%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP048^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:08 AM UTC 2026
% Result : Theorem 241.67s 35.85s
% Output : Refutation 241.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP048^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n013.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:24:23 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP048^2 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer EdmondsKarp_Termination_Abstract problem prob_146__7582994_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : EdmondsKarp_Termination_Abstract/prob_146__7582994_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.33 v9.0.0, 0.00 v8.1.0, 0.25 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 356 ( 82 unt; 55 typ; 0 def)
% 0.20/0.46 % Number of atoms : 868 ( 171 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.20/0.46 % Number of connectives : 3538 ( 62 ~; 10 |; 48 &;2953 @)
% 0.20/0.46 % ( 0 <=>; 465 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 19 ( 8 avg)
% 0.20/0.46 % Number of types : 4 ( 3 usr)
% 0.20/0.46 % Number of type conns : 135 ( 135 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 53 ( 52 usr; 12 con; 0-5 aty)
% 0.20/0.46 % Number of variables : 1002 ( 61 ^; 872 !; 34 ?;1002 :)
% 0.20/0.46 % ( 35 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.46 % SPC : TH1_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:15:44.477
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (6)
% 0.20/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.20/0.46 product_prod: $tType > $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_List_Olist,type,
% 0.20/0.46 list: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_tf_capacity,type,
% 0.20/0.46 capacity: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Set_Oset,type,
% 0.20/0.46 set: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Nat_Onat,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_tf_a,type,
% 0.20/0.46 a: $tType ).
% 0.20/0.46
% 0.20/0.46 % Explicit typings (49)
% 0.20/0.46 thf(sy_cl_HOL_Otype,type,
% 0.20/0.46 type:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Nat_Osize,type,
% 0.20/0.46 size:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.20/0.46 ord:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.20/0.46 order:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.20/0.46 group_add:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Ono__bot,type,
% 0.20/0.46 no_bot:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Ono__top,type,
% 0.20/0.46 no_top:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.46 linorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.20/0.46 preorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Owellorder,type,
% 0.20/0.46 wellorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.20/0.46 semigroup_add:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Odense__order,type,
% 0.20/0.46 dense_order:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.20/0.46 linordered_idom:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.20/0.46 comm_monoid_add:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.31/0.47 ab_semigroup_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.31/0.47 cancel_semigroup_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.31/0.47 ordere779506340up_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.31/0.47 canoni770627133id_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.31/0.47 ordere236663937imp_le:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.31/0.47 ordere223160158up_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.31/0.47 strict2144017051up_add:
% 0.31/0.47 !>[A: $tType] : $o ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Graph_OGraph_Oconnected,type,
% 0.31/0.47 connected:
% 0.31/0.47 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > nat > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Graph_OGraph_Odist,type,
% 0.31/0.47 dist:
% 0.31/0.47 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > nat > nat > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Graph_OGraph_OisPath,type,
% 0.31/0.47 isPath:
% 0.31/0.47 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Graph_OGraph_OisShortestPath,type,
% 0.31/0.47 isShortestPath:
% 0.31/0.47 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Graph_OGraph_OisSimplePath,type,
% 0.31/0.47 isSimplePath:
% 0.31/0.47 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Graph_OGraph_Omin__dist,type,
% 0.31/0.47 min_dist:
% 0.31/0.47 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > nat > nat ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Graph_OGraph_OreachableNodes,type,
% 0.31/0.47 reachableNodes:
% 0.31/0.47 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > ( set @ nat ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.31/0.47 plus_plus:
% 0.31/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.31/0.47 size_size:
% 0.31/0.47 !>[A: $tType] : ( A > nat ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Oord__class_OLeast,type,
% 0.31/0.47 ord_Least:
% 0.31/0.47 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.31/0.47 ord_less:
% 0.31/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/0.47 ord_less_eq:
% 0.31/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_Set_OCollect,type,
% 0.31/0.47 collect:
% 0.31/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_c_member,type,
% 0.31/0.47 member:
% 0.31/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_c,type,
% 0.31/0.47 c: ( product_prod @ nat @ nat ) > capacity ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_c_H,type,
% 0.31/0.47 c2: ( product_prod @ nat @ nat ) > a ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_p,type,
% 0.31/0.47 p: list @ ( product_prod @ nat @ nat ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_p1____,type,
% 0.31/0.47 p1: list @ ( product_prod @ nat @ nat ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_p1a____,type,
% 0.31/0.47 p1a: list @ ( product_prod @ nat @ nat ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_p2_H____,type,
% 0.31/0.47 p2: list @ ( product_prod @ nat @ nat ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_p2_Ha____,type,
% 0.31/0.47 p2_a: list @ ( product_prod @ nat @ nat ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_p_H,type,
% 0.31/0.47 p3: list @ ( product_prod @ nat @ nat ) ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_s,type,
% 0.31/0.47 s: nat ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_t,type,
% 0.31/0.47 t: nat ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_u____,type,
% 0.31/0.47 u: nat ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_ua____,type,
% 0.31/0.47 ua: nat ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_v____,type,
% 0.31/0.47 v: nat ).
% 0.31/0.47
% 0.31/0.47 thf(sy_v_va____,type,
% 0.31/0.47 va: nat ).
% 0.31/0.47
% 0.31/0.47 % Relevant facts (256)
% 0.31/0.47 thf(fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062,axiom,
% 0.31/0.47 ( ( min_dist @ capacity @ c @ s @ t )
% 0.31/0.47 = ( plus_plus @ nat @ ( min_dist @ capacity @ c @ s @ ua ) @ ( min_dist @ capacity @ c @ ua @ t ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>min_dist s t = min_dist s u + min_dist u t\<close>
% 0.31/0.47 thf(fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062,axiom,
% 0.31/0.47 ord_less @ nat @ ( min_dist @ capacity @ c @ s @ ua ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p1a ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>min_dist s u < length p1\<close>
% 0.31/0.47 thf(fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062,axiom,
% 0.31/0.47 ord_less_eq @ nat @ ( min_dist @ capacity @ c @ ua @ t ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2_a ) ).
% 0.31/0.47
% 0.31/0.47 % \<open>min_dist u t \<le> length p2'\<close>
% 0.31/0.47 thf(fact_3_nat__add__left__cancel__less,axiom,
% 0.31/0.47 ! [K: nat,M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.31/0.47 = ( ord_less @ nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_add_left_cancel_less
% 0.31/0.47 thf(fact_4_add__less__cancel__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [C: A,A2: A,B: A] :
% 0.31/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.31/0.47 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_less_cancel_left
% 0.31/0.47 thf(fact_5_add__less__cancel__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_less_cancel_right
% 0.31/0.47 thf(fact_6__C1_Oprems_C_I2_J,axiom,
% 0.31/0.47 isPath @ capacity @ c @ s @ p1a @ va ).
% 0.31/0.47
% 0.31/0.47 % "1.prems"(2)
% 0.31/0.47 thf(fact_7_SP,axiom,
% 0.31/0.47 isShortestPath @ capacity @ c @ s @ p @ t ).
% 0.31/0.47
% 0.31/0.47 % SP
% 0.31/0.47 thf(fact_8_min__dist__split_I2_J,axiom,
% 0.31/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ capacity @ c @ W @ D2 @ V )
% 0.31/0.47 => ( ( ( min_dist @ capacity @ c @ U @ V )
% 0.31/0.47 = ( plus_plus @ nat @ D1 @ D2 ) )
% 0.31/0.47 => ( ( min_dist @ capacity @ c @ W @ V )
% 0.31/0.47 = D2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_dist_split(2)
% 0.31/0.47 thf(fact_9_min__dist__split_I1_J,axiom,
% 0.31/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ capacity @ c @ W @ D2 @ V )
% 0.31/0.47 => ( ( ( min_dist @ capacity @ c @ U @ V )
% 0.31/0.47 = ( plus_plus @ nat @ D1 @ D2 ) )
% 0.31/0.47 => ( ( min_dist @ capacity @ c @ U @ W )
% 0.31/0.47 = D1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_dist_split(1)
% 0.31/0.47 thf(fact_10_min__dist__less,axiom,
% 0.31/0.47 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 0.31/0.47 ( ( connected @ capacity @ c @ Src @ V )
% 0.31/0.47 => ( ( ( min_dist @ capacity @ c @ Src @ V )
% 0.31/0.47 = D )
% 0.31/0.47 => ( ( ord_less @ nat @ D3 @ D )
% 0.31/0.47 => ? [V2: nat] :
% 0.31/0.47 ( ( connected @ capacity @ c @ Src @ V2 )
% 0.31/0.47 & ( ( min_dist @ capacity @ c @ Src @ V2 )
% 0.31/0.47 = D3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_dist_less
% 0.31/0.47 thf(fact_11_add__left__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel_semigroup_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/0.47 = ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_left_cancel
% 0.31/0.47 thf(fact_12_add__right__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel_semigroup_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.31/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/0.47 = ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_right_cancel
% 0.31/0.47 thf(fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062,axiom,
% 0.31/0.47 isPath @ capacity @ c @ ua @ p2_a @ t ).
% 0.31/0.47
% 0.31/0.47 % \<open>isPath u p2' t\<close>
% 0.31/0.47 thf(fact_14_dist__trans,axiom,
% 0.31/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ capacity @ c @ W @ D2 @ V )
% 0.31/0.47 => ( dist @ capacity @ c @ U @ ( plus_plus @ nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_trans
% 0.31/0.47 thf(fact_15_connected__def,axiom,
% 0.31/0.47 ! [U: nat,V: nat] :
% 0.31/0.47 ( ( connected @ capacity @ c @ U @ V )
% 0.31/0.47 = ( ? [P: list @ ( product_prod @ nat @ nat )] : ( isPath @ capacity @ c @ U @ P @ V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % connected_def
% 0.31/0.47 thf(fact_16_shortestPath__is__path,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ capacity @ c @ U @ P2 @ V )
% 0.31/0.47 => ( isPath @ capacity @ c @ U @ P2 @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % shortestPath_is_path
% 0.31/0.47 thf(fact_17_connected__by__dist,axiom,
% 0.31/0.47 ! [V: nat,V3: nat] :
% 0.31/0.47 ( ( connected @ capacity @ c @ V @ V3 )
% 0.31/0.47 = ( ? [D4: nat] : ( dist @ capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % connected_by_dist
% 0.31/0.47 thf(fact_18_obtain__shortest__path,axiom,
% 0.31/0.47 ! [U: nat,V: nat] :
% 0.31/0.47 ( ( connected @ capacity @ c @ U @ V )
% 0.31/0.47 => ~ ! [P3: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ~ ( isShortestPath @ capacity @ c @ U @ P3 @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % obtain_shortest_path
% 0.31/0.47 thf(fact_19_min__dist__le,axiom,
% 0.31/0.47 ! [Src: nat,V: nat,D3: nat] :
% 0.31/0.47 ( ( connected @ capacity @ c @ Src @ V )
% 0.31/0.47 => ( ( ord_less_eq @ nat @ D3 @ ( min_dist @ capacity @ c @ Src @ V ) )
% 0.31/0.47 => ? [V2: nat] :
% 0.31/0.47 ( ( connected @ capacity @ c @ Src @ V2 )
% 0.31/0.47 & ( ( min_dist @ capacity @ c @ Src @ V2 )
% 0.31/0.47 = D3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_dist_le
% 0.31/0.47 thf(fact_20_min__dist__minD,axiom,
% 0.31/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ V @ D @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( min_dist @ capacity @ c @ V @ V3 ) @ D ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_dist_minD
% 0.31/0.47 thf(fact_21_min__distI__eq,axiom,
% 0.31/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ V @ D @ V3 )
% 0.31/0.47 => ( ! [D5: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ V @ D5 @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ D @ D5 ) )
% 0.31/0.47 => ( ( min_dist @ capacity @ c @ V @ V3 )
% 0.31/0.47 = D ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_distI_eq
% 0.31/0.47 thf(fact_22_isPath__distD,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isPath @ capacity @ c @ U @ P2 @ V )
% 0.31/0.47 => ( dist @ capacity @ c @ U @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % isPath_distD
% 0.31/0.47 thf(fact_23_dist__def,axiom,
% 0.31/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ V @ D @ V3 )
% 0.31/0.47 = ( ? [P: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ( ( isPath @ capacity @ c @ V @ P @ V3 )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 0.31/0.47 = D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dist_def
% 0.31/0.47 thf(fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062,axiom,
% 0.31/0.47 isPath @ capacity @ c @ s @ p1 @ v ).
% 0.31/0.47
% 0.31/0.47 % \<open>isPath s p1__ v__\<close>
% 0.31/0.47 thf(fact_25_min__dist__is__dist,axiom,
% 0.31/0.47 ! [V: nat,V3: nat] :
% 0.31/0.47 ( ( connected @ capacity @ c @ V @ V3 )
% 0.31/0.47 => ( dist @ capacity @ c @ V @ ( min_dist @ capacity @ c @ V @ V3 ) @ V3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_dist_is_dist
% 0.31/0.47 thf(fact_26_isShortestPath__def,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ capacity @ c @ U @ P2 @ V )
% 0.31/0.47 = ( ( isPath @ capacity @ c @ U @ P2 @ V )
% 0.31/0.47 & ! [P4: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ( ( isPath @ capacity @ c @ U @ P4 @ V )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isShortestPath_def
% 0.31/0.47 thf(fact_27_min__distI2,axiom,
% 0.31/0.47 ! [V: nat,V3: nat,Q: nat > $o] :
% 0.31/0.47 ( ( connected @ capacity @ c @ V @ V3 )
% 0.31/0.47 => ( ! [D6: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ V @ D6 @ V3 )
% 0.31/0.47 => ( ! [D7: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ V @ D7 @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ D6 @ D7 ) )
% 0.31/0.47 => ( Q @ D6 ) ) )
% 0.31/0.47 => ( Q @ ( min_dist @ capacity @ c @ V @ V3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_distI2
% 0.31/0.47 thf(fact_28_isShortestPath__min__dist__def,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ capacity @ c @ U @ P2 @ V )
% 0.31/0.47 = ( ( isPath @ capacity @ c @ U @ P2 @ V )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 )
% 0.31/0.47 = ( min_dist @ capacity @ c @ U @ V ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isShortestPath_min_dist_def
% 0.31/0.47 thf(fact_29__092_060open_062connected_As_Au_092_060close_062,axiom,
% 0.31/0.47 connected @ capacity @ c @ s @ ua ).
% 0.31/0.47
% 0.31/0.47 % \<open>connected s u\<close>
% 0.31/0.47 thf(fact_30_add__le__cancel__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_cancel_right
% 0.31/0.47 thf(fact_31_add__le__cancel__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [C: A,A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.31/0.47 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_cancel_left
% 0.31/0.47 thf(fact_32_nat__add__left__cancel__le,axiom,
% 0.31/0.47 ! [K: nat,M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.31/0.47 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_add_left_cancel_le
% 0.31/0.47 thf(fact_33_P1,axiom,
% 0.31/0.47 isPath @ capacity @ c @ s @ p1a @ va ).
% 0.31/0.47
% 0.31/0.47 % P1
% 0.31/0.47 thf(fact_34_connected__refl,axiom,
% 0.31/0.47 ! [V: nat] : ( connected @ capacity @ c @ V @ V ) ).
% 0.31/0.47
% 0.31/0.47 % connected_refl
% 0.31/0.47 thf(fact_35_connected__distI,axiom,
% 0.31/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ capacity @ c @ V @ D @ V3 )
% 0.31/0.47 => ( connected @ capacity @ c @ V @ V3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % connected_distI
% 0.31/0.47 thf(fact_36_le__refl,axiom,
% 0.31/0.47 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.31/0.47
% 0.31/0.47 % le_refl
% 0.31/0.47 thf(fact_37_le__trans,axiom,
% 0.31/0.47 ! [I: nat,J: nat,K: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.47 => ( ( ord_less_eq @ nat @ J @ K )
% 0.31/0.47 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_trans
% 0.31/0.47 thf(fact_38_eq__imp__le,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( M = N )
% 0.31/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_imp_le
% 0.31/0.47 thf(fact_39_le__antisym,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/0.47 => ( ( ord_less_eq @ nat @ N @ M )
% 0.31/0.47 => ( M = N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_antisym
% 0.31/0.47 thf(fact_40_nat__le__linear,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/0.47 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_le_linear
% 0.31/0.47 thf(fact_41_Nat_Oex__has__greatest__nat,axiom,
% 0.31/0.47 ! [P5: nat > $o,K: nat,B: nat] :
% 0.31/0.47 ( ( P5 @ K )
% 0.31/0.47 => ( ! [Y: nat] :
% 0.31/0.47 ( ( P5 @ Y )
% 0.31/0.47 => ( ord_less_eq @ nat @ Y @ B ) )
% 0.31/0.47 => ? [X: nat] :
% 0.31/0.47 ( ( P5 @ X )
% 0.31/0.47 & ! [Y2: nat] :
% 0.31/0.47 ( ( P5 @ Y2 )
% 0.31/0.47 => ( ord_less_eq @ nat @ Y2 @ X ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Nat.ex_has_greatest_nat
% 0.31/0.47 thf(fact_42_add__le__imp__le__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_imp_le_right
% 0.31/0.47 thf(fact_43_add__le__imp__le__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [C: A,A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_imp_le_left
% 0.31/0.47 thf(fact_44_le__iff__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( canoni770627133id_add @ A )
% 0.31/0.47 => ( ( ord_less_eq @ A )
% 0.31/0.47 = ( ^ [A3: A,B2: A] :
% 0.31/0.47 ? [C2: A] :
% 0.31/0.47 ( B2
% 0.31/0.47 = ( plus_plus @ A @ A3 @ C2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_iff_add
% 0.31/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/0.47 ! [A: $tType,A2: A,P5: A > $o] :
% 0.31/0.47 ( ( member @ A @ A2 @ ( collect @ A @ P5 ) )
% 0.31/0.47 = ( P5 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % mem_Collect_eq
% 0.31/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/0.47 ! [A: $tType,A4: set @ A] :
% 0.31/0.47 ( ( collect @ A
% 0.31/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 0.31/0.47 = A4 ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mem_eq
% 0.31/0.47 thf(fact_47_Collect__cong,axiom,
% 0.31/0.47 ! [A: $tType,P5: A > $o,Q: A > $o] :
% 0.31/0.47 ( ! [X: A] :
% 0.31/0.47 ( ( P5 @ X )
% 0.31/0.47 = ( Q @ X ) )
% 0.31/0.47 => ( ( collect @ A @ P5 )
% 0.31/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_cong
% 0.31/0.47 thf(fact_48_ext,axiom,
% 0.31/0.47 ! [B3: $tType,A: $tType,F: A > B3,G: A > B3] :
% 0.31/0.47 ( ! [X: A] :
% 0.31/0.47 ( ( F @ X )
% 0.31/0.47 = ( G @ X ) )
% 0.31/0.47 => ( F = G ) ) ).
