (12213)Termination reason: Unknown
% 9.93/2.76 % (12213)Termination phase: Saturation
% 9.93/2.76
% 9.93/2.76 % (12213)Memory used [KB]: 8699
% 9.93/2.76 % (12213)Time elapsed: 0.306 s
% 9.93/2.76 % (12213)Instructions burned: 1023 (million)
% 9.93/2.76 % (12213)------------------------------
% 9.93/2.76 % (12213)------------------------------
% 9.93/2.77 % (12226)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_11849 for (2988ds/31Mi)
% 9.93/2.78 % (12226)Instruction limit reached!
% 9.93/2.78 % (12226)------------------------------
% 9.93/2.78 % (12226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.93/2.78 % (12226)Termination reason: Unknown
% 9.93/2.78 % (12226)Termination phase: Property scanning
% 9.93/2.78
% 9.93/2.78 % (12226)Memory used [KB]: 1918
% 9.93/2.78 % (12226)Time elapsed: 0.011 s
% 9.93/2.78 % (12226)Instructions burned: 32 (million)
% 9.93/2.78 % (12226)------------------------------
% 9.93/2.78 % (12226)------------------------------
% 9.93/2.79 % (12227)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_11849 for (2987ds/279Mi)
% 10.29/2.83 % (12225)Instruction limit reached!
% 10.29/2.83 % (12225)------------------------------
% 10.29/2.83 % (12225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/2.83 % (12225)Termination reason: Unknown
% 10.29/2.83 % (12225)Termination phase: Saturation
% 10.29/2.83
% 10.29/2.83 % (12225)Memory used [KB]: 7675
% 10.29/2.83 % (12225)Time elapsed: 0.138 s
% 10.29/2.83 % (12225)Instructions burned: 360 (million)
% 10.29/2.83 % (12225)------------------------------
% 10.29/2.83 % (12225)------------------------------
% 10.29/2.84 % (12228)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_11849 for (2987ds/258Mi)
% 10.29/2.87 % (12227)Instruction limit reached!
% 10.29/2.87 % (12227)------------------------------
% 10.29/2.87 % (12227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/2.87 % (12227)Termination reason: Unknown
% 10.29/2.87 % (12227)Termination phase: Saturation
% 10.29/2.87
% 10.29/2.87 % (12227)Memory used [KB]: 7547
% 10.29/2.87 % (12227)Time elapsed: 0.105 s
% 10.29/2.87 % (12227)Instructions burned: 282 (million)
% 10.29/2.87 % (12227)------------------------------
% 10.29/2.87 % (12227)------------------------------
% 10.29/2.88 % (12229)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_11849 for (2986ds/26Mi)
% 10.29/2.89 % (12229)Instruction limit reached!
% 10.29/2.89 % (12229)------------------------------
% 10.29/2.89 % (12229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/2.89 % (12229)Termination reason: Unknown
% 10.29/2.89 % (12229)Termination phase: shuffling
% 10.29/2.89
% 10.29/2.89 % (12229)Memory used [KB]: 2046
% 10.29/2.89 % (12229)Time elapsed: 0.009 s
% 10.29/2.89 % (12229)Instructions burned: 29 (million)
% 10.29/2.89 % (12229)------------------------------
% 10.29/2.89 % (12229)------------------------------
% 10.29/2.90 % (12230)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_11849 for (2986ds/995Mi)
% 10.55/2.92 % (12228)Instruction limit reached!
% 10.55/2.92 % (12228)------------------------------
% 10.55/2.92 % (12228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.92 % (12228)Termination reason: Unknown
% 10.55/2.92 % (12228)Termination phase: Saturation
% 10.55/2.92
% 10.55/2.92 % (12228)Memory used [KB]: 7803
% 10.55/2.92 % (12228)Time elapsed: 0.082 s
% 10.55/2.92 % (12228)Instructions burned: 259 (million)
% 10.55/2.92 % (12228)------------------------------
% 10.55/2.92 % (12228)------------------------------
% 10.55/2.93 % (12231)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_11849 for (2986ds/373Mi)
% 10.55/2.99 % (12219)Instruction limit reached!
% 10.55/2.99 % (12219)------------------------------
% 10.55/2.99 % (12219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.55/2.99 % (12219)Termination reason: Unknown
% 10.55/2.99 % (12219)Termination phase: Saturation
% 10.55/2.99
% 10.55/2.99 % (12219)Memory used [KB]: 12409
% 10.55/2.99 % (12219)Time elapsed: 0.476 s
% 10.55/2.99 % (12219)Instructions burned: 1542 (million)
% 10.55/2.99 % (12219)------------------------------
% 10.55/2.99 % (12219)------------------------------
% 10.55/3.00 % (12232)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_11849 for (2985ds/253Mi)
% 12.98/3.05 % (12231)Instruction limit reached!
% 12.98/3.05 % (12231)------------------------------
% 12.98/3.05 % (12231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.98/3.05 % (12231)Termination reason: Unknown
% 12.98/3.05 % (12231)Termination phase: Saturation
% 12.98/3.05
% 12.98/3.05 % (12231)Memory used [KB]: 8571
% 12.98/3.05 % (12231)Time elapsed: 0.122 s
% 12.98/3.05 % (12231)Instructions burned: 374 (million)
% 12.98/3.05 % (12231)------------------------------
% 12.98/3.05 % (12231)------------------------------
% 12.98/3.06 % (12233)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_11849 for (2985ds/832Mi)
% 12.98/3.07 % (12232)Instruction limit reached!
% 12.98/3.07 % (12232)------------------------------
% 12.98/3.07 % (12232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.98/3.07 % (12232)Termination reason: Unknown
% 12.98/3.07 % (12232)Termination phase: Saturation
% 12.98/3.07
% 12.98/3.07 % (12232)Memory used [KB]: 7675
% 12.98/3.07 % (12232)Time elapsed: 0.074 s
% 12.98/3.07 % (12232)Instructions burned: 253 (million)
% 12.98/3.07 % (12232)------------------------------
% 12.98/3.07 % (12232)------------------------------
% 12.98/3.08 % (12234)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_11849 for (2984ds/668Mi)
% 13.62/3.19 % (12230)Instruction limit reached!
% 13.62/3.19 % (12230)------------------------------
% 13.62/3.19 % (12230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.62/3.19 % (12230)Termination reason: Unknown
% 13.62/3.19 % (12230)Termination phase: Saturation
% 13.62/3.19
% 13.62/3.19 % (12230)Memory used [KB]: 9850
% 13.62/3.19 % (12230)Time elapsed: 0.300 s
% 13.62/3.19 % (12230)Instructions burned: 995 (million)
% 13.62/3.19 % (12230)------------------------------
% 13.62/3.19 % (12230)------------------------------
% 13.99/3.20 % (12235)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_11849 for (2983ds/40Mi)
% 13.99/3.22 % (12235)Instruction limit reached!
% 13.99/3.22 % (12235)------------------------------
% 13.99/3.22 % (12235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.99/3.22 % (12235)Termination reason: Unknown
% 13.99/3.22 % (12235)Termination phase: shuffling
% 13.99/3.22
% 13.99/3.22 % (12235)Memory used [KB]: 2174
% 13.99/3.22 % (12235)Time elapsed: 0.013 s
% 13.99/3.22 % (12235)Instructions burned: 41 (million)
% 13.99/3.22 % (12235)------------------------------
% 13.99/3.22 % (12235)------------------------------
% 13.99/3.23 % (12236)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_11849 for (2983ds/294Mi)
% 13.99/3.23 % (12222)Instruction limit reached!
% 13.99/3.23 % (12222)------------------------------
% 13.99/3.23 % (12222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.99/3.23 % (12222)Termination reason: Unknown
% 13.99/3.23 % (12222)Termination phase: Saturation
% 13.99/3.23
% 13.99/3.23 % (12222)Memory used [KB]: 6396
% 13.99/3.23 % (12222)Time elapsed: 0.619 s
% 13.99/3.23 % (12222)Instructions burned: 1915 (million)
% 13.99/3.23 % (12222)------------------------------
% 13.99/3.23 % (12222)------------------------------
% 13.99/3.24 % (12237)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_11849 for (2983ds/187Mi)
% 13.99/3.28 % (12234)Instruction limit reached!
% 13.99/3.28 % (12234)------------------------------
% 13.99/3.28 % (12234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.99/3.28 % (12234)Termination reason: Unknown
% 13.99/3.28 % (12234)Termination phase: Saturation
% 13.99/3.28
% 13.99/3.28 % (12234)Memory used [KB]: 14328
% 13.99/3.28 % (12234)Time elapsed: 0.204 s
% 13.99/3.28 % (12234)Instructions burned: 670 (million)
% 13.99/3.28 % (12234)------------------------------
% 13.99/3.28 % (12234)------------------------------
% 13.99/3.29 % (12238)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_11849 for (2982ds/371Mi)
% 14.57/3.30 % (12237)Instruction limit reached!
% 14.57/3.30 % (12237)------------------------------
% 14.57/3.30 % (12237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.30 % (12237)Termination reason: Unknown
% 14.57/3.30 % (12237)Termination phase: Saturation
% 14.57/3.30
% 14.57/3.30 % (12237)Memory used [KB]: 7419
% 14.57/3.30 % (12237)Time elapsed: 0.064 s
% 14.57/3.30 % (12237)Instructions burned: 189 (million)
% 14.57/3.30 % (12237)------------------------------
% 14.57/3.30 % (12237)------------------------------
% 14.57/3.31 % (12236)Instruction limit reached!
% 14.57/3.31 % (12236)------------------------------
% 14.57/3.31 % (12236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.31 % (12236)Termination reason: Unknown
% 14.57/3.31 % (12236)Termination phase: Saturation
% 14.57/3.31
% 14.57/3.31 % (12236)Memory used [KB]: 7675
% 14.57/3.31 % (12236)Time elapsed: 0.086 s
% 14.57/3.31 % (12236)Instructions burned: 295 (million)
% 14.57/3.31 % (12236)------------------------------
% 14.57/3.31 % (12236)------------------------------
% 14.57/3.31 % (12239)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_11849 for (2982ds/1827Mi)
% 14.57/3.32 % (12233)Instruction limit reached!
