%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP168^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 08:56:06 AM UTC 2026
% Result : Theorem 9.39s 2.67s
% Output : Refutation 9.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP168^2 : TPTP v9.2.1. Released v7.5.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n016.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 08:28:51 EST 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.41 ---- Original DTF file ---
% 0.14/0.41 thf(spec,logic,$$dhol).
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 % File : ITP168^2 : TPTP v9.2.1. Released v7.5.0.
% 0.14/0.41 % Domain : Interactive Theorem Proving
% 0.14/0.41 % Problem : Sledgehammer Safety_Regular problem prob_110__3347974_1
% 0.14/0.41 % Version : Especial.
% 0.14/0.41 % English :
% 0.14/0.41
% 0.14/0.41 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.14/0.41 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.14/0.41 % Source : [Des21]
% 0.14/0.41 % Names : Safety_Regular/prob_110__3347974_1 [Des21]
% 0.14/0.41
% 0.14/0.41 % Status : Theorem
% 0.14/0.41 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.14/0.41 % Syntax : Number of formulae : 381 ( 114 unt; 67 typ; 0 def)
% 0.14/0.41 % Number of atoms : 937 ( 222 equ; 0 cnn)
% 0.14/0.41 % Maximal formula atoms : 13 ( 2 avg)
% 0.14/0.41 % Number of connectives : 3532 ( 81 ~; 27 |; 140 &;2816 @)
% 0.14/0.41 % ( 0 <=>; 468 =>; 0 <=; 0 <~>)
% 0.14/0.41 % Maximal formula depth : 22 ( 8 avg)
% 0.14/0.41 % Number of types : 8 ( 7 usr)
% 0.14/0.41 % Number of type conns : 234 ( 234 >; 0 *; 0 +; 0 <<)
% 0.14/0.41 % Number of symbols : 63 ( 60 usr; 8 con; 0-6 aty)
% 0.14/0.41 % Number of variables : 1170 ( 78 ^; 948 !; 113 ?;1170 :)
% 0.14/0.41 % ( 31 !>; 0 ?*; 0 @-; 0 @+)
% 0.14/0.41 % SPC : TH1_THM_EQU_NAR
% 0.14/0.41
% 0.14/0.41 % Comments : This file was generated by Sledgehammer 2021-02-23 16:21:50.823
% 0.14/0.41 %------------------------------------------------------------------------------
% 0.14/0.41 % Could-be-implicit typings (8)
% 0.14/0.41 thf(ty_t_Views_Oview_Oview__ext,type,
% 0.14/0.41 view_ext: $tType > $tType ).
% 0.14/0.41
% 0.14/0.41 thf(ty_t_Product__Type_Ounit,type,
% 0.14/0.41 product_unit: $tType ).
% 0.14/0.41
% 0.14/0.41 thf(ty_t_RealInt_Oreal__int,type,
% 0.14/0.41 real_int: $tType ).
% 0.14/0.41
% 0.14/0.41 thf(ty_t_Traffic_Otraffic,type,
% 0.14/0.41 traffic: $tType ).
% 0.14/0.41
% 0.14/0.41 thf(ty_t_NatInt_Onat__int,type,
% 0.14/0.41 nat_int: $tType ).
% 0.14/0.41
% 0.14/0.41 thf(ty_t_Real_Oreal,type,
% 0.14/0.41 real: $tType ).
% 0.14/0.41
% 0.14/0.41 thf(ty_t_Cars_Ocars,type,
% 0.14/0.41 cars: $tType ).
% 0.14/0.41
% 0.14/0.41 thf(ty_t_Nat_Onat,type,
% 0.14/0.41 nat: $tType ).
% 0.14/0.41
% 0.14/0.41 % Explicit typings (59)
% 0.14/0.41 thf(sy_cl_HOL_Otype,type,
% 0.14/0.41 type:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Groups_Ominus,type,
% 0.14/0.41 minus:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Obot,type,
% 0.14/0.41 bot:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Oord,type,
% 0.14/0.41 ord:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Oorder,type,
% 0.14/0.41 order:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Groups_Ogroup__add,type,
% 0.14/0.41 group_add:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Ono__bot,type,
% 0.14/0.41 no_bot:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Ono__top,type,
% 0.14/0.41 no_top:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Olinorder,type,
% 0.14/0.41 linorder:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Opreorder,type,
% 0.14/0.41 preorder:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Oorder__bot,type,
% 0.14/0.41 order_bot:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Owellorder,type,
% 0.14/0.41 wellorder:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Odense__order,type,
% 0.14/0.41 dense_order:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.14/0.41 dense_linorder:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.14/0.41 ordered_ab_group_add:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.14/0.41 cancel146912293up_add:
% 0.14/0.41 !>[A: $tType] : $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Fun_Ofun__upd,type,
% 0.14/0.41 fun_upd:
% 0.14/0.41 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.14/0.41 minus_minus:
% 0.14/0.41 !>[A: $tType] : ( A > A > A ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 0.14/0.41 default_default:
% 0.14/0.41 !>[A: $tType] : A ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_If,type,
% 0.14/0.41 if:
% 0.14/0.41 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Move_Otraffic_Omove,type,
% 0.14/0.41 move: traffic > traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_NatInt_Onat__int_ON__Chop,type,
% 0.14/0.41 nat_N_Chop: nat_int > nat_int > nat_int > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_NatInt_Onat__int_Ocard_H,type,
% 0.14/0.41 nat_card: nat_int > nat ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_NatInt_Onat__int_Oconsec,type,
% 0.14/0.41 nat_consec: nat_int > nat_int > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_NatInt_Onat__int_Onot__in,type,
% 0.14/0.41 nat_not_in: nat > nat_int > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_NatInt_Onat__int_Ounion,type,
% 0.14/0.41 nat_union: nat_int > nat_int > nat_int ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.14/0.41 bot_bot:
% 0.14/0.41 !>[A: $tType] : A ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.14/0.41 ord_less:
% 0.14/0.41 !>[A: $tType] : ( A > A > $o ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.14/0.41 ord_less_eq:
% 0.14/0.41 !>[A: $tType] : ( A > A > $o ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 0.14/0.41 order_Greatest:
% 0.14/0.41 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Product__Type_OUnity,type,
% 0.14/0.41 product_Unity: product_unit ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 0.14/0.41 product_rec_unit:
% 0.14/0.41 !>[T: $tType] : ( T > product_unit > T ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_RealInt_Oreal__int_OR__Chop,type,
% 0.14/0.41 real_R_Chop: real_int > real_int > real_int > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_RealInt_Oreal__int_Oshift,type,
% 0.14/0.41 real_shift: real_int > real > real_int ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Oabstract,type,
% 0.14/0.41 abstract: traffic > traffic > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Obraking__distance,type,
% 0.14/0.41 braking_distance: traffic > cars > real ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Ochange__dyn,type,
% 0.14/0.41 change_dyn: traffic > cars > ( real > real ) > traffic > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Oclm,type,
% 0.14/0.41 clm: traffic > cars > nat_int ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Ocreate__claim,type,
% 0.14/0.41 create_claim: traffic > cars > nat > traffic > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Ocreate__reservation,type,
% 0.14/0.41 create_reservation: traffic > cars > traffic > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Odyn,type,
% 0.14/0.41 dyn: traffic > cars > real > real ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Oevolve,type,
% 0.14/0.41 evolve: traffic > traffic > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Ophysical__size,type,
% 0.14/0.41 physical_size: traffic > cars > real ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Opos,type,
% 0.14/0.41 pos: traffic > cars > real ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Ores,type,
% 0.14/0.41 res: traffic > cars > nat_int ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Owithdraw__claim,type,
% 0.14/0.41 withdraw_claim: traffic > cars > traffic > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Traffic_Otraffic_Owithdraw__reservation,type,
% 0.14/0.41 withdraw_reservation: traffic > cars > nat > traffic > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Views_Oview_Oext,type,
% 0.14/0.41 ext:
% 0.14/0.41 !>[Z: $tType] : ( ( view_ext @ Z ) > real_int ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Views_Oview_Ohchop,type,
% 0.14/0.41 hchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Views_Oview_Olan,type,
% 0.14/0.41 lan:
% 0.14/0.41 !>[Z: $tType] : ( ( view_ext @ Z ) > nat_int ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Views_Oview_Omore,type,
% 0.14/0.41 more:
% 0.14/0.41 !>[Z: $tType] : ( ( view_ext @ Z ) > Z ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Views_Oview_Oown,type,
% 0.14/0.41 own:
% 0.14/0.41 !>[Z: $tType] : ( ( view_ext @ Z ) > cars ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Views_Oview_Oswitch,type,
% 0.14/0.41 switch: ( view_ext @ product_unit ) > cars > ( view_ext @ product_unit ) > $o ).
% 0.14/0.41
% 0.14/0.41 thf(sy_c_Views_Oview_Oview__ext,type,
% 0.14/0.41 view_ext2:
% 0.14/0.41 !>[Z: $tType] : ( real_int > nat_int > cars > Z > ( view_ext @ Z ) ) ).
% 0.14/0.41
% 0.14/0.41 thf(sy_v_ts_H_H____,type,
% 0.14/0.41 ts: traffic ).
% 0.14/0.41
% 0.14/0.41 thf(sy_v_ts_H____,type,
% 0.14/0.41 ts2: traffic ).
% 0.14/0.41
% 0.14/0.41 thf(sy_v_ts_Ha____,type,
% 0.14/0.41 ts_a: traffic ).
% 0.14/0.41
% 0.14/0.41 thf(sy_v_ts____,type,
% 0.14/0.41 ts3: traffic ).
% 0.14/0.41
% 0.14/0.41 thf(sy_v_v____,type,
% 0.14/0.41 v: view_ext @ product_unit ).
% 0.14/0.41
% 0.14/0.41 % Relevant facts (256)
% 0.14/0.41 thf(fact_0_cr__res_Ohyps_I1_J,axiom,
% 0.14/0.41 abstract @ ts3 @ ts_a ).
% 0.14/0.41
% 0.14/0.41 % cr_res.hyps(1)
% 0.14/0.41 thf(fact_1_cr__res_Ohyps_I2_J,axiom,
% 0.14/0.41 ? [C: cars] : ( create_reservation @ ts_a @ C @ ts ) ).
% 0.14/0.41
% 0.14/0.41 % cr_res.hyps(2)
% 0.14/0.41 thf(fact_2_local_Ohmlsl_Oglobally__4,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ! [Ts2: traffic] :
% 0.14/0.41 ( ( abstract @ Ts @ Ts2 )
% 0.14/0.41 => ( Phi @ Ts2 @ ( move @ Ts @ Ts2 @ V ) ) )
% 0.14/0.41 => ! [Ts3: traffic] :
% 0.14/0.41 ( ( abstract @ Ts @ Ts3 )
% 0.14/0.41 => ! [Ts_a: traffic] :
% 0.14/0.41 ( ( abstract @ Ts3 @ Ts_a )
% 0.14/0.41 => ( Phi @ Ts_a @ ( move @ Ts3 @ Ts_a @ ( move @ Ts @ Ts3 @ V ) ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.globally_4
% 0.14/0.41 thf(fact_3_local_Ohmlsl_Oglobally__all__iff,axiom,
% 0.14/0.41 ! [A: $tType,B: $tType,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( ! [Ts4: traffic] :
% 0.14/0.41 ( ( abstract @ Ts @ Ts4 )
% 0.14/0.41 => ! [X: A] : ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V ) ) ) )
% 0.14/0.41 = ( ! [X: B,Ts4: traffic] :
% 0.14/0.41 ( ( abstract @ Ts @ Ts4 )
% 0.14/0.41 => ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.globally_all_iff
% 0.14/0.41 thf(fact_4_local_Ohmlsl_Oglobally__all__iff_H,axiom,
% 0.14/0.41 ! [A: $tType,B: $tType,Ts5: traffic,Phi: traffic > ( view_ext @ product_unit ) > $o,V2: view_ext @ product_unit] :
% 0.14/0.41 ( ( ! [Ts4: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts4 )
% 0.14/0.41 => ! [X: A] : ( Phi @ Ts4 @ ( move @ Ts5 @ Ts4 @ V2 ) ) ) )
% 0.14/0.41 = ( ! [X: B,Ts4: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts4 )
% 0.14/0.41 => ( Phi @ Ts4 @ ( move @ Ts5 @ Ts4 @ V2 ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.globally_all_iff'
% 0.14/0.41 thf(fact_5_local_Ohmlsl_Oglobally__refl,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ! [Ts2: traffic] :
% 0.14/0.41 ( ( abstract @ Ts @ Ts2 )
% 0.14/0.41 => ( Phi @ Ts2 @ ( move @ Ts @ Ts2 @ V ) ) )
% 0.14/0.41 => ( Phi @ Ts @ V ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.globally_refl
% 0.14/0.41 thf(fact_6_abs,axiom,
% 0.14/0.41 abstract @ ts3 @ ts2 ).
% 0.14/0.41
% 0.14/0.41 % abs
% 0.14/0.41 thf(fact_7__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,axiom,
% 0.14/0.41 ( ( move @ ts3 @ ts_a @ v )
% 0.14/0.41 = ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % \<open>move ts ts' v = move ts' ts'' (move ts ts' v)\<close>
% 0.14/0.41 thf(fact_8_traffic_Omove__nothing,axiom,
% 0.14/0.41 ! [Ts5: traffic,V2: view_ext @ product_unit] :
% 0.14/0.41 ( ( move @ Ts5 @ Ts5 @ V2 )
% 0.14/0.41 = V2 ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_nothing
% 0.14/0.41 thf(fact_9_traffic_Omove__def,axiom,
% 0.14/0.41 ( move
% 0.14/0.41 = ( ^ [Ts6: traffic,Ts4: traffic,V3: view_ext @ product_unit] : ( view_ext2 @ product_unit @ ( real_shift @ ( ext @ product_unit @ V3 ) @ ( minus_minus @ real @ ( pos @ Ts4 @ ( own @ product_unit @ V3 ) ) @ ( pos @ Ts6 @ ( own @ product_unit @ V3 ) ) ) ) @ ( lan @ product_unit @ V3 ) @ ( own @ product_unit @ V3 ) @ product_Unity ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_def
% 0.14/0.41 thf(fact_10_traffic_Omove__stability__res,axiom,
% 0.14/0.41 ! [Ts5: traffic,C2: cars,Ts7: traffic,V2: view_ext @ product_unit] :
% 0.14/0.41 ( ( create_reservation @ Ts5 @ C2 @ Ts7 )
% 0.14/0.41 => ( ( move @ Ts5 @ Ts7 @ V2 )
% 0.14/0.41 = V2 ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_stability_res
% 0.14/0.41 thf(fact_11_traffic_Omove__keeps__owner,axiom,
% 0.14/0.41 ! [Ts5: traffic,Ts7: traffic] :
% 0.14/0.41 ( ( own @ product_unit )
% 0.14/0.41 = ( ^ [V3: view_ext @ product_unit] : ( own @ product_unit @ ( move @ Ts5 @ Ts7 @ V3 ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_keeps_owner
% 0.14/0.41 thf(fact_12_traffic_Omove__trans,axiom,
% 0.14/0.41 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic,V2: view_ext @ product_unit] :
% 0.14/0.41 ( ( ( abstract @ Ts5 @ Ts7 )
% 0.14/0.41 & ( abstract @ Ts7 @ Ts8 ) )
% 0.14/0.41 => ( ( move @ Ts7 @ Ts8 @ ( move @ Ts5 @ Ts7 @ V2 ) )
% 0.14/0.41 = ( move @ Ts5 @ Ts8 @ V2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_trans
% 0.14/0.41 thf(fact_13_traffic_Omove__keeps__lanes,axiom,
% 0.14/0.41 ! [Ts5: traffic,Ts7: traffic] :
% 0.14/0.41 ( ( lan @ product_unit )
% 0.14/0.41 = ( ^ [V3: view_ext @ product_unit] : ( lan @ product_unit @ ( move @ Ts5 @ Ts7 @ V3 ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_keeps_lanes
% 0.14/0.41 thf(fact_14_traffic_Omove__stability__clm,axiom,
% 0.14/0.41 ! [Ts5: traffic,C2: cars,N: nat,Ts7: traffic,V2: view_ext @ product_unit] :
% 0.14/0.41 ( ( create_claim @ Ts5 @ C2 @ N @ Ts7 )
% 0.14/0.41 => ( ( move @ Ts5 @ Ts7 @ V2 )
% 0.14/0.41 = V2 ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_stability_clm
% 0.14/0.41 thf(fact_15_traffic_Omove__stability__wdc,axiom,
% 0.14/0.41 ! [Ts5: traffic,C2: cars,Ts7: traffic,V2: view_ext @ product_unit] :
% 0.14/0.41 ( ( withdraw_claim @ Ts5 @ C2 @ Ts7 )
% 0.14/0.41 => ( ( move @ Ts5 @ Ts7 @ V2 )
% 0.14/0.41 = V2 ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_stability_wdc
% 0.14/0.41 thf(fact_16_traffic_Omove__stability__wdr,axiom,
% 0.14/0.41 ! [Ts5: traffic,C2: cars,N: nat,Ts7: traffic,V2: view_ext @ product_unit] :
% 0.14/0.41 ( ( withdraw_reservation @ Ts5 @ C2 @ N @ Ts7 )
% 0.14/0.41 => ( ( move @ Ts5 @ Ts7 @ V2 )
% 0.14/0.41 = V2 ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.move_stability_wdr
% 0.14/0.41 thf(fact_17_local_Ohmlsl_Ohchop__assoc,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ( Phi @ Ts @ W )
% 0.14/0.41 & ? [X: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ U @ X @ Y )
% 0.14/0.41 & ( Psi @ Ts @ X )
% 0.14/0.41 & ( Chi @ Ts @ Y ) ) ) )
% 0.14/0.41 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ? [X: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ W @ X @ Y )
% 0.14/0.41 & ( Phi @ Ts @ X )
% 0.14/0.41 & ( Psi @ Ts @ Y ) )
% 0.14/0.41 & ( Chi @ Ts @ U ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.hchop_assoc
% 0.14/0.41 thf(fact_18_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ( Phi @ Ts @ W )
% 0.14/0.41 & ( ( Psi @ Ts @ U )
% 0.14/0.41 | ( Chi @ Ts @ U ) ) ) )
% 0.14/0.41 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ( Phi @ Ts @ W )
% 0.14/0.41 & ( Psi @ Ts @ U ) )
% 0.14/0.41 | ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ( Phi @ Ts @ W )
% 0.14/0.41 & ( Chi @ Ts @ U ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.hchop_disj_distr1
% 0.14/0.41 thf(fact_19_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 0.14/0.41 ! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ( ( Psi @ Ts @ W )
% 0.14/0.41 | ( Chi @ Ts @ W ) )
% 0.14/0.41 & ( Phi @ Ts @ U ) ) )
% 0.14/0.41 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ( Psi @ Ts @ W )
% 0.14/0.41 & ( Phi @ Ts @ U ) )
% 0.14/0.41 | ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ( Chi @ Ts @ W )
% 0.14/0.41 & ( Phi @ Ts @ U ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.hchop_disj_distr2
% 0.14/0.41 thf(fact_20_local_Ohmlsl_Ohchop__weaken2,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( Phi @ Ts @ V )
% 0.14/0.41 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ Va @ U2 )
% 0.14/0.41 & ( Phi @ Ts @ U2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.hchop_weaken2
% 0.14/0.41 thf(fact_21_local_Ohmlsl_Ohchop__weaken1,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( Phi @ Ts @ V )
% 0.14/0.41 => ? [Va: view_ext @ product_unit] :
% 0.14/0.41 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
% 0.14/0.41 & ( Phi @ Ts @ Va ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.hchop_weaken1
% 0.14/0.41 thf(fact_22_local_Ohmlsl_Ohchop__weaken,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( Phi @ Ts @ V )
% 0.14/0.41 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ Va @ U2 )
% 0.14/0.41 & ? [Vb: view_ext @ product_unit] :
% 0.14/0.41 ( ? [X_1: view_ext @ product_unit] : ( hchop @ U2 @ Vb @ X_1 )
% 0.14/0.41 & ( Phi @ Ts @ Vb ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.hchop_weaken
% 0.14/0.41 thf(fact_23_local_Ohmlsl_Ohchop__neg2,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ~ ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ Va @ U2 )
% 0.14/0.41 & ( Phi @ Ts @ U2 ) )
% 0.14/0.41 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ Va @ U2 )
% 0.14/0.41 & ~ ( Phi @ Ts @ U2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.hchop_neg2
% 0.14/0.41 thf(fact_24_local_Ohmlsl_Ohchop__neg1,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ~ ? [Va: view_ext @ product_unit] :
% 0.14/0.41 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
% 0.14/0.41 & ( Phi @ Ts @ Va ) )
% 0.14/0.41 => ? [Va: view_ext @ product_unit] :
% 0.14/0.41 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
% 0.14/0.41 & ~ ( Phi @ Ts @ Va ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.hchop_neg1
% 0.14/0.41 thf(fact_25_ext__inject,axiom,
% 0.14/0.41 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z,Ext2: real_int,Lan2: nat_int,Own2: cars,More2: Z] :
% 0.14/0.41 ( ( ( view_ext2 @ Z @ Ext @ Lan @ Own @ More )
% 0.14/0.41 = ( view_ext2 @ Z @ Ext2 @ Lan2 @ Own2 @ More2 ) )
% 0.14/0.41 = ( ( Ext = Ext2 )
% 0.14/0.41 & ( Lan = Lan2 )
% 0.14/0.41 & ( Own = Own2 )
% 0.14/0.41 & ( More = More2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % ext_inject
% 0.14/0.41 thf(fact_26_cases,axiom,
% 0.14/0.41 ! [R: view_ext @ product_unit] :
% 0.14/0.41 ~ ! [Ext3: real_int,Lan3: nat_int,Own3: cars] :
% 0.14/0.41 ( R
% 0.14/0.41 != ( view_ext2 @ product_unit @ Ext3 @ Lan3 @ Own3 @ product_Unity ) ) ).
% 0.14/0.41
% 0.14/0.41 % cases
% 0.14/0.41 thf(fact_27_induct,axiom,
% 0.14/0.41 ! [P: ( view_ext @ product_unit ) > $o,R: view_ext @ product_unit] :
% 0.14/0.41 ( ! [Ext3: real_int,Lan3: nat_int,Own3: cars] : ( P @ ( view_ext2 @ product_unit @ Ext3 @ Lan3 @ Own3 @ product_Unity ) )
% 0.14/0.41 => ( P @ R ) ) ).
% 0.14/0.41
% 0.14/0.41 % induct
% 0.14/0.41 thf(fact_28_traffic_Ocr__clm,axiom,
% 0.14/0.41 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts7 )
% 0.14/0.41 => ( ? [C3: cars,N2: nat] : ( create_claim @ Ts7 @ C3 @ N2 @ Ts8 )
% 0.14/0.41 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.cr_clm
% 0.14/0.41 thf(fact_29_traffic_Owd__clm,axiom,
% 0.14/0.41 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts7 )
% 0.14/0.41 => ( ? [C3: cars] : ( withdraw_claim @ Ts7 @ C3 @ Ts8 )
% 0.14/0.41 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.wd_clm
% 0.14/0.41 thf(fact_30_traffic_Owd__res,axiom,
% 0.14/0.41 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts7 )
% 0.14/0.41 => ( ? [C3: cars,N2: nat] : ( withdraw_reservation @ Ts7 @ C3 @ N2 @ Ts8 )
% 0.14/0.41 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.wd_res
% 0.14/0.41 thf(fact_31_minus__apply,axiom,
% 0.14/0.41 ! [B: $tType,A: $tType] :
% 0.14/0.41 ( ( minus @ B )
% 0.14/0.41 => ( ( minus_minus @ ( A > B ) )
% 0.14/0.41 = ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % minus_apply
% 0.14/0.41 thf(fact_32_traffic_Ocr__res,axiom,
% 0.14/0.41 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts7 )
% 0.14/0.41 => ( ? [C3: cars] : ( create_reservation @ Ts7 @ C3 @ Ts8 )
% 0.14/0.41 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.cr_res
% 0.14/0.41 thf(fact_33_select__convs_I3_J,axiom,
% 0.14/0.41 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
% 0.14/0.41 ( ( own @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
% 0.14/0.41 = Own ) ).
% 0.14/0.41
% 0.14/0.41 % select_convs(3)
% 0.14/0.41 thf(fact_34_select__convs_I2_J,axiom,
% 0.14/0.41 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
% 0.14/0.41 ( ( lan @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
% 0.14/0.41 = Lan ) ).
% 0.14/0.41
% 0.14/0.41 % select_convs(2)
% 0.14/0.41 thf(fact_35_fun__diff__def,axiom,
% 0.14/0.41 ! [B: $tType,A: $tType] :
% 0.14/0.41 ( ( minus @ B )
% 0.14/0.41 => ( ( minus_minus @ ( A > B ) )
% 0.14/0.41 = ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_diff_def
% 0.14/0.41 thf(fact_36_view_Ohorizontal__chop__empty__right,axiom,
% 0.14/0.41 ! [V: view_ext @ product_unit] :
% 0.14/0.41 ? [X_1: view_ext @ product_unit] : ( hchop @ V @ V @ X_1 ) ).
% 0.14/0.41
% 0.14/0.41 % view.horizontal_chop_empty_right
% 0.14/0.41 thf(fact_37_view_Ohorizontal__chop__empty__left,axiom,
% 0.14/0.41 ! [V: view_ext @ product_unit] :
% 0.14/0.41 ? [U2: view_ext @ product_unit] : ( hchop @ V @ U2 @ V ) ).
% 0.14/0.41
% 0.14/0.41 % view.horizontal_chop_empty_left
% 0.14/0.41 thf(fact_38_view_Ohorizontal__chop__assoc2,axiom,
% 0.14/0.41 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 0.14/0.41 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.14/0.41 & ( hchop @ V1 @ V32 @ V4 ) )
% 0.14/0.41 => ? [V5: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V2 @ V32 @ V5 )
% 0.14/0.41 & ( hchop @ V5 @ V4 @ V22 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % view.horizontal_chop_assoc2
% 0.14/0.41 thf(fact_39_view_Ohorizontal__chop__assoc1,axiom,
% 0.14/0.41 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 0.14/0.41 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.14/0.41 & ( hchop @ V22 @ V32 @ V4 ) )
% 0.14/0.41 => ? [V5: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V2 @ V5 @ V4 )
% 0.14/0.41 & ( hchop @ V5 @ V1 @ V32 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % view.horizontal_chop_assoc1
% 0.14/0.41 thf(fact_40_view_Ohorizontal__chop1,axiom,
% 0.14/0.41 ! [V2: view_ext @ product_unit] :
% 0.14/0.41 ? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( hchop @ V2 @ U2 @ X_1 ) ).
% 0.14/0.41
% 0.14/0.41 % view.horizontal_chop1
% 0.14/0.41 thf(fact_41_traffic_Oabstract_Orefl,axiom,
% 0.14/0.41 ! [Ts5: traffic] : ( abstract @ Ts5 @ Ts5 ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.abstract.refl
% 0.14/0.41 thf(fact_42_traffic_Oabs__trans,axiom,
% 0.14/0.41 ! [Ts1: traffic,Ts22: traffic,Ts0: traffic] :
% 0.14/0.41 ( ( abstract @ Ts1 @ Ts22 )
% 0.14/0.41 => ( ( abstract @ Ts0 @ Ts1 )
% 0.14/0.41 => ( abstract @ Ts0 @ Ts22 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.abs_trans
% 0.14/0.41 thf(fact_43_induct__scheme,axiom,
% 0.14/0.41 ! [Z: $tType,P: ( view_ext @ Z ) > $o,R: view_ext @ Z] :
% 0.14/0.41 ( ! [Ext3: real_int,Lan3: nat_int,Own3: cars,More3: Z] : ( P @ ( view_ext2 @ Z @ Ext3 @ Lan3 @ Own3 @ More3 ) )
% 0.14/0.41 => ( P @ R ) ) ).
% 0.14/0.41
% 0.14/0.41 % induct_scheme
% 0.14/0.41 thf(fact_44_cases__scheme,axiom,
% 0.14/0.41 ! [Z: $tType,R: view_ext @ Z] :
% 0.14/0.41 ~ ! [Ext3: real_int,Lan3: nat_int,Own3: cars,More3: Z] :
% 0.14/0.41 ( R
% 0.14/0.41 != ( view_ext2 @ Z @ Ext3 @ Lan3 @ Own3 @ More3 ) ) ).
% 0.14/0.41
% 0.14/0.41 % cases_scheme
% 0.14/0.41 thf(fact_45_ext,axiom,
% 0.14/0.41 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.14/0.41 ( ! [X2: A] :
% 0.14/0.41 ( ( F @ X2 )
% 0.14/0.41 = ( G @ X2 ) )
% 0.14/0.41 => ( F = G ) ) ).
% 0.14/0.41
% 0.14/0.41 % ext
% 0.14/0.41 thf(fact_46_traffic_Oalways__create__res,axiom,
% 0.14/0.41 ! [C2: cars,Ts: traffic] :
% 0.14/0.41 ? [X_1: traffic] : ( create_reservation @ Ts @ C2 @ X_1 ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.always_create_res
% 0.14/0.41 thf(fact_47_view_Ohorizontal__chop__own__trans,axiom,
% 0.14/0.41 ! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V2 @ U3 @ W2 )
% 0.14/0.41 => ( ( own @ product_unit @ U3 )
% 0.14/0.41 = ( own @ product_unit @ W2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % view.horizontal_chop_own_trans
% 0.14/0.41 thf(fact_48_select__convs_I1_J,axiom,
% 0.14/0.41 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
% 0.14/0.41 ( ( ext @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
% 0.14/0.41 = Ext ) ).
% 0.14/0.41
% 0.14/0.41 % select_convs(1)
% 0.14/0.41 thf(fact_49_traffic_Ocreate__reservation__def,axiom,
% 0.14/0.41 ( create_reservation
% 0.14/0.41 = ( ^ [Ts6: traffic,C4: cars,Ts4: traffic] :
% 0.14/0.41 ( ( ( pos @ Ts4 )
% 0.14/0.41 = ( pos @ Ts6 ) )
% 0.14/0.41 & ( ( res @ Ts4 )
% 0.14/0.41 = ( fun_upd @ cars @ nat_int @ ( res @ Ts6 ) @ C4 @ ( nat_union @ ( res @ Ts6 @ C4 ) @ ( clm @ Ts6 @ C4 ) ) ) )
% 0.14/0.41 & ( ( dyn @ Ts4 )
% 0.14/0.41 = ( dyn @ Ts6 ) )
% 0.14/0.41 & ( ( clm @ Ts4 )
% 0.14/0.41 = ( fun_upd @ cars @ nat_int @ ( clm @ Ts6 ) @ C4 @ ( bot_bot @ nat_int ) ) )
% 0.14/0.41 & ( ( physical_size @ Ts4 )
% 0.14/0.41 = ( physical_size @ Ts6 ) )
% 0.14/0.41 & ( ( braking_distance @ Ts4 )
% 0.14/0.41 = ( braking_distance @ Ts6 ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.create_reservation_def
% 0.14/0.41 thf(fact_50_traffic_Oabstract_Oinducts,axiom,
% 0.14/0.41 ! [Ts5: traffic,X3: traffic,P: traffic > $o] :
% 0.14/0.41 ( ( abstract @ Ts5 @ X3 )
% 0.14/0.41 => ( ( P @ Ts5 )
% 0.14/0.41 => ( ! [Ts2: traffic,Ts9: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ( ( P @ Ts2 )
% 0.14/0.41 => ( ( evolve @ Ts2 @ Ts9 )
% 0.14/0.41 => ( P @ Ts9 ) ) ) )
% 0.14/0.41 => ( ! [Ts2: traffic,Ts9: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ( ( P @ Ts2 )
% 0.14/0.41 => ( ? [C: cars,N3: nat] : ( create_claim @ Ts2 @ C @ N3 @ Ts9 )
% 0.14/0.41 => ( P @ Ts9 ) ) ) )
% 0.14/0.41 => ( ! [Ts2: traffic,Ts9: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ( ( P @ Ts2 )
% 0.14/0.41 => ( ? [C: cars] : ( withdraw_claim @ Ts2 @ C @ Ts9 )
% 0.14/0.41 => ( P @ Ts9 ) ) ) )
% 0.14/0.41 => ( ! [Ts2: traffic,Ts9: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ( ( P @ Ts2 )
% 0.14/0.41 => ( ? [C: cars] : ( create_reservation @ Ts2 @ C @ Ts9 )
% 0.14/0.41 => ( P @ Ts9 ) ) ) )
% 0.14/0.41 => ( ! [Ts2: traffic,Ts9: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ( ( P @ Ts2 )
% 0.14/0.41 => ( ? [C: cars,N3: nat] : ( withdraw_reservation @ Ts2 @ C @ N3 @ Ts9 )
% 0.14/0.41 => ( P @ Ts9 ) ) ) )
% 0.14/0.41 => ( P @ X3 ) ) ) ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.abstract.inducts
% 0.14/0.41 thf(fact_51_traffic_Oabstract_Osimps,axiom,
% 0.14/0.41 ( abstract
% 0.14/0.41 = ( ^ [Ts6: traffic,A3: traffic] :
% 0.14/0.41 ( ( A3 = Ts6 )
% 0.14/0.41 | ? [Ts4: traffic,Ts10: traffic] :
% 0.14/0.41 ( ( A3 = Ts10 )
% 0.14/0.41 & ( abstract @ Ts6 @ Ts4 )
% 0.14/0.41 & ( evolve @ Ts4 @ Ts10 ) )
% 0.14/0.41 | ? [Ts4: traffic,Ts10: traffic] :
% 0.14/0.41 ( ( A3 = Ts10 )
% 0.14/0.41 & ( abstract @ Ts6 @ Ts4 )
% 0.14/0.41 & ? [C4: cars,N4: nat] : ( create_claim @ Ts4 @ C4 @ N4 @ Ts10 ) )
% 0.14/0.41 | ? [Ts4: traffic,Ts10: traffic] :
% 0.14/0.41 ( ( A3 = Ts10 )
% 0.14/0.41 & ( abstract @ Ts6 @ Ts4 )
% 0.14/0.41 & ? [C4: cars] : ( withdraw_claim @ Ts4 @ C4 @ Ts10 ) )
% 0.14/0.41 | ? [Ts4: traffic,Ts10: traffic] :
% 0.14/0.41 ( ( A3 = Ts10 )
% 0.14/0.41 & ( abstract @ Ts6 @ Ts4 )
% 0.14/0.41 & ? [C4: cars] : ( create_reservation @ Ts4 @ C4 @ Ts10 ) )
% 0.14/0.41 | ? [Ts4: traffic,Ts10: traffic] :
% 0.14/0.41 ( ( A3 = Ts10 )
% 0.14/0.41 & ( abstract @ Ts6 @ Ts4 )
% 0.14/0.41 & ? [C4: cars,N4: nat] : ( withdraw_reservation @ Ts4 @ C4 @ N4 @ Ts10 ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.abstract.simps
% 0.14/0.41 thf(fact_52_traffic_Oabstract_Ocases,axiom,
% 0.14/0.41 ! [Ts5: traffic,A4: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ A4 )
% 0.14/0.41 => ( ( A4 != Ts5 )
% 0.14/0.41 => ( ! [Ts2: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ~ ( evolve @ Ts2 @ A4 ) )
% 0.14/0.41 => ( ! [Ts2: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ~ ? [C: cars,N3: nat] : ( create_claim @ Ts2 @ C @ N3 @ A4 ) )
% 0.14/0.41 => ( ! [Ts2: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ~ ? [C: cars] : ( withdraw_claim @ Ts2 @ C @ A4 ) )
% 0.14/0.41 => ( ! [Ts2: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ~ ? [C: cars] : ( create_reservation @ Ts2 @ C @ A4 ) )
% 0.14/0.41 => ~ ! [Ts2: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts2 )
% 0.14/0.41 => ~ ? [C: cars,N3: nat] : ( withdraw_reservation @ Ts2 @ C @ N3 @ A4 ) ) ) ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.abstract.cases
% 0.14/0.41 thf(fact_53_surjective,axiom,
% 0.14/0.41 ! [Z: $tType,R: view_ext @ Z] :
% 0.14/0.41 ( R
% 0.14/0.41 = ( view_ext2 @ Z @ ( ext @ Z @ R ) @ ( lan @ Z @ R ) @ ( own @ Z @ R ) @ ( more @ Z @ R ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % surjective
% 0.14/0.41 thf(fact_54_traffic_Owithdraw__clm__eq__res,axiom,
% 0.14/0.41 ! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
% 0.14/0.41 ( ( withdraw_claim @ Ts5 @ D @ Ts7 )
% 0.14/0.41 => ( ( res @ Ts5 @ C2 )
% 0.14/0.41 = ( res @ Ts7 @ C2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.withdraw_clm_eq_res
% 0.14/0.41 thf(fact_55_traffic_Ocreate__clm__eq__res,axiom,
% 0.14/0.41 ! [Ts5: traffic,D: cars,N: nat,Ts7: traffic,C2: cars] :
% 0.14/0.41 ( ( create_claim @ Ts5 @ D @ N @ Ts7 )
% 0.14/0.41 => ( ( res @ Ts5 @ C2 )
% 0.14/0.41 = ( res @ Ts7 @ C2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.create_clm_eq_res
% 0.14/0.41 thf(fact_56_traffic_Ocreate__res__subseteq1__neq,axiom,
% 0.14/0.41 ! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
% 0.14/0.41 ( ( ( create_reservation @ Ts5 @ D @ Ts7 )
% 0.14/0.41 & ( D != C2 ) )
% 0.14/0.41 => ( ( res @ Ts5 @ C2 )
% 0.14/0.41 = ( res @ Ts7 @ C2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.create_res_subseteq1_neq
% 0.14/0.41 thf(fact_57_traffic_Ocreate__res__subseteq2__neq,axiom,
% 0.14/0.41 ! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
% 0.14/0.41 ( ( ( create_reservation @ Ts5 @ D @ Ts7 )
% 0.14/0.41 & ( D != C2 ) )
% 0.14/0.41 => ( ( clm @ Ts5 @ C2 )
% 0.14/0.41 = ( clm @ Ts7 @ C2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.create_res_subseteq2_neq
% 0.14/0.41 thf(fact_58_traffic_Oevolve__trans,axiom,
% 0.14/0.41 ! [Ts0: traffic,Ts1: traffic,Ts22: traffic] :
% 0.14/0.41 ( ( evolve @ Ts0 @ Ts1 )
% 0.14/0.41 => ( ( evolve @ Ts1 @ Ts22 )
% 0.14/0.41 => ( evolve @ Ts0 @ Ts22 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.evolve_trans
% 0.14/0.41 thf(fact_59_traffic_Oevolve_Orefl,axiom,
% 0.14/0.41 ! [Ts5: traffic] : ( evolve @ Ts5 @ Ts5 ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.evolve.refl
% 0.14/0.41 thf(fact_60_traffic_Owithdraw__claim__def,axiom,
% 0.14/0.41 ( withdraw_claim
% 0.14/0.41 = ( ^ [Ts6: traffic,C4: cars,Ts4: traffic] :
% 0.14/0.41 ( ( ( pos @ Ts4 )
% 0.14/0.41 = ( pos @ Ts6 ) )
% 0.14/0.41 & ( ( res @ Ts4 )
% 0.14/0.41 = ( res @ Ts6 ) )
% 0.14/0.41 & ( ( dyn @ Ts4 )
% 0.14/0.41 = ( dyn @ Ts6 ) )
% 0.14/0.41 & ( ( physical_size @ Ts4 )
% 0.14/0.41 = ( physical_size @ Ts6 ) )
% 0.14/0.41 & ( ( braking_distance @ Ts4 )
% 0.14/0.41 = ( braking_distance @ Ts6 ) )
% 0.14/0.41 & ( ( clm @ Ts4 )
% 0.14/0.41 = ( fun_upd @ cars @ nat_int @ ( clm @ Ts6 ) @ C4 @ ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.withdraw_claim_def
% 0.14/0.41 thf(fact_61_traffic_Oevolve,axiom,
% 0.14/0.41 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 0.14/0.41 ( ( abstract @ Ts5 @ Ts7 )
% 0.14/0.41 => ( ( evolve @ Ts7 @ Ts8 )
% 0.14/0.41 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.evolve
% 0.14/0.41 thf(fact_62_select__convs_I4_J,axiom,
% 0.14/0.41 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
% 0.14/0.41 ( ( more @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
% 0.14/0.41 = More ) ).
% 0.14/0.41
% 0.14/0.41 % select_convs(4)
% 0.14/0.41 thf(fact_63_equality,axiom,
% 0.14/0.41 ! [Z: $tType,R: view_ext @ Z,R2: view_ext @ Z] :
% 0.14/0.41 ( ( ( ext @ Z @ R )
% 0.14/0.41 = ( ext @ Z @ R2 ) )
% 0.14/0.41 => ( ( ( lan @ Z @ R )
% 0.14/0.41 = ( lan @ Z @ R2 ) )
% 0.14/0.41 => ( ( ( own @ Z @ R )
% 0.14/0.41 = ( own @ Z @ R2 ) )
% 0.14/0.41 => ( ( ( more @ Z @ R )
% 0.14/0.41 = ( more @ Z @ R2 ) )
% 0.14/0.41 => ( R = R2 ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % equality
% 0.14/0.41 thf(fact_64_fun__upd__upd,axiom,
% 0.14/0.41 ! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B,Z2: B] :
% 0.14/0.41 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X3 @ Y2 ) @ X3 @ Z2 )
% 0.14/0.41 = ( fun_upd @ A @ B @ F @ X3 @ Z2 ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_upd
% 0.14/0.41 thf(fact_65_fun__upd__triv,axiom,
% 0.14/0.41 ! [B: $tType,A: $tType,F: A > B,X3: A] :
% 0.14/0.41 ( ( fun_upd @ A @ B @ F @ X3 @ ( F @ X3 ) )
% 0.14/0.41 = F ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_triv
% 0.14/0.41 thf(fact_66_fun__upd__apply,axiom,
% 0.14/0.41 ! [A: $tType,B: $tType] :
% 0.14/0.41 ( ( fun_upd @ B @ A )
% 0.14/0.41 = ( ^ [F2: B > A,X: B,Y: A,Z3: B] : ( if @ A @ ( Z3 = X ) @ Y @ ( F2 @ Z3 ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_apply
% 0.14/0.41 thf(fact_67_bot__apply,axiom,
% 0.14/0.41 ! [C5: $tType,D2: $tType] :
% 0.14/0.41 ( ( bot @ C5 )
% 0.14/0.41 => ( ( bot_bot @ ( D2 > C5 ) )
% 0.14/0.41 = ( ^ [X: D2] : ( bot_bot @ C5 ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % bot_apply
% 0.14/0.41 thf(fact_68_un__empty__absorb1,axiom,
% 0.14/0.41 ! [I: nat_int] :
% 0.14/0.41 ( ( nat_union @ I @ ( bot_bot @ nat_int ) )
% 0.14/0.41 = I ) ).
% 0.14/0.41
% 0.14/0.41 % un_empty_absorb1
% 0.14/0.41 thf(fact_69_un__empty__absorb2,axiom,
% 0.14/0.41 ! [I: nat_int] :
% 0.14/0.41 ( ( nat_union @ ( bot_bot @ nat_int ) @ I )
% 0.14/0.41 = I ) ).
% 0.14/0.41
% 0.14/0.41 % un_empty_absorb2
% 0.14/0.41 thf(fact_70_view_Ohchop__def,axiom,
% 0.14/0.41 ( hchop
% 0.14/0.41 = ( ^ [V3: view_ext @ product_unit,U: view_ext @ product_unit,W: view_ext @ product_unit] :
% 0.14/0.41 ( ( real_R_Chop @ ( ext @ product_unit @ V3 ) @ ( ext @ product_unit @ U ) @ ( ext @ product_unit @ W ) )
% 0.14/0.41 & ( ( lan @ product_unit @ V3 )
% 0.14/0.41 = ( lan @ product_unit @ U ) )
% 0.14/0.41 & ( ( lan @ product_unit @ V3 )
% 0.14/0.41 = ( lan @ product_unit @ W ) )
% 0.14/0.41 & ( ( own @ product_unit @ V3 )
% 0.14/0.41 = ( own @ product_unit @ U ) )
% 0.14/0.41 & ( ( own @ product_unit @ V3 )
% 0.14/0.41 = ( own @ product_unit @ W ) )
% 0.14/0.41 & ( ( more @ product_unit @ V3 )
% 0.14/0.41 = ( more @ product_unit @ W ) )
% 0.14/0.41 & ( ( more @ product_unit @ V3 )
% 0.14/0.41 = ( more @ product_unit @ U ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % view.hchop_def
% 0.14/0.41 thf(fact_71_bot__fun__def,axiom,
% 0.14/0.41 ! [B: $tType,A: $tType] :
% 0.14/0.41 ( ( bot @ B )
% 0.14/0.41 => ( ( bot_bot @ ( A > B ) )
% 0.14/0.41 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % bot_fun_def
% 0.14/0.41 thf(fact_72_fun__upd__idem__iff,axiom,
% 0.14/0.41 ! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B] :
% 0.14/0.41 ( ( ( fun_upd @ A @ B @ F @ X3 @ Y2 )
% 0.14/0.41 = F )
% 0.14/0.41 = ( ( F @ X3 )
% 0.14/0.41 = Y2 ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_idem_iff
% 0.14/0.41 thf(fact_73_fun__upd__twist,axiom,
% 0.14/0.41 ! [A: $tType,B: $tType,A4: A,C2: A,M: A > B,B3: B,D: B] :
% 0.14/0.41 ( ( A4 != C2 )
% 0.14/0.41 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ A4 @ B3 ) @ C2 @ D )
% 0.14/0.41 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ C2 @ D ) @ A4 @ B3 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_twist
% 0.14/0.41 thf(fact_74_fun__upd__other,axiom,
% 0.14/0.41 ! [B: $tType,A: $tType,Z2: A,X3: A,F: A > B,Y2: B] :
% 0.14/0.41 ( ( Z2 != X3 )
% 0.14/0.41 => ( ( fun_upd @ A @ B @ F @ X3 @ Y2 @ Z2 )
% 0.14/0.41 = ( F @ Z2 ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_other
% 0.14/0.41 thf(fact_75_fun__upd__same,axiom,
% 0.14/0.41 ! [B: $tType,A: $tType,F: B > A,X3: B,Y2: A] :
% 0.14/0.41 ( ( fun_upd @ B @ A @ F @ X3 @ Y2 @ X3 )
% 0.14/0.41 = Y2 ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_same
% 0.14/0.41 thf(fact_76_fun__upd__idem,axiom,
% 0.14/0.41 ! [A: $tType,B: $tType,F: B > A,X3: B,Y2: A] :
% 0.14/0.41 ( ( ( F @ X3 )
% 0.14/0.41 = Y2 )
% 0.14/0.41 => ( ( fun_upd @ B @ A @ F @ X3 @ Y2 )
% 0.14/0.41 = F ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_idem
% 0.14/0.41 thf(fact_77_fun__upd__eqD,axiom,
% 0.14/0.41 ! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B,G: A > B,Z2: B] :
% 0.14/0.41 ( ( ( fun_upd @ A @ B @ F @ X3 @ Y2 )
% 0.14/0.41 = ( fun_upd @ A @ B @ G @ X3 @ Z2 ) )
% 0.14/0.41 => ( Y2 = Z2 ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_eqD
% 0.14/0.41 thf(fact_78_fun__upd__def,axiom,
% 0.14/0.41 ! [B: $tType,A: $tType] :
% 0.14/0.41 ( ( fun_upd @ A @ B )
% 0.14/0.41 = ( ^ [F2: A > B,A3: A,B4: B,X: A] : ( if @ B @ ( X = A3 ) @ B4 @ ( F2 @ X ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % fun_upd_def
% 0.14/0.41 thf(fact_79_traffic_Ochange__dyn__def,axiom,
% 0.14/0.41 ( change_dyn
% 0.14/0.41 = ( ^ [Ts6: traffic,C4: cars,F2: real > real,Ts4: traffic] :
% 0.14/0.41 ( ( ( pos @ Ts4 )
% 0.14/0.41 = ( pos @ Ts6 ) )
% 0.14/0.41 & ( ( res @ Ts4 )
% 0.14/0.41 = ( res @ Ts6 ) )
% 0.14/0.41 & ( ( clm @ Ts4 )
% 0.14/0.41 = ( clm @ Ts6 ) )
% 0.14/0.41 & ( ( dyn @ Ts4 )
% 0.14/0.41 = ( fun_upd @ cars @ ( real > real ) @ ( dyn @ Ts6 ) @ C4 @ F2 ) )
% 0.14/0.41 & ( ( physical_size @ Ts4 )
% 0.14/0.41 = ( physical_size @ Ts6 ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % traffic.change_dyn_def
% 0.14/0.41 thf(fact_80_local_Ohmlsl_Owidth__hchop__stable,axiom,
% 0.14/0.41 ! [X3: nat,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 0.14/0.41 = X3 )
% 0.14/0.41 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.41 ( ( hchop @ V @ W @ U )
% 0.14/0.41 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 0.14/0.41 = X3 )
% 0.14/0.41 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 0.14/0.41 = X3 ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.width_hchop_stable
% 0.14/0.41 thf(fact_81_chop__singleton__right,axiom,
% 0.14/0.41 ! [R3: real_int] :
% 0.14/0.41 ? [X_1: real_int] : ( real_R_Chop @ R3 @ R3 @ X_1 ) ).