% 0.31/0.47
% 0.31/0.47 % ext
% 0.31/0.47 thf(fact_49_add__right__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_right_mono
% 0.31/0.47 thf(fact_50_less__eqE,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( canoni770627133id_add @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ~ ! [C3: A] :
% 0.31/0.47 ( B
% 0.31/0.47 != ( plus_plus @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_eqE
% 0.31/0.47 thf(fact_51_add__left__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_left_mono
% 0.31/0.47 thf(fact_52_add__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ C @ D )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono
% 0.31/0.47 thf(fact_53_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/0.47 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_semiring(1)
% 0.31/0.47 thf(fact_54_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( I = J )
% 0.31/0.47 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_semiring(2)
% 0.31/0.47 thf(fact_55_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/0.47 & ( K = L ) )
% 0.31/0.47 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_semiring(3)
% 0.31/0.47 thf(fact_56_less__mono__imp__le__mono,axiom,
% 0.31/0.47 ! [F: nat > nat,I: nat,J: nat] :
% 0.31/0.47 ( ! [I2: nat,J2: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ I2 @ J2 )
% 0.31/0.47 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.31/0.47 => ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_mono_imp_le_mono
% 0.31/0.47 thf(fact_57_le__neq__implies__less,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/0.47 => ( ( M != N )
% 0.31/0.47 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_neq_implies_less
% 0.31/0.47 thf(fact_58_less__or__eq__imp__le,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ( ord_less @ nat @ M @ N )
% 0.31/0.47 | ( M = N ) )
% 0.31/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_or_eq_imp_le
% 0.31/0.47 thf(fact_59_le__eq__less__or__eq,axiom,
% 0.31/0.47 ( ( ord_less_eq @ nat )
% 0.31/0.47 = ( ^ [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ M2 @ N2 )
% 0.31/0.47 | ( M2 = N2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_eq_less_or_eq
% 0.31/0.47 thf(fact_60_less__imp__le__nat,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ M @ N )
% 0.31/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_le_nat
% 0.31/0.47 thf(fact_61_nat__less__le,axiom,
% 0.31/0.47 ( ( ord_less @ nat )
% 0.31/0.47 = ( ^ [M2: nat,N2: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ M2 @ N2 )
% 0.31/0.47 & ( M2 != N2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_less_le
% 0.31/0.47 thf(fact_62_nat__le__iff__add,axiom,
% 0.31/0.47 ( ( ord_less_eq @ nat )
% 0.31/0.47 = ( ^ [M2: nat,N2: nat] :
% 0.31/0.47 ? [K2: nat] :
% 0.31/0.47 ( N2
% 0.31/0.47 = ( plus_plus @ nat @ M2 @ K2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_le_iff_add
% 0.31/0.47 thf(fact_63_trans__le__add2,axiom,
% 0.31/0.47 ! [I: nat,J: nat,M: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.47 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trans_le_add2
% 0.31/0.47 thf(fact_64_trans__le__add1,axiom,
% 0.31/0.47 ! [I: nat,J: nat,M: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.47 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trans_le_add1
% 0.31/0.47 thf(fact_65_add__le__mono1,axiom,
% 0.31/0.47 ! [I: nat,J: nat,K: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_mono1
% 0.31/0.47 thf(fact_66_add__le__mono,axiom,
% 0.31/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/0.47 => ( ( ord_less_eq @ nat @ K @ L )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_mono
% 0.31/0.47 thf(fact_67_le__Suc__ex,axiom,
% 0.31/0.47 ! [K: nat,L: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ K @ L )
% 0.31/0.47 => ? [N3: nat] :
% 0.31/0.47 ( L
% 0.31/0.47 = ( plus_plus @ nat @ K @ N3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_Suc_ex
% 0.31/0.47 thf(fact_68_add__leD2,axiom,
% 0.31/0.47 ! [M: nat,K: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.31/0.47 => ( ord_less_eq @ nat @ K @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_leD2
% 0.31/0.47 thf(fact_69_add__leD1,axiom,
% 0.31/0.47 ! [M: nat,K: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.31/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_leD1
% 0.31/0.47 thf(fact_70_le__add2,axiom,
% 0.31/0.47 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_add2
% 0.31/0.47 thf(fact_71_le__add1,axiom,
% 0.31/0.47 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_add1
% 0.31/0.47 thf(fact_72_add__leE,axiom,
% 0.31/0.47 ! [M: nat,K: nat,N: nat] :
% 0.31/0.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.31/0.47 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 0.31/0.47 => ~ ( ord_less_eq @ nat @ K @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_leE
% 0.31/0.47 thf(fact_73_measure__induct__rule,axiom,
% 0.31/0.47 ! [B3: $tType,A: $tType] :
% 0.31/0.47 ( ( wellorder @ B3 )
% 0.31/0.47 => ! [F: A > B3,P5: A > $o,A2: A] :
% 0.31/0.47 ( ! [X: A] :
% 0.31/0.47 ( ! [Y2: A] :
% 0.31/0.47 ( ( ord_less @ B3 @ ( F @ Y2 ) @ ( F @ X ) )
% 0.31/0.47 => ( P5 @ Y2 ) )
% 0.31/0.47 => ( P5 @ X ) )
% 0.31/0.47 => ( P5 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % measure_induct_rule
% 0.31/0.47 thf(fact_74_measure__induct,axiom,
% 0.31/0.47 ! [B3: $tType,A: $tType] :
% 0.31/0.47 ( ( wellorder @ B3 )
% 0.31/0.47 => ! [F: A > B3,P5: A > $o,A2: A] :
% 0.31/0.47 ( ! [X: A] :
% 0.31/0.47 ( ! [Y2: A] :
% 0.31/0.47 ( ( ord_less @ B3 @ ( F @ Y2 ) @ ( F @ X ) )
% 0.31/0.47 => ( P5 @ Y2 ) )
% 0.31/0.47 => ( P5 @ X ) )
% 0.31/0.47 => ( P5 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % measure_induct
% 0.31/0.47 thf(fact_75_add__right__imp__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel_semigroup_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.31/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/0.47 => ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_right_imp_eq
% 0.31/0.47 thf(fact_76_add__left__imp__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( cancel_semigroup_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/0.47 => ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_left_imp_eq
% 0.31/0.47 thf(fact_77_add_Oleft__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.left_commute
% 0.31/0.47 thf(fact_78_add_Ocommute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_add @ A )
% 0.31/0.47 => ( ( plus_plus @ A )
% 0.31/0.47 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.commute
% 0.31/0.47 thf(fact_79_add_Oright__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ B @ A2 )
% 0.31/0.47 = ( plus_plus @ A @ C @ A2 ) )
% 0.31/0.47 = ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.right_cancel
% 0.31/0.47 thf(fact_80_add_Oleft__cancel,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( group_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ( plus_plus @ A @ A2 @ B )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ C ) )
% 0.31/0.47 = ( B = C ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.left_cancel
% 0.31/0.47 thf(fact_81_add_Oassoc,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( semigroup_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add.assoc
% 0.31/0.47 thf(fact_82_group__cancel_Oadd2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_monoid_add @ A )
% 0.31/0.47 => ! [B4: A,K: A,B: A,A2: A] :
% 0.31/0.47 ( ( B4
% 0.31/0.47 = ( plus_plus @ A @ K @ B ) )
% 0.31/0.47 => ( ( plus_plus @ A @ A2 @ B4 )
% 0.31/0.47 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % group_cancel.add2
% 0.31/0.47 thf(fact_83_group__cancel_Oadd1,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( comm_monoid_add @ A )
% 0.31/0.47 => ! [A4: A,K: A,A2: A,B: A] :
% 0.31/0.47 ( ( A4
% 0.31/0.47 = ( plus_plus @ A @ K @ A2 ) )
% 0.31/0.47 => ( ( plus_plus @ A @ A4 @ B )
% 0.31/0.47 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % group_cancel.add1
% 0.31/0.47 thf(fact_84_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere779506340up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( I = J )
% 0.31/0.47 & ( K = L ) )
% 0.31/0.47 => ( ( plus_plus @ A @ I @ K )
% 0.31/0.47 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_semiring(4)
% 0.31/0.47 thf(fact_85_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ab_semigroup_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 0.31/0.47 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.31/0.47 thf(fact_86_infinite__descent__measure,axiom,
% 0.31/0.47 ! [A: $tType,P5: A > $o,V4: A > nat,X3: A] :
% 0.31/0.47 ( ! [X: A] :
% 0.31/0.47 ( ~ ( P5 @ X )
% 0.31/0.47 => ? [Y2: A] :
% 0.31/0.47 ( ( ord_less @ nat @ ( V4 @ Y2 ) @ ( V4 @ X ) )
% 0.31/0.47 & ~ ( P5 @ Y2 ) ) )
% 0.31/0.47 => ( P5 @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % infinite_descent_measure
% 0.31/0.47 thf(fact_87_linorder__neqE__nat,axiom,
% 0.31/0.47 ! [X3: nat,Y3: nat] :
% 0.31/0.47 ( ( X3 != Y3 )
% 0.31/0.47 => ( ~ ( ord_less @ nat @ X3 @ Y3 )
% 0.31/0.47 => ( ord_less @ nat @ Y3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_neqE_nat
% 0.31/0.47 thf(fact_88_infinite__descent,axiom,
% 0.31/0.47 ! [P5: nat > $o,N: nat] :
% 0.31/0.47 ( ! [N3: nat] :
% 0.31/0.47 ( ~ ( P5 @ N3 )
% 0.31/0.47 => ? [M3: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ M3 @ N3 )
% 0.31/0.47 & ~ ( P5 @ M3 ) ) )
% 0.31/0.47 => ( P5 @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % infinite_descent
% 0.31/0.47 thf(fact_89_nat__less__induct,axiom,
% 0.31/0.47 ! [P5: nat > $o,N: nat] :
% 0.31/0.47 ( ! [N3: nat] :
% 0.31/0.47 ( ! [M3: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ M3 @ N3 )
% 0.31/0.47 => ( P5 @ M3 ) )
% 0.31/0.47 => ( P5 @ N3 ) )
% 0.31/0.47 => ( P5 @ N ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_less_induct
% 0.31/0.47 thf(fact_90_less__irrefl__nat,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ~ ( ord_less @ nat @ N @ N ) ).
% 0.31/0.47
% 0.31/0.47 % less_irrefl_nat
% 0.31/0.47 thf(fact_91_less__not__refl3,axiom,
% 0.31/0.47 ! [S: nat,T: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ S @ T )
% 0.31/0.47 => ( S != T ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_refl3
% 0.31/0.47 thf(fact_92_less__not__refl2,axiom,
% 0.31/0.47 ! [N: nat,M: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ N @ M )
% 0.31/0.47 => ( M != N ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_refl2
% 0.31/0.47 thf(fact_93_less__not__refl,axiom,
% 0.31/0.47 ! [N: nat] :
% 0.31/0.47 ~ ( ord_less @ nat @ N @ N ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_refl
% 0.31/0.47 thf(fact_94_nat__neq__iff,axiom,
% 0.31/0.47 ! [M: nat,N: nat] :
% 0.31/0.47 ( ( M != N )
% 0.31/0.47 = ( ( ord_less @ nat @ M @ N )
% 0.31/0.47 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % nat_neq_iff
% 0.31/0.47 thf(fact_95_size__neq__size__imp__neq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( size @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ( size_size @ A @ X3 )
% 0.31/0.47 != ( size_size @ A @ Y3 ) )
% 0.31/0.47 => ( X3 != Y3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % size_neq_size_imp_neq
% 0.31/0.47 thf(fact_96_add__less__le__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ C @ D )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_less_le_mono
% 0.31/0.47 thf(fact_97_add__le__less__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less @ A @ C @ D )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_le_less_mono
% 0.31/0.47 thf(fact_98_add__mono__thms__linordered__field_I3_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( ord_less @ A @ I @ J )
% 0.31/0.47 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_field(3)
% 0.31/0.47 thf(fact_99_add__mono__thms__linordered__field_I4_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/0.47 & ( ord_less @ A @ K @ L ) )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_field(4)
% 0.31/0.47 thf(fact_100_mono__nat__linear__lb,axiom,
% 0.31/0.47 ! [F: nat > nat,M: nat,K: nat] :
% 0.31/0.47 ( ! [M4: nat,N3: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ M4 @ N3 )
% 0.31/0.47 => ( ord_less @ nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus @ nat @ M @ K ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mono_nat_linear_lb
% 0.31/0.47 thf(fact_101_add__less__imp__less__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [A2: A,C: A,B: A] :
% 0.31/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 0.31/0.47 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_less_imp_less_right
% 0.31/0.47 thf(fact_102_add__less__imp__less__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere236663937imp_le @ A )
% 0.31/0.47 => ! [C: A,A2: A,B: A] :
% 0.31/0.47 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 0.31/0.47 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_less_imp_less_left
% 0.31/0.47 thf(fact_103_add__strict__right__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_strict_right_mono
% 0.31/0.47 thf(fact_104_add__strict__left__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_strict_left_mono
% 0.31/0.47 thf(fact_105_add__strict__mono,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( strict2144017051up_add @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A,D: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less @ A @ C @ D )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_strict_mono
% 0.31/0.47 thf(fact_106_add__mono__thms__linordered__field_I1_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( ord_less @ A @ I @ J )
% 0.31/0.47 & ( K = L ) )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_field(1)
% 0.31/0.47 thf(fact_107_add__mono__thms__linordered__field_I2_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( I = J )
% 0.31/0.47 & ( ord_less @ A @ K @ L ) )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_field(2)
% 0.31/0.47 thf(fact_108_add__mono__thms__linordered__field_I5_J,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ordere223160158up_add @ A )
% 0.31/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.31/0.47 ( ( ( ord_less @ A @ I @ J )
% 0.31/0.47 & ( ord_less @ A @ K @ L ) )
% 0.31/0.47 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_mono_thms_linordered_field(5)
% 0.31/0.47 thf(fact_109_less__add__eq__less,axiom,
% 0.31/0.47 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ K @ L )
% 0.31/0.47 => ( ( ( plus_plus @ nat @ M @ L )
% 0.31/0.47 = ( plus_plus @ nat @ K @ N ) )
% 0.31/0.47 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_add_eq_less
% 0.31/0.47 thf(fact_110_trans__less__add2,axiom,
% 0.31/0.47 ! [I: nat,J: nat,M: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ I @ J )
% 0.31/0.47 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trans_less_add2
% 0.31/0.47 thf(fact_111_trans__less__add1,axiom,
% 0.31/0.47 ! [I: nat,J: nat,M: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ I @ J )
% 0.31/0.47 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % trans_less_add1
% 0.31/0.47 thf(fact_112_add__less__mono1,axiom,
% 0.31/0.47 ! [I: nat,J: nat,K: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ I @ J )
% 0.31/0.47 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_less_mono1
% 0.31/0.47 thf(fact_113_not__add__less2,axiom,
% 0.31/0.47 ! [J: nat,I: nat] :
% 0.31/0.47 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 0.31/0.47
% 0.31/0.47 % not_add_less2
% 0.31/0.47 thf(fact_114_not__add__less1,axiom,
% 0.31/0.47 ! [I: nat,J: nat] :
% 0.31/0.47 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 0.31/0.47
% 0.31/0.47 % not_add_less1
% 0.31/0.47 thf(fact_115_add__less__mono,axiom,
% 0.31/0.47 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ I @ J )
% 0.31/0.47 => ( ( ord_less @ nat @ K @ L )
% 0.31/0.47 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_less_mono
% 0.31/0.47 thf(fact_116_add__lessD1,axiom,
% 0.31/0.47 ! [I: nat,J: nat,K: nat] :
% 0.31/0.47 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 0.31/0.47 => ( ord_less @ nat @ I @ K ) ) ).
% 0.31/0.47
% 0.31/0.47 % add_lessD1
% 0.31/0.47 thf(fact_117_reachableNodes__def,axiom,
% 0.31/0.47 ! [U: nat] :
% 0.31/0.47 ( ( reachableNodes @ capacity @ c @ U )
% 0.31/0.47 = ( collect @ nat @ ( connected @ capacity @ c @ U ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % reachableNodes_def
% 0.31/0.47 thf(fact_118_min__dist__def,axiom,
% 0.31/0.47 ! [V: nat,V3: nat] :
% 0.31/0.47 ( ( min_dist @ capacity @ c @ V @ V3 )
% 0.31/0.47 = ( ord_Least @ nat
% 0.31/0.47 @ ^ [D4: nat] : ( dist @ capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_dist_def
% 0.31/0.47 thf(fact_119_Graph_OisShortestPath__min__dist__def,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( isShortestPath @ Capacity )
% 0.31/0.47 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat,P: list @ ( product_prod @ nat @ nat ),V5: nat] :
% 0.31/0.47 ( ( isPath @ Capacity @ C2 @ U2 @ P @ V5 )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 0.31/0.47 = ( min_dist @ Capacity @ C2 @ U2 @ V5 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.isShortestPath_min_dist_def
% 0.31/0.47 thf(fact_120_Graph_OisShortestPath__def,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( isShortestPath @ Capacity )
% 0.31/0.47 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat,P: list @ ( product_prod @ nat @ nat ),V5: nat] :
% 0.31/0.47 ( ( isPath @ Capacity @ C2 @ U2 @ P @ V5 )
% 0.31/0.47 & ! [P4: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ( ( isPath @ Capacity @ C2 @ U2 @ P4 @ V5 )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P4 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.isShortestPath_def
% 0.31/0.47 thf(fact_121_Graph_Omin__distI2,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,V3: nat,Q: nat > $o] :
% 0.31/0.47 ( ( connected @ Capacity @ C @ V @ V3 )
% 0.31/0.47 => ( ! [D6: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ V @ D6 @ V3 )
% 0.31/0.47 => ( ! [D7: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ V @ D7 @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ D6 @ D7 ) )
% 0.31/0.47 => ( Q @ D6 ) ) )
% 0.31/0.47 => ( Q @ ( min_dist @ Capacity @ C @ V @ V3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_distI2
% 0.31/0.47 thf(fact_122_isShortestPath__alt,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ capacity @ c @ U @ P2 @ V )
% 0.31/0.47 = ( ( isSimplePath @ capacity @ c @ U @ P2 @ V )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 )
% 0.31/0.47 = ( min_dist @ capacity @ c @ U @ V ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % isShortestPath_alt
% 0.31/0.47 thf(fact_123_Graph_Odist__def,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( dist @ Capacity )
% 0.31/0.47 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,V5: nat,D4: nat,V6: nat] :
% 0.31/0.47 ? [P: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ( ( isPath @ Capacity @ C2 @ V5 @ P @ V6 )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 0.31/0.47 = D4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.dist_def
% 0.31/0.47 thf(fact_124_Graph_OisPath__distD,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isPath @ Capacity @ C @ U @ P2 @ V )
% 0.31/0.47 => ( dist @ Capacity @ C @ U @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.isPath_distD
% 0.31/0.47 thf(fact_125_Graph_Omin__dist__is__dist,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,V3: nat] :
% 0.31/0.47 ( ( connected @ Capacity @ C @ V @ V3 )
% 0.31/0.47 => ( dist @ Capacity @ C @ V @ ( min_dist @ Capacity @ C @ V @ V3 ) @ V3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_dist_is_dist
% 0.31/0.47 thf(fact_126_Graph_Omin__dist__split_I1_J,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ Capacity @ C @ W @ D2 @ V )
% 0.31/0.47 => ( ( ( min_dist @ Capacity @ C @ U @ V )
% 0.31/0.47 = ( plus_plus @ nat @ D1 @ D2 ) )
% 0.31/0.47 => ( ( min_dist @ Capacity @ C @ U @ W )
% 0.31/0.47 = D1 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_dist_split(1)
% 0.31/0.47 thf(fact_127_isSPath__pathLE,axiom,
% 0.31/0.47 ! [S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 0.31/0.47 ( ( isPath @ capacity @ c @ S @ P2 @ T )
% 0.31/0.47 => ? [P6: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ capacity @ c @ S @ P6 @ T ) ) ).
% 0.31/0.47
% 0.31/0.47 % isSPath_pathLE
% 0.31/0.47 thf(fact_128_shortestPath__is__simple,axiom,
% 0.31/0.47 ! [S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 0.31/0.47 ( ( isShortestPath @ capacity @ c @ S @ P2 @ T )
% 0.31/0.47 => ( isSimplePath @ capacity @ c @ S @ P2 @ T ) ) ).
% 0.31/0.47
% 0.31/0.47 % shortestPath_is_simple
% 0.31/0.47 thf(fact_129_Graph_OreachableNodes_Ocong,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( reachableNodes @ Capacity )
% 0.31/0.47 = ( reachableNodes @ Capacity ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.reachableNodes.cong
% 0.31/0.47 thf(fact_130_Graph_OisSimplePath_Ocong,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( isSimplePath @ Capacity )
% 0.31/0.47 = ( isSimplePath @ Capacity ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.isSimplePath.cong
% 0.31/0.47 thf(fact_131_Graph_OisSPath__pathLE,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 0.31/0.47 ( ( isPath @ Capacity @ C @ S @ P2 @ T )
% 0.31/0.47 => ? [P6: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ Capacity @ C @ S @ P6 @ T ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.isSPath_pathLE
% 0.31/0.47 thf(fact_132_Graph_OshortestPath__is__simple,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 0.31/0.47 ( ( isShortestPath @ Capacity @ C @ S @ P2 @ T )
% 0.31/0.47 => ( isSimplePath @ Capacity @ C @ S @ P2 @ T ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.shortestPath_is_simple
% 0.31/0.47 thf(fact_133_Graph_OreachableNodes__def,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( reachableNodes @ Capacity )
% 0.31/0.47 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat] : ( collect @ nat @ ( connected @ Capacity @ C2 @ U2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.reachableNodes_def
% 0.31/0.47 thf(fact_134_Graph_Omin__dist__def,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( min_dist @ Capacity )
% 0.31/0.47 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,V5: nat,V6: nat] :
% 0.31/0.47 ( ord_Least @ nat
% 0.31/0.47 @ ^ [D4: nat] : ( dist @ Capacity @ C2 @ V5 @ D4 @ V6 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_dist_def
% 0.31/0.47 thf(fact_135_Graph_OisShortestPath__alt,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( isShortestPath @ Capacity )
% 0.31/0.47 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat,P: list @ ( product_prod @ nat @ nat ),V5: nat] :
% 0.31/0.47 ( ( isSimplePath @ Capacity @ C2 @ U2 @ P @ V5 )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 0.31/0.47 = ( min_dist @ Capacity @ C2 @ U2 @ V5 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.isShortestPath_alt
% 0.31/0.47 thf(fact_136_Graph_OisPath_Ocong,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( isPath @ Capacity )
% 0.31/0.47 = ( isPath @ Capacity ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.isPath.cong
% 0.31/0.47 thf(fact_137_Graph_Omin__dist_Ocong,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( min_dist @ Capacity )
% 0.31/0.47 = ( min_dist @ Capacity ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_dist.cong
% 0.31/0.47 thf(fact_138_Graph_Oconnected__refl,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat] : ( connected @ Capacity @ C @ V @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.connected_refl
% 0.31/0.47 thf(fact_139_Graph_Oconnected_Ocong,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( connected @ Capacity )
% 0.31/0.47 = ( connected @ Capacity ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.connected.cong
% 0.31/0.47 thf(fact_140_Graph_Odist_Ocong,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( dist @ Capacity )
% 0.31/0.47 = ( dist @ Capacity ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.dist.cong
% 0.31/0.47 thf(fact_141_Graph_OisShortestPath_Ocong,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( isShortestPath @ Capacity )
% 0.31/0.47 = ( isShortestPath @ Capacity ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.isShortestPath.cong
% 0.31/0.47 thf(fact_142_Graph_Odist__trans,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ Capacity @ C @ W @ D2 @ V )
% 0.31/0.47 => ( dist @ Capacity @ C @ U @ ( plus_plus @ nat @ D1 @ D2 ) @ V ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.dist_trans
% 0.31/0.47 thf(fact_143_Graph_Oconnected__def,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( connected @ Capacity )
% 0.31/0.47 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat,V5: nat] :
% 0.31/0.47 ? [P: list @ ( product_prod @ nat @ nat )] : ( isPath @ Capacity @ C2 @ U2 @ P @ V5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.connected_def
% 0.31/0.47 thf(fact_144_Graph_OshortestPath__is__path,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ Capacity @ C @ U @ P2 @ V )
% 0.31/0.47 => ( isPath @ Capacity @ C @ U @ P2 @ V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.shortestPath_is_path
% 0.31/0.47 thf(fact_145_Graph_Oconnected__by__dist,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ( ( connected @ Capacity )
% 0.31/0.47 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,V5: nat,V6: nat] :
% 0.31/0.47 ? [D4: nat] : ( dist @ Capacity @ C2 @ V5 @ D4 @ V6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.connected_by_dist
% 0.31/0.47 thf(fact_146_Graph_Oconnected__distI,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ V @ D @ V3 )
% 0.31/0.47 => ( connected @ Capacity @ C @ V @ V3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.connected_distI
% 0.31/0.47 thf(fact_147_Graph_Oobtain__shortest__path,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,V: nat] :
% 0.31/0.47 ( ( connected @ Capacity @ C @ U @ V )
% 0.31/0.47 => ~ ! [P3: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ~ ( isShortestPath @ Capacity @ C @ U @ P3 @ V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.obtain_shortest_path
% 0.31/0.47 thf(fact_148_Graph_Omin__dist__less,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,Src: nat,V: nat,D: nat,D3: nat] :
% 0.31/0.47 ( ( connected @ Capacity @ C @ Src @ V )
% 0.31/0.47 => ( ( ( min_dist @ Capacity @ C @ Src @ V )
% 0.31/0.47 = D )
% 0.31/0.47 => ( ( ord_less @ nat @ D3 @ D )
% 0.31/0.47 => ? [V2: nat] :
% 0.31/0.47 ( ( connected @ Capacity @ C @ Src @ V2 )
% 0.31/0.47 & ( ( min_dist @ Capacity @ C @ Src @ V2 )
% 0.31/0.47 = D3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_dist_less
% 0.31/0.47 thf(fact_149_Graph_Omin__dist__le,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,Src: nat,V: nat,D3: nat] :
% 0.31/0.47 ( ( connected @ Capacity @ C @ Src @ V )
% 0.31/0.47 => ( ( ord_less_eq @ nat @ D3 @ ( min_dist @ Capacity @ C @ Src @ V ) )
% 0.31/0.47 => ? [V2: nat] :
% 0.31/0.47 ( ( connected @ Capacity @ C @ Src @ V2 )
% 0.31/0.47 & ( ( min_dist @ Capacity @ C @ Src @ V2 )
% 0.31/0.47 = D3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_dist_le
% 0.31/0.47 thf(fact_150_Graph_Omin__distI__eq,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ V @ D @ V3 )
% 0.31/0.47 => ( ! [D5: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ V @ D5 @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ D @ D5 ) )
% 0.31/0.47 => ( ( min_dist @ Capacity @ C @ V @ V3 )
% 0.31/0.47 = D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_distI_eq
% 0.31/0.47 thf(fact_151_Graph_Omin__dist__minD,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ V @ D @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( min_dist @ Capacity @ C @ V @ V3 ) @ D ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_dist_minD
% 0.31/0.47 thf(fact_152_Graph_Omin__dist__split_I2_J,axiom,
% 0.31/0.47 ! [Capacity: $tType] :
% 0.31/0.47 ( ( linordered_idom @ Capacity )
% 0.31/0.47 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ Capacity @ C @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ Capacity @ C @ W @ D2 @ V )
% 0.31/0.47 => ( ( ( min_dist @ Capacity @ C @ U @ V )
% 0.31/0.47 = ( plus_plus @ nat @ D1 @ D2 ) )
% 0.31/0.47 => ( ( min_dist @ Capacity @ C @ W @ V )
% 0.31/0.47 = D2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Graph.min_dist_split(2)
% 0.31/0.47 thf(fact_153__C1_Oprems_C_I3_J,axiom,
% 0.31/0.47 isPath @ a @ c2 @ ua @ p2_a @ t ).