% 14.57/3.32 % (12233)------------------------------
% 14.57/3.32 % (12233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.32 % (12233)Termination reason: Unknown
% 14.57/3.32 % (12233)Termination phase: Saturation
% 14.57/3.32
% 14.57/3.32 % (12233)Memory used [KB]: 8571
% 14.57/3.32 % (12233)Time elapsed: 0.259 s
% 14.57/3.32 % (12233)Instructions burned: 832 (million)
% 14.57/3.32 % (12233)------------------------------
% 14.57/3.32 % (12233)------------------------------
% 14.57/3.32 % (12240)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_11849 for (2982ds/70Mi)
% 14.57/3.33 % (12241)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_11849 for (2982ds/316Mi)
% 14.57/3.34 % (12240)Instruction limit reached!
% 14.57/3.34 % (12240)------------------------------
% 14.57/3.34 % (12240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.57/3.34 % (12240)Termination reason: Unknown
% 14.57/3.34 % (12240)Termination phase: Preprocessing 1
% 14.57/3.34
% 14.57/3.34 % (12240)Memory used [KB]: 2302
% 14.57/3.34 % (12240)Time elapsed: 0.021 s
% 14.57/3.34 % (12240)Instructions burned: 71 (million)
% 14.57/3.34 % (12240)------------------------------
% 14.57/3.34 % (12240)------------------------------
% 14.57/3.35 % (12242)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_11849 for (2982ds/932Mi)
% 15.32/3.41 % (12238)Instruction limit reached!
% 15.32/3.41 % (12238)------------------------------
% 15.32/3.41 % (12238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.32/3.41 % (12238)Termination reason: Unknown
% 15.32/3.41 % (12238)Termination phase: Saturation
% 15.32/3.41
% 15.32/3.41 % (12238)Memory used [KB]: 8315
% 15.32/3.41 % (12238)Time elapsed: 0.117 s
% 15.32/3.41 % (12238)Instructions burned: 373 (million)
% 15.32/3.41 % (12238)------------------------------
% 15.32/3.41 % (12238)------------------------------
% 15.32/3.42 % (12241)Instruction limit reached!
% 15.32/3.42 % (12241)------------------------------
% 15.32/3.42 % (12241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.32/3.42 % (12241)Termination reason: Unknown
% 15.32/3.42 % (12241)Termination phase: Saturation
% 15.32/3.42
% 15.32/3.42 % (12241)Memory used [KB]: 8059
% 15.32/3.42 % (12241)Time elapsed: 0.091 s
% 15.32/3.42 % (12241)Instructions burned: 316 (million)
% 15.32/3.42 % (12241)------------------------------
% 15.32/3.42 % (12241)------------------------------
% 15.32/3.42 % (12243)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_11849 for (2981ds/4714Mi)
% 15.32/3.43 % (12244)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_11849 for (2981ds/8250Mi)
% 16.17/3.62 % (12242)Instruction limit reached!
% 16.17/3.62 % (12242)------------------------------
% 16.17/3.62 % (12242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.17/3.62 % (12242)Termination reason: Unknown
% 16.17/3.62 % (12242)Termination phase: Saturation
% 16.17/3.62
% 16.17/3.62 % (12242)Memory used [KB]: 9594
% 16.17/3.62 % (12242)Time elapsed: 0.271 s
% 16.17/3.62 % (12242)Instructions burned: 933 (million)
% 16.17/3.62 % (12242)------------------------------
% 16.17/3.62 % (12242)------------------------------
% 16.17/3.63 % (12245)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_11849 for (2979ds/770Mi)
% 17.05/3.81 % (12245)Instruction limit reached!
% 17.05/3.81 % (12245)------------------------------
% 17.05/3.81 % (12245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.81 % (12245)Termination reason: Unknown
% 17.05/3.81 % (12245)Termination phase: Saturation
% 17.05/3.81
% 17.05/3.81 % (12245)Memory used [KB]: 7419
% 17.05/3.81 % (12245)Time elapsed: 0.178 s
% 17.05/3.81 % (12245)Instructions burned: 770 (million)
% 17.05/3.81 % (12245)------------------------------
% 17.05/3.81 % (12245)------------------------------
% 17.05/3.82 % (12246)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_11849 for (2977ds/794Mi)
% 17.05/3.87 % (12218)Instruction limit reached!
% 17.05/3.87 % (12218)------------------------------
% 17.05/3.87 % (12218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.87 % (12218)Termination reason: Unknown
% 17.05/3.87 % (12218)Termination phase: Saturation
% 17.05/3.87
% 17.05/3.87 % (12218)Memory used [KB]: 12281
% 17.05/3.87 % (12218)Time elapsed: 1.363 s
% 17.05/3.87 % (12218)Instructions burned: 4436 (million)
% 17.05/3.87 % (12218)------------------------------
% 17.05/3.87 % (12218)------------------------------
% 17.05/3.88 % (12248)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_11849 for (2976ds/464Mi)
% 17.05/3.89 % (12239)Instruction limit reached!
% 17.05/3.89 % (12239)------------------------------
% 17.05/3.89 % (12239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.05/3.89 % (12239)Termination reason: Unknown
% 17.05/3.89 % (12239)Termination phase: Saturation
% 17.05/3.89
% 17.05/3.89 % (12239)Memory used [KB]: 11513
% 17.05/3.89 % (12239)Time elapsed: 0.584 s
% 17.05/3.89 % (12239)Instructions burned: 1830 (million)
% 17.05/3.89 % (12239)------------------------------
% 17.05/3.89 % (12239)------------------------------
% 18.13/3.90 % (12249)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_11849 for (2976ds/1376Mi)
% 18.13/3.93 % (12223)Instruction limit reached!
% 18.13/3.93 % (12223)------------------------------
% 18.13/3.93 % (12223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.13/3.93 % (12223)Termination reason: Unknown
% 18.13/3.93 % (12223)Termination phase: Saturation
% 18.13/3.93
% 18.13/3.93 % (12223)Memory used [KB]: 13688
% 18.13/3.93 % (12223)Time elapsed: 1.269 s
% 18.13/3.93 % (12223)Instructions burned: 4351 (million)
% 18.13/3.93 % (12223)------------------------------
% 18.13/3.93 % (12223)------------------------------
% 18.13/3.94 % (12250)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_11849 for (2976ds/906Mi)
% 20.03/4.03 % (12248)Instruction limit reached!
% 20.03/4.03 % (12248)------------------------------
% 20.03/4.03 % (12248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.03 % (12248)Termination reason: Unknown
% 20.03/4.03 % (12248)Termination phase: Saturation
% 20.03/4.03
% 20.03/4.03 % (12248)Memory used [KB]: 7931
% 20.03/4.03 % (12248)Time elapsed: 0.146 s
% 20.03/4.03 % (12248)Instructions burned: 464 (million)
% 20.03/4.03 % (12248)------------------------------
% 20.03/4.03 % (12248)------------------------------
% 20.03/4.04 % (12251)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_11849 for (2975ds/434Mi)
% 20.03/4.07 % (12246)Instruction limit reached!
% 20.03/4.07 % (12246)------------------------------
% 20.03/4.07 % (12246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.07 % (12246)Termination reason: Unknown
% 20.03/4.07 % (12246)Termination phase: Saturation
% 20.03/4.07
% 20.03/4.07 % (12246)Memory used [KB]: 5500
% 20.03/4.07 % (12246)Time elapsed: 0.255 s
% 20.03/4.07 % (12246)Instructions burned: 795 (million)
% 20.03/4.07 % (12246)------------------------------
% 20.03/4.07 % (12246)------------------------------
% 20.03/4.08 % (12252)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_11849 for (2974ds/865Mi)
% 20.61/4.13 % (12221)Instruction limit reached!
% 20.61/4.13 % (12221)------------------------------
% 20.61/4.13 % (12221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.61/4.13 % (12221)Termination reason: Unknown
% 20.61/4.13 % (12221)Termination phase: Saturation
% 20.61/4.13
% 20.61/4.13 % (12221)Memory used [KB]: 14967
% 20.61/4.13 % (12221)Time elapsed: 1.564 s
% 20.61/4.13 % (12221)Instructions burned: 5207 (million)
% 20.61/4.13 % (12221)------------------------------
% 20.61/4.13 % (12221)------------------------------
% 20.61/4.14 % (12253)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_11849 for (2974ds/593Mi)
% 20.61/4.17 % (12251)Instruction limit reached!
% 20.61/4.17 % (12251)------------------------------
% 20.61/4.17 % (12251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.61/4.17 % (12251)Termination reason: Unknown
% 20.61/4.17 % (12251)Termination phase: Saturation
% 20.61/4.17
% 20.61/4.17 % (12251)Memory used [KB]: 7931
% 20.61/4.17 % (12251)Time elapsed: 0.135 s
% 20.61/4.17 % (12251)Instructions burned: 435 (million)
% 20.61/4.17 % (12251)------------------------------
% 20.61/4.17 % (12251)------------------------------
% 20.61/4.18 % (12254)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_11849 for (2973ds/443Mi)
% 21.07/4.24 % (12250)Instruction limit reached!
% 21.07/4.24 % (12250)------------------------------
% 21.07/4.24 % (12250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.07/4.24 % (12250)Termination reason: Unknown
% 21.07/4.24 % (12250)Termination phase: Saturation
% 21.07/4.24
% 21.07/4.24 % (12250)Memory used [KB]: 11129
% 21.07/4.24 % (12250)Time elapsed: 0.301 s
% 21.07/4.24 % (12250)Instructions burned: 906 (million)
% 21.07/4.24 % (12250)------------------------------
% 21.07/4.24 % (12250)------------------------------
% 21.07/4.25 % (12255)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_11849 for (2973ds/594Mi)
% 21.42/4.31 % (12253)Instruction limit reached!