% 0.14/0.41
% 0.14/0.41 % chop_singleton_right
% 0.14/0.41 thf(fact_82_real__int__class_Ochop__always__possible,axiom,
% 0.14/0.41 ! [R3: real_int] :
% 0.14/0.41 ? [S: real_int,X_1: real_int] : ( real_R_Chop @ R3 @ S @ X_1 ) ).
% 0.14/0.41
% 0.14/0.41 % real_int_class.chop_always_possible
% 0.14/0.41 thf(fact_83_chop__singleton__left,axiom,
% 0.14/0.41 ! [R3: real_int] :
% 0.14/0.41 ? [S: real_int] : ( real_R_Chop @ R3 @ S @ R3 ) ).
% 0.14/0.41
% 0.14/0.41 % chop_singleton_left
% 0.14/0.41 thf(fact_84_view_Oswitch__def,axiom,
% 0.14/0.41 ( switch
% 0.14/0.41 = ( ^ [V3: view_ext @ product_unit,C4: cars,W: view_ext @ product_unit] :
% 0.14/0.41 ( ( ( ext @ product_unit @ V3 )
% 0.14/0.41 = ( ext @ product_unit @ W ) )
% 0.14/0.41 & ( ( lan @ product_unit @ V3 )
% 0.14/0.41 = ( lan @ product_unit @ W ) )
% 0.14/0.41 & ( ( own @ product_unit @ W )
% 0.14/0.41 = C4 )
% 0.14/0.41 & ( ( more @ product_unit @ V3 )
% 0.14/0.41 = ( more @ product_unit @ W ) ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % view.switch_def
% 0.14/0.41 thf(fact_85_local_Ohmlsl_Oat__conj__distr,axiom,
% 0.14/0.41 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( ! [V6: view_ext @ product_unit] :
% 0.14/0.41 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.41 => ( ( Phi @ Ts @ V6 )
% 0.14/0.41 & ( Psi @ Ts @ V6 ) ) ) )
% 0.14/0.41 = ( ! [V6: view_ext @ product_unit] :
% 0.14/0.41 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.41 => ( Phi @ Ts @ V6 ) )
% 0.14/0.41 & ! [V6: view_ext @ product_unit] :
% 0.14/0.41 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.41 => ( Psi @ Ts @ V6 ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.at_conj_distr
% 0.14/0.41 thf(fact_86_local_Ohmlsl_Oat__disj__dist,axiom,
% 0.14/0.41 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( ! [V6: view_ext @ product_unit] :
% 0.14/0.41 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.41 => ( ( Phi @ Ts @ V6 )
% 0.14/0.41 | ( Psi @ Ts @ V6 ) ) ) )
% 0.14/0.41 = ( ! [V6: view_ext @ product_unit] :
% 0.14/0.41 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.41 => ( Phi @ Ts @ V6 ) )
% 0.14/0.41 | ! [V6: view_ext @ product_unit] :
% 0.14/0.41 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.41 => ( Psi @ Ts @ V6 ) ) ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.at_disj_dist
% 0.14/0.41 thf(fact_87_local_Ohmlsl_Oat__eq,axiom,
% 0.14/0.41 ! [A: $tType,E: cars,C2: A,D: A,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.41 ( ( ! [V6: view_ext @ product_unit] :
% 0.14/0.41 ( ( switch @ V @ E @ V6 )
% 0.14/0.41 => ( C2 = D ) ) )
% 0.14/0.41 = ( C2 = D ) ) ).
% 0.14/0.41
% 0.14/0.41 % local.hmlsl.at_eq
% 0.14/0.41 thf(fact_88_local_Ohmlsl_Oat__exists,axiom,
% 0.14/0.41 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ( Phi @ Ts @ V )
% 0.14/0.42 => ? [X2: cars] :
% 0.14/0.42 ! [V7: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ X2 @ V7 )
% 0.14/0.42 => ( Phi @ Ts @ V7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_exists
% 0.14/0.42 thf(fact_89_local_Ohmlsl_Oat__neg,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ( ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.42 => ~ ( Phi @ Ts @ V6 ) ) )
% 0.14/0.42 = ( ~ ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.42 => ( Phi @ Ts @ V6 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_neg
% 0.14/0.42 thf(fact_90_local_Ohmlsl_Oat__neg_H,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts5: traffic] :
% 0.14/0.42 ( ( ~ ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V2 @ C2 @ V6 )
% 0.14/0.42 => ( Phi @ Ts5 @ V6 ) ) )
% 0.14/0.42 = ( ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V2 @ C2 @ V6 )
% 0.14/0.42 => ~ ( Phi @ Ts5 @ V6 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_neg'
% 0.14/0.42 thf(fact_91_local_Ohmlsl_Oat__neg1,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ! [V5: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V5 )
% 0.14/0.42 => ~ ( Phi @ Ts @ V5 ) )
% 0.14/0.42 => ~ ! [V5: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V5 )
% 0.14/0.42 => ( Phi @ Ts @ V5 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_neg1
% 0.14/0.42 thf(fact_92_local_Ohmlsl_Oat__neg2,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ~ ! [V7: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V7 )
% 0.14/0.42 => ( Phi @ Ts @ V7 ) )
% 0.14/0.42 => ! [V7: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V7 )
% 0.14/0.42 => ~ ( Phi @ Ts @ V7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_neg2
% 0.14/0.42 thf(fact_93_local_Ohmlsl_Oat__neg__neg,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ( ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.42 => ( Phi @ Ts @ V6 ) ) )
% 0.14/0.42 = ( ~ ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.42 => ~ ( Phi @ Ts @ V6 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_neg_neg
% 0.14/0.42 thf(fact_94_local_Ohmlsl_Oat__neg__neg1,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ! [V5: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V5 )
% 0.14/0.42 => ( Phi @ Ts @ V5 ) )
% 0.14/0.42 => ~ ! [V5: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V5 )
% 0.14/0.42 => ~ ( Phi @ Ts @ V5 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_neg_neg1
% 0.14/0.42 thf(fact_95_local_Ohmlsl_Oat__neg__neg2,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ~ ! [V7: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V7 )
% 0.14/0.42 => ~ ( Phi @ Ts @ V7 ) )
% 0.14/0.42 => ! [V7: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V7 )
% 0.14/0.42 => ( Phi @ Ts @ V7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_neg_neg2
% 0.14/0.42 thf(fact_96_local_Ohmlsl_Oat__hchop__dist,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V @ W @ U )
% 0.14/0.42 & ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ W @ C2 @ V6 )
% 0.14/0.42 => ( Phi @ Ts @ V6 ) )
% 0.14/0.42 & ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ U @ C2 @ V6 )
% 0.14/0.42 => ( Psi @ Ts @ V6 ) ) ) )
% 0.14/0.42 = ( ! [V6: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V6 )
% 0.14/0.42 => ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V6 @ W @ U )
% 0.14/0.42 & ( Phi @ Ts @ W )
% 0.14/0.42 & ( Psi @ Ts @ U ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_hchop_dist
% 0.14/0.42 thf(fact_97_local_Ohmlsl_Oat__hchop__dist1,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ! [V5: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V5 )
% 0.14/0.42 => ? [Va2: view_ext @ product_unit,U4: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V5 @ Va2 @ U4 )
% 0.14/0.42 & ( Phi @ Ts @ Va2 )
% 0.14/0.42 & ( Psi @ Ts @ U4 ) ) )
% 0.14/0.42 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V @ Va @ U2 )
% 0.14/0.42 & ! [V7: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ Va @ C2 @ V7 )
% 0.14/0.42 => ( Phi @ Ts @ V7 ) )
% 0.14/0.42 & ! [V7: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ U2 @ C2 @ V7 )
% 0.14/0.42 => ( Psi @ Ts @ V7 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_hchop_dist1
% 0.14/0.42 thf(fact_98_local_Ohmlsl_Oat__hchop__dist2,axiom,
% 0.14/0.42 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 0.14/0.42 ( ? [Va2: view_ext @ product_unit,U4: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V @ Va2 @ U4 )
% 0.14/0.42 & ! [V5: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ Va2 @ C2 @ V5 )
% 0.14/0.42 => ( Phi @ Ts @ V5 ) )
% 0.14/0.42 & ! [V5: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ U4 @ C2 @ V5 )
% 0.14/0.42 => ( Psi @ Ts @ V5 ) ) )
% 0.14/0.42 => ! [V7: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V @ C2 @ V7 )
% 0.14/0.42 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V7 @ Va @ U2 )
% 0.14/0.42 & ( Phi @ Ts @ Va )
% 0.14/0.42 & ( Psi @ Ts @ U2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % local.hmlsl.at_hchop_dist2
% 0.14/0.42 thf(fact_99_view_Oswitch__always__exists,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,C3: cars] :
% 0.14/0.42 ? [X_1: view_ext @ product_unit] : ( switch @ V2 @ C3 @ X_1 ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_always_exists
% 0.14/0.42 thf(fact_100_view_Oswitch__triangle,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,D: cars,W2: view_ext @ product_unit] :
% 0.14/0.42 ( ( ( switch @ V2 @ C2 @ U3 )
% 0.14/0.42 & ( switch @ V2 @ D @ W2 ) )
% 0.14/0.42 => ( switch @ U3 @ D @ W2 ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_triangle
% 0.14/0.42 thf(fact_101_view_Oswitch__unique,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.14/0.42 ( ( ( switch @ V2 @ C2 @ U3 )
% 0.14/0.42 & ( switch @ V2 @ C2 @ W2 ) )
% 0.14/0.42 => ( U3 = W2 ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_unique
% 0.14/0.42 thf(fact_102_view_Oswitch__exists,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit] :
% 0.14/0.42 ? [C: cars,X_1: view_ext @ product_unit] : ( switch @ V2 @ C @ X_1 ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_exists
% 0.14/0.42 thf(fact_103_view_Oswitch__trans,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,D: cars,W2: view_ext @ product_unit] :
% 0.14/0.42 ( ( ( switch @ V2 @ C2 @ U3 )
% 0.14/0.42 & ( switch @ U3 @ D @ W2 ) )
% 0.14/0.42 => ( switch @ V2 @ D @ W2 ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_trans
% 0.14/0.42 thf(fact_104_view_Oswitch__hchop1,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,C2: cars,V8: view_ext @ product_unit] :
% 0.14/0.42 ( ( ( hchop @ V2 @ V1 @ V22 )
% 0.14/0.42 & ( switch @ V2 @ C2 @ V8 ) )
% 0.14/0.42 => ? [V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V1 @ C2 @ V12 )
% 0.14/0.42 & ( switch @ V22 @ C2 @ V23 )
% 0.14/0.42 & ( hchop @ V8 @ V12 @ V23 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_hchop1
% 0.14/0.42 thf(fact_105_view_Oswitch__hchop2,axiom,
% 0.14/0.42 ! [V8: view_ext @ product_unit,V13: view_ext @ product_unit,V24: view_ext @ product_unit,V2: view_ext @ product_unit,C2: cars] :
% 0.14/0.42 ( ( ( hchop @ V8 @ V13 @ V24 )
% 0.14/0.42 & ( switch @ V2 @ C2 @ V8 ) )
% 0.14/0.42 => ? [V14: view_ext @ product_unit,V25: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V14 @ C2 @ V13 )
% 0.14/0.42 & ( switch @ V25 @ C2 @ V24 )
% 0.14/0.42 & ( hchop @ V2 @ V14 @ V25 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_hchop2
% 0.14/0.42 thf(fact_106_view_Oswitch__refl,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit] : ( switch @ V2 @ ( own @ product_unit @ V2 ) @ V2 ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_refl
% 0.14/0.42 thf(fact_107_view_Oswitch__symm,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V2 @ C2 @ U3 )
% 0.14/0.42 => ( switch @ U3 @ ( own @ product_unit @ V2 ) @ V2 ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_symm
% 0.14/0.42 thf(fact_108_view_Oswitch__origin,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit] :
% 0.14/0.42 ? [U2: view_ext @ product_unit] : ( switch @ U2 @ ( own @ product_unit @ V2 ) @ V2 ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_origin
% 0.14/0.42 thf(fact_109_view_Ohorizontal__chop__width__stable,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V2 @ U3 @ W2 )
% 0.14/0.42 => ( ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.14/0.42 = ( nat_card @ ( lan @ product_unit @ U3 ) ) )
% 0.14/0.42 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 0.14/0.42 = ( nat_card @ ( lan @ product_unit @ W2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.horizontal_chop_width_stable
% 0.14/0.42 thf(fact_110_traffic_Ochange,axiom,
% 0.14/0.42 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 0.14/0.42 ( ? [C3: cars,F3: real > real] : ( change_dyn @ Ts5 @ C3 @ F3 @ Ts7 )
% 0.14/0.42 => ( ( evolve @ Ts7 @ Ts8 )
% 0.14/0.42 => ( evolve @ Ts5 @ Ts8 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % traffic.change
% 0.14/0.42 thf(fact_111_old_Ounit_Oexhaust,axiom,
% 0.14/0.42 ! [Y2: product_unit] : ( Y2 = product_Unity ) ).
% 0.14/0.42
% 0.14/0.42 % old.unit.exhaust
% 0.14/0.42 thf(fact_112_old_Ounit_Oinducts,axiom,
% 0.14/0.42 ! [P: product_unit > $o,Unit: product_unit] :
% 0.14/0.42 ( ( P @ product_Unity )
% 0.14/0.42 => ( P @ Unit ) ) ).
% 0.14/0.42
% 0.14/0.42 % old.unit.inducts
% 0.14/0.42 thf(fact_113_unit__all__impI,axiom,
% 0.14/0.42 ! [P: product_unit > $o,Q: product_unit > $o] :
% 0.14/0.42 ( ( ( P @ product_Unity )
% 0.14/0.42 => ( Q @ product_Unity ) )
% 0.14/0.42 => ! [X4: product_unit] :
% 0.14/0.42 ( ( P @ X4 )
% 0.14/0.42 => ( Q @ X4 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % unit_all_impI
% 0.14/0.42 thf(fact_114_eq__sym__Unity__conv,axiom,
% 0.14/0.42 ! [X3: $o] :
% 0.14/0.42 ( ( X3
% 0.14/0.42 = ( product_Unity = product_Unity ) )
% 0.14/0.42 = X3 ) ).
% 0.14/0.42
% 0.14/0.42 % eq_sym_Unity_conv
% 0.14/0.42 thf(fact_115_bot__unit__def,axiom,
% 0.14/0.42 ( ( bot_bot @ product_unit )
% 0.14/0.42 = product_Unity ) ).
% 0.14/0.42
% 0.14/0.42 % bot_unit_def
% 0.14/0.42 thf(fact_116_traffic_Ocreate__res__subseteq2,axiom,
% 0.14/0.42 ! [Ts5: traffic,C2: cars,Ts7: traffic] :
% 0.14/0.42 ( ( create_reservation @ Ts5 @ C2 @ Ts7 )
% 0.14/0.42 => ( ord_less_eq @ nat_int @ ( clm @ Ts5 @ C2 ) @ ( res @ Ts7 @ C2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % traffic.create_res_subseteq2
% 0.14/0.42 thf(fact_117_order__refl,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_refl
% 0.14/0.42 thf(fact_118_le__funD,axiom,
% 0.14/0.42 ! [B: $tType,A: $tType] :
% 0.14/0.42 ( ( ord @ B )
% 0.14/0.42 => ! [F: A > B,G: A > B,X3: A] :
% 0.14/0.42 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.14/0.42 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_funD
% 0.14/0.42 thf(fact_119_le__funE,axiom,
% 0.14/0.42 ! [B: $tType,A: $tType] :
% 0.14/0.42 ( ( ord @ B )
% 0.14/0.42 => ! [F: A > B,G: A > B,X3: A] :
% 0.14/0.42 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.14/0.42 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_funE
% 0.14/0.42 thf(fact_120_le__funI,axiom,
% 0.14/0.42 ! [B: $tType,A: $tType] :
% 0.14/0.42 ( ( ord @ B )
% 0.14/0.42 => ! [F: A > B,G: A > B] :
% 0.14/0.42 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.14/0.42 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_funI
% 0.14/0.42 thf(fact_121_le__fun__def,axiom,
% 0.14/0.42 ! [B: $tType,A: $tType] :
% 0.14/0.42 ( ( ord @ B )
% 0.14/0.42 => ( ( ord_less_eq @ ( A > B ) )
% 0.14/0.42 = ( ^ [F2: A > B,G2: A > B] :
% 0.14/0.42 ! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_fun_def
% 0.14/0.42 thf(fact_122_order__subst1,axiom,
% 0.14/0.42 ! [A: $tType,B: $tType] :
% 0.14/0.42 ( ( ( order @ B )
% 0.14/0.42 & ( order @ A ) )
% 0.14/0.42 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
% 0.14/0.42 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.14/0.42 => ( ! [X2: B,Y3: B] :
% 0.14/0.42 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_subst1
% 0.14/0.42 thf(fact_123_order__subst2,axiom,
% 0.14/0.42 ! [A: $tType,C5: $tType] :
% 0.14/0.42 ( ( ( order @ C5 )
% 0.14/0.42 & ( order @ A ) )
% 0.14/0.42 => ! [A4: A,B3: A,F: A > C5,C2: C5] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less_eq @ C5 @ ( F @ B3 ) @ C2 )
% 0.14/0.42 => ( ! [X2: A,Y3: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less_eq @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less_eq @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_subst2
% 0.14/0.42 thf(fact_124_ord__eq__le__subst,axiom,
% 0.14/0.42 ! [A: $tType,B: $tType] :
% 0.14/0.42 ( ( ( ord @ B )
% 0.14/0.42 & ( ord @ A ) )
% 0.14/0.42 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 0.14/0.42 ( ( A4
% 0.14/0.42 = ( F @ B3 ) )
% 0.14/0.42 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.14/0.42 => ( ! [X2: B,Y3: B] :
% 0.14/0.42 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % ord_eq_le_subst
% 0.14/0.42 thf(fact_125_ord__le__eq__subst,axiom,
% 0.14/0.42 ! [A: $tType,B: $tType] :
% 0.14/0.42 ( ( ( ord @ B )
% 0.14/0.42 & ( ord @ A ) )
% 0.14/0.42 => ! [A4: A,B3: A,F: A > B,C2: B] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ( F @ B3 )
% 0.14/0.42 = C2 )
% 0.14/0.42 => ( ! [X2: A,Y3: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % ord_le_eq_subst
% 0.14/0.42 thf(fact_126_eq__iff,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ^ [Y4: A,Z4: A] : ( Y4 = Z4 ) )
% 0.14/0.42 = ( ^ [X: A,Y: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X @ Y )
% 0.14/0.42 & ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % eq_iff
% 0.14/0.42 thf(fact_127_antisym,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.14/0.42 => ( X3 = Y2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % antisym
% 0.14/0.42 thf(fact_128_linear,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 | ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % linear
% 0.14/0.42 thf(fact_129_eq__refl,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( X3 = Y2 )
% 0.14/0.42 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % eq_refl
% 0.14/0.42 thf(fact_130_le__cases,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ~ ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_cases
% 0.14/0.42 thf(fact_131_order_Otrans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.14/0.42 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.trans
% 0.14/0.42 thf(fact_132_le__cases3,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A,Z2: A] :
% 0.14/0.42 ( ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 0.14/0.42 => ( ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.14/0.42 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.14/0.42 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.14/0.42 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 0.14/0.42 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 0.14/0.42 => ~ ( ord_less_eq @ A @ Y2 @ X3 ) )
% 0.14/0.42 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.14/0.42 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.14/0.42 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.14/0.42 => ~ ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_cases3
% 0.14/0.42 thf(fact_133_antisym__conv,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [Y2: A,X3: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 = ( X3 = Y2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % antisym_conv
% 0.14/0.42 thf(fact_134_order__class_Oorder_Oeq__iff,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ^ [Y4: A,Z4: A] : ( Y4 = Z4 ) )
% 0.14/0.42 = ( ^ [A3: A,B4: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.14/0.42 & ( ord_less_eq @ A @ B4 @ A3 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_class.order.eq_iff
% 0.14/0.42 thf(fact_135_ord__eq__le__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ord @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( A4 = B3 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.14/0.42 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % ord_eq_le_trans
% 0.14/0.42 thf(fact_136_ord__le__eq__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ord @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( B3 = C2 )
% 0.14/0.42 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % ord_le_eq_trans
% 0.14/0.42 thf(fact_137_order__class_Oorder_Oantisym,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.14/0.42 => ( A4 = B3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_class.order.antisym
% 0.14/0.42 thf(fact_138_order__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A,Z2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.14/0.42 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_trans
% 0.14/0.42 thf(fact_139_dual__order_Orefl,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.refl
% 0.14/0.42 thf(fact_140_linorder__wlog,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [P: A > A > $o,A4: A,B3: A] :
% 0.14/0.42 ( ! [A5: A,B5: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.14/0.42 => ( P @ A5 @ B5 ) )
% 0.14/0.42 => ( ! [A5: A,B5: A] :
% 0.14/0.42 ( ( P @ B5 @ A5 )
% 0.14/0.42 => ( P @ A5 @ B5 ) )
% 0.14/0.42 => ( P @ A4 @ B3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % linorder_wlog
% 0.14/0.42 thf(fact_141_dual__order_Otrans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [B3: A,A4: A,C2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 0.14/0.42 => ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.trans
% 0.14/0.42 thf(fact_142_dual__order_Oeq__iff,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ^ [Y4: A,Z4: A] : ( Y4 = Z4 ) )
% 0.14/0.42 = ( ^ [A3: A,B4: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.14/0.42 & ( ord_less_eq @ A @ A3 @ B4 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.eq_iff
% 0.14/0.42 thf(fact_143_dual__order_Oantisym,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [B3: A,A4: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( A4 = B3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.antisym
% 0.14/0.42 thf(fact_144_less__eq__view__ext__def,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ord_less_eq @ ( view_ext @ A ) )
% 0.14/0.42 = ( ^ [V9: view_ext @ A,V10: view_ext @ A] :
% 0.14/0.42 ( ( ord_less_eq @ real_int @ ( ext @ A @ V9 ) @ ( ext @ A @ V10 ) )
% 0.14/0.42 & ( ord_less_eq @ nat_int @ ( lan @ A @ V9 ) @ ( lan @ A @ V10 ) )
% 0.14/0.42 & ( ( own @ A @ V9 )
% 0.14/0.42 = ( own @ A @ V10 ) )
% 0.14/0.42 & ( ord_less_eq @ A @ ( more @ A @ V9 ) @ ( more @ A @ V10 ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_eq_view_ext_def
% 0.14/0.42 thf(fact_145_bot_Oextremum,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order_bot @ A )
% 0.14/0.42 => ! [A4: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A4 ) ) ).
% 0.14/0.42
% 0.14/0.42 % bot.extremum
% 0.14/0.42 thf(fact_146_bot_Oextremum__unique,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order_bot @ A )
% 0.14/0.42 => ! [A4: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ ( bot_bot @ A ) )
% 0.14/0.42 = ( A4
% 0.14/0.42 = ( bot_bot @ A ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % bot.extremum_unique
% 0.14/0.42 thf(fact_147_bot_Oextremum__uniqueI,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order_bot @ A )
% 0.14/0.42 => ! [A4: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ ( bot_bot @ A ) )
% 0.14/0.42 => ( A4
% 0.14/0.42 = ( bot_bot @ A ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % bot.extremum_uniqueI
% 0.14/0.42 thf(fact_148_traffic_Ocreate__res__subseteq1,axiom,
% 0.14/0.42 ! [Ts5: traffic,C2: cars,Ts7: traffic] :
% 0.14/0.42 ( ( create_reservation @ Ts5 @ C2 @ Ts7 )
% 0.14/0.42 => ( ord_less_eq @ nat_int @ ( res @ Ts5 @ C2 ) @ ( res @ Ts7 @ C2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % traffic.create_res_subseteq1
% 0.14/0.42 thf(fact_149_traffic_Owithdraw__res__subseteq,axiom,
% 0.14/0.42 ! [Ts5: traffic,D: cars,N: nat,Ts7: traffic,C2: cars] :
% 0.14/0.42 ( ( withdraw_reservation @ Ts5 @ D @ N @ Ts7 )
% 0.14/0.42 => ( ord_less_eq @ nat_int @ ( res @ Ts7 @ C2 ) @ ( res @ Ts5 @ C2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % traffic.withdraw_res_subseteq
% 0.14/0.42 thf(fact_150_old_Ounit_Orec,axiom,
% 0.14/0.42 ! [T: $tType,F1: T] :
% 0.14/0.42 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 0.14/0.42 = F1 ) ).
% 0.14/0.42
% 0.14/0.42 % old.unit.rec
% 0.14/0.42 thf(fact_151_default__unit__def,axiom,
% 0.14/0.42 ( ( default_default @ product_unit )
% 0.14/0.42 = product_Unity ) ).
% 0.14/0.42
% 0.14/0.42 % default_unit_def
% 0.14/0.42 thf(fact_152_less__view__ext__def,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ord_less @ ( view_ext @ A ) )
% 0.14/0.42 = ( ^ [V9: view_ext @ A,V10: view_ext @ A] :
% 0.14/0.42 ( ( ord_less_eq @ real_int @ ( ext @ A @ V9 ) @ ( ext @ A @ V10 ) )
% 0.14/0.42 & ( ord_less_eq @ nat_int @ ( lan @ A @ V9 ) @ ( lan @ A @ V10 ) )
% 0.14/0.42 & ( ( own @ A @ V10 )
% 0.14/0.42 = ( own @ A @ V9 ) )
% 0.14/0.42 & ( ord_less_eq @ A @ ( more @ A @ V9 ) @ ( more @ A @ V10 ) )
% 0.14/0.42 & ~ ( ( ord_less_eq @ real_int @ ( ext @ A @ V10 ) @ ( ext @ A @ V9 ) )
% 0.14/0.42 & ( ord_less_eq @ nat_int @ ( lan @ A @ V10 ) @ ( lan @ A @ V9 ) )
% 0.14/0.42 & ( ( own @ A @ V10 )
% 0.14/0.42 = ( own @ A @ V9 ) )
% 0.14/0.42 & ( ord_less_eq @ A @ ( more @ A @ V10 ) @ ( more @ A @ V9 ) ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_view_ext_def
% 0.14/0.42 thf(fact_153_diff__mono,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ordered_ab_group_add @ A )
% 0.14/0.42 => ! [A4: A,B3: A,D: A,C2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ D @ C2 )
% 0.14/0.42 => ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_mono
% 0.14/0.42 thf(fact_154_leD,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [Y2: A,X3: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 0.14/0.42 => ~ ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % leD
% 0.14/0.42 thf(fact_155_leI,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % leI
% 0.14/0.42 thf(fact_156_le__less,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ord_less_eq @ A )
% 0.14/0.42 = ( ^ [X: A,Y: A] :
% 0.14/0.42 ( ( ord_less @ A @ X @ Y )
% 0.14/0.42 | ( X = Y ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_less
% 0.14/0.42 thf(fact_157_less__le,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ord_less @ A )
% 0.14/0.42 = ( ^ [X: A,Y: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X @ Y )
% 0.14/0.42 & ( X != Y ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_le
% 0.14/0.42 thf(fact_158_order__le__less__subst1,axiom,
% 0.14/0.42 ! [A: $tType,B: $tType] :
% 0.14/0.42 ( ( ( order @ B )
% 0.14/0.42 & ( order @ A ) )
% 0.14/0.42 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
% 0.14/0.42 => ( ( ord_less @ B @ B3 @ C2 )
% 0.14/0.42 => ( ! [X2: B,Y3: B] :
% 0.14/0.42 ( ( ord_less @ B @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_le_less_subst1
% 0.14/0.42 thf(fact_159_order__le__less__subst2,axiom,
% 0.14/0.42 ! [A: $tType,C5: $tType] :
% 0.14/0.42 ( ( ( order @ C5 )
% 0.14/0.42 & ( order @ A ) )
% 0.14/0.42 => ! [A4: A,B3: A,F: A > C5,C2: C5] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less @ C5 @ ( F @ B3 ) @ C2 )
% 0.14/0.42 => ( ! [X2: A,Y3: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less_eq @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_le_less_subst2
% 0.14/0.42 thf(fact_160_order__less__le__subst1,axiom,
% 0.14/0.42 ! [A: $tType,B: $tType] :
% 0.14/0.42 ( ( ( order @ B )
% 0.14/0.42 & ( order @ A ) )
% 0.14/0.42 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ ( F @ B3 ) )
% 0.14/0.42 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 0.14/0.42 => ( ! [X2: B,Y3: B] :
% 0.14/0.42 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_less_le_subst1
% 0.14/0.42 thf(fact_161_order__less__le__subst2,axiom,
% 0.14/0.42 ! [A: $tType,C5: $tType] :
% 0.14/0.42 ( ( ( order @ C5 )
% 0.14/0.42 & ( order @ A ) )
% 0.14/0.42 => ! [A4: A,B3: A,F: A > C5,C2: C5] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less_eq @ C5 @ ( F @ B3 ) @ C2 )
% 0.14/0.42 => ( ! [X2: A,Y3: A] :
% 0.14/0.42 ( ( ord_less @ A @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_less_le_subst2
% 0.14/0.42 thf(fact_162_not__le,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ~ ( ord_less_eq @ A @ X3 @ Y2 ) )
% 0.14/0.42 = ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % not_le
% 0.14/0.42 thf(fact_163_not__less,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.14/0.42 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % not_less
% 0.14/0.42 thf(fact_164_le__neq__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( A4 != B3 )
% 0.14/0.42 => ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_neq_trans
% 0.14/0.42 thf(fact_165_antisym__conv1,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 = ( X3 = Y2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % antisym_conv1
% 0.14/0.42 thf(fact_166_antisym__conv2,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.14/0.42 = ( X3 = Y2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % antisym_conv2
% 0.14/0.42 thf(fact_167_less__imp__le,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_imp_le
% 0.14/0.42 thf(fact_168_le__less__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A,Z2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ord_less @ A @ Y2 @ Z2 )
% 0.14/0.42 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_less_trans
% 0.14/0.42 thf(fact_169_less__le__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A,Z2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.14/0.42 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_le_trans
% 0.14/0.42 thf(fact_170_dense__ge,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( dense_linorder @ A )
% 0.14/0.42 => ! [Z2: A,Y2: A] :
% 0.14/0.42 ( ! [X2: A] :
% 0.14/0.42 ( ( ord_less @ A @ Z2 @ X2 )
% 0.14/0.42 => ( ord_less_eq @ A @ Y2 @ X2 ) )
% 0.14/0.42 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dense_ge
% 0.14/0.42 thf(fact_171_dense__le,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( dense_linorder @ A )
% 0.14/0.42 => ! [Y2: A,Z2: A] :
% 0.14/0.42 ( ! [X2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X2 @ Y2 )
% 0.14/0.42 => ( ord_less_eq @ A @ X2 @ Z2 ) )
% 0.14/0.42 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dense_le
% 0.14/0.42 thf(fact_172_le__less__linear,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_less_linear
% 0.14/0.42 thf(fact_173_le__imp__less__or__eq,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 | ( X3 = Y2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % le_imp_less_or_eq
% 0.14/0.42 thf(fact_174_less__le__not__le,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ( ( ord_less @ A )
% 0.14/0.42 = ( ^ [X: A,Y: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ X @ Y )
% 0.14/0.42 & ~ ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_le_not_le
% 0.14/0.42 thf(fact_175_not__le__imp__less,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [Y2: A,X3: A] :
% 0.14/0.42 ( ~ ( ord_less_eq @ A @ Y2 @ X3 )
% 0.14/0.42 => ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % not_le_imp_less
% 0.14/0.42 thf(fact_176_order_Ostrict__trans1,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less @ A @ B3 @ C2 )
% 0.14/0.42 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.strict_trans1
% 0.14/0.42 thf(fact_177_order_Ostrict__trans2,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 0.14/0.42 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.strict_trans2
% 0.14/0.42 thf(fact_178_order_Oorder__iff__strict,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ord_less_eq @ A )
% 0.14/0.42 = ( ^ [A3: A,B4: A] :
% 0.14/0.42 ( ( ord_less @ A @ A3 @ B4 )
% 0.14/0.42 | ( A3 = B4 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.order_iff_strict
% 0.14/0.42 thf(fact_179_order_Ostrict__iff__order,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ord_less @ A )
% 0.14/0.42 = ( ^ [A3: A,B4: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A3 @ B4 )
% 0.14/0.42 & ( A3 != B4 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.strict_iff_order
% 0.14/0.42 thf(fact_180_dual__order_Ostrict__trans1,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [B3: A,A4: A,C2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.14/0.42 => ( ( ord_less @ A @ C2 @ B3 )
% 0.14/0.42 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.strict_trans1
% 0.14/0.42 thf(fact_181_dual__order_Ostrict__trans2,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [B3: A,A4: A,C2: A] :
% 0.14/0.42 ( ( ord_less @ A @ B3 @ A4 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 0.14/0.42 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.strict_trans2
% 0.14/0.42 thf(fact_182_dense__ge__bounded,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( dense_linorder @ A )
% 0.14/0.42 => ! [Z2: A,X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ Z2 @ X3 )
% 0.14/0.42 => ( ! [W3: A] :
% 0.14/0.42 ( ( ord_less @ A @ Z2 @ W3 )
% 0.14/0.42 => ( ( ord_less @ A @ W3 @ X3 )
% 0.14/0.42 => ( ord_less_eq @ A @ Y2 @ W3 ) ) )
% 0.14/0.42 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dense_ge_bounded
% 0.14/0.42 thf(fact_183_dense__le__bounded,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( dense_linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A,Z2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ! [W3: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ W3 )
% 0.14/0.42 => ( ( ord_less @ A @ W3 @ Y2 )
% 0.14/0.42 => ( ord_less_eq @ A @ W3 @ Z2 ) ) )
% 0.14/0.42 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dense_le_bounded
% 0.14/0.42 thf(fact_184_order_Ostrict__implies__order,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ord_less_eq @ A @ A4 @ B3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.strict_implies_order
% 0.14/0.42 thf(fact_185_dual__order_Oorder__iff__strict,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ord_less_eq @ A )
% 0.14/0.42 = ( ^ [B4: A,A3: A] :
% 0.14/0.42 ( ( ord_less @ A @ B4 @ A3 )
% 0.14/0.42 | ( A3 = B4 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.order_iff_strict
% 0.14/0.42 thf(fact_186_dual__order_Ostrict__iff__order,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ( ( ord_less @ A )
% 0.14/0.42 = ( ^ [B4: A,A3: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ B4 @ A3 )
% 0.14/0.42 & ( A3 != B4 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.strict_iff_order
% 0.14/0.42 thf(fact_187_dual__order_Ostrict__implies__order,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [B3: A,A4: A] :
% 0.14/0.42 ( ( ord_less @ A @ B3 @ A4 )
% 0.14/0.42 => ( ord_less_eq @ A @ B3 @ A4 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.strict_implies_order
% 0.14/0.42 thf(fact_188_order_Onot__eq__order__implies__strict,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A] :
% 0.14/0.42 ( ( A4 != B3 )
% 0.14/0.42 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.not_eq_order_implies_strict
% 0.14/0.42 thf(fact_189_bot_Oextremum__strict,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order_bot @ A )
% 0.14/0.42 => ! [A4: A] :
% 0.14/0.42 ~ ( ord_less @ A @ A4 @ ( bot_bot @ A ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % bot.extremum_strict
% 0.14/0.42 thf(fact_190_bot_Onot__eq__extremum,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order_bot @ A )
% 0.14/0.42 => ! [A4: A] :
% 0.14/0.42 ( ( A4
% 0.14/0.42 != ( bot_bot @ A ) )
% 0.14/0.42 = ( ord_less @ A @ ( bot_bot @ A ) @ A4 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % bot.not_eq_extremum
% 0.14/0.42 thf(fact_191_view_Ohorizontal__chop__leq2,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V2 @ U3 @ W2 )
% 0.14/0.42 => ( ord_less_eq @ ( view_ext @ product_unit ) @ W2 @ V2 ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.horizontal_chop_leq2
% 0.14/0.42 thf(fact_192_view_Ohorizontal__chop__leq1,axiom,
% 0.14/0.42 ! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 0.14/0.42 ( ( hchop @ V2 @ U3 @ W2 )
% 0.14/0.42 => ( ord_less_eq @ ( view_ext @ product_unit ) @ U3 @ V2 ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.horizontal_chop_leq1
% 0.14/0.42 thf(fact_193_view_Oswitch__leq,axiom,
% 0.14/0.42 ! [U5: view_ext @ product_unit,U3: view_ext @ product_unit,V2: view_ext @ product_unit,C2: cars] :
% 0.14/0.42 ( ( ( ord_less_eq @ ( view_ext @ product_unit ) @ U5 @ U3 )
% 0.14/0.42 & ( switch @ V2 @ C2 @ U3 ) )
% 0.14/0.42 => ? [V5: view_ext @ product_unit] :
% 0.14/0.42 ( ( switch @ V5 @ C2 @ U5 )
% 0.14/0.42 & ( ord_less_eq @ ( view_ext @ product_unit ) @ V5 @ V2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % view.switch_leq
% 0.14/0.42 thf(fact_194_dual__order_Ostrict__implies__not__eq,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [B3: A,A4: A] :
% 0.14/0.42 ( ( ord_less @ A @ B3 @ A4 )
% 0.14/0.42 => ( A4 != B3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.strict_implies_not_eq
% 0.14/0.42 thf(fact_195_order_Ostrict__implies__not__eq,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( A4 != B3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.strict_implies_not_eq
% 0.14/0.42 thf(fact_196_not__less__iff__gr__or__eq,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.14/0.42 = ( ( ord_less @ A @ Y2 @ X3 )
% 0.14/0.42 | ( X3 = Y2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % not_less_iff_gr_or_eq
% 0.14/0.42 thf(fact_197_dual__order_Ostrict__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [B3: A,A4: A,C2: A] :
% 0.14/0.42 ( ( ord_less @ A @ B3 @ A4 )
% 0.14/0.42 => ( ( ord_less @ A @ C2 @ B3 )
% 0.14/0.42 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.strict_trans
% 0.14/0.42 thf(fact_198_linorder__less__wlog,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [P: A > A > $o,A4: A,B3: A] :
% 0.14/0.42 ( ! [A5: A,B5: A] :
% 0.14/0.42 ( ( ord_less @ A @ A5 @ B5 )
% 0.14/0.42 => ( P @ A5 @ B5 ) )
% 0.14/0.42 => ( ! [A5: A] : ( P @ A5 @ A5 )
% 0.14/0.42 => ( ! [A5: A,B5: A] :
% 0.14/0.42 ( ( P @ B5 @ A5 )
% 0.14/0.42 => ( P @ A5 @ B5 ) )
% 0.14/0.42 => ( P @ A4 @ B3 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % linorder_less_wlog
% 0.14/0.42 thf(fact_199_exists__least__iff,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( wellorder @ A )
% 0.14/0.42 => ( ( ^ [P2: A > $o] :
% 0.14/0.42 ? [X5: A] : ( P2 @ X5 ) )
% 0.14/0.42 = ( ^ [P3: A > $o] :
% 0.14/0.42 ? [N4: A] :
% 0.14/0.42 ( ( P3 @ N4 )
% 0.14/0.42 & ! [M2: A] :
% 0.14/0.42 ( ( ord_less @ A @ M2 @ N4 )
% 0.14/0.42 => ~ ( P3 @ M2 ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % exists_least_iff
% 0.14/0.42 thf(fact_200_less__imp__not__less,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_imp_not_less
% 0.14/0.42 thf(fact_201_order_Ostrict__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less @ A @ B3 @ C2 )
% 0.14/0.42 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.strict_trans
% 0.14/0.42 thf(fact_202_dual__order_Oirrefl,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A] :
% 0.14/0.42 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.irrefl
% 0.14/0.42 thf(fact_203_linorder__cases,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( X3 != Y2 )
% 0.14/0.42 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % linorder_cases
% 0.14/0.42 thf(fact_204_less__imp__triv,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A,P: $o] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ord_less @ A @ Y2 @ X3 )
% 0.14/0.42 => P ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_imp_triv
% 0.14/0.42 thf(fact_205_less__imp__not__eq2,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( Y2 != X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_imp_not_eq2
% 0.14/0.42 thf(fact_206_antisym__conv3,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [Y2: A,X3: A] :
% 0.14/0.42 ( ~ ( ord_less @ A @ Y2 @ X3 )
% 0.14/0.42 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 0.14/0.42 = ( X3 = Y2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % antisym_conv3
% 0.14/0.42 thf(fact_207_less__induct,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( wellorder @ A )
% 0.14/0.42 => ! [P: A > $o,A4: A] :
% 0.14/0.42 ( ! [X2: A] :
% 0.14/0.42 ( ! [Y5: A] :
% 0.14/0.42 ( ( ord_less @ A @ Y5 @ X2 )
% 0.14/0.42 => ( P @ Y5 ) )
% 0.14/0.42 => ( P @ X2 ) )
% 0.14/0.42 => ( P @ A4 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_induct
% 0.14/0.42 thf(fact_208_less__not__sym,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_not_sym
% 0.14/0.42 thf(fact_209_less__imp__not__eq,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( X3 != Y2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_imp_not_eq
% 0.14/0.42 thf(fact_210_dual__order_Oasym,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [B3: A,A4: A] :
% 0.14/0.42 ( ( ord_less @ A @ B3 @ A4 )
% 0.14/0.42 => ~ ( ord_less @ A @ A4 @ B3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dual_order.asym
% 0.14/0.42 thf(fact_211_ord__less__eq__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ord @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( B3 = C2 )
% 0.14/0.42 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % ord_less_eq_trans
% 0.14/0.42 thf(fact_212_ord__eq__less__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ord @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( A4 = B3 )
% 0.14/0.42 => ( ( ord_less @ A @ B3 @ C2 )
% 0.14/0.42 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % ord_eq_less_trans
% 0.14/0.42 thf(fact_213_less__irrefl,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A] :
% 0.14/0.42 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_irrefl
% 0.14/0.42 thf(fact_214_less__linear,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 | ( X3 = Y2 )
% 0.14/0.42 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_linear
% 0.14/0.42 thf(fact_215_less__trans,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A,Z2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ( ord_less @ A @ Y2 @ Z2 )
% 0.14/0.42 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_trans
% 0.14/0.42 thf(fact_216_less__asym_H,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [A4: A,B3: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_asym'
% 0.14/0.42 thf(fact_217_less__asym,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( preorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_asym
% 0.14/0.42 thf(fact_218_less__imp__neq,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( X3 != Y2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_imp_neq
% 0.14/0.42 thf(fact_219_dense,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( dense_order @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ? [Z5: A] :
% 0.14/0.42 ( ( ord_less @ A @ X3 @ Z5 )
% 0.14/0.42 & ( ord_less @ A @ Z5 @ Y2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % dense
% 0.14/0.42 thf(fact_220_order_Oasym,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [A4: A,B3: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order.asym
% 0.14/0.42 thf(fact_221_neq__iff,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( X3 != Y2 )
% 0.14/0.42 = ( ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 | ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % neq_iff
% 0.14/0.42 thf(fact_222_neqE,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( linorder @ A )
% 0.14/0.42 => ! [X3: A,Y2: A] :
% 0.14/0.42 ( ( X3 != Y2 )
% 0.14/0.42 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 0.14/0.42 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % neqE
% 0.14/0.42 thf(fact_223_gt__ex,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( no_top @ A )
% 0.14/0.42 => ! [X3: A] :
% 0.14/0.42 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 0.14/0.42
% 0.14/0.42 % gt_ex
% 0.14/0.42 thf(fact_224_lt__ex,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( no_bot @ A )
% 0.14/0.42 => ! [X3: A] :
% 0.14/0.42 ? [Y3: A] : ( ord_less @ A @ Y3 @ X3 ) ) ).