% 0.31/0.47
% 0.31/0.47 % "1.prems"(3)
% 0.31/0.47 thf(fact_154_ex__has__greatest__nat__lemma,axiom,
% 0.31/0.47 ! [A: $tType,P5: A > $o,K: A,F: A > nat,N: nat] :
% 0.31/0.47 ( ( P5 @ K )
% 0.31/0.47 => ( ! [X: A] :
% 0.31/0.47 ( ( P5 @ X )
% 0.31/0.47 => ? [Y2: A] :
% 0.31/0.47 ( ( P5 @ Y2 )
% 0.31/0.47 & ~ ( ord_less_eq @ nat @ ( F @ Y2 ) @ ( F @ X ) ) ) )
% 0.31/0.47 => ? [Y: A] :
% 0.31/0.47 ( ( P5 @ Y )
% 0.31/0.47 & ~ ( ord_less @ nat @ ( F @ Y ) @ ( plus_plus @ nat @ ( F @ K ) @ N ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_has_greatest_nat_lemma
% 0.31/0.47 thf(fact_155_not__less__Least,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ! [K: A,P5: A > $o] :
% 0.31/0.47 ( ( ord_less @ A @ K @ ( ord_Least @ A @ P5 ) )
% 0.31/0.47 => ~ ( P5 @ K ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_Least
% 0.31/0.47 thf(fact_156_Least__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ! [P5: A > $o,K: A] :
% 0.31/0.47 ( ( P5 @ K )
% 0.31/0.47 => ( ord_less_eq @ A @ ( ord_Least @ A @ P5 ) @ K ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Least_le
% 0.31/0.47 thf(fact_157_g_H_Oconnected__by__dist,axiom,
% 0.31/0.47 ! [V: nat,V3: nat] :
% 0.31/0.47 ( ( connected @ a @ c2 @ V @ V3 )
% 0.31/0.47 = ( ? [D4: nat] : ( dist @ a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.connected_by_dist
% 0.31/0.47 thf(fact_158_g_H_Omin__dist__is__dist,axiom,
% 0.31/0.47 ! [V: nat,V3: nat] :
% 0.31/0.47 ( ( connected @ a @ c2 @ V @ V3 )
% 0.31/0.47 => ( dist @ a @ c2 @ V @ ( min_dist @ a @ c2 @ V @ V3 ) @ V3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_dist_is_dist
% 0.31/0.47 thf(fact_159_g_H_Oobtain__shortest__path,axiom,
% 0.31/0.47 ! [U: nat,V: nat] :
% 0.31/0.47 ( ( connected @ a @ c2 @ U @ V )
% 0.31/0.47 => ~ ! [P3: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ~ ( isShortestPath @ a @ c2 @ U @ P3 @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.obtain_shortest_path
% 0.31/0.47 thf(fact_160_g_H_OshortestPath__is__simple,axiom,
% 0.31/0.47 ! [S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 0.31/0.47 ( ( isShortestPath @ a @ c2 @ S @ P2 @ T )
% 0.31/0.47 => ( isSimplePath @ a @ c2 @ S @ P2 @ T ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.shortestPath_is_simple
% 0.31/0.47 thf(fact_161_g_H_OreachableNodes__def,axiom,
% 0.31/0.47 ! [U: nat] :
% 0.31/0.47 ( ( reachableNodes @ a @ c2 @ U )
% 0.31/0.47 = ( collect @ nat @ ( connected @ a @ c2 @ U ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.reachableNodes_def
% 0.31/0.47 thf(fact_162_g_H_Omin__dist__less,axiom,
% 0.31/0.47 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 0.31/0.47 ( ( connected @ a @ c2 @ Src @ V )
% 0.31/0.47 => ( ( ( min_dist @ a @ c2 @ Src @ V )
% 0.31/0.47 = D )
% 0.31/0.47 => ( ( ord_less @ nat @ D3 @ D )
% 0.31/0.47 => ? [V2: nat] :
% 0.31/0.47 ( ( connected @ a @ c2 @ Src @ V2 )
% 0.31/0.47 & ( ( min_dist @ a @ c2 @ Src @ V2 )
% 0.31/0.47 = D3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_dist_less
% 0.31/0.47 thf(fact_163_g_H_Omin__distI2,axiom,
% 0.31/0.47 ! [V: nat,V3: nat,Q: nat > $o] :
% 0.31/0.47 ( ( connected @ a @ c2 @ V @ V3 )
% 0.31/0.47 => ( ! [D6: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ V @ D6 @ V3 )
% 0.31/0.47 => ( ! [D7: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ V @ D7 @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ D6 @ D7 ) )
% 0.31/0.47 => ( Q @ D6 ) ) )
% 0.31/0.47 => ( Q @ ( min_dist @ a @ c2 @ V @ V3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_distI2
% 0.31/0.47 thf(fact_164_g_H_Omin__distI__eq,axiom,
% 0.31/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ V @ D @ V3 )
% 0.31/0.47 => ( ! [D5: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ V @ D5 @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ D @ D5 ) )
% 0.31/0.47 => ( ( min_dist @ a @ c2 @ V @ V3 )
% 0.31/0.47 = D ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_distI_eq
% 0.31/0.47 thf(fact_165_g_H_Omin__dist__le,axiom,
% 0.31/0.47 ! [Src: nat,V: nat,D3: nat] :
% 0.31/0.47 ( ( connected @ a @ c2 @ Src @ V )
% 0.31/0.47 => ( ( ord_less_eq @ nat @ D3 @ ( min_dist @ a @ c2 @ Src @ V ) )
% 0.31/0.47 => ? [V2: nat] :
% 0.31/0.47 ( ( connected @ a @ c2 @ Src @ V2 )
% 0.31/0.47 & ( ( min_dist @ a @ c2 @ Src @ V2 )
% 0.31/0.47 = D3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_dist_le
% 0.31/0.47 thf(fact_166_g_H_Omin__dist__minD,axiom,
% 0.31/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ V @ D @ V3 )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( min_dist @ a @ c2 @ V @ V3 ) @ D ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_dist_minD
% 0.31/0.47 thf(fact_167_g_H_Omin__dist__split_I2_J,axiom,
% 0.31/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ a @ c2 @ W @ D2 @ V )
% 0.31/0.47 => ( ( ( min_dist @ a @ c2 @ U @ V )
% 0.31/0.47 = ( plus_plus @ nat @ D1 @ D2 ) )
% 0.31/0.47 => ( ( min_dist @ a @ c2 @ W @ V )
% 0.31/0.47 = D2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_dist_split(2)
% 0.31/0.47 thf(fact_168_g_H_Omin__dist__split_I1_J,axiom,
% 0.31/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ a @ c2 @ W @ D2 @ V )
% 0.31/0.47 => ( ( ( min_dist @ a @ c2 @ U @ V )
% 0.31/0.47 = ( plus_plus @ nat @ D1 @ D2 ) )
% 0.31/0.47 => ( ( min_dist @ a @ c2 @ U @ W )
% 0.31/0.47 = D1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_dist_split(1)
% 0.31/0.47 thf(fact_169_g_H_Odist__trans,axiom,
% 0.31/0.47 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ U @ D1 @ W )
% 0.31/0.47 => ( ( dist @ a @ c2 @ W @ D2 @ V )
% 0.31/0.47 => ( dist @ a @ c2 @ U @ ( plus_plus @ nat @ D1 @ D2 ) @ V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.dist_trans
% 0.31/0.47 thf(fact_170_g_H_Oconnected__def,axiom,
% 0.31/0.47 ! [U: nat,V: nat] :
% 0.31/0.47 ( ( connected @ a @ c2 @ U @ V )
% 0.31/0.47 = ( ? [P: list @ ( product_prod @ nat @ nat )] : ( isPath @ a @ c2 @ U @ P @ V ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.connected_def
% 0.31/0.47 thf(fact_171_g_H_OisSPath__pathLE,axiom,
% 0.31/0.47 ! [S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 0.31/0.47 ( ( isPath @ a @ c2 @ S @ P2 @ T )
% 0.31/0.47 => ? [P6: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ a @ c2 @ S @ P6 @ T ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.isSPath_pathLE
% 0.31/0.47 thf(fact_172_g_H_OshortestPath__is__path,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ a @ c2 @ U @ P2 @ V )
% 0.31/0.47 => ( isPath @ a @ c2 @ U @ P2 @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.shortestPath_is_path
% 0.31/0.47 thf(fact_173_g_H_OisShortestPath__alt,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ a @ c2 @ U @ P2 @ V )
% 0.31/0.47 = ( ( isSimplePath @ a @ c2 @ U @ P2 @ V )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 )
% 0.31/0.47 = ( min_dist @ a @ c2 @ U @ V ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.isShortestPath_alt
% 0.31/0.47 thf(fact_174_g_H_Omin__dist__def,axiom,
% 0.31/0.47 ! [V: nat,V3: nat] :
% 0.31/0.47 ( ( min_dist @ a @ c2 @ V @ V3 )
% 0.31/0.47 = ( ord_Least @ nat
% 0.31/0.47 @ ^ [D4: nat] : ( dist @ a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.min_dist_def
% 0.31/0.47 thf(fact_175_g_H_Odist__def,axiom,
% 0.31/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ V @ D @ V3 )
% 0.31/0.47 = ( ? [P: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ( ( isPath @ a @ c2 @ V @ P @ V3 )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 0.31/0.47 = D ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.dist_def
% 0.31/0.47 thf(fact_176_g_H_OisPath__distD,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isPath @ a @ c2 @ U @ P2 @ V )
% 0.31/0.47 => ( dist @ a @ c2 @ U @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ V ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.isPath_distD
% 0.31/0.47 thf(fact_177_g_H_OisShortestPath__min__dist__def,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ a @ c2 @ U @ P2 @ V )
% 0.31/0.47 = ( ( isPath @ a @ c2 @ U @ P2 @ V )
% 0.31/0.47 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 )
% 0.31/0.47 = ( min_dist @ a @ c2 @ U @ V ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.isShortestPath_min_dist_def
% 0.31/0.47 thf(fact_178_order__refl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_refl
% 0.31/0.47 thf(fact_179_g_H_OisShortestPath__def,axiom,
% 0.31/0.47 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 0.31/0.47 ( ( isShortestPath @ a @ c2 @ U @ P2 @ V )
% 0.31/0.47 = ( ( isPath @ a @ c2 @ U @ P2 @ V )
% 0.31/0.47 & ! [P4: list @ ( product_prod @ nat @ nat )] :
% 0.31/0.47 ( ( isPath @ a @ c2 @ U @ P4 @ V )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.isShortestPath_def
% 0.31/0.47 thf(fact_180_assms_I5_J,axiom,
% 0.31/0.47 isPath @ a @ c2 @ s @ p3 @ t ).
% 0.31/0.47
% 0.31/0.47 % assms(5)
% 0.31/0.47 thf(fact_181__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062,axiom,
% 0.31/0.47 isPath @ a @ c2 @ u @ p2 @ t ).
% 0.31/0.47
% 0.31/0.47 % \<open>g'.isPath u__ p2'__ t\<close>
% 0.31/0.47 thf(fact_182_g_H_Oconnected__distI,axiom,
% 0.31/0.47 ! [V: nat,D: nat,V3: nat] :
% 0.31/0.47 ( ( dist @ a @ c2 @ V @ D @ V3 )
% 0.31/0.47 => ( connected @ a @ c2 @ V @ V3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % g'.connected_distI
% 0.31/0.47 thf(fact_183_g_H_Oconnected__refl,axiom,
% 0.31/0.47 ! [V: nat] : ( connected @ a @ c2 @ V @ V ) ).
% 0.31/0.47
% 0.31/0.47 % g'.connected_refl
% 0.31/0.47 thf(fact_184_P2_H,axiom,
% 0.31/0.47 isPath @ a @ c2 @ ua @ p2_a @ t ).
% 0.31/0.47
% 0.31/0.47 % P2'
% 0.31/0.47 thf(fact_185_le__funD,axiom,
% 0.31/0.47 ! [B3: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B3 )
% 0.31/0.47 => ! [F: A > B3,G: A > B3,X3: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 0.31/0.47 => ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funD
% 0.31/0.47 thf(fact_186_le__funE,axiom,
% 0.31/0.47 ! [B3: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B3 )
% 0.31/0.47 => ! [F: A > B3,G: A > B3,X3: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 0.31/0.47 => ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funE
% 0.31/0.47 thf(fact_187_le__funI,axiom,
% 0.31/0.47 ! [B3: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B3 )
% 0.31/0.47 => ! [F: A > B3,G: A > B3] :
% 0.31/0.47 ( ! [X: A] : ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) )
% 0.31/0.47 => ( ord_less_eq @ ( A > B3 ) @ F @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funI
% 0.31/0.47 thf(fact_188_le__fun__def,axiom,
% 0.31/0.47 ! [B3: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ ( A > B3 ) )
% 0.31/0.47 = ( ^ [F2: A > B3,G2: A > B3] :
% 0.31/0.47 ! [X2: A] : ( ord_less_eq @ B3 @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_fun_def
% 0.31/0.47 thf(fact_189_order__subst1,axiom,
% 0.31/0.47 ! [A: $tType,B3: $tType] :
% 0.31/0.47 ( ( ( order @ B3 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B ) )
% 0.31/0.47 => ( ( ord_less_eq @ B3 @ B @ C )
% 0.31/0.47 => ( ! [X: B3,Y: B3] :
% 0.31/0.47 ( ( ord_less_eq @ B3 @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst1
% 0.31/0.47 thf(fact_190_order__subst2,axiom,
% 0.31/0.47 ! [A: $tType,C4: $tType] :
% 0.31/0.47 ( ( ( order @ C4 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,B: A,F: A > C4,C: C4] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ C4 @ ( F @ B ) @ C )
% 0.31/0.47 => ( ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ C4 @ ( F @ X ) @ ( F @ Y ) ) )
% 0.31/0.47 => ( ord_less_eq @ C4 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst2
% 0.31/0.47 thf(fact_191_ord__eq__le__subst,axiom,
% 0.31/0.47 ! [A: $tType,B3: $tType] :
% 0.31/0.47 ( ( ( ord @ B3 )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( F @ B ) )
% 0.31/0.47 => ( ( ord_less_eq @ B3 @ B @ C )
% 0.31/0.47 => ( ! [X: B3,Y: B3] :
% 0.31/0.47 ( ( ord_less_eq @ B3 @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_subst
% 0.31/0.47 thf(fact_192_ord__le__eq__subst,axiom,
% 0.31/0.47 ! [A: $tType,B3: $tType] :
% 0.31/0.47 ( ( ( ord @ B3 )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A2: A,B: A,F: A > B3,C: B3] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ( F @ B )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( F @ Y ) ) )
% 0.31/0.47 => ( ord_less_eq @ B3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_subst
% 0.31/0.47 thf(fact_193_eq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.31/0.47 = ( ^ [X2: A,Y5: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X2 @ Y5 )
% 0.31/0.47 & ( ord_less_eq @ A @ Y5 @ X2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_iff
% 0.31/0.47 thf(fact_194_antisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.31/0.47 => ( X3 = Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym
% 0.31/0.47 thf(fact_195_linear,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.31/0.47 | ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linear
% 0.31/0.47 thf(fact_196_eq__refl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( X3 = Y3 )
% 0.31/0.47 => ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_refl
% 0.31/0.47 thf(fact_197_le__cases,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ~ ( ord_less_eq @ A @ X3 @ Y3 )
% 0.31/0.47 => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_cases
% 0.31/0.47 thf(fact_198_order_Otrans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B @ C )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.trans
% 0.31/0.47 thf(fact_199_le__cases3,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A,Z2: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Y3 @ X3 ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 0.31/0.47 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_cases3
% 0.31/0.47 thf(fact_200_antisym__conv,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [Y3: A,X3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.31/0.47 = ( X3 = Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv
% 0.31/0.47 thf(fact_201_order__class_Oorder_Oeq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.31/0.47 = ( ^ [A3: A,B2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.31/0.47 & ( ord_less_eq @ A @ B2 @ A3 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.eq_iff
% 0.31/0.47 thf(fact_202_ord__eq__le__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( A2 = B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B @ C )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_trans
% 0.31/0.47 thf(fact_203_ord__le__eq__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( B = C )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_trans
% 0.31/0.47 thf(fact_204_order__class_Oorder_Oantisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.47 => ( A2 = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.antisym
% 0.31/0.47 thf(fact_205_order__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A,Z2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.31/0.47 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_trans
% 0.31/0.47 thf(fact_206_dual__order_Orefl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.refl
% 0.31/0.47 thf(fact_207_linorder__wlog,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [P5: A > A > $o,A2: A,B: A] :
% 0.31/0.47 ( ! [A5: A,B5: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A5 @ B5 )
% 0.31/0.47 => ( P5 @ A5 @ B5 ) )
% 0.31/0.47 => ( ! [A5: A,B5: A] :
% 0.31/0.47 ( ( P5 @ B5 @ A5 )
% 0.31/0.47 => ( P5 @ A5 @ B5 ) )
% 0.31/0.47 => ( P5 @ A2 @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_wlog
% 0.31/0.47 thf(fact_208_dual__order_Otrans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ C @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.trans
% 0.31/0.47 thf(fact_209_dual__order_Oeq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.31/0.47 = ( ^ [A3: A,B2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.31/0.47 & ( ord_less_eq @ A @ A3 @ B2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.eq_iff
% 0.31/0.47 thf(fact_210_dual__order_Oantisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B: A,A2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B @ A2 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( A2 = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.antisym
% 0.31/0.47 thf(fact_211_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B: A,A2: A] :
% 0.31/0.47 ( ( ord_less @ A @ B @ A2 )
% 0.31/0.47 => ( A2 != B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_implies_not_eq
% 0.31/0.47 thf(fact_212_order_Ostrict__implies__not__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( A2 != B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_implies_not_eq
% 0.31/0.47 thf(fact_213_not__less__iff__gr__or__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ~ ( ord_less @ A @ X3 @ Y3 ) )
% 0.31/0.47 = ( ( ord_less @ A @ Y3 @ X3 )
% 0.31/0.47 | ( X3 = Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_less_iff_gr_or_eq
% 0.31/0.47 thf(fact_214_dual__order_Ostrict__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B: A,A2: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ B @ A2 )
% 0.31/0.47 => ( ( ord_less @ A @ C @ B )
% 0.31/0.47 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_trans
% 0.31/0.47 thf(fact_215_linorder__less__wlog,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [P5: A > A > $o,A2: A,B: A] :
% 0.31/0.47 ( ! [A5: A,B5: A] :
% 0.31/0.47 ( ( ord_less @ A @ A5 @ B5 )
% 0.31/0.47 => ( P5 @ A5 @ B5 ) )
% 0.31/0.47 => ( ! [A5: A] : ( P5 @ A5 @ A5 )
% 0.31/0.47 => ( ! [A5: A,B5: A] :
% 0.31/0.47 ( ( P5 @ B5 @ A5 )
% 0.31/0.47 => ( P5 @ A5 @ B5 ) )
% 0.31/0.47 => ( P5 @ A2 @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_less_wlog
% 0.31/0.47 thf(fact_216_exists__least__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ( ( ^ [P7: A > $o] :
% 0.31/0.47 ? [X4: A] : ( P7 @ X4 ) )
% 0.31/0.47 = ( ^ [P8: A > $o] :
% 0.31/0.47 ? [N2: A] :
% 0.31/0.47 ( ( P8 @ N2 )
% 0.31/0.47 & ! [M2: A] :
% 0.31/0.47 ( ( ord_less @ A @ M2 @ N2 )
% 0.31/0.47 => ~ ( P8 @ M2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % exists_least_iff
% 0.31/0.47 thf(fact_217_less__imp__not__less,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ~ ( ord_less @ A @ Y3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_less
% 0.31/0.47 thf(fact_218_order_Ostrict__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less @ A @ B @ C )
% 0.31/0.47 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_trans
% 0.31/0.47 thf(fact_219_dual__order_Oirrefl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A] :
% 0.31/0.47 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.irrefl
% 0.31/0.47 thf(fact_220_linorder__cases,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ~ ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ( ( X3 != Y3 )
% 0.31/0.47 => ( ord_less @ A @ Y3 @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_cases
% 0.31/0.47 thf(fact_221_less__imp__triv,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A,P5: $o] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ( ( ord_less @ A @ Y3 @ X3 )
% 0.31/0.47 => P5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_triv
% 0.31/0.47 thf(fact_222_less__imp__not__eq2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ( Y3 != X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_eq2
% 0.31/0.47 thf(fact_223_antisym__conv3,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [Y3: A,X3: A] :
% 0.31/0.47 ( ~ ( ord_less @ A @ Y3 @ X3 )
% 0.31/0.47 => ( ( ~ ( ord_less @ A @ X3 @ Y3 ) )
% 0.31/0.47 = ( X3 = Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv3
% 0.31/0.47 thf(fact_224_less__induct,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ! [P5: A > $o,A2: A] :
% 0.31/0.47 ( ! [X: A] :
% 0.31/0.47 ( ! [Y2: A] :
% 0.31/0.47 ( ( ord_less @ A @ Y2 @ X )
% 0.31/0.47 => ( P5 @ Y2 ) )
% 0.31/0.47 => ( P5 @ X ) )
% 0.31/0.47 => ( P5 @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_induct
% 0.31/0.47 thf(fact_225_less__not__sym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ~ ( ord_less @ A @ Y3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_not_sym
% 0.31/0.47 thf(fact_226_less__imp__not__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ( X3 != Y3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_not_eq
% 0.31/0.47 thf(fact_227_dual__order_Oasym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B: A,A2: A] :