% 21.42/4.31 % (12253)------------------------------
% 21.42/4.31 % (12253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.42/4.31 % (12253)Termination reason: Unknown
% 21.42/4.31 % (12253)Termination phase: Saturation
% 21.42/4.31
% 21.42/4.31 % (12253)Memory used [KB]: 9210
% 21.42/4.31 % (12253)Time elapsed: 0.175 s
% 21.42/4.31 % (12253)Instructions burned: 594 (million)
% 21.42/4.31 % (12253)------------------------------
% 21.42/4.31 % (12253)------------------------------
% 21.42/4.32 % (12249)Instruction limit reached!
% 21.42/4.32 % (12249)------------------------------
% 21.42/4.32 % (12249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.42/4.32 % (12249)Termination reason: Unknown
% 21.42/4.32 % (12249)Termination phase: Saturation
% 21.42/4.32
% 21.42/4.32 % (12249)Memory used [KB]: 13944
% 21.42/4.32 % (12249)Time elapsed: 0.414 s
% 21.42/4.32 % (12249)Instructions burned: 1377 (million)
% 21.42/4.32 % (12249)------------------------------
% 21.42/4.32 % (12249)------------------------------
% 21.42/4.32 % (12256)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_11849 for (2972ds/327Mi)
% 21.42/4.32 % (12254)Instruction limit reached!
% 21.42/4.32 % (12254)------------------------------
% 21.42/4.32 % (12254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.42/4.32 % (12254)Termination reason: Unknown
% 21.42/4.32 % (12254)Termination phase: Saturation
% 21.42/4.32
% 21.42/4.32 % (12254)Memory used [KB]: 8187
% 21.42/4.32 % (12254)Time elapsed: 0.147 s
% 21.42/4.32 % (12254)Instructions burned: 444 (million)
% 21.42/4.32 % (12254)------------------------------
% 21.42/4.32 % (12254)------------------------------
% 21.42/4.33 % (12257)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_11849 for (2972ds/5411Mi)
% 21.42/4.33 % (12258)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_11849 for (2972ds/1762Mi)
% 21.42/4.34 % (12252)Instruction limit reached!
% 21.42/4.34 % (12252)------------------------------
% 21.42/4.34 % (12252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.42/4.34 % (12252)Termination reason: Unknown
% 21.42/4.34 % (12252)Termination phase: Saturation
% 21.42/4.34
% 21.42/4.34 % (12252)Memory used [KB]: 8443
% 21.42/4.34 % (12252)Time elapsed: 0.257 s
% 21.42/4.34 % (12252)Instructions burned: 865 (million)
% 21.42/4.34 % (12252)------------------------------
% 21.42/4.34 % (12252)------------------------------
% 21.42/4.35 % (12259)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_11849 for (2972ds/96Mi)
% 21.42/4.37 % (12259)Instruction limit reached!
% 21.42/4.37 % (12259)------------------------------
% 21.42/4.37 % (12259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.42/4.37 % (12259)Termination reason: Unknown
% 21.42/4.37 % (12259)Termination phase: Property scanning
% 21.42/4.37
% 21.42/4.37 % (12259)Memory used [KB]: 2430
% 21.42/4.37 % (12259)Time elapsed: 0.027 s
% 21.42/4.37 % (12259)Instructions burned: 96 (million)
% 21.42/4.37 % (12259)------------------------------
% 21.42/4.37 % (12259)------------------------------
% 21.42/4.38 % (12260)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_11849 for (2971ds/503Mi)
% 22.29/4.43 % (12256)Instruction limit reached!
% 22.29/4.43 % (12256)------------------------------
% 22.29/4.43 % (12256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.29/4.43 % (12256)Termination reason: Unknown
% 22.29/4.43 % (12256)Termination phase: Saturation
% 22.29/4.43
% 22.29/4.43 % (12256)Memory used [KB]: 7931
% 22.29/4.43 % (12256)Time elapsed: 0.106 s
% 22.29/4.43 % (12256)Instructions burned: 328 (million)
% 22.29/4.43 % (12256)------------------------------
% 22.29/4.43 % (12256)------------------------------
% 22.29/4.44 % (12261)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_11849 for (2971ds/90Mi)
% 22.29/4.44 % (12255)Instruction limit reached!
% 22.29/4.44 % (12255)------------------------------
% 22.29/4.44 % (12255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.29/4.44 % (12255)Termination reason: Unknown
% 22.29/4.44 % (12255)Termination phase: Saturation
% 22.29/4.44
% 22.29/4.44 % (12255)Memory used [KB]: 8571
% 22.29/4.44 % (12255)Time elapsed: 0.188 s
% 22.29/4.44 % (12255)Instructions burned: 595 (million)
% 22.29/4.44 % (12255)------------------------------
% 22.29/4.44 % (12255)------------------------------
% 22.29/4.45 % (12262)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_11849 for (2971ds/593Mi)
% 22.29/4.46 % (12261)Instruction limit reached!
% 22.29/4.46 % (12261)------------------------------
% 22.29/4.46 % (12261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.29/4.46 % (12261)Termination reason: Unknown
% 22.29/4.46 % (12261)Termination phase: Saturation
% 22.29/4.46
% 22.29/4.46 % (12261)Memory used [KB]: 6780
% 22.29/4.46 % (12261)Time elapsed: 0.028 s
% 22.29/4.46 % (12261)Instructions burned: 90 (million)
% 22.29/4.46 % (12261)------------------------------
% 22.29/4.46 % (12261)------------------------------
% 22.29/4.47 % (12263)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_11849 for (2971ds/1512Mi)
% 22.84/4.53 % (12260)Instruction limit reached!
% 22.84/4.53 % (12260)------------------------------
% 22.84/4.53 % (12260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.84/4.53 % (12260)Termination reason: Unknown
% 22.84/4.53 % (12260)Termination phase: Saturation
% 22.84/4.53
% 22.84/4.53 % (12260)Memory used [KB]: 8827
% 22.84/4.53 % (12260)Time elapsed: 0.152 s
% 22.84/4.53 % (12260)Instructions burned: 506 (million)
% 22.84/4.53 % (12260)------------------------------
% 22.84/4.53 % (12260)------------------------------
% 22.84/4.54 % (12264)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_11849 for (2970ds/569Mi)
% 23.21/4.64 % (12262)Instruction limit reached!
% 23.21/4.64 % (12262)------------------------------
% 23.21/4.64 % (12262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.21/4.64 % (12262)Termination reason: Unknown
% 23.21/4.64 % (12262)Termination phase: Saturation
% 23.21/4.64
% 23.21/4.64 % (12262)Memory used [KB]: 8571
% 23.21/4.64 % (12262)Time elapsed: 0.212 s
% 23.21/4.64 % (12262)Instructions burned: 594 (million)
% 23.21/4.64 % (12262)------------------------------
% 23.21/4.64 % (12262)------------------------------
% 23.21/4.65 % (12265)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_11849 for (2969ds/501Mi)
% 23.61/4.71 % (12264)Instruction limit reached!
% 23.61/4.71 % (12264)------------------------------
% 23.61/4.71 % (12264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.61/4.71 % (12264)Termination reason: Unknown
% 23.61/4.71 % (12264)Termination phase: Saturation
% 23.61/4.71
% 23.61/4.71 % (12264)Memory used [KB]: 8699
% 23.61/4.71 % (12264)Time elapsed: 0.166 s
% 23.61/4.71 % (12264)Instructions burned: 570 (million)
% 23.61/4.71 % (12264)------------------------------
% 23.61/4.71 % (12264)------------------------------
% 23.61/4.72 % (12266)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_11849 for (2968ds/562Mi)
% 23.61/4.79 % (12243)Instruction limit reached!
% 23.61/4.79 % (12243)------------------------------
% 23.61/4.79 % (12243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.61/4.79 % (12243)Termination reason: Unknown
% 23.61/4.79 % (12243)Termination phase: Saturation
% 23.61/4.79
% 23.61/4.79 % (12243)Memory used [KB]: 15863
% 23.61/4.79 % (12243)Time elapsed: 1.392 s
% 23.61/4.79 % (12243)Instructions burned: 4714 (million)
% 23.61/4.79 % (12243)------------------------------
% 23.61/4.79 % (12243)------------------------------
% 24.00/4.80 % (12267)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_11849 for (2967ds/406Mi)
% 24.00/4.81 % (12265)Instruction limit reached!
% 24.00/4.81 % (12265)------------------------------
% 24.00/4.81 % (12265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/4.81 % (12265)Termination reason: Unknown
% 24.00/4.81 % (12265)Termination phase: Saturation
% 24.00/4.81
% 24.00/4.81 % (12265)Memory used [KB]: 8571
% 24.00/4.81 % (12265)Time elapsed: 0.180 s
% 24.00/4.81 % (12265)Instructions burned: 502 (million)
% 24.00/4.81 % (12265)------------------------------
% 24.00/4.81 % (12265)------------------------------
% 24.00/4.82 % (12268)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_11849 for (2967ds/582Mi)
% 24.00/4.87 % (12258)Instruction limit reached!
% 24.00/4.87 % (12258)------------------------------
% 24.00/4.87 % (12258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/4.87 % (12258)Termination reason: Unknown
% 24.00/4.87 % (12258)Termination phase: Saturation
% 24.00/4.87
% 24.00/4.87 % (12258)Memory used [KB]: 11129
% 24.00/4.87 % (12258)Time elapsed: 0.536 s
% 24.00/4.87 % (12258)Instructions burned: 1763 (million)
% 24.00/4.87 % (12258)------------------------------
% 24.00/4.87 % (12258)------------------------------
% 24.00/4.88 % (12269)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_11849 for (2966ds/456Mi)
% 24.00/4.89 % (12266)Instruction limit reached!
% 24.00/4.89 % (12266)------------------------------
% 24.00/4.89 % (12266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.00/4.89 % (12266)Termination reason: Unknown
% 24.00/4.89 % (12266)Termination phase: Saturation
% 24.00/4.89
% 24.00/4.89 % (12266)Memory used [KB]: 7803
% 24.00/4.89 % (12266)Time elapsed: 0.198 s
% 24.00/4.89 % (12266)Instructions burned: 562 (million)
% 24.00/4.89 % (12266)------------------------------
% 24.00/4.89 % (12266)------------------------------
% 24.99/4.90 % (12270)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_11849 for (2966ds/393Mi)
% 24.99/4.90 % (12263)Instruction limit reached!