% 0.14/0.42
% 0.14/0.42 % lt_ex
% 0.14/0.42 thf(fact_225_order__less__subst2,axiom,
% 0.14/0.42 ! [A: $tType,C5: $tType] :
% 0.14/0.42 ( ( ( order @ C5 )
% 0.14/0.42 & ( order @ A ) )
% 0.14/0.42 => ! [A4: A,B3: A,F: A > C5,C2: C5] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less @ C5 @ ( F @ B3 ) @ C2 )
% 0.14/0.42 => ( ! [X2: A,Y3: A] :
% 0.14/0.42 ( ( ord_less @ A @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_less_subst2
% 0.14/0.42 thf(fact_226_order__less__subst1,axiom,
% 0.14/0.42 ! [A: $tType,B: $tType] :
% 0.14/0.42 ( ( ( order @ B )
% 0.14/0.42 & ( order @ A ) )
% 0.14/0.42 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ ( F @ B3 ) )
% 0.14/0.42 => ( ( ord_less @ B @ B3 @ C2 )
% 0.14/0.42 => ( ! [X2: B,Y3: B] :
% 0.14/0.42 ( ( ord_less @ B @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % order_less_subst1
% 0.14/0.42 thf(fact_227_ord__less__eq__subst,axiom,
% 0.14/0.42 ! [A: $tType,B: $tType] :
% 0.14/0.42 ( ( ( ord @ B )
% 0.14/0.42 & ( ord @ A ) )
% 0.14/0.42 => ! [A4: A,B3: A,F: A > B,C2: B] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ( F @ B3 )
% 0.14/0.42 = C2 )
% 0.14/0.42 => ( ! [X2: A,Y3: A] :
% 0.14/0.42 ( ( ord_less @ A @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % ord_less_eq_subst
% 0.14/0.42 thf(fact_228_ord__eq__less__subst,axiom,
% 0.14/0.42 ! [A: $tType,B: $tType] :
% 0.14/0.42 ( ( ( ord @ B )
% 0.14/0.42 & ( ord @ A ) )
% 0.14/0.42 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 0.14/0.42 ( ( A4
% 0.14/0.42 = ( F @ B3 ) )
% 0.14/0.42 => ( ( ord_less @ B @ B3 @ C2 )
% 0.14/0.42 => ( ! [X2: B,Y3: B] :
% 0.14/0.42 ( ( ord_less @ B @ X2 @ Y3 )
% 0.14/0.42 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.14/0.42 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % ord_eq_less_subst
% 0.14/0.42 thf(fact_229_diff__strict__right__mono,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ordered_ab_group_add @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_strict_right_mono
% 0.14/0.42 thf(fact_230_diff__strict__left__mono,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ordered_ab_group_add @ A )
% 0.14/0.42 => ! [B3: A,A4: A,C2: A] :
% 0.14/0.42 ( ( ord_less @ A @ B3 @ A4 )
% 0.14/0.42 => ( ord_less @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_strict_left_mono
% 0.14/0.42 thf(fact_231_diff__eq__diff__less,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ordered_ab_group_add @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A,D: A] :
% 0.14/0.42 ( ( ( minus_minus @ A @ A4 @ B3 )
% 0.14/0.42 = ( minus_minus @ A @ C2 @ D ) )
% 0.14/0.42 => ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 = ( ord_less @ A @ C2 @ D ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_eq_diff_less
% 0.14/0.42 thf(fact_232_diff__strict__mono,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ordered_ab_group_add @ A )
% 0.14/0.42 => ! [A4: A,B3: A,D: A,C2: A] :
% 0.14/0.42 ( ( ord_less @ A @ A4 @ B3 )
% 0.14/0.42 => ( ( ord_less @ A @ D @ C2 )
% 0.14/0.42 => ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_strict_mono
% 0.14/0.42 thf(fact_233_chop__leq2,axiom,
% 0.14/0.42 ! [R: real_int,S2: real_int,T2: real_int] :
% 0.14/0.42 ( ( real_R_Chop @ R @ S2 @ T2 )
% 0.14/0.42 => ( ord_less_eq @ real_int @ T2 @ R ) ) ).
% 0.14/0.42
% 0.14/0.42 % chop_leq2
% 0.14/0.42 thf(fact_234_chop__leq1,axiom,
% 0.14/0.42 ! [R: real_int,S2: real_int,T2: real_int] :
% 0.14/0.42 ( ( real_R_Chop @ R @ S2 @ T2 )
% 0.14/0.42 => ( ord_less_eq @ real_int @ S2 @ R ) ) ).
% 0.14/0.42
% 0.14/0.42 % chop_leq1
% 0.14/0.42 thf(fact_235_card__subset__le,axiom,
% 0.14/0.42 ! [I: nat_int,I2: nat_int] :
% 0.14/0.42 ( ( ord_less_eq @ nat_int @ I @ I2 )
% 0.14/0.42 => ( ord_less_eq @ nat @ ( nat_card @ I ) @ ( nat_card @ I2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % card_subset_le
% 0.14/0.42 thf(fact_236_diff__eq__diff__eq,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( group_add @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A,D: A] :
% 0.14/0.42 ( ( ( minus_minus @ A @ A4 @ B3 )
% 0.14/0.42 = ( minus_minus @ A @ C2 @ D ) )
% 0.14/0.42 => ( ( A4 = B3 )
% 0.14/0.42 = ( C2 = D ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_eq_diff_eq
% 0.14/0.42 thf(fact_237_diff__right__commute,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( cancel146912293up_add @ A )
% 0.14/0.42 => ! [A4: A,C2: A,B3: A] :
% 0.14/0.42 ( ( minus_minus @ A @ ( minus_minus @ A @ A4 @ C2 ) @ B3 )
% 0.14/0.42 = ( minus_minus @ A @ ( minus_minus @ A @ A4 @ B3 ) @ C2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_right_commute
% 0.14/0.42 thf(fact_238_diff__eq__diff__less__eq,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ordered_ab_group_add @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A,D: A] :
% 0.14/0.42 ( ( ( minus_minus @ A @ A4 @ B3 )
% 0.14/0.42 = ( minus_minus @ A @ C2 @ D ) )
% 0.14/0.42 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 = ( ord_less_eq @ A @ C2 @ D ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_eq_diff_less_eq
% 0.14/0.42 thf(fact_239_diff__right__mono,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ordered_ab_group_add @ A )
% 0.14/0.42 => ! [A4: A,B3: A,C2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.14/0.42 => ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_right_mono
% 0.14/0.42 thf(fact_240_diff__left__mono,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( ordered_ab_group_add @ A )
% 0.14/0.42 => ! [B3: A,A4: A,C2: A] :
% 0.14/0.42 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.14/0.42 => ( ord_less_eq @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % diff_left_mono
% 0.14/0.42 thf(fact_241_traffic_Oclm__consec__res,axiom,
% 0.14/0.42 ! [Ts5: traffic,C2: cars] :
% 0.14/0.42 ( ( ( clm @ Ts5 @ C2 )
% 0.14/0.42 != ( bot_bot @ nat_int ) )
% 0.14/0.42 => ( ( nat_consec @ ( clm @ Ts5 @ C2 ) @ ( res @ Ts5 @ C2 ) )
% 0.14/0.42 | ( nat_consec @ ( res @ Ts5 @ C2 ) @ ( clm @ Ts5 @ C2 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % traffic.clm_consec_res
% 0.14/0.42 thf(fact_242_Greatest__equality,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [P: A > $o,X3: A] :
% 0.14/0.42 ( ( P @ X3 )
% 0.14/0.42 => ( ! [Y3: A] :
% 0.14/0.42 ( ( P @ Y3 )
% 0.14/0.42 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.14/0.42 => ( ( order_Greatest @ A @ P )
% 0.14/0.42 = X3 ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % Greatest_equality
% 0.14/0.42 thf(fact_243_GreatestI2__order,axiom,
% 0.14/0.42 ! [A: $tType] :
% 0.14/0.42 ( ( order @ A )
% 0.14/0.42 => ! [P: A > $o,X3: A,Q: A > $o] :
% 0.14/0.42 ( ( P @ X3 )
% 0.14/0.42 => ( ! [Y3: A] :
% 0.14/0.42 ( ( P @ Y3 )
% 0.14/0.42 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.14/0.42 => ( ! [X2: A] :
% 0.14/0.42 ( ( P @ X2 )
% 0.14/0.42 => ( ! [Y5: A] :
% 0.14/0.42 ( ( P @ Y5 )
% 0.14/0.42 => ( ord_less_eq @ A @ Y5 @ X2 ) )
% 0.14/0.42 => ( Q @ X2 ) ) )
% 0.14/0.42 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % GreatestI2_order
% 0.14/0.42 thf(fact_244_less__fun__def,axiom,
% 0.14/0.42 ! [B: $tType,A: $tType] :
% 0.14/0.42 ( ( ord @ B )
% 0.14/0.42 => ( ( ord_less @ ( A > B ) )
% 0.14/0.42 = ( ^ [F2: A > B,G2: A > B] :
% 0.14/0.42 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.14/0.42 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % less_fun_def
% 0.14/0.42 thf(fact_245_card__subset__less,axiom,
% 0.14/0.42 ! [I: nat_int,I2: nat_int] :
% 0.14/0.42 ( ( ord_less @ nat_int @ I @ I2 )
% 0.14/0.42 => ( ord_less @ nat @ ( nat_card @ I ) @ ( nat_card @ I2 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % card_subset_less
% 0.14/0.42 thf(fact_246_consec__intermediate2,axiom,
% 0.14/0.42 ! [I: nat_int,J: nat_int,K: nat_int] :
% 0.14/0.42 ( ( ( nat_consec @ I @ J )
% 0.14/0.42 & ( nat_consec @ ( nat_union @ I @ J ) @ K ) )
% 0.14/0.42 => ( nat_consec @ J @ K ) ) ).
% 0.14/0.42
% 0.14/0.42 % consec_intermediate2
% 0.14/0.42 thf(fact_247_consec__intermediate1,axiom,
% 0.14/0.42 ! [J: nat_int,K: nat_int,I: nat_int] :
% 0.14/0.42 ( ( ( nat_consec @ J @ K )
% 0.14/0.42 & ( nat_consec @ I @ ( nat_union @ J @ K ) ) )
% 0.14/0.42 => ( nat_consec @ I @ J ) ) ).
% 0.14/0.42
% 0.14/0.42 % consec_intermediate1
% 0.14/0.42 thf(fact_248_consec__assoc2,axiom,
% 0.14/0.42 ! [I: nat_int,J: nat_int,K: nat_int] :
% 0.14/0.42 ( ( ( nat_consec @ I @ J )
% 0.14/0.42 & ( nat_consec @ ( nat_union @ I @ J ) @ K ) )
% 0.14/0.42 => ( nat_consec @ I @ ( nat_union @ J @ K ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % consec_assoc2
% 0.14/0.42 thf(fact_249_consec__assoc1,axiom,
% 0.14/0.42 ! [J: nat_int,K: nat_int,I: nat_int] :
% 0.14/0.42 ( ( ( nat_consec @ J @ K )
% 0.14/0.42 & ( nat_consec @ I @ ( nat_union @ J @ K ) ) )
% 0.14/0.42 => ( nat_consec @ ( nat_union @ I @ J ) @ K ) ) ).
% 0.14/0.42
% 0.14/0.42 % consec_assoc1
% 0.14/0.42 thf(fact_250_un__assoc,axiom,
% 0.14/0.42 ! [I: nat_int,J: nat_int,K: nat_int] :
% 0.14/0.42 ( ( ( nat_consec @ I @ J )
% 0.14/0.42 & ( nat_consec @ J @ K ) )
% 0.14/0.42 => ( ( nat_union @ ( nat_union @ I @ J ) @ K )
% 0.14/0.42 = ( nat_union @ I @ ( nat_union @ J @ K ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % un_assoc
% 0.14/0.42 thf(fact_251_consec__assoc__mult,axiom,
% 0.14/0.42 ! [I22: nat_int,I1: nat_int,I3: nat_int,I4: nat_int] :
% 0.14/0.42 ( ( ( ( I22
% 0.14/0.42 = ( bot_bot @ nat_int ) )
% 0.14/0.42 | ( nat_consec @ I1 @ I22 ) )
% 0.14/0.42 & ( ( I3
% 0.14/0.42 = ( bot_bot @ nat_int ) )
% 0.14/0.42 | ( nat_consec @ I3 @ I4 ) )
% 0.14/0.42 & ( nat_consec @ ( nat_union @ I1 @ I22 ) @ ( nat_union @ I3 @ I4 ) ) )
% 0.14/0.42 => ( ( nat_union @ ( nat_union @ I1 @ I22 ) @ ( nat_union @ I3 @ I4 ) )
% 0.14/0.42 = ( nat_union @ ( nat_union @ I1 @ ( nat_union @ I22 @ I3 ) ) @ I4 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % consec_assoc_mult
% 0.14/0.42 thf(fact_252_un__subset2,axiom,
% 0.14/0.42 ! [I: nat_int,J: nat_int] :
% 0.14/0.42 ( ( nat_consec @ I @ J )
% 0.14/0.42 => ( ord_less_eq @ nat_int @ J @ ( nat_union @ I @ J ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % un_subset2
% 0.14/0.42 thf(fact_253_un__subset1,axiom,
% 0.14/0.42 ! [I: nat_int,J: nat_int] :
% 0.14/0.42 ( ( nat_consec @ I @ J )
% 0.14/0.42 => ( ord_less_eq @ nat_int @ I @ ( nat_union @ I @ J ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % un_subset1
% 0.14/0.42 thf(fact_254_nchop__def,axiom,
% 0.14/0.42 ( nat_N_Chop
% 0.14/0.42 = ( ^ [I5: nat_int,J2: nat_int,K2: nat_int] :
% 0.14/0.42 ( ( I5
% 0.14/0.42 = ( nat_union @ J2 @ K2 ) )
% 0.14/0.42 & ( ( J2
% 0.14/0.42 = ( bot_bot @ nat_int ) )
% 0.14/0.42 | ( K2
% 0.14/0.42 = ( bot_bot @ nat_int ) )
% 0.14/0.42 | ( nat_consec @ J2 @ K2 ) ) ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % nchop_def
% 0.14/0.42 thf(fact_255_consec__un__not__elem2,axiom,
% 0.14/0.42 ! [I: nat_int,J: nat_int,N: nat] :
% 0.14/0.42 ( ( ( nat_consec @ I @ J )
% 0.14/0.42 & ( nat_not_in @ N @ ( nat_union @ I @ J ) ) )
% 0.14/0.42 => ( nat_not_in @ N @ J ) ) ).
% 0.14/0.42
% 0.14/0.42 % consec_un_not_elem2
% 0.14/0.42
% 0.14/0.42 % Type constructors (54)
% 0.14/0.42 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 0.14/0.42 ! [A6: $tType,A7: $tType] :
% 0.14/0.42 ( ( order_bot @ A7 )
% 0.14/0.42 => ( order_bot @ ( A6 > A7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.14/0.42 ! [A6: $tType,A7: $tType] :
% 0.14/0.42 ( ( preorder @ A7 )
% 0.14/0.42 => ( preorder @ ( A6 > A7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.14/0.42 ! [A6: $tType,A7: $tType] :
% 0.14/0.42 ( ( order @ A7 )
% 0.14/0.42 => ( order @ ( A6 > A7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_fun___Orderings_Oord,axiom,
% 0.14/0.42 ! [A6: $tType,A7: $tType] :
% 0.14/0.42 ( ( ord @ A7 )
% 0.14/0.42 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_fun___Orderings_Obot,axiom,
% 0.14/0.42 ! [A6: $tType,A7: $tType] :
% 0.14/0.42 ( ( bot @ A7 )
% 0.14/0.42 => ( bot @ ( A6 > A7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_fun___Groups_Ominus,axiom,
% 0.14/0.42 ! [A6: $tType,A7: $tType] :
% 0.14/0.42 ( ( minus @ A7 )
% 0.14/0.42 => ( minus @ ( A6 > A7 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.14/0.42 cancel146912293up_add @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.14/0.42 wellorder @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1,axiom,
% 0.14/0.42 order_bot @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
% 0.14/0.42 preorder @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.14/0.42 linorder @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.14/0.42 no_top @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Orderings_Oorder_3,axiom,
% 0.14/0.42 order @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Orderings_Oord_4,axiom,
% 0.14/0.42 ord @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
% 0.14/0.42 bot @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Nat_Onat___Groups_Ominus_6,axiom,
% 0.14/0.42 minus @ nat ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_HOL_Obool___Orderings_Oorder__bot_7,axiom,
% 0.14/0.42 order_bot @ $o ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 0.14/0.42 preorder @ $o ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_HOL_Obool___Orderings_Olinorder_9,axiom,
% 0.14/0.42 linorder @ $o ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_HOL_Obool___Orderings_Oorder_10,axiom,
% 0.14/0.42 order @ $o ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_HOL_Obool___Orderings_Oord_11,axiom,
% 0.14/0.42 ord @ $o ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_HOL_Obool___Orderings_Obot_12,axiom,
% 0.14/0.42 bot @ $o ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_HOL_Obool___Groups_Ominus_13,axiom,
% 0.14/0.42 minus @ $o ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_14,axiom,
% 0.14/0.42 cancel146912293up_add @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
% 0.14/0.42 ordered_ab_group_add @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
% 0.14/0.42 dense_linorder @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
% 0.14/0.42 dense_order @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Orderings_Opreorder_15,axiom,
% 0.14/0.42 preorder @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Orderings_Olinorder_16,axiom,
% 0.14/0.42 linorder @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Orderings_Ono__top_17,axiom,
% 0.14/0.42 no_top @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Orderings_Ono__bot,axiom,
% 0.14/0.42 no_bot @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 0.14/0.42 group_add @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Orderings_Oorder_18,axiom,
% 0.14/0.42 order @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Orderings_Oord_19,axiom,
% 0.14/0.42 ord @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Real_Oreal___Groups_Ominus_20,axiom,
% 0.14/0.42 minus @ real ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_NatInt_Onat__int___Orderings_Oorder__bot_21,axiom,
% 0.14/0.42 order_bot @ nat_int ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_NatInt_Onat__int___Orderings_Opreorder_22,axiom,
% 0.14/0.42 preorder @ nat_int ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_NatInt_Onat__int___Orderings_Oorder_23,axiom,
% 0.14/0.42 order @ nat_int ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_NatInt_Onat__int___Orderings_Oord_24,axiom,
% 0.14/0.42 ord @ nat_int ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_NatInt_Onat__int___Orderings_Obot_25,axiom,
% 0.14/0.42 bot @ nat_int ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_RealInt_Oreal__int___Orderings_Opreorder_26,axiom,
% 0.14/0.42 preorder @ real_int ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_RealInt_Oreal__int___Orderings_Oorder_27,axiom,
% 0.14/0.42 order @ real_int ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_RealInt_Oreal__int___Orderings_Oord_28,axiom,
% 0.14/0.42 ord @ real_int ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_29,axiom,
% 0.14/0.42 wellorder @ product_unit ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_30,axiom,
% 0.14/0.42 order_bot @ product_unit ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_31,axiom,
% 0.14/0.42 preorder @ product_unit ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_32,axiom,
% 0.14/0.42 linorder @ product_unit ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Product__Type_Ounit___Orderings_Oorder_33,axiom,
% 0.14/0.42 order @ product_unit ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Product__Type_Ounit___Orderings_Oord_34,axiom,
% 0.14/0.42 ord @ product_unit ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Product__Type_Ounit___Orderings_Obot_35,axiom,
% 0.14/0.42 bot @ product_unit ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Product__Type_Ounit___Groups_Ominus_36,axiom,
% 0.14/0.42 minus @ product_unit ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Views_Oview_Oview__ext___Orderings_Opreorder_37,axiom,
% 0.14/0.42 ! [A6: $tType] :
% 0.14/0.42 ( ( order @ A6 )
% 0.14/0.42 => ( preorder @ ( view_ext @ A6 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Views_Oview_Oview__ext___Orderings_Oorder_38,axiom,
% 0.14/0.42 ! [A6: $tType] :
% 0.14/0.42 ( ( order @ A6 )
% 0.14/0.42 => ( order @ ( view_ext @ A6 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(tcon_Views_Oview_Oview__ext___Orderings_Oord_39,axiom,
% 0.14/0.42 ! [A6: $tType] :
% 0.14/0.42 ( ( order @ A6 )
% 0.14/0.42 => ( ord @ ( view_ext @ A6 ) ) ) ).
% 0.14/0.42
% 0.14/0.42 % Helper facts (3)
% 0.14/0.42 thf(help_If_3_1_T,axiom,
% 0.14/0.42 ! [P: $o] :
% 0.14/0.42 ( ( P = $true )
% 0.14/0.42 | ( P = $false ) ) ).
% 0.14/0.42
% 0.14/0.42 thf(help_If_2_1_T,axiom,
% 0.14/0.42 ! [A: $tType,X3: A,Y2: A] :
% 0.14/0.42 ( ( if @ A @ $false @ X3 @ Y2 )
% 0.14/0.42 = Y2 ) ).
% 0.14/0.42
% 0.14/0.42 thf(help_If_1_1_T,axiom,
% 0.14/0.42 ! [A: $tType,X3: A,Y2: A] :
% 0.14/0.42 ( ( if @ A @ $true @ X3 @ Y2 )
% 0.14/0.42 = X3 ) ).
% 0.14/0.42
% 0.14/0.42 % Conjectures (1)
% 0.14/0.42 thf(conj_0,conjecture,
% 0.14/0.42 ( ( move @ ts3 @ ts_a @ v )
% 0.14/0.42 = ( move @ ts3 @ ts @ v ) ) ).
% 0.14/0.42
% 0.14/0.42 %------------------------------------------------------------------------------
% 0.14/0.42 ------------------------
% 2.61/1.47 ---- Embedded in THF ---
% 2.61/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.61/1.48 %%% Generated on Tue Feb 24 08:28:52 EST 2026
% 2.61/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.61/1.48 %%% Logic specification used:
% 2.61/1.48 %%% thf(spec, logic, $$dhol).
% 2.61/1.48
% 2.61/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2DTF13762.p
% 2.61/1.48 thf(ty_t_Views_Oview_Oview__ext, type, view_ext: ($tType > $tType)).
% 2.61/1.48 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.61/1.48 thf(ty_t_RealInt_Oreal__int, type, real_int: $tType).
% 2.61/1.48 thf(ty_t_Traffic_Otraffic, type, traffic: $tType).
% 2.61/1.48 thf(ty_t_NatInt_Onat__int, type, nat_int: $tType).
% 2.61/1.48 thf(ty_t_Real_Oreal, type, real: $tType).
% 2.61/1.48 thf(ty_t_Cars_Ocars, type, cars: $tType).
% 2.61/1.48 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.61/1.48 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Oorder__bot, type, order_bot: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 2.61/1.48 thf(sy_c_Fun_Ofun__upd, type, fun_upd: (!> [A:$tType,B:$tType]: (((A > B) > (A > (B > (A > B))))))).
% 2.61/1.48 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.61/1.48 thf(sy_c_HOL_Odefault__class_Odefault, type, default_default: (!> [A:$tType]: (A))).
% 2.61/1.48 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.61/1.48 thf(sy_c_Move_Otraffic_Omove, type, move: (traffic > (traffic > ((view_ext @ product_unit) > (view_ext @ product_unit))))).
% 2.61/1.48 thf(sy_c_NatInt_Onat__int_ON__Chop, type, nat_N_Chop: (nat_int > (nat_int > (nat_int > $o)))).
% 2.61/1.48 thf(sy_c_NatInt_Onat__int_Ocard_H, type, nat_card: (nat_int > nat)).
% 2.61/1.48 thf(sy_c_NatInt_Onat__int_Oconsec, type, nat_consec: (nat_int > (nat_int > $o))).
% 2.61/1.48 thf(sy_c_NatInt_Onat__int_Onot__in, type, nat_not_in: (nat > (nat_int > $o))).
% 2.61/1.48 thf(sy_c_NatInt_Onat__int_Ounion, type, nat_union: (nat_int > (nat_int > nat_int))).
% 2.61/1.48 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.61/1.48 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.61/1.48 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.61/1.48 thf(sy_c_Orderings_Oorder__class_OGreatest, type, order_Greatest: (!> [A:$tType]: (((A > $o) > A)))).
% 2.61/1.48 thf(sy_c_Product__Type_OUnity, type, product_Unity: product_unit).
% 2.61/1.48 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit, type, product_rec_unit: (!> [T:$tType]: ((T > (product_unit > T))))).
% 2.61/1.48 thf(sy_c_RealInt_Oreal__int_OR__Chop, type, real_R_Chop: (real_int > (real_int > (real_int > $o)))).
% 2.61/1.48 thf(sy_c_RealInt_Oreal__int_Oshift, type, real_shift: (real_int > (real > real_int))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Oabstract, type, abstract: (traffic > (traffic > $o))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Obraking__distance, type, braking_distance: (traffic > (cars > real))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Ochange__dyn, type, change_dyn: (traffic > (cars > ((real > real) > (traffic > $o))))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Oclm, type, clm: (traffic > (cars > nat_int))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Ocreate__claim, type, create_claim: (traffic > (cars > (nat > (traffic > $o))))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Ocreate__reservation, type, create_reservation: (traffic > (cars > (traffic > $o)))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Odyn, type, dyn: (traffic > (cars > (real > real)))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Oevolve, type, evolve: (traffic > (traffic > $o))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Ophysical__size, type, physical_size: (traffic > (cars > real))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Opos, type, pos: (traffic > (cars > real))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Ores, type, res: (traffic > (cars > nat_int))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Owithdraw__claim, type, withdraw_claim: (traffic > (cars > (traffic > $o)))).
% 2.61/1.48 thf(sy_c_Traffic_Otraffic_Owithdraw__reservation, type, withdraw_reservation: (traffic > (cars > (nat > (traffic > $o))))).
% 2.61/1.48 thf(sy_c_Views_Oview_Oext, type, ext: (!> [Z:$tType]: (((view_ext @ Z) > real_int)))).
% 2.61/1.48 thf(sy_c_Views_Oview_Ohchop, type, hchop: ((view_ext @ product_unit) > ((view_ext @ product_unit) > ((view_ext @ product_unit) > $o)))).
% 2.61/1.48 thf(sy_c_Views_Oview_Olan, type, lan: (!> [Z:$tType]: (((view_ext @ Z) > nat_int)))).
% 2.61/1.48 thf(sy_c_Views_Oview_Omore, type, more: (!> [Z:$tType]: (((view_ext @ Z) > Z)))).
% 2.61/1.48 thf(sy_c_Views_Oview_Oown, type, own: (!> [Z:$tType]: (((view_ext @ Z) > cars)))).
% 2.61/1.48 thf(sy_c_Views_Oview_Oswitch, type, switch: ((view_ext @ product_unit) > (cars > ((view_ext @ product_unit) > $o)))).
% 2.61/1.48 thf(sy_c_Views_Oview_Oview__ext, type, view_ext2: (!> [Z:$tType]: ((real_int > (nat_int > (cars > (Z > (view_ext @ Z)))))))).
% 2.61/1.48 thf(sy_v_ts_H_H____, type, ts: traffic).
% 2.61/1.48 thf(sy_v_ts_H____, type, ts2: traffic).
% 2.61/1.48 thf(sy_v_ts_Ha____, type, ts_a: traffic).
% 2.61/1.48 thf(sy_v_ts____, type, ts3: traffic).
% 2.61/1.48 thf(sy_v_v____, type, v: (view_ext @ product_unit)).
% 2.61/1.48 thf(fact_0_cr__res_Ohyps_I1_J, axiom, ((abstract @ ts3) @ ts_a)).
% 2.61/1.48 thf(fact_1_cr__res_Ohyps_I2_J, axiom, (? [C:cars]: ((((create_reservation @ ts_a) @ C) @ ts)))).
% 2.61/1.48 thf(fact_2_local_Ohmlsl_Oglobally__4, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [Ts2:traffic]: ((((abstract @ Ts) @ Ts2) => ((Phi @ Ts2) @ (((move @ Ts) @ Ts2) @ V))))) => (! [Ts3:traffic]: ((((abstract @ Ts) @ Ts3) => (! [Ts_a:traffic]: ((((abstract @ Ts3) @ Ts_a) => ((Phi @ Ts_a) @ (((move @ Ts3) @ Ts_a) @ (((move @ Ts) @ Ts3) @ V))))))))))))).
% 2.61/1.48 thf(fact_3_local_Ohmlsl_Oglobally__all__iff, axiom, (! [A:$tType,B:$tType,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [Ts4:traffic]: ((((abstract @ Ts) @ Ts4) => (! [X:A]: (((Phi @ Ts4) @ (((move @ Ts) @ Ts4) @ V))))))) = (! [X:B,Ts4:traffic]: ((((abstract @ Ts) @ Ts4) => ((Phi @ Ts4) @ (((move @ Ts) @ Ts4) @ V))))))))).
% 2.61/1.48 thf(fact_4_local_Ohmlsl_Oglobally__all__iff_H, axiom, (! [A:$tType,B:$tType,Ts5:traffic,Phi:(traffic > ((view_ext @ product_unit) > $o)),V2:(view_ext @ product_unit)]: (((! [Ts4:traffic]: ((((abstract @ Ts5) @ Ts4) => (! [X:A]: (((Phi @ Ts4) @ (((move @ Ts5) @ Ts4) @ V2))))))) = (! [X:B,Ts4:traffic]: ((((abstract @ Ts5) @ Ts4) => ((Phi @ Ts4) @ (((move @ Ts5) @ Ts4) @ V2))))))))).
% 2.61/1.48 thf(fact_5_local_Ohmlsl_Oglobally__refl, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [Ts2:traffic]: ((((abstract @ Ts) @ Ts2) => ((Phi @ Ts2) @ (((move @ Ts) @ Ts2) @ V))))) => ((Phi @ Ts) @ V))))).
% 2.61/1.48 thf(fact_6_abs, axiom, ((abstract @ ts3) @ ts2)).
% 2.61/1.48 thf(fact_7__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062, axiom, ((((move @ ts3) @ ts_a) @ v) = (((move @ ts_a) @ ts) @ (((move @ ts3) @ ts_a) @ v)))).
% 2.61/1.48 thf(fact_8_traffic_Omove__nothing, axiom, (! [Ts5:traffic,V2:(view_ext @ product_unit)]: (((((move @ Ts5) @ Ts5) @ V2) = V2)))).
% 2.61/1.48 thf(fact_9_traffic_Omove__def, axiom, (move = (^ [Ts6:traffic,Ts4:traffic,V3:(view_ext @ product_unit)]: ((((((view_ext2 @ product_unit) @ ((real_shift @ ((ext @ product_unit) @ V3)) @ (((minus_minus @ real) @ ((pos @ Ts4) @ ((own @ product_unit) @ V3))) @ ((pos @ Ts6) @ ((own @ product_unit) @ V3))))) @ ((lan @ product_unit) @ V3)) @ ((own @ product_unit) @ V3)) @ product_Unity))))).
% 2.61/1.48 thf(fact_10_traffic_Omove__stability__res, axiom, (! [Ts5:traffic,C2:cars,Ts7:traffic,V2:(view_ext @ product_unit)]: (((((create_reservation @ Ts5) @ C2) @ Ts7) => ((((move @ Ts5) @ Ts7) @ V2) = V2))))).
% 2.61/1.48 thf(fact_11_traffic_Omove__keeps__owner, axiom, (! [Ts5:traffic,Ts7:traffic]: (((own @ product_unit) = (^ [V3:(view_ext @ product_unit)]: (((own @ product_unit) @ (((move @ Ts5) @ Ts7) @ V3)))))))).
% 2.61/1.48 thf(fact_12_traffic_Omove__trans, axiom, (! [Ts5:traffic,Ts7:traffic,Ts8:traffic,V2:(view_ext @ product_unit)]: (((((abstract @ Ts5) @ Ts7) & ((abstract @ Ts7) @ Ts8)) => ((((move @ Ts7) @ Ts8) @ (((move @ Ts5) @ Ts7) @ V2)) = (((move @ Ts5) @ Ts8) @ V2)))))).
% 2.61/1.48 thf(fact_13_traffic_Omove__keeps__lanes, axiom, (! [Ts5:traffic,Ts7:traffic]: (((lan @ product_unit) = (^ [V3:(view_ext @ product_unit)]: (((lan @ product_unit) @ (((move @ Ts5) @ Ts7) @ V3)))))))).
% 2.61/1.48 thf(fact_14_traffic_Omove__stability__clm, axiom, (! [Ts5:traffic,C2:cars,N:nat,Ts7:traffic,V2:(view_ext @ product_unit)]: ((((((create_claim @ Ts5) @ C2) @ N) @ Ts7) => ((((move @ Ts5) @ Ts7) @ V2) = V2))))).
% 2.61/1.48 thf(fact_15_traffic_Omove__stability__wdc, axiom, (! [Ts5:traffic,C2:cars,Ts7:traffic,V2:(view_ext @ product_unit)]: (((((withdraw_claim @ Ts5) @ C2) @ Ts7) => ((((move @ Ts5) @ Ts7) @ V2) = V2))))).
% 2.61/1.48 thf(fact_16_traffic_Omove__stability__wdr, axiom, (! [Ts5:traffic,C2:cars,N:nat,Ts7:traffic,V2:(view_ext @ product_unit)]: ((((((withdraw_reservation @ Ts5) @ C2) @ N) @ Ts7) => ((((move @ Ts5) @ Ts7) @ V2) = V2))))).
% 2.61/1.48 thf(fact_17_local_Ohmlsl_Ohchop__assoc, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & (((Phi @ Ts) @ W) & (? [X:(view_ext @ product_unit),Y:(view_ext @ product_unit)]: (((((hchop @ U) @ X) @ Y) & (((Psi @ Ts) @ X) & ((Chi @ Ts) @ Y))))))))) = (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & ((? [X:(view_ext @ product_unit),Y:(view_ext @ product_unit)]: (((((hchop @ W) @ X) @ Y) & (((Phi @ Ts) @ X) & ((Psi @ Ts) @ Y))))) & ((Chi @ Ts) @ U))))))))).
% 2.61/1.48 thf(fact_18_local_Ohmlsl_Ohchop__disj__distr1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & (((Phi @ Ts) @ W) & (((Psi @ Ts) @ U) | ((Chi @ Ts) @ U)))))) = ((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & (((Phi @ Ts) @ W) & ((Psi @ Ts) @ U))))) | (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & (((Phi @ Ts) @ W) & ((Chi @ Ts) @ U)))))))))).
% 2.61/1.48 thf(fact_19_local_Ohmlsl_Ohchop__disj__distr2, axiom, (! [Psi:(traffic > ((view_ext @ product_unit) > $o)),Chi:(traffic > ((view_ext @ product_unit) > $o)),Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & ((((Psi @ Ts) @ W) | ((Chi @ Ts) @ W)) & ((Phi @ Ts) @ U))))) = ((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & (((Psi @ Ts) @ W) & ((Phi @ Ts) @ U))))) | (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & (((Chi @ Ts) @ W) & ((Phi @ Ts) @ U)))))))))).
% 2.61/1.48 thf(fact_20_local_Ohmlsl_Ohchop__weaken2, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts) @ V) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U2) & ((Phi @ Ts) @ U2)))))))).
% 2.61/1.48 thf(fact_21_local_Ohmlsl_Ohchop__weaken1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts) @ V) => (? [Va:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ Va) @ X_1))) & ((Phi @ Ts) @ Va)))))))).
% 2.61/1.48 thf(fact_22_local_Ohmlsl_Ohchop__weaken, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts) @ V) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U2) & (? [Vb:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ U2) @ Vb) @ X_1))) & ((Phi @ Ts) @ Vb))))))))))).
% 2.61/1.48 thf(fact_23_local_Ohmlsl_Ohchop__neg2, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((~ ((? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U2) & ((Phi @ Ts) @ U2)))))) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U2) & (~ (((Phi @ Ts) @ U2)))))))))).
% 2.61/1.48 thf(fact_24_local_Ohmlsl_Ohchop__neg1, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((~ ((? [Va:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ Va) @ X_1))) & ((Phi @ Ts) @ Va)))))) => (? [Va:(view_ext @ product_unit)]: (((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ Va) @ X_1))) & (~ (((Phi @ Ts) @ Va)))))))))).
% 2.61/1.48 thf(fact_25_ext__inject, axiom, (! [Z:$tType,Ext:real_int,Lan:nat_int,Own:cars,More:Z,Ext2:real_int,Lan2:nat_int,Own2:cars,More2:Z]: ((((((((view_ext2 @ Z) @ Ext) @ Lan) @ Own) @ More) = (((((view_ext2 @ Z) @ Ext2) @ Lan2) @ Own2) @ More2)) = ((Ext = Ext2) & ((Lan = Lan2) & ((Own = Own2) & (More = More2)))))))).
% 2.61/1.48 thf(fact_26_cases, axiom, (! [R:(view_ext @ product_unit)]: ((~ ((! [Ext3:real_int,Lan3:nat_int,Own3:cars]: ((R != (((((view_ext2 @ product_unit) @ Ext3) @ Lan3) @ Own3) @ product_Unity))))))))).
% 2.61/1.48 thf(fact_27_induct, axiom, (! [P:((view_ext @ product_unit) > $o),R:(view_ext @ product_unit)]: (((! [Ext3:real_int,Lan3:nat_int,Own3:cars]: ((P @ (((((view_ext2 @ product_unit) @ Ext3) @ Lan3) @ Own3) @ product_Unity)))) => (P @ R))))).
% 2.61/1.48 thf(fact_28_traffic_Ocr__clm, axiom, (! [Ts5:traffic,Ts7:traffic,Ts8:traffic]: ((((abstract @ Ts5) @ Ts7) => ((? [C3:cars,N2:nat]: (((((create_claim @ Ts7) @ C3) @ N2) @ Ts8))) => ((abstract @ Ts5) @ Ts8)))))).
% 2.61/1.48 thf(fact_29_traffic_Owd__clm, axiom, (! [Ts5:traffic,Ts7:traffic,Ts8:traffic]: ((((abstract @ Ts5) @ Ts7) => ((? [C3:cars]: ((((withdraw_claim @ Ts7) @ C3) @ Ts8))) => ((abstract @ Ts5) @ Ts8)))))).
% 2.61/1.48 thf(fact_30_traffic_Owd__res, axiom, (! [Ts5:traffic,Ts7:traffic,Ts8:traffic]: ((((abstract @ Ts5) @ Ts7) => ((? [C3:cars,N2:nat]: (((((withdraw_reservation @ Ts7) @ C3) @ N2) @ Ts8))) => ((abstract @ Ts5) @ Ts8)))))).
% 2.61/1.48 thf(fact_31_minus__apply, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A2:(A > B),B2:(A > B),X:A]: ((((minus_minus @ B) @ (A2 @ X)) @ (B2 @ X))))))))).
% 2.61/1.48 thf(fact_32_traffic_Ocr__res, axiom, (! [Ts5:traffic,Ts7:traffic,Ts8:traffic]: ((((abstract @ Ts5) @ Ts7) => ((? [C3:cars]: ((((create_reservation @ Ts7) @ C3) @ Ts8))) => ((abstract @ Ts5) @ Ts8)))))).
% 2.61/1.48 thf(fact_33_select__convs_I3_J, axiom, (! [Z:$tType,Ext:real_int,Lan:nat_int,Own:cars,More:Z]: ((((own @ Z) @ (((((view_ext2 @ Z) @ Ext) @ Lan) @ Own) @ More)) = Own)))).
% 2.61/1.48 thf(fact_34_select__convs_I2_J, axiom, (! [Z:$tType,Ext:real_int,Lan:nat_int,Own:cars,More:Z]: ((((lan @ Z) @ (((((view_ext2 @ Z) @ Ext) @ Lan) @ Own) @ More)) = Lan)))).
% 2.61/1.48 thf(fact_35_fun__diff__def, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A2:(A > B),B2:(A > B),X:A]: ((((minus_minus @ B) @ (A2 @ X)) @ (B2 @ X))))))))).
% 2.61/1.48 thf(fact_36_view_Ohorizontal__chop__empty__right, axiom, (! [V:(view_ext @ product_unit)]: ((? [X_1:(view_ext @ product_unit)]: ((((hchop @ V) @ V) @ X_1)))))).
% 2.61/1.48 thf(fact_37_view_Ohorizontal__chop__empty__left, axiom, (! [V:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit)]: ((((hchop @ V) @ U2) @ V)))))).
% 2.61/1.48 thf(fact_38_view_Ohorizontal__chop__assoc2, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V32:(view_ext @ product_unit),V4:(view_ext @ product_unit)]: ((((((hchop @ V2) @ V1) @ V22) & (((hchop @ V1) @ V32) @ V4)) => (? [V5:(view_ext @ product_unit)]: (((((hchop @ V2) @ V32) @ V5) & (((hchop @ V5) @ V4) @ V22)))))))).
% 2.61/1.48 thf(fact_39_view_Ohorizontal__chop__assoc1, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),V32:(view_ext @ product_unit),V4:(view_ext @ product_unit)]: ((((((hchop @ V2) @ V1) @ V22) & (((hchop @ V22) @ V32) @ V4)) => (? [V5:(view_ext @ product_unit)]: (((((hchop @ V2) @ V5) @ V4) & (((hchop @ V5) @ V1) @ V32)))))))).
% 2.61/1.48 thf(fact_40_view_Ohorizontal__chop1, axiom, (! [V2:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit),X_1:(view_ext @ product_unit)]: ((((hchop @ V2) @ U2) @ X_1)))))).
% 2.61/1.48 thf(fact_41_traffic_Oabstract_Orefl, axiom, (! [Ts5:traffic]: (((abstract @ Ts5) @ Ts5)))).
% 2.61/1.48 thf(fact_42_traffic_Oabs__trans, axiom, (! [Ts1:traffic,Ts22:traffic,Ts0:traffic]: ((((abstract @ Ts1) @ Ts22) => (((abstract @ Ts0) @ Ts1) => ((abstract @ Ts0) @ Ts22)))))).
% 2.61/1.48 thf(fact_43_induct__scheme, axiom, (! [Z:$tType,P:((view_ext @ Z) > $o),R:(view_ext @ Z)]: (((! [Ext3:real_int,Lan3:nat_int,Own3:cars,More3:Z]: ((P @ (((((view_ext2 @ Z) @ Ext3) @ Lan3) @ Own3) @ More3)))) => (P @ R))))).
% 2.61/1.48 thf(fact_44_cases__scheme, axiom, (! [Z:$tType,R:(view_ext @ Z)]: ((~ ((! [Ext3:real_int,Lan3:nat_int,Own3:cars,More3:Z]: ((R != (((((view_ext2 @ Z) @ Ext3) @ Lan3) @ Own3) @ More3))))))))).
% 2.61/1.48 thf(fact_45_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.61/1.48 thf(fact_46_traffic_Oalways__create__res, axiom, (! [C2:cars,Ts:traffic]: ((? [X_1:traffic]: ((((create_reservation @ Ts) @ C2) @ X_1)))))).
% 2.61/1.48 thf(fact_47_view_Ohorizontal__chop__own__trans, axiom, (! [V2:(view_ext @ product_unit),U3:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V2) @ U3) @ W2) => (((own @ product_unit) @ U3) = ((own @ product_unit) @ W2)))))).
% 2.61/1.48 thf(fact_48_select__convs_I1_J, axiom, (! [Z:$tType,Ext:real_int,Lan:nat_int,Own:cars,More:Z]: ((((ext @ Z) @ (((((view_ext2 @ Z) @ Ext) @ Lan) @ Own) @ More)) = Ext)))).
% 2.61/1.48 thf(fact_49_traffic_Ocreate__reservation__def, axiom, (create_reservation = (^ [Ts6:traffic,C4:cars,Ts4:traffic]: ((((pos @ Ts4) = (pos @ Ts6)) & (((res @ Ts4) = (((((fun_upd @ cars) @ nat_int) @ (res @ Ts6)) @ C4) @ ((nat_union @ ((res @ Ts6) @ C4)) @ ((clm @ Ts6) @ C4)))) & (((dyn @ Ts4) = (dyn @ Ts6)) & (((clm @ Ts4) = (((((fun_upd @ cars) @ nat_int) @ (clm @ Ts6)) @ C4) @ (bot_bot @ nat_int))) & (((physical_size @ Ts4) = (physical_size @ Ts6)) & ((braking_distance @ Ts4) = (braking_distance @ Ts6))))))))))).
% 2.61/1.48 thf(fact_50_traffic_Oabstract_Oinducts, axiom, (! [Ts5:traffic,X3:traffic,P:(traffic > $o)]: ((((abstract @ Ts5) @ X3) => ((P @ Ts5) => ((! [Ts2:traffic,Ts9:traffic]: ((((abstract @ Ts5) @ Ts2) => ((P @ Ts2) => (((evolve @ Ts2) @ Ts9) => (P @ Ts9)))))) => ((! [Ts2:traffic,Ts9:traffic]: ((((abstract @ Ts5) @ Ts2) => ((P @ Ts2) => ((? [C:cars,N3:nat]: (((((create_claim @ Ts2) @ C) @ N3) @ Ts9))) => (P @ Ts9)))))) => ((! [Ts2:traffic,Ts9:traffic]: ((((abstract @ Ts5) @ Ts2) => ((P @ Ts2) => ((? [C:cars]: ((((withdraw_claim @ Ts2) @ C) @ Ts9))) => (P @ Ts9)))))) => ((! [Ts2:traffic,Ts9:traffic]: ((((abstract @ Ts5) @ Ts2) => ((P @ Ts2) => ((? [C:cars]: ((((create_reservation @ Ts2) @ C) @ Ts9))) => (P @ Ts9)))))) => ((! [Ts2:traffic,Ts9:traffic]: ((((abstract @ Ts5) @ Ts2) => ((P @ Ts2) => ((? [C:cars,N3:nat]: (((((withdraw_reservation @ Ts2) @ C) @ N3) @ Ts9))) => (P @ Ts9)))))) => (P @ X3))))))))))).
% 2.61/1.48 thf(fact_51_traffic_Oabstract_Osimps, axiom, (abstract = (^ [Ts6:traffic,A3:traffic]: (((A3 = Ts6) | ((? [Ts4:traffic,Ts10:traffic]: (((A3 = Ts10) & (((abstract @ Ts6) @ Ts4) & ((evolve @ Ts4) @ Ts10))))) | ((? [Ts4:traffic,Ts10:traffic]: (((A3 = Ts10) & (((abstract @ Ts6) @ Ts4) & (? [C4:cars,N4:nat]: (((((create_claim @ Ts4) @ C4) @ N4) @ Ts10))))))) | ((? [Ts4:traffic,Ts10:traffic]: (((A3 = Ts10) & (((abstract @ Ts6) @ Ts4) & (? [C4:cars]: ((((withdraw_claim @ Ts4) @ C4) @ Ts10))))))) | ((? [Ts4:traffic,Ts10:traffic]: (((A3 = Ts10) & (((abstract @ Ts6) @ Ts4) & (? [C4:cars]: ((((create_reservation @ Ts4) @ C4) @ Ts10))))))) | (? [Ts4:traffic,Ts10:traffic]: (((A3 = Ts10) & (((abstract @ Ts6) @ Ts4) & (? [C4:cars,N4:nat]: (((((withdraw_reservation @ Ts4) @ C4) @ N4) @ Ts10)))))))))))))))).
% 2.61/1.48 thf(fact_52_traffic_Oabstract_Ocases, axiom, (! [Ts5:traffic,A4:traffic]: ((((abstract @ Ts5) @ A4) => ((A4 != Ts5) => ((! [Ts2:traffic]: ((((abstract @ Ts5) @ Ts2) => (~ (((evolve @ Ts2) @ A4)))))) => ((! [Ts2:traffic]: ((((abstract @ Ts5) @ Ts2) => (~ ((? [C:cars,N3:nat]: (((((create_claim @ Ts2) @ C) @ N3) @ A4)))))))) => ((! [Ts2:traffic]: ((((abstract @ Ts5) @ Ts2) => (~ ((? [C:cars]: ((((withdraw_claim @ Ts2) @ C) @ A4)))))))) => ((! [Ts2:traffic]: ((((abstract @ Ts5) @ Ts2) => (~ ((? [C:cars]: ((((create_reservation @ Ts2) @ C) @ A4)))))))) => (~ ((! [Ts2:traffic]: ((((abstract @ Ts5) @ Ts2) => (~ ((? [C:cars,N3:nat]: (((((withdraw_reservation @ Ts2) @ C) @ N3) @ A4))))))))))))))))))).
% 2.61/1.48 thf(fact_53_surjective, axiom, (! [Z:$tType,R:(view_ext @ Z)]: ((R = (((((view_ext2 @ Z) @ ((ext @ Z) @ R)) @ ((lan @ Z) @ R)) @ ((own @ Z) @ R)) @ ((more @ Z) @ R)))))).