% 0.31/0.47 ( ( ord_less @ A @ B @ A2 )
% 0.31/0.47 => ~ ( ord_less @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.asym
% 0.31/0.47 thf(fact_228_ord__less__eq__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ( B = C )
% 0.31/0.47 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_less_eq_trans
% 0.31/0.47 thf(fact_229_ord__eq__less__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A2: A,B: A,C: A] :
% 0.31/0.47 ( ( A2 = B )
% 0.31/0.47 => ( ( ord_less @ A @ B @ C )
% 0.31/0.47 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_less_trans
% 0.31/0.47 thf(fact_230_less__irrefl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A] :
% 0.31/0.47 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_irrefl
% 0.31/0.47 thf(fact_231_less__linear,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 | ( X3 = Y3 )
% 0.31/0.47 | ( ord_less @ A @ Y3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_linear
% 0.31/0.47 thf(fact_232_less__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A,Z2: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ( ( ord_less @ A @ Y3 @ Z2 )
% 0.31/0.47 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_trans
% 0.31/0.47 thf(fact_233_less__asym_H,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ~ ( ord_less @ A @ B @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_asym'
% 0.31/0.47 thf(fact_234_less__asym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ~ ( ord_less @ A @ Y3 @ X3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_asym
% 0.31/0.47 thf(fact_235_less__imp__neq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ( X3 != Y3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % less_imp_neq
% 0.31/0.47 thf(fact_236_dense,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( dense_order @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ? [Z3: A] :
% 0.31/0.47 ( ( ord_less @ A @ X3 @ Z3 )
% 0.31/0.47 & ( ord_less @ A @ Z3 @ Y3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dense
% 0.31/0.47 thf(fact_237_order_Oasym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ~ ( ord_less @ A @ B @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.asym
% 0.31/0.47 thf(fact_238_neq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( X3 != Y3 )
% 0.31/0.47 = ( ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 | ( ord_less @ A @ Y3 @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_iff
% 0.31/0.47 thf(fact_239_neqE,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X3: A,Y3: A] :
% 0.31/0.47 ( ( X3 != Y3 )
% 0.31/0.47 => ( ~ ( ord_less @ A @ X3 @ Y3 )
% 0.31/0.47 => ( ord_less @ A @ Y3 @ X3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neqE
% 0.31/0.47 thf(fact_240_gt__ex,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( no_top @ A )
% 0.31/0.47 => ! [X3: A] :
% 0.31/0.47 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 0.31/0.47
% 0.31/0.47 % gt_ex
% 0.31/0.47 thf(fact_241_lt__ex,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( no_bot @ A )
% 0.31/0.47 => ! [X3: A] :
% 0.31/0.47 ? [Y: A] : ( ord_less @ A @ Y @ X3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % lt_ex
% 0.31/0.47 thf(fact_242_order__less__subst2,axiom,
% 0.31/0.47 ! [A: $tType,C4: $tType] :
% 0.31/0.47 ( ( ( order @ C4 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,B: A,F: A > C4,C: C4] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ( ord_less @ C4 @ ( F @ B ) @ C )
% 0.31/0.47 => ( ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ord_less @ C4 @ ( F @ X ) @ ( F @ Y ) ) )
% 0.31/0.47 => ( ord_less @ C4 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_subst2
% 0.31/0.47 thf(fact_243_order__less__subst1,axiom,
% 0.31/0.47 ! [A: $tType,B3: $tType] :
% 0.31/0.47 ( ( ( order @ B3 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ ( F @ B ) )
% 0.31/0.47 => ( ( ord_less @ B3 @ B @ C )
% 0.31/0.47 => ( ! [X: B3,Y: B3] :
% 0.31/0.47 ( ( ord_less @ B3 @ X @ Y )
% 0.31/0.47 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y ) ) )
% 0.31/0.47 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_less_subst1
% 0.31/0.47 thf(fact_244_ord__less__eq__subst,axiom,
% 0.31/0.47 ! [A: $tType,B3: $tType] :
% 0.31/0.47 ( ( ( ord @ B3 )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A2: A,B: A,F: A > B3,C: B3] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ( ( F @ B )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less @ A @ X @ Y )
% 0.31/0.47 => ( ord_less @ B3 @ ( F @ X ) @ ( F @ Y ) ) )
% 0.31/0.47 => ( ord_less @ B3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_less_eq_subst
% 0.31/0.47 thf(fact_245_ord__eq__less__subst,axiom,
% 0.31/0.47 ! [A: $tType,B3: $tType] :
% 0.31/0.47 ( ( ( ord @ B3 )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 0.31/0.47 ( ( A2
% 0.31/0.47 = ( F @ B ) )
% 0.31/0.47 => ( ( ord_less @ B3 @ B @ C )
% 0.31/0.47 => ( ! [X: B3,Y: B3] :
% 0.31/0.47 ( ( ord_less @ B3 @ X @ Y )
% 0.31/0.47 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y ) ) )
% 0.31/0.47 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_less_subst
% 0.31/0.47 thf(fact_246_ex__has__least__nat,axiom,
% 0.31/0.47 ! [A: $tType,P5: A > $o,K: A,M: A > nat] :
% 0.31/0.47 ( ( P5 @ K )
% 0.31/0.47 => ? [X: A] :
% 0.31/0.47 ( ( P5 @ X )
% 0.31/0.47 & ! [Y2: A] :
% 0.31/0.47 ( ( P5 @ Y2 )
% 0.31/0.47 => ( ord_less_eq @ nat @ ( M @ X ) @ ( M @ Y2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ex_has_least_nat
% 0.31/0.47 thf(fact_247_LeastI2,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ! [P5: A > $o,A2: A,Q: A > $o] :
% 0.31/0.47 ( ( P5 @ A2 )
% 0.31/0.47 => ( ! [X: A] :
% 0.31/0.47 ( ( P5 @ X )
% 0.31/0.47 => ( Q @ X ) )
% 0.31/0.47 => ( Q @ ( ord_Least @ A @ P5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LeastI2
% 0.31/0.47 thf(fact_248_LeastI__ex,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ! [P5: A > $o] :
% 0.31/0.47 ( ? [X_12: A] : ( P5 @ X_12 )
% 0.31/0.47 => ( P5 @ ( ord_Least @ A @ P5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LeastI_ex
% 0.31/0.47 thf(fact_249_LeastI2__ex,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ! [P5: A > $o,Q: A > $o] :
% 0.31/0.47 ( ? [X_12: A] : ( P5 @ X_12 )
% 0.31/0.47 => ( ! [X: A] :
% 0.31/0.47 ( ( P5 @ X )
% 0.31/0.47 => ( Q @ X ) )
% 0.31/0.47 => ( Q @ ( ord_Least @ A @ P5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LeastI2_ex
% 0.31/0.47 thf(fact_250_LeastI,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( wellorder @ A )
% 0.31/0.47 => ! [P5: A > $o,K: A] :
% 0.31/0.47 ( ( P5 @ K )
% 0.31/0.47 => ( P5 @ ( ord_Least @ A @ P5 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LeastI
% 0.31/0.47 thf(fact_251_order_Onot__eq__order__implies__strict,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( A2 != B )
% 0.31/0.47 => ( ( ord_less_eq @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less @ A @ A2 @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.not_eq_order_implies_strict
% 0.31/0.47 thf(fact_252_dual__order_Ostrict__implies__order,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B: A,A2: A] :
% 0.31/0.47 ( ( ord_less @ A @ B @ A2 )
% 0.31/0.47 => ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_implies_order
% 0.31/0.47 thf(fact_253_dual__order_Ostrict__iff__order,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ord_less @ A )
% 0.31/0.47 = ( ^ [B2: A,A3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.31/0.47 & ( A3 != B2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.strict_iff_order
% 0.31/0.47 thf(fact_254_dual__order_Oorder__iff__strict,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ord_less_eq @ A )
% 0.31/0.47 = ( ^ [B2: A,A3: A] :
% 0.31/0.47 ( ( ord_less @ A @ B2 @ A3 )
% 0.31/0.47 | ( A3 = B2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.order_iff_strict
% 0.31/0.47 thf(fact_255_order_Ostrict__implies__order,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A2: A,B: A] :
% 0.31/0.47 ( ( ord_less @ A @ A2 @ B )
% 0.31/0.47 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.strict_implies_order
% 0.31/0.47
% 0.31/0.47 % Subclasses (14)
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___HOL_Otype,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( type @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Orderings_Oord,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( ord @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Orderings_Oorder,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( order @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Ogroup__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( group_add @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Orderings_Olinorder,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( linorder @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Orderings_Opreorder,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( preorder @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Osemigroup__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( semigroup_add @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( comm_monoid_add @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( ab_semigroup_add @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Ocancel__semigroup__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( cancel_semigroup_add @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( ordere779506340up_add @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( ordere236663937imp_le @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( ordere223160158up_add @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subcl_Rings_Olinordered__idom___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linordered_idom @ A )
% 0.31/0.47 => ( strict2144017051up_add @ A ) ) ).
% 0.31/0.47
% 0.31/0.47 % Type constructors (28)
% 0.31/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/0.47 ! [A6: $tType,A7: $tType] :
% 0.31/0.47 ( ( preorder @ A7 )
% 0.31/0.47 => ( preorder @ ( A6 > A7 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/0.47 ! [A6: $tType,A7: $tType] :
% 0.31/0.47 ( ( order @ A7 )
% 0.31/0.47 => ( order @ ( A6 > A7 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/0.47 ! [A6: $tType,A7: $tType] :
% 0.31/0.47 ( ( ord @ A7 )
% 0.31/0.47 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.31/0.47 strict2144017051up_add @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.31/0.47 ordere223160158up_add @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.31/0.47 ordere236663937imp_le @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.31/0.47 canoni770627133id_add @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.31/0.47 ordere779506340up_add @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.31/0.47 cancel_semigroup_add @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.31/0.47 ab_semigroup_add @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.31/0.47 comm_monoid_add @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.31/0.47 semigroup_add @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.31/0.47 wellorder @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.31/0.47 preorder @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.31/0.47 linorder @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.31/0.47 no_top @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.31/0.47 order @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.31/0.47 ord @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.31/0.47 size @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 0.31/0.47 ! [A6: $tType] : ( preorder @ ( set @ A6 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 0.31/0.47 ! [A6: $tType] : ( order @ ( set @ A6 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 0.31/0.47 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 0.31/0.47 preorder @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 0.31/0.47 linorder @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 0.31/0.47 order @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 0.31/0.47 ord @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_List_Olist___Nat_Osize_11,axiom,
% 0.31/0.47 ! [A6: $tType] : ( size @ ( list @ A6 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Product__Type_Oprod___Nat_Osize_12,axiom,
% 0.31/0.47 ! [A6: $tType,A7: $tType] : ( size @ ( product_prod @ A6 @ A7 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Free types (2)
% 0.31/0.47 thf(tfree_0,hypothesis,
% 0.31/0.47 linordered_idom @ capacity ).
% 0.31/0.47
% 0.31/0.47 thf(tfree_1,hypothesis,
% 0.31/0.47 linordered_idom @ a ).
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ord_less @ nat @ ( min_dist @ capacity @ c @ s @ t ) @ ( plus_plus @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p1a ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2_a ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.67/1.55 ---- Embedded in THF ---
% 2.67/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.67/1.55 %%% Generated on Tue Feb 24 08:24:24 EST 2026
% 2.67/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.67/1.55 %%% Logic specification used:
% 2.67/1.55 %%% thf(spec, logic, $$dhol).
% 2.67/1.55
% 2.67/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2DTF7288.p
% 2.67/1.55 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.67/1.55 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.67/1.55 thf(ty_tf_capacity, type, capacity: $tType).
% 2.67/1.55 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.67/1.55 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.67/1.55 thf(ty_tf_a, type, a: $tType).
% 2.67/1.55 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: ($o))).
% 2.67/1.55 thf(sy_c_Graph_OGraph_Oconnected, type, connected: (!> [Capacity:$tType]: (((((product_prod @ nat) @ nat) > Capacity) > (nat > (nat > $o)))))).
% 2.67/1.55 thf(sy_c_Graph_OGraph_Odist, type, dist: (!> [Capacity:$tType]: (((((product_prod @ nat) @ nat) > Capacity) > (nat > (nat > (nat > $o))))))).
% 2.67/1.55 thf(sy_c_Graph_OGraph_OisPath, type, isPath: (!> [Capacity:$tType]: (((((product_prod @ nat) @ nat) > Capacity) > (nat > ((list @ ((product_prod @ nat) @ nat)) > (nat > $o))))))).
% 2.67/1.55 thf(sy_c_Graph_OGraph_OisShortestPath, type, isShortestPath: (!> [Capacity:$tType]: (((((product_prod @ nat) @ nat) > Capacity) > (nat > ((list @ ((product_prod @ nat) @ nat)) > (nat > $o))))))).
% 2.67/1.55 thf(sy_c_Graph_OGraph_OisSimplePath, type, isSimplePath: (!> [Capacity:$tType]: (((((product_prod @ nat) @ nat) > Capacity) > (nat > ((list @ ((product_prod @ nat) @ nat)) > (nat > $o))))))).
% 2.67/1.55 thf(sy_c_Graph_OGraph_Omin__dist, type, min_dist: (!> [Capacity:$tType]: (((((product_prod @ nat) @ nat) > Capacity) > (nat > (nat > nat)))))).
% 2.67/1.55 thf(sy_c_Graph_OGraph_OreachableNodes, type, reachableNodes: (!> [Capacity:$tType]: (((((product_prod @ nat) @ nat) > Capacity) > (nat > (set @ nat)))))).
% 2.67/1.55 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.67/1.55 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.67/1.55 thf(sy_c_Orderings_Oord__class_OLeast, type, ord_Least: (!> [A:$tType]: (((A > $o) > A)))).
% 2.67/1.55 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.67/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.67/1.55 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.67/1.55 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.67/1.55 thf(sy_v_c, type, c: (((product_prod @ nat) @ nat) > capacity)).
% 2.67/1.55 thf(sy_v_c_H, type, c2: (((product_prod @ nat) @ nat) > a)).
% 2.67/1.55 thf(sy_v_p, type, p: (list @ ((product_prod @ nat) @ nat))).
% 2.67/1.55 thf(sy_v_p1____, type, p1: (list @ ((product_prod @ nat) @ nat))).
% 2.67/1.55 thf(sy_v_p1a____, type, p1a: (list @ ((product_prod @ nat) @ nat))).
% 2.67/1.55 thf(sy_v_p2_H____, type, p2: (list @ ((product_prod @ nat) @ nat))).
% 2.67/1.55 thf(sy_v_p2_Ha____, type, p2_a: (list @ ((product_prod @ nat) @ nat))).
% 2.67/1.55 thf(sy_v_p_H, type, p3: (list @ ((product_prod @ nat) @ nat))).
% 2.67/1.55 thf(sy_v_s, type, s: nat).
% 2.67/1.55 thf(sy_v_t, type, t: nat).
% 2.67/1.55 thf(sy_v_u____, type, u: nat).
% 2.67/1.55 thf(sy_v_ua____, type, ua: nat).
% 2.67/1.55 thf(sy_v_v____, type, v: nat).
% 2.67/1.55 thf(sy_v_va____, type, va: nat).
% 2.67/1.55 thf(fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062, axiom, (((((min_dist @ capacity) @ c) @ s) @ t) = (((plus_plus @ nat) @ ((((min_dist @ capacity) @ c) @ s) @ ua)) @ ((((min_dist @ capacity) @ c) @ ua) @ t)))).
% 2.67/1.55 thf(fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062, axiom, (((ord_less @ nat) @ ((((min_dist @ capacity) @ c) @ s) @ ua)) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ p1a))).
% 2.67/1.55 thf(fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062, axiom, (((ord_less_eq @ nat) @ ((((min_dist @ capacity) @ c) @ ua) @ t)) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ p2_a))).
% 2.67/1.55 thf(fact_3_nat__add__left__cancel__less, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.67/1.55 thf(fact_4_add__less__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) = (((ord_less @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(fact_5_add__less__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) = (((ord_less @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(fact_6__C1_Oprems_C_I2_J, axiom, (((((isPath @ capacity) @ c) @ s) @ p1a) @ va)).
% 2.67/1.55 thf(fact_7_SP, axiom, (((((isShortestPath @ capacity) @ c) @ s) @ p) @ t)).
% 2.67/1.55 thf(fact_8_min__dist__split_I2_J, axiom, (! [U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ capacity) @ c) @ U) @ D1) @ W) => ((((((dist @ capacity) @ c) @ W) @ D2) @ V) => ((((((min_dist @ capacity) @ c) @ U) @ V) = (((plus_plus @ nat) @ D1) @ D2)) => (((((min_dist @ capacity) @ c) @ W) @ V) = D2))))))).
% 2.67/1.55 thf(fact_9_min__dist__split_I1_J, axiom, (! [U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ capacity) @ c) @ U) @ D1) @ W) => ((((((dist @ capacity) @ c) @ W) @ D2) @ V) => ((((((min_dist @ capacity) @ c) @ U) @ V) = (((plus_plus @ nat) @ D1) @ D2)) => (((((min_dist @ capacity) @ c) @ U) @ W) = D1))))))).
% 2.67/1.55 thf(fact_10_min__dist__less, axiom, (! [Src:nat,V:nat,D:nat,D3:nat]: ((((((connected @ capacity) @ c) @ Src) @ V) => ((((((min_dist @ capacity) @ c) @ Src) @ V) = D) => ((((ord_less @ nat) @ D3) @ D) => (? [V2:nat]: ((((((connected @ capacity) @ c) @ Src) @ V2) & (((((min_dist @ capacity) @ c) @ Src) @ V2) = D3)))))))))).
% 2.67/1.55 thf(fact_11_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) = (B = C)))))))).
% 2.67/1.55 thf(fact_12_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B = C)))))))).
% 2.67/1.55 thf(fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062, axiom, (((((isPath @ capacity) @ c) @ ua) @ p2_a) @ t)).
% 2.67/1.55 thf(fact_14_dist__trans, axiom, (! [U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ capacity) @ c) @ U) @ D1) @ W) => ((((((dist @ capacity) @ c) @ W) @ D2) @ V) => (((((dist @ capacity) @ c) @ U) @ (((plus_plus @ nat) @ D1) @ D2)) @ V)))))).
% 2.67/1.55 thf(fact_15_connected__def, axiom, (! [U:nat,V:nat]: ((((((connected @ capacity) @ c) @ U) @ V) = (? [P:(list @ ((product_prod @ nat) @ nat))]: ((((((isPath @ capacity) @ c) @ U) @ P) @ V))))))).
% 2.67/1.55 thf(fact_16_shortestPath__is__path, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ capacity) @ c) @ U) @ P2) @ V) => (((((isPath @ capacity) @ c) @ U) @ P2) @ V))))).
% 2.67/1.55 thf(fact_17_connected__by__dist, axiom, (! [V:nat,V3:nat]: ((((((connected @ capacity) @ c) @ V) @ V3) = (? [D4:nat]: ((((((dist @ capacity) @ c) @ V) @ D4) @ V3))))))).
% 2.67/1.55 thf(fact_18_obtain__shortest__path, axiom, (! [U:nat,V:nat]: ((((((connected @ capacity) @ c) @ U) @ V) => (~ ((! [P3:(list @ ((product_prod @ nat) @ nat))]: ((~ ((((((isShortestPath @ capacity) @ c) @ U) @ P3) @ V))))))))))).
% 2.67/1.55 thf(fact_19_min__dist__le, axiom, (! [Src:nat,V:nat,D3:nat]: ((((((connected @ capacity) @ c) @ Src) @ V) => ((((ord_less_eq @ nat) @ D3) @ ((((min_dist @ capacity) @ c) @ Src) @ V)) => (? [V2:nat]: ((((((connected @ capacity) @ c) @ Src) @ V2) & (((((min_dist @ capacity) @ c) @ Src) @ V2) = D3))))))))).
% 2.67/1.55 thf(fact_20_min__dist__minD, axiom, (! [V:nat,D:nat,V3:nat]: (((((((dist @ capacity) @ c) @ V) @ D) @ V3) => (((ord_less_eq @ nat) @ ((((min_dist @ capacity) @ c) @ V) @ V3)) @ D))))).