% 24.99/4.90 % (12263)------------------------------
% 24.99/4.90 % (12263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/4.90 % (12263)Termination reason: Unknown
% 24.99/4.90 % (12263)Termination phase: Saturation
% 24.99/4.90
% 24.99/4.90 % (12263)Memory used [KB]: 8571
% 24.99/4.90 % (12263)Time elapsed: 0.452 s
% 24.99/4.90 % (12263)Instructions burned: 1513 (million)
% 24.99/4.90 % (12263)------------------------------
% 24.99/4.90 % (12263)------------------------------
% 24.99/4.91 % (12271)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_11849 for (2966ds/1335Mi)
% 24.99/4.93 % (12267)Instruction limit reached!
% 24.99/4.93 % (12267)------------------------------
% 24.99/4.93 % (12267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/4.93 % (12267)Termination reason: Unknown
% 24.99/4.93 % (12267)Termination phase: Saturation
% 24.99/4.93
% 24.99/4.93 % (12267)Memory used [KB]: 8187
% 24.99/4.93 % (12267)Time elapsed: 0.130 s
% 24.99/4.93 % (12267)Instructions burned: 407 (million)
% 24.99/4.93 % (12267)------------------------------
% 24.99/4.93 % (12267)------------------------------
% 24.99/4.94 % (12272)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_11849 for (2966ds/3373Mi)
% 24.99/5.00 % (12268)Instruction limit reached!
% 24.99/5.00 % (12268)------------------------------
% 24.99/5.00 % (12268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/5.00 % (12268)Termination reason: Unknown
% 24.99/5.00 % (12268)Termination phase: Saturation
% 24.99/5.00
% 24.99/5.00 % (12268)Memory used [KB]: 9338
% 24.99/5.00 % (12268)Time elapsed: 0.189 s
% 24.99/5.00 % (12268)Instructions burned: 584 (million)
% 24.99/5.00 % (12268)------------------------------
% 24.99/5.00 % (12268)------------------------------
% 24.99/5.01 % (12270)Instruction limit reached!
% 24.99/5.01 % (12270)------------------------------
% 24.99/5.01 % (12270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/5.01 % (12270)Termination reason: Unknown
% 24.99/5.01 % (12270)Termination phase: Saturation
% 24.99/5.01
% 24.99/5.01 % (12270)Memory used [KB]: 7675
% 24.99/5.01 % (12270)Time elapsed: 0.115 s
% 24.99/5.01 % (12270)Instructions burned: 395 (million)
% 24.99/5.01 % (12270)------------------------------
% 24.99/5.01 % (12270)------------------------------
% 24.99/5.01 % (12273)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_11849 for (2965ds/474Mi)
% 24.99/5.02 % (12269)Instruction limit reached!
% 24.99/5.02 % (12269)------------------------------
% 24.99/5.02 % (12269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.99/5.02 % (12269)Termination reason: Unknown
% 24.99/5.02 % (12269)Termination phase: Saturation
% 24.99/5.02
% 24.99/5.02 % (12269)Memory used [KB]: 8571
% 24.99/5.02 % (12269)Time elapsed: 0.144 s
% 24.99/5.02 % (12269)Instructions burned: 456 (million)
% 24.99/5.02 % (12269)------------------------------
% 24.99/5.02 % (12269)------------------------------
% 27.04/5.02 % (12274)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_11849 for (2965ds/157Mi)
% 27.04/5.03 % (12275)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_11849 for (2965ds/590Mi)
% 27.04/5.07 % (12274)Instruction limit reached!
% 27.04/5.07 % (12274)------------------------------
% 27.04/5.07 % (12274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/5.07 % (12274)Termination reason: Unknown
% 27.04/5.07 % (12274)Termination phase: Saturation
% 27.04/5.07
% 27.04/5.07 % (12274)Memory used [KB]: 7036
% 27.04/5.07 % (12274)Time elapsed: 0.044 s
% 27.04/5.07 % (12274)Instructions burned: 158 (million)
% 27.04/5.07 % (12274)------------------------------
% 27.04/5.07 % (12274)------------------------------
% 27.04/5.08 % (12276)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_11849 for (2964ds/104Mi)
% 27.04/5.11 % (12276)Instruction limit reached!
% 27.04/5.11 % (12276)------------------------------
% 27.04/5.11 % (12276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/5.11 % (12276)Termination reason: Unknown
% 27.04/5.11 % (12276)Termination phase: Saturation
% 27.04/5.11
% 27.04/5.11 % (12276)Memory used [KB]: 2814
% 27.04/5.11 % (12276)Time elapsed: 0.032 s
% 27.04/5.11 % (12276)Instructions burned: 106 (million)
% 27.04/5.11 % (12276)------------------------------
% 27.04/5.11 % (12276)------------------------------
% 27.04/5.12 % (12277)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_11849 for (2964ds/414Mi)
% 27.58/5.16 % (12273)Instruction limit reached!
% 27.58/5.16 % (12273)------------------------------
% 27.58/5.16 % (12273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.58/5.16 % (12273)Termination reason: Unknown
% 27.58/5.16 % (12273)Termination phase: Saturation
% 27.58/5.16
% 27.58/5.16 % (12273)Memory used [KB]: 8443
% 27.58/5.16 % (12273)Time elapsed: 0.149 s
% 27.58/5.16 % (12273)Instructions burned: 477 (million)
% 27.58/5.16 % (12273)------------------------------
% 27.58/5.16 % (12273)------------------------------
% 27.58/5.17 % (12278)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_11849 for (2964ds/715Mi)
% 28.03/5.21 % (12275)Instruction limit reached!
% 28.03/5.21 % (12275)------------------------------
% 28.03/5.21 % (12275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.03/5.21 % (12275)Termination reason: Unknown
% 28.03/5.21 % (12275)Termination phase: Saturation
% 28.03/5.21
% 28.03/5.21 % (12275)Memory used [KB]: 8315
% 28.03/5.21 % (12275)Time elapsed: 0.177 s
% 28.03/5.21 % (12275)Instructions burned: 591 (million)
% 28.03/5.21 % (12275)------------------------------
% 28.03/5.21 % (12275)------------------------------
% 28.03/5.22 % (12279)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_11849 for (2963ds/961Mi)
% 28.03/5.24 % (12277)Instruction limit reached!
% 28.03/5.24 % (12277)------------------------------
% 28.03/5.24 % (12277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.03/5.24 % (12277)Termination reason: Unknown
% 28.03/5.24 % (12277)Termination phase: Saturation
% 28.03/5.24
% 28.03/5.24 % (12277)Memory used [KB]: 7675
% 28.03/5.24 % (12277)Time elapsed: 0.122 s
% 28.03/5.24 % (12277)Instructions burned: 414 (million)
% 28.03/5.24 % (12277)------------------------------
% 28.03/5.24 % (12277)------------------------------
% 28.03/5.25 % (12280)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_11849 for (2963ds/1213Mi)
% 28.74/5.31 % (12271)Instruction limit reached!
% 28.74/5.31 % (12271)------------------------------
% 28.74/5.31 % (12271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.74/5.31 % (12271)Termination reason: Unknown
% 28.74/5.31 % (12271)Termination phase: Saturation
% 28.74/5.31
% 28.74/5.31 % (12271)Memory used [KB]: 8571
% 28.74/5.31 % (12271)Time elapsed: 0.400 s
% 28.74/5.31 % (12271)Instructions burned: 1335 (million)
% 28.74/5.31 % (12271)------------------------------
% 28.74/5.31 % (12271)------------------------------
% 28.74/5.32 % (12281)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_11849 for (2962ds/1979Mi)
% 28.74/5.40 % (12278)Instruction limit reached!
% 28.74/5.40 % (12278)------------------------------
% 28.74/5.40 % (12278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.74/5.40 % (12278)Termination reason: Unknown
% 28.74/5.40 % (12278)Termination phase: Saturation
% 28.74/5.40
% 28.74/5.40 % (12278)Memory used [KB]: 4605
% 28.74/5.40 % (12278)Time elapsed: 0.226 s
% 28.74/5.40 % (12278)Instructions burned: 717 (million)
% 28.74/5.40 % (12278)------------------------------
% 28.74/5.40 % (12278)------------------------------
% 29.07/5.41 % (12282)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_11849 for (2961ds/481Mi)
% 29.61/5.52 % (12279)Instruction limit reached!
% 29.61/5.52 % (12279)------------------------------
% 29.61/5.52 % (12279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.61/5.52 % (12279)Termination reason: Unknown
% 29.61/5.52 % (12279)Termination phase: Saturation
% 29.61/5.52
% 29.61/5.52 % (12279)Memory used [KB]: 8059
% 29.61/5.52 % (12279)Time elapsed: 0.300 s
% 29.61/5.52 % (12279)Instructions burned: 961 (million)
% 29.61/5.52 % (12279)------------------------------
% 29.61/5.52 % (12279)------------------------------
% 29.61/5.53 % (12283)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_11849 for (2960ds/783Mi)
% 29.61/5.56 % (12282)Instruction limit reached!
% 29.61/5.56 % (12282)------------------------------
% 29.61/5.56 % (12282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.61/5.56 % (12282)Termination reason: Unknown
% 29.61/5.56 % (12282)Termination phase: Saturation
% 29.61/5.56
% 29.61/5.56 % (12282)Memory used [KB]: 8315
% 29.61/5.56 % (12282)Time elapsed: 0.150 s
% 29.61/5.56 % (12282)Instructions burned: 482 (million)
% 29.61/5.56 % (12282)------------------------------
% 29.61/5.56 % (12282)------------------------------
% 29.61/5.57 % (12284)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_11849 for (2960ds/432Mi)
% 30.37/5.63 % (12280)Instruction limit reached!