% 2.61/1.48 thf(fact_54_traffic_Owithdraw__clm__eq__res, axiom, (! [Ts5:traffic,D:cars,Ts7:traffic,C2:cars]: (((((withdraw_claim @ Ts5) @ D) @ Ts7) => (((res @ Ts5) @ C2) = ((res @ Ts7) @ C2)))))).
% 2.61/1.48 thf(fact_55_traffic_Ocreate__clm__eq__res, axiom, (! [Ts5:traffic,D:cars,N:nat,Ts7:traffic,C2:cars]: ((((((create_claim @ Ts5) @ D) @ N) @ Ts7) => (((res @ Ts5) @ C2) = ((res @ Ts7) @ C2)))))).
% 2.61/1.48 thf(fact_56_traffic_Ocreate__res__subseteq1__neq, axiom, (! [Ts5:traffic,D:cars,Ts7:traffic,C2:cars]: ((((((create_reservation @ Ts5) @ D) @ Ts7) & (D != C2)) => (((res @ Ts5) @ C2) = ((res @ Ts7) @ C2)))))).
% 2.61/1.48 thf(fact_57_traffic_Ocreate__res__subseteq2__neq, axiom, (! [Ts5:traffic,D:cars,Ts7:traffic,C2:cars]: ((((((create_reservation @ Ts5) @ D) @ Ts7) & (D != C2)) => (((clm @ Ts5) @ C2) = ((clm @ Ts7) @ C2)))))).
% 2.61/1.48 thf(fact_58_traffic_Oevolve__trans, axiom, (! [Ts0:traffic,Ts1:traffic,Ts22:traffic]: ((((evolve @ Ts0) @ Ts1) => (((evolve @ Ts1) @ Ts22) => ((evolve @ Ts0) @ Ts22)))))).
% 2.61/1.48 thf(fact_59_traffic_Oevolve_Orefl, axiom, (! [Ts5:traffic]: (((evolve @ Ts5) @ Ts5)))).
% 2.61/1.48 thf(fact_60_traffic_Owithdraw__claim__def, axiom, (withdraw_claim = (^ [Ts6:traffic,C4:cars,Ts4:traffic]: ((((pos @ Ts4) = (pos @ Ts6)) & (((res @ Ts4) = (res @ Ts6)) & (((dyn @ Ts4) = (dyn @ Ts6)) & (((physical_size @ Ts4) = (physical_size @ Ts6)) & (((braking_distance @ Ts4) = (braking_distance @ Ts6)) & ((clm @ Ts4) = (((((fun_upd @ cars) @ nat_int) @ (clm @ Ts6)) @ C4) @ (bot_bot @ nat_int)))))))))))).
% 2.61/1.48 thf(fact_61_traffic_Oevolve, axiom, (! [Ts5:traffic,Ts7:traffic,Ts8:traffic]: ((((abstract @ Ts5) @ Ts7) => (((evolve @ Ts7) @ Ts8) => ((abstract @ Ts5) @ Ts8)))))).
% 2.61/1.48 thf(fact_62_select__convs_I4_J, axiom, (! [Z:$tType,Ext:real_int,Lan:nat_int,Own:cars,More:Z]: ((((more @ Z) @ (((((view_ext2 @ Z) @ Ext) @ Lan) @ Own) @ More)) = More)))).
% 2.61/1.48 thf(fact_63_equality, axiom, (! [Z:$tType,R:(view_ext @ Z),R2:(view_ext @ Z)]: (((((ext @ Z) @ R) = ((ext @ Z) @ R2)) => ((((lan @ Z) @ R) = ((lan @ Z) @ R2)) => ((((own @ Z) @ R) = ((own @ Z) @ R2)) => ((((more @ Z) @ R) = ((more @ Z) @ R2)) => (R = R2)))))))).
% 2.61/1.48 thf(fact_64_fun__upd__upd, axiom, (! [A:$tType,B:$tType,F:(A > B),X3:A,Y2:B,Z2:B]: (((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ F) @ X3) @ Y2)) @ X3) @ Z2) = (((((fun_upd @ A) @ B) @ F) @ X3) @ Z2))))).
% 2.61/1.48 thf(fact_65_fun__upd__triv, axiom, (! [B:$tType,A:$tType,F:(A > B),X3:A]: (((((((fun_upd @ A) @ B) @ F) @ X3) @ (F @ X3)) = F)))).
% 2.61/1.48 thf(fact_66_fun__upd__apply, axiom, (! [A:$tType,B:$tType]: ((((fun_upd @ B) @ A) = (^ [F2:(B > A),X:B,Y:A,Z3:B]: (((((if @ A) @ (Z3 = X)) @ Y) @ (F2 @ Z3)))))))).
% 2.61/1.48 thf(fact_67_bot__apply, axiom, (! [C5:$tType,D2:$tType]: (((bot @ C5) => ((bot_bot @ (D2 > C5)) = (^ [X:D2]: ((bot_bot @ C5)))))))).
% 2.61/1.48 thf(fact_68_un__empty__absorb1, axiom, (! [I:nat_int]: ((((nat_union @ I) @ (bot_bot @ nat_int)) = I)))).
% 2.61/1.48 thf(fact_69_un__empty__absorb2, axiom, (! [I:nat_int]: ((((nat_union @ (bot_bot @ nat_int)) @ I) = I)))).
% 2.61/1.48 thf(fact_70_view_Ohchop__def, axiom, (hchop = (^ [V3:(view_ext @ product_unit),U:(view_ext @ product_unit),W:(view_ext @ product_unit)]: (((((real_R_Chop @ ((ext @ product_unit) @ V3)) @ ((ext @ product_unit) @ U)) @ ((ext @ product_unit) @ W)) & ((((lan @ product_unit) @ V3) = ((lan @ product_unit) @ U)) & ((((lan @ product_unit) @ V3) = ((lan @ product_unit) @ W)) & ((((own @ product_unit) @ V3) = ((own @ product_unit) @ U)) & ((((own @ product_unit) @ V3) = ((own @ product_unit) @ W)) & ((((more @ product_unit) @ V3) = ((more @ product_unit) @ W)) & (((more @ product_unit) @ V3) = ((more @ product_unit) @ U)))))))))))).
% 2.61/1.48 thf(fact_71_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X:A]: ((bot_bot @ B)))))))).
% 2.61/1.48 thf(fact_72_fun__upd__idem__iff, axiom, (! [A:$tType,B:$tType,F:(A > B),X3:A,Y2:B]: ((((((((fun_upd @ A) @ B) @ F) @ X3) @ Y2) = F) = ((F @ X3) = Y2))))).
% 2.61/1.48 thf(fact_73_fun__upd__twist, axiom, (! [A:$tType,B:$tType,A4:A,C2:A,M:(A > B),B3:B,D:B]: (((A4 != C2) => ((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M) @ A4) @ B3)) @ C2) @ D) = (((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M) @ C2) @ D)) @ A4) @ B3)))))).
% 2.61/1.48 thf(fact_74_fun__upd__other, axiom, (! [B:$tType,A:$tType,Z2:A,X3:A,F:(A > B),Y2:B]: (((Z2 != X3) => (((((((fun_upd @ A) @ B) @ F) @ X3) @ Y2) @ Z2) = (F @ Z2)))))).
% 2.61/1.48 thf(fact_75_fun__upd__same, axiom, (! [B:$tType,A:$tType,F:(B > A),X3:B,Y2:A]: ((((((((fun_upd @ B) @ A) @ F) @ X3) @ Y2) @ X3) = Y2)))).
% 2.61/1.48 thf(fact_76_fun__upd__idem, axiom, (! [A:$tType,B:$tType,F:(B > A),X3:B,Y2:A]: ((((F @ X3) = Y2) => ((((((fun_upd @ B) @ A) @ F) @ X3) @ Y2) = F))))).
% 2.61/1.48 thf(fact_77_fun__upd__eqD, axiom, (! [A:$tType,B:$tType,F:(A > B),X3:A,Y2:B,G:(A > B),Z2:B]: ((((((((fun_upd @ A) @ B) @ F) @ X3) @ Y2) = (((((fun_upd @ A) @ B) @ G) @ X3) @ Z2)) => (Y2 = Z2))))).
% 2.61/1.48 thf(fact_78_fun__upd__def, axiom, (! [B:$tType,A:$tType]: ((((fun_upd @ A) @ B) = (^ [F2:(A > B),A3:A,B4:B,X:A]: (((((if @ B) @ (X = A3)) @ B4) @ (F2 @ X)))))))).
% 2.61/1.48 thf(fact_79_traffic_Ochange__dyn__def, axiom, (change_dyn = (^ [Ts6:traffic,C4:cars,F2:(real > real),Ts4:traffic]: ((((pos @ Ts4) = (pos @ Ts6)) & (((res @ Ts4) = (res @ Ts6)) & (((clm @ Ts4) = (clm @ Ts6)) & (((dyn @ Ts4) = (((((fun_upd @ cars) @ (real > real)) @ (dyn @ Ts6)) @ C4) @ F2)) & ((physical_size @ Ts4) = (physical_size @ Ts6)))))))))).
% 2.61/1.48 thf(fact_80_local_Ohmlsl_Owidth__hchop__stable, axiom, (! [X3:nat,Ts:traffic,V:(view_ext @ product_unit)]: ((((nat_card @ ((lan @ product_unit) @ V)) = X3) = (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & (((nat_card @ ((lan @ product_unit) @ W)) = X3) & ((nat_card @ ((lan @ product_unit) @ U)) = X3))))))))).
% 2.61/1.48 thf(fact_81_chop__singleton__right, axiom, (! [R3:real_int]: ((? [X_1:real_int]: ((((real_R_Chop @ R3) @ R3) @ X_1)))))).
% 2.61/1.48 thf(fact_82_real__int__class_Ochop__always__possible, axiom, (! [R3:real_int]: ((? [S:real_int,X_1:real_int]: ((((real_R_Chop @ R3) @ S) @ X_1)))))).
% 2.61/1.48 thf(fact_83_chop__singleton__left, axiom, (! [R3:real_int]: ((? [S:real_int]: ((((real_R_Chop @ R3) @ S) @ R3)))))).
% 2.61/1.48 thf(fact_84_view_Oswitch__def, axiom, (switch = (^ [V3:(view_ext @ product_unit),C4:cars,W:(view_ext @ product_unit)]: (((((ext @ product_unit) @ V3) = ((ext @ product_unit) @ W)) & ((((lan @ product_unit) @ V3) = ((lan @ product_unit) @ W)) & ((((own @ product_unit) @ W) = C4) & (((more @ product_unit) @ V3) = ((more @ product_unit) @ W))))))))).
% 2.61/1.48 thf(fact_85_local_Ohmlsl_Oat__conj__distr, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => (((Phi @ Ts) @ V6) & ((Psi @ Ts) @ V6))))) = ((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => ((Phi @ Ts) @ V6)))) & (! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => ((Psi @ Ts) @ V6))))))))).
% 2.61/1.48 thf(fact_86_local_Ohmlsl_Oat__disj__dist, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => (((Phi @ Ts) @ V6) | ((Psi @ Ts) @ V6))))) = ((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => ((Phi @ Ts) @ V6)))) | (! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => ((Psi @ Ts) @ V6))))))))).
% 2.61/1.48 thf(fact_87_local_Ohmlsl_Oat__eq, axiom, (! [A:$tType,E:cars,C2:A,D:A,Ts:traffic,V:(view_ext @ product_unit)]: (((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ E) @ V6) => (C2 = D)))) = (C2 = D))))).
% 2.61/1.48 thf(fact_88_local_Ohmlsl_Oat__exists, axiom, (! [Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: ((((Phi @ Ts) @ V) => (? [X2:cars]: ((! [V7:(view_ext @ product_unit)]: (((((switch @ V) @ X2) @ V7) => ((Phi @ Ts) @ V7)))))))))).
% 2.61/1.48 thf(fact_89_local_Ohmlsl_Oat__neg, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => (~ (((Phi @ Ts) @ V6)))))) = (~ ((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => ((Phi @ Ts) @ V6)))))))))).
% 2.61/1.48 thf(fact_90_local_Ohmlsl_Oat__neg_H, axiom, (! [V2:(view_ext @ product_unit),C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts5:traffic]: (((~ ((! [V6:(view_ext @ product_unit)]: (((((switch @ V2) @ C2) @ V6) => ((Phi @ Ts5) @ V6)))))) = (! [V6:(view_ext @ product_unit)]: (((((switch @ V2) @ C2) @ V6) => (~ (((Phi @ Ts5) @ V6)))))))))).
% 2.61/1.48 thf(fact_91_local_Ohmlsl_Oat__neg1, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [V5:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V5) => (~ (((Phi @ Ts) @ V5)))))) => (~ ((! [V5:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V5) => ((Phi @ Ts) @ V5)))))))))).
% 2.61/1.48 thf(fact_92_local_Ohmlsl_Oat__neg2, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((~ ((! [V7:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V7) => ((Phi @ Ts) @ V7)))))) => (! [V7:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V7) => (~ (((Phi @ Ts) @ V7)))))))))).
% 2.61/1.48 thf(fact_93_local_Ohmlsl_Oat__neg__neg, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => ((Phi @ Ts) @ V6)))) = (~ ((! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => (~ (((Phi @ Ts) @ V6)))))))))))).
% 2.61/1.48 thf(fact_94_local_Ohmlsl_Oat__neg__neg1, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [V5:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V5) => ((Phi @ Ts) @ V5)))) => (~ ((! [V5:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V5) => (~ (((Phi @ Ts) @ V5)))))))))))).
% 2.61/1.48 thf(fact_95_local_Ohmlsl_Oat__neg__neg2, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((~ ((! [V7:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V7) => (~ (((Phi @ Ts) @ V7)))))))) => (! [V7:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V7) => ((Phi @ Ts) @ V7)))))))).
% 2.61/1.48 thf(fact_96_local_Ohmlsl_Oat__hchop__dist, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V) @ W) @ U) & ((! [V6:(view_ext @ product_unit)]: (((((switch @ W) @ C2) @ V6) => ((Phi @ Ts) @ V6)))) & (! [V6:(view_ext @ product_unit)]: (((((switch @ U) @ C2) @ V6) => ((Psi @ Ts) @ V6)))))))) = (! [V6:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V6) => (? [W:(view_ext @ product_unit),U:(view_ext @ product_unit)]: (((((hchop @ V6) @ W) @ U) & (((Phi @ Ts) @ W) & ((Psi @ Ts) @ U)))))))))))).
% 2.61/1.48 thf(fact_97_local_Ohmlsl_Oat__hchop__dist1, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((! [V5:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V5) => (? [Va2:(view_ext @ product_unit),U4:(view_ext @ product_unit)]: (((((hchop @ V5) @ Va2) @ U4) & (((Phi @ Ts) @ Va2) & ((Psi @ Ts) @ U4)))))))) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V) @ Va) @ U2) & ((! [V7:(view_ext @ product_unit)]: (((((switch @ Va) @ C2) @ V7) => ((Phi @ Ts) @ V7)))) & (! [V7:(view_ext @ product_unit)]: (((((switch @ U2) @ C2) @ V7) => ((Psi @ Ts) @ V7)))))))))))).
% 2.61/1.48 thf(fact_98_local_Ohmlsl_Oat__hchop__dist2, axiom, (! [C2:cars,Phi:(traffic > ((view_ext @ product_unit) > $o)),Psi:(traffic > ((view_ext @ product_unit) > $o)),Ts:traffic,V:(view_ext @ product_unit)]: (((? [Va2:(view_ext @ product_unit),U4:(view_ext @ product_unit)]: (((((hchop @ V) @ Va2) @ U4) & ((! [V5:(view_ext @ product_unit)]: (((((switch @ Va2) @ C2) @ V5) => ((Phi @ Ts) @ V5)))) & (! [V5:(view_ext @ product_unit)]: (((((switch @ U4) @ C2) @ V5) => ((Psi @ Ts) @ V5)))))))) => (! [V7:(view_ext @ product_unit)]: (((((switch @ V) @ C2) @ V7) => (? [Va:(view_ext @ product_unit),U2:(view_ext @ product_unit)]: (((((hchop @ V7) @ Va) @ U2) & (((Phi @ Ts) @ Va) & ((Psi @ Ts) @ U2)))))))))))).
% 2.61/1.48 thf(fact_99_view_Oswitch__always__exists, axiom, (! [V2:(view_ext @ product_unit),C3:cars]: ((? [X_1:(view_ext @ product_unit)]: ((((switch @ V2) @ C3) @ X_1)))))).
% 2.61/1.48 thf(fact_100_view_Oswitch__triangle, axiom, (! [V2:(view_ext @ product_unit),C2:cars,U3:(view_ext @ product_unit),D:cars,W2:(view_ext @ product_unit)]: ((((((switch @ V2) @ C2) @ U3) & (((switch @ V2) @ D) @ W2)) => (((switch @ U3) @ D) @ W2))))).
% 2.61/1.48 thf(fact_101_view_Oswitch__unique, axiom, (! [V2:(view_ext @ product_unit),C2:cars,U3:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: ((((((switch @ V2) @ C2) @ U3) & (((switch @ V2) @ C2) @ W2)) => (U3 = W2))))).
% 2.61/1.48 thf(fact_102_view_Oswitch__exists, axiom, (! [V2:(view_ext @ product_unit)]: ((? [C:cars,X_1:(view_ext @ product_unit)]: ((((switch @ V2) @ C) @ X_1)))))).
% 2.61/1.48 thf(fact_103_view_Oswitch__trans, axiom, (! [V2:(view_ext @ product_unit),C2:cars,U3:(view_ext @ product_unit),D:cars,W2:(view_ext @ product_unit)]: ((((((switch @ V2) @ C2) @ U3) & (((switch @ U3) @ D) @ W2)) => (((switch @ V2) @ D) @ W2))))).
% 2.61/1.48 thf(fact_104_view_Oswitch__hchop1, axiom, (! [V2:(view_ext @ product_unit),V1:(view_ext @ product_unit),V22:(view_ext @ product_unit),C2:cars,V8:(view_ext @ product_unit)]: ((((((hchop @ V2) @ V1) @ V22) & (((switch @ V2) @ C2) @ V8)) => (? [V12:(view_ext @ product_unit),V23:(view_ext @ product_unit)]: (((((switch @ V1) @ C2) @ V12) & ((((switch @ V22) @ C2) @ V23) & (((hchop @ V8) @ V12) @ V23))))))))).
% 2.61/1.48 thf(fact_105_view_Oswitch__hchop2, axiom, (! [V8:(view_ext @ product_unit),V13:(view_ext @ product_unit),V24:(view_ext @ product_unit),V2:(view_ext @ product_unit),C2:cars]: ((((((hchop @ V8) @ V13) @ V24) & (((switch @ V2) @ C2) @ V8)) => (? [V14:(view_ext @ product_unit),V25:(view_ext @ product_unit)]: (((((switch @ V14) @ C2) @ V13) & ((((switch @ V25) @ C2) @ V24) & (((hchop @ V2) @ V14) @ V25))))))))).
% 2.61/1.48 thf(fact_106_view_Oswitch__refl, axiom, (! [V2:(view_ext @ product_unit)]: ((((switch @ V2) @ ((own @ product_unit) @ V2)) @ V2)))).
% 2.61/1.48 thf(fact_107_view_Oswitch__symm, axiom, (! [V2:(view_ext @ product_unit),C2:cars,U3:(view_ext @ product_unit)]: (((((switch @ V2) @ C2) @ U3) => (((switch @ U3) @ ((own @ product_unit) @ V2)) @ V2))))).
% 2.61/1.48 thf(fact_108_view_Oswitch__origin, axiom, (! [V2:(view_ext @ product_unit)]: ((? [U2:(view_ext @ product_unit)]: ((((switch @ U2) @ ((own @ product_unit) @ V2)) @ V2)))))).
% 2.61/1.48 thf(fact_109_view_Ohorizontal__chop__width__stable, axiom, (! [V2:(view_ext @ product_unit),U3:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V2) @ U3) @ W2) => (((nat_card @ ((lan @ product_unit) @ V2)) = (nat_card @ ((lan @ product_unit) @ U3))) & ((nat_card @ ((lan @ product_unit) @ V2)) = (nat_card @ ((lan @ product_unit) @ W2)))))))).
% 2.61/1.48 thf(fact_110_traffic_Ochange, axiom, (! [Ts5:traffic,Ts7:traffic,Ts8:traffic]: (((? [C3:cars,F3:(real > real)]: (((((change_dyn @ Ts5) @ C3) @ F3) @ Ts7))) => (((evolve @ Ts7) @ Ts8) => ((evolve @ Ts5) @ Ts8)))))).
% 2.61/1.48 thf(fact_111_old_Ounit_Oexhaust, axiom, (! [Y2:product_unit]: ((Y2 = product_Unity)))).
% 2.61/1.48 thf(fact_112_old_Ounit_Oinducts, axiom, (! [P:(product_unit > $o),Unit:product_unit]: (((P @ product_Unity) => (P @ Unit))))).
% 2.61/1.48 thf(fact_113_unit__all__impI, axiom, (! [P:(product_unit > $o),Q:(product_unit > $o)]: ((((P @ product_Unity) => (Q @ product_Unity)) => (! [X4:product_unit]: (((P @ X4) => (Q @ X4)))))))).
% 2.61/1.48 thf(fact_114_eq__sym__Unity__conv, axiom, (! [X3:$o]: (((X3 = (product_Unity = product_Unity)) = X3)))).
% 2.61/1.48 thf(fact_115_bot__unit__def, axiom, ((bot_bot @ product_unit) = product_Unity)).
% 2.61/1.48 thf(fact_116_traffic_Ocreate__res__subseteq2, axiom, (! [Ts5:traffic,C2:cars,Ts7:traffic]: (((((create_reservation @ Ts5) @ C2) @ Ts7) => (((ord_less_eq @ nat_int) @ ((clm @ Ts5) @ C2)) @ ((res @ Ts7) @ C2)))))).
% 2.61/1.48 thf(fact_117_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.61/1.48 thf(fact_118_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3))))))))).
% 2.61/1.48 thf(fact_119_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X3:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3))))))))).
% 2.61/1.48 thf(fact_120_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X2:A]: ((((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.61/1.48 thf(fact_121_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X:A]: ((((ord_less_eq @ B) @ (F2 @ X)) @ (G2 @ X))))))))))).
% 2.61/1.48 thf(fact_122_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B3:B,C2:B]: (((((ord_less_eq @ A) @ A4) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A4) @ (F @ C2))))))))))).
% 2.61/1.48 thf(fact_123_order__subst2, axiom, (! [A:$tType,C5:$tType]: ((((order @ C5) & (order @ A)) => (! [A4:A,B3:A,F:(A > C5),C2:C5]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less_eq @ C5) @ (F @ B3)) @ C2) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ C5) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ C5) @ (F @ A4)) @ C2)))))))))).
% 2.61/1.48 thf(fact_124_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,F:(B > A),B3:B,C2:B]: (((A4 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A4) @ (F @ C2))))))))))).
% 2.61/1.48 thf(fact_125_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,B3:A,F:(A > B),C2:B]: (((((ord_less_eq @ A) @ A4) @ B3) => (((F @ B3) = C2) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ B) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ B) @ (F @ A4)) @ C2)))))))))).
% 2.61/1.48 thf(fact_126_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z4:A]: ((Y4 = Z4))) = (^ [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) & (((ord_less_eq @ A) @ Y) @ X))))))))).
% 2.61/1.48 thf(fact_127_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ X3) => (X3 = Y2))))))))).
% 2.61/1.48 thf(fact_128_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) | (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 2.61/1.48 thf(fact_129_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((X3 = Y2) => (((ord_less_eq @ A) @ X3) @ Y2)))))))).
% 2.61/1.48 thf(fact_130_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 2.61/1.48 thf(fact_131_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less_eq @ A) @ B3) @ C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 2.61/1.48 thf(fact_132_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z2)))) => (((((ord_less_eq @ A) @ Y2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y2)))) => (((((ord_less_eq @ A) @ Z2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X3)))) => (((((ord_less_eq @ A) @ Y2) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y2))))))))))))))))).
% 2.61/1.48 thf(fact_133_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ Y2) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y2) = (X3 = Y2))))))))).
% 2.61/1.48 thf(fact_134_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z4:A]: ((Y4 = Z4))) = (^ [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ B4) & (((ord_less_eq @ A) @ B4) @ A3))))))))).
% 2.61/1.48 thf(fact_135_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B3:A,C2:A]: (((A4 = B3) => ((((ord_less_eq @ A) @ B3) @ C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 2.61/1.48 thf(fact_136_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((B3 = C2) => (((ord_less_eq @ A) @ A4) @ C2))))))))).
% 2.61/1.48 thf(fact_137_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less_eq @ A) @ B3) @ A4) => (A4 = B3))))))))).
% 2.61/1.48 thf(fact_138_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 2.61/1.48 thf(fact_139_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A]: ((((ord_less_eq @ A) @ A4) @ A4))))))).
% 2.61/1.48 thf(fact_140_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A4:A,B3:A]: (((! [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) => ((P @ A5) @ B5)))) => ((! [A5:A,B5:A]: ((((P @ B5) @ A5) => ((P @ A5) @ B5)))) => ((P @ A4) @ B3))))))))).
% 2.61/1.48 thf(fact_141_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B3) @ A4) => ((((ord_less_eq @ A) @ C2) @ B3) => (((ord_less_eq @ A) @ C2) @ A4))))))))).
% 2.61/1.48 thf(fact_142_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z4:A]: ((Y4 = Z4))) = (^ [A3:A,B4:A]: (((((ord_less_eq @ A) @ B4) @ A3) & (((ord_less_eq @ A) @ A3) @ B4))))))))).
% 2.61/1.48 thf(fact_143_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A4:A]: (((((ord_less_eq @ A) @ B3) @ A4) => ((((ord_less_eq @ A) @ A4) @ B3) => (A4 = B3))))))))).
% 2.61/1.48 thf(fact_144_less__eq__view__ext__def, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ (view_ext @ A)) = (^ [V9:(view_ext @ A),V10:(view_ext @ A)]: (((((ord_less_eq @ real_int) @ ((ext @ A) @ V9)) @ ((ext @ A) @ V10)) & ((((ord_less_eq @ nat_int) @ ((lan @ A) @ V9)) @ ((lan @ A) @ V10)) & ((((own @ A) @ V9) = ((own @ A) @ V10)) & (((ord_less_eq @ A) @ ((more @ A) @ V9)) @ ((more @ A) @ V10)))))))))))).
% 2.61/1.48 thf(fact_145_bot_Oextremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A4:A]: ((((ord_less_eq @ A) @ (bot_bot @ A)) @ A4))))))).
% 2.61/1.48 thf(fact_146_bot_Oextremum__unique, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A4:A]: (((((ord_less_eq @ A) @ A4) @ (bot_bot @ A)) = (A4 = (bot_bot @ A))))))))).
% 2.61/1.48 thf(fact_147_bot_Oextremum__uniqueI, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A4:A]: (((((ord_less_eq @ A) @ A4) @ (bot_bot @ A)) => (A4 = (bot_bot @ A))))))))).
% 2.61/1.48 thf(fact_148_traffic_Ocreate__res__subseteq1, axiom, (! [Ts5:traffic,C2:cars,Ts7:traffic]: (((((create_reservation @ Ts5) @ C2) @ Ts7) => (((ord_less_eq @ nat_int) @ ((res @ Ts5) @ C2)) @ ((res @ Ts7) @ C2)))))).
% 2.61/1.48 thf(fact_149_traffic_Owithdraw__res__subseteq, axiom, (! [Ts5:traffic,D:cars,N:nat,Ts7:traffic,C2:cars]: ((((((withdraw_reservation @ Ts5) @ D) @ N) @ Ts7) => (((ord_less_eq @ nat_int) @ ((res @ Ts7) @ C2)) @ ((res @ Ts5) @ C2)))))).
% 2.61/1.48 thf(fact_150_old_Ounit_Orec, axiom, (! [T:$tType,F1:T]: (((((product_rec_unit @ T) @ F1) @ product_Unity) = F1)))).
% 2.61/1.48 thf(fact_151_default__unit__def, axiom, ((default_default @ product_unit) = product_Unity)).
% 2.61/1.48 thf(fact_152_less__view__ext__def, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ (view_ext @ A)) = (^ [V9:(view_ext @ A),V10:(view_ext @ A)]: (((((ord_less_eq @ real_int) @ ((ext @ A) @ V9)) @ ((ext @ A) @ V10)) & ((((ord_less_eq @ nat_int) @ ((lan @ A) @ V9)) @ ((lan @ A) @ V10)) & ((((own @ A) @ V10) = ((own @ A) @ V9)) & ((((ord_less_eq @ A) @ ((more @ A) @ V9)) @ ((more @ A) @ V10)) & (~ (((((ord_less_eq @ real_int) @ ((ext @ A) @ V10)) @ ((ext @ A) @ V9)) & ((((ord_less_eq @ nat_int) @ ((lan @ A) @ V10)) @ ((lan @ A) @ V9)) & ((((own @ A) @ V10) = ((own @ A) @ V9)) & (((ord_less_eq @ A) @ ((more @ A) @ V10)) @ ((more @ A) @ V9)))))))))))))))))).
% 2.61/1.48 thf(fact_153_diff__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B3:A,D:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less_eq @ A) @ D) @ C2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ (((minus_minus @ A) @ B3) @ D)))))))))).
% 2.61/1.48 thf(fact_154_leD, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X3:A]: (((((ord_less_eq @ A) @ Y2) @ X3) => (~ ((((ord_less @ A) @ X3) @ Y2)))))))))).
% 2.61/1.48 thf(fact_155_leI, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 2.61/1.48 thf(fact_156_le__less, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | (X = Y))))))))).
% 2.61/1.48 thf(fact_157_less__le, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) & (X != Y))))))))).
% 2.61/1.48 thf(fact_158_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B3:B,C2:B]: (((((ord_less_eq @ A) @ A4) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 2.61/1.48 thf(fact_159_order__le__less__subst2, axiom, (! [A:$tType,C5:$tType]: ((((order @ C5) & (order @ A)) => (! [A4:A,B3:A,F:(A > C5),C2:C5]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less @ C5) @ (F @ B3)) @ C2) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ C5) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ C5) @ (F @ A4)) @ C2)))))))))).
% 2.61/1.48 thf(fact_160_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B3:B,C2:B]: (((((ord_less @ A) @ A4) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 2.61/1.48 thf(fact_161_order__less__le__subst2, axiom, (! [A:$tType,C5:$tType]: ((((order @ C5) & (order @ A)) => (! [A4:A,B3:A,F:(A > C5),C2:C5]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less_eq @ C5) @ (F @ B3)) @ C2) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ C5) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ C5) @ (F @ A4)) @ C2)))))))))).
% 2.61/1.48 thf(fact_162_not__le, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y2))) = (((ord_less @ A) @ Y2) @ X3)))))))).
% 2.61/1.48 thf(fact_163_not__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) = (((ord_less_eq @ A) @ Y2) @ X3)))))))).
% 2.61/1.48 thf(fact_164_le__neq__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((A4 != B3) => (((ord_less @ A) @ A4) @ B3))))))))).
% 2.61/1.48 thf(fact_165_antisym__conv1, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => ((((ord_less_eq @ A) @ X3) @ Y2) = (X3 = Y2))))))))).
% 2.61/1.48 thf(fact_166_antisym__conv2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((~ ((((ord_less @ A) @ X3) @ Y2))) = (X3 = Y2))))))))).
% 2.61/1.48 thf(fact_167_less__imp__le, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less_eq @ A) @ X3) @ Y2)))))))).
% 2.61/1.48 thf(fact_168_le__less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ Z2) => (((ord_less @ A) @ X3) @ Z2))))))))).
% 2.61/1.48 thf(fact_169_less__le__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z2) => (((ord_less @ A) @ X3) @ Z2))))))))).
% 2.61/1.48 thf(fact_170_dense__ge, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z2:A,Y2:A]: (((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => (((ord_less_eq @ A) @ Y2) @ X2)))) => (((ord_less_eq @ A) @ Y2) @ Z2)))))))).
% 2.61/1.48 thf(fact_171_dense__le, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Y2:A,Z2:A]: (((! [X2:A]: (((((ord_less @ A) @ X2) @ Y2) => (((ord_less_eq @ A) @ X2) @ Z2)))) => (((ord_less_eq @ A) @ Y2) @ Z2)))))))).
% 2.61/1.48 thf(fact_172_le__less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) | (((ord_less @ A) @ Y2) @ X3)))))))).
% 2.61/1.48 thf(fact_173_le__imp__less__or__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => ((((ord_less @ A) @ X3) @ Y2) | (X3 = Y2))))))))).
% 2.61/1.48 thf(fact_174_less__le__not__le, axiom, (! [A:$tType]: (((preorder @ A) => ((ord_less @ A) = (^ [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) & (~ ((((ord_less_eq @ A) @ Y) @ X))))))))))).
% 2.61/1.48 thf(fact_175_not__le__imp__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X3:A]: (((~ ((((ord_less_eq @ A) @ Y2) @ X3))) => (((ord_less @ A) @ X3) @ Y2)))))))).
% 2.61/1.48 thf(fact_176_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.61/1.48 thf(fact_177_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A,C2:A]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less_eq @ A) @ B3) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.61/1.48 thf(fact_178_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A3:A,B4:A]: (((((ord_less @ A) @ A3) @ B4) | (A3 = B4))))))))).
% 2.61/1.48 thf(fact_179_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A3:A,B4:A]: (((((ord_less_eq @ A) @ A3) @ B4) & (A3 != B4))))))))).
% 2.61/1.48 thf(fact_180_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B3) @ A4) => ((((ord_less @ A) @ C2) @ B3) => (((ord_less @ A) @ C2) @ A4))))))))).
% 2.61/1.48 thf(fact_181_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A4:A,C2:A]: (((((ord_less @ A) @ B3) @ A4) => ((((ord_less_eq @ A) @ C2) @ B3) => (((ord_less @ A) @ C2) @ A4))))))))).
% 2.61/1.48 thf(fact_182_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z2:A,X3:A,Y2:A]: (((((ord_less @ A) @ Z2) @ X3) => ((! [W3:A]: (((((ord_less @ A) @ Z2) @ W3) => ((((ord_less @ A) @ W3) @ X3) => (((ord_less_eq @ A) @ Y2) @ W3))))) => (((ord_less_eq @ A) @ Y2) @ Z2))))))))).
% 2.61/1.48 thf(fact_183_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less @ A) @ X3) @ Y2) => ((! [W3:A]: (((((ord_less @ A) @ X3) @ W3) => ((((ord_less @ A) @ W3) @ Y2) => (((ord_less_eq @ A) @ W3) @ Z2))))) => (((ord_less_eq @ A) @ Y2) @ Z2))))))))).
% 2.61/1.48 thf(fact_184_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (((ord_less_eq @ A) @ A4) @ B3)))))))).
% 2.61/1.48 thf(fact_185_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B4:A,A3:A]: (((((ord_less @ A) @ B4) @ A3) | (A3 = B4))))))))).
% 2.61/1.48 thf(fact_186_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B4:A,A3:A]: (((((ord_less_eq @ A) @ B4) @ A3) & (A3 != B4))))))))).
% 2.61/1.48 thf(fact_187_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) => (((ord_less_eq @ A) @ B3) @ A4)))))))).
% 2.61/1.48 thf(fact_188_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A]: (((A4 != B3) => ((((ord_less_eq @ A) @ A4) @ B3) => (((ord_less @ A) @ A4) @ B3))))))))).
% 2.61/1.48 thf(fact_189_bot_Oextremum__strict, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ (bot_bot @ A)))))))))).
% 2.61/1.48 thf(fact_190_bot_Onot__eq__extremum, axiom, (! [A:$tType]: (((order_bot @ A) => (! [A4:A]: (((A4 != (bot_bot @ A)) = (((ord_less @ A) @ (bot_bot @ A)) @ A4)))))))).
% 2.61/1.48 thf(fact_191_view_Ohorizontal__chop__leq2, axiom, (! [V2:(view_ext @ product_unit),U3:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V2) @ U3) @ W2) => (((ord_less_eq @ (view_ext @ product_unit)) @ W2) @ V2))))).
% 2.61/1.48 thf(fact_192_view_Ohorizontal__chop__leq1, axiom, (! [V2:(view_ext @ product_unit),U3:(view_ext @ product_unit),W2:(view_ext @ product_unit)]: (((((hchop @ V2) @ U3) @ W2) => (((ord_less_eq @ (view_ext @ product_unit)) @ U3) @ V2))))).
% 2.61/1.48 thf(fact_193_view_Oswitch__leq, axiom, (! [U5:(view_ext @ product_unit),U3:(view_ext @ product_unit),V2:(view_ext @ product_unit),C2:cars]: ((((((ord_less_eq @ (view_ext @ product_unit)) @ U5) @ U3) & (((switch @ V2) @ C2) @ U3)) => (? [V5:(view_ext @ product_unit)]: (((((switch @ V5) @ C2) @ U5) & (((ord_less_eq @ (view_ext @ product_unit)) @ V5) @ V2)))))))).
% 2.61/1.48 thf(fact_194_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) => (A4 != B3)))))))).
% 2.61/1.48 thf(fact_195_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (A4 != B3)))))))).
% 2.61/1.48 thf(fact_196_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) = ((((ord_less @ A) @ Y2) @ X3) | (X3 = Y2))))))))).
% 2.61/1.48 thf(fact_197_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A4:A,C2:A]: (((((ord_less @ A) @ B3) @ A4) => ((((ord_less @ A) @ C2) @ B3) => (((ord_less @ A) @ C2) @ A4))))))))).
% 2.61/1.48 thf(fact_198_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A4:A,B3:A]: (((! [A5:A,B5:A]: (((((ord_less @ A) @ A5) @ B5) => ((P @ A5) @ B5)))) => ((! [A5:A]: (((P @ A5) @ A5))) => ((! [A5:A,B5:A]: ((((P @ B5) @ A5) => ((P @ A5) @ B5)))) => ((P @ A4) @ B3)))))))))).
% 2.61/1.48 thf(fact_199_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P2:(A > $o)]: ((? [X5:A]: ((P2 @ X5))))) = (^ [P3:(A > $o)]: ((? [N4:A]: (((P3 @ N4) & (! [M2:A]: (((((ord_less @ A) @ M2) @ N4) => (~ ((P3 @ M2)))))))))))))))).
% 2.61/1.48 thf(fact_200_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 2.61/1.48 thf(fact_201_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A,C2:A]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.61/1.48 thf(fact_202_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ A4))))))))).
% 2.61/1.48 thf(fact_203_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((~ ((((ord_less @ A) @ X3) @ Y2))) => ((X3 != Y2) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 2.61/1.48 thf(fact_204_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,P:$o]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ X3) => P)))))))).
% 2.61/1.48 thf(fact_205_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (Y2 != X3)))))))).
% 2.61/1.48 thf(fact_206_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y2:A,X3:A]: (((~ ((((ord_less @ A) @ Y2) @ X3))) => ((~ ((((ord_less @ A) @ X3) @ Y2))) = (X3 = Y2))))))))).
% 2.61/1.48 thf(fact_207_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A4:A]: (((! [X2:A]: (((! [Y5:A]: (((((ord_less @ A) @ Y5) @ X2) => (P @ Y5)))) => (P @ X2)))) => (P @ A4)))))))).
% 2.61/1.48 thf(fact_208_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 2.61/1.48 thf(fact_209_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (X3 != Y2)))))))).
% 2.61/1.48 thf(fact_210_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) => (~ ((((ord_less @ A) @ A4) @ B3)))))))))).
% 2.61/1.48 thf(fact_211_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B3:A,C2:A]: (((((ord_less @ A) @ A4) @ B3) => ((B3 = C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.61/1.48 thf(fact_212_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A4:A,B3:A,C2:A]: (((A4 = B3) => ((((ord_less @ A) @ B3) @ C2) => (((ord_less @ A) @ A4) @ C2))))))))).
% 2.61/1.48 thf(fact_213_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((~ ((((ord_less @ A) @ X3) @ X3))))))))).
% 2.61/1.48 thf(fact_214_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) | ((X3 = Y2) | (((ord_less @ A) @ Y2) @ X3))))))))).
% 2.61/1.48 thf(fact_215_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A,Z2:A]: (((((ord_less @ A) @ X3) @ Y2) => ((((ord_less @ A) @ Y2) @ Z2) => (((ord_less @ A) @ X3) @ Z2))))))))).
% 2.61/1.48 thf(fact_216_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (~ ((((ord_less @ A) @ B3) @ A4)))))))))).
% 2.61/1.48 thf(fact_217_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (~ ((((ord_less @ A) @ Y2) @ X3)))))))))).
% 2.61/1.48 thf(fact_218_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (X3 != Y2)))))))).
% 2.61/1.48 thf(fact_219_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (? [Z5:A]: (((((ord_less @ A) @ X3) @ Z5) & (((ord_less @ A) @ Z5) @ Y2))))))))))).
% 2.61/1.48 thf(fact_220_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (~ ((((ord_less @ A) @ B3) @ A4)))))))))).
% 2.61/1.48 thf(fact_221_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((X3 != Y2) = ((((ord_less @ A) @ X3) @ Y2) | (((ord_less @ A) @ Y2) @ X3))))))))).
% 2.61/1.48 thf(fact_222_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y2:A]: (((X3 != Y2) => ((~ ((((ord_less @ A) @ X3) @ Y2))) => (((ord_less @ A) @ Y2) @ X3))))))))).
% 2.61/1.48 thf(fact_223_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X3:A]: ((? [X_1:A]: ((((ord_less @ A) @ X3) @ X_1))))))))).
% 2.61/1.48 thf(fact_224_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X3:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X3))))))))).
% 2.61/1.48 thf(fact_225_order__less__subst2, axiom, (! [A:$tType,C5:$tType]: ((((order @ C5) & (order @ A)) => (! [A4:A,B3:A,F:(A > C5),C2:C5]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less @ C5) @ (F @ B3)) @ C2) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ C5) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ C5) @ (F @ A4)) @ C2)))))))))).
% 2.61/1.48 thf(fact_226_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A4:A,F:(B > A),B3:B,C2:B]: (((((ord_less @ A) @ A4) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 2.61/1.48 thf(fact_227_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,B3:A,F:(A > B),C2:B]: (((((ord_less @ A) @ A4) @ B3) => (((F @ B3) = C2) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ B) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ B) @ (F @ A4)) @ C2)))))))))).
% 2.61/1.48 thf(fact_228_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A4:A,F:(B > A),B3:B,C2:B]: (((A4 = (F @ B3)) => ((((ord_less @ B) @ B3) @ C2) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less @ A) @ A4) @ (F @ C2))))))))))).
% 2.61/1.48 thf(fact_229_diff__strict__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B3:A,C2:A]: (((((ord_less @ A) @ A4) @ B3) => (((ord_less @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ (((minus_minus @ A) @ B3) @ C2))))))))).
% 2.61/1.48 thf(fact_230_diff__strict__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A4:A,C2:A]: (((((ord_less @ A) @ B3) @ A4) => (((ord_less @ A) @ (((minus_minus @ A) @ C2) @ A4)) @ (((minus_minus @ A) @ C2) @ B3))))))))).
% 2.61/1.48 thf(fact_231_diff__eq__diff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B3:A,C2:A,D:A]: ((((((minus_minus @ A) @ A4) @ B3) = (((minus_minus @ A) @ C2) @ D)) => ((((ord_less @ A) @ A4) @ B3) = (((ord_less @ A) @ C2) @ D))))))))).
% 2.61/1.48 thf(fact_232_diff__strict__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B3:A,D:A,C2:A]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less @ A) @ D) @ C2) => (((ord_less @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ (((minus_minus @ A) @ B3) @ D)))))))))).
% 2.61/1.48 thf(fact_233_chop__leq2, axiom, (! [R:real_int,S2:real_int,T2:real_int]: (((((real_R_Chop @ R) @ S2) @ T2) => (((ord_less_eq @ real_int) @ T2) @ R))))).
% 2.61/1.48 thf(fact_234_chop__leq1, axiom, (! [R:real_int,S2:real_int,T2:real_int]: (((((real_R_Chop @ R) @ S2) @ T2) => (((ord_less_eq @ real_int) @ S2) @ R))))).
% 2.61/1.48 thf(fact_235_card__subset__le, axiom, (! [I:nat_int,I2:nat_int]: (((((ord_less_eq @ nat_int) @ I) @ I2) => (((ord_less_eq @ nat) @ (nat_card @ I)) @ (nat_card @ I2)))))).
% 2.61/1.48 thf(fact_236_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A4:A,B3:A,C2:A,D:A]: ((((((minus_minus @ A) @ A4) @ B3) = (((minus_minus @ A) @ C2) @ D)) => ((A4 = B3) = (C2 = D))))))))).
% 2.61/1.48 thf(fact_237_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A4:A,C2:A,B3:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ B3) = (((minus_minus @ A) @ (((minus_minus @ A) @ A4) @ B3)) @ C2)))))))).
% 2.61/1.48 thf(fact_238_diff__eq__diff__less__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B3:A,C2:A,D:A]: ((((((minus_minus @ A) @ A4) @ B3) = (((minus_minus @ A) @ C2) @ D)) => ((((ord_less_eq @ A) @ A4) @ B3) = (((ord_less_eq @ A) @ C2) @ D))))))))).
% 2.61/1.48 thf(fact_239_diff__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A4:A,B3:A,C2:A]: (((((ord_less_eq @ A) @ A4) @ B3) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A4) @ C2)) @ (((minus_minus @ A) @ B3) @ C2))))))))).
% 2.61/1.48 thf(fact_240_diff__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A4:A,C2:A]: (((((ord_less_eq @ A) @ B3) @ A4) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C2) @ A4)) @ (((minus_minus @ A) @ C2) @ B3))))))))).
% 2.61/1.48 thf(fact_241_traffic_Oclm__consec__res, axiom, (! [Ts5:traffic,C2:cars]: (((((clm @ Ts5) @ C2) != (bot_bot @ nat_int)) => (((nat_consec @ ((clm @ Ts5) @ C2)) @ ((res @ Ts5) @ C2)) | ((nat_consec @ ((res @ Ts5) @ C2)) @ ((clm @ Ts5) @ C2))))))).
% 2.61/1.48 thf(fact_242_Greatest__equality, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X3:A]: (((P @ X3) => ((! [Y3:A]: (((P @ Y3) => (((ord_less_eq @ A) @ Y3) @ X3)))) => (((order_Greatest @ A) @ P) = X3))))))))).
% 2.61/1.48 thf(fact_243_GreatestI2__order, axiom, (! [A:$tType]: (((order @ A) => (! [P:(A > $o),X3:A,Q:(A > $o)]: (((P @ X3) => ((! [Y3:A]: (((P @ Y3) => (((ord_less_eq @ A) @ Y3) @ X3)))) => ((! [X2:A]: (((P @ X2) => ((! [Y5:A]: (((P @ Y5) => (((ord_less_eq @ A) @ Y5) @ X2)))) => (Q @ X2))))) => (Q @ ((order_Greatest @ A) @ P))))))))))).
% 2.61/1.48 thf(fact_244_less__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) & (~ ((((ord_less_eq @ (A > B)) @ G2) @ F2))))))))))).
% 2.61/1.48 thf(fact_245_card__subset__less, axiom, (! [I:nat_int,I2:nat_int]: (((((ord_less @ nat_int) @ I) @ I2) => (((ord_less @ nat) @ (nat_card @ I)) @ (nat_card @ I2)))))).