% 2.67/1.55 thf(fact_21_min__distI__eq, axiom, (! [V:nat,D:nat,V3:nat]: (((((((dist @ capacity) @ c) @ V) @ D) @ V3) => ((! [D5:nat]: (((((((dist @ capacity) @ c) @ V) @ D5) @ V3) => (((ord_less_eq @ nat) @ D) @ D5)))) => (((((min_dist @ capacity) @ c) @ V) @ V3) = D)))))).
% 2.67/1.55 thf(fact_22_isPath__distD, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isPath @ capacity) @ c) @ U) @ P2) @ V) => (((((dist @ capacity) @ c) @ U) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2)) @ V))))).
% 2.67/1.55 thf(fact_23_dist__def, axiom, (! [V:nat,D:nat,V3:nat]: (((((((dist @ capacity) @ c) @ V) @ D) @ V3) = (? [P:(list @ ((product_prod @ nat) @ nat))]: (((((((isPath @ capacity) @ c) @ V) @ P) @ V3) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P) = D)))))))).
% 2.67/1.55 thf(fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062, axiom, (((((isPath @ capacity) @ c) @ s) @ p1) @ v)).
% 2.67/1.55 thf(fact_25_min__dist__is__dist, axiom, (! [V:nat,V3:nat]: ((((((connected @ capacity) @ c) @ V) @ V3) => (((((dist @ capacity) @ c) @ V) @ ((((min_dist @ capacity) @ c) @ V) @ V3)) @ V3))))).
% 2.67/1.55 thf(fact_26_isShortestPath__def, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ capacity) @ c) @ U) @ P2) @ V) = ((((((isPath @ capacity) @ c) @ U) @ P2) @ V) & (! [P4:(list @ ((product_prod @ nat) @ nat))]: (((((((isPath @ capacity) @ c) @ U) @ P4) @ V) => (((ord_less_eq @ nat) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2)) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P4)))))))))).
% 2.67/1.55 thf(fact_27_min__distI2, axiom, (! [V:nat,V3:nat,Q:(nat > $o)]: ((((((connected @ capacity) @ c) @ V) @ V3) => ((! [D6:nat]: (((((((dist @ capacity) @ c) @ V) @ D6) @ V3) => ((! [D7:nat]: (((((((dist @ capacity) @ c) @ V) @ D7) @ V3) => (((ord_less_eq @ nat) @ D6) @ D7)))) => (Q @ D6))))) => (Q @ ((((min_dist @ capacity) @ c) @ V) @ V3))))))).
% 2.67/1.55 thf(fact_28_isShortestPath__min__dist__def, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ capacity) @ c) @ U) @ P2) @ V) = ((((((isPath @ capacity) @ c) @ U) @ P2) @ V) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2) = ((((min_dist @ capacity) @ c) @ U) @ V))))))).
% 2.67/1.55 thf(fact_29__092_060open_062connected_As_Au_092_060close_062, axiom, ((((connected @ capacity) @ c) @ s) @ ua)).
% 2.67/1.55 thf(fact_30_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) = (((ord_less_eq @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(fact_31_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) = (((ord_less_eq @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(fact_32_nat__add__left__cancel__le, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.55 thf(fact_33_P1, axiom, (((((isPath @ capacity) @ c) @ s) @ p1a) @ va)).
% 2.67/1.55 thf(fact_34_connected__refl, axiom, (! [V:nat]: (((((connected @ capacity) @ c) @ V) @ V)))).
% 2.67/1.55 thf(fact_35_connected__distI, axiom, (! [V:nat,D:nat,V3:nat]: (((((((dist @ capacity) @ c) @ V) @ D) @ V3) => ((((connected @ capacity) @ c) @ V) @ V3))))).
% 2.67/1.55 thf(fact_36_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 2.67/1.55 thf(fact_37_le__trans, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I) @ K)))))).
% 2.67/1.55 thf(fact_38_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.55 thf(fact_39_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 2.67/1.55 thf(fact_40_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 2.67/1.55 thf(fact_41_Nat_Oex__has__greatest__nat, axiom, (! [P5:(nat > $o),K:nat,B:nat]: (((P5 @ K) => ((! [Y:nat]: (((P5 @ Y) => (((ord_less_eq @ nat) @ Y) @ B)))) => (? [X:nat]: (((P5 @ X) & (! [Y2:nat]: (((P5 @ Y2) => (((ord_less_eq @ nat) @ Y2) @ X)))))))))))).
% 2.67/1.55 thf(fact_42_add__le__imp__le__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(fact_43_add__le__imp__le__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(fact_44_le__iff__add, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => ((ord_less_eq @ A) = (^ [A3:A,B2:A]: ((? [C2:A]: ((B2 = (((plus_plus @ A) @ A3) @ C2))))))))))).
% 2.67/1.55 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P5:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P5)) = (P5 @ A2))))).
% 2.67/1.55 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A4)))) = A4)))).
% 2.67/1.55 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P5:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P5 @ X) = (Q @ X)))) => (((collect @ A) @ P5) = ((collect @ A) @ Q)))))).
% 2.67/1.55 thf(fact_48_ext, axiom, (! [B3:$tType,A:$tType,F:(A > B3),G:(A > B3)]: (((! [X:A]: (((F @ X) = (G @ X)))) => (F = G))))).
% 2.67/1.55 thf(fact_49_add__right__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.67/1.55 thf(fact_50_less__eqE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => (~ ((! [C3:A]: ((B != (((plus_plus @ A) @ A2) @ C3))))))))))))).
% 2.67/1.55 thf(fact_51_add__left__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B))))))))).
% 2.67/1.55 thf(fact_52_add__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ C) @ D) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 2.67/1.55 thf(fact_53_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_54_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_55_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (K = L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_56_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I:nat,J:nat]: (((! [I2:nat,J2:nat]: (((((ord_less @ nat) @ I2) @ J2) => (((ord_less @ nat) @ (F @ I2)) @ (F @ J2))))) => ((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (F @ I)) @ (F @ J))))))).
% 2.67/1.55 thf(fact_57_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 2.67/1.55 thf(fact_58_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.55 thf(fact_59_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M2:nat,N2:nat]: (((((ord_less @ nat) @ M2) @ N2) | (M2 = N2)))))).
% 2.67/1.55 thf(fact_60_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.55 thf(fact_61_nat__less__le, axiom, ((ord_less @ nat) = (^ [M2:nat,N2:nat]: (((((ord_less_eq @ nat) @ M2) @ N2) & (M2 != N2)))))).
% 2.67/1.55 thf(fact_62_nat__le__iff__add, axiom, ((ord_less_eq @ nat) = (^ [M2:nat,N2:nat]: ((? [K2:nat]: ((N2 = (((plus_plus @ nat) @ M2) @ K2)))))))).
% 2.67/1.55 thf(fact_63_trans__le__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.67/1.55 thf(fact_64_trans__le__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.67/1.55 thf(fact_65_add__le__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ K)))))).
% 2.67/1.55 thf(fact_66_add__le__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ K) @ L) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 2.67/1.55 thf(fact_67_le__Suc__ex, axiom, (! [K:nat,L:nat]: (((((ord_less_eq @ nat) @ K) @ L) => (? [N3:nat]: ((L = (((plus_plus @ nat) @ K) @ N3)))))))).
% 2.67/1.55 thf(fact_68_add__leD2, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (((ord_less_eq @ nat) @ K) @ N))))).
% 2.67/1.55 thf(fact_69_add__leD1, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.67/1.55 thf(fact_70_le__add2, axiom, (! [N:nat,M:nat]: ((((ord_less_eq @ nat) @ N) @ (((plus_plus @ nat) @ M) @ N))))).
% 2.67/1.55 thf(fact_71_le__add1, axiom, (! [N:nat,M:nat]: ((((ord_less_eq @ nat) @ N) @ (((plus_plus @ nat) @ N) @ M))))).
% 2.67/1.55 thf(fact_72_add__leE, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (~ (((((ord_less_eq @ nat) @ M) @ N) => (~ ((((ord_less_eq @ nat) @ K) @ N)))))))))).
% 2.67/1.55 thf(fact_73_measure__induct__rule, axiom, (! [B3:$tType,A:$tType]: (((wellorder @ B3) => (! [F:(A > B3),P5:(A > $o),A2:A]: (((! [X:A]: (((! [Y2:A]: (((((ord_less @ B3) @ (F @ Y2)) @ (F @ X)) => (P5 @ Y2)))) => (P5 @ X)))) => (P5 @ A2)))))))).
% 2.67/1.55 thf(fact_74_measure__induct, axiom, (! [B3:$tType,A:$tType]: (((wellorder @ B3) => (! [F:(A > B3),P5:(A > $o),A2:A]: (((! [X:A]: (((! [Y2:A]: (((((ord_less @ B3) @ (F @ Y2)) @ (F @ X)) => (P5 @ Y2)))) => (P5 @ X)))) => (P5 @ A2)))))))).
% 2.67/1.55 thf(fact_75_add__right__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) => (B = C)))))))).
% 2.67/1.55 thf(fact_76_add__left__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) => (B = C)))))))).
% 2.67/1.55 thf(fact_77_add_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [B:A,A2:A,C:A]: (((((plus_plus @ A) @ B) @ (((plus_plus @ A) @ A2) @ C)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.67/1.55 thf(fact_78_add_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => ((plus_plus @ A) = (^ [A3:A,B2:A]: ((((plus_plus @ A) @ B2) @ A3)))))))).
% 2.67/1.55 thf(fact_79_add_Oright__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [B:A,A2:A,C:A]: ((((((plus_plus @ A) @ B) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B = C)))))))).
% 2.67/1.55 thf(fact_80_add_Oleft__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B:A,C:A]: ((((((plus_plus @ A) @ A2) @ B) = (((plus_plus @ A) @ A2) @ C)) = (B = C)))))))).
% 2.67/1.55 thf(fact_81_add_Oassoc, axiom, (! [A:$tType]: (((semigroup_add @ A) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.67/1.55 thf(fact_82_group__cancel_Oadd2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [B4:A,K:A,B:A,A2:A]: (((B4 = (((plus_plus @ A) @ K) @ B)) => ((((plus_plus @ A) @ A2) @ B4) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B)))))))))).
% 2.67/1.55 thf(fact_83_group__cancel_Oadd1, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A4:A,K:A,A2:A,B:A]: (((A4 = (((plus_plus @ A) @ K) @ A2)) => ((((plus_plus @ A) @ A4) @ B) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B)))))))))).
% 2.67/1.55 thf(fact_84_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_85_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [A2:A,B:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.67/1.55 thf(fact_86_infinite__descent__measure, axiom, (! [A:$tType,P5:(A > $o),V4:(A > nat),X3:A]: (((! [X:A]: (((~ ((P5 @ X))) => (? [Y2:A]: (((((ord_less @ nat) @ (V4 @ Y2)) @ (V4 @ X)) & (~ ((P5 @ Y2))))))))) => (P5 @ X3))))).
% 2.67/1.55 thf(fact_87_linorder__neqE__nat, axiom, (! [X3:nat,Y3:nat]: (((X3 != Y3) => ((~ ((((ord_less @ nat) @ X3) @ Y3))) => (((ord_less @ nat) @ Y3) @ X3)))))).
% 2.67/1.55 thf(fact_88_infinite__descent, axiom, (! [P5:(nat > $o),N:nat]: (((! [N3:nat]: (((~ ((P5 @ N3))) => (? [M3:nat]: (((((ord_less @ nat) @ M3) @ N3) & (~ ((P5 @ M3))))))))) => (P5 @ N))))).
% 2.67/1.55 thf(fact_89_nat__less__induct, axiom, (! [P5:(nat > $o),N:nat]: (((! [N3:nat]: (((! [M3:nat]: (((((ord_less @ nat) @ M3) @ N3) => (P5 @ M3)))) => (P5 @ N3)))) => (P5 @ N))))).
% 2.67/1.55 thf(fact_90_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.67/1.55 thf(fact_91_less__not__refl3, axiom, (! [S:nat,T:nat]: (((((ord_less @ nat) @ S) @ T) => (S != T))))).
% 2.67/1.55 thf(fact_92_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.67/1.55 thf(fact_93_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.67/1.55 thf(fact_94_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.67/1.55 thf(fact_95_size__neq__size__imp__neq, axiom, (! [A:$tType]: (((size @ A) => (! [X3:A,Y3:A]: (((((size_size @ A) @ X3) != ((size_size @ A) @ Y3)) => (X3 != Y3)))))))).
% 2.67/1.55 thf(fact_96_add__less__le__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 2.67/1.55 thf(fact_97_add__le__less__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 2.67/1.55 thf(fact_98_add__mono__thms__linordered__field_I3_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_99_add__mono__thms__linordered__field_I4_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_100_mono__nat__linear__lb, axiom, (! [F:(nat > nat),M:nat,K:nat]: (((! [M4:nat,N3:nat]: (((((ord_less @ nat) @ M4) @ N3) => (((ord_less @ nat) @ (F @ M4)) @ (F @ N3))))) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (F @ M)) @ K)) @ (F @ (((plus_plus @ nat) @ M) @ K))))))).
% 2.67/1.55 thf(fact_101_add__less__imp__less__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C)) => (((ord_less @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(fact_102_add__less__imp__less__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C:A,A2:A,B:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B)) => (((ord_less @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(fact_103_add__strict__right__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ C))))))))).
% 2.67/1.55 thf(fact_104_add__strict__left__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B))))))))).
% 2.67/1.55 thf(fact_105_add__strict__mono, axiom, (! [A:$tType]: (((strict2144017051up_add @ A) => (! [A2:A,B:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B) @ D)))))))))).
% 2.67/1.55 thf(fact_106_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_107_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_108_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.67/1.55 thf(fact_109_less__add__eq__less, axiom, (! [K:nat,L:nat,M:nat,N:nat]: (((((ord_less @ nat) @ K) @ L) => (((((plus_plus @ nat) @ M) @ L) = (((plus_plus @ nat) @ K) @ N)) => (((ord_less @ nat) @ M) @ N)))))).
% 2.67/1.55 thf(fact_110_trans__less__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.67/1.55 thf(fact_111_trans__less__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.67/1.55 thf(fact_112_add__less__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ K)))))).
% 2.67/1.55 thf(fact_113_not__add__less2, axiom, (! [J:nat,I:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ J) @ I)) @ I)))))).
% 2.67/1.55 thf(fact_114_not__add__less1, axiom, (! [I:nat,J:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ I)))))).
% 2.67/1.55 thf(fact_115_add__less__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ K) @ L) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 2.67/1.55 thf(fact_116_add__lessD1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ K) => (((ord_less @ nat) @ I) @ K))))).
% 2.67/1.55 thf(fact_117_reachableNodes__def, axiom, (! [U:nat]: (((((reachableNodes @ capacity) @ c) @ U) = ((collect @ nat) @ (((connected @ capacity) @ c) @ U)))))).
% 2.67/1.55 thf(fact_118_min__dist__def, axiom, (! [V:nat,V3:nat]: ((((((min_dist @ capacity) @ c) @ V) @ V3) = ((ord_Least @ nat) @ (^ [D4:nat]: ((((((dist @ capacity) @ c) @ V) @ D4) @ V3)))))))).
% 2.67/1.55 thf(fact_119_Graph_OisShortestPath__min__dist__def, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((isShortestPath @ Capacity) = (^ [C2:(((product_prod @ nat) @ nat) > Capacity),U2:nat,P:(list @ ((product_prod @ nat) @ nat)),V5:nat]: (((((((isPath @ Capacity) @ C2) @ U2) @ P) @ V5) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P) = ((((min_dist @ Capacity) @ C2) @ U2) @ V5)))))))))).
% 2.67/1.55 thf(fact_120_Graph_OisShortestPath__def, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((isShortestPath @ Capacity) = (^ [C2:(((product_prod @ nat) @ nat) > Capacity),U2:nat,P:(list @ ((product_prod @ nat) @ nat)),V5:nat]: (((((((isPath @ Capacity) @ C2) @ U2) @ P) @ V5) & (! [P4:(list @ ((product_prod @ nat) @ nat))]: (((((((isPath @ Capacity) @ C2) @ U2) @ P4) @ V5) => (((ord_less_eq @ nat) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P)) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P4))))))))))))).
% 2.67/1.55 thf(fact_121_Graph_Omin__distI2, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),V:nat,V3:nat,Q:(nat > $o)]: ((((((connected @ Capacity) @ C) @ V) @ V3) => ((! [D6:nat]: (((((((dist @ Capacity) @ C) @ V) @ D6) @ V3) => ((! [D7:nat]: (((((((dist @ Capacity) @ C) @ V) @ D7) @ V3) => (((ord_less_eq @ nat) @ D6) @ D7)))) => (Q @ D6))))) => (Q @ ((((min_dist @ Capacity) @ C) @ V) @ V3)))))))))).
% 2.67/1.55 thf(fact_122_isShortestPath__alt, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ capacity) @ c) @ U) @ P2) @ V) = ((((((isSimplePath @ capacity) @ c) @ U) @ P2) @ V) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2) = ((((min_dist @ capacity) @ c) @ U) @ V))))))).
% 2.67/1.55 thf(fact_123_Graph_Odist__def, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((dist @ Capacity) = (^ [C2:(((product_prod @ nat) @ nat) > Capacity),V5:nat,D4:nat,V6:nat]: ((? [P:(list @ ((product_prod @ nat) @ nat))]: (((((((isPath @ Capacity) @ C2) @ V5) @ P) @ V6) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P) = D4))))))))))).
% 2.67/1.55 thf(fact_124_Graph_OisPath__distD, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isPath @ Capacity) @ C) @ U) @ P2) @ V) => (((((dist @ Capacity) @ C) @ U) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2)) @ V)))))))).
% 2.67/1.55 thf(fact_125_Graph_Omin__dist__is__dist, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),V:nat,V3:nat]: ((((((connected @ Capacity) @ C) @ V) @ V3) => (((((dist @ Capacity) @ C) @ V) @ ((((min_dist @ Capacity) @ C) @ V) @ V3)) @ V3)))))))).
% 2.67/1.55 thf(fact_126_Graph_Omin__dist__split_I1_J, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ Capacity) @ C) @ U) @ D1) @ W) => ((((((dist @ Capacity) @ C) @ W) @ D2) @ V) => ((((((min_dist @ Capacity) @ C) @ U) @ V) = (((plus_plus @ nat) @ D1) @ D2)) => (((((min_dist @ Capacity) @ C) @ U) @ W) = D1)))))))))).
% 2.67/1.55 thf(fact_127_isSPath__pathLE, axiom, (! [S:nat,P2:(list @ ((product_prod @ nat) @ nat)),T:nat]: (((((((isPath @ capacity) @ c) @ S) @ P2) @ T) => (? [P6:(list @ ((product_prod @ nat) @ nat))]: ((((((isSimplePath @ capacity) @ c) @ S) @ P6) @ T))))))).
% 2.67/1.55 thf(fact_128_shortestPath__is__simple, axiom, (! [S:nat,P2:(list @ ((product_prod @ nat) @ nat)),T:nat]: (((((((isShortestPath @ capacity) @ c) @ S) @ P2) @ T) => (((((isSimplePath @ capacity) @ c) @ S) @ P2) @ T))))).
% 2.67/1.55 thf(fact_129_Graph_OreachableNodes_Ocong, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((reachableNodes @ Capacity) = (reachableNodes @ Capacity)))))).
% 2.67/1.55 thf(fact_130_Graph_OisSimplePath_Ocong, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((isSimplePath @ Capacity) = (isSimplePath @ Capacity)))))).
% 2.67/1.55 thf(fact_131_Graph_OisSPath__pathLE, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),S:nat,P2:(list @ ((product_prod @ nat) @ nat)),T:nat]: (((((((isPath @ Capacity) @ C) @ S) @ P2) @ T) => (? [P6:(list @ ((product_prod @ nat) @ nat))]: ((((((isSimplePath @ Capacity) @ C) @ S) @ P6) @ T)))))))))).
% 2.67/1.55 thf(fact_132_Graph_OshortestPath__is__simple, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),S:nat,P2:(list @ ((product_prod @ nat) @ nat)),T:nat]: (((((((isShortestPath @ Capacity) @ C) @ S) @ P2) @ T) => (((((isSimplePath @ Capacity) @ C) @ S) @ P2) @ T)))))))).
% 2.67/1.55 thf(fact_133_Graph_OreachableNodes__def, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((reachableNodes @ Capacity) = (^ [C2:(((product_prod @ nat) @ nat) > Capacity),U2:nat]: (((collect @ nat) @ (((connected @ Capacity) @ C2) @ U2))))))))).
% 2.67/1.55 thf(fact_134_Graph_Omin__dist__def, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((min_dist @ Capacity) = (^ [C2:(((product_prod @ nat) @ nat) > Capacity),V5:nat,V6:nat]: (((ord_Least @ nat) @ (^ [D4:nat]: ((((((dist @ Capacity) @ C2) @ V5) @ D4) @ V6))))))))))).
% 2.67/1.55 thf(fact_135_Graph_OisShortestPath__alt, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((isShortestPath @ Capacity) = (^ [C2:(((product_prod @ nat) @ nat) > Capacity),U2:nat,P:(list @ ((product_prod @ nat) @ nat)),V5:nat]: (((((((isSimplePath @ Capacity) @ C2) @ U2) @ P) @ V5) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P) = ((((min_dist @ Capacity) @ C2) @ U2) @ V5)))))))))).
% 2.67/1.55 thf(fact_136_Graph_OisPath_Ocong, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((isPath @ Capacity) = (isPath @ Capacity)))))).
% 2.67/1.55 thf(fact_137_Graph_Omin__dist_Ocong, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((min_dist @ Capacity) = (min_dist @ Capacity)))))).
% 2.67/1.55 thf(fact_138_Graph_Oconnected__refl, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),V:nat]: (((((connected @ Capacity) @ C) @ V) @ V))))))).
% 2.67/1.55 thf(fact_139_Graph_Oconnected_Ocong, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((connected @ Capacity) = (connected @ Capacity)))))).
% 2.67/1.55 thf(fact_140_Graph_Odist_Ocong, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((dist @ Capacity) = (dist @ Capacity)))))).
% 2.67/1.55 thf(fact_141_Graph_OisShortestPath_Ocong, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((isShortestPath @ Capacity) = (isShortestPath @ Capacity)))))).