% 30.37/5.63 % (12280)------------------------------
% 30.37/5.63 % (12280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.37/5.63 % (12280)Termination reason: Unknown
% 30.37/5.63 % (12280)Termination phase: Saturation
% 30.37/5.63
% 30.37/5.63 % (12280)Memory used [KB]: 8571
% 30.37/5.63 % (12280)Time elapsed: 0.387 s
% 30.37/5.63 % (12280)Instructions burned: 1215 (million)
% 30.37/5.63 % (12280)------------------------------
% 30.37/5.63 % (12280)------------------------------
% 30.37/5.64 % (12285)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_11849 for (2959ds/1670Mi)
% 31.07/5.70 % (12284)Instruction limit reached!
% 31.07/5.70 % (12284)------------------------------
% 31.07/5.70 % (12284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.07/5.70 % (12284)Termination reason: Unknown
% 31.07/5.70 % (12284)Termination phase: Saturation
% 31.07/5.70
% 31.07/5.70 % (12284)Memory used [KB]: 9466
% 31.07/5.70 % (12284)Time elapsed: 0.160 s
% 31.07/5.70 % (12284)Instructions burned: 432 (million)
% 31.07/5.70 % (12284)------------------------------
% 31.07/5.70 % (12284)------------------------------
% 31.07/5.71 % (12286)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_11849 for (2958ds/90Mi)
% 31.07/5.74 % (12286)Instruction limit reached!
% 31.07/5.74 % (12286)------------------------------
% 31.07/5.74 % (12286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.07/5.74 % (12286)Termination reason: Unknown
% 31.07/5.74 % (12286)Termination phase: Saturation
% 31.07/5.74
% 31.07/5.74 % (12286)Memory used [KB]: 6780
% 31.07/5.74 % (12286)Time elapsed: 0.028 s
% 31.07/5.74 % (12286)Instructions burned: 93 (million)
% 31.07/5.74 % (12286)------------------------------
% 31.07/5.74 % (12286)------------------------------
% 31.07/5.75 % (12287)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_11849 for (2958ds/346Mi)
% 31.07/5.76 % (12283)Instruction limit reached!
% 31.07/5.76 % (12283)------------------------------
% 31.07/5.76 % (12283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.07/5.76 % (12283)Termination reason: Unknown
% 31.07/5.76 % (12283)Termination phase: Saturation
% 31.07/5.76
% 31.07/5.76 % (12283)Memory used [KB]: 9722
% 31.07/5.76 % (12283)Time elapsed: 0.235 s
% 31.07/5.76 % (12283)Instructions burned: 783 (million)
% 31.07/5.76 % (12283)------------------------------
% 31.07/5.76 % (12283)------------------------------
% 31.07/5.77 % (12288)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_11849 for (2957ds/401Mi)
% 31.07/5.78 % (12244)Instruction limit reached!
% 31.07/5.78 % (12244)------------------------------
% 31.07/5.78 % (12244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.07/5.78 % (12244)Termination reason: Unknown
% 31.07/5.78 % (12244)Termination phase: Saturation
% 31.07/5.78
% 31.07/5.78 % (12244)Memory used [KB]: 13048
% 31.07/5.78 % (12244)Time elapsed: 2.353 s
% 31.07/5.78 % (12244)Instructions burned: 8250 (million)
% 31.07/5.78 % (12244)------------------------------
% 31.07/5.78 % (12244)------------------------------
% 31.07/5.79 % (12289)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_11849 for (2957ds/6454Mi)
% 31.79/5.85 % (12287)Instruction limit reached!
% 31.79/5.85 % (12287)------------------------------
% 31.79/5.85 % (12287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.79/5.85 % (12287)Termination reason: Unknown
% 31.79/5.85 % (12287)Termination phase: Saturation
% 31.79/5.85
% 31.79/5.85 % (12287)Memory used [KB]: 7803
% 31.79/5.85 % (12287)Time elapsed: 0.106 s
% 31.79/5.85 % (12287)Instructions burned: 347 (million)
% 31.79/5.85 % (12287)------------------------------
% 31.79/5.85 % (12287)------------------------------
% 31.79/5.86 % (12290)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_11849 for (2956ds/283Mi)
% 31.79/5.89 % (12288)Instruction limit reached!
% 31.79/5.89 % (12288)------------------------------
% 31.79/5.89 % (12288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.79/5.89 % (12288)Termination reason: Unknown
% 31.79/5.89 % (12288)Termination phase: Saturation
% 31.79/5.89
% 31.79/5.89 % (12288)Memory used [KB]: 8827
% 31.79/5.89 % (12288)Time elapsed: 0.117 s
% 31.79/5.89 % (12288)Instructions burned: 402 (million)
% 31.79/5.89 % (12288)------------------------------
% 31.79/5.89 % (12288)------------------------------
% 31.79/5.89 % (12257)Instruction limit reached!
% 31.79/5.89 % (12257)------------------------------
% 31.79/5.89 % (12257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.79/5.89 % (12257)Termination reason: Unknown
% 31.79/5.89 % (12257)Termination phase: Saturation
% 31.79/5.89
% 31.79/5.89 % (12257)Memory used [KB]: 10362
% 31.79/5.89 % (12257)Time elapsed: 1.560 s
% 31.79/5.89 % (12257)Instructions burned: 5411 (million)
% 31.79/5.89 % (12257)------------------------------
% 31.79/5.89 % (12257)------------------------------
% 31.79/5.90 % (12291)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_11849 for (2956ds/865Mi)
% 32.23/5.90 % (12292)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_11849 for (2956ds/4528Mi)
% 32.23/5.94 % (12281)Instruction limit reached!
% 32.23/5.94 % (12281)------------------------------
% 32.23/5.94 % (12281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.23/5.94 % (12281)Termination reason: Unknown
% 32.23/5.94 % (12281)Termination phase: Saturation
% 32.23/5.94
% 32.23/5.94 % (12281)Memory used [KB]: 7931
% 32.23/5.94 % (12281)Time elapsed: 0.618 s
% 32.23/5.94 % (12281)Instructions burned: 1979 (million)
% 32.23/5.94 % (12281)------------------------------
% 32.23/5.94 % (12281)------------------------------
% 32.23/5.95 % (12293)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_11849 for (2956ds/1001Mi)
% 32.23/5.96 % (12290)Instruction limit reached!
% 32.23/5.96 % (12290)------------------------------
% 32.23/5.96 % (12290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.23/5.96 % (12290)Termination reason: Unknown
% 32.23/5.96 % (12290)Termination phase: Saturation
% 32.23/5.96
% 32.23/5.96 % (12290)Memory used [KB]: 7931
% 32.23/5.96 % (12290)Time elapsed: 0.095 s
% 32.23/5.96 % (12290)Instructions burned: 284 (million)
% 32.23/5.96 % (12290)------------------------------
% 32.23/5.96 % (12290)------------------------------
% 32.23/5.96 % (12272)Instruction limit reached!
% 32.23/5.96 % (12272)------------------------------
% 32.23/5.96 % (12272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.23/5.96 % (12272)Termination reason: Unknown
% 32.23/5.96 % (12272)Termination phase: Saturation
% 32.23/5.96
% 32.23/5.96 % (12272)Memory used [KB]: 12025
% 32.23/5.96 % (12272)Time elapsed: 1.022 s
% 32.23/5.96 % (12272)Instructions burned: 3373 (million)
% 32.23/5.96 % (12272)------------------------------
% 32.23/5.96 % (12272)------------------------------
% 32.23/5.97 % (12294)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_11849 for (2955ds/102Mi)
% 32.23/5.97 % (12295)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_11849 for (2955ds/952Mi)
% 32.23/6.00 % (12294)Instruction limit reached!
% 32.23/6.00 % (12294)------------------------------
% 32.23/6.00 % (12294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.23/6.00 % (12294)Termination reason: Unknown
% 32.23/6.00 % (12294)Termination phase: Property scanning
% 32.23/6.00
% 32.23/6.00 % (12294)Memory used [KB]: 2302
% 32.23/6.00 % (12294)Time elapsed: 0.030 s
% 32.23/6.00 % (12294)Instructions burned: 104 (million)
% 32.23/6.00 % (12294)------------------------------
% 32.23/6.00 % (12294)------------------------------
% 32.23/6.01 % (12296)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_11849 for (2955ds/578Mi)
% 34.67/6.15 % (12285)Instruction limit reached!
% 34.67/6.15 % (12285)------------------------------
% 34.67/6.15 % (12285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.67/6.15 % (12285)Termination reason: Unknown
% 34.67/6.15 % (12285)Termination phase: Saturation
% 34.67/6.15
% 34.67/6.15 % (12285)Memory used [KB]: 10362
% 34.67/6.15 % (12285)Time elapsed: 0.534 s
% 34.67/6.15 % (12285)Instructions burned: 1672 (million)
% 34.67/6.15 % (12285)------------------------------
% 34.67/6.15 % (12285)------------------------------
% 34.67/6.16 % (12297)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_11849 for (2954ds/643Mi)
% 34.67/6.18 % (12291)Instruction limit reached!
% 34.67/6.18 % (12291)------------------------------
% 34.67/6.18 % (12291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.67/6.18 % (12291)Termination reason: Unknown
% 34.67/6.18 % (12291)Termination phase: Saturation
% 34.67/6.18
% 34.67/6.18 % (12291)Memory used [KB]: 9594
% 34.67/6.18 % (12291)Time elapsed: 0.285 s
% 34.67/6.18 % (12291)Instructions burned: 867 (million)
% 34.67/6.18 % (12291)------------------------------
% 34.67/6.18 % (12291)------------------------------
% 34.67/6.18 % (12296)Instruction limit reached!
% 34.67/6.18 % (12296)------------------------------
% 34.67/6.18 % (12296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.67/6.18 % (12296)Termination reason: Unknown
% 34.67/6.18 % (12296)Termination phase: Saturation
% 34.67/6.18
% 34.67/6.18 % (12296)Memory used [KB]: 9210
% 34.67/6.18 % (12296)Time elapsed: 0.179 s
% 34.67/6.18 % (12296)Instructions burned: 578 (million)
% 34.67/6.18 % (12296)------------------------------
% 34.67/6.18 % (12296)------------------------------
% 34.67/6.19 % (12298)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_11849 for (2953ds/865Mi)
% 34.67/6.19 % (12299)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_11849 for (2953ds/1174Mi)
% 35.27/6.26 % (12293)Instruction limit reached!