% 2.61/1.48 thf(fact_246_consec__intermediate2, axiom, (! [I:nat_int,J:nat_int,K:nat_int]: (((((nat_consec @ I) @ J) & ((nat_consec @ ((nat_union @ I) @ J)) @ K)) => ((nat_consec @ J) @ K))))).
% 2.61/1.48 thf(fact_247_consec__intermediate1, axiom, (! [J:nat_int,K:nat_int,I:nat_int]: (((((nat_consec @ J) @ K) & ((nat_consec @ I) @ ((nat_union @ J) @ K))) => ((nat_consec @ I) @ J))))).
% 2.61/1.48 thf(fact_248_consec__assoc2, axiom, (! [I:nat_int,J:nat_int,K:nat_int]: (((((nat_consec @ I) @ J) & ((nat_consec @ ((nat_union @ I) @ J)) @ K)) => ((nat_consec @ I) @ ((nat_union @ J) @ K)))))).
% 2.61/1.48 thf(fact_249_consec__assoc1, axiom, (! [J:nat_int,K:nat_int,I:nat_int]: (((((nat_consec @ J) @ K) & ((nat_consec @ I) @ ((nat_union @ J) @ K))) => ((nat_consec @ ((nat_union @ I) @ J)) @ K))))).
% 2.61/1.48 thf(fact_250_un__assoc, axiom, (! [I:nat_int,J:nat_int,K:nat_int]: (((((nat_consec @ I) @ J) & ((nat_consec @ J) @ K)) => (((nat_union @ ((nat_union @ I) @ J)) @ K) = ((nat_union @ I) @ ((nat_union @ J) @ K))))))).
% 2.61/1.48 thf(fact_251_consec__assoc__mult, axiom, (! [I22:nat_int,I1:nat_int,I3:nat_int,I4:nat_int]: (((((I22 = (bot_bot @ nat_int)) | ((nat_consec @ I1) @ I22)) & (((I3 = (bot_bot @ nat_int)) | ((nat_consec @ I3) @ I4)) & ((nat_consec @ ((nat_union @ I1) @ I22)) @ ((nat_union @ I3) @ I4)))) => (((nat_union @ ((nat_union @ I1) @ I22)) @ ((nat_union @ I3) @ I4)) = ((nat_union @ ((nat_union @ I1) @ ((nat_union @ I22) @ I3))) @ I4)))))).
% 2.61/1.48 thf(fact_252_un__subset2, axiom, (! [I:nat_int,J:nat_int]: ((((nat_consec @ I) @ J) => (((ord_less_eq @ nat_int) @ J) @ ((nat_union @ I) @ J)))))).
% 2.61/1.48 thf(fact_253_un__subset1, axiom, (! [I:nat_int,J:nat_int]: ((((nat_consec @ I) @ J) => (((ord_less_eq @ nat_int) @ I) @ ((nat_union @ I) @ J)))))).
% 2.61/1.48 thf(fact_254_nchop__def, axiom, (nat_N_Chop = (^ [I5:nat_int,J2:nat_int,K2:nat_int]: (((I5 = ((nat_union @ J2) @ K2)) & ((J2 = (bot_bot @ nat_int)) | ((K2 = (bot_bot @ nat_int)) | ((nat_consec @ J2) @ K2)))))))).
% 2.61/1.48 thf(fact_255_consec__un__not__elem2, axiom, (! [I:nat_int,J:nat_int,N:nat]: (((((nat_consec @ I) @ J) & ((nat_not_in @ N) @ ((nat_union @ I) @ J))) => ((nat_not_in @ N) @ J))))).
% 2.61/1.48 thf(tcon_fun___Orderings_Oorder__bot, axiom, (! [A6:$tType,A7:$tType]: (((order_bot @ A7) => (order_bot @ (A6 > A7)))))).
% 2.61/1.48 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A6:$tType,A7:$tType]: (((preorder @ A7) => (preorder @ (A6 > A7)))))).
% 2.61/1.48 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: (((order @ A7) => (order @ (A6 > A7)))))).
% 2.61/1.48 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.61/1.48 thf(tcon_fun___Orderings_Obot, axiom, (! [A6:$tType,A7:$tType]: (((bot @ A7) => (bot @ (A6 > A7)))))).
% 2.61/1.48 thf(tcon_fun___Groups_Ominus, axiom, (! [A6:$tType,A7:$tType]: (((minus @ A7) => (minus @ (A6 > A7)))))).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1, axiom, (order_bot @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Opreorder_2, axiom, (preorder @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, (no_top @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Oorder_3, axiom, (order @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Oord_4, axiom, (ord @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Orderings_Obot_5, axiom, (bot @ nat)).
% 2.61/1.48 thf(tcon_Nat_Onat___Groups_Ominus_6, axiom, (minus @ nat)).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Oorder__bot_7, axiom, (order_bot @ $o)).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Opreorder_8, axiom, (preorder @ $o)).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Olinorder_9, axiom, (linorder @ $o)).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Oorder_10, axiom, (order @ $o)).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Oord_11, axiom, (ord @ $o)).
% 2.61/1.48 thf(tcon_HOL_Obool___Orderings_Obot_12, axiom, (bot @ $o)).
% 2.61/1.48 thf(tcon_HOL_Obool___Groups_Ominus_13, axiom, (minus @ $o)).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_14, axiom, (cancel146912293up_add @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add, axiom, (ordered_ab_group_add @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Odense__linorder, axiom, (dense_linorder @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Odense__order, axiom, (dense_order @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Opreorder_15, axiom, (preorder @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Olinorder_16, axiom, (linorder @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Ono__top_17, axiom, (no_top @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Ono__bot, axiom, (no_bot @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Ogroup__add, axiom, (group_add @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Oorder_18, axiom, (order @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Orderings_Oord_19, axiom, (ord @ real)).
% 2.61/1.48 thf(tcon_Real_Oreal___Groups_Ominus_20, axiom, (minus @ real)).
% 2.61/1.48 thf(tcon_NatInt_Onat__int___Orderings_Oorder__bot_21, axiom, (order_bot @ nat_int)).
% 2.61/1.48 thf(tcon_NatInt_Onat__int___Orderings_Opreorder_22, axiom, (preorder @ nat_int)).
% 2.61/1.48 thf(tcon_NatInt_Onat__int___Orderings_Oorder_23, axiom, (order @ nat_int)).
% 2.61/1.48 thf(tcon_NatInt_Onat__int___Orderings_Oord_24, axiom, (ord @ nat_int)).
% 2.61/1.48 thf(tcon_NatInt_Onat__int___Orderings_Obot_25, axiom, (bot @ nat_int)).
% 2.61/1.48 thf(tcon_RealInt_Oreal__int___Orderings_Opreorder_26, axiom, (preorder @ real_int)).
% 2.61/1.48 thf(tcon_RealInt_Oreal__int___Orderings_Oorder_27, axiom, (order @ real_int)).
% 2.61/1.48 thf(tcon_RealInt_Oreal__int___Orderings_Oord_28, axiom, (ord @ real_int)).
% 2.61/1.48 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_29, axiom, (wellorder @ product_unit)).
% 2.61/1.48 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_30, axiom, (order_bot @ product_unit)).
% 2.61/1.48 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_31, axiom, (preorder @ product_unit)).
% 2.61/1.48 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_32, axiom, (linorder @ product_unit)).
% 2.61/1.48 thf(tcon_Product__Type_Ounit___Orderings_Oorder_33, axiom, (order @ product_unit)).
% 2.61/1.48 thf(tcon_Product__Type_Ounit___Orderings_Oord_34, axiom, (ord @ product_unit)).
% 2.61/1.48 thf(tcon_Product__Type_Ounit___Orderings_Obot_35, axiom, (bot @ product_unit)).
% 2.61/1.48 thf(tcon_Product__Type_Ounit___Groups_Ominus_36, axiom, (minus @ product_unit)).
% 2.61/1.48 thf(tcon_Views_Oview_Oview__ext___Orderings_Opreorder_37, axiom, (! [A6:$tType]: (((order @ A6) => (preorder @ (view_ext @ A6)))))).
% 2.61/1.48 thf(tcon_Views_Oview_Oview__ext___Orderings_Oorder_38, axiom, (! [A6:$tType]: (((order @ A6) => (order @ (view_ext @ A6)))))).
% 2.61/1.48 thf(tcon_Views_Oview_Oview__ext___Orderings_Oord_39, axiom, (! [A6:$tType]: (((order @ A6) => (ord @ (view_ext @ A6)))))).
% 2.61/1.48 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.61/1.48 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y2:A]: ((((((if @ A) @ $false) @ X3) @ Y2) = Y2)))).
% 2.61/1.48 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y2:A]: ((((((if @ A) @ $true) @ X3) @ Y2) = X3)))).
% 2.61/1.48 thf(conj_0, conjecture, ((((move @ ts3) @ ts_a) @ v) = (((move @ ts3) @ ts) @ v))).
% 2.61/1.48 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2DTF13762.p
% 2.61/1.48 ------------------------
% 2.81/1.52 ---- Cleaned THF ---
% 2.81/1.52 thf(ty_t_Views_Oview_Oview__ext,type,
% 2.81/1.52 view_ext: $tType > $tType ).
% 2.81/1.52
% 2.81/1.52 thf(ty_t_Product__Type_Ounit,type,
% 2.81/1.52 product_unit: $tType ).
% 2.81/1.52
% 2.81/1.52 thf(ty_t_RealInt_Oreal__int,type,
% 2.81/1.52 real_int: $tType ).
% 2.81/1.52
% 2.81/1.52 thf(ty_t_Traffic_Otraffic,type,
% 2.81/1.52 traffic: $tType ).
% 2.81/1.52
% 2.81/1.52 thf(ty_t_NatInt_Onat__int,type,
% 2.81/1.52 nat_int: $tType ).
% 2.81/1.52
% 2.81/1.52 thf(ty_t_Real_Oreal,type,
% 2.81/1.52 real: $tType ).
% 2.81/1.52
% 2.81/1.52 thf(ty_t_Cars_Ocars,type,
% 2.81/1.52 cars: $tType ).
% 2.81/1.52
% 2.81/1.52 thf(ty_t_Nat_Onat,type,
% 2.81/1.52 nat: $tType ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_HOL_Otype,type,
% 2.81/1.52 type:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Groups_Ominus,type,
% 2.81/1.52 minus:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Obot,type,
% 2.81/1.52 bot:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Oord,type,
% 2.81/1.52 ord:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Oorder,type,
% 2.81/1.52 order:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Groups_Ogroup__add,type,
% 2.81/1.52 group_add:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Ono__bot,type,
% 2.81/1.52 no_bot:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Ono__top,type,
% 2.81/1.52 no_top:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Olinorder,type,
% 2.81/1.52 linorder:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Opreorder,type,
% 2.81/1.52 preorder:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Oorder__bot,type,
% 2.81/1.52 order_bot:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Owellorder,type,
% 2.81/1.52 wellorder:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Odense__order,type,
% 2.81/1.52 dense_order:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Orderings_Odense__linorder,type,
% 2.81/1.52 dense_linorder:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.81/1.52 ordered_ab_group_add:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 2.81/1.52 cancel146912293up_add:
% 2.81/1.52 !>[A: $tType] : $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Fun_Ofun__upd,type,
% 2.81/1.52 fun_upd:
% 2.81/1.52 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.81/1.52 minus_minus:
% 2.81/1.52 !>[A: $tType] : ( A > A > A ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_HOL_Odefault__class_Odefault,type,
% 2.81/1.52 default_default:
% 2.81/1.52 !>[A: $tType] : A ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_If,type,
% 2.81/1.52 if:
% 2.81/1.52 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Move_Otraffic_Omove,type,
% 2.81/1.52 move: traffic > traffic > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_NatInt_Onat__int_ON__Chop,type,
% 2.81/1.52 nat_N_Chop: nat_int > nat_int > nat_int > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_NatInt_Onat__int_Ocard_H,type,
% 2.81/1.52 nat_card: nat_int > nat ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_NatInt_Onat__int_Oconsec,type,
% 2.81/1.52 nat_consec: nat_int > nat_int > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_NatInt_Onat__int_Onot__in,type,
% 2.81/1.52 nat_not_in: nat > nat_int > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_NatInt_Onat__int_Ounion,type,
% 2.81/1.52 nat_union: nat_int > nat_int > nat_int ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.81/1.52 bot_bot:
% 2.81/1.52 !>[A: $tType] : A ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.81/1.52 ord_less:
% 2.81/1.52 !>[A: $tType] : ( A > A > $o ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.81/1.52 ord_less_eq:
% 2.81/1.52 !>[A: $tType] : ( A > A > $o ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Orderings_Oorder__class_OGreatest,type,
% 2.81/1.52 order_Greatest:
% 2.81/1.52 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Product__Type_OUnity,type,
% 2.81/1.52 product_Unity: product_unit ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Product__Type_Oold_Ounit_Orec__unit,type,
% 2.81/1.52 product_rec_unit:
% 2.81/1.52 !>[T: $tType] : ( T > product_unit > T ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_RealInt_Oreal__int_OR__Chop,type,
% 2.81/1.52 real_R_Chop: real_int > real_int > real_int > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_RealInt_Oreal__int_Oshift,type,
% 2.81/1.52 real_shift: real_int > real > real_int ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Oabstract,type,
% 2.81/1.52 abstract: traffic > traffic > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Obraking__distance,type,
% 2.81/1.52 braking_distance: traffic > cars > real ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Ochange__dyn,type,
% 2.81/1.52 change_dyn: traffic > cars > ( real > real ) > traffic > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Oclm,type,
% 2.81/1.52 clm: traffic > cars > nat_int ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Ocreate__claim,type,
% 2.81/1.52 create_claim: traffic > cars > nat > traffic > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Ocreate__reservation,type,
% 2.81/1.52 create_reservation: traffic > cars > traffic > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Odyn,type,
% 2.81/1.52 dyn: traffic > cars > real > real ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Oevolve,type,
% 2.81/1.52 evolve: traffic > traffic > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Ophysical__size,type,
% 2.81/1.52 physical_size: traffic > cars > real ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Opos,type,
% 2.81/1.52 pos: traffic > cars > real ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Ores,type,
% 2.81/1.52 res: traffic > cars > nat_int ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Owithdraw__claim,type,
% 2.81/1.52 withdraw_claim: traffic > cars > traffic > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Traffic_Otraffic_Owithdraw__reservation,type,
% 2.81/1.52 withdraw_reservation: traffic > cars > nat > traffic > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Views_Oview_Oext,type,
% 2.81/1.52 ext:
% 2.81/1.52 !>[Z: $tType] : ( ( view_ext @ Z ) > real_int ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Views_Oview_Ohchop,type,
% 2.81/1.52 hchop: ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > ( view_ext @ product_unit ) > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Views_Oview_Olan,type,
% 2.81/1.52 lan:
% 2.81/1.52 !>[Z: $tType] : ( ( view_ext @ Z ) > nat_int ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Views_Oview_Omore,type,
% 2.81/1.52 more:
% 2.81/1.52 !>[Z: $tType] : ( ( view_ext @ Z ) > Z ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Views_Oview_Oown,type,
% 2.81/1.52 own:
% 2.81/1.52 !>[Z: $tType] : ( ( view_ext @ Z ) > cars ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Views_Oview_Oswitch,type,
% 2.81/1.52 switch: ( view_ext @ product_unit ) > cars > ( view_ext @ product_unit ) > $o ).
% 2.81/1.52
% 2.81/1.52 thf(sy_c_Views_Oview_Oview__ext,type,
% 2.81/1.52 view_ext2:
% 2.81/1.52 !>[Z: $tType] : ( real_int > nat_int > cars > Z > ( view_ext @ Z ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(sy_v_ts_H_H____,type,
% 2.81/1.52 ts: traffic ).
% 2.81/1.52
% 2.81/1.52 thf(sy_v_ts_H____,type,
% 2.81/1.52 ts2: traffic ).
% 2.81/1.52
% 2.81/1.52 thf(sy_v_ts_Ha____,type,
% 2.81/1.52 ts_a: traffic ).
% 2.81/1.52
% 2.81/1.52 thf(sy_v_ts____,type,
% 2.81/1.52 ts3: traffic ).
% 2.81/1.52
% 2.81/1.52 thf(sy_v_v____,type,
% 2.81/1.52 v: view_ext @ product_unit ).
% 2.81/1.52
% 2.81/1.52 thf(fact_0_cr__res_Ohyps_I1_J,axiom,
% 2.81/1.52 abstract @ ts3 @ ts_a ).
% 2.81/1.52
% 2.81/1.52 thf(fact_1_cr__res_Ohyps_I2_J,axiom,
% 2.81/1.52 ? [C: cars] : ( create_reservation @ ts_a @ C @ ts ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_2_local_Ohmlsl_Oglobally__4,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ! [Ts2: traffic] :
% 2.81/1.52 ( ( abstract @ Ts @ Ts2 )
% 2.81/1.52 => ( Phi @ Ts2 @ ( move @ Ts @ Ts2 @ V ) ) )
% 2.81/1.52 => ! [Ts3: traffic] :
% 2.81/1.52 ( ( abstract @ Ts @ Ts3 )
% 2.81/1.52 => ! [Ts_a: traffic] :
% 2.81/1.52 ( ( abstract @ Ts3 @ Ts_a )
% 2.81/1.52 => ( Phi @ Ts_a @ ( move @ Ts3 @ Ts_a @ ( move @ Ts @ Ts3 @ V ) ) ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_3_local_Ohmlsl_Oglobally__all__iff,axiom,
% 2.81/1.52 ! [A: $tType,B: $tType,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ( ! [Ts4: traffic] :
% 2.81/1.52 ( ( abstract @ Ts @ Ts4 )
% 2.81/1.52 => ! [X: A] : ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V ) ) ) )
% 2.81/1.52 = ( ! [X: B,Ts4: traffic] :
% 2.81/1.52 ( ( abstract @ Ts @ Ts4 )
% 2.81/1.52 => ( Phi @ Ts4 @ ( move @ Ts @ Ts4 @ V ) ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_4_local_Ohmlsl_Oglobally__all__iff_H,axiom,
% 2.81/1.52 ! [A: $tType,B: $tType,Ts5: traffic,Phi: traffic > ( view_ext @ product_unit ) > $o,V2: view_ext @ product_unit] :
% 2.81/1.52 ( ( ! [Ts4: traffic] :
% 2.81/1.52 ( ( abstract @ Ts5 @ Ts4 )
% 2.81/1.52 => ! [X: A] : ( Phi @ Ts4 @ ( move @ Ts5 @ Ts4 @ V2 ) ) ) )
% 2.81/1.52 = ( ! [X: B,Ts4: traffic] :
% 2.81/1.52 ( ( abstract @ Ts5 @ Ts4 )
% 2.81/1.52 => ( Phi @ Ts4 @ ( move @ Ts5 @ Ts4 @ V2 ) ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_5_local_Ohmlsl_Oglobally__refl,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ! [Ts2: traffic] :
% 2.81/1.52 ( ( abstract @ Ts @ Ts2 )
% 2.81/1.52 => ( Phi @ Ts2 @ ( move @ Ts @ Ts2 @ V ) ) )
% 2.81/1.52 => ( Phi @ Ts @ V ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_6_abs,axiom,
% 2.81/1.52 abstract @ ts3 @ ts2 ).
% 2.81/1.52
% 2.81/1.52 thf(fact_7__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062,axiom,
% 2.81/1.52 ( ( move @ ts3 @ ts_a @ v )
% 2.81/1.52 = ( move @ ts_a @ ts @ ( move @ ts3 @ ts_a @ v ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_8_traffic_Omove__nothing,axiom,
% 2.81/1.52 ! [Ts5: traffic,V2: view_ext @ product_unit] :
% 2.81/1.52 ( ( move @ Ts5 @ Ts5 @ V2 )
% 2.81/1.52 = V2 ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_9_traffic_Omove__def,axiom,
% 2.81/1.52 ( move
% 2.81/1.52 = ( ^ [Ts6: traffic,Ts4: traffic,V3: view_ext @ product_unit] : ( view_ext2 @ product_unit @ ( real_shift @ ( ext @ product_unit @ V3 ) @ ( minus_minus @ real @ ( pos @ Ts4 @ ( own @ product_unit @ V3 ) ) @ ( pos @ Ts6 @ ( own @ product_unit @ V3 ) ) ) ) @ ( lan @ product_unit @ V3 ) @ ( own @ product_unit @ V3 ) @ product_Unity ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_10_traffic_Omove__stability__res,axiom,
% 2.81/1.52 ! [Ts5: traffic,C2: cars,Ts7: traffic,V2: view_ext @ product_unit] :
% 2.81/1.52 ( ( create_reservation @ Ts5 @ C2 @ Ts7 )
% 2.81/1.52 => ( ( move @ Ts5 @ Ts7 @ V2 )
% 2.81/1.52 = V2 ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_11_traffic_Omove__keeps__owner,axiom,
% 2.81/1.52 ! [Ts5: traffic,Ts7: traffic] :
% 2.81/1.52 ( ( own @ product_unit )
% 2.81/1.52 = ( ^ [V3: view_ext @ product_unit] : ( own @ product_unit @ ( move @ Ts5 @ Ts7 @ V3 ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_12_traffic_Omove__trans,axiom,
% 2.81/1.52 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic,V2: view_ext @ product_unit] :
% 2.81/1.52 ( ( ( abstract @ Ts5 @ Ts7 )
% 2.81/1.52 & ( abstract @ Ts7 @ Ts8 ) )
% 2.81/1.52 => ( ( move @ Ts7 @ Ts8 @ ( move @ Ts5 @ Ts7 @ V2 ) )
% 2.81/1.52 = ( move @ Ts5 @ Ts8 @ V2 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_13_traffic_Omove__keeps__lanes,axiom,
% 2.81/1.52 ! [Ts5: traffic,Ts7: traffic] :
% 2.81/1.52 ( ( lan @ product_unit )
% 2.81/1.52 = ( ^ [V3: view_ext @ product_unit] : ( lan @ product_unit @ ( move @ Ts5 @ Ts7 @ V3 ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_14_traffic_Omove__stability__clm,axiom,
% 2.81/1.52 ! [Ts5: traffic,C2: cars,N: nat,Ts7: traffic,V2: view_ext @ product_unit] :
% 2.81/1.52 ( ( create_claim @ Ts5 @ C2 @ N @ Ts7 )
% 2.81/1.52 => ( ( move @ Ts5 @ Ts7 @ V2 )
% 2.81/1.52 = V2 ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_15_traffic_Omove__stability__wdc,axiom,
% 2.81/1.52 ! [Ts5: traffic,C2: cars,Ts7: traffic,V2: view_ext @ product_unit] :
% 2.81/1.52 ( ( withdraw_claim @ Ts5 @ C2 @ Ts7 )
% 2.81/1.52 => ( ( move @ Ts5 @ Ts7 @ V2 )
% 2.81/1.52 = V2 ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_16_traffic_Omove__stability__wdr,axiom,
% 2.81/1.52 ! [Ts5: traffic,C2: cars,N: nat,Ts7: traffic,V2: view_ext @ product_unit] :
% 2.81/1.52 ( ( withdraw_reservation @ Ts5 @ C2 @ N @ Ts7 )
% 2.81/1.52 => ( ( move @ Ts5 @ Ts7 @ V2 )
% 2.81/1.52 = V2 ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_17_local_Ohmlsl_Ohchop__assoc,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ W @ U )
% 2.81/1.52 & ( Phi @ Ts @ W )
% 2.81/1.52 & ? [X: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ U @ X @ Y )
% 2.81/1.52 & ( Psi @ Ts @ X )
% 2.81/1.52 & ( Chi @ Ts @ Y ) ) ) )
% 2.81/1.52 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ W @ U )
% 2.81/1.52 & ? [X: view_ext @ product_unit,Y: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ W @ X @ Y )
% 2.81/1.52 & ( Phi @ Ts @ X )
% 2.81/1.52 & ( Psi @ Ts @ Y ) )
% 2.81/1.52 & ( Chi @ Ts @ U ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_18_local_Ohmlsl_Ohchop__disj__distr1,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ W @ U )
% 2.81/1.52 & ( Phi @ Ts @ W )
% 2.81/1.52 & ( ( Psi @ Ts @ U )
% 2.81/1.52 | ( Chi @ Ts @ U ) ) ) )
% 2.81/1.52 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ W @ U )
% 2.81/1.52 & ( Phi @ Ts @ W )
% 2.81/1.52 & ( Psi @ Ts @ U ) )
% 2.81/1.52 | ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ W @ U )
% 2.81/1.52 & ( Phi @ Ts @ W )
% 2.81/1.52 & ( Chi @ Ts @ U ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_19_local_Ohmlsl_Ohchop__disj__distr2,axiom,
% 2.81/1.52 ! [Psi: traffic > ( view_ext @ product_unit ) > $o,Chi: traffic > ( view_ext @ product_unit ) > $o,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ W @ U )
% 2.81/1.52 & ( ( Psi @ Ts @ W )
% 2.81/1.52 | ( Chi @ Ts @ W ) )
% 2.81/1.52 & ( Phi @ Ts @ U ) ) )
% 2.81/1.52 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ W @ U )
% 2.81/1.52 & ( Psi @ Ts @ W )
% 2.81/1.52 & ( Phi @ Ts @ U ) )
% 2.81/1.52 | ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ W @ U )
% 2.81/1.52 & ( Chi @ Ts @ W )
% 2.81/1.52 & ( Phi @ Ts @ U ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_20_local_Ohmlsl_Ohchop__weaken2,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ( Phi @ Ts @ V )
% 2.81/1.52 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ Va @ U2 )
% 2.81/1.52 & ( Phi @ Ts @ U2 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_21_local_Ohmlsl_Ohchop__weaken1,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ( Phi @ Ts @ V )
% 2.81/1.52 => ? [Va: view_ext @ product_unit] :
% 2.81/1.52 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
% 2.81/1.52 & ( Phi @ Ts @ Va ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_22_local_Ohmlsl_Ohchop__weaken,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ( Phi @ Ts @ V )
% 2.81/1.52 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ Va @ U2 )
% 2.81/1.52 & ? [Vb: view_ext @ product_unit] :
% 2.81/1.52 ( ? [X_1: view_ext @ product_unit] : ( hchop @ U2 @ Vb @ X_1 )
% 2.81/1.52 & ( Phi @ Ts @ Vb ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_23_local_Ohmlsl_Ohchop__neg2,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ~ ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ Va @ U2 )
% 2.81/1.52 & ( Phi @ Ts @ U2 ) )
% 2.81/1.52 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V @ Va @ U2 )
% 2.81/1.52 & ~ ( Phi @ Ts @ U2 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_24_local_Ohmlsl_Ohchop__neg1,axiom,
% 2.81/1.52 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.52 ( ~ ? [Va: view_ext @ product_unit] :
% 2.81/1.52 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
% 2.81/1.52 & ( Phi @ Ts @ Va ) )
% 2.81/1.52 => ? [Va: view_ext @ product_unit] :
% 2.81/1.52 ( ? [X_1: view_ext @ product_unit] : ( hchop @ V @ Va @ X_1 )
% 2.81/1.52 & ~ ( Phi @ Ts @ Va ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_25_ext__inject,axiom,
% 2.81/1.52 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z,Ext2: real_int,Lan2: nat_int,Own2: cars,More2: Z] :
% 2.81/1.52 ( ( ( view_ext2 @ Z @ Ext @ Lan @ Own @ More )
% 2.81/1.52 = ( view_ext2 @ Z @ Ext2 @ Lan2 @ Own2 @ More2 ) )
% 2.81/1.52 = ( ( Ext = Ext2 )
% 2.81/1.52 & ( Lan = Lan2 )
% 2.81/1.52 & ( Own = Own2 )
% 2.81/1.52 & ( More = More2 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_26_cases,axiom,
% 2.81/1.52 ! [R: view_ext @ product_unit] :
% 2.81/1.52 ~ ! [Ext3: real_int,Lan3: nat_int,Own3: cars] :
% 2.81/1.52 ( R
% 2.81/1.52 != ( view_ext2 @ product_unit @ Ext3 @ Lan3 @ Own3 @ product_Unity ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_27_induct,axiom,
% 2.81/1.52 ! [P: ( view_ext @ product_unit ) > $o,R: view_ext @ product_unit] :
% 2.81/1.52 ( ! [Ext3: real_int,Lan3: nat_int,Own3: cars] : ( P @ ( view_ext2 @ product_unit @ Ext3 @ Lan3 @ Own3 @ product_Unity ) )
% 2.81/1.52 => ( P @ R ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_28_traffic_Ocr__clm,axiom,
% 2.81/1.52 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 2.81/1.52 ( ( abstract @ Ts5 @ Ts7 )
% 2.81/1.52 => ( ? [C3: cars,N2: nat] : ( create_claim @ Ts7 @ C3 @ N2 @ Ts8 )
% 2.81/1.52 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_29_traffic_Owd__clm,axiom,
% 2.81/1.52 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 2.81/1.52 ( ( abstract @ Ts5 @ Ts7 )
% 2.81/1.52 => ( ? [C3: cars] : ( withdraw_claim @ Ts7 @ C3 @ Ts8 )
% 2.81/1.52 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_30_traffic_Owd__res,axiom,
% 2.81/1.52 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 2.81/1.52 ( ( abstract @ Ts5 @ Ts7 )
% 2.81/1.52 => ( ? [C3: cars,N2: nat] : ( withdraw_reservation @ Ts7 @ C3 @ N2 @ Ts8 )
% 2.81/1.52 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_31_minus__apply,axiom,
% 2.81/1.52 ! [B: $tType,A: $tType] :
% 2.81/1.52 ( ( minus @ B )
% 2.81/1.52 => ( ( minus_minus @ ( A > B ) )
% 2.81/1.52 = ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_32_traffic_Ocr__res,axiom,
% 2.81/1.52 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 2.81/1.52 ( ( abstract @ Ts5 @ Ts7 )
% 2.81/1.52 => ( ? [C3: cars] : ( create_reservation @ Ts7 @ C3 @ Ts8 )
% 2.81/1.52 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_33_select__convs_I3_J,axiom,
% 2.81/1.52 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
% 2.81/1.52 ( ( own @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
% 2.81/1.52 = Own ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_34_select__convs_I2_J,axiom,
% 2.81/1.52 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
% 2.81/1.52 ( ( lan @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
% 2.81/1.52 = Lan ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_35_fun__diff__def,axiom,
% 2.81/1.52 ! [B: $tType,A: $tType] :
% 2.81/1.52 ( ( minus @ B )
% 2.81/1.52 => ( ( minus_minus @ ( A > B ) )
% 2.81/1.52 = ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_36_view_Ohorizontal__chop__empty__right,axiom,
% 2.81/1.52 ! [V: view_ext @ product_unit] :
% 2.81/1.52 ? [X_1: view_ext @ product_unit] : ( hchop @ V @ V @ X_1 ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_37_view_Ohorizontal__chop__empty__left,axiom,
% 2.81/1.52 ! [V: view_ext @ product_unit] :
% 2.81/1.52 ? [U2: view_ext @ product_unit] : ( hchop @ V @ U2 @ V ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_38_view_Ohorizontal__chop__assoc2,axiom,
% 2.81/1.52 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 2.81/1.52 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.81/1.52 & ( hchop @ V1 @ V32 @ V4 ) )
% 2.81/1.52 => ? [V5: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V2 @ V32 @ V5 )
% 2.81/1.52 & ( hchop @ V5 @ V4 @ V22 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_39_view_Ohorizontal__chop__assoc1,axiom,
% 2.81/1.52 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,V32: view_ext @ product_unit,V4: view_ext @ product_unit] :
% 2.81/1.52 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.81/1.52 & ( hchop @ V22 @ V32 @ V4 ) )
% 2.81/1.52 => ? [V5: view_ext @ product_unit] :
% 2.81/1.52 ( ( hchop @ V2 @ V5 @ V4 )
% 2.81/1.52 & ( hchop @ V5 @ V1 @ V32 ) ) ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_40_view_Ohorizontal__chop1,axiom,
% 2.81/1.52 ! [V2: view_ext @ product_unit] :
% 2.81/1.52 ? [U2: view_ext @ product_unit,X_1: view_ext @ product_unit] : ( hchop @ V2 @ U2 @ X_1 ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_41_traffic_Oabstract_Orefl,axiom,
% 2.81/1.52 ! [Ts5: traffic] : ( abstract @ Ts5 @ Ts5 ) ).
% 2.81/1.52
% 2.81/1.52 thf(fact_42_traffic_Oabs__trans,axiom,
% 2.81/1.52 ! [Ts1: traffic,Ts22: traffic,Ts0: traffic] :
% 2.81/1.53 ( ( abstract @ Ts1 @ Ts22 )
% 2.81/1.53 => ( ( abstract @ Ts0 @ Ts1 )
% 2.81/1.53 => ( abstract @ Ts0 @ Ts22 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_43_induct__scheme,axiom,
% 2.81/1.53 ! [Z: $tType,P: ( view_ext @ Z ) > $o,R: view_ext @ Z] :
% 2.81/1.53 ( ! [Ext3: real_int,Lan3: nat_int,Own3: cars,More3: Z] : ( P @ ( view_ext2 @ Z @ Ext3 @ Lan3 @ Own3 @ More3 ) )
% 2.81/1.53 => ( P @ R ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_44_cases__scheme,axiom,
% 2.81/1.53 ! [Z: $tType,R: view_ext @ Z] :
% 2.81/1.53 ~ ! [Ext3: real_int,Lan3: nat_int,Own3: cars,More3: Z] :
% 2.81/1.53 ( R
% 2.81/1.53 != ( view_ext2 @ Z @ Ext3 @ Lan3 @ Own3 @ More3 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_45_ext,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.81/1.53 ( ! [X2: A] :
% 2.81/1.53 ( ( F @ X2 )
% 2.81/1.53 = ( G @ X2 ) )
% 2.81/1.53 => ( F = G ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_46_traffic_Oalways__create__res,axiom,
% 2.81/1.53 ! [C2: cars,Ts: traffic] :
% 2.81/1.53 ? [X_1: traffic] : ( create_reservation @ Ts @ C2 @ X_1 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_47_view_Ohorizontal__chop__own__trans,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V2 @ U3 @ W2 )
% 2.81/1.53 => ( ( own @ product_unit @ U3 )
% 2.81/1.53 = ( own @ product_unit @ W2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_48_select__convs_I1_J,axiom,
% 2.81/1.53 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
% 2.81/1.53 ( ( ext @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
% 2.81/1.53 = Ext ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_49_traffic_Ocreate__reservation__def,axiom,
% 2.81/1.53 ( create_reservation
% 2.81/1.53 = ( ^ [Ts6: traffic,C4: cars,Ts4: traffic] :
% 2.81/1.53 ( ( ( pos @ Ts4 )
% 2.81/1.53 = ( pos @ Ts6 ) )
% 2.81/1.53 & ( ( res @ Ts4 )
% 2.81/1.53 = ( fun_upd @ cars @ nat_int @ ( res @ Ts6 ) @ C4 @ ( nat_union @ ( res @ Ts6 @ C4 ) @ ( clm @ Ts6 @ C4 ) ) ) )
% 2.81/1.53 & ( ( dyn @ Ts4 )
% 2.81/1.53 = ( dyn @ Ts6 ) )
% 2.81/1.53 & ( ( clm @ Ts4 )
% 2.81/1.53 = ( fun_upd @ cars @ nat_int @ ( clm @ Ts6 ) @ C4 @ ( bot_bot @ nat_int ) ) )
% 2.81/1.53 & ( ( physical_size @ Ts4 )
% 2.81/1.53 = ( physical_size @ Ts6 ) )
% 2.81/1.53 & ( ( braking_distance @ Ts4 )
% 2.81/1.53 = ( braking_distance @ Ts6 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_50_traffic_Oabstract_Oinducts,axiom,
% 2.81/1.53 ! [Ts5: traffic,X3: traffic,P: traffic > $o] :
% 2.81/1.53 ( ( abstract @ Ts5 @ X3 )
% 2.81/1.53 => ( ( P @ Ts5 )
% 2.81/1.53 => ( ! [Ts2: traffic,Ts9: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ( ( P @ Ts2 )
% 2.81/1.53 => ( ( evolve @ Ts2 @ Ts9 )
% 2.81/1.53 => ( P @ Ts9 ) ) ) )
% 2.81/1.53 => ( ! [Ts2: traffic,Ts9: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ( ( P @ Ts2 )
% 2.81/1.53 => ( ? [C: cars,N3: nat] : ( create_claim @ Ts2 @ C @ N3 @ Ts9 )
% 2.81/1.53 => ( P @ Ts9 ) ) ) )
% 2.81/1.53 => ( ! [Ts2: traffic,Ts9: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ( ( P @ Ts2 )
% 2.81/1.53 => ( ? [C: cars] : ( withdraw_claim @ Ts2 @ C @ Ts9 )
% 2.81/1.53 => ( P @ Ts9 ) ) ) )
% 2.81/1.53 => ( ! [Ts2: traffic,Ts9: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ( ( P @ Ts2 )
% 2.81/1.53 => ( ? [C: cars] : ( create_reservation @ Ts2 @ C @ Ts9 )
% 2.81/1.53 => ( P @ Ts9 ) ) ) )
% 2.81/1.53 => ( ! [Ts2: traffic,Ts9: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ( ( P @ Ts2 )
% 2.81/1.53 => ( ? [C: cars,N3: nat] : ( withdraw_reservation @ Ts2 @ C @ N3 @ Ts9 )
% 2.81/1.53 => ( P @ Ts9 ) ) ) )
% 2.81/1.53 => ( P @ X3 ) ) ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_51_traffic_Oabstract_Osimps,axiom,
% 2.81/1.53 ( abstract
% 2.81/1.53 = ( ^ [Ts6: traffic,A3: traffic] :
% 2.81/1.53 ( ( A3 = Ts6 )
% 2.81/1.53 | ? [Ts4: traffic,Ts10: traffic] :
% 2.81/1.53 ( ( A3 = Ts10 )
% 2.81/1.53 & ( abstract @ Ts6 @ Ts4 )
% 2.81/1.53 & ( evolve @ Ts4 @ Ts10 ) )
% 2.81/1.53 | ? [Ts4: traffic,Ts10: traffic] :
% 2.81/1.53 ( ( A3 = Ts10 )
% 2.81/1.53 & ( abstract @ Ts6 @ Ts4 )
% 2.81/1.53 & ? [C4: cars,N4: nat] : ( create_claim @ Ts4 @ C4 @ N4 @ Ts10 ) )
% 2.81/1.53 | ? [Ts4: traffic,Ts10: traffic] :
% 2.81/1.53 ( ( A3 = Ts10 )
% 2.81/1.53 & ( abstract @ Ts6 @ Ts4 )
% 2.81/1.53 & ? [C4: cars] : ( withdraw_claim @ Ts4 @ C4 @ Ts10 ) )
% 2.81/1.53 | ? [Ts4: traffic,Ts10: traffic] :
% 2.81/1.53 ( ( A3 = Ts10 )
% 2.81/1.53 & ( abstract @ Ts6 @ Ts4 )
% 2.81/1.53 & ? [C4: cars] : ( create_reservation @ Ts4 @ C4 @ Ts10 ) )
% 2.81/1.53 | ? [Ts4: traffic,Ts10: traffic] :
% 2.81/1.53 ( ( A3 = Ts10 )
% 2.81/1.53 & ( abstract @ Ts6 @ Ts4 )
% 2.81/1.53 & ? [C4: cars,N4: nat] : ( withdraw_reservation @ Ts4 @ C4 @ N4 @ Ts10 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_52_traffic_Oabstract_Ocases,axiom,
% 2.81/1.53 ! [Ts5: traffic,A4: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ A4 )
% 2.81/1.53 => ( ( A4 != Ts5 )
% 2.81/1.53 => ( ! [Ts2: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ~ ( evolve @ Ts2 @ A4 ) )
% 2.81/1.53 => ( ! [Ts2: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ~ ? [C: cars,N3: nat] : ( create_claim @ Ts2 @ C @ N3 @ A4 ) )
% 2.81/1.53 => ( ! [Ts2: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ~ ? [C: cars] : ( withdraw_claim @ Ts2 @ C @ A4 ) )
% 2.81/1.53 => ( ! [Ts2: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ~ ? [C: cars] : ( create_reservation @ Ts2 @ C @ A4 ) )
% 2.81/1.53 => ~ ! [Ts2: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts2 )
% 2.81/1.53 => ~ ? [C: cars,N3: nat] : ( withdraw_reservation @ Ts2 @ C @ N3 @ A4 ) ) ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_53_surjective,axiom,
% 2.81/1.53 ! [Z: $tType,R: view_ext @ Z] :
% 2.81/1.53 ( R
% 2.81/1.53 = ( view_ext2 @ Z @ ( ext @ Z @ R ) @ ( lan @ Z @ R ) @ ( own @ Z @ R ) @ ( more @ Z @ R ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_54_traffic_Owithdraw__clm__eq__res,axiom,
% 2.81/1.53 ! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
% 2.81/1.53 ( ( withdraw_claim @ Ts5 @ D @ Ts7 )
% 2.81/1.53 => ( ( res @ Ts5 @ C2 )
% 2.81/1.53 = ( res @ Ts7 @ C2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_55_traffic_Ocreate__clm__eq__res,axiom,
% 2.81/1.53 ! [Ts5: traffic,D: cars,N: nat,Ts7: traffic,C2: cars] :
% 2.81/1.53 ( ( create_claim @ Ts5 @ D @ N @ Ts7 )
% 2.81/1.53 => ( ( res @ Ts5 @ C2 )
% 2.81/1.53 = ( res @ Ts7 @ C2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_56_traffic_Ocreate__res__subseteq1__neq,axiom,
% 2.81/1.53 ! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
% 2.81/1.53 ( ( ( create_reservation @ Ts5 @ D @ Ts7 )
% 2.81/1.53 & ( D != C2 ) )
% 2.81/1.53 => ( ( res @ Ts5 @ C2 )
% 2.81/1.53 = ( res @ Ts7 @ C2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_57_traffic_Ocreate__res__subseteq2__neq,axiom,
% 2.81/1.53 ! [Ts5: traffic,D: cars,Ts7: traffic,C2: cars] :
% 2.81/1.53 ( ( ( create_reservation @ Ts5 @ D @ Ts7 )
% 2.81/1.53 & ( D != C2 ) )
% 2.81/1.53 => ( ( clm @ Ts5 @ C2 )
% 2.81/1.53 = ( clm @ Ts7 @ C2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_58_traffic_Oevolve__trans,axiom,
% 2.81/1.53 ! [Ts0: traffic,Ts1: traffic,Ts22: traffic] :
% 2.81/1.53 ( ( evolve @ Ts0 @ Ts1 )
% 2.81/1.53 => ( ( evolve @ Ts1 @ Ts22 )
% 2.81/1.53 => ( evolve @ Ts0 @ Ts22 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_59_traffic_Oevolve_Orefl,axiom,
% 2.81/1.53 ! [Ts5: traffic] : ( evolve @ Ts5 @ Ts5 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_60_traffic_Owithdraw__claim__def,axiom,
% 2.81/1.53 ( withdraw_claim
% 2.81/1.53 = ( ^ [Ts6: traffic,C4: cars,Ts4: traffic] :
% 2.81/1.53 ( ( ( pos @ Ts4 )
% 2.81/1.53 = ( pos @ Ts6 ) )
% 2.81/1.53 & ( ( res @ Ts4 )
% 2.81/1.53 = ( res @ Ts6 ) )
% 2.81/1.53 & ( ( dyn @ Ts4 )
% 2.81/1.53 = ( dyn @ Ts6 ) )
% 2.81/1.53 & ( ( physical_size @ Ts4 )
% 2.81/1.53 = ( physical_size @ Ts6 ) )
% 2.81/1.53 & ( ( braking_distance @ Ts4 )
% 2.81/1.53 = ( braking_distance @ Ts6 ) )
% 2.81/1.53 & ( ( clm @ Ts4 )
% 2.81/1.53 = ( fun_upd @ cars @ nat_int @ ( clm @ Ts6 ) @ C4 @ ( bot_bot @ nat_int ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_61_traffic_Oevolve,axiom,
% 2.81/1.53 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 2.81/1.53 ( ( abstract @ Ts5 @ Ts7 )
% 2.81/1.53 => ( ( evolve @ Ts7 @ Ts8 )
% 2.81/1.53 => ( abstract @ Ts5 @ Ts8 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_62_select__convs_I4_J,axiom,
% 2.81/1.53 ! [Z: $tType,Ext: real_int,Lan: nat_int,Own: cars,More: Z] :
% 2.81/1.53 ( ( more @ Z @ ( view_ext2 @ Z @ Ext @ Lan @ Own @ More ) )
% 2.81/1.53 = More ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_63_equality,axiom,
% 2.81/1.53 ! [Z: $tType,R: view_ext @ Z,R2: view_ext @ Z] :
% 2.81/1.53 ( ( ( ext @ Z @ R )
% 2.81/1.53 = ( ext @ Z @ R2 ) )
% 2.81/1.53 => ( ( ( lan @ Z @ R )
% 2.81/1.53 = ( lan @ Z @ R2 ) )
% 2.81/1.53 => ( ( ( own @ Z @ R )
% 2.81/1.53 = ( own @ Z @ R2 ) )
% 2.81/1.53 => ( ( ( more @ Z @ R )
% 2.81/1.53 = ( more @ Z @ R2 ) )
% 2.81/1.53 => ( R = R2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_64_fun__upd__upd,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B,Z2: B] :
% 2.81/1.53 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F @ X3 @ Y2 ) @ X3 @ Z2 )
% 2.81/1.53 = ( fun_upd @ A @ B @ F @ X3 @ Z2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_65_fun__upd__triv,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType,F: A > B,X3: A] :
% 2.81/1.53 ( ( fun_upd @ A @ B @ F @ X3 @ ( F @ X3 ) )
% 2.81/1.53 = F ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_66_fun__upd__apply,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( fun_upd @ B @ A )
% 2.81/1.53 = ( ^ [F2: B > A,X: B,Y: A,Z3: B] : ( if @ A @ ( Z3 = X ) @ Y @ ( F2 @ Z3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_67_bot__apply,axiom,
% 2.81/1.53 ! [C5: $tType,D2: $tType] :
% 2.81/1.53 ( ( bot @ C5 )
% 2.81/1.53 => ( ( bot_bot @ ( D2 > C5 ) )
% 2.81/1.53 = ( ^ [X: D2] : ( bot_bot @ C5 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_68_un__empty__absorb1,axiom,
% 2.81/1.53 ! [I: nat_int] :
% 2.81/1.53 ( ( nat_union @ I @ ( bot_bot @ nat_int ) )
% 2.81/1.53 = I ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_69_un__empty__absorb2,axiom,
% 2.81/1.53 ! [I: nat_int] :
% 2.81/1.53 ( ( nat_union @ ( bot_bot @ nat_int ) @ I )
% 2.81/1.53 = I ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_70_view_Ohchop__def,axiom,
% 2.81/1.53 ( hchop
% 2.81/1.53 = ( ^ [V3: view_ext @ product_unit,U: view_ext @ product_unit,W: view_ext @ product_unit] :
% 2.81/1.53 ( ( real_R_Chop @ ( ext @ product_unit @ V3 ) @ ( ext @ product_unit @ U ) @ ( ext @ product_unit @ W ) )
% 2.81/1.53 & ( ( lan @ product_unit @ V3 )
% 2.81/1.53 = ( lan @ product_unit @ U ) )
% 2.81/1.53 & ( ( lan @ product_unit @ V3 )
% 2.81/1.53 = ( lan @ product_unit @ W ) )
% 2.81/1.53 & ( ( own @ product_unit @ V3 )
% 2.81/1.53 = ( own @ product_unit @ U ) )
% 2.81/1.53 & ( ( own @ product_unit @ V3 )
% 2.81/1.53 = ( own @ product_unit @ W ) )
% 2.81/1.53 & ( ( more @ product_unit @ V3 )
% 2.81/1.53 = ( more @ product_unit @ W ) )
% 2.81/1.53 & ( ( more @ product_unit @ V3 )
% 2.81/1.53 = ( more @ product_unit @ U ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_71_bot__fun__def,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType] :
% 2.81/1.53 ( ( bot @ B )
% 2.81/1.53 => ( ( bot_bot @ ( A > B ) )
% 2.81/1.53 = ( ^ [X: A] : ( bot_bot @ B ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_72_fun__upd__idem__iff,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B] :
% 2.81/1.53 ( ( ( fun_upd @ A @ B @ F @ X3 @ Y2 )
% 2.81/1.53 = F )
% 2.81/1.53 = ( ( F @ X3 )
% 2.81/1.53 = Y2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_73_fun__upd__twist,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType,A4: A,C2: A,M: A > B,B3: B,D: B] :
% 2.81/1.53 ( ( A4 != C2 )
% 2.81/1.53 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ A4 @ B3 ) @ C2 @ D )
% 2.81/1.53 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M @ C2 @ D ) @ A4 @ B3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_74_fun__upd__other,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType,Z2: A,X3: A,F: A > B,Y2: B] :
% 2.81/1.53 ( ( Z2 != X3 )
% 2.81/1.53 => ( ( fun_upd @ A @ B @ F @ X3 @ Y2 @ Z2 )
% 2.81/1.53 = ( F @ Z2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_75_fun__upd__same,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType,F: B > A,X3: B,Y2: A] :
% 2.81/1.53 ( ( fun_upd @ B @ A @ F @ X3 @ Y2 @ X3 )
% 2.81/1.53 = Y2 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_76_fun__upd__idem,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType,F: B > A,X3: B,Y2: A] :
% 2.81/1.53 ( ( ( F @ X3 )
% 2.81/1.53 = Y2 )
% 2.81/1.53 => ( ( fun_upd @ B @ A @ F @ X3 @ Y2 )
% 2.81/1.53 = F ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_77_fun__upd__eqD,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType,F: A > B,X3: A,Y2: B,G: A > B,Z2: B] :
% 2.81/1.53 ( ( ( fun_upd @ A @ B @ F @ X3 @ Y2 )
% 2.81/1.53 = ( fun_upd @ A @ B @ G @ X3 @ Z2 ) )
% 2.81/1.53 => ( Y2 = Z2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_78_fun__upd__def,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType] :
% 2.81/1.53 ( ( fun_upd @ A @ B )
% 2.81/1.53 = ( ^ [F2: A > B,A3: A,B4: B,X: A] : ( if @ B @ ( X = A3 ) @ B4 @ ( F2 @ X ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_79_traffic_Ochange__dyn__def,axiom,
% 2.81/1.53 ( change_dyn
% 2.81/1.53 = ( ^ [Ts6: traffic,C4: cars,F2: real > real,Ts4: traffic] :
% 2.81/1.53 ( ( ( pos @ Ts4 )
% 2.81/1.53 = ( pos @ Ts6 ) )
% 2.81/1.53 & ( ( res @ Ts4 )
% 2.81/1.53 = ( res @ Ts6 ) )
% 2.81/1.53 & ( ( clm @ Ts4 )
% 2.81/1.53 = ( clm @ Ts6 ) )
% 2.81/1.53 & ( ( dyn @ Ts4 )
% 2.81/1.53 = ( fun_upd @ cars @ ( real > real ) @ ( dyn @ Ts6 ) @ C4 @ F2 ) )
% 2.81/1.53 & ( ( physical_size @ Ts4 )
% 2.81/1.53 = ( physical_size @ Ts6 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_80_local_Ohmlsl_Owidth__hchop__stable,axiom,
% 2.81/1.53 ! [X3: nat,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ( ( nat_card @ ( lan @ product_unit @ V ) )
% 2.81/1.53 = X3 )
% 2.81/1.53 = ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V @ W @ U )
% 2.81/1.53 & ( ( nat_card @ ( lan @ product_unit @ W ) )
% 2.81/1.53 = X3 )
% 2.81/1.53 & ( ( nat_card @ ( lan @ product_unit @ U ) )
% 2.81/1.53 = X3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_81_chop__singleton__right,axiom,
% 2.81/1.53 ! [R3: real_int] :
% 2.81/1.53 ? [X_1: real_int] : ( real_R_Chop @ R3 @ R3 @ X_1 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_82_real__int__class_Ochop__always__possible,axiom,
% 2.81/1.53 ! [R3: real_int] :
% 2.81/1.53 ? [S: real_int,X_1: real_int] : ( real_R_Chop @ R3 @ S @ X_1 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_83_chop__singleton__left,axiom,
% 2.81/1.53 ! [R3: real_int] :
% 2.81/1.53 ? [S: real_int] : ( real_R_Chop @ R3 @ S @ R3 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_84_view_Oswitch__def,axiom,
% 2.81/1.53 ( switch
% 2.81/1.53 = ( ^ [V3: view_ext @ product_unit,C4: cars,W: view_ext @ product_unit] :
% 2.81/1.53 ( ( ( ext @ product_unit @ V3 )
% 2.81/1.53 = ( ext @ product_unit @ W ) )
% 2.81/1.53 & ( ( lan @ product_unit @ V3 )
% 2.81/1.53 = ( lan @ product_unit @ W ) )
% 2.81/1.53 & ( ( own @ product_unit @ W )
% 2.81/1.53 = C4 )
% 2.81/1.53 & ( ( more @ product_unit @ V3 )
% 2.81/1.53 = ( more @ product_unit @ W ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_85_local_Ohmlsl_Oat__conj__distr,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ( ( Phi @ Ts @ V6 )
% 2.81/1.53 & ( Psi @ Ts @ V6 ) ) ) )
% 2.81/1.53 = ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ( Phi @ Ts @ V6 ) )
% 2.81/1.53 & ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ( Psi @ Ts @ V6 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_86_local_Ohmlsl_Oat__disj__dist,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ( ( Phi @ Ts @ V6 )
% 2.81/1.53 | ( Psi @ Ts @ V6 ) ) ) )
% 2.81/1.53 = ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ( Phi @ Ts @ V6 ) )
% 2.81/1.53 | ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ( Psi @ Ts @ V6 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_87_local_Ohmlsl_Oat__eq,axiom,
% 2.81/1.53 ! [A: $tType,E: cars,C2: A,D: A,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ E @ V6 )
% 2.81/1.53 => ( C2 = D ) ) )
% 2.81/1.53 = ( C2 = D ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_88_local_Ohmlsl_Oat__exists,axiom,
% 2.81/1.53 ! [Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ( Phi @ Ts @ V )
% 2.81/1.53 => ? [X2: cars] :
% 2.81/1.53 ! [V7: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ X2 @ V7 )
% 2.81/1.53 => ( Phi @ Ts @ V7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_89_local_Ohmlsl_Oat__neg,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ~ ( Phi @ Ts @ V6 ) ) )
% 2.81/1.53 = ( ~ ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ( Phi @ Ts @ V6 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_90_local_Ohmlsl_Oat__neg_H,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts5: traffic] :
% 2.81/1.53 ( ( ~ ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V2 @ C2 @ V6 )
% 2.81/1.53 => ( Phi @ Ts5 @ V6 ) ) )
% 2.81/1.53 = ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V2 @ C2 @ V6 )
% 2.81/1.53 => ~ ( Phi @ Ts5 @ V6 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_91_local_Ohmlsl_Oat__neg1,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ! [V5: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V5 )
% 2.81/1.53 => ~ ( Phi @ Ts @ V5 ) )
% 2.81/1.53 => ~ ! [V5: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V5 )
% 2.81/1.53 => ( Phi @ Ts @ V5 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_92_local_Ohmlsl_Oat__neg2,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ~ ! [V7: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V7 )
% 2.81/1.53 => ( Phi @ Ts @ V7 ) )
% 2.81/1.53 => ! [V7: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V7 )
% 2.81/1.53 => ~ ( Phi @ Ts @ V7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_93_local_Ohmlsl_Oat__neg__neg,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ( Phi @ Ts @ V6 ) ) )
% 2.81/1.53 = ( ~ ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ~ ( Phi @ Ts @ V6 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_94_local_Ohmlsl_Oat__neg__neg1,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ! [V5: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V5 )
% 2.81/1.53 => ( Phi @ Ts @ V5 ) )
% 2.81/1.53 => ~ ! [V5: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V5 )
% 2.81/1.53 => ~ ( Phi @ Ts @ V5 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_95_local_Ohmlsl_Oat__neg__neg2,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ~ ! [V7: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V7 )
% 2.81/1.53 => ~ ( Phi @ Ts @ V7 ) )
% 2.81/1.53 => ! [V7: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V7 )
% 2.81/1.53 => ( Phi @ Ts @ V7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_96_local_Ohmlsl_Oat__hchop__dist,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ( ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V @ W @ U )
% 2.81/1.53 & ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ W @ C2 @ V6 )
% 2.81/1.53 => ( Phi @ Ts @ V6 ) )
% 2.81/1.53 & ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ U @ C2 @ V6 )
% 2.81/1.53 => ( Psi @ Ts @ V6 ) ) ) )
% 2.81/1.53 = ( ! [V6: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V6 )
% 2.81/1.53 => ? [W: view_ext @ product_unit,U: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V6 @ W @ U )
% 2.81/1.53 & ( Phi @ Ts @ W )
% 2.81/1.53 & ( Psi @ Ts @ U ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_97_local_Ohmlsl_Oat__hchop__dist1,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ! [V5: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V5 )
% 2.81/1.53 => ? [Va2: view_ext @ product_unit,U4: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V5 @ Va2 @ U4 )
% 2.81/1.53 & ( Phi @ Ts @ Va2 )
% 2.81/1.53 & ( Psi @ Ts @ U4 ) ) )
% 2.81/1.53 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V @ Va @ U2 )
% 2.81/1.53 & ! [V7: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ Va @ C2 @ V7 )
% 2.81/1.53 => ( Phi @ Ts @ V7 ) )
% 2.81/1.53 & ! [V7: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ U2 @ C2 @ V7 )
% 2.81/1.53 => ( Psi @ Ts @ V7 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_98_local_Ohmlsl_Oat__hchop__dist2,axiom,
% 2.81/1.53 ! [C2: cars,Phi: traffic > ( view_ext @ product_unit ) > $o,Psi: traffic > ( view_ext @ product_unit ) > $o,Ts: traffic,V: view_ext @ product_unit] :
% 2.81/1.53 ( ? [Va2: view_ext @ product_unit,U4: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V @ Va2 @ U4 )
% 2.81/1.53 & ! [V5: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ Va2 @ C2 @ V5 )
% 2.81/1.53 => ( Phi @ Ts @ V5 ) )