% 2.67/1.55 thf(fact_142_Graph_Odist__trans, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ Capacity) @ C) @ U) @ D1) @ W) => ((((((dist @ Capacity) @ C) @ W) @ D2) @ V) => (((((dist @ Capacity) @ C) @ U) @ (((plus_plus @ nat) @ D1) @ D2)) @ V))))))))).
% 2.67/1.55 thf(fact_143_Graph_Oconnected__def, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((connected @ Capacity) = (^ [C2:(((product_prod @ nat) @ nat) > Capacity),U2:nat,V5:nat]: ((? [P:(list @ ((product_prod @ nat) @ nat))]: ((((((isPath @ Capacity) @ C2) @ U2) @ P) @ V5)))))))))).
% 2.67/1.55 thf(fact_144_Graph_OshortestPath__is__path, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ Capacity) @ C) @ U) @ P2) @ V) => (((((isPath @ Capacity) @ C) @ U) @ P2) @ V)))))))).
% 2.67/1.55 thf(fact_145_Graph_Oconnected__by__dist, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => ((connected @ Capacity) = (^ [C2:(((product_prod @ nat) @ nat) > Capacity),V5:nat,V6:nat]: ((? [D4:nat]: ((((((dist @ Capacity) @ C2) @ V5) @ D4) @ V6)))))))))).
% 2.67/1.55 thf(fact_146_Graph_Oconnected__distI, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),V:nat,D:nat,V3:nat]: (((((((dist @ Capacity) @ C) @ V) @ D) @ V3) => ((((connected @ Capacity) @ C) @ V) @ V3)))))))).
% 2.67/1.55 thf(fact_147_Graph_Oobtain__shortest__path, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),U:nat,V:nat]: ((((((connected @ Capacity) @ C) @ U) @ V) => (~ ((! [P3:(list @ ((product_prod @ nat) @ nat))]: ((~ ((((((isShortestPath @ Capacity) @ C) @ U) @ P3) @ V)))))))))))))).
% 2.67/1.55 thf(fact_148_Graph_Omin__dist__less, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),Src:nat,V:nat,D:nat,D3:nat]: ((((((connected @ Capacity) @ C) @ Src) @ V) => ((((((min_dist @ Capacity) @ C) @ Src) @ V) = D) => ((((ord_less @ nat) @ D3) @ D) => (? [V2:nat]: ((((((connected @ Capacity) @ C) @ Src) @ V2) & (((((min_dist @ Capacity) @ C) @ Src) @ V2) = D3))))))))))))).
% 2.67/1.55 thf(fact_149_Graph_Omin__dist__le, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),Src:nat,V:nat,D3:nat]: ((((((connected @ Capacity) @ C) @ Src) @ V) => ((((ord_less_eq @ nat) @ D3) @ ((((min_dist @ Capacity) @ C) @ Src) @ V)) => (? [V2:nat]: ((((((connected @ Capacity) @ C) @ Src) @ V2) & (((((min_dist @ Capacity) @ C) @ Src) @ V2) = D3)))))))))))).
% 2.67/1.55 thf(fact_150_Graph_Omin__distI__eq, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),V:nat,D:nat,V3:nat]: (((((((dist @ Capacity) @ C) @ V) @ D) @ V3) => ((! [D5:nat]: (((((((dist @ Capacity) @ C) @ V) @ D5) @ V3) => (((ord_less_eq @ nat) @ D) @ D5)))) => (((((min_dist @ Capacity) @ C) @ V) @ V3) = D))))))))).
% 2.67/1.55 thf(fact_151_Graph_Omin__dist__minD, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),V:nat,D:nat,V3:nat]: (((((((dist @ Capacity) @ C) @ V) @ D) @ V3) => (((ord_less_eq @ nat) @ ((((min_dist @ Capacity) @ C) @ V) @ V3)) @ D)))))))).
% 2.67/1.55 thf(fact_152_Graph_Omin__dist__split_I2_J, axiom, (! [Capacity:$tType]: (((linordered_idom @ Capacity) => (! [C:(((product_prod @ nat) @ nat) > Capacity),U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ Capacity) @ C) @ U) @ D1) @ W) => ((((((dist @ Capacity) @ C) @ W) @ D2) @ V) => ((((((min_dist @ Capacity) @ C) @ U) @ V) = (((plus_plus @ nat) @ D1) @ D2)) => (((((min_dist @ Capacity) @ C) @ W) @ V) = D2)))))))))).
% 2.67/1.55 thf(fact_153__C1_Oprems_C_I3_J, axiom, (((((isPath @ a) @ c2) @ ua) @ p2_a) @ t)).
% 2.67/1.55 thf(fact_154_ex__has__greatest__nat__lemma, axiom, (! [A:$tType,P5:(A > $o),K:A,F:(A > nat),N:nat]: (((P5 @ K) => ((! [X:A]: (((P5 @ X) => (? [Y2:A]: (((P5 @ Y2) & (~ ((((ord_less_eq @ nat) @ (F @ Y2)) @ (F @ X)))))))))) => (? [Y:A]: (((P5 @ Y) & (~ ((((ord_less @ nat) @ (F @ Y)) @ (((plus_plus @ nat) @ (F @ K)) @ N)))))))))))).
% 2.67/1.55 thf(fact_155_not__less__Least, axiom, (! [A:$tType]: (((wellorder @ A) => (! [K:A,P5:(A > $o)]: (((((ord_less @ A) @ K) @ ((ord_Least @ A) @ P5)) => (~ ((P5 @ K)))))))))).
% 2.67/1.55 thf(fact_156_Least__le, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P5:(A > $o),K:A]: (((P5 @ K) => (((ord_less_eq @ A) @ ((ord_Least @ A) @ P5)) @ K)))))))).
% 2.67/1.55 thf(fact_157_g_H_Oconnected__by__dist, axiom, (! [V:nat,V3:nat]: ((((((connected @ a) @ c2) @ V) @ V3) = (? [D4:nat]: ((((((dist @ a) @ c2) @ V) @ D4) @ V3))))))).
% 2.67/1.55 thf(fact_158_g_H_Omin__dist__is__dist, axiom, (! [V:nat,V3:nat]: ((((((connected @ a) @ c2) @ V) @ V3) => (((((dist @ a) @ c2) @ V) @ ((((min_dist @ a) @ c2) @ V) @ V3)) @ V3))))).
% 2.67/1.55 thf(fact_159_g_H_Oobtain__shortest__path, axiom, (! [U:nat,V:nat]: ((((((connected @ a) @ c2) @ U) @ V) => (~ ((! [P3:(list @ ((product_prod @ nat) @ nat))]: ((~ ((((((isShortestPath @ a) @ c2) @ U) @ P3) @ V))))))))))).
% 2.67/1.55 thf(fact_160_g_H_OshortestPath__is__simple, axiom, (! [S:nat,P2:(list @ ((product_prod @ nat) @ nat)),T:nat]: (((((((isShortestPath @ a) @ c2) @ S) @ P2) @ T) => (((((isSimplePath @ a) @ c2) @ S) @ P2) @ T))))).
% 2.67/1.55 thf(fact_161_g_H_OreachableNodes__def, axiom, (! [U:nat]: (((((reachableNodes @ a) @ c2) @ U) = ((collect @ nat) @ (((connected @ a) @ c2) @ U)))))).
% 2.67/1.55 thf(fact_162_g_H_Omin__dist__less, axiom, (! [Src:nat,V:nat,D:nat,D3:nat]: ((((((connected @ a) @ c2) @ Src) @ V) => ((((((min_dist @ a) @ c2) @ Src) @ V) = D) => ((((ord_less @ nat) @ D3) @ D) => (? [V2:nat]: ((((((connected @ a) @ c2) @ Src) @ V2) & (((((min_dist @ a) @ c2) @ Src) @ V2) = D3)))))))))).
% 2.67/1.55 thf(fact_163_g_H_Omin__distI2, axiom, (! [V:nat,V3:nat,Q:(nat > $o)]: ((((((connected @ a) @ c2) @ V) @ V3) => ((! [D6:nat]: (((((((dist @ a) @ c2) @ V) @ D6) @ V3) => ((! [D7:nat]: (((((((dist @ a) @ c2) @ V) @ D7) @ V3) => (((ord_less_eq @ nat) @ D6) @ D7)))) => (Q @ D6))))) => (Q @ ((((min_dist @ a) @ c2) @ V) @ V3))))))).
% 2.67/1.55 thf(fact_164_g_H_Omin__distI__eq, axiom, (! [V:nat,D:nat,V3:nat]: (((((((dist @ a) @ c2) @ V) @ D) @ V3) => ((! [D5:nat]: (((((((dist @ a) @ c2) @ V) @ D5) @ V3) => (((ord_less_eq @ nat) @ D) @ D5)))) => (((((min_dist @ a) @ c2) @ V) @ V3) = D)))))).
% 2.67/1.55 thf(fact_165_g_H_Omin__dist__le, axiom, (! [Src:nat,V:nat,D3:nat]: ((((((connected @ a) @ c2) @ Src) @ V) => ((((ord_less_eq @ nat) @ D3) @ ((((min_dist @ a) @ c2) @ Src) @ V)) => (? [V2:nat]: ((((((connected @ a) @ c2) @ Src) @ V2) & (((((min_dist @ a) @ c2) @ Src) @ V2) = D3))))))))).
% 2.67/1.55 thf(fact_166_g_H_Omin__dist__minD, axiom, (! [V:nat,D:nat,V3:nat]: (((((((dist @ a) @ c2) @ V) @ D) @ V3) => (((ord_less_eq @ nat) @ ((((min_dist @ a) @ c2) @ V) @ V3)) @ D))))).
% 2.67/1.55 thf(fact_167_g_H_Omin__dist__split_I2_J, axiom, (! [U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ a) @ c2) @ U) @ D1) @ W) => ((((((dist @ a) @ c2) @ W) @ D2) @ V) => ((((((min_dist @ a) @ c2) @ U) @ V) = (((plus_plus @ nat) @ D1) @ D2)) => (((((min_dist @ a) @ c2) @ W) @ V) = D2))))))).
% 2.67/1.55 thf(fact_168_g_H_Omin__dist__split_I1_J, axiom, (! [U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ a) @ c2) @ U) @ D1) @ W) => ((((((dist @ a) @ c2) @ W) @ D2) @ V) => ((((((min_dist @ a) @ c2) @ U) @ V) = (((plus_plus @ nat) @ D1) @ D2)) => (((((min_dist @ a) @ c2) @ U) @ W) = D1))))))).
% 2.67/1.55 thf(fact_169_g_H_Odist__trans, axiom, (! [U:nat,D1:nat,W:nat,D2:nat,V:nat]: (((((((dist @ a) @ c2) @ U) @ D1) @ W) => ((((((dist @ a) @ c2) @ W) @ D2) @ V) => (((((dist @ a) @ c2) @ U) @ (((plus_plus @ nat) @ D1) @ D2)) @ V)))))).
% 2.67/1.55 thf(fact_170_g_H_Oconnected__def, axiom, (! [U:nat,V:nat]: ((((((connected @ a) @ c2) @ U) @ V) = (? [P:(list @ ((product_prod @ nat) @ nat))]: ((((((isPath @ a) @ c2) @ U) @ P) @ V))))))).
% 2.67/1.55 thf(fact_171_g_H_OisSPath__pathLE, axiom, (! [S:nat,P2:(list @ ((product_prod @ nat) @ nat)),T:nat]: (((((((isPath @ a) @ c2) @ S) @ P2) @ T) => (? [P6:(list @ ((product_prod @ nat) @ nat))]: ((((((isSimplePath @ a) @ c2) @ S) @ P6) @ T))))))).
% 2.67/1.55 thf(fact_172_g_H_OshortestPath__is__path, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ a) @ c2) @ U) @ P2) @ V) => (((((isPath @ a) @ c2) @ U) @ P2) @ V))))).
% 2.67/1.55 thf(fact_173_g_H_OisShortestPath__alt, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ a) @ c2) @ U) @ P2) @ V) = ((((((isSimplePath @ a) @ c2) @ U) @ P2) @ V) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2) = ((((min_dist @ a) @ c2) @ U) @ V))))))).
% 2.67/1.55 thf(fact_174_g_H_Omin__dist__def, axiom, (! [V:nat,V3:nat]: ((((((min_dist @ a) @ c2) @ V) @ V3) = ((ord_Least @ nat) @ (^ [D4:nat]: ((((((dist @ a) @ c2) @ V) @ D4) @ V3)))))))).
% 2.67/1.55 thf(fact_175_g_H_Odist__def, axiom, (! [V:nat,D:nat,V3:nat]: (((((((dist @ a) @ c2) @ V) @ D) @ V3) = (? [P:(list @ ((product_prod @ nat) @ nat))]: (((((((isPath @ a) @ c2) @ V) @ P) @ V3) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P) = D)))))))).
% 2.67/1.55 thf(fact_176_g_H_OisPath__distD, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isPath @ a) @ c2) @ U) @ P2) @ V) => (((((dist @ a) @ c2) @ U) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2)) @ V))))).
% 2.67/1.55 thf(fact_177_g_H_OisShortestPath__min__dist__def, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ a) @ c2) @ U) @ P2) @ V) = ((((((isPath @ a) @ c2) @ U) @ P2) @ V) & (((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2) = ((((min_dist @ a) @ c2) @ U) @ V))))))).
% 2.67/1.55 thf(fact_178_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ X3) @ X3))))))).
% 2.67/1.55 thf(fact_179_g_H_OisShortestPath__def, axiom, (! [U:nat,P2:(list @ ((product_prod @ nat) @ nat)),V:nat]: (((((((isShortestPath @ a) @ c2) @ U) @ P2) @ V) = ((((((isPath @ a) @ c2) @ U) @ P2) @ V) & (! [P4:(list @ ((product_prod @ nat) @ nat))]: (((((((isPath @ a) @ c2) @ U) @ P4) @ V) => (((ord_less_eq @ nat) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P2)) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ P4)))))))))).
% 2.67/1.55 thf(fact_180_assms_I5_J, axiom, (((((isPath @ a) @ c2) @ s) @ p3) @ t)).
% 2.67/1.55 thf(fact_181__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062, axiom, (((((isPath @ a) @ c2) @ u) @ p2) @ t)).
% 2.67/1.55 thf(fact_182_g_H_Oconnected__distI, axiom, (! [V:nat,D:nat,V3:nat]: (((((((dist @ a) @ c2) @ V) @ D) @ V3) => ((((connected @ a) @ c2) @ V) @ V3))))).
% 2.67/1.55 thf(fact_183_g_H_Oconnected__refl, axiom, (! [V:nat]: (((((connected @ a) @ c2) @ V) @ V)))).
% 2.67/1.55 thf(fact_184_P2_H, axiom, (((((isPath @ a) @ c2) @ ua) @ p2_a) @ t)).
% 2.67/1.55 thf(fact_185_le__funD, axiom, (! [B3:$tType,A:$tType]: (((ord @ B3) => (! [F:(A > B3),G:(A > B3),X3:A]: (((((ord_less_eq @ (A > B3)) @ F) @ G) => (((ord_less_eq @ B3) @ (F @ X3)) @ (G @ X3))))))))).
% 2.67/1.55 thf(fact_186_le__funE, axiom, (! [B3:$tType,A:$tType]: (((ord @ B3) => (! [F:(A > B3),G:(A > B3),X3:A]: (((((ord_less_eq @ (A > B3)) @ F) @ G) => (((ord_less_eq @ B3) @ (F @ X3)) @ (G @ X3))))))))).
% 2.67/1.55 thf(fact_187_le__funI, axiom, (! [B3:$tType,A:$tType]: (((ord @ B3) => (! [F:(A > B3),G:(A > B3)]: (((! [X:A]: ((((ord_less_eq @ B3) @ (F @ X)) @ (G @ X)))) => (((ord_less_eq @ (A > B3)) @ F) @ G)))))))).
% 2.67/1.55 thf(fact_188_le__fun__def, axiom, (! [B3:$tType,A:$tType]: (((ord @ B3) => ((ord_less_eq @ (A > B3)) = (^ [F2:(A > B3),G2:(A > B3)]: ((! [X2:A]: ((((ord_less_eq @ B3) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 2.67/1.55 thf(fact_189_order__subst1, axiom, (! [A:$tType,B3:$tType]: ((((order @ B3) & (order @ A)) => (! [A2:A,F:(B3 > A),B:B3,C:B3]: (((((ord_less_eq @ A) @ A2) @ (F @ B)) => ((((ord_less_eq @ B3) @ B) @ C) => ((! [X:B3,Y:B3]: (((((ord_less_eq @ B3) @ X) @ Y) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 2.67/1.55 thf(fact_190_order__subst2, axiom, (! [A:$tType,C4:$tType]: ((((order @ C4) & (order @ A)) => (! [A2:A,B:A,F:(A > C4),C:C4]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ C4) @ (F @ B)) @ C) => ((! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => (((ord_less_eq @ C4) @ (F @ X)) @ (F @ Y))))) => (((ord_less_eq @ C4) @ (F @ A2)) @ C)))))))))).
% 2.67/1.55 thf(fact_191_ord__eq__le__subst, axiom, (! [A:$tType,B3:$tType]: ((((ord @ B3) & (ord @ A)) => (! [A2:A,F:(B3 > A),B:B3,C:B3]: (((A2 = (F @ B)) => ((((ord_less_eq @ B3) @ B) @ C) => ((! [X:B3,Y:B3]: (((((ord_less_eq @ B3) @ X) @ Y) => (((ord_less_eq @ A) @ (F @ X)) @ (F @ Y))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 2.67/1.55 thf(fact_192_ord__le__eq__subst, axiom, (! [A:$tType,B3:$tType]: ((((ord @ B3) & (ord @ A)) => (! [A2:A,B:A,F:(A > B3),C:B3]: (((((ord_less_eq @ A) @ A2) @ B) => (((F @ B) = C) => ((! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => (((ord_less_eq @ B3) @ (F @ X)) @ (F @ Y))))) => (((ord_less_eq @ B3) @ (F @ A2)) @ C)))))))))).
% 2.67/1.55 thf(fact_193_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [X2:A,Y5:A]: (((((ord_less_eq @ A) @ X2) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X2))))))))).
% 2.67/1.55 thf(fact_194_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ X3) => (X3 = Y3))))))))).
% 2.67/1.55 thf(fact_195_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) | (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 2.67/1.55 thf(fact_196_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A]: (((X3 = Y3) => (((ord_less_eq @ A) @ X3) @ Y3)))))))).
% 2.67/1.55 thf(fact_197_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((~ ((((ord_less_eq @ A) @ X3) @ Y3))) => (((ord_less_eq @ A) @ Y3) @ X3)))))))).
% 2.67/1.55 thf(fact_198_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ B) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.67/1.55 thf(fact_199_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A,Z2:A]: ((((((ord_less_eq @ A) @ X3) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ Z2)))) => (((((ord_less_eq @ A) @ Y3) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Z2)))) => (((((ord_less_eq @ A) @ X3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y3)))) => (((((ord_less_eq @ A) @ Z2) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ X3)))) => (((((ord_less_eq @ A) @ Y3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X3)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ Y3))))))))))))))))).
% 2.67/1.55 thf(fact_200_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y3:A,X3:A]: (((((ord_less_eq @ A) @ Y3) @ X3) => ((((ord_less_eq @ A) @ X3) @ Y3) = (X3 = Y3))))))))).
% 2.67/1.55 thf(fact_201_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ B2) & (((ord_less_eq @ A) @ B2) @ A3))))))))).
% 2.67/1.55 thf(fact_202_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B:A,C:A]: (((A2 = B) => ((((ord_less_eq @ A) @ B) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.67/1.55 thf(fact_203_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((B = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.67/1.55 thf(fact_204_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A]: (((((ord_less_eq @ A) @ A2) @ B) => ((((ord_less_eq @ A) @ B) @ A2) => (A2 = B))))))))).
% 2.67/1.55 thf(fact_205_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ Z2) => (((ord_less_eq @ A) @ X3) @ Z2))))))))).
% 2.67/1.55 thf(fact_206_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.67/1.55 thf(fact_207_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P5:(A > (A > $o)),A2:A,B:A]: (((! [A5:A,B5:A]: (((((ord_less_eq @ A) @ A5) @ B5) => ((P5 @ A5) @ B5)))) => ((! [A5:A,B5:A]: ((((P5 @ B5) @ A5) => ((P5 @ A5) @ B5)))) => ((P5 @ A2) @ B))))))))).
% 2.67/1.55 thf(fact_208_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((ord_less_eq @ A) @ C) @ B) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 2.67/1.55 thf(fact_209_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A3:A,B2:A]: (((((ord_less_eq @ A) @ B2) @ A3) & (((ord_less_eq @ A) @ A3) @ B2))))))))).
% 2.67/1.55 thf(fact_210_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B:A,A2:A]: (((((ord_less_eq @ A) @ B) @ A2) => ((((ord_less_eq @ A) @ A2) @ B) => (A2 = B))))))))).
% 2.67/1.55 thf(fact_211_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B:A,A2:A]: (((((ord_less @ A) @ B) @ A2) => (A2 != B)))))))).
% 2.67/1.55 thf(fact_212_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ B) => (A2 != B)))))))).
% 2.67/1.55 thf(fact_213_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((~ ((((ord_less @ A) @ X3) @ Y3))) = ((((ord_less @ A) @ Y3) @ X3) | (X3 = Y3))))))))).
% 2.67/1.55 thf(fact_214_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B:A,A2:A,C:A]: (((((ord_less @ A) @ B) @ A2) => ((((ord_less @ A) @ C) @ B) => (((ord_less @ A) @ C) @ A2))))))))).
% 2.67/1.55 thf(fact_215_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P5:(A > (A > $o)),A2:A,B:A]: (((! [A5:A,B5:A]: (((((ord_less @ A) @ A5) @ B5) => ((P5 @ A5) @ B5)))) => ((! [A5:A]: (((P5 @ A5) @ A5))) => ((! [A5:A,B5:A]: ((((P5 @ B5) @ A5) => ((P5 @ A5) @ B5)))) => ((P5 @ A2) @ B)))))))))).