% 35.27/6.26 % (12293)------------------------------
% 35.27/6.26 % (12293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.27/6.26 % (12293)Termination reason: Unknown
% 35.27/6.26 % (12293)Termination phase: Saturation
% 35.27/6.26
% 35.27/6.26 % (12293)Memory used [KB]: 8059
% 35.27/6.26 % (12293)Time elapsed: 0.314 s
% 35.27/6.26 % (12293)Instructions burned: 1002 (million)
% 35.27/6.26 % (12293)------------------------------
% 35.27/6.26 % (12293)------------------------------
% 35.27/6.27 % (12295)Instruction limit reached!
% 35.27/6.27 % (12295)------------------------------
% 35.27/6.27 % (12295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.27/6.27 % (12295)Termination reason: Unknown
% 35.27/6.27 % (12295)Termination phase: Saturation
% 35.27/6.27
% 35.27/6.27 % (12295)Memory used [KB]: 10490
% 35.27/6.27 % (12295)Time elapsed: 0.299 s
% 35.27/6.27 % (12295)Instructions burned: 952 (million)
% 35.27/6.27 % (12295)------------------------------
% 35.27/6.27 % (12295)------------------------------
% 35.27/6.27 % (12300)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_11849 for (2952ds/644Mi)
% 35.27/6.28 % (12301)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_11849 for (2952ds/1201Mi)
% 35.63/6.36 % (12297)Instruction limit reached!
% 35.63/6.36 % (12297)------------------------------
% 35.63/6.36 % (12297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.63/6.36 % (12297)Termination reason: Unknown
% 35.63/6.36 % (12297)Termination phase: Saturation
% 35.63/6.36
% 35.63/6.36 % (12297)Memory used [KB]: 9466
% 35.63/6.36 % (12297)Time elapsed: 0.196 s
% 35.63/6.36 % (12297)Instructions burned: 643 (million)
% 35.63/6.36 % (12297)------------------------------
% 35.63/6.36 % (12297)------------------------------
% 35.63/6.36 % (12299)First to succeed.
% 35.63/6.37 % (12299)Refutation found. Thanks to Tanya!
% 35.63/6.37 % SZS status Theorem for DTF2THF_11849
% 35.63/6.37 % SZS output start Proof for DTF2THF_11849
% 35.63/6.37 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 35.63/6.37 thf(type_def_7, type, set: ($tType) > $tType).
% 35.63/6.37 thf(type_def_8, type, real: $tType).
% 35.63/6.37 thf(type_def_9, type, a: $tType).
% 35.63/6.37 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 35.63/6.37 thf(func_def_1, type, real: $tType).
% 35.63/6.37 thf(func_def_2, type, set: ($tType) > $tType).
% 35.63/6.37 thf(func_def_3, type, a: $tType).
% 35.63/6.37 thf(func_def_4, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_5, type, type: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_6, type, one: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_7, type, plus: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_8, type, zero: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_9, type, ord: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_10, type, neg_numeral: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_11, type, order: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_12, type, group_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_13, type, monoid_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_16, type, zero_neq_one: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_17, type, zero_less_one: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_18, type, semigroup_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_19, type, linordered_idom: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_20, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_21, type, linordered_field: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_22, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_23, type, linordered_semidom: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_24, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_25, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_26, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_27, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_28, type, real_V1076094709vector: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_29, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_30, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_31, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_32, type, ordere1818651114id_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_33, type, strict797366125id_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_34, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_35, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_36, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_37, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_38, type, real_V1587248058vector: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_39, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_40, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 35.63/6.37 thf(func_def_41, type, unique455577585es_aux: !>[X0: $tType]:(product_prod @ X0 @ X0 > $o)).
% 35.63/6.37 thf(func_def_42, type, one_one: !>[X0: $tType]:(X0)).
% 35.63/6.37 thf(func_def_43, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 35.63/6.37 thf(func_def_44, type, zero_zero: !>[X0: $tType]:(X0)).
% 35.63/6.37 thf(func_def_45, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 35.63/6.37 thf(func_def_46, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 35.63/6.37 thf(func_def_47, type, prefer1289595409x_pref: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > $o)).
% 35.63/6.37 thf(func_def_48, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 35.63/6.37 thf(func_def_49, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 35.63/6.37 thf(func_def_50, type, real_V1908273582scaleR: !>[X0: $tType]:(real > X0 > X0)).
% 35.63/6.37 thf(func_def_51, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 35.63/6.37 thf(func_def_52, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 35.63/6.37 thf(func_def_53, type, relation: set @ product_prod @ a @ a).
% 35.63/6.37 thf(func_def_54, type, u: real).
% 35.63/6.37 thf(func_def_55, type, v: real).
% 35.63/6.37 thf(func_def_56, type, x: a).
% 35.63/6.37 thf(func_def_57, type, y: a).
% 35.63/6.37 thf(func_def_74, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 35.63/6.37 thf(func_def_75, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 35.63/6.37 thf(func_def_76, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 35.63/6.37 thf(func_def_77, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 35.63/6.37 thf(func_def_78, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 35.63/6.37 thf(func_def_79, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 35.63/6.37 thf(func_def_80, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 35.63/6.37 thf(func_def_81, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 35.63/6.37 thf(func_def_82, type, sK8: !>[X0: $tType]:(X0 > X0 > X0)).
% 35.63/6.37 thf(func_def_83, type, sK9: !>[X0: $tType]:(X0 > X0 > X0)).
% 35.63/6.37 thf(func_def_84, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 35.63/6.37 thf(func_def_85, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 35.63/6.37 thf(func_def_86, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 35.63/6.37 thf(func_def_87, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 35.63/6.37 thf(func_def_88, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 35.63/6.37 thf(func_def_89, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_90, type, sK16: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 35.63/6.37 thf(func_def_91, type, sK17: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 35.63/6.37 thf(func_def_92, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 35.63/6.37 thf(func_def_93, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 35.63/6.37 thf(func_def_94, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_95, type, sK21: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 35.63/6.37 thf(func_def_96, type, sK22: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 35.63/6.37 thf(func_def_97, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 35.63/6.37 thf(func_def_98, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 35.63/6.37 thf(func_def_99, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 35.63/6.37 thf(func_def_100, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 35.63/6.37 thf(func_def_101, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 35.63/6.37 thf(func_def_102, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 35.63/6.37 thf(func_def_103, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 35.63/6.37 thf(func_def_104, type, sK30: !>[X0: $tType]:(X0 > X0)).
% 35.63/6.37 thf(func_def_105, type, sK31: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 35.63/6.37 thf(func_def_106, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 35.63/6.37 thf(func_def_107, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 35.63/6.37 thf(func_def_108, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 35.63/6.37 thf(func_def_109, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 35.63/6.37 thf(func_def_110, type, sK36: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 35.63/6.37 thf(func_def_111, type, sK37: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 35.63/6.37 thf(func_def_112, type, sK38: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > real)).
% 35.63/6.37 thf(func_def_113, type, sK39: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > real)).
% 35.63/6.37 thf(func_def_114, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 35.63/6.37 thf(func_def_115, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 35.63/6.37 thf(func_def_116, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 35.63/6.37 thf(func_def_117, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 35.63/6.37 thf(func_def_118, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 35.63/6.37 thf(func_def_119, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 35.63/6.37 thf(func_def_120, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 35.63/6.37 thf(func_def_121, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 35.63/6.37 thf(func_def_122, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 35.63/6.37 thf(func_def_123, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 35.63/6.37 thf(func_def_124, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 35.63/6.37 thf(func_def_125, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 35.63/6.37 thf(func_def_126, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_127, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 35.63/6.37 thf(func_def_128, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 35.63/6.37 thf(func_def_129, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 35.63/6.37 thf(func_def_130, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_131, type, sK57: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_132, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 35.63/6.37 thf(func_def_133, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 35.63/6.37 thf(func_def_134, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 35.63/6.37 thf(func_def_135, type, sK61: !>[X0: $tType]:(X0 > X0)).
% 35.63/6.37 thf(func_def_136, type, sK62: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 35.63/6.37 thf(func_def_137, type, sK63: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > X0)).
% 35.63/6.37 thf(func_def_138, type, sK64: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > real)).
% 35.63/6.37 thf(func_def_139, type, sK65: !>[X0: $tType]:(set @ product_prod @ X0 @ X0 > real)).
% 35.63/6.37 thf(func_def_140, type, sK66: !>[X0: $tType]:(X0 > X0 > X0)).
% 35.63/6.37 thf(func_def_141, type, sK67: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 35.63/6.37 thf(func_def_142, type, sK68: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 35.63/6.37 thf(func_def_143, type, sK69: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 35.63/6.37 thf(func_def_144, type, sK70: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 35.63/6.37 thf(func_def_145, type, sK71: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 35.63/6.37 thf(func_def_146, type, sK72: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_147, type, sK73: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 35.63/6.37 thf(func_def_148, type, sK74: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 35.63/6.37 thf(func_def_149, type, sK75: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 35.63/6.37 thf(func_def_150, type, sK76: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_151, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 35.63/6.37 thf(func_def_152, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 35.63/6.37 thf(func_def_153, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 35.63/6.37 thf(func_def_154, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 35.63/6.37 thf(func_def_155, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_156, type, sK82: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0)).
% 35.63/6.37 thf(func_def_157, type, sK83: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0)).
% 35.63/6.37 thf(func_def_158, type, sK84: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 35.63/6.37 thf(func_def_159, type, sK85: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 35.63/6.37 thf(func_def_160, type, sK86: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 35.63/6.37 thf(func_def_161, type, sK87: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 35.63/6.37 thf(func_def_163, type, ph89: !>[X0: $tType]:(X0)).