% 2.81/1.53 & ! [V5: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ U4 @ C2 @ V5 )
% 2.81/1.53 => ( Psi @ Ts @ V5 ) ) )
% 2.81/1.53 => ! [V7: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V @ C2 @ V7 )
% 2.81/1.53 => ? [Va: view_ext @ product_unit,U2: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V7 @ Va @ U2 )
% 2.81/1.53 & ( Phi @ Ts @ Va )
% 2.81/1.53 & ( Psi @ Ts @ U2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_99_view_Oswitch__always__exists,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,C3: cars] :
% 2.81/1.53 ? [X_1: view_ext @ product_unit] : ( switch @ V2 @ C3 @ X_1 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_100_view_Oswitch__triangle,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,D: cars,W2: view_ext @ product_unit] :
% 2.81/1.53 ( ( ( switch @ V2 @ C2 @ U3 )
% 2.81/1.53 & ( switch @ V2 @ D @ W2 ) )
% 2.81/1.53 => ( switch @ U3 @ D @ W2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_101_view_Oswitch__unique,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.81/1.53 ( ( ( switch @ V2 @ C2 @ U3 )
% 2.81/1.53 & ( switch @ V2 @ C2 @ W2 ) )
% 2.81/1.53 => ( U3 = W2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_102_view_Oswitch__exists,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit] :
% 2.81/1.53 ? [C: cars,X_1: view_ext @ product_unit] : ( switch @ V2 @ C @ X_1 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_103_view_Oswitch__trans,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit,D: cars,W2: view_ext @ product_unit] :
% 2.81/1.53 ( ( ( switch @ V2 @ C2 @ U3 )
% 2.81/1.53 & ( switch @ U3 @ D @ W2 ) )
% 2.81/1.53 => ( switch @ V2 @ D @ W2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_104_view_Oswitch__hchop1,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,V1: view_ext @ product_unit,V22: view_ext @ product_unit,C2: cars,V8: view_ext @ product_unit] :
% 2.81/1.53 ( ( ( hchop @ V2 @ V1 @ V22 )
% 2.81/1.53 & ( switch @ V2 @ C2 @ V8 ) )
% 2.81/1.53 => ? [V12: view_ext @ product_unit,V23: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V1 @ C2 @ V12 )
% 2.81/1.53 & ( switch @ V22 @ C2 @ V23 )
% 2.81/1.53 & ( hchop @ V8 @ V12 @ V23 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_105_view_Oswitch__hchop2,axiom,
% 2.81/1.53 ! [V8: view_ext @ product_unit,V13: view_ext @ product_unit,V24: view_ext @ product_unit,V2: view_ext @ product_unit,C2: cars] :
% 2.81/1.53 ( ( ( hchop @ V8 @ V13 @ V24 )
% 2.81/1.53 & ( switch @ V2 @ C2 @ V8 ) )
% 2.81/1.53 => ? [V14: view_ext @ product_unit,V25: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V14 @ C2 @ V13 )
% 2.81/1.53 & ( switch @ V25 @ C2 @ V24 )
% 2.81/1.53 & ( hchop @ V2 @ V14 @ V25 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_106_view_Oswitch__refl,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit] : ( switch @ V2 @ ( own @ product_unit @ V2 ) @ V2 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_107_view_Oswitch__symm,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,C2: cars,U3: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V2 @ C2 @ U3 )
% 2.81/1.53 => ( switch @ U3 @ ( own @ product_unit @ V2 ) @ V2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_108_view_Oswitch__origin,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit] :
% 2.81/1.53 ? [U2: view_ext @ product_unit] : ( switch @ U2 @ ( own @ product_unit @ V2 ) @ V2 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_109_view_Ohorizontal__chop__width__stable,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V2 @ U3 @ W2 )
% 2.81/1.53 => ( ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.81/1.53 = ( nat_card @ ( lan @ product_unit @ U3 ) ) )
% 2.81/1.53 & ( ( nat_card @ ( lan @ product_unit @ V2 ) )
% 2.81/1.53 = ( nat_card @ ( lan @ product_unit @ W2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_110_traffic_Ochange,axiom,
% 2.81/1.53 ! [Ts5: traffic,Ts7: traffic,Ts8: traffic] :
% 2.81/1.53 ( ? [C3: cars,F3: real > real] : ( change_dyn @ Ts5 @ C3 @ F3 @ Ts7 )
% 2.81/1.53 => ( ( evolve @ Ts7 @ Ts8 )
% 2.81/1.53 => ( evolve @ Ts5 @ Ts8 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_111_old_Ounit_Oexhaust,axiom,
% 2.81/1.53 ! [Y2: product_unit] : ( Y2 = product_Unity ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_112_old_Ounit_Oinducts,axiom,
% 2.81/1.53 ! [P: product_unit > $o,Unit: product_unit] :
% 2.81/1.53 ( ( P @ product_Unity )
% 2.81/1.53 => ( P @ Unit ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_113_unit__all__impI,axiom,
% 2.81/1.53 ! [P: product_unit > $o,Q: product_unit > $o] :
% 2.81/1.53 ( ( ( P @ product_Unity )
% 2.81/1.53 => ( Q @ product_Unity ) )
% 2.81/1.53 => ! [X4: product_unit] :
% 2.81/1.53 ( ( P @ X4 )
% 2.81/1.53 => ( Q @ X4 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_114_eq__sym__Unity__conv,axiom,
% 2.81/1.53 ! [X3: $o] :
% 2.81/1.53 ( ( X3
% 2.81/1.53 = ( product_Unity = product_Unity ) )
% 2.81/1.53 = X3 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_115_bot__unit__def,axiom,
% 2.81/1.53 ( ( bot_bot @ product_unit )
% 2.81/1.53 = product_Unity ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_116_traffic_Ocreate__res__subseteq2,axiom,
% 2.81/1.53 ! [Ts5: traffic,C2: cars,Ts7: traffic] :
% 2.81/1.53 ( ( create_reservation @ Ts5 @ C2 @ Ts7 )
% 2.81/1.53 => ( ord_less_eq @ nat_int @ ( clm @ Ts5 @ C2 ) @ ( res @ Ts7 @ C2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_117_order__refl,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_118_le__funD,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType] :
% 2.81/1.53 ( ( ord @ B )
% 2.81/1.53 => ! [F: A > B,G: A > B,X3: A] :
% 2.81/1.53 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.81/1.53 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_119_le__funE,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType] :
% 2.81/1.53 ( ( ord @ B )
% 2.81/1.53 => ! [F: A > B,G: A > B,X3: A] :
% 2.81/1.53 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.81/1.53 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_120_le__funI,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType] :
% 2.81/1.53 ( ( ord @ B )
% 2.81/1.53 => ! [F: A > B,G: A > B] :
% 2.81/1.53 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 2.81/1.53 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_121_le__fun__def,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType] :
% 2.81/1.53 ( ( ord @ B )
% 2.81/1.53 => ( ( ord_less_eq @ ( A > B ) )
% 2.81/1.53 = ( ^ [F2: A > B,G2: A > B] :
% 2.81/1.53 ! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_122_order__subst1,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( ( order @ B )
% 2.81/1.53 & ( order @ A ) )
% 2.81/1.53 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
% 2.81/1.53 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 2.81/1.53 => ( ! [X2: B,Y3: B] :
% 2.81/1.53 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_123_order__subst2,axiom,
% 2.81/1.53 ! [A: $tType,C5: $tType] :
% 2.81/1.53 ( ( ( order @ C5 )
% 2.81/1.53 & ( order @ A ) )
% 2.81/1.53 => ! [A4: A,B3: A,F: A > C5,C2: C5] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less_eq @ C5 @ ( F @ B3 ) @ C2 )
% 2.81/1.53 => ( ! [X2: A,Y3: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less_eq @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less_eq @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_124_ord__eq__le__subst,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( ( ord @ B )
% 2.81/1.53 & ( ord @ A ) )
% 2.81/1.53 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 2.81/1.53 ( ( A4
% 2.81/1.53 = ( F @ B3 ) )
% 2.81/1.53 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 2.81/1.53 => ( ! [X2: B,Y3: B] :
% 2.81/1.53 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less_eq @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_125_ord__le__eq__subst,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( ( ord @ B )
% 2.81/1.53 & ( ord @ A ) )
% 2.81/1.53 => ! [A4: A,B3: A,F: A > B,C2: B] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ( F @ B3 )
% 2.81/1.53 = C2 )
% 2.81/1.53 => ( ! [X2: A,Y3: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less_eq @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_126_eq__iff,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ^ [Y4: A,Z4: A] : ( Y4 = Z4 ) )
% 2.81/1.53 = ( ^ [X: A,Y: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X @ Y )
% 2.81/1.53 & ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_127_antisym,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ Y2 @ X3 )
% 2.81/1.53 => ( X3 = Y2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_128_linear,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 | ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_129_eq__refl,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( X3 = Y2 )
% 2.81/1.53 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_130_le__cases,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ~ ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_131_order_Otrans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 2.81/1.53 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_132_le__cases3,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A,Z2: A] :
% 2.81/1.53 ( ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 2.81/1.53 => ( ( ( ord_less_eq @ A @ Y2 @ X3 )
% 2.81/1.53 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 2.81/1.53 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 2.81/1.53 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 2.81/1.53 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 2.81/1.53 => ~ ( ord_less_eq @ A @ Y2 @ X3 ) )
% 2.81/1.53 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 2.81/1.53 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 2.81/1.53 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 2.81/1.53 => ~ ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_133_antisym__conv,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [Y2: A,X3: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 = ( X3 = Y2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_134_order__class_Oorder_Oeq__iff,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ^ [Y4: A,Z4: A] : ( Y4 = Z4 ) )
% 2.81/1.53 = ( ^ [A3: A,B4: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.81/1.53 & ( ord_less_eq @ A @ B4 @ A3 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_135_ord__eq__le__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ord @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( A4 = B3 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 2.81/1.53 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_136_ord__le__eq__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ord @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( B3 = C2 )
% 2.81/1.53 => ( ord_less_eq @ A @ A4 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_137_order__class_Oorder_Oantisym,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ B3 @ A4 )
% 2.81/1.53 => ( A4 = B3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_138_order__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A,Z2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 2.81/1.53 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_139_dual__order_Orefl,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_140_linorder__wlog,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [P: A > A > $o,A4: A,B3: A] :
% 2.81/1.53 ( ! [A5: A,B5: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A5 @ B5 )
% 2.81/1.53 => ( P @ A5 @ B5 ) )
% 2.81/1.53 => ( ! [A5: A,B5: A] :
% 2.81/1.53 ( ( P @ B5 @ A5 )
% 2.81/1.53 => ( P @ A5 @ B5 ) )
% 2.81/1.53 => ( P @ A4 @ B3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_141_dual__order_Otrans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [B3: A,A4: A,C2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ B3 @ A4 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 2.81/1.53 => ( ord_less_eq @ A @ C2 @ A4 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_142_dual__order_Oeq__iff,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ^ [Y4: A,Z4: A] : ( Y4 = Z4 ) )
% 2.81/1.53 = ( ^ [A3: A,B4: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.81/1.53 & ( ord_less_eq @ A @ A3 @ B4 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_143_dual__order_Oantisym,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [B3: A,A4: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ B3 @ A4 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( A4 = B3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_144_less__eq__view__ext__def,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ord_less_eq @ ( view_ext @ A ) )
% 2.81/1.53 = ( ^ [V9: view_ext @ A,V10: view_ext @ A] :
% 2.81/1.53 ( ( ord_less_eq @ real_int @ ( ext @ A @ V9 ) @ ( ext @ A @ V10 ) )
% 2.81/1.53 & ( ord_less_eq @ nat_int @ ( lan @ A @ V9 ) @ ( lan @ A @ V10 ) )
% 2.81/1.53 & ( ( own @ A @ V9 )
% 2.81/1.53 = ( own @ A @ V10 ) )
% 2.81/1.53 & ( ord_less_eq @ A @ ( more @ A @ V9 ) @ ( more @ A @ V10 ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_145_bot_Oextremum,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order_bot @ A )
% 2.81/1.53 => ! [A4: A] : ( ord_less_eq @ A @ ( bot_bot @ A ) @ A4 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_146_bot_Oextremum__unique,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order_bot @ A )
% 2.81/1.53 => ! [A4: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ ( bot_bot @ A ) )
% 2.81/1.53 = ( A4
% 2.81/1.53 = ( bot_bot @ A ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_147_bot_Oextremum__uniqueI,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order_bot @ A )
% 2.81/1.53 => ! [A4: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ ( bot_bot @ A ) )
% 2.81/1.53 => ( A4
% 2.81/1.53 = ( bot_bot @ A ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_148_traffic_Ocreate__res__subseteq1,axiom,
% 2.81/1.53 ! [Ts5: traffic,C2: cars,Ts7: traffic] :
% 2.81/1.53 ( ( create_reservation @ Ts5 @ C2 @ Ts7 )
% 2.81/1.53 => ( ord_less_eq @ nat_int @ ( res @ Ts5 @ C2 ) @ ( res @ Ts7 @ C2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_149_traffic_Owithdraw__res__subseteq,axiom,
% 2.81/1.53 ! [Ts5: traffic,D: cars,N: nat,Ts7: traffic,C2: cars] :
% 2.81/1.53 ( ( withdraw_reservation @ Ts5 @ D @ N @ Ts7 )
% 2.81/1.53 => ( ord_less_eq @ nat_int @ ( res @ Ts7 @ C2 ) @ ( res @ Ts5 @ C2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_150_old_Ounit_Orec,axiom,
% 2.81/1.53 ! [T: $tType,F1: T] :
% 2.81/1.53 ( ( product_rec_unit @ T @ F1 @ product_Unity )
% 2.81/1.53 = F1 ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_151_default__unit__def,axiom,
% 2.81/1.53 ( ( default_default @ product_unit )
% 2.81/1.53 = product_Unity ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_152_less__view__ext__def,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ord_less @ ( view_ext @ A ) )
% 2.81/1.53 = ( ^ [V9: view_ext @ A,V10: view_ext @ A] :
% 2.81/1.53 ( ( ord_less_eq @ real_int @ ( ext @ A @ V9 ) @ ( ext @ A @ V10 ) )
% 2.81/1.53 & ( ord_less_eq @ nat_int @ ( lan @ A @ V9 ) @ ( lan @ A @ V10 ) )
% 2.81/1.53 & ( ( own @ A @ V10 )
% 2.81/1.53 = ( own @ A @ V9 ) )
% 2.81/1.53 & ( ord_less_eq @ A @ ( more @ A @ V9 ) @ ( more @ A @ V10 ) )
% 2.81/1.53 & ~ ( ( ord_less_eq @ real_int @ ( ext @ A @ V10 ) @ ( ext @ A @ V9 ) )
% 2.81/1.53 & ( ord_less_eq @ nat_int @ ( lan @ A @ V10 ) @ ( lan @ A @ V9 ) )
% 2.81/1.53 & ( ( own @ A @ V10 )
% 2.81/1.53 = ( own @ A @ V9 ) )
% 2.81/1.53 & ( ord_less_eq @ A @ ( more @ A @ V10 ) @ ( more @ A @ V9 ) ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_153_diff__mono,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ordered_ab_group_add @ A )
% 2.81/1.53 => ! [A4: A,B3: A,D: A,C2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ D @ C2 )
% 2.81/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_154_leD,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [Y2: A,X3: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ Y2 @ X3 )
% 2.81/1.53 => ~ ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_155_leI,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_156_le__less,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ord_less_eq @ A )
% 2.81/1.53 = ( ^ [X: A,Y: A] :
% 2.81/1.53 ( ( ord_less @ A @ X @ Y )
% 2.81/1.53 | ( X = Y ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_157_less__le,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ord_less @ A )
% 2.81/1.53 = ( ^ [X: A,Y: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X @ Y )
% 2.81/1.53 & ( X != Y ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_158_order__le__less__subst1,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( ( order @ B )
% 2.81/1.53 & ( order @ A ) )
% 2.81/1.53 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
% 2.81/1.53 => ( ( ord_less @ B @ B3 @ C2 )
% 2.81/1.53 => ( ! [X2: B,Y3: B] :
% 2.81/1.53 ( ( ord_less @ B @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_159_order__le__less__subst2,axiom,
% 2.81/1.53 ! [A: $tType,C5: $tType] :
% 2.81/1.53 ( ( ( order @ C5 )
% 2.81/1.53 & ( order @ A ) )
% 2.81/1.53 => ! [A4: A,B3: A,F: A > C5,C2: C5] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less @ C5 @ ( F @ B3 ) @ C2 )
% 2.81/1.53 => ( ! [X2: A,Y3: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less_eq @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_160_order__less__le__subst1,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( ( order @ B )
% 2.81/1.53 & ( order @ A ) )
% 2.81/1.53 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ ( F @ B3 ) )
% 2.81/1.53 => ( ( ord_less_eq @ B @ B3 @ C2 )
% 2.81/1.53 => ( ! [X2: B,Y3: B] :
% 2.81/1.53 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_161_order__less__le__subst2,axiom,
% 2.81/1.53 ! [A: $tType,C5: $tType] :
% 2.81/1.53 ( ( ( order @ C5 )
% 2.81/1.53 & ( order @ A ) )
% 2.81/1.53 => ! [A4: A,B3: A,F: A > C5,C2: C5] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less_eq @ C5 @ ( F @ B3 ) @ C2 )
% 2.81/1.53 => ( ! [X2: A,Y3: A] :
% 2.81/1.53 ( ( ord_less @ A @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_162_not__le,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ~ ( ord_less_eq @ A @ X3 @ Y2 ) )
% 2.81/1.53 = ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_163_not__less,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 2.81/1.53 = ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_164_le__neq__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( A4 != B3 )
% 2.81/1.53 => ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_165_antisym__conv1,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 = ( X3 = Y2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_166_antisym__conv2,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 2.81/1.53 = ( X3 = Y2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_167_less__imp__le,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ord_less_eq @ A @ X3 @ Y2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_168_le__less__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A,Z2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ord_less @ A @ Y2 @ Z2 )
% 2.81/1.53 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_169_less__le__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A,Z2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 2.81/1.53 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_170_dense__ge,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( dense_linorder @ A )
% 2.81/1.53 => ! [Z2: A,Y2: A] :
% 2.81/1.53 ( ! [X2: A] :
% 2.81/1.53 ( ( ord_less @ A @ Z2 @ X2 )
% 2.81/1.53 => ( ord_less_eq @ A @ Y2 @ X2 ) )
% 2.81/1.53 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_171_dense__le,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( dense_linorder @ A )
% 2.81/1.53 => ! [Y2: A,Z2: A] :
% 2.81/1.53 ( ! [X2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X2 @ Y2 )
% 2.81/1.53 => ( ord_less_eq @ A @ X2 @ Z2 ) )
% 2.81/1.53 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_172_le__less__linear,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_173_le__imp__less__or__eq,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 | ( X3 = Y2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_174_less__le__not__le,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ( ( ord_less @ A )
% 2.81/1.53 = ( ^ [X: A,Y: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ X @ Y )
% 2.81/1.53 & ~ ( ord_less_eq @ A @ Y @ X ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_175_not__le__imp__less,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [Y2: A,X3: A] :
% 2.81/1.53 ( ~ ( ord_less_eq @ A @ Y2 @ X3 )
% 2.81/1.53 => ( ord_less @ A @ X3 @ Y2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_176_order_Ostrict__trans1,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less @ A @ B3 @ C2 )
% 2.81/1.53 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_177_order_Ostrict__trans2,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ B3 @ C2 )
% 2.81/1.53 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_178_order_Oorder__iff__strict,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ord_less_eq @ A )
% 2.81/1.53 = ( ^ [A3: A,B4: A] :
% 2.81/1.53 ( ( ord_less @ A @ A3 @ B4 )
% 2.81/1.53 | ( A3 = B4 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_179_order_Ostrict__iff__order,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ord_less @ A )
% 2.81/1.53 = ( ^ [A3: A,B4: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A3 @ B4 )
% 2.81/1.53 & ( A3 != B4 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_180_dual__order_Ostrict__trans1,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [B3: A,A4: A,C2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ B3 @ A4 )
% 2.81/1.53 => ( ( ord_less @ A @ C2 @ B3 )
% 2.81/1.53 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_181_dual__order_Ostrict__trans2,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [B3: A,A4: A,C2: A] :
% 2.81/1.53 ( ( ord_less @ A @ B3 @ A4 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ C2 @ B3 )
% 2.81/1.53 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_182_dense__ge__bounded,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( dense_linorder @ A )
% 2.81/1.53 => ! [Z2: A,X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ Z2 @ X3 )
% 2.81/1.53 => ( ! [W3: A] :
% 2.81/1.53 ( ( ord_less @ A @ Z2 @ W3 )
% 2.81/1.53 => ( ( ord_less @ A @ W3 @ X3 )
% 2.81/1.53 => ( ord_less_eq @ A @ Y2 @ W3 ) ) )
% 2.81/1.53 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_183_dense__le__bounded,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( dense_linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A,Z2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ! [W3: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ W3 )
% 2.81/1.53 => ( ( ord_less @ A @ W3 @ Y2 )
% 2.81/1.53 => ( ord_less_eq @ A @ W3 @ Z2 ) ) )
% 2.81/1.53 => ( ord_less_eq @ A @ Y2 @ Z2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_184_order_Ostrict__implies__order,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ord_less_eq @ A @ A4 @ B3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_185_dual__order_Oorder__iff__strict,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ord_less_eq @ A )
% 2.81/1.53 = ( ^ [B4: A,A3: A] :
% 2.81/1.53 ( ( ord_less @ A @ B4 @ A3 )
% 2.81/1.53 | ( A3 = B4 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_186_dual__order_Ostrict__iff__order,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ( ( ord_less @ A )
% 2.81/1.53 = ( ^ [B4: A,A3: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ B4 @ A3 )
% 2.81/1.53 & ( A3 != B4 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_187_dual__order_Ostrict__implies__order,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [B3: A,A4: A] :
% 2.81/1.53 ( ( ord_less @ A @ B3 @ A4 )
% 2.81/1.53 => ( ord_less_eq @ A @ B3 @ A4 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_188_order_Onot__eq__order__implies__strict,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A] :
% 2.81/1.53 ( ( A4 != B3 )
% 2.81/1.53 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_189_bot_Oextremum__strict,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order_bot @ A )
% 2.81/1.53 => ! [A4: A] :
% 2.81/1.53 ~ ( ord_less @ A @ A4 @ ( bot_bot @ A ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_190_bot_Onot__eq__extremum,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order_bot @ A )
% 2.81/1.53 => ! [A4: A] :
% 2.81/1.53 ( ( A4
% 2.81/1.53 != ( bot_bot @ A ) )
% 2.81/1.53 = ( ord_less @ A @ ( bot_bot @ A ) @ A4 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_191_view_Ohorizontal__chop__leq2,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V2 @ U3 @ W2 )
% 2.81/1.53 => ( ord_less_eq @ ( view_ext @ product_unit ) @ W2 @ V2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_192_view_Ohorizontal__chop__leq1,axiom,
% 2.81/1.53 ! [V2: view_ext @ product_unit,U3: view_ext @ product_unit,W2: view_ext @ product_unit] :
% 2.81/1.53 ( ( hchop @ V2 @ U3 @ W2 )
% 2.81/1.53 => ( ord_less_eq @ ( view_ext @ product_unit ) @ U3 @ V2 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_193_view_Oswitch__leq,axiom,
% 2.81/1.53 ! [U5: view_ext @ product_unit,U3: view_ext @ product_unit,V2: view_ext @ product_unit,C2: cars] :
% 2.81/1.53 ( ( ( ord_less_eq @ ( view_ext @ product_unit ) @ U5 @ U3 )
% 2.81/1.53 & ( switch @ V2 @ C2 @ U3 ) )
% 2.81/1.53 => ? [V5: view_ext @ product_unit] :
% 2.81/1.53 ( ( switch @ V5 @ C2 @ U5 )
% 2.81/1.53 & ( ord_less_eq @ ( view_ext @ product_unit ) @ V5 @ V2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_194_dual__order_Ostrict__implies__not__eq,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [B3: A,A4: A] :
% 2.81/1.53 ( ( ord_less @ A @ B3 @ A4 )
% 2.81/1.53 => ( A4 != B3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_195_order_Ostrict__implies__not__eq,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( A4 != B3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_196_not__less__iff__gr__or__eq,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 2.81/1.53 = ( ( ord_less @ A @ Y2 @ X3 )
% 2.81/1.53 | ( X3 = Y2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_197_dual__order_Ostrict__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [B3: A,A4: A,C2: A] :
% 2.81/1.53 ( ( ord_less @ A @ B3 @ A4 )
% 2.81/1.53 => ( ( ord_less @ A @ C2 @ B3 )
% 2.81/1.53 => ( ord_less @ A @ C2 @ A4 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_198_linorder__less__wlog,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [P: A > A > $o,A4: A,B3: A] :
% 2.81/1.53 ( ! [A5: A,B5: A] :
% 2.81/1.53 ( ( ord_less @ A @ A5 @ B5 )
% 2.81/1.53 => ( P @ A5 @ B5 ) )
% 2.81/1.53 => ( ! [A5: A] : ( P @ A5 @ A5 )
% 2.81/1.53 => ( ! [A5: A,B5: A] :
% 2.81/1.53 ( ( P @ B5 @ A5 )
% 2.81/1.53 => ( P @ A5 @ B5 ) )
% 2.81/1.53 => ( P @ A4 @ B3 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_199_exists__least__iff,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( wellorder @ A )
% 2.81/1.53 => ( ( ^ [P2: A > $o] :
% 2.81/1.53 ? [X5: A] : ( P2 @ X5 ) )
% 2.81/1.53 = ( ^ [P3: A > $o] :
% 2.81/1.53 ? [N4: A] :
% 2.81/1.53 ( ( P3 @ N4 )
% 2.81/1.53 & ! [M2: A] :
% 2.81/1.53 ( ( ord_less @ A @ M2 @ N4 )
% 2.81/1.53 => ~ ( P3 @ M2 ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_200_less__imp__not__less,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_201_order_Ostrict__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less @ A @ B3 @ C2 )
% 2.81/1.53 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_202_dual__order_Oirrefl,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A] :
% 2.81/1.53 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_203_linorder__cases,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ~ ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( X3 != Y2 )
% 2.81/1.53 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_204_less__imp__triv,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A,P: $o] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ord_less @ A @ Y2 @ X3 )
% 2.81/1.53 => P ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_205_less__imp__not__eq2,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( Y2 != X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_206_antisym__conv3,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [Y2: A,X3: A] :
% 2.81/1.53 ( ~ ( ord_less @ A @ Y2 @ X3 )
% 2.81/1.53 => ( ( ~ ( ord_less @ A @ X3 @ Y2 ) )
% 2.81/1.53 = ( X3 = Y2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_207_less__induct,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( wellorder @ A )
% 2.81/1.53 => ! [P: A > $o,A4: A] :
% 2.81/1.53 ( ! [X2: A] :
% 2.81/1.53 ( ! [Y5: A] :
% 2.81/1.53 ( ( ord_less @ A @ Y5 @ X2 )
% 2.81/1.53 => ( P @ Y5 ) )
% 2.81/1.53 => ( P @ X2 ) )
% 2.81/1.53 => ( P @ A4 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_208_less__not__sym,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_209_less__imp__not__eq,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( X3 != Y2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_210_dual__order_Oasym,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [B3: A,A4: A] :
% 2.81/1.53 ( ( ord_less @ A @ B3 @ A4 )
% 2.81/1.53 => ~ ( ord_less @ A @ A4 @ B3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_211_ord__less__eq__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ord @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( B3 = C2 )
% 2.81/1.53 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_212_ord__eq__less__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ord @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( A4 = B3 )
% 2.81/1.53 => ( ( ord_less @ A @ B3 @ C2 )
% 2.81/1.53 => ( ord_less @ A @ A4 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_213_less__irrefl,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A] :
% 2.81/1.53 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_214_less__linear,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 | ( X3 = Y2 )
% 2.81/1.53 | ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_215_less__trans,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A,Z2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ( ord_less @ A @ Y2 @ Z2 )
% 2.81/1.53 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_216_less__asym_H,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [A4: A,B3: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_217_less__asym,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( preorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ~ ( ord_less @ A @ Y2 @ X3 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_218_less__imp__neq,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( X3 != Y2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_219_dense,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( dense_order @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ? [Z5: A] :
% 2.81/1.53 ( ( ord_less @ A @ X3 @ Z5 )
% 2.81/1.53 & ( ord_less @ A @ Z5 @ Y2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_220_order_Oasym,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [A4: A,B3: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_221_neq__iff,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( X3 != Y2 )
% 2.81/1.53 = ( ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 | ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_222_neqE,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( linorder @ A )
% 2.81/1.53 => ! [X3: A,Y2: A] :
% 2.81/1.53 ( ( X3 != Y2 )
% 2.81/1.53 => ( ~ ( ord_less @ A @ X3 @ Y2 )
% 2.81/1.53 => ( ord_less @ A @ Y2 @ X3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_223_gt__ex,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( no_top @ A )
% 2.81/1.53 => ! [X3: A] :
% 2.81/1.53 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_224_lt__ex,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( no_bot @ A )
% 2.81/1.53 => ! [X3: A] :
% 2.81/1.53 ? [Y3: A] : ( ord_less @ A @ Y3 @ X3 ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_225_order__less__subst2,axiom,
% 2.81/1.53 ! [A: $tType,C5: $tType] :
% 2.81/1.53 ( ( ( order @ C5 )
% 2.81/1.53 & ( order @ A ) )
% 2.81/1.53 => ! [A4: A,B3: A,F: A > C5,C2: C5] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less @ C5 @ ( F @ B3 ) @ C2 )
% 2.81/1.53 => ( ! [X2: A,Y3: A] :
% 2.81/1.53 ( ( ord_less @ A @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less @ C5 @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less @ C5 @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_226_order__less__subst1,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( ( order @ B )
% 2.81/1.53 & ( order @ A ) )
% 2.81/1.53 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ ( F @ B3 ) )
% 2.81/1.53 => ( ( ord_less @ B @ B3 @ C2 )
% 2.81/1.53 => ( ! [X2: B,Y3: B] :
% 2.81/1.53 ( ( ord_less @ B @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_227_ord__less__eq__subst,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( ( ord @ B )
% 2.81/1.53 & ( ord @ A ) )
% 2.81/1.53 => ! [A4: A,B3: A,F: A > B,C2: B] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ( F @ B3 )
% 2.81/1.53 = C2 )
% 2.81/1.53 => ( ! [X2: A,Y3: A] :
% 2.81/1.53 ( ( ord_less @ A @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less @ B @ ( F @ A4 ) @ C2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_228_ord__eq__less__subst,axiom,
% 2.81/1.53 ! [A: $tType,B: $tType] :
% 2.81/1.53 ( ( ( ord @ B )
% 2.81/1.53 & ( ord @ A ) )
% 2.81/1.53 => ! [A4: A,F: B > A,B3: B,C2: B] :
% 2.81/1.53 ( ( A4
% 2.81/1.53 = ( F @ B3 ) )
% 2.81/1.53 => ( ( ord_less @ B @ B3 @ C2 )
% 2.81/1.53 => ( ! [X2: B,Y3: B] :
% 2.81/1.53 ( ( ord_less @ B @ X2 @ Y3 )
% 2.81/1.53 => ( ord_less @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.81/1.53 => ( ord_less @ A @ A4 @ ( F @ C2 ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_229_diff__strict__right__mono,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ordered_ab_group_add @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_230_diff__strict__left__mono,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ordered_ab_group_add @ A )
% 2.81/1.53 => ! [B3: A,A4: A,C2: A] :
% 2.81/1.53 ( ( ord_less @ A @ B3 @ A4 )
% 2.81/1.53 => ( ord_less @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_231_diff__eq__diff__less,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ordered_ab_group_add @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A,D: A] :
% 2.81/1.53 ( ( ( minus_minus @ A @ A4 @ B3 )
% 2.81/1.53 = ( minus_minus @ A @ C2 @ D ) )
% 2.81/1.53 => ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 = ( ord_less @ A @ C2 @ D ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_232_diff__strict__mono,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ordered_ab_group_add @ A )
% 2.81/1.53 => ! [A4: A,B3: A,D: A,C2: A] :
% 2.81/1.53 ( ( ord_less @ A @ A4 @ B3 )
% 2.81/1.53 => ( ( ord_less @ A @ D @ C2 )
% 2.81/1.53 => ( ord_less @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_233_chop__leq2,axiom,
% 2.81/1.53 ! [R: real_int,S2: real_int,T2: real_int] :
% 2.81/1.53 ( ( real_R_Chop @ R @ S2 @ T2 )
% 2.81/1.53 => ( ord_less_eq @ real_int @ T2 @ R ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_234_chop__leq1,axiom,
% 2.81/1.53 ! [R: real_int,S2: real_int,T2: real_int] :
% 2.81/1.53 ( ( real_R_Chop @ R @ S2 @ T2 )
% 2.81/1.53 => ( ord_less_eq @ real_int @ S2 @ R ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_235_card__subset__le,axiom,
% 2.81/1.53 ! [I: nat_int,I2: nat_int] :
% 2.81/1.53 ( ( ord_less_eq @ nat_int @ I @ I2 )
% 2.81/1.53 => ( ord_less_eq @ nat @ ( nat_card @ I ) @ ( nat_card @ I2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_236_diff__eq__diff__eq,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( group_add @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A,D: A] :
% 2.81/1.53 ( ( ( minus_minus @ A @ A4 @ B3 )
% 2.81/1.53 = ( minus_minus @ A @ C2 @ D ) )
% 2.81/1.53 => ( ( A4 = B3 )
% 2.81/1.53 = ( C2 = D ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_237_diff__right__commute,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( cancel146912293up_add @ A )
% 2.81/1.53 => ! [A4: A,C2: A,B3: A] :
% 2.81/1.53 ( ( minus_minus @ A @ ( minus_minus @ A @ A4 @ C2 ) @ B3 )
% 2.81/1.53 = ( minus_minus @ A @ ( minus_minus @ A @ A4 @ B3 ) @ C2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_238_diff__eq__diff__less__eq,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ordered_ab_group_add @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A,D: A] :
% 2.81/1.53 ( ( ( minus_minus @ A @ A4 @ B3 )
% 2.81/1.53 = ( minus_minus @ A @ C2 @ D ) )
% 2.81/1.53 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 = ( ord_less_eq @ A @ C2 @ D ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_239_diff__right__mono,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ordered_ab_group_add @ A )
% 2.81/1.53 => ! [A4: A,B3: A,C2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.81/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ A4 @ C2 ) @ ( minus_minus @ A @ B3 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_240_diff__left__mono,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( ordered_ab_group_add @ A )
% 2.81/1.53 => ! [B3: A,A4: A,C2: A] :
% 2.81/1.53 ( ( ord_less_eq @ A @ B3 @ A4 )
% 2.81/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ C2 @ A4 ) @ ( minus_minus @ A @ C2 @ B3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_241_traffic_Oclm__consec__res,axiom,
% 2.81/1.53 ! [Ts5: traffic,C2: cars] :
% 2.81/1.53 ( ( ( clm @ Ts5 @ C2 )
% 2.81/1.53 != ( bot_bot @ nat_int ) )
% 2.81/1.53 => ( ( nat_consec @ ( clm @ Ts5 @ C2 ) @ ( res @ Ts5 @ C2 ) )
% 2.81/1.53 | ( nat_consec @ ( res @ Ts5 @ C2 ) @ ( clm @ Ts5 @ C2 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_242_Greatest__equality,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [P: A > $o,X3: A] :
% 2.81/1.53 ( ( P @ X3 )
% 2.81/1.53 => ( ! [Y3: A] :
% 2.81/1.53 ( ( P @ Y3 )
% 2.81/1.53 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 2.81/1.53 => ( ( order_Greatest @ A @ P )
% 2.81/1.53 = X3 ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_243_GreatestI2__order,axiom,
% 2.81/1.53 ! [A: $tType] :
% 2.81/1.53 ( ( order @ A )
% 2.81/1.53 => ! [P: A > $o,X3: A,Q: A > $o] :
% 2.81/1.53 ( ( P @ X3 )
% 2.81/1.53 => ( ! [Y3: A] :
% 2.81/1.53 ( ( P @ Y3 )
% 2.81/1.53 => ( ord_less_eq @ A @ Y3 @ X3 ) )
% 2.81/1.53 => ( ! [X2: A] :
% 2.81/1.53 ( ( P @ X2 )
% 2.81/1.53 => ( ! [Y5: A] :
% 2.81/1.53 ( ( P @ Y5 )
% 2.81/1.53 => ( ord_less_eq @ A @ Y5 @ X2 ) )
% 2.81/1.53 => ( Q @ X2 ) ) )
% 2.81/1.53 => ( Q @ ( order_Greatest @ A @ P ) ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_244_less__fun__def,axiom,
% 2.81/1.53 ! [B: $tType,A: $tType] :
% 2.81/1.53 ( ( ord @ B )
% 2.81/1.53 => ( ( ord_less @ ( A > B ) )
% 2.81/1.53 = ( ^ [F2: A > B,G2: A > B] :
% 2.81/1.53 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 2.81/1.53 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_245_card__subset__less,axiom,
% 2.81/1.53 ! [I: nat_int,I2: nat_int] :
% 2.81/1.53 ( ( ord_less @ nat_int @ I @ I2 )
% 2.81/1.53 => ( ord_less @ nat @ ( nat_card @ I ) @ ( nat_card @ I2 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_246_consec__intermediate2,axiom,
% 2.81/1.53 ! [I: nat_int,J: nat_int,K: nat_int] :
% 2.81/1.53 ( ( ( nat_consec @ I @ J )
% 2.81/1.53 & ( nat_consec @ ( nat_union @ I @ J ) @ K ) )
% 2.81/1.53 => ( nat_consec @ J @ K ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_247_consec__intermediate1,axiom,
% 2.81/1.53 ! [J: nat_int,K: nat_int,I: nat_int] :
% 2.81/1.53 ( ( ( nat_consec @ J @ K )
% 2.81/1.53 & ( nat_consec @ I @ ( nat_union @ J @ K ) ) )
% 2.81/1.53 => ( nat_consec @ I @ J ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_248_consec__assoc2,axiom,
% 2.81/1.53 ! [I: nat_int,J: nat_int,K: nat_int] :
% 2.81/1.53 ( ( ( nat_consec @ I @ J )
% 2.81/1.53 & ( nat_consec @ ( nat_union @ I @ J ) @ K ) )
% 2.81/1.53 => ( nat_consec @ I @ ( nat_union @ J @ K ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_249_consec__assoc1,axiom,
% 2.81/1.53 ! [J: nat_int,K: nat_int,I: nat_int] :
% 2.81/1.53 ( ( ( nat_consec @ J @ K )
% 2.81/1.53 & ( nat_consec @ I @ ( nat_union @ J @ K ) ) )
% 2.81/1.53 => ( nat_consec @ ( nat_union @ I @ J ) @ K ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_250_un__assoc,axiom,
% 2.81/1.53 ! [I: nat_int,J: nat_int,K: nat_int] :
% 2.81/1.53 ( ( ( nat_consec @ I @ J )
% 2.81/1.53 & ( nat_consec @ J @ K ) )
% 2.81/1.53 => ( ( nat_union @ ( nat_union @ I @ J ) @ K )
% 2.81/1.53 = ( nat_union @ I @ ( nat_union @ J @ K ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_251_consec__assoc__mult,axiom,
% 2.81/1.53 ! [I22: nat_int,I1: nat_int,I3: nat_int,I4: nat_int] :
% 2.81/1.53 ( ( ( ( I22
% 2.81/1.53 = ( bot_bot @ nat_int ) )
% 2.81/1.53 | ( nat_consec @ I1 @ I22 ) )
% 2.81/1.53 & ( ( I3
% 2.81/1.53 = ( bot_bot @ nat_int ) )
% 2.81/1.53 | ( nat_consec @ I3 @ I4 ) )
% 2.81/1.53 & ( nat_consec @ ( nat_union @ I1 @ I22 ) @ ( nat_union @ I3 @ I4 ) ) )
% 2.81/1.53 => ( ( nat_union @ ( nat_union @ I1 @ I22 ) @ ( nat_union @ I3 @ I4 ) )
% 2.81/1.53 = ( nat_union @ ( nat_union @ I1 @ ( nat_union @ I22 @ I3 ) ) @ I4 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_252_un__subset2,axiom,
% 2.81/1.53 ! [I: nat_int,J: nat_int] :
% 2.81/1.53 ( ( nat_consec @ I @ J )
% 2.81/1.53 => ( ord_less_eq @ nat_int @ J @ ( nat_union @ I @ J ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_253_un__subset1,axiom,
% 2.81/1.53 ! [I: nat_int,J: nat_int] :
% 2.81/1.53 ( ( nat_consec @ I @ J )
% 2.81/1.53 => ( ord_less_eq @ nat_int @ I @ ( nat_union @ I @ J ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_254_nchop__def,axiom,
% 2.81/1.53 ( nat_N_Chop
% 2.81/1.53 = ( ^ [I5: nat_int,J2: nat_int,K2: nat_int] :
% 2.81/1.53 ( ( I5
% 2.81/1.53 = ( nat_union @ J2 @ K2 ) )
% 2.81/1.53 & ( ( J2
% 2.81/1.53 = ( bot_bot @ nat_int ) )
% 2.81/1.53 | ( K2
% 2.81/1.53 = ( bot_bot @ nat_int ) )
% 2.81/1.53 | ( nat_consec @ J2 @ K2 ) ) ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(fact_255_consec__un__not__elem2,axiom,
% 2.81/1.53 ! [I: nat_int,J: nat_int,N: nat] :
% 2.81/1.53 ( ( ( nat_consec @ I @ J )
% 2.81/1.53 & ( nat_not_in @ N @ ( nat_union @ I @ J ) ) )
% 2.81/1.53 => ( nat_not_in @ N @ J ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_fun___Orderings_Oorder__bot,axiom,
% 2.81/1.53 ! [A6: $tType,A7: $tType] :
% 2.81/1.53 ( ( order_bot @ A7 )
% 2.81/1.53 => ( order_bot @ ( A6 > A7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.81/1.53 ! [A6: $tType,A7: $tType] :
% 2.81/1.53 ( ( preorder @ A7 )
% 2.81/1.53 => ( preorder @ ( A6 > A7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.81/1.53 ! [A6: $tType,A7: $tType] :
% 2.81/1.53 ( ( order @ A7 )
% 2.81/1.53 => ( order @ ( A6 > A7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_fun___Orderings_Oord,axiom,
% 2.81/1.53 ! [A6: $tType,A7: $tType] :
% 2.81/1.53 ( ( ord @ A7 )
% 2.81/1.53 => ( ord @ ( A6 > A7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_fun___Orderings_Obot,axiom,
% 2.81/1.53 ! [A6: $tType,A7: $tType] :
% 2.81/1.53 ( ( bot @ A7 )
% 2.81/1.53 => ( bot @ ( A6 > A7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_fun___Groups_Ominus,axiom,
% 2.81/1.53 ! [A6: $tType,A7: $tType] :
% 2.81/1.53 ( ( minus @ A7 )
% 2.81/1.53 => ( minus @ ( A6 > A7 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 2.81/1.53 cancel146912293up_add @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.81/1.53 wellorder @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Oorder__bot_1,axiom,
% 2.81/1.53 order_bot @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
% 2.81/1.53 preorder @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.81/1.53 linorder @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 2.81/1.53 no_top @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Oorder_3,axiom,
% 2.81/1.53 order @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Oord_4,axiom,
% 2.81/1.53 ord @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Orderings_Obot_5,axiom,
% 2.81/1.53 bot @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Nat_Onat___Groups_Ominus_6,axiom,
% 2.81/1.53 minus @ nat ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_HOL_Obool___Orderings_Oorder__bot_7,axiom,
% 2.81/1.53 order_bot @ $o ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_HOL_Obool___Orderings_Opreorder_8,axiom,
% 2.81/1.53 preorder @ $o ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder_9,axiom,
% 2.81/1.53 linorder @ $o ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_HOL_Obool___Orderings_Oorder_10,axiom,
% 2.81/1.53 order @ $o ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_HOL_Obool___Orderings_Oord_11,axiom,
% 2.81/1.53 ord @ $o ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_HOL_Obool___Orderings_Obot_12,axiom,
% 2.81/1.53 bot @ $o ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_HOL_Obool___Groups_Ominus_13,axiom,
% 2.81/1.53 minus @ $o ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_14,axiom,
% 2.81/1.53 cancel146912293up_add @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Groups_Oordered__ab__group__add,axiom,
% 2.81/1.53 ordered_ab_group_add @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Orderings_Odense__linorder,axiom,
% 2.81/1.53 dense_linorder @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Orderings_Odense__order,axiom,
% 2.81/1.53 dense_order @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Orderings_Opreorder_15,axiom,
% 2.81/1.53 preorder @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Orderings_Olinorder_16,axiom,
% 2.81/1.53 linorder @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Orderings_Ono__top_17,axiom,
% 2.81/1.53 no_top @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Orderings_Ono__bot,axiom,
% 2.81/1.53 no_bot @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Groups_Ogroup__add,axiom,
% 2.81/1.53 group_add @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Orderings_Oorder_18,axiom,
% 2.81/1.53 order @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Orderings_Oord_19,axiom,
% 2.81/1.53 ord @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Real_Oreal___Groups_Ominus_20,axiom,
% 2.81/1.53 minus @ real ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_NatInt_Onat__int___Orderings_Oorder__bot_21,axiom,
% 2.81/1.53 order_bot @ nat_int ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_NatInt_Onat__int___Orderings_Opreorder_22,axiom,
% 2.81/1.53 preorder @ nat_int ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_NatInt_Onat__int___Orderings_Oorder_23,axiom,
% 2.81/1.53 order @ nat_int ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_NatInt_Onat__int___Orderings_Oord_24,axiom,
% 2.81/1.53 ord @ nat_int ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_NatInt_Onat__int___Orderings_Obot_25,axiom,
% 2.81/1.53 bot @ nat_int ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_RealInt_Oreal__int___Orderings_Opreorder_26,axiom,
% 2.81/1.53 preorder @ real_int ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_RealInt_Oreal__int___Orderings_Oorder_27,axiom,
% 2.81/1.53 order @ real_int ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_RealInt_Oreal__int___Orderings_Oord_28,axiom,
% 2.81/1.53 ord @ real_int ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_29,axiom,
% 2.81/1.53 wellorder @ product_unit ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Product__Type_Ounit___Orderings_Oorder__bot_30,axiom,
% 2.81/1.53 order_bot @ product_unit ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_31,axiom,
% 2.81/1.53 preorder @ product_unit ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_32,axiom,
% 2.81/1.53 linorder @ product_unit ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Product__Type_Ounit___Orderings_Oorder_33,axiom,
% 2.81/1.53 order @ product_unit ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Product__Type_Ounit___Orderings_Oord_34,axiom,
% 2.81/1.53 ord @ product_unit ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Product__Type_Ounit___Orderings_Obot_35,axiom,
% 2.81/1.53 bot @ product_unit ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Product__Type_Ounit___Groups_Ominus_36,axiom,
% 2.81/1.53 minus @ product_unit ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Views_Oview_Oview__ext___Orderings_Opreorder_37,axiom,
% 2.81/1.53 ! [A6: $tType] :
% 2.81/1.53 ( ( order @ A6 )
% 2.81/1.53 => ( preorder @ ( view_ext @ A6 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Views_Oview_Oview__ext___Orderings_Oorder_38,axiom,
% 2.81/1.53 ! [A6: $tType] :
% 2.81/1.53 ( ( order @ A6 )
% 2.81/1.53 => ( order @ ( view_ext @ A6 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(tcon_Views_Oview_Oview__ext___Orderings_Oord_39,axiom,
% 2.81/1.53 ! [A6: $tType] :
% 2.81/1.53 ( ( order @ A6 )
% 2.81/1.53 => ( ord @ ( view_ext @ A6 ) ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(help_If_3_1_T,axiom,
% 2.81/1.53 ! [P: $o] :
% 2.81/1.53 ( ( P = $true )
% 2.81/1.53 | ( P = $false ) ) ).