% 2.67/1.55 thf(fact_216_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P7:(A > $o)]: ((? [X4:A]: ((P7 @ X4))))) = (^ [P8:(A > $o)]: ((? [N2:A]: (((P8 @ N2) & (! [M2:A]: (((((ord_less @ A) @ M2) @ N2) => (~ ((P8 @ M2)))))))))))))))).
% 2.67/1.55 thf(fact_217_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (~ ((((ord_less @ A) @ Y3) @ X3)))))))))).
% 2.67/1.55 thf(fact_218_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ A) @ B) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.67/1.55 thf(fact_219_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 2.67/1.55 thf(fact_220_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((~ ((((ord_less @ A) @ X3) @ Y3))) => ((X3 != Y3) => (((ord_less @ A) @ Y3) @ X3))))))))).
% 2.67/1.55 thf(fact_221_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A,P5:$o]: (((((ord_less @ A) @ X3) @ Y3) => ((((ord_less @ A) @ Y3) @ X3) => P5)))))))).
% 2.67/1.55 thf(fact_222_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (Y3 != X3)))))))).
% 2.67/1.55 thf(fact_223_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y3:A,X3:A]: (((~ ((((ord_less @ A) @ Y3) @ X3))) => ((~ ((((ord_less @ A) @ X3) @ Y3))) = (X3 = Y3))))))))).
% 2.67/1.55 thf(fact_224_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P5:(A > $o),A2:A]: (((! [X:A]: (((! [Y2:A]: (((((ord_less @ A) @ Y2) @ X) => (P5 @ Y2)))) => (P5 @ X)))) => (P5 @ A2)))))))).
% 2.67/1.55 thf(fact_225_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (~ ((((ord_less @ A) @ Y3) @ X3)))))))))).
% 2.67/1.55 thf(fact_226_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (X3 != Y3)))))))).
% 2.67/1.55 thf(fact_227_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B:A,A2:A]: (((((ord_less @ A) @ B) @ A2) => (~ ((((ord_less @ A) @ A2) @ B)))))))))).
% 2.67/1.55 thf(fact_228_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B:A,C:A]: (((((ord_less @ A) @ A2) @ B) => ((B = C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.67/1.55 thf(fact_229_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B:A,C:A]: (((A2 = B) => ((((ord_less @ A) @ B) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.67/1.55 thf(fact_230_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A]: ((~ ((((ord_less @ A) @ X3) @ X3))))))))).
% 2.67/1.55 thf(fact_231_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) | ((X3 = Y3) | (((ord_less @ A) @ Y3) @ X3))))))))).
% 2.67/1.55 thf(fact_232_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A,Z2:A]: (((((ord_less @ A) @ X3) @ Y3) => ((((ord_less @ A) @ Y3) @ Z2) => (((ord_less @ A) @ X3) @ Z2))))))))).
% 2.67/1.55 thf(fact_233_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ B) => (~ ((((ord_less @ A) @ B) @ A2)))))))))).
% 2.67/1.55 thf(fact_234_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (~ ((((ord_less @ A) @ Y3) @ X3)))))))))).
% 2.67/1.55 thf(fact_235_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (X3 != Y3)))))))).
% 2.67/1.55 thf(fact_236_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (? [Z3:A]: (((((ord_less @ A) @ X3) @ Z3) & (((ord_less @ A) @ Z3) @ Y3))))))))))).
% 2.67/1.55 thf(fact_237_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ B) => (~ ((((ord_less @ A) @ B) @ A2)))))))))).
% 2.67/1.55 thf(fact_238_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((X3 != Y3) = ((((ord_less @ A) @ X3) @ Y3) | (((ord_less @ A) @ Y3) @ X3))))))))).
% 2.67/1.55 thf(fact_239_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:A,Y3:A]: (((X3 != Y3) => ((~ ((((ord_less @ A) @ X3) @ Y3))) => (((ord_less @ A) @ Y3) @ X3))))))))).
% 2.67/1.55 thf(fact_240_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X3:A]: ((? [X_1:A]: ((((ord_less @ A) @ X3) @ X_1))))))))).
% 2.67/1.55 thf(fact_241_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X3:A]: ((? [Y:A]: ((((ord_less @ A) @ Y) @ X3))))))))).
% 2.67/1.55 thf(fact_242_order__less__subst2, axiom, (! [A:$tType,C4:$tType]: ((((order @ C4) & (order @ A)) => (! [A2:A,B:A,F:(A > C4),C:C4]: (((((ord_less @ A) @ A2) @ B) => ((((ord_less @ C4) @ (F @ B)) @ C) => ((! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (((ord_less @ C4) @ (F @ X)) @ (F @ Y))))) => (((ord_less @ C4) @ (F @ A2)) @ C)))))))))).
% 2.67/1.55 thf(fact_243_order__less__subst1, axiom, (! [A:$tType,B3:$tType]: ((((order @ B3) & (order @ A)) => (! [A2:A,F:(B3 > A),B:B3,C:B3]: (((((ord_less @ A) @ A2) @ (F @ B)) => ((((ord_less @ B3) @ B) @ C) => ((! [X:B3,Y:B3]: (((((ord_less @ B3) @ X) @ Y) => (((ord_less @ A) @ (F @ X)) @ (F @ Y))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 2.67/1.55 thf(fact_244_ord__less__eq__subst, axiom, (! [A:$tType,B3:$tType]: ((((ord @ B3) & (ord @ A)) => (! [A2:A,B:A,F:(A > B3),C:B3]: (((((ord_less @ A) @ A2) @ B) => (((F @ B) = C) => ((! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (((ord_less @ B3) @ (F @ X)) @ (F @ Y))))) => (((ord_less @ B3) @ (F @ A2)) @ C)))))))))).
% 2.67/1.55 thf(fact_245_ord__eq__less__subst, axiom, (! [A:$tType,B3:$tType]: ((((ord @ B3) & (ord @ A)) => (! [A2:A,F:(B3 > A),B:B3,C:B3]: (((A2 = (F @ B)) => ((((ord_less @ B3) @ B) @ C) => ((! [X:B3,Y:B3]: (((((ord_less @ B3) @ X) @ Y) => (((ord_less @ A) @ (F @ X)) @ (F @ Y))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 2.67/1.55 thf(fact_246_ex__has__least__nat, axiom, (! [A:$tType,P5:(A > $o),K:A,M:(A > nat)]: (((P5 @ K) => (? [X:A]: (((P5 @ X) & (! [Y2:A]: (((P5 @ Y2) => (((ord_less_eq @ nat) @ (M @ X)) @ (M @ Y2)))))))))))).
% 2.67/1.55 thf(fact_247_LeastI2, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P5:(A > $o),A2:A,Q:(A > $o)]: (((P5 @ A2) => ((! [X:A]: (((P5 @ X) => (Q @ X)))) => (Q @ ((ord_Least @ A) @ P5)))))))))).
% 2.67/1.55 thf(fact_248_LeastI__ex, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P5:(A > $o)]: (((? [X_12:A]: ((P5 @ X_12))) => (P5 @ ((ord_Least @ A) @ P5))))))))).
% 2.67/1.55 thf(fact_249_LeastI2__ex, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P5:(A > $o),Q:(A > $o)]: (((? [X_12:A]: ((P5 @ X_12))) => ((! [X:A]: (((P5 @ X) => (Q @ X)))) => (Q @ ((ord_Least @ A) @ P5)))))))))).
% 2.67/1.55 thf(fact_250_LeastI, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P5:(A > $o),K:A]: (((P5 @ K) => (P5 @ ((ord_Least @ A) @ P5))))))))).
% 2.67/1.55 thf(fact_251_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A]: (((A2 != B) => ((((ord_less_eq @ A) @ A2) @ B) => (((ord_less @ A) @ A2) @ B))))))))).
% 2.67/1.55 thf(fact_252_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B:A,A2:A]: (((((ord_less @ A) @ B) @ A2) => (((ord_less_eq @ A) @ B) @ A2)))))))).
% 2.67/1.55 thf(fact_253_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B2:A,A3:A]: (((((ord_less_eq @ A) @ B2) @ A3) & (A3 != B2))))))))).
% 2.67/1.55 thf(fact_254_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B2:A,A3:A]: (((((ord_less @ A) @ B2) @ A3) | (A3 = B2))))))))).
% 2.67/1.55 thf(fact_255_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B:A]: (((((ord_less @ A) @ A2) @ B) => (((ord_less_eq @ A) @ A2) @ B)))))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___HOL_Otype, axiom, (! [A:$tType]: (((linordered_idom @ A) => (type @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Orderings_Oord, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ord @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Orderings_Oorder, axiom, (! [A:$tType]: (((linordered_idom @ A) => (order @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Ogroup__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (group_add @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Orderings_Olinorder, axiom, (! [A:$tType]: (((linordered_idom @ A) => (linorder @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Orderings_Opreorder, axiom, (! [A:$tType]: (((linordered_idom @ A) => (preorder @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Osemigroup__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (semigroup_add @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (comm_monoid_add @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ab_semigroup_add @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Ocancel__semigroup__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (cancel_semigroup_add @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ordere779506340up_add @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add__imp__le, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ordere236663937imp_le @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__cancel__ab__semigroup__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (ordere223160158up_add @ A))))).
% 2.67/1.55 thf(subcl_Rings_Olinordered__idom___Groups_Ostrict__ordered__ab__semigroup__add, axiom, (! [A:$tType]: (((linordered_idom @ A) => (strict2144017051up_add @ A))))).
% 2.67/1.55 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A6:$tType,A7:$tType]: (((preorder @ A7) => (preorder @ (A6 > A7)))))).
% 2.67/1.55 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: (((order @ A7) => (order @ (A6 > A7)))))).
% 2.67/1.55 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, (strict2144017051up_add @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, axiom, (ordere223160158up_add @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, (ordere236663937imp_le @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, (ordere779506340up_add @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, (cancel_semigroup_add @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, (ab_semigroup_add @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, (semigroup_add @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, (preorder @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, (no_top @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, (order @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, (ord @ nat)).
% 2.67/1.55 thf(tcon_Nat_Onat___Nat_Osize, axiom, (size @ nat)).
% 2.67/1.55 thf(tcon_Set_Oset___Orderings_Opreorder_4, axiom, (! [A6:$tType]: ((preorder @ (set @ A6))))).
% 2.67/1.55 thf(tcon_Set_Oset___Orderings_Oorder_5, axiom, (! [A6:$tType]: ((order @ (set @ A6))))).
% 2.67/1.55 thf(tcon_Set_Oset___Orderings_Oord_6, axiom, (! [A6:$tType]: ((ord @ (set @ A6))))).
% 2.67/1.55 thf(tcon_HOL_Obool___Orderings_Opreorder_7, axiom, (preorder @ $o)).
% 2.67/1.55 thf(tcon_HOL_Obool___Orderings_Olinorder_8, axiom, (linorder @ $o)).
% 2.67/1.55 thf(tcon_HOL_Obool___Orderings_Oorder_9, axiom, (order @ $o)).
% 2.67/1.55 thf(tcon_HOL_Obool___Orderings_Oord_10, axiom, (ord @ $o)).
% 2.67/1.55 thf(tcon_List_Olist___Nat_Osize_11, axiom, (! [A6:$tType]: ((size @ (list @ A6))))).
% 2.67/1.55 thf(tcon_Product__Type_Oprod___Nat_Osize_12, axiom, (! [A6:$tType,A7:$tType]: ((size @ ((product_prod @ A6) @ A7))))).
% 2.67/1.55 thf(tfree_0, hypothesis, (linordered_idom @ capacity)).
% 2.67/1.55 thf(tfree_1, hypothesis, (linordered_idom @ a)).
% 2.67/1.55 thf(conj_0, conjecture, (((ord_less @ nat) @ ((((min_dist @ capacity) @ c) @ s) @ t)) @ (((plus_plus @ nat) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ p1a)) @ ((size_size @ (list @ ((product_prod @ nat) @ nat))) @ p2_a)))).
% 2.67/1.55 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2DTF7288.p
% 2.67/1.55 ------------------------
% 2.67/1.58 ---- Cleaned THF ---
% 2.67/1.58 thf(ty_t_Product__Type_Oprod,type,
% 2.67/1.58 product_prod: $tType > $tType > $tType ).
% 2.67/1.58
% 2.67/1.58 thf(ty_t_List_Olist,type,
% 2.67/1.58 list: $tType > $tType ).
% 2.67/1.58
% 2.67/1.58 thf(ty_tf_capacity,type,
% 2.67/1.58 capacity: $tType ).
% 2.67/1.58
% 2.67/1.58 thf(ty_t_Set_Oset,type,
% 2.67/1.58 set: $tType > $tType ).
% 2.67/1.58
% 2.67/1.58 thf(ty_t_Nat_Onat,type,
% 2.67/1.58 nat: $tType ).
% 2.67/1.58
% 2.67/1.58 thf(ty_tf_a,type,
% 2.67/1.58 a: $tType ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_HOL_Otype,type,
% 2.67/1.58 type:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Nat_Osize,type,
% 2.67/1.58 size:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Orderings_Oord,type,
% 2.67/1.58 ord:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Orderings_Oorder,type,
% 2.67/1.58 order:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Ogroup__add,type,
% 2.67/1.58 group_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Orderings_Ono__bot,type,
% 2.67/1.58 no_bot:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Orderings_Ono__top,type,
% 2.67/1.58 no_top:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Orderings_Olinorder,type,
% 2.67/1.58 linorder:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Orderings_Opreorder,type,
% 2.67/1.58 preorder:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Orderings_Owellorder,type,
% 2.67/1.58 wellorder:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.67/1.58 semigroup_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Orderings_Odense__order,type,
% 2.67/1.58 dense_order:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.67/1.58 linordered_idom:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.67/1.58 comm_monoid_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.67/1.58 ab_semigroup_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.67/1.58 cancel_semigroup_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.67/1.58 ordere779506340up_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.67/1.58 canoni770627133id_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.67/1.58 ordere236663937imp_le:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 2.67/1.58 ordere223160158up_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 2.67/1.58 strict2144017051up_add:
% 2.67/1.58 !>[A: $tType] : $o ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Graph_OGraph_Oconnected,type,
% 2.67/1.58 connected:
% 2.67/1.58 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > nat > $o ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Graph_OGraph_Odist,type,
% 2.67/1.58 dist:
% 2.67/1.58 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > nat > nat > $o ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Graph_OGraph_OisPath,type,
% 2.67/1.58 isPath:
% 2.67/1.58 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Graph_OGraph_OisShortestPath,type,
% 2.67/1.58 isShortestPath:
% 2.67/1.58 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Graph_OGraph_OisSimplePath,type,
% 2.67/1.58 isSimplePath:
% 2.67/1.58 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > ( list @ ( product_prod @ nat @ nat ) ) > nat > $o ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Graph_OGraph_Omin__dist,type,
% 2.67/1.58 min_dist:
% 2.67/1.58 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > nat > nat ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Graph_OGraph_OreachableNodes,type,
% 2.67/1.58 reachableNodes:
% 2.67/1.58 !>[Capacity: $tType] : ( ( ( product_prod @ nat @ nat ) > Capacity ) > nat > ( set @ nat ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.67/1.58 plus_plus:
% 2.67/1.58 !>[A: $tType] : ( A > A > A ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Nat_Osize__class_Osize,type,
% 2.67/1.58 size_size:
% 2.67/1.58 !>[A: $tType] : ( A > nat ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Orderings_Oord__class_OLeast,type,
% 2.67/1.58 ord_Least:
% 2.67/1.58 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.67/1.58 ord_less:
% 2.67/1.58 !>[A: $tType] : ( A > A > $o ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.67/1.58 ord_less_eq:
% 2.67/1.58 !>[A: $tType] : ( A > A > $o ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_Set_OCollect,type,
% 2.67/1.58 collect:
% 2.67/1.58 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_c_member,type,
% 2.67/1.58 member:
% 2.67/1.58 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_c,type,
% 2.67/1.58 c: ( product_prod @ nat @ nat ) > capacity ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_c_H,type,
% 2.67/1.58 c2: ( product_prod @ nat @ nat ) > a ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_p,type,
% 2.67/1.58 p: list @ ( product_prod @ nat @ nat ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_p1____,type,
% 2.67/1.58 p1: list @ ( product_prod @ nat @ nat ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_p1a____,type,
% 2.67/1.58 p1a: list @ ( product_prod @ nat @ nat ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_p2_H____,type,
% 2.67/1.58 p2: list @ ( product_prod @ nat @ nat ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_p2_Ha____,type,
% 2.67/1.58 p2_a: list @ ( product_prod @ nat @ nat ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_p_H,type,
% 2.67/1.58 p3: list @ ( product_prod @ nat @ nat ) ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_s,type,
% 2.67/1.58 s: nat ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_t,type,
% 2.67/1.58 t: nat ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_u____,type,
% 2.67/1.58 u: nat ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_ua____,type,
% 2.67/1.58 ua: nat ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_v____,type,
% 2.67/1.58 v: nat ).
% 2.67/1.58
% 2.67/1.58 thf(sy_v_va____,type,
% 2.67/1.58 va: nat ).
% 2.67/1.58
% 2.67/1.58 thf(fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062,axiom,
% 2.67/1.58 ( ( min_dist @ capacity @ c @ s @ t )
% 2.67/1.58 = ( plus_plus @ nat @ ( min_dist @ capacity @ c @ s @ ua ) @ ( min_dist @ capacity @ c @ ua @ t ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062,axiom,
% 2.67/1.58 ord_less @ nat @ ( min_dist @ capacity @ c @ s @ ua ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p1a ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062,axiom,
% 2.67/1.58 ord_less_eq @ nat @ ( min_dist @ capacity @ c @ ua @ t ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2_a ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_3_nat__add__left__cancel__less,axiom,
% 2.67/1.58 ! [K: nat,M: nat,N: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.67/1.58 = ( ord_less @ nat @ M @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_4_add__less__cancel__left,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere236663937imp_le @ A )
% 2.67/1.58 => ! [C: A,A2: A,B: A] :
% 2.67/1.58 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.67/1.58 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_5_add__less__cancel__right,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere236663937imp_le @ A )
% 2.67/1.58 => ! [A2: A,C: A,B: A] :
% 2.67/1.58 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.67/1.58 = ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_6__C1_Oprems_C_I2_J,axiom,
% 2.67/1.58 isPath @ capacity @ c @ s @ p1a @ va ).
% 2.67/1.58
% 2.67/1.58 thf(fact_7_SP,axiom,
% 2.67/1.58 isShortestPath @ capacity @ c @ s @ p @ t ).
% 2.67/1.58
% 2.67/1.58 thf(fact_8_min__dist__split_I2_J,axiom,
% 2.67/1.58 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ capacity @ c @ W @ D2 @ V )
% 2.67/1.58 => ( ( ( min_dist @ capacity @ c @ U @ V )
% 2.67/1.58 = ( plus_plus @ nat @ D1 @ D2 ) )
% 2.67/1.58 => ( ( min_dist @ capacity @ c @ W @ V )
% 2.67/1.58 = D2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_9_min__dist__split_I1_J,axiom,
% 2.67/1.58 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ capacity @ c @ W @ D2 @ V )
% 2.67/1.58 => ( ( ( min_dist @ capacity @ c @ U @ V )
% 2.67/1.58 = ( plus_plus @ nat @ D1 @ D2 ) )
% 2.67/1.58 => ( ( min_dist @ capacity @ c @ U @ W )
% 2.67/1.58 = D1 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_10_min__dist__less,axiom,
% 2.67/1.58 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 2.67/1.58 ( ( connected @ capacity @ c @ Src @ V )
% 2.67/1.58 => ( ( ( min_dist @ capacity @ c @ Src @ V )
% 2.67/1.58 = D )
% 2.67/1.58 => ( ( ord_less @ nat @ D3 @ D )
% 2.67/1.58 => ? [V2: nat] :
% 2.67/1.58 ( ( connected @ capacity @ c @ Src @ V2 )
% 2.67/1.58 & ( ( min_dist @ capacity @ c @ Src @ V2 )
% 2.67/1.58 = D3 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_11_add__left__cancel,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( cancel_semigroup_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ( plus_plus @ A @ A2 @ B )
% 2.67/1.58 = ( plus_plus @ A @ A2 @ C ) )
% 2.67/1.58 = ( B = C ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_12_add__right__cancel,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( cancel_semigroup_add @ A )
% 2.67/1.58 => ! [B: A,A2: A,C: A] :
% 2.67/1.58 ( ( ( plus_plus @ A @ B @ A2 )
% 2.67/1.58 = ( plus_plus @ A @ C @ A2 ) )
% 2.67/1.58 = ( B = C ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062,axiom,
% 2.67/1.58 isPath @ capacity @ c @ ua @ p2_a @ t ).
% 2.67/1.58
% 2.67/1.58 thf(fact_14_dist__trans,axiom,
% 2.67/1.58 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ capacity @ c @ W @ D2 @ V )
% 2.67/1.58 => ( dist @ capacity @ c @ U @ ( plus_plus @ nat @ D1 @ D2 ) @ V ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_15_connected__def,axiom,
% 2.67/1.58 ! [U: nat,V: nat] :
% 2.67/1.58 ( ( connected @ capacity @ c @ U @ V )
% 2.67/1.58 = ( ? [P: list @ ( product_prod @ nat @ nat )] : ( isPath @ capacity @ c @ U @ P @ V ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_16_shortestPath__is__path,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ capacity @ c @ U @ P2 @ V )
% 2.67/1.58 => ( isPath @ capacity @ c @ U @ P2 @ V ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_17_connected__by__dist,axiom,
% 2.67/1.58 ! [V: nat,V3: nat] :
% 2.67/1.58 ( ( connected @ capacity @ c @ V @ V3 )
% 2.67/1.58 = ( ? [D4: nat] : ( dist @ capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_18_obtain__shortest__path,axiom,
% 2.67/1.58 ! [U: nat,V: nat] :
% 2.67/1.58 ( ( connected @ capacity @ c @ U @ V )
% 2.67/1.58 => ~ ! [P3: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ~ ( isShortestPath @ capacity @ c @ U @ P3 @ V ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_19_min__dist__le,axiom,
% 2.67/1.58 ! [Src: nat,V: nat,D3: nat] :
% 2.67/1.58 ( ( connected @ capacity @ c @ Src @ V )
% 2.67/1.58 => ( ( ord_less_eq @ nat @ D3 @ ( min_dist @ capacity @ c @ Src @ V ) )
% 2.67/1.58 => ? [V2: nat] :
% 2.67/1.58 ( ( connected @ capacity @ c @ Src @ V2 )
% 2.67/1.58 & ( ( min_dist @ capacity @ c @ Src @ V2 )
% 2.67/1.58 = D3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_20_min__dist__minD,axiom,
% 2.67/1.58 ! [V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ V @ D @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( min_dist @ capacity @ c @ V @ V3 ) @ D ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_21_min__distI__eq,axiom,
% 2.67/1.58 ! [V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ V @ D @ V3 )
% 2.67/1.58 => ( ! [D5: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ V @ D5 @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ D @ D5 ) )
% 2.67/1.58 => ( ( min_dist @ capacity @ c @ V @ V3 )
% 2.67/1.58 = D ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_22_isPath__distD,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isPath @ capacity @ c @ U @ P2 @ V )
% 2.67/1.58 => ( dist @ capacity @ c @ U @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ V ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_23_dist__def,axiom,
% 2.67/1.58 ! [V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ V @ D @ V3 )
% 2.67/1.58 = ( ? [P: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ( ( isPath @ capacity @ c @ V @ P @ V3 )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 2.67/1.58 = D ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062,axiom,
% 2.67/1.58 isPath @ capacity @ c @ s @ p1 @ v ).