% 35.63/6.37 thf(f2781,plain,(
% 35.63/6.37 $false),
% 35.63/6.37 inference(avatar_sat_refutation,[status(thm)],[f2046,f2053,f2772])).
% 35.63/6.37 thf(f2772,plain,(
% 35.63/6.37 ~spl88_6),
% 35.63/6.37 inference(avatar_contradiction_clause,[status(thm)],[f2771])).
% 35.63/6.37 thf(f2771,plain,(
% 35.63/6.37 $false | ~spl88_6),
% 35.63/6.37 inference(subsumption_resolution,[status(thm)],[f2770,f1790])).
% 35.63/6.37 thf(f1790,plain,(
% 35.63/6.37 ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation) = $true)),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f929])).
% 35.63/6.37 thf(f929,plain,(
% 35.63/6.37 ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation) = $true)),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f928])).
% 35.63/6.37 thf(f928,plain,(
% 35.63/6.37 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)),
% 35.63/6.37 inference(rectify,[status(thm)],[f6])).
% 35.63/6.37 thf(f6,axiom,(
% 35.63/6.37 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',fact_5_assms_I2_J)).
% 35.63/6.37 thf(f2770,plain,(
% 35.63/6.37 ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation) != $true) | ~spl88_6),
% 35.63/6.37 inference(subsumption_resolution,[status(thm)],[f2744,f1979])).
% 35.63/6.37 thf(f1979,plain,(
% 35.63/6.37 (comm_monoid_add @ a = $true)),
% 35.63/6.37 inference(trivial_inequality_removal,[status(thm)],[f1874])).
% 35.63/6.37 thf(f1874,plain,(
% 35.63/6.37 (comm_monoid_add @ a = $true) | ($true != $true)),
% 35.63/6.37 inference(superposition,[status(thm)],[f1608,f1531])).
% 35.63/6.37 thf(f1531,plain,(
% 35.63/6.37 (real_V1076094709vector @ a = $true)),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f761])).
% 35.63/6.37 thf(f761,plain,(
% 35.63/6.37 (real_V1076094709vector @ a = $true)),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f760])).
% 35.63/6.37 thf(f760,plain,(
% 35.63/6.37 real_V1076094709vector @ a),
% 35.63/6.37 inference(rectify,[status(thm)],[f340])).
% 35.63/6.37 thf(f340,axiom,(
% 35.63/6.37 real_V1076094709vector @ a),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',tfree_0)).
% 35.63/6.37 thf(f1608,plain,(
% 35.63/6.37 ( ! [X0 : $tType] : ((real_V1076094709vector @ X0 != $true) | (comm_monoid_add @ X0 = $true)) )),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f1237])).
% 35.63/6.37 thf(f1237,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((real_V1076094709vector @ X0 != $true) | (comm_monoid_add @ X0 = $true))),
% 35.63/6.37 inference(ennf_transformation,[status(thm)],[f881])).
% 35.63/6.37 thf(f881,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((real_V1076094709vector @ X0 = $true) => (comm_monoid_add @ X0 = $true))),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f880])).
% 35.63/6.37 thf(f880,plain,(
% 35.63/6.37 ! [X0 : $tType] : (real_V1076094709vector @ X0 => comm_monoid_add @ X0)),
% 35.63/6.37 inference(rectify,[status(thm)],[f261])).
% 35.63/6.37 thf(f261,axiom,(
% 35.63/6.37 ! [X0 : $tType] : (real_V1076094709vector @ X0 => comm_monoid_add @ X0)),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',subcl_Real__Vector__Spaces_Oreal__vector___Groups_Ocomm__monoid__add)).
% 35.63/6.37 thf(f2744,plain,(
% 35.63/6.37 (comm_monoid_add @ a != $true) | ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation) != $true) | ~spl88_6),
% 35.63/6.37 inference(superposition,[status(thm)],[f2629,f1802])).
% 35.63/6.37 thf(f1802,plain,(
% 35.63/6.37 ( ! [X0 : $tType,X1 : X0] : (((plus_plus @ X0 @ X1 @ zero_zero @ X0) = X1) | (comm_monoid_add @ X0 != $true)) )),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f1305])).
% 35.63/6.37 thf(f1305,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((comm_monoid_add @ X0 != $true) | ! [X1 : X0] : ((plus_plus @ X0 @ X1 @ zero_zero @ X0) = X1))),
% 35.63/6.37 inference(ennf_transformation,[status(thm)],[f445])).
% 35.63/6.37 thf(f445,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((comm_monoid_add @ X0 = $true) => ! [X1 : X0] : ((plus_plus @ X0 @ X1 @ zero_zero @ X0) = X1))),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f444])).
% 35.63/6.37 thf(f444,plain,(
% 35.63/6.37 ! [X0 : $tType] : (comm_monoid_add @ X0 => ! [X1 : X0] : ((plus_plus @ X0 @ X1 @ zero_zero @ X0) = X1))),
% 35.63/6.37 inference(rectify,[status(thm)],[f68])).
% 35.63/6.37 thf(f68,axiom,(
% 35.63/6.37 ! [X0 : $tType] : (comm_monoid_add @ X0 => ! [X7 : X0] : ((plus_plus @ X0 @ X7 @ zero_zero @ X0) = X7))),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',fact_67_add_Ocomm__neutral)).
% 35.63/6.37 thf(f2629,plain,(
% 35.63/6.37 ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ zero_zero @ a) @ y) @ relation) != $true) | ~spl88_6),
% 35.63/6.37 inference(backward_demodulation,[status(thm)],[f2102,f2542])).
% 35.63/6.37 thf(f2542,plain,(
% 35.63/6.37 ( ! [X0 : a] : (((real_V1908273582scaleR @ a @ v @ X0) = zero_zero @ a)) ) | ~spl88_6),
% 35.63/6.37 inference(backward_demodulation,[status(thm)],[f1983,f2505])).
% 35.63/6.37 thf(f2505,plain,(
% 35.63/6.37 (zero_zero @ real = v) | ~spl88_6),
% 35.63/6.37 inference(subsumption_resolution,[status(thm)],[f2334,f1513])).
% 35.63/6.37 thf(f1513,plain,(
% 35.63/6.37 (cancel1352612707id_add @ real = $true)),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f411])).
% 35.63/6.37 thf(f411,plain,(
% 35.63/6.37 (cancel1352612707id_add @ real = $true)),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f410])).
% 35.63/6.37 thf(f410,plain,(
% 35.63/6.37 cancel1352612707id_add @ real),
% 35.63/6.37 inference(rectify,[status(thm)],[f297])).
% 35.63/6.37 thf(f297,axiom,(
% 35.63/6.37 cancel1352612707id_add @ real),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add)).
% 35.63/6.37 thf(f2334,plain,(
% 35.63/6.37 (zero_zero @ real = v) | (cancel1352612707id_add @ real != $true) | ~spl88_6),
% 35.63/6.37 inference(equality_proxy_clausification,[status(thm)],[f2333])).
% 35.63/6.37 thf(f2333,plain,(
% 35.63/6.37 (cancel1352612707id_add @ real != $true) | ($true = (zero_zero @ real = v)) | ~spl88_6),
% 35.63/6.37 inference(boolean_simplification,[status(thm)],[f2243])).
% 35.63/6.37 thf(f2243,plain,(
% 35.63/6.37 (cancel1352612707id_add @ real != $true) | ((u = u) = (zero_zero @ real = v)) | ~spl88_6),
% 35.63/6.37 inference(superposition,[status(thm)],[f1695,f2077])).
% 35.63/6.37 thf(f2077,plain,(
% 35.63/6.37 (u = (plus_plus @ real @ u @ v)) | ~spl88_6),
% 35.63/6.37 inference(backward_demodulation,[status(thm)],[f1698,f2045])).
% 35.63/6.37 thf(f2045,plain,(
% 35.63/6.37 (u = one_one @ real) | ~spl88_6),
% 35.63/6.37 inference(avatar_component_clause,[status(thm)],[f2043])).
% 35.63/6.37 thf(f2043,definition,(
% 35.63/6.37 spl88_6 <=> (u = one_one @ real)),
% 35.63/6.37 introduced(definition,[new_symbols(naming,[spl88_6])],[avatar_definition])).
% 35.63/6.37 thf(f1698,plain,(
% 35.63/6.37 (one_one @ real = (plus_plus @ real @ u @ v))),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f10])).
% 35.63/6.37 thf(f10,axiom,(
% 35.63/6.37 (one_one @ real = (plus_plus @ real @ u @ v))),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',fact_9_assms_I5_J)).
% 35.63/6.37 thf(f1695,plain,(
% 35.63/6.37 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((zero_zero @ X0 = X2) = ((plus_plus @ X0 @ X1 @ X2) = X1)) | (cancel1352612707id_add @ X0 != $true)) )),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f1378])).
% 35.63/6.37 thf(f1378,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((cancel1352612707id_add @ X0 != $true) | ! [X1 : X0,X2 : X0] : ((zero_zero @ X0 = X2) = ((plus_plus @ X0 @ X1 @ X2) = X1)))),
% 35.63/6.37 inference(ennf_transformation,[status(thm)],[f643])).
% 35.63/6.37 thf(f643,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((cancel1352612707id_add @ X0 = $true) => ! [X1 : X0,X2 : X0] : ((zero_zero @ X0 = X2) = ((plus_plus @ X0 @ X1 @ X2) = X1)))),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f642])).
% 35.63/6.37 thf(f642,plain,(
% 35.63/6.37 ! [X0 : $tType] : (cancel1352612707id_add @ X0 => ! [X1 : X0,X2 : X0] : (((plus_plus @ X0 @ X1 @ X2) = X1) = (zero_zero @ X0 = X2)))),
% 35.63/6.37 inference(rectify,[status(thm)],[f26])).
% 35.63/6.37 thf(f26,axiom,(
% 35.63/6.37 ! [X0 : $tType] : (cancel1352612707id_add @ X0 => ! [X7 : X0,X8 : X0] : (((plus_plus @ X0 @ X7 @ X8) = X7) = (zero_zero @ X0 = X8)))),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',fact_25_add__cancel__right__right)).