% 2.81/1.53
% 2.81/1.53 thf(help_If_2_1_T,axiom,
% 2.81/1.53 ! [A: $tType,X3: A,Y2: A] :
% 2.81/1.53 ( ( if @ A @ $false @ X3 @ Y2 )
% 2.81/1.53 = Y2 ) ).
% 2.81/1.53
% 2.81/1.53 thf(help_If_1_1_T,axiom,
% 2.81/1.53 ! [A: $tType,X3: A,Y2: A] :
% 2.81/1.53 ( ( if @ A @ $true @ X3 @ Y2 )
% 2.81/1.53 = X3 ) ).
% 2.81/1.53
% 2.81/1.53 thf(conj_0,conjecture,
% 2.81/1.53 ( ( move @ ts3 @ ts_a @ v )
% 2.81/1.53 = ( move @ ts3 @ ts @ v ) ) ).
% 2.81/1.53 ------------------------
% 2.81/1.55 % (13869)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/183Mi)
% 2.81/1.55 % (13872)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/2Mi)
% 2.81/1.55 % (13870)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_13762 for (2999ds/4Mi)
% 2.81/1.55 % (13871)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_13762 for (2999ds/27Mi)
% 2.81/1.55 % (13873)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_13762 for (2999ds/2Mi)
% 2.81/1.55 % (13874)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_13762 for (2999ds/275Mi)
% 2.81/1.55 % (13875)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/18Mi)
% 2.81/1.55 % (13872)Instruction limit reached!
% 2.81/1.55 % (13872)------------------------------
% 2.81/1.55 % (13872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.55 % (13872)Termination reason: Unknown
% 2.81/1.55 % (13873)Instruction limit reached!
% 2.81/1.55 % (13873)------------------------------
% 2.81/1.55 % (13873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.55 % (13872)Termination phase: shuffling
% 2.81/1.55
% 2.81/1.55 % (13872)Memory used [KB]: 1407
% 2.81/1.55 % (13872)Time elapsed: 0.003 s
% 2.81/1.56 % (13872)Instructions burned: 3 (million)
% 2.81/1.56 % (13872)------------------------------
% 2.81/1.56 % (13872)------------------------------
% 2.81/1.56 % (13873)Termination reason: Unknown
% 2.81/1.56 % (13873)Termination phase: shuffling
% 2.81/1.56
% 2.81/1.56 % (13873)Memory used [KB]: 1407
% 2.81/1.56 % (13873)Time elapsed: 0.003 s
% 2.81/1.56 % (13873)Instructions burned: 3 (million)
% 2.81/1.56 % (13873)------------------------------
% 2.81/1.56 % (13873)------------------------------
% 2.81/1.56 % (13870)Instruction limit reached!
% 2.81/1.56 % (13870)------------------------------
% 2.81/1.56 % (13870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.56 % (13870)Termination reason: Unknown
% 2.81/1.56 % (13870)Termination phase: shuffling
% 2.81/1.56
% 2.81/1.56 % (13870)Memory used [KB]: 1535
% 2.81/1.56 % (13870)Time elapsed: 0.004 s
% 2.81/1.56 % (13870)Instructions burned: 5 (million)
% 2.81/1.56 % (13870)------------------------------
% 2.81/1.56 % (13870)------------------------------
% 2.81/1.56 % (13875)Instruction limit reached!
% 2.81/1.56 % (13875)------------------------------
% 2.81/1.56 % (13875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.56 % (13875)Termination reason: Unknown
% 2.81/1.56 % (13875)Termination phase: shuffling
% 2.81/1.56
% 2.81/1.56 % (13875)Memory used [KB]: 1918
% 2.81/1.56 % (13875)Time elapsed: 0.011 s
% 2.81/1.56 % (13875)Instructions burned: 18 (million)
% 2.81/1.56 % (13875)------------------------------
% 2.81/1.56 % (13875)------------------------------
% 2.81/1.57 % (13871)Instruction limit reached!
% 2.81/1.57 % (13871)------------------------------
% 2.81/1.57 % (13871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.57 % (13871)Termination reason: Unknown
% 2.81/1.57 % (13871)Termination phase: Property scanning
% 2.81/1.57
% 2.81/1.57 % (13871)Memory used [KB]: 2046
% 2.81/1.57 % (13871)Time elapsed: 0.015 s
% 2.81/1.57 % (13871)Instructions burned: 27 (million)
% 2.81/1.57 % (13871)------------------------------
% 2.81/1.57 % (13871)------------------------------
% 2.81/1.57 % (13876)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/3Mi)
% 2.81/1.57 % (13877)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_13762 for (2999ds/37Mi)
% 2.81/1.57 % (13878)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_13762 for (2999ds/15Mi)
% 2.81/1.57 % (13876)Instruction limit reached!
% 2.81/1.57 % (13876)------------------------------
% 2.81/1.57 % (13876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.57 % (13876)Termination reason: Unknown
% 2.81/1.57 % (13876)Termination phase: shuffling
% 2.81/1.57
% 2.81/1.57 % (13876)Memory used [KB]: 1407
% 2.81/1.57 % (13876)Time elapsed: 0.003 s
% 2.81/1.57 % (13876)Instructions burned: 4 (million)
% 2.81/1.57 % (13876)------------------------------
% 2.81/1.57 % (13876)------------------------------
% 2.81/1.58 % (13874)Refutation not found, incomplete strategy
% 2.81/1.58 % (13874)------------------------------
% 2.81/1.58 % (13874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.58 % (13874)Termination reason: Refutation not found, incomplete strategy
% 2.81/1.58
% 2.81/1.58
% 2.81/1.58 % (13874)Memory used [KB]: 6652
% 2.81/1.58 % (13874)Time elapsed: 0.026 s
% 2.81/1.58 % (13874)Instructions burned: 50 (million)
% 2.81/1.58 % (13874)------------------------------
% 2.81/1.58 % (13874)------------------------------
% 2.81/1.58 % (13879)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_13762 for (2999ds/3Mi)
% 2.81/1.58 % (13878)Instruction limit reached!
% 2.81/1.58 % (13878)------------------------------
% 2.81/1.58 % (13878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.58 % (13878)Termination reason: Unknown
% 2.81/1.58 % (13878)Termination phase: shuffling
% 2.81/1.58
% 2.81/1.58 % (13878)Memory used [KB]: 1791
% 2.81/1.58 % (13878)Time elapsed: 0.009 s
% 2.81/1.58 % (13878)Instructions burned: 15 (million)
% 2.81/1.58 % (13878)------------------------------
% 2.81/1.58 % (13878)------------------------------
% 2.81/1.58 % (13879)Instruction limit reached!
% 2.81/1.58 % (13879)------------------------------
% 2.81/1.58 % (13879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.58 % (13879)Termination reason: Unknown
% 2.81/1.58 % (13879)Termination phase: shuffling
% 2.81/1.58
% 2.81/1.58 % (13879)Memory used [KB]: 1407
% 2.81/1.58 % (13879)Time elapsed: 0.003 s
% 2.81/1.58 % (13879)Instructions burned: 3 (million)
% 2.81/1.58 % (13879)------------------------------
% 2.81/1.58 % (13879)------------------------------
% 2.81/1.58 % (13880)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_13762 for (2999ds/1041Mi)
% 2.81/1.59 % (13881)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/7Mi)
% 2.81/1.59 % (13877)Instruction limit reached!
% 2.81/1.59 % (13877)------------------------------
% 2.81/1.59 % (13877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.59 % (13877)Termination reason: Unknown
% 2.81/1.59 % (13877)Termination phase: shuffling
% 2.81/1.59
% 2.81/1.59 % (13877)Memory used [KB]: 2174
% 2.81/1.59 % (13877)Time elapsed: 0.019 s
% 2.81/1.59 % (13877)Instructions burned: 38 (million)
% 2.81/1.59 % (13877)------------------------------
% 2.81/1.59 % (13877)------------------------------
% 2.81/1.59 % (13881)Instruction limit reached!
% 2.81/1.59 % (13881)------------------------------
% 2.81/1.59 % (13881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.81/1.59 % (13881)Termination reason: Unknown
% 2.81/1.59 % (13881)Termination phase: shuffling
% 2.81/1.59
% 2.81/1.59 % (13881)Memory used [KB]: 1535
% 2.81/1.59 % (13881)Time elapsed: 0.006 s
% 2.81/1.59 % (13881)Instructions burned: 8 (million)
% 2.81/1.59 % (13881)------------------------------
% 2.81/1.59 % (13881)------------------------------
% 2.81/1.59 % (13882)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/16Mi)
% 2.86/1.60 % (13884)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_13762 for (2999ds/3Mi)
% 2.86/1.60 % (13883)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_13762 for (2999ds/3Mi)
% 2.86/1.60 % (13869)Instruction limit reached!
% 2.86/1.60 % (13869)------------------------------
% 2.86/1.60 % (13869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.60 % (13869)Termination reason: Unknown
% 2.86/1.60 % (13884)Instruction limit reached!
% 2.86/1.60 % (13884)------------------------------
% 2.86/1.60 % (13884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.60 % (13869)Termination phase: Saturation
% 2.86/1.60
% 2.86/1.60 % (13884)Termination reason: Unknown
% 2.86/1.60 % (13869)Memory used [KB]: 7291
% 2.86/1.60 % (13869)Time elapsed: 0.052 s
% 2.86/1.60 % (13884)Termination phase: shuffling
% 2.86/1.60 % (13869)Instructions burned: 186 (million)
% 2.86/1.60
% 2.86/1.60 % (13869)------------------------------
% 2.86/1.60 % (13869)------------------------------
% 2.86/1.60 % (13884)Memory used [KB]: 1407
% 2.86/1.60 % (13884)Time elapsed: 0.003 s
% 2.86/1.60 % (13884)Instructions burned: 4 (million)
% 2.86/1.60 % (13884)------------------------------
% 2.86/1.60 % (13884)------------------------------
% 2.86/1.60 % (13883)Instruction limit reached!
% 2.86/1.60 % (13883)------------------------------
% 2.86/1.60 % (13883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.60 % (13883)Termination reason: Unknown
% 2.86/1.60 % (13883)Termination phase: shuffling
% 2.86/1.60
% 2.86/1.60 % (13883)Memory used [KB]: 1535
% 2.86/1.60 % (13883)Time elapsed: 0.004 s
% 2.86/1.60 % (13883)Instructions burned: 5 (million)
% 2.86/1.60 % (13883)------------------------------
% 2.86/1.60 % (13883)------------------------------
% 2.86/1.60 % (13882)Instruction limit reached!
% 2.86/1.60 % (13882)------------------------------
% 2.86/1.60 % (13882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.60 % (13882)Termination reason: Unknown
% 2.86/1.60 % (13882)Termination phase: shuffling
% 2.86/1.60
% 2.86/1.60 % (13882)Memory used [KB]: 1791
% 2.86/1.60 % (13882)Time elapsed: 0.009 s
% 2.86/1.60 % (13882)Instructions burned: 16 (million)
% 2.86/1.60 % (13882)------------------------------
% 2.86/1.60 % (13882)------------------------------
% 2.86/1.60 % (13885)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/7Mi)
% 2.86/1.61 % (13887)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/4Mi)
% 2.86/1.61 % (13885)Instruction limit reached!
% 2.86/1.61 % (13885)------------------------------
% 2.86/1.61 % (13885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.61 % (13885)Termination reason: Unknown
% 2.86/1.61 % (13885)Termination phase: shuffling
% 2.86/1.61
% 2.86/1.61 % (13885)Memory used [KB]: 1535
% 2.86/1.61 % (13885)Time elapsed: 0.005 s
% 2.86/1.61 % (13885)Instructions burned: 7 (million)
% 2.86/1.61 % (13885)------------------------------
% 2.86/1.61 % (13885)------------------------------
% 2.86/1.61 % (13886)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/3Mi)
% 2.86/1.61 % (13887)Instruction limit reached!
% 2.86/1.61 % (13887)------------------------------
% 2.86/1.61 % (13887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.61 % (13887)Termination reason: Unknown
% 2.86/1.61 % (13887)Termination phase: shuffling
% 2.86/1.61
% 2.86/1.61 % (13887)Memory used [KB]: 1535
% 2.86/1.61 % (13887)Time elapsed: 0.003 s
% 2.86/1.61 % (13887)Instructions burned: 6 (million)
% 2.86/1.61 % (13887)------------------------------
% 2.86/1.61 % (13887)------------------------------
% 2.86/1.61 % (13886)Instruction limit reached!
% 2.86/1.61 % (13886)------------------------------
% 2.86/1.61 % (13886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.61 % (13886)Termination reason: Unknown
% 2.86/1.61 % (13886)Termination phase: shuffling
% 2.86/1.61
% 2.86/1.61 % (13886)Memory used [KB]: 1407
% 2.86/1.61 % (13886)Time elapsed: 0.003 s
% 2.86/1.61 % (13886)Instructions burned: 4 (million)
% 2.86/1.61 % (13886)------------------------------
% 2.86/1.61 % (13886)------------------------------
% 2.86/1.61 % (13888)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/18Mi)
% 2.86/1.62 % (13889)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/710Mi)
% 2.86/1.62 % (13890)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/6Mi)
% 2.86/1.62 % (13892)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_13762 for (2999ds/21Mi)
% 2.86/1.62 % (13890)Instruction limit reached!
% 2.86/1.62 % (13890)------------------------------
% 2.86/1.62 % (13890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.62 % (13890)Termination reason: Unknown
% 2.86/1.62 % (13890)Termination phase: shuffling
% 2.86/1.62
% 2.86/1.62 % (13890)Memory used [KB]: 1535
% 2.86/1.62 % (13890)Time elapsed: 0.004 s
% 2.86/1.62 % (13890)Instructions burned: 6 (million)
% 2.86/1.62 % (13890)------------------------------
% 2.86/1.62 % (13890)------------------------------
% 2.86/1.62 % (13888)Instruction limit reached!
% 2.86/1.62 % (13888)------------------------------
% 2.86/1.62 % (13888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.62 % (13888)Termination reason: Unknown
% 2.86/1.62 % (13888)Termination phase: shuffling
% 2.86/1.62
% 2.86/1.62 % (13888)Memory used [KB]: 1918
% 2.86/1.62 % (13888)Time elapsed: 0.010 s
% 2.86/1.62 % (13888)Instructions burned: 18 (million)
% 2.86/1.62 % (13888)------------------------------
% 2.86/1.62 % (13888)------------------------------
% 2.86/1.62 % (13891)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_13762 for (2999ds/902Mi)
% 2.86/1.63 % (13892)Instruction limit reached!
% 2.86/1.63 % (13892)------------------------------
% 2.86/1.63 % (13892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.63 % (13892)Termination reason: Unknown
% 2.86/1.63 % (13892)Termination phase: shuffling
% 2.86/1.63
% 2.86/1.63 % (13892)Memory used [KB]: 1918
% 2.86/1.63 % (13892)Time elapsed: 0.008 s
% 2.86/1.63 % (13892)Instructions burned: 22 (million)
% 2.86/1.63 % (13892)------------------------------
% 2.86/1.63 % (13892)------------------------------
% 2.86/1.63 % (13893)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/5Mi)
% 2.86/1.63 % (13893)Instruction limit reached!
% 2.86/1.63 % (13893)------------------------------
% 2.86/1.63 % (13893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.63 % (13893)Termination reason: Unknown
% 2.86/1.63 % (13893)Termination phase: shuffling
% 2.86/1.63
% 2.86/1.63 % (13893)Memory used [KB]: 1535
% 2.86/1.63 % (13893)Time elapsed: 0.004 s
% 2.86/1.63 % (13893)Instructions burned: 6 (million)
% 2.86/1.63 % (13893)------------------------------
% 2.86/1.63 % (13893)------------------------------
% 2.86/1.64 % (13896)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_13762 for (2999ds/779Mi)
% 2.86/1.64 % (13894)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_13762 for (2999ds/6Mi)
% 2.86/1.64 % (13895)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13762 for (2999ds/377Mi)
% 2.86/1.64 % (13894)Instruction limit reached!
% 2.86/1.64 % (13894)------------------------------
% 2.86/1.64 % (13894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.64 % (13894)Termination reason: Unknown
% 2.86/1.64 % (13894)Termination phase: shuffling
% 2.86/1.64
% 2.86/1.64 % (13894)Memory used [KB]: 1535
% 2.86/1.64 % (13894)Time elapsed: 0.004 s
% 2.86/1.64 % (13894)Instructions burned: 6 (million)
% 2.86/1.64 % (13894)------------------------------
% 2.86/1.64 % (13894)------------------------------
% 2.86/1.66 % (13898)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13762 for (2998ds/879Mi)
% 2.86/1.66 % (13897)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_13762 for (2999ds/19Mi)
% 2.86/1.67 % (13897)Instruction limit reached!
% 2.86/1.67 % (13897)------------------------------
% 2.86/1.67 % (13897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.67 % (13897)Termination reason: Unknown
% 2.86/1.67 % (13897)Termination phase: shuffling
% 2.86/1.67
% 2.86/1.67 % (13897)Memory used [KB]: 1791
% 2.86/1.67 % (13897)Time elapsed: 0.010 s
% 2.86/1.67 % (13897)Instructions burned: 19 (million)
% 2.86/1.67 % (13897)------------------------------
% 2.86/1.67 % (13897)------------------------------
% 2.86/1.69 % (13899)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13762 for (2998ds/17Mi)
% 2.86/1.69 % (13899)Instruction limit reached!
% 2.86/1.69 % (13899)------------------------------
% 2.86/1.69 % (13899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.69 % (13899)Termination reason: Unknown
% 2.86/1.69 % (13899)Termination phase: shuffling
% 2.86/1.69
% 2.86/1.69 % (13899)Memory used [KB]: 1791
% 2.86/1.69 % (13899)Time elapsed: 0.010 s
% 2.86/1.69 % (13899)Instructions burned: 17 (million)
% 2.86/1.69 % (13899)------------------------------
% 2.86/1.69 % (13899)------------------------------
% 2.86/1.70 % (13891)Refutation not found, incomplete strategy
% 2.86/1.70 % (13891)------------------------------
% 2.86/1.70 % (13891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.70 % (13891)Termination reason: Refutation not found, incomplete strategy
% 2.86/1.70
% 2.86/1.70
% 2.86/1.70 % (13891)Memory used [KB]: 7803
% 2.86/1.70 % (13891)Time elapsed: 0.077 s
% 2.86/1.70 % (13891)Instructions burned: 158 (million)
% 2.86/1.70 % (13891)------------------------------
% 2.86/1.70 % (13891)------------------------------
% 2.86/1.71 % (13900)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13762 for (2998ds/3Mi)
% 2.86/1.71 % (13900)Instruction limit reached!
% 2.86/1.71 % (13900)------------------------------
% 2.86/1.71 % (13900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.71 % (13900)Termination reason: Unknown
% 2.86/1.71 % (13900)Termination phase: shuffling
% 2.86/1.71
% 2.86/1.71 % (13900)Memory used [KB]: 1407
% 2.86/1.71 % (13900)Time elapsed: 0.003 s
% 2.86/1.71 % (13900)Instructions burned: 3 (million)
% 2.86/1.71 % (13900)------------------------------
% 2.86/1.71 % (13900)------------------------------
% 2.86/1.72 % (13901)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13762 for (2998ds/30Mi)
% 2.86/1.73 % (13902)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13762 for (2998ds/127Mi)
% 2.86/1.73 % (13901)Instruction limit reached!
% 2.86/1.73 % (13901)------------------------------
% 2.86/1.73 % (13901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.73 % (13901)Termination reason: Unknown
% 2.86/1.73 % (13901)Termination phase: Property scanning
% 2.86/1.73
% 2.86/1.73 % (13901)Memory used [KB]: 2046
% 2.86/1.73 % (13901)Time elapsed: 0.016 s
% 2.86/1.73 % (13901)Instructions burned: 30 (million)
% 2.86/1.73 % (13901)------------------------------
% 2.86/1.73 % (13901)------------------------------
% 2.86/1.75 % (13903)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13762 for (2998ds/100Mi)
% 2.86/1.79 % (13902)Instruction limit reached!
% 2.86/1.79 % (13902)------------------------------
% 2.86/1.79 % (13902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.79 % (13902)Termination reason: Unknown
% 2.86/1.79 % (13902)Termination phase: Property scanning
% 2.86/1.79
% 2.86/1.79 % (13902)Memory used [KB]: 2686
% 2.86/1.79 % (13902)Time elapsed: 0.060 s
% 2.86/1.79 % (13902)Instructions burned: 128 (million)
% 2.86/1.79 % (13902)------------------------------
% 2.86/1.79 % (13902)------------------------------
% 2.86/1.79 % (13903)Instruction limit reached!
% 2.86/1.79 % (13903)------------------------------
% 2.86/1.79 % (13903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.79 % (13903)Termination reason: Unknown
% 2.86/1.79 % (13903)Termination phase: Property scanning
% 2.86/1.79
% 2.86/1.79 % (13903)Memory used [KB]: 2430
% 2.86/1.79 % (13903)Time elapsed: 0.047 s
% 2.86/1.79 % (13903)Instructions burned: 100 (million)
% 2.86/1.79 % (13903)------------------------------
% 2.86/1.79 % (13903)------------------------------
% 2.86/1.80 % (13904)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_13762 for (2997ds/3Mi)
% 2.86/1.80 % (13904)Instruction limit reached!
% 2.86/1.80 % (13904)------------------------------
% 2.86/1.80 % (13904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.80 % (13904)Termination reason: Unknown
% 2.86/1.80 % (13904)Termination phase: shuffling
% 2.86/1.80
% 2.86/1.80 % (13904)Memory used [KB]: 1535
% 2.86/1.80 % (13904)Time elapsed: 0.003 s
% 2.86/1.80 % (13904)Instructions burned: 5 (million)
% 2.86/1.80 % (13904)------------------------------
% 2.86/1.80 % (13904)------------------------------
% 2.86/1.81 % (13905)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_13762 for (2997ds/20Mi)
% 2.86/1.81 % (13895)Instruction limit reached!
% 2.86/1.81 % (13895)------------------------------
% 2.86/1.81 % (13895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.81 % (13895)Termination reason: Unknown
% 2.86/1.81 % (13895)Termination phase: Saturation
% 2.86/1.81
% 2.86/1.81 % (13895)Memory used [KB]: 7675
% 2.86/1.81 % (13895)Time elapsed: 0.172 s
% 2.86/1.81 % (13895)Instructions burned: 378 (million)
% 2.86/1.81 % (13895)------------------------------
% 2.86/1.81 % (13895)------------------------------
% 2.86/1.81 % (13906)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_13762 for (2997ds/86Mi)
% 2.86/1.81 % (13905)Instruction limit reached!
% 2.86/1.81 % (13905)------------------------------
% 2.86/1.81 % (13905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.81 % (13905)Termination reason: Unknown
% 2.86/1.81 % (13905)Termination phase: shuffling
% 2.86/1.81
% 2.86/1.81 % (13905)Memory used [KB]: 1918
% 2.86/1.81 % (13905)Time elapsed: 0.008 s
% 2.86/1.81 % (13905)Instructions burned: 21 (million)
% 2.86/1.81 % (13905)------------------------------
% 2.86/1.81 % (13905)------------------------------
% 2.86/1.82 % (13908)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_13762 for (2997ds/39Mi)
% 2.86/1.83 % (13907)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_13762 for (2997ds/107Mi)
% 2.86/1.83 % (13908)Instruction limit reached!
% 2.86/1.83 % (13908)------------------------------
% 2.86/1.83 % (13908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.83 % (13908)Termination reason: Unknown
% 2.86/1.83 % (13908)Termination phase: shuffling
% 2.86/1.83
% 2.86/1.83 % (13908)Memory used [KB]: 2174
% 2.86/1.83 % (13908)Time elapsed: 0.012 s
% 2.86/1.83 % (13908)Instructions burned: 39 (million)
% 2.86/1.83 % (13908)------------------------------
% 2.86/1.83 % (13908)------------------------------
% 2.86/1.84 % (13909)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_13762 for (2997ds/448Mi)
% 2.86/1.85 % (13906)Instruction limit reached!
% 2.86/1.85 % (13906)------------------------------
% 2.86/1.85 % (13906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.85 % (13906)Termination reason: Unknown
% 2.86/1.85 % (13906)Termination phase: Function definition elimination
% 2.86/1.85
% 2.86/1.85 % (13906)Memory used [KB]: 2686
% 2.86/1.85 % (13906)Time elapsed: 0.042 s
% 2.86/1.85 % (13906)Instructions burned: 88 (million)
% 2.86/1.85 % (13906)------------------------------
% 2.86/1.85 % (13906)------------------------------
% 2.86/1.88 % (13907)Instruction limit reached!
% 2.86/1.88 % (13907)------------------------------
% 2.86/1.88 % (13907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.88 % (13907)Termination reason: Unknown
% 2.86/1.88 % (13907)Termination phase: Property scanning
% 2.86/1.88
% 2.86/1.88 % (13907)Memory used [KB]: 2558
% 2.86/1.88 % (13907)Time elapsed: 0.051 s
% 2.86/1.88 % (13907)Instructions burned: 109 (million)
% 2.86/1.88 % (13907)------------------------------
% 2.86/1.88 % (13907)------------------------------
% 2.86/1.88 % (13911)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_13762 for (2996ds/46Mi)
% 2.86/1.89 % (13912)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_13762 for (2996ds/98Mi)
% 2.86/1.91 % (13911)Instruction limit reached!
% 2.86/1.91 % (13911)------------------------------
% 2.86/1.91 % (13911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.91 % (13911)Termination reason: Unknown
% 2.86/1.91 % (13911)Termination phase: SInE selection
% 2.86/1.91
% 2.86/1.91 % (13911)Memory used [KB]: 2046
% 2.86/1.91 % (13911)Time elapsed: 0.017 s
% 2.86/1.91 % (13911)Instructions burned: 49 (million)
% 2.86/1.91 % (13911)------------------------------
% 2.86/1.91 % (13911)------------------------------
% 2.86/1.92 % (13913)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_13762 for (2996ds/507Mi)
% 2.86/1.92 % (13896)Instruction limit reached!
% 2.86/1.92 % (13896)------------------------------
% 2.86/1.92 % (13896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.92 % (13896)Termination reason: Unknown
% 2.86/1.92 % (13896)Termination phase: Saturation
% 2.86/1.92
% 2.86/1.92 % (13896)Memory used [KB]: 8187
% 2.86/1.92 % (13896)Time elapsed: 0.289 s
% 2.86/1.92 % (13896)Instructions burned: 779 (million)
% 2.86/1.92 % (13896)------------------------------
% 2.86/1.92 % (13896)------------------------------
% 2.86/1.94 % (13912)Instruction limit reached!
% 2.86/1.94 % (13912)------------------------------
% 2.86/1.94 % (13912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.94 % (13912)Termination reason: Unknown
% 2.86/1.94 % (13912)Termination phase: Property scanning
% 2.86/1.94
% 2.86/1.94 % (13912)Memory used [KB]: 2430
% 2.86/1.94 % (13912)Time elapsed: 0.046 s
% 2.86/1.94 % (13912)Instructions burned: 99 (million)
% 2.86/1.94 % (13912)------------------------------
% 2.86/1.94 % (13912)------------------------------
% 2.86/1.94 % (13914)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_13762 for (2996ds/149Mi)
% 2.86/1.95 % (13915)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13762 for (2995ds/39Mi)
% 2.86/1.96 % (13889)Instruction limit reached!
% 2.86/1.96 % (13889)------------------------------
% 2.86/1.96 % (13889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.96 % (13889)Termination reason: Unknown
% 2.86/1.96 % (13889)Termination phase: Saturation
% 2.86/1.96
% 2.86/1.96 % (13889)Memory used [KB]: 8059
% 2.86/1.96 % (13889)Time elapsed: 0.346 s
% 2.86/1.96 % (13889)Instructions burned: 710 (million)
% 2.86/1.96 % (13889)------------------------------
% 2.86/1.96 % (13889)------------------------------
% 2.86/1.97 % (13915)Instruction limit reached!
% 2.86/1.97 % (13915)------------------------------
% 2.86/1.97 % (13915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.97 % (13915)Termination reason: Unknown
% 2.86/1.97 % (13915)Termination phase: Property scanning
% 2.86/1.97
% 2.86/1.97 % (13915)Memory used [KB]: 2046
% 2.86/1.97 % (13915)Time elapsed: 0.020 s
% 2.86/1.97 % (13915)Instructions burned: 39 (million)
% 2.86/1.97 % (13915)------------------------------
% 2.86/1.97 % (13915)------------------------------
% 2.86/1.99 % (13917)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_13762 for (2995ds/1087Mi)
% 2.86/1.99 % (13916)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_13762 for (2995ds/6Mi)
% 2.86/1.99 % (13909)Instruction limit reached!
% 2.86/1.99 % (13909)------------------------------
% 2.86/1.99 % (13909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.99 % (13909)Termination reason: Unknown
% 2.86/1.99 % (13909)Termination phase: Saturation
% 2.86/1.99
% 2.86/1.99 % (13909)Memory used [KB]: 7675
% 2.86/1.99 % (13909)Time elapsed: 0.126 s
% 2.86/1.99 % (13909)Instructions burned: 448 (million)
% 2.86/1.99 % (13909)------------------------------
% 2.86/1.99 % (13909)------------------------------
% 2.86/1.99 % (13916)Instruction limit reached!
% 2.86/1.99 % (13916)------------------------------
% 2.86/1.99 % (13916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.99 % (13916)Termination reason: Unknown
% 2.86/1.99 % (13916)Termination phase: shuffling
% 2.86/1.99
% 2.86/1.99 % (13916)Memory used [KB]: 1535
% 2.86/1.99 % (13916)Time elapsed: 0.005 s
% 2.86/1.99 % (13916)Instructions burned: 7 (million)
% 2.86/1.99 % (13916)------------------------------
% 2.86/1.99 % (13916)------------------------------
% 2.86/2.01 % (13919)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_13762 for (2995ds/44Mi)
% 2.86/2.01 % (13914)Instruction limit reached!
% 2.86/2.01 % (13914)------------------------------
% 2.86/2.01 % (13914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/2.01 % (13914)Termination reason: Unknown
% 2.86/2.01 % (13914)Termination phase: Property scanning
% 2.86/2.01
% 2.86/2.01 % (13914)Memory used [KB]: 2686
% 2.86/2.01 % (13914)Time elapsed: 0.069 s
% 2.86/2.01 % (13914)Instructions burned: 150 (million)
% 2.86/2.01 % (13914)------------------------------
% 2.86/2.01 % (13914)------------------------------
% 6.01/2.02 % (13918)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_13762 for (2995ds/47Mi)
% 6.01/2.03 % (13920)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_13762 for (2995ds/432Mi)
% 6.01/2.03 % (13919)Instruction limit reached!
% 6.01/2.03 % (13919)------------------------------
% 6.01/2.03 % (13919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.03 % (13919)Termination reason: Unknown
% 6.01/2.03 % (13919)Termination phase: shuffling
% 6.01/2.03
% 6.01/2.03 % (13919)Memory used [KB]: 2302
% 6.01/2.03 % (13919)Time elapsed: 0.022 s
% 6.01/2.03 % (13919)Instructions burned: 44 (million)
% 6.01/2.03 % (13919)------------------------------
% 6.01/2.03 % (13919)------------------------------
% 6.01/2.03 % (13918)Instruction limit reached!
% 6.01/2.03 % (13918)------------------------------
% 6.01/2.03 % (13918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.03 % (13918)Termination reason: Unknown
% 6.01/2.03 % (13918)Termination phase: Preprocessing 3
% 6.01/2.03
% 6.01/2.03 % (13918)Memory used [KB]: 2174
% 6.01/2.03 % (13918)Time elapsed: 0.016 s
% 6.01/2.03 % (13918)Instructions burned: 48 (million)
% 6.01/2.03 % (13918)------------------------------
% 6.01/2.03 % (13918)------------------------------
% 6.01/2.04 % (13923)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_13762 for (2994ds/31Mi)
% 6.01/2.04 % (13922)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_13762 for (2994ds/62Mi)
% 6.01/2.05 % (13923)Instruction limit reached!
% 6.01/2.05 % (13923)------------------------------
% 6.01/2.05 % (13923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.05 % (13923)Termination reason: Unknown
% 6.01/2.05 % (13923)Termination phase: Property scanning
% 6.01/2.05
% 6.01/2.05 % (13923)Memory used [KB]: 2046
% 6.01/2.05 % (13923)Time elapsed: 0.011 s
% 6.01/2.05 % (13923)Instructions burned: 33 (million)
% 6.01/2.05 % (13923)------------------------------
% 6.01/2.05 % (13923)------------------------------
% 6.01/2.06 % (13898)Instruction limit reached!
% 6.01/2.06 % (13898)------------------------------
% 6.01/2.06 % (13898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.06 % (13898)Termination reason: Unknown
% 6.01/2.06 % (13898)Termination phase: Saturation
% 6.01/2.06
% 6.01/2.06 % (13898)Memory used [KB]: 8827
% 6.01/2.06 % (13898)Time elapsed: 0.403 s
% 6.01/2.06 % (13898)Instructions burned: 880 (million)
% 6.01/2.06 % (13898)------------------------------
% 6.01/2.06 % (13898)------------------------------
% 6.01/2.06 % (13924)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_13762 for (2994ds/96Mi)
% 6.01/2.07 % (13880)Instruction limit reached!
% 6.01/2.07 % (13880)------------------------------
% 6.01/2.07 % (13880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.07 % (13880)Termination reason: Unknown
% 6.01/2.07 % (13880)Termination phase: Saturation
% 6.01/2.07
% 6.01/2.07 % (13880)Memory used [KB]: 9722
% 6.01/2.07 % (13880)Time elapsed: 0.486 s
% 6.01/2.07 % (13880)Instructions burned: 1041 (million)
% 6.01/2.07 % (13880)------------------------------
% 6.01/2.07 % (13880)------------------------------
% 6.01/2.07 % (13922)Instruction limit reached!
% 6.01/2.07 % (13922)------------------------------
% 6.01/2.07 % (13922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.07 % (13922)Termination reason: Unknown
% 6.01/2.07 % (13922)Termination phase: Property scanning
% 6.01/2.07
% 6.01/2.07 % (13922)Memory used [KB]: 2302
% 6.01/2.07 % (13922)Time elapsed: 0.030 s
% 6.01/2.07 % (13922)Instructions burned: 62 (million)
% 6.01/2.07 % (13922)------------------------------
% 6.01/2.07 % (13922)------------------------------
% 6.01/2.07 % (13925)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_13762 for (2994ds/453Mi)
% 6.01/2.08 % (13926)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_13762 for (2994ds/71Mi)
% 6.01/2.09 % (13927)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_13762 for (2994ds/83Mi)
% 6.01/2.10 % (13926)Instruction limit reached!
% 6.01/2.10 % (13926)------------------------------
% 6.01/2.10 % (13926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.10 % (13926)Termination reason: Unknown
% 6.01/2.10 % (13926)Termination phase: Property scanning
% 6.01/2.10
% 6.01/2.10 % (13926)Memory used [KB]: 2558
% 6.01/2.10 % (13926)Time elapsed: 0.022 s
% 6.01/2.10 % (13926)Instructions burned: 71 (million)
% 6.01/2.10 % (13926)------------------------------
% 6.01/2.10 % (13926)------------------------------
% 6.01/2.11 % (13924)Instruction limit reached!
% 6.01/2.11 % (13924)------------------------------
% 6.01/2.11 % (13924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.11 % (13924)Termination reason: Unknown
% 6.01/2.11 % (13924)Termination phase: Property scanning
% 6.01/2.11
% 6.01/2.11 % (13924)Memory used [KB]: 2686
% 6.01/2.11 % (13924)Time elapsed: 0.044 s
% 6.01/2.11 % (13924)Instructions burned: 97 (million)
% 6.01/2.11 % (13924)------------------------------
% 6.01/2.11 % (13924)------------------------------
% 6.01/2.11 % (13928)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_13762 for (2994ds/11Mi)
% 6.54/2.12 % (13928)Instruction limit reached!
% 6.54/2.12 % (13928)------------------------------
% 6.54/2.12 % (13928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.12 % (13928)Termination reason: Unknown
% 6.54/2.12 % (13928)Termination phase: shuffling
% 6.54/2.12
% 6.54/2.12 % (13928)Memory used [KB]: 1663
% 6.54/2.12 % (13928)Time elapsed: 0.007 s
% 6.54/2.12 % (13928)Instructions burned: 13 (million)
% 6.54/2.12 % (13928)------------------------------
% 6.54/2.12 % (13928)------------------------------
% 6.54/2.12 % (13929)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_13762 for (2994ds/41Mi)
% 6.54/2.13 % (13931)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13762 for (2994ds/6Mi)
% 6.54/2.13 % (13931)Instruction limit reached!
% 6.54/2.13 % (13931)------------------------------
% 6.54/2.13 % (13931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.13 % (13931)Termination reason: Unknown
% 6.54/2.13 % (13931)Termination phase: shuffling
% 6.54/2.13
% 6.54/2.13 % (13931)Memory used [KB]: 1535
% 6.54/2.13 % (13931)Time elapsed: 0.003 s
% 6.54/2.13 % (13931)Instructions burned: 6 (million)
% 6.54/2.13 % (13931)------------------------------
% 6.54/2.13 % (13931)------------------------------
% 6.54/2.13 % (13927)Instruction limit reached!
% 6.54/2.13 % (13927)------------------------------
% 6.54/2.13 % (13927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.13 % (13927)Termination reason: Unknown
% 6.54/2.13 % (13927)Termination phase: Saturation
% 6.54/2.13
% 6.54/2.13 % (13927)Memory used [KB]: 6780
% 6.54/2.13 % (13927)Time elapsed: 0.042 s
% 6.54/2.13 % (13927)Instructions burned: 83 (million)
% 6.54/2.13 % (13927)------------------------------
% 6.54/2.13 % (13927)------------------------------
% 6.54/2.14 % (13932)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_13762 for (2994ds/150Mi)
% 6.54/2.14 % (13929)Instruction limit reached!
% 6.54/2.14 % (13929)------------------------------
% 6.54/2.14 % (13929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.14 % (13929)Termination reason: Unknown
% 6.54/2.14 % (13929)Termination phase: shuffling
% 6.54/2.14
% 6.54/2.14 % (13929)Memory used [KB]: 2302
% 6.54/2.14 % (13929)Time elapsed: 0.021 s
% 6.54/2.14 % (13929)Instructions burned: 42 (million)
% 6.54/2.14 % (13929)------------------------------
% 6.54/2.14 % (13929)------------------------------
% 6.54/2.15 % (13933)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_13762 for (2994ds/343Mi)
% 6.54/2.16 % (13934)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_13762 for (2993ds/109Mi)
% 6.54/2.17 % (13913)Instruction limit reached!
% 6.54/2.17 % (13913)------------------------------
% 6.54/2.17 % (13913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.17 % (13913)Termination reason: Unknown
% 6.54/2.17 % (13913)Termination phase: Saturation
% 6.54/2.17
% 6.54/2.17 % (13913)Memory used [KB]: 9083
% 6.54/2.17 % (13913)Time elapsed: 0.246 s
% 6.54/2.17 % (13913)Instructions burned: 507 (million)
% 6.54/2.17 % (13913)------------------------------
% 6.54/2.17 % (13913)------------------------------
% 6.54/2.18 % (13935)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_13762 for (2993ds/253Mi)
% 6.81/2.20 % (13932)Instruction limit reached!
% 6.81/2.20 % (13932)------------------------------
% 6.81/2.20 % (13932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.20 % (13932)Termination reason: Unknown
% 6.81/2.20 % (13932)Termination phase: Property scanning
% 6.81/2.20
% 6.81/2.20 % (13932)Memory used [KB]: 2942
% 6.81/2.20 % (13932)Time elapsed: 0.044 s
% 6.81/2.20 % (13932)Instructions burned: 154 (million)
% 6.81/2.20 % (13932)------------------------------
% 6.81/2.20 % (13932)------------------------------
% 6.81/2.21 % (13935)Refutation not found, incomplete strategy
% 6.81/2.21 % (13935)------------------------------
% 6.81/2.21 % (13935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.21 % (13935)Termination reason: Refutation not found, incomplete strategy
% 6.81/2.21
% 6.81/2.21
% 6.81/2.21 % (13935)Memory used [KB]: 6780
% 6.81/2.21 % (13935)Time elapsed: 0.029 s
% 6.81/2.21 % (13935)Instructions burned: 54 (million)
% 6.81/2.21 % (13935)------------------------------
% 6.81/2.21 % (13935)------------------------------
% 6.81/2.22 % (13934)Instruction limit reached!
% 6.81/2.22 % (13934)------------------------------
% 6.81/2.22 % (13934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.22 % (13934)Termination reason: Unknown
% 6.81/2.22 % (13934)Termination phase: Property scanning
% 6.81/2.22
% 6.81/2.22 % (13934)Memory used [KB]: 2686
% 6.81/2.22 % (13934)Time elapsed: 0.034 s
% 6.81/2.22 % (13934)Instructions burned: 110 (million)
% 6.81/2.22 % (13934)------------------------------
% 6.81/2.22 % (13934)------------------------------
% 6.81/2.22 % (13936)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_13762 for (2993ds/140Mi)
% 6.81/2.23 % (13920)Instruction limit reached!
% 6.81/2.23 % (13920)------------------------------
% 6.81/2.23 % (13920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.23 % (13920)Termination reason: Unknown
% 6.81/2.23 % (13920)Termination phase: Saturation
% 6.81/2.23
% 6.81/2.23 % (13920)Memory used [KB]: 4733
% 6.81/2.23 % (13920)Time elapsed: 0.202 s
% 6.81/2.23 % (13920)Instructions burned: 432 (million)
% 6.81/2.23 % (13920)------------------------------
% 6.81/2.23 % (13920)------------------------------
% 6.81/2.23 % (13937)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_13762 for (2993ds/614Mi)
% 6.81/2.23 % (13938)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_13762 for (2993ds/202Mi)
% 6.81/2.24 % (13939)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_13762 for (2993ds/339Mi)
% 6.81/2.26 % (13938)Refutation not found, incomplete strategy
% 6.81/2.26 % (13938)------------------------------
% 6.81/2.26 % (13938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.26 % (13938)Termination reason: Refutation not found, incomplete strategy
% 6.81/2.26
% 6.81/2.26
% 6.81/2.26 % (13938)Memory used [KB]: 6652
% 6.81/2.26 % (13938)Time elapsed: 0.027 s
% 6.81/2.26 % (13938)Instructions burned: 53 (million)
% 6.81/2.26 % (13938)------------------------------
% 6.81/2.26 % (13938)------------------------------
% 6.81/2.28 % (13925)Instruction limit reached!
% 6.81/2.28 % (13925)------------------------------
% 6.81/2.28 % (13925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.28 % (13925)Termination reason: Unknown
% 6.81/2.28 % (13925)Termination phase: Saturation
% 6.81/2.28
% 6.81/2.28 % (13925)Memory used [KB]: 7931
% 6.81/2.28 % (13925)Time elapsed: 0.207 s
% 6.81/2.28 % (13925)Instructions burned: 453 (million)
% 6.81/2.28 % (13925)------------------------------
% 6.81/2.28 % (13925)------------------------------
% 6.81/2.29 % (13940)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_13762 for (2992ds/283Mi)
% 6.81/2.29 % (13936)Instruction limit reached!
% 6.81/2.29 % (13936)------------------------------
% 6.81/2.29 % (13936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.81/2.29 % (13936)Termination reason: Unknown
% 6.81/2.29 % (13936)Termination phase: Saturation
% 6.81/2.29
% 6.81/2.29 % (13936)Memory used [KB]: 7164
% 6.81/2.29 % (13936)Time elapsed: 0.070 s
% 6.81/2.29 % (13936)Instructions burned: 141 (million)
% 6.81/2.29 % (13936)------------------------------
% 6.81/2.29 % (13936)------------------------------
% 7.61/2.30 % (13941)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_13762 for (2992ds/134Mi)
% 7.61/2.30 % (13933)Instruction limit reached!
% 7.61/2.30 % (13933)------------------------------
% 7.61/2.30 % (13933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.30 % (13933)Termination reason: Unknown
% 7.61/2.30 % (13933)Termination phase: Saturation
% 7.61/2.30
% 7.61/2.30 % (13933)Memory used [KB]: 7419
% 7.61/2.30 % (13933)Time elapsed: 0.156 s
% 7.61/2.30 % (13933)Instructions burned: 343 (million)
% 7.61/2.30 % (13933)------------------------------
% 7.61/2.30 % (13933)------------------------------
% 7.61/2.31 % (13942)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_13762 for (2992ds/298Mi)
% 7.61/2.32 % (13943)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_13762 for (2992ds/192Mi)
% 7.61/2.36 % (13941)Instruction limit reached!
% 7.61/2.36 % (13941)------------------------------
% 7.61/2.36 % (13941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.61/2.36 % (13941)Termination reason: Unknown
% 7.61/2.36 % (13941)Termination phase: Property scanning
% 7.61/2.36
% 7.61/2.36 % (13941)Memory used [KB]: 2686
% 7.61/2.36 % (13941)Time elapsed: 0.063 s
% 7.61/2.36 % (13941)Instructions burned: 135 (million)
% 7.61/2.36 % (13941)------------------------------
% 7.61/2.36 % (13941)------------------------------
% 7.61/2.38 % (13944)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_13762 for (2991ds/258Mi)
% 7.96/2.40 % (13939)Instruction limit reached!
% 7.96/2.40 % (13939)------------------------------
% 7.96/2.40 % (13939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.40 % (13939)Termination reason: Unknown
% 7.96/2.40 % (13939)Termination phase: Saturation
% 7.96/2.40
% 7.96/2.40 % (13939)Memory used [KB]: 7419
% 7.96/2.40 % (13939)Time elapsed: 0.156 s
% 7.96/2.40 % (13939)Instructions burned: 339 (million)
% 7.96/2.40 % (13939)------------------------------
% 7.96/2.40 % (13939)------------------------------
% 7.96/2.40 % (13937)Instruction limit reached!
% 7.96/2.40 % (13937)------------------------------
% 7.96/2.40 % (13937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.40 % (13937)Termination reason: Unknown
% 7.96/2.40 % (13937)Termination phase: Saturation
% 7.96/2.40
% 7.96/2.40 % (13937)Memory used [KB]: 8187
% 7.96/2.40 % (13937)Time elapsed: 0.176 s
% 7.96/2.40 % (13937)Instructions burned: 616 (million)
% 7.96/2.40 % (13937)------------------------------
% 7.96/2.40 % (13937)------------------------------
% 7.96/2.40 % (13943)Instruction limit reached!
% 7.96/2.40 % (13943)------------------------------
% 7.96/2.40 % (13943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.40 % (13943)Termination reason: Unknown
% 7.96/2.40 % (13943)Termination phase: Saturation
% 7.96/2.40
% 7.96/2.40 % (13943)Memory used [KB]: 3454
% 7.96/2.40 % (13943)Time elapsed: 0.089 s
% 7.96/2.40 % (13943)Instructions burned: 193 (million)
% 7.96/2.40 % (13943)------------------------------
% 7.96/2.40 % (13943)------------------------------
% 7.96/2.41 % (13940)Instruction limit reached!
% 7.96/2.41 % (13940)------------------------------
% 7.96/2.41 % (13940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.41 % (13940)Termination reason: Unknown
% 7.96/2.41 % (13940)Termination phase: Saturation
% 7.96/2.41
% 7.96/2.41 % (13940)Memory used [KB]: 7547
% 7.96/2.41 % (13946)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_13762 for (2991ds/231Mi)
% 7.96/2.41 % (13940)Time elapsed: 0.149 s
% 7.96/2.41 % (13940)Instructions burned: 283 (million)
% 7.96/2.41 % (13940)------------------------------
% 7.96/2.41 % (13940)------------------------------
% 7.96/2.42 % (13945)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_13762 for (2991ds/90Mi)
% 7.96/2.42 % (13947)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_13762 for (2991ds/458Mi)
% 7.96/2.43 % (13948)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_13762 for (2991ds/31Mi)
% 7.96/2.44 % (13942)Instruction limit reached!
% 7.96/2.44 % (13942)------------------------------
% 7.96/2.44 % (13942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.44 % (13942)Termination reason: Unknown
% 7.96/2.44 % (13942)Termination phase: Saturation
% 7.96/2.44
% 7.96/2.44 % (13942)Memory used [KB]: 7419
% 7.96/2.44 % (13942)Time elapsed: 0.131 s
% 7.96/2.44 % (13942)Instructions burned: 298 (million)
% 7.96/2.44 % (13942)------------------------------
% 7.96/2.44 % (13942)------------------------------
% 7.96/2.44 % (13948)Instruction limit reached!
% 7.96/2.44 % (13948)------------------------------
% 7.96/2.44 % (13948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.44 % (13948)Termination reason: Unknown
% 7.96/2.44 % (13948)Termination phase: Property scanning
% 7.96/2.44
% 7.96/2.44 % (13948)Memory used [KB]: 2046
% 7.96/2.44 % (13948)Time elapsed: 0.017 s
% 7.96/2.44 % (13948)Instructions burned: 32 (million)
% 7.96/2.44 % (13948)------------------------------
% 7.96/2.44 % (13948)------------------------------
% 7.96/2.46 % (13945)Instruction limit reached!
% 7.96/2.46 % (13945)------------------------------
% 7.96/2.46 % (13945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.46 % (13945)Termination reason: Unknown
% 7.96/2.46 % (13945)Termination phase: Equality resolution with deletion
% 7.96/2.46
% 7.96/2.46 % (13945)Memory used [KB]: 2686
% 7.96/2.46 % (13945)Time elapsed: 0.044 s
% 7.96/2.46 % (13945)Instructions burned: 91 (million)
% 7.96/2.46 % (13945)------------------------------
% 7.96/2.46 % (13945)------------------------------
% 7.96/2.46 % (13951)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_13762 for (2990ds/987Mi)
% 7.96/2.46 % (13949)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_13762 for (2991ds/297Mi)
% 7.96/2.47 % (13946)Instruction limit reached!
% 7.96/2.47 % (13946)------------------------------
% 7.96/2.47 % (13946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.47 % (13946)Termination reason: Unknown
% 7.96/2.47 % (13946)Termination phase: Saturation
% 7.96/2.47
% 7.96/2.47 % (13946)Memory used [KB]: 7419
% 7.96/2.47 % (13946)Time elapsed: 0.061 s
% 7.96/2.47 % (13946)Instructions burned: 233 (million)
% 7.96/2.47 % (13946)------------------------------
% 7.96/2.47 % (13946)------------------------------
% 7.96/2.47 % (13952)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_13762 for (2990ds/182Mi)
% 7.96/2.48 % (13953)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_13762 for (2990ds/182Mi)
% 7.96/2.48 % (13944)Instruction limit reached!
% 7.96/2.48 % (13944)------------------------------
% 7.96/2.48 % (13944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.48 % (13944)Termination reason: Unknown
% 7.96/2.48 % (13944)Termination phase: Function definition elimination
% 7.96/2.48
% 7.96/2.48 % (13944)Memory used [KB]: 2430
% 7.96/2.48 % (13944)Time elapsed: 0.110 s
% 7.96/2.48 % (13944)Instructions burned: 258 (million)
% 7.96/2.48 % (13944)------------------------------
% 7.96/2.48 % (13944)------------------------------
% 9.09/2.50 % (13954)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_13762 for (2990ds/154Mi)
% 9.09/2.50 % (13917)Instruction limit reached!
% 9.09/2.50 % (13917)------------------------------
% 9.09/2.50 % (13917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.50 % (13917)Termination reason: Unknown
% 9.09/2.50 % (13917)Termination phase: Saturation
% 9.09/2.50
% 9.09/2.50 % (13917)Memory used [KB]: 8315
% 9.09/2.50 % (13917)Time elapsed: 0.517 s
% 9.09/2.50 % (13917)Instructions burned: 1087 (million)
% 9.09/2.50 % (13917)------------------------------
% 9.09/2.50 % (13917)------------------------------
% 9.09/2.53 % (13955)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_13762 for (2990ds/79Mi)
% 9.09/2.55 % (13953)Instruction limit reached!
% 9.09/2.55 % (13953)------------------------------
% 9.09/2.55 % (13953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.55 % (13953)Termination reason: Unknown
% 9.09/2.55 % (13953)Termination phase: Saturation
% 9.09/2.55
% 9.09/2.55 % (13953)Memory used [KB]: 7547
% 9.09/2.55 % (13953)Time elapsed: 0.085 s
% 9.09/2.55 % (13953)Instructions burned: 183 (million)
% 9.09/2.55 % (13953)------------------------------
% 9.09/2.55 % (13953)------------------------------
% 9.09/2.55 % (13952)Instruction limit reached!
% 9.09/2.55 % (13952)------------------------------
% 9.09/2.55 % (13952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.55 % (13952)Termination reason: Unknown
% 9.09/2.55 % (13952)Termination phase: Property scanning
% 9.09/2.55
% 9.09/2.55 % (13952)Memory used [KB]: 2686
% 9.09/2.55 % (13952)Time elapsed: 0.082 s
% 9.09/2.55 % (13952)Instructions burned: 183 (million)
% 9.09/2.55 % (13952)------------------------------
% 9.09/2.55 % (13952)------------------------------
% 9.09/2.55 % (13955)Instruction limit reached!
% 9.09/2.55 % (13955)------------------------------
% 9.09/2.55 % (13955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.55 % (13955)Termination reason: Unknown
% 9.09/2.55 % (13955)Termination phase: Function definition elimination
% 9.09/2.55
% 9.09/2.55 % (13955)Memory used [KB]: 2558
% 9.09/2.55 % (13955)Time elapsed: 0.025 s
% 9.09/2.55 % (13955)Instructions burned: 82 (million)
% 9.09/2.55 % (13955)------------------------------
% 9.09/2.55 % (13955)------------------------------
% 9.09/2.56 % (13956)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_13762 for (2989ds/216Mi)
% 9.09/2.57 % (13954)Instruction limit reached!
% 9.09/2.57 % (13954)------------------------------
% 9.09/2.57 % (13954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.09/2.57 % (13954)Termination reason: Unknown
% 9.09/2.57 % (13954)Termination phase: Property scanning
% 9.09/2.57
% 9.09/2.57 % (13954)Memory used [KB]: 2814
% 9.09/2.57 % (13954)Time elapsed: 0.071 s
% 9.09/2.57 % (13954)Instructions burned: 155 (million)
% 9.09/2.57 % (13954)------------------------------
% 9.09/2.57 % (13954)------------------------------
% 9.09/2.57 % (13957)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_13762 for (2989ds/114Mi)
% 9.09/2.57 % (13958)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_13762 for (2989ds/922Mi)
% 9.09/2.59 % (13959)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_13762 for (2989ds/182Mi)
% 9.39/2.60 % (13949)Instruction limit reached!
% 9.39/2.60 % (13949)------------------------------
% 9.39/2.60 % (13949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.60 % (13949)Termination reason: Unknown
% 9.39/2.60 % (13949)Termination phase: Saturation
% 9.39/2.60
% 9.39/2.60 % (13949)Memory used [KB]: 7675
% 9.39/2.60 % (13949)Time elapsed: 0.164 s
% 9.39/2.60 % (13949)Instructions burned: 297 (million)
% 9.39/2.60 % (13949)------------------------------
% 9.39/2.60 % (13949)------------------------------
% 9.39/2.62 % (13956)Instruction limit reached!
% 9.39/2.62 % (13956)------------------------------
% 9.39/2.62 % (13956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.62 % (13956)Termination reason: Unknown
% 9.39/2.62 % (13956)Termination phase: Saturation
% 9.39/2.62
% 9.39/2.62 % (13956)Memory used [KB]: 7291
% 9.39/2.62 % (13956)Time elapsed: 0.057 s
% 9.39/2.62 % (13956)Instructions burned: 218 (million)
% 9.39/2.62 % (13956)------------------------------
% 9.39/2.62 % (13956)------------------------------
% 9.39/2.62 % (13960)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_13762 for (2989ds/164Mi)
% 9.39/2.62 % (13957)Instruction limit reached!
% 9.39/2.62 % (13957)------------------------------
% 9.39/2.62 % (13957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.62 % (13957)Termination reason: Unknown
% 9.39/2.62 % (13957)Termination phase: Property scanning
% 9.39/2.62
% 9.39/2.62 % (13957)Memory used [KB]: 2686
% 9.39/2.62 % (13957)Time elapsed: 0.054 s
% 9.39/2.62 % (13957)Instructions burned: 115 (million)
% 9.39/2.62 % (13957)------------------------------
% 9.39/2.62 % (13957)------------------------------
% 9.39/2.63 % (13947)Instruction limit reached!
% 9.39/2.63 % (13947)------------------------------
% 9.39/2.63 % (13947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.63 % (13947)Termination reason: Unknown
% 9.39/2.63 % (13947)Termination phase: Saturation
% 9.39/2.63
% 9.39/2.63 % (13947)Memory used [KB]: 7675
% 9.39/2.63 % (13947)Time elapsed: 0.207 s
% 9.39/2.63 % (13947)Instructions burned: 458 (million)
% 9.39/2.63 % (13947)------------------------------
% 9.39/2.63 % (13947)------------------------------
% 9.39/2.63 % (13962)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_13762 for (2989ds/368Mi)
% 9.39/2.63 % (13961)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_13762 for (2989ds/50Mi)
% 9.39/2.66 % (13961)Instruction limit reached!
% 9.39/2.66 % (13961)------------------------------
% 9.39/2.66 % (13961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.66 % (13961)Termination reason: Unknown
% 9.39/2.66 % (13961)Termination phase: Property scanning
% 9.39/2.66
% 9.39/2.66 % (13961)Memory used [KB]: 2302
% 9.39/2.66 % (13961)Time elapsed: 0.025 s
% 9.39/2.66 % (13961)Instructions burned: 51 (million)
% 9.39/2.66 % (13961)------------------------------
% 9.39/2.66 % (13961)------------------------------
% 9.39/2.66 % (13963)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_13762 for (2989ds/1021Mi)
% 9.39/2.66 % (13958)First to succeed.
% 9.39/2.67 % (13958)Refutation found. Thanks to Tanya!
% 9.39/2.67 % SZS status Theorem for DTF2THF_13762
% 9.39/2.67 % SZS output start Proof for DTF2THF_13762
% 9.39/2.67 thf(type_def_6, type, traffic: $tType).
% 9.39/2.67 thf(type_def_7, type, product_unit: $tType).
% 9.39/2.67 thf(type_def_8, type, view_ext: ($tType) > $tType).
% 9.39/2.67 thf(type_def_9, type, nat_int: $tType).
% 9.39/2.67 thf(type_def_10, type, nat: $tType).
% 9.39/2.67 thf(type_def_11, type, real_int: $tType).
% 9.39/2.67 thf(type_def_12, type, real: $tType).
% 9.39/2.67 thf(type_def_13, type, cars: $tType).
% 9.39/2.67 thf(func_def_0, type, view_ext: ($tType) > $tType).
% 9.39/2.67 thf(func_def_1, type, product_unit: $tType).
% 9.39/2.67 thf(func_def_2, type, real_int: $tType).
% 9.39/2.67 thf(func_def_3, type, traffic: $tType).
% 9.39/2.67 thf(func_def_4, type, nat_int: $tType).
% 9.39/2.67 thf(func_def_5, type, real: $tType).
% 9.39/2.67 thf(func_def_6, type, cars: $tType).
% 9.39/2.67 thf(func_def_7, type, nat: $tType).
% 9.39/2.67 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_9, type, minus: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_10, type, bot: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_11, type, ord: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_12, type, order: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_13, type, group_add: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_14, type, no_bot: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_15, type, no_top: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_16, type, linorder: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_17, type, preorder: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_18, type, order_bot: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_19, type, wellorder: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_20, type, dense_order: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_21, type, dense_linorder: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_22, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_23, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 9.39/2.67 thf(func_def_24, type, fun_upd: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0 > X1 > X0 > X1)).
% 9.39/2.67 thf(func_def_25, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 9.39/2.67 thf(func_def_26, type, default_default: !>[X0: $tType]:(X0)).
% 9.39/2.67 thf(func_def_27, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 9.39/2.67 thf(func_def_28, type, move: traffic > traffic > view_ext @ product_unit > view_ext @ product_unit).
% 9.39/2.67 thf(func_def_29, type, nat_N_Chop: nat_int > nat_int > nat_int > $o).
% 9.39/2.67 thf(func_def_30, type, nat_card: nat_int > nat).
% 9.39/2.67 thf(func_def_31, type, nat_consec: nat_int > nat_int > $o).
% 9.39/2.67 thf(func_def_32, type, nat_not_in: nat > nat_int > $o).
% 9.39/2.67 thf(func_def_33, type, nat_union: nat_int > nat_int > nat_int).
% 9.39/2.67 thf(func_def_34, type, bot_bot: !>[X0: $tType]:(X0)).
% 9.39/2.67 thf(func_def_35, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 9.39/2.67 thf(func_def_36, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 9.39/2.67 thf(func_def_37, type, order_Greatest: !>[X0: $tType]:((X0 > $o) > X0)).
% 9.39/2.67 thf(func_def_38, type, product_Unity: product_unit).
% 9.39/2.67 thf(func_def_39, type, product_rec_unit: !>[X0: $tType]:(X0 > product_unit > X0)).
% 9.39/2.67 thf(func_def_40, type, real_R_Chop: real_int > real_int > real_int > $o).
% 9.39/2.67 thf(func_def_41, type, real_shift: real_int > real > real_int).
% 9.39/2.67 thf(func_def_42, type, abstract: traffic > traffic > $o).
% 9.39/2.67 thf(func_def_43, type, braking_distance: traffic > cars > real).
% 9.39/2.67 thf(func_def_44, type, change_dyn: traffic > cars > (real > real) > traffic > $o).
% 9.39/2.67 thf(func_def_45, type, clm: traffic > cars > nat_int).
% 9.39/2.67 thf(func_def_46, type, create_claim: traffic > cars > nat > traffic > $o).
% 9.39/2.67 thf(func_def_47, type, create_reservation: traffic > cars > traffic > $o).
% 9.39/2.67 thf(func_def_48, type, dyn: traffic > cars > real > real).
% 9.39/2.67 thf(func_def_49, type, evolve: traffic > traffic > $o).
% 9.39/2.67 thf(func_def_50, type, physical_size: traffic > cars > real).
% 9.39/2.67 thf(func_def_51, type, pos: traffic > cars > real).
% 9.39/2.67 thf(func_def_52, type, res: traffic > cars > nat_int).
% 9.39/2.67 thf(func_def_53, type, withdraw_claim: traffic > cars > traffic > $o).
% 9.39/2.67 thf(func_def_54, type, withdraw_reservation: traffic > cars > nat > traffic > $o).
% 9.39/2.67 thf(func_def_55, type, ext: !>[X0: $tType]:(view_ext @ X0 > real_int)).
% 9.39/2.67 thf(func_def_56, type, hchop: view_ext @ product_unit > view_ext @ product_unit > view_ext @ product_unit > $o).
% 9.39/2.67 thf(func_def_57, type, lan: !>[X0: $tType]:(view_ext @ X0 > nat_int)).
% 9.39/2.67 thf(func_def_58, type, more: !>[X0: $tType]:(view_ext @ X0 > X0)).
% 9.39/2.67 thf(func_def_59, type, own: !>[X0: $tType]:(view_ext @ X0 > cars)).
% 9.39/2.67 thf(func_def_60, type, switch: view_ext @ product_unit > cars > view_ext @ product_unit > $o).
% 9.39/2.67 thf(func_def_61, type, view_ext2: !>[X0: $tType]:(real_int > nat_int > cars > X0 > view_ext @ X0)).
% 9.39/2.67 thf(func_def_62, type, ts: traffic).
% 9.39/2.67 thf(func_def_63, type, ts2: traffic).
% 9.39/2.67 thf(func_def_64, type, ts_a: traffic).
% 9.39/2.67 thf(func_def_65, type, ts3: traffic).
% 9.39/2.67 thf(func_def_66, type, v: view_ext @ product_unit).
% 9.39/2.67 thf(func_def_82, type, sK0: traffic > cars > traffic).
% 9.39/2.67 thf(func_def_83, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 9.39/2.67 thf(func_def_84, type, sK2: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > traffic).
% 9.39/2.67 thf(func_def_85, type, sK3: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > traffic).
% 9.39/2.67 thf(func_def_86, type, sK4: view_ext @ product_unit > (traffic > view_ext @ product_unit > $o) > traffic > traffic).
% 9.39/2.67 thf(func_def_87, type, sK5: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > traffic).
% 9.39/2.67 thf(func_def_88, type, sK6: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > traffic).
% 9.39/2.67 thf(func_def_89, type, sK7: view_ext @ product_unit > traffic > (traffic > view_ext @ product_unit > $o) > traffic).
% 9.39/2.67 thf(func_def_90, type, sK8: cars).
% 9.39/2.67 thf(func_def_92, type, ph10: !>[X0: $tType]:(X0)).
% 9.39/2.67 thf(f1323,plain,(
% 9.39/2.67 $false),
% 9.39/2.67 inference(avatar_sat_refutation,[status(thm)],[f966,f971,f976,f981,f1310,f1322])).
% 9.39/2.67 thf(f1322,plain,(
% 9.39/2.67 ~spl9_2 | spl9_11),
% 9.39/2.67 inference(avatar_contradiction_clause,[status(thm)],[f1321])).
% 9.39/2.67 thf(f1321,plain,(
% 9.39/2.67 $false | (~spl9_2 | spl9_11)),
% 9.39/2.67 inference(subsumption_resolution,[status(thm)],[f1316,f951])).
% 9.39/2.67 thf(f951,plain,(
% 9.39/2.67 ( ! [X0 : traffic] : (($true = (abstract @ X0 @ X0))) )),
% 9.39/2.67 inference(cnf_transformation,[status(thm)],[f870])).
% 9.39/2.67 thf(f870,plain,(
% 9.39/2.67 ! [X0 : traffic] : ($true = (abstract @ X0 @ X0))),
% 9.39/2.67 inference(fool_elimination,[status(thm)],[f869])).
% 9.39/2.67 thf(f869,plain,(
% 9.39/2.67 ! [X0 : traffic] : (abstract @ X0 @ X0)),
% 9.39/2.67 inference(rectify,[status(thm)],[f42])).
% 9.39/2.67 thf(f42,axiom,(
% 9.39/2.67 ! [X13 : traffic] : (abstract @ X13 @ X13)),
% 9.39/2.67 file('/export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2THF_13762.p',fact_41_traffic_Oabstract_Orefl)).
% 9.39/2.67 thf(f1316,plain,(
% 9.39/2.67 ((abstract @ ts_a @ ts_a) != $true) | (~spl9_2 | spl9_11)),
% 9.39/2.67 inference(trivial_inequality_removal,[status(thm)],[f1311])).
% 9.39/2.67 thf(f1311,plain,(
% 9.39/2.67 ($true != $true) | ((abstract @ ts_a @ ts_a) != $true) | (~spl9_2 | spl9_11)),
% 9.39/2.67 inference(superposition,[status(thm)],[f1298,f990])).
% 9.39/2.67 thf(f990,plain,(
% 9.39/2.67 ( ! [X0 : traffic] : (((abstract @ X0 @ ts) = $true) | ((abstract @ X0 @ ts_a) != $true)) ) | ~spl9_2),
% 9.39/2.67 inference(trivial_inequality_removal,[status(thm)],[f987])).
% 9.39/2.67 thf(f987,plain,(
% 9.39/2.67 ( ! [X0 : traffic] : (((abstract @ X0 @ ts) = $true) | ((abstract @ X0 @ ts_a) != $true) | ($true != $true)) ) | ~spl9_2),
% 9.39/2.67 inference(superposition,[status(thm)],[f959,f970])).
% 9.39/2.67 thf(f970,plain,(
% 9.39/2.67 ((create_reservation @ ts_a @ sK8 @ ts) = $true) | ~spl9_2),
% 9.39/2.67 inference(avatar_component_clause,[status(thm)],[f968])).
% 9.39/2.67 thf(f968,definition,(
% 9.39/2.67 spl9_2 <=> ((create_reservation @ ts_a @ sK8 @ ts) = $true)),
% 9.39/2.67 introduced(definition,[new_symbols(naming,[spl9_2])],[avatar_definition])).
% 9.39/2.67 thf(f959,plain,(
% 9.39/2.67 ( ! [X2 : traffic,X3 : cars,X0 : traffic,X1 : traffic] : (((create_reservation @ X1 @ X3 @ X2) != $true) | ($true = (abstract @ X0 @ X2)) | ((abstract @ X0 @ X1) != $true)) )),
% 9.39/2.67 inference(cnf_transformation,[status(thm)],[f906])).
% 9.39/2.67 thf(f906,plain,(
% 9.39/2.67 ! [X0 : traffic,X1 : traffic,X2 : traffic] : (! [X3 : cars] : ((create_reservation @ X1 @ X3 @ X2) != $true) | ($true = (abstract @ X0 @ X2)) | ((abstract @ X0 @ X1) != $true))),
% 9.39/2.67 inference(flattening,[status(thm)],[f905])).
% 9.39/2.67 thf(f905,plain,(
% 9.39/2.67 ! [X0 : traffic,X1 : traffic,X2 : traffic] : ((($true = (abstract @ X0 @ X2)) | ! [X3 : cars] : ((create_reservation @ X1 @ X3 @ X2) != $true)) | ((abstract @ X0 @ X1) != $true))),
% 9.39/2.67 inference(ennf_transformation,[status(thm)],[f824])).
% 9.39/2.67 thf(f824,plain,(
% 9.39/2.67 ! [X0 : traffic,X1 : traffic,X2 : traffic] : (((abstract @ X0 @ X1) = $true) => (? [X3 : cars] : ((create_reservation @ X1 @ X3 @ X2) = $true) => ($true = (abstract @ X0 @ X2))))),
% 9.39/2.67 inference(fool_elimination,[status(thm)],[f823])).
% 9.39/2.67 thf(f823,plain,(
% 9.39/2.67 ! [X0 : traffic,X1 : traffic,X2 : traffic] : ((abstract @ X0 @ X1) => (? [X3 : cars] : (create_reservation @ X1 @ X3 @ X2) => (abstract @ X0 @ X2)))),
% 9.39/2.67 inference(rectify,[status(thm)],[f33])).
% 9.39/2.67 thf(f33,axiom,(
% 9.39/2.67 ! [X13 : traffic,X18 : traffic,X19 : traffic] : ((abstract @ X13 @ X18) => (? [X43 : cars] : (create_reservation @ X18 @ X43 @ X19) => (abstract @ X13 @ X19)))),
% 9.39/2.67 file('/export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2THF_13762.p',fact_32_traffic_Ocr__res)).
% 9.39/2.67 thf(f1298,plain,(
% 9.39/2.67 ((abstract @ ts_a @ ts) != $true) | spl9_11),
% 9.39/2.67 inference(avatar_component_clause,[status(thm)],[f1296])).
% 9.39/2.67 thf(f1296,definition,(
% 9.39/2.67 spl9_11 <=> ((abstract @ ts_a @ ts) = $true)),
% 9.39/2.67 introduced(definition,[new_symbols(naming,[spl9_11])],[avatar_definition])).
% 9.39/2.67 thf(f1310,plain,(
% 9.39/2.67 ~spl9_11 | ~spl9_1 | ~spl9_3 | spl9_4),
% 9.39/2.67 inference(avatar_split_clause,[status(thm)],[f1309,f978,f973,f963,f1296])).
% 9.39/2.67 thf(f963,definition,(
% 9.39/2.67 spl9_1 <=> ((move @ ts3 @ ts_a @ v) = (move @ ts_a @ ts @ (move @ ts3 @ ts_a @ v)))),
% 9.39/2.67 introduced(definition,[new_symbols(naming,[spl9_1])],[avatar_definition])).
% 9.39/2.67 thf(f973,definition,(
% 9.39/2.67 spl9_3 <=> ((abstract @ ts3 @ ts_a) = $true)),
% 9.39/2.67 introduced(definition,[new_symbols(naming,[spl9_3])],[avatar_definition])).
% 9.39/2.67 thf(f978,definition,(
% 9.39/2.67 spl9_4 <=> ((move @ ts3 @ ts_a @ v) = (move @ ts3 @ ts @ v))),
% 9.39/2.67 introduced(definition,[new_symbols(naming,[spl9_4])],[avatar_definition])).
% 9.39/2.67 thf(f1309,plain,(
% 9.39/2.67 ((abstract @ ts_a @ ts) != $true) | (~spl9_1 | ~spl9_3 | spl9_4)),
% 9.39/2.67 inference(subsumption_resolution,[status(thm)],[f1308,f975])).
% 9.39/2.67 thf(f975,plain,(
% 9.39/2.67 ((abstract @ ts3 @ ts_a) = $true) | ~spl9_3),
% 9.39/2.67 inference(avatar_component_clause,[status(thm)],[f973])).
% 9.39/2.67 thf(f1308,plain,(
% 9.39/2.67 ((abstract @ ts_a @ ts) != $true) | ((abstract @ ts3 @ ts_a) != $true) | (~spl9_1 | spl9_4)),
% 9.39/2.67 inference(subsumption_resolution,[status(thm)],[f1289,f980])).
% 9.39/2.67 thf(f980,plain,(
% 9.39/2.67 ((move @ ts3 @ ts_a @ v) != (move @ ts3 @ ts @ v)) | spl9_4),
% 9.39/2.67 inference(avatar_component_clause,[status(thm)],[f978])).
% 9.39/2.67 thf(f1289,plain,(
% 9.39/2.67 ((abstract @ ts_a @ ts) != $true) | ((move @ ts3 @ ts_a @ v) = (move @ ts3 @ ts @ v)) | ((abstract @ ts3 @ ts_a) != $true) | ~spl9_1),
% 9.39/2.67 inference(superposition,[status(thm)],[f965,f938])).
% 9.39/2.67 thf(f938,plain,(
% 9.39/2.67 ( ! [X2 : traffic,X3 : view_ext @ product_unit,X0 : traffic,X1 : traffic] : (((move @ X1 @ X2 @ (move @ X0 @ X1 @ X3)) = (move @ X0 @ X2 @ X3)) | ((abstract @ X0 @ X1) != $true) | ((abstract @ X1 @ X2) != $true)) )),
% 9.39/2.67 inference(cnf_transformation,[status(thm)],[f908])).
% 9.39/2.67 thf(f908,plain,(
% 9.39/2.67 ! [X0 : traffic,X1 : traffic,X2 : traffic,X3 : view_ext @ product_unit] : (((abstract @ X0 @ X1) != $true) | ((move @ X1 @ X2 @ (move @ X0 @ X1 @ X3)) = (move @ X0 @ X2 @ X3)) | ((abstract @ X1 @ X2) != $true))),
% 9.39/2.67 inference(flattening,[status(thm)],[f907])).
% 9.39/2.67 thf(f907,plain,(
% 9.39/2.67 ! [X0 : traffic,X1 : traffic,X2 : traffic,X3 : view_ext @ product_unit] : (((move @ X1 @ X2 @ (move @ X0 @ X1 @ X3)) = (move @ X0 @ X2 @ X3)) | (((abstract @ X0 @ X1) != $true) | ((abstract @ X1 @ X2) != $true)))),
% 9.39/2.67 inference(ennf_transformation,[status(thm)],[f846])).
% 9.39/2.67 thf(f846,plain,(
% 9.39/2.67 ! [X0 : traffic,X1 : traffic,X2 : traffic,X3 : view_ext @ product_unit] : ((((abstract @ X0 @ X1) = $true) & ((abstract @ X1 @ X2) = $true)) => ((move @ X1 @ X2 @ (move @ X0 @ X1 @ X3)) = (move @ X0 @ X2 @ X3)))),
% 9.39/2.67 inference(fool_elimination,[status(thm)],[f845])).
% 9.39/2.67 thf(f845,plain,(
% 9.39/2.67 ! [X0 : traffic,X1 : traffic,X2 : traffic,X3 : view_ext @ product_unit] : (((abstract @ X1 @ X2) & (abstract @ X0 @ X1)) => ((move @ X1 @ X2 @ (move @ X0 @ X1 @ X3)) = (move @ X0 @ X2 @ X3)))),
% 9.39/2.67 inference(rectify,[status(thm)],[f13])).
% 9.39/2.67 thf(f13,axiom,(
% 9.39/2.67 ! [X13 : traffic,X18 : traffic,X19 : traffic,X14 : view_ext @ product_unit] : (((abstract @ X18 @ X19) & (abstract @ X13 @ X18)) => ((move @ X18 @ X19 @ (move @ X13 @ X18 @ X14)) = (move @ X13 @ X19 @ X14)))),
% 9.39/2.67 file('/export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2THF_13762.p',fact_12_traffic_Omove__trans)).
% 9.39/2.67 thf(f965,plain,(
% 9.39/2.67 ((move @ ts3 @ ts_a @ v) = (move @ ts_a @ ts @ (move @ ts3 @ ts_a @ v))) | ~spl9_1),
% 9.39/2.67 inference(avatar_component_clause,[status(thm)],[f963])).
% 9.39/2.67 thf(f981,plain,(
% 9.39/2.67 ~spl9_4),
% 9.39/2.67 inference(avatar_split_clause,[status(thm)],[f939,f978])).
% 9.39/2.67 thf(f939,plain,(
% 9.39/2.67 ((move @ ts3 @ ts_a @ v) != (move @ ts3 @ ts @ v))),
% 9.39/2.67 inference(cnf_transformation,[status(thm)],[f895])).
% 9.39/2.67 thf(f895,plain,(
% 9.39/2.67 ((move @ ts3 @ ts_a @ v) != (move @ ts3 @ ts @ v))),
% 9.39/2.67 inference(flattening,[status(thm)],[f315])).
% 9.39/2.67 thf(f315,negated_conjecture,(
% 9.39/2.67 ~((move @ ts3 @ ts_a @ v) = (move @ ts3 @ ts @ v))),
% 9.39/2.67 inference(negated_conjecture,[status(cth)],[f314])).
% 9.39/2.67 thf(f314,conjecture,(
% 9.39/2.67 ((move @ ts3 @ ts_a @ v) = (move @ ts3 @ ts @ v))),
% 9.39/2.67 file('/export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2THF_13762.p',conj_0)).
% 9.39/2.67 thf(f976,plain,(
% 9.39/2.67 spl9_3),
% 9.39/2.67 inference(avatar_split_clause,[status(thm)],[f942,f973])).
% 9.39/2.67 thf(f942,plain,(
% 9.39/2.67 ((abstract @ ts3 @ ts_a) = $true)),
% 9.39/2.67 inference(cnf_transformation,[status(thm)],[f394])).
% 9.39/2.67 thf(f394,plain,(
% 9.39/2.67 ((abstract @ ts3 @ ts_a) = $true)),
% 9.39/2.67 inference(fool_elimination,[status(thm)],[f393])).
% 9.39/2.67 thf(f393,plain,(
% 9.39/2.67 (abstract @ ts3 @ ts_a)),
% 9.39/2.67 inference(rectify,[status(thm)],[f1])).
% 9.39/2.67 thf(f1,axiom,(
% 9.39/2.67 (abstract @ ts3 @ ts_a)),
% 9.39/2.67 file('/export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2THF_13762.p',fact_0_cr__res_Ohyps_I1_J)).
% 9.39/2.67 thf(f971,plain,(
% 9.39/2.67 spl9_2),
% 9.39/2.67 inference(avatar_split_clause,[status(thm)],[f960,f968])).
% 9.39/2.67 thf(f960,plain,(
% 9.39/2.67 ((create_reservation @ ts_a @ sK8 @ ts) = $true)),
% 9.39/2.67 inference(cnf_transformation,[status(thm)],[f934])).
% 9.39/2.67 thf(f934,plain,(
% 9.39/2.67 ((create_reservation @ ts_a @ sK8 @ ts) = $true)),
% 9.39/2.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f680,f933])).
% 9.39/2.67 thf(f933,plain,(
% 9.39/2.67 ? [X0 : cars] : ($true = (create_reservation @ ts_a @ X0 @ ts)) => ((create_reservation @ ts_a @ sK8 @ ts) = $true)),
% 9.39/2.67 introduced(definition,[],[choice_axiom])).
% 9.39/2.67 thf(f680,plain,(
% 9.39/2.67 ? [X0 : cars] : ($true = (create_reservation @ ts_a @ X0 @ ts))),
% 9.39/2.67 inference(fool_elimination,[status(thm)],[f679])).
% 9.39/2.67 thf(f679,plain,(
% 9.39/2.67 ? [X0 : cars] : (create_reservation @ ts_a @ X0 @ ts)),
% 9.39/2.67 inference(rectify,[status(thm)],[f2])).
% 9.39/2.67 thf(f2,axiom,(
% 9.39/2.67 ? [X4 : cars] : (create_reservation @ ts_a @ X4 @ ts)),
% 9.39/2.67 file('/export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2THF_13762.p',fact_1_cr__res_Ohyps_I2_J)).
% 9.39/2.67 thf(f966,plain,(
% 9.39/2.67 spl9_1),
% 9.39/2.67 inference(avatar_split_clause,[status(thm)],[f952,f963])).
% 9.39/2.67 thf(f952,plain,(
% 9.39/2.67 ((move @ ts3 @ ts_a @ v) = (move @ ts_a @ ts @ (move @ ts3 @ ts_a @ v)))),
% 9.39/2.67 inference(cnf_transformation,[status(thm)],[f8])).
% 9.39/2.67 thf(f8,axiom,(
% 9.39/2.67 ((move @ ts3 @ ts_a @ v) = (move @ ts_a @ ts @ (move @ ts3 @ ts_a @ v)))),
% 9.39/2.67 file('/export/starexec/sandbox/tmp/tmp.V7v881CDeh/DTF2THF_13762.p',fact_7__092_060open_062move_Ats_Ats_H_Av_A_061_Amove_Ats_H_Ats_H_H_A_Imove_Ats_Ats_H_Av_J_092_060close_062)).
% 9.39/2.67 % SZS output end Proof for DTF2THF_13762
% 9.39/2.67 % (13958)------------------------------
% 9.39/2.67 % (13958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.39/2.67 % (13958)Termination reason: Refutation
% 9.39/2.67
% 9.39/2.67 % (13958)Memory used [KB]: 6908
% 9.39/2.67 % (13958)Time elapsed: 0.095 s
% 9.39/2.67 % (13958)Instructions burned: 188 (million)
% 9.39/2.67 % (13958)------------------------------
% 9.39/2.67 % (13958)------------------------------
% 9.39/2.67 % (13868)Success in time 1.134 s
%------------------------------------------------------------------------------