% 35.63/6.37 thf(f1983,plain,(
% 35.63/6.37 ( ! [X0 : a] : (((real_V1908273582scaleR @ a @ zero_zero @ real @ X0) = zero_zero @ a)) )),
% 35.63/6.37 inference(trivial_inequality_removal,[status(thm)],[f1887])).
% 35.63/6.37 thf(f1887,plain,(
% 35.63/6.37 ( ! [X0 : a] : (((real_V1908273582scaleR @ a @ zero_zero @ real @ X0) = zero_zero @ a) | ($true != $true)) )),
% 35.63/6.37 inference(superposition,[status(thm)],[f1669,f1531])).
% 35.63/6.37 thf(f1669,plain,(
% 35.63/6.37 ( ! [X0 : $tType,X1 : X0] : ((real_V1076094709vector @ X0 != $true) | (zero_zero @ X0 = (real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1))) )),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f1346])).
% 35.63/6.37 thf(f1346,plain,(
% 35.63/6.37 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero @ X0 = (real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1)) | (real_V1076094709vector @ X0 != $true))),
% 35.63/6.37 inference(ennf_transformation,[status(thm)],[f769])).
% 35.63/6.37 thf(f769,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((real_V1076094709vector @ X0 = $true) => ! [X1 : X0] : (zero_zero @ X0 = (real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1)))),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f768])).
% 35.63/6.37 thf(f768,plain,(
% 35.63/6.37 ! [X0 : $tType] : (real_V1076094709vector @ X0 => ! [X1 : X0] : (zero_zero @ X0 = (real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1)))),
% 35.63/6.37 inference(rectify,[status(thm)],[f115])).
% 35.63/6.37 thf(f115,axiom,(
% 35.63/6.37 ! [X0 : $tType] : (real_V1076094709vector @ X0 => ! [X3 : X0] : (zero_zero @ X0 = (real_V1908273582scaleR @ X0 @ zero_zero @ real @ X3)))),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',fact_114_scale__zero__left)).
% 35.63/6.37 thf(f2102,plain,(
% 35.63/6.37 ($true != (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) | ~spl88_6),
% 35.63/6.37 inference(backward_demodulation,[status(thm)],[f1694,f2084])).
% 35.63/6.37 thf(f2084,plain,(
% 35.63/6.37 ( ! [X0 : a] : (((real_V1908273582scaleR @ a @ u @ X0) = X0)) ) | ~spl88_6),
% 35.63/6.37 inference(backward_demodulation,[status(thm)],[f1920,f2045])).
% 35.63/6.37 thf(f1920,plain,(
% 35.63/6.37 ( ! [X0 : a] : (((real_V1908273582scaleR @ a @ one_one @ real @ X0) = X0)) )),
% 35.63/6.37 inference(trivial_inequality_removal,[status(thm)],[f1902])).
% 35.63/6.37 thf(f1902,plain,(
% 35.63/6.37 ( ! [X0 : a] : (((real_V1908273582scaleR @ a @ one_one @ real @ X0) = X0) | ($true != $true)) )),
% 35.63/6.37 inference(superposition,[status(thm)],[f1840,f1531])).
% 35.63/6.37 thf(f1840,plain,(
% 35.63/6.37 ( ! [X0 : $tType,X1 : X0] : ((real_V1076094709vector @ X0 != $true) | ((real_V1908273582scaleR @ X0 @ one_one @ real @ X1) = X1)) )),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f1201])).
% 35.63/6.37 thf(f1201,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((real_V1076094709vector @ X0 != $true) | ! [X1 : X0] : ((real_V1908273582scaleR @ X0 @ one_one @ real @ X1) = X1))),
% 35.63/6.37 inference(ennf_transformation,[status(thm)],[f421])).
% 35.63/6.37 thf(f421,plain,(
% 35.63/6.37 ! [X0 : $tType] : ((real_V1076094709vector @ X0 = $true) => ! [X1 : X0] : ((real_V1908273582scaleR @ X0 @ one_one @ real @ X1) = X1))),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f420])).
% 35.63/6.37 thf(f420,plain,(
% 35.63/6.37 ! [X0 : $tType] : (real_V1076094709vector @ X0 => ! [X1 : X0] : ((real_V1908273582scaleR @ X0 @ one_one @ real @ X1) = X1))),
% 35.63/6.37 inference(rectify,[status(thm)],[f117])).
% 35.63/6.37 thf(f117,axiom,(
% 35.63/6.37 ! [X0 : $tType] : (real_V1076094709vector @ X0 => ! [X3 : X0] : ((real_V1908273582scaleR @ X0 @ one_one @ real @ X3) = X3))),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',fact_116_scaleR__one)).
% 35.63/6.37 thf(f1694,plain,(
% 35.63/6.37 ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) != $true)),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f1024])).
% 35.63/6.37 thf(f1024,plain,(
% 35.63/6.37 ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) != $true)),
% 35.63/6.37 inference(flattening,[status(thm)],[f997])).
% 35.63/6.37 thf(f997,plain,(
% 35.63/6.37 ~((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) = $true)),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f996])).
% 35.63/6.37 thf(f996,plain,(
% 35.63/6.37 ~(member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 35.63/6.37 inference(rectify,[status(thm)],[f342])).
% 35.63/6.37 thf(f342,negated_conjecture,(
% 35.63/6.37 ~(member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 35.63/6.37 inference(negated_conjecture,[status(cth)],[f341])).
% 35.63/6.37 thf(f341,conjecture,(
% 35.63/6.37 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',conj_0)).
% 35.63/6.37 thf(f2053,plain,(
% 35.63/6.37 ~spl88_5),
% 35.63/6.37 inference(avatar_split_clause,[status(thm)],[f2015,f2039])).
% 35.63/6.37 thf(f2039,definition,(
% 35.63/6.37 spl88_5 <=> (u = zero_zero @ real)),
% 35.63/6.37 introduced(definition,[new_symbols(naming,[spl88_5])],[avatar_definition])).
% 35.63/6.37 thf(f2015,plain,(
% 35.63/6.37 (u != zero_zero @ real)),
% 35.63/6.37 inference(trivial_inequality_removal,[status(thm)],[f1997])).
% 35.63/6.37 thf(f1997,plain,(
% 35.63/6.37 ($true != $true) | (u != zero_zero @ real)),
% 35.63/6.37 inference(superposition,[status(thm)],[f1694,f1646])).
% 35.63/6.37 thf(f1646,plain,(
% 35.63/6.37 (u != zero_zero @ real) | ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) = $true)),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f1330])).
% 35.63/6.37 thf(f1330,plain,(
% 35.63/6.37 ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) = $true) | (u != zero_zero @ real)),
% 35.63/6.37 inference(ennf_transformation,[status(thm)],[f663])).
% 35.63/6.37 thf(f663,plain,(
% 35.63/6.37 (u = zero_zero @ real) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) = $true)),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f662])).
% 35.63/6.37 thf(f662,plain,(
% 35.63/6.37 (u = zero_zero @ real) => (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 35.63/6.37 inference(rectify,[status(thm)],[f8])).
% 35.63/6.37 thf(f8,axiom,(
% 35.63/6.37 (u = zero_zero @ real) => (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',fact_7_u__0)).
% 35.63/6.37 thf(f2046,plain,(
% 35.63/6.37 spl88_5 | spl88_6),
% 35.63/6.37 inference(avatar_split_clause,[status(thm)],[f2019,f2043,f2039])).
% 35.63/6.37 thf(f2019,plain,(
% 35.63/6.37 (u = one_one @ real) | (u = zero_zero @ real)),
% 35.63/6.37 inference(trivial_inequality_removal,[status(thm)],[f1996])).
% 35.63/6.37 thf(f1996,plain,(
% 35.63/6.37 (u = one_one @ real) | ($true != $true) | (u = zero_zero @ real)),
% 35.63/6.37 inference(superposition,[status(thm)],[f1694,f1517])).
% 35.63/6.37 thf(f1517,plain,(
% 35.63/6.37 (u = one_one @ real) | ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) = $true) | (u = zero_zero @ real)),
% 35.63/6.37 inference(cnf_transformation,[status(thm)],[f1322])).
% 35.63/6.37 thf(f1322,plain,(
% 35.63/6.37 (u = zero_zero @ real) | ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) = $true) | (u = one_one @ real)),
% 35.63/6.37 inference(flattening,[status(thm)],[f1321])).
% 35.63/6.37 thf(f1321,plain,(
% 35.63/6.37 ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) = $true) | ((u = one_one @ real) | (u = zero_zero @ real))),
% 35.63/6.37 inference(ennf_transformation,[status(thm)],[f367])).
% 35.63/6.37 thf(f367,plain,(
% 35.63/6.37 ((u != one_one @ real) & (u != zero_zero @ real)) => ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation) = $true)),
% 35.63/6.37 inference(fool_elimination,[status(thm)],[f366])).
% 35.63/6.37 thf(f366,plain,(
% 35.63/6.37 ((u != one_one @ real) & (u != zero_zero @ real)) => (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 35.63/6.37 inference(rectify,[status(thm)],[f7])).
% 35.63/6.37 thf(f7,axiom,(
% 35.63/6.37 ((u != one_one @ real) & (u != zero_zero @ real)) => (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 35.63/6.37 file('/export/starexec/sandbox2/tmp/tmp.SgO4W3MFj7/DTF2THF_11849.p',fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062)).
% 35.63/6.37 % SZS output end Proof for DTF2THF_11849
% 35.63/6.37 % (12299)------------------------------
% 35.63/6.37 % (12299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.63/6.37 % (12299)Termination reason: Refutation
% 35.63/6.37
% 35.63/6.37 % (12299)Memory used [KB]: 8571
% 35.63/6.37 % (12299)Time elapsed: 0.171 s
% 35.63/6.37 % (12299)Instructions burned: 526 (million)
% 35.63/6.37 % (12299)------------------------------
% 35.63/6.37 % (12299)------------------------------
% 35.63/6.37 % (12122)Success in time 4.807 s
%------------------------------------------------------------------------------