% 2.67/1.58
% 2.67/1.58 thf(fact_25_min__dist__is__dist,axiom,
% 2.67/1.58 ! [V: nat,V3: nat] :
% 2.67/1.58 ( ( connected @ capacity @ c @ V @ V3 )
% 2.67/1.58 => ( dist @ capacity @ c @ V @ ( min_dist @ capacity @ c @ V @ V3 ) @ V3 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_26_isShortestPath__def,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ capacity @ c @ U @ P2 @ V )
% 2.67/1.58 = ( ( isPath @ capacity @ c @ U @ P2 @ V )
% 2.67/1.58 & ! [P4: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ( ( isPath @ capacity @ c @ U @ P4 @ V )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P4 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_27_min__distI2,axiom,
% 2.67/1.58 ! [V: nat,V3: nat,Q: nat > $o] :
% 2.67/1.58 ( ( connected @ capacity @ c @ V @ V3 )
% 2.67/1.58 => ( ! [D6: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ V @ D6 @ V3 )
% 2.67/1.58 => ( ! [D7: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ V @ D7 @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ D6 @ D7 ) )
% 2.67/1.58 => ( Q @ D6 ) ) )
% 2.67/1.58 => ( Q @ ( min_dist @ capacity @ c @ V @ V3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_28_isShortestPath__min__dist__def,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ capacity @ c @ U @ P2 @ V )
% 2.67/1.58 = ( ( isPath @ capacity @ c @ U @ P2 @ V )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 )
% 2.67/1.58 = ( min_dist @ capacity @ c @ U @ V ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_29__092_060open_062connected_As_Au_092_060close_062,axiom,
% 2.67/1.58 connected @ capacity @ c @ s @ ua ).
% 2.67/1.58
% 2.67/1.58 thf(fact_30_add__le__cancel__right,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere236663937imp_le @ A )
% 2.67/1.58 => ! [A2: A,C: A,B: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.67/1.58 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_31_add__le__cancel__left,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere236663937imp_le @ A )
% 2.67/1.58 => ! [C: A,A2: A,B: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.67/1.58 = ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_32_nat__add__left__cancel__le,axiom,
% 2.67/1.58 ! [K: nat,M: nat,N: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.67/1.58 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_33_P1,axiom,
% 2.67/1.58 isPath @ capacity @ c @ s @ p1a @ va ).
% 2.67/1.58
% 2.67/1.58 thf(fact_34_connected__refl,axiom,
% 2.67/1.58 ! [V: nat] : ( connected @ capacity @ c @ V @ V ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_35_connected__distI,axiom,
% 2.67/1.58 ! [V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ capacity @ c @ V @ D @ V3 )
% 2.67/1.58 => ( connected @ capacity @ c @ V @ V3 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_36_le__refl,axiom,
% 2.67/1.58 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_37_le__trans,axiom,
% 2.67/1.58 ! [I: nat,J: nat,K: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.58 => ( ( ord_less_eq @ nat @ J @ K )
% 2.67/1.58 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_38_eq__imp__le,axiom,
% 2.67/1.58 ! [M: nat,N: nat] :
% 2.67/1.58 ( ( M = N )
% 2.67/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_39_le__antisym,axiom,
% 2.67/1.58 ! [M: nat,N: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ M @ N )
% 2.67/1.58 => ( ( ord_less_eq @ nat @ N @ M )
% 2.67/1.58 => ( M = N ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_40_nat__le__linear,axiom,
% 2.67/1.58 ! [M: nat,N: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ M @ N )
% 2.67/1.58 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_41_Nat_Oex__has__greatest__nat,axiom,
% 2.67/1.58 ! [P5: nat > $o,K: nat,B: nat] :
% 2.67/1.58 ( ( P5 @ K )
% 2.67/1.58 => ( ! [Y: nat] :
% 2.67/1.58 ( ( P5 @ Y )
% 2.67/1.58 => ( ord_less_eq @ nat @ Y @ B ) )
% 2.67/1.58 => ? [X: nat] :
% 2.67/1.58 ( ( P5 @ X )
% 2.67/1.58 & ! [Y2: nat] :
% 2.67/1.58 ( ( P5 @ Y2 )
% 2.67/1.58 => ( ord_less_eq @ nat @ Y2 @ X ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_42_add__le__imp__le__right,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere236663937imp_le @ A )
% 2.67/1.58 => ! [A2: A,C: A,B: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.67/1.58 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_43_add__le__imp__le__left,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere236663937imp_le @ A )
% 2.67/1.58 => ! [C: A,A2: A,B: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.67/1.58 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_44_le__iff__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( canoni770627133id_add @ A )
% 2.67/1.58 => ( ( ord_less_eq @ A )
% 2.67/1.58 = ( ^ [A3: A,B2: A] :
% 2.67/1.58 ? [C2: A] :
% 2.67/1.58 ( B2
% 2.67/1.58 = ( plus_plus @ A @ A3 @ C2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_45_mem__Collect__eq,axiom,
% 2.67/1.58 ! [A: $tType,A2: A,P5: A > $o] :
% 2.67/1.58 ( ( member @ A @ A2 @ ( collect @ A @ P5 ) )
% 2.67/1.58 = ( P5 @ A2 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_46_Collect__mem__eq,axiom,
% 2.67/1.58 ! [A: $tType,A4: set @ A] :
% 2.67/1.58 ( ( collect @ A
% 2.67/1.58 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 2.67/1.58 = A4 ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_47_Collect__cong,axiom,
% 2.67/1.58 ! [A: $tType,P5: A > $o,Q: A > $o] :
% 2.67/1.58 ( ! [X: A] :
% 2.67/1.58 ( ( P5 @ X )
% 2.67/1.58 = ( Q @ X ) )
% 2.67/1.58 => ( ( collect @ A @ P5 )
% 2.67/1.58 = ( collect @ A @ Q ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_48_ext,axiom,
% 2.67/1.58 ! [B3: $tType,A: $tType,F: A > B3,G: A > B3] :
% 2.67/1.58 ( ! [X: A] :
% 2.67/1.58 ( ( F @ X )
% 2.67/1.58 = ( G @ X ) )
% 2.67/1.58 => ( F = G ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_49_add__right__mono,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere779506340up_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_50_less__eqE,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( canoni770627133id_add @ A )
% 2.67/1.58 => ! [A2: A,B: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ~ ! [C3: A] :
% 2.67/1.58 ( B
% 2.67/1.58 != ( plus_plus @ A @ A2 @ C3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_51_add__left__mono,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere779506340up_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_52_add__mono,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere779506340up_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A,D: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less_eq @ A @ C @ D )
% 2.67/1.58 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_53_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere779506340up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( ord_less_eq @ A @ I @ J )
% 2.67/1.58 & ( ord_less_eq @ A @ K @ L ) )
% 2.67/1.58 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_54_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere779506340up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( I = J )
% 2.67/1.58 & ( ord_less_eq @ A @ K @ L ) )
% 2.67/1.58 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_55_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere779506340up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( ord_less_eq @ A @ I @ J )
% 2.67/1.58 & ( K = L ) )
% 2.67/1.58 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_56_less__mono__imp__le__mono,axiom,
% 2.67/1.58 ! [F: nat > nat,I: nat,J: nat] :
% 2.67/1.58 ( ! [I2: nat,J2: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ I2 @ J2 )
% 2.67/1.58 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 2.67/1.58 => ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_57_le__neq__implies__less,axiom,
% 2.67/1.58 ! [M: nat,N: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ M @ N )
% 2.67/1.58 => ( ( M != N )
% 2.67/1.58 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_58_less__or__eq__imp__le,axiom,
% 2.67/1.58 ! [M: nat,N: nat] :
% 2.67/1.58 ( ( ( ord_less @ nat @ M @ N )
% 2.67/1.58 | ( M = N ) )
% 2.67/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_59_le__eq__less__or__eq,axiom,
% 2.67/1.58 ( ( ord_less_eq @ nat )
% 2.67/1.58 = ( ^ [M2: nat,N2: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ M2 @ N2 )
% 2.67/1.58 | ( M2 = N2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_60_less__imp__le__nat,axiom,
% 2.67/1.58 ! [M: nat,N: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ M @ N )
% 2.67/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_61_nat__less__le,axiom,
% 2.67/1.58 ( ( ord_less @ nat )
% 2.67/1.58 = ( ^ [M2: nat,N2: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ M2 @ N2 )
% 2.67/1.58 & ( M2 != N2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_62_nat__le__iff__add,axiom,
% 2.67/1.58 ( ( ord_less_eq @ nat )
% 2.67/1.58 = ( ^ [M2: nat,N2: nat] :
% 2.67/1.58 ? [K2: nat] :
% 2.67/1.58 ( N2
% 2.67/1.58 = ( plus_plus @ nat @ M2 @ K2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_63_trans__le__add2,axiom,
% 2.67/1.58 ! [I: nat,J: nat,M: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.58 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_64_trans__le__add1,axiom,
% 2.67/1.58 ! [I: nat,J: nat,M: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.58 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_65_add__le__mono1,axiom,
% 2.67/1.58 ! [I: nat,J: nat,K: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_66_add__le__mono,axiom,
% 2.67/1.58 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ I @ J )
% 2.67/1.58 => ( ( ord_less_eq @ nat @ K @ L )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_67_le__Suc__ex,axiom,
% 2.67/1.58 ! [K: nat,L: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ K @ L )
% 2.67/1.58 => ? [N3: nat] :
% 2.67/1.58 ( L
% 2.67/1.58 = ( plus_plus @ nat @ K @ N3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_68_add__leD2,axiom,
% 2.67/1.58 ! [M: nat,K: nat,N: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.67/1.58 => ( ord_less_eq @ nat @ K @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_69_add__leD1,axiom,
% 2.67/1.58 ! [M: nat,K: nat,N: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.67/1.58 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_70_le__add2,axiom,
% 2.67/1.58 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_71_le__add1,axiom,
% 2.67/1.58 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_72_add__leE,axiom,
% 2.67/1.58 ! [M: nat,K: nat,N: nat] :
% 2.67/1.58 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 2.67/1.58 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 2.67/1.58 => ~ ( ord_less_eq @ nat @ K @ N ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_73_measure__induct__rule,axiom,
% 2.67/1.58 ! [B3: $tType,A: $tType] :
% 2.67/1.58 ( ( wellorder @ B3 )
% 2.67/1.58 => ! [F: A > B3,P5: A > $o,A2: A] :
% 2.67/1.58 ( ! [X: A] :
% 2.67/1.58 ( ! [Y2: A] :
% 2.67/1.58 ( ( ord_less @ B3 @ ( F @ Y2 ) @ ( F @ X ) )
% 2.67/1.58 => ( P5 @ Y2 ) )
% 2.67/1.58 => ( P5 @ X ) )
% 2.67/1.58 => ( P5 @ A2 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_74_measure__induct,axiom,
% 2.67/1.58 ! [B3: $tType,A: $tType] :
% 2.67/1.58 ( ( wellorder @ B3 )
% 2.67/1.58 => ! [F: A > B3,P5: A > $o,A2: A] :
% 2.67/1.58 ( ! [X: A] :
% 2.67/1.58 ( ! [Y2: A] :
% 2.67/1.58 ( ( ord_less @ B3 @ ( F @ Y2 ) @ ( F @ X ) )
% 2.67/1.58 => ( P5 @ Y2 ) )
% 2.67/1.58 => ( P5 @ X ) )
% 2.67/1.58 => ( P5 @ A2 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_75_add__right__imp__eq,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( cancel_semigroup_add @ A )
% 2.67/1.58 => ! [B: A,A2: A,C: A] :
% 2.67/1.58 ( ( ( plus_plus @ A @ B @ A2 )
% 2.67/1.58 = ( plus_plus @ A @ C @ A2 ) )
% 2.67/1.58 => ( B = C ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_76_add__left__imp__eq,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( cancel_semigroup_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ( plus_plus @ A @ A2 @ B )
% 2.67/1.58 = ( plus_plus @ A @ A2 @ C ) )
% 2.67/1.58 => ( B = C ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_77_add_Oleft__commute,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ab_semigroup_add @ A )
% 2.67/1.58 => ! [B: A,A2: A,C: A] :
% 2.67/1.58 ( ( plus_plus @ A @ B @ ( plus_plus @ A @ A2 @ C ) )
% 2.67/1.58 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_78_add_Ocommute,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ab_semigroup_add @ A )
% 2.67/1.58 => ( ( plus_plus @ A )
% 2.67/1.58 = ( ^ [A3: A,B2: A] : ( plus_plus @ A @ B2 @ A3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_79_add_Oright__cancel,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( group_add @ A )
% 2.67/1.58 => ! [B: A,A2: A,C: A] :
% 2.67/1.58 ( ( ( plus_plus @ A @ B @ A2 )
% 2.67/1.58 = ( plus_plus @ A @ C @ A2 ) )
% 2.67/1.58 = ( B = C ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_80_add_Oleft__cancel,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( group_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ( plus_plus @ A @ A2 @ B )
% 2.67/1.58 = ( plus_plus @ A @ A2 @ C ) )
% 2.67/1.58 = ( B = C ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_81_add_Oassoc,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( semigroup_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.67/1.58 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_82_group__cancel_Oadd2,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( comm_monoid_add @ A )
% 2.67/1.58 => ! [B4: A,K: A,B: A,A2: A] :
% 2.67/1.58 ( ( B4
% 2.67/1.58 = ( plus_plus @ A @ K @ B ) )
% 2.67/1.58 => ( ( plus_plus @ A @ A2 @ B4 )
% 2.67/1.58 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_83_group__cancel_Oadd1,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( comm_monoid_add @ A )
% 2.67/1.58 => ! [A4: A,K: A,A2: A,B: A] :
% 2.67/1.58 ( ( A4
% 2.67/1.58 = ( plus_plus @ A @ K @ A2 ) )
% 2.67/1.58 => ( ( plus_plus @ A @ A4 @ B )
% 2.67/1.58 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_84_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere779506340up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( I = J )
% 2.67/1.58 & ( K = L ) )
% 2.67/1.58 => ( ( plus_plus @ A @ I @ K )
% 2.67/1.58 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_85_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ab_semigroup_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B ) @ C )
% 2.67/1.58 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_86_infinite__descent__measure,axiom,
% 2.67/1.58 ! [A: $tType,P5: A > $o,V4: A > nat,X3: A] :
% 2.67/1.58 ( ! [X: A] :
% 2.67/1.58 ( ~ ( P5 @ X )
% 2.67/1.58 => ? [Y2: A] :
% 2.67/1.58 ( ( ord_less @ nat @ ( V4 @ Y2 ) @ ( V4 @ X ) )
% 2.67/1.58 & ~ ( P5 @ Y2 ) ) )
% 2.67/1.58 => ( P5 @ X3 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_87_linorder__neqE__nat,axiom,
% 2.67/1.58 ! [X3: nat,Y3: nat] :
% 2.67/1.58 ( ( X3 != Y3 )
% 2.67/1.58 => ( ~ ( ord_less @ nat @ X3 @ Y3 )
% 2.67/1.58 => ( ord_less @ nat @ Y3 @ X3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_88_infinite__descent,axiom,
% 2.67/1.58 ! [P5: nat > $o,N: nat] :
% 2.67/1.58 ( ! [N3: nat] :
% 2.67/1.58 ( ~ ( P5 @ N3 )
% 2.67/1.58 => ? [M3: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ M3 @ N3 )
% 2.67/1.58 & ~ ( P5 @ M3 ) ) )
% 2.67/1.58 => ( P5 @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_89_nat__less__induct,axiom,
% 2.67/1.58 ! [P5: nat > $o,N: nat] :
% 2.67/1.58 ( ! [N3: nat] :
% 2.67/1.58 ( ! [M3: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ M3 @ N3 )
% 2.67/1.58 => ( P5 @ M3 ) )
% 2.67/1.58 => ( P5 @ N3 ) )
% 2.67/1.58 => ( P5 @ N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_90_less__irrefl__nat,axiom,
% 2.67/1.58 ! [N: nat] :
% 2.67/1.58 ~ ( ord_less @ nat @ N @ N ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_91_less__not__refl3,axiom,
% 2.67/1.58 ! [S: nat,T: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ S @ T )
% 2.67/1.58 => ( S != T ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_92_less__not__refl2,axiom,
% 2.67/1.58 ! [N: nat,M: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ N @ M )
% 2.67/1.58 => ( M != N ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_93_less__not__refl,axiom,
% 2.67/1.58 ! [N: nat] :
% 2.67/1.58 ~ ( ord_less @ nat @ N @ N ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_94_nat__neq__iff,axiom,
% 2.67/1.58 ! [M: nat,N: nat] :
% 2.67/1.58 ( ( M != N )
% 2.67/1.58 = ( ( ord_less @ nat @ M @ N )
% 2.67/1.58 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_95_size__neq__size__imp__neq,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( size @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ( size_size @ A @ X3 )
% 2.67/1.58 != ( size_size @ A @ Y3 ) )
% 2.67/1.58 => ( X3 != Y3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_96_add__less__le__mono,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A,D: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less_eq @ A @ C @ D )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_97_add__le__less__mono,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A,D: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less @ A @ C @ D )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_98_add__mono__thms__linordered__field_I3_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( ord_less @ A @ I @ J )
% 2.67/1.58 & ( ord_less_eq @ A @ K @ L ) )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_99_add__mono__thms__linordered__field_I4_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( ord_less_eq @ A @ I @ J )
% 2.67/1.58 & ( ord_less @ A @ K @ L ) )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_100_mono__nat__linear__lb,axiom,
% 2.67/1.58 ! [F: nat > nat,M: nat,K: nat] :
% 2.67/1.58 ( ! [M4: nat,N3: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ M4 @ N3 )
% 2.67/1.58 => ( ord_less @ nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus @ nat @ M @ K ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_101_add__less__imp__less__right,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere236663937imp_le @ A )
% 2.67/1.58 => ! [A2: A,C: A,B: A] :
% 2.67/1.58 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) )
% 2.67/1.58 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_102_add__less__imp__less__left,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere236663937imp_le @ A )
% 2.67/1.58 => ! [C: A,A2: A,B: A] :
% 2.67/1.58 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) )
% 2.67/1.58 => ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_103_add__strict__right__mono,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_104_add__strict__left__mono,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_105_add__strict__mono,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( strict2144017051up_add @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A,D: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less @ A @ C @ D )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B @ D ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_106_add__mono__thms__linordered__field_I1_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( ord_less @ A @ I @ J )
% 2.67/1.58 & ( K = L ) )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_107_add__mono__thms__linordered__field_I2_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( I = J )
% 2.67/1.58 & ( ord_less @ A @ K @ L ) )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_108_add__mono__thms__linordered__field_I5_J,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ordere223160158up_add @ A )
% 2.67/1.58 => ! [I: A,J: A,K: A,L: A] :
% 2.67/1.58 ( ( ( ord_less @ A @ I @ J )
% 2.67/1.58 & ( ord_less @ A @ K @ L ) )
% 2.67/1.58 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_109_less__add__eq__less,axiom,
% 2.67/1.58 ! [K: nat,L: nat,M: nat,N: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ K @ L )
% 2.67/1.58 => ( ( ( plus_plus @ nat @ M @ L )
% 2.67/1.58 = ( plus_plus @ nat @ K @ N ) )
% 2.67/1.58 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_110_trans__less__add2,axiom,
% 2.67/1.58 ! [I: nat,J: nat,M: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ I @ J )
% 2.67/1.58 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_111_trans__less__add1,axiom,
% 2.67/1.58 ! [I: nat,J: nat,M: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ I @ J )
% 2.67/1.58 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_112_add__less__mono1,axiom,
% 2.67/1.58 ! [I: nat,J: nat,K: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ I @ J )
% 2.67/1.58 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_113_not__add__less2,axiom,
% 2.67/1.58 ! [J: nat,I: nat] :
% 2.67/1.58 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_114_not__add__less1,axiom,
% 2.67/1.58 ! [I: nat,J: nat] :
% 2.67/1.58 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_115_add__less__mono,axiom,
% 2.67/1.58 ! [I: nat,J: nat,K: nat,L: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ I @ J )
% 2.67/1.58 => ( ( ord_less @ nat @ K @ L )
% 2.67/1.58 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_116_add__lessD1,axiom,
% 2.67/1.58 ! [I: nat,J: nat,K: nat] :
% 2.67/1.58 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 2.67/1.58 => ( ord_less @ nat @ I @ K ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_117_reachableNodes__def,axiom,
% 2.67/1.58 ! [U: nat] :
% 2.67/1.58 ( ( reachableNodes @ capacity @ c @ U )
% 2.67/1.58 = ( collect @ nat @ ( connected @ capacity @ c @ U ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_118_min__dist__def,axiom,
% 2.67/1.58 ! [V: nat,V3: nat] :
% 2.67/1.58 ( ( min_dist @ capacity @ c @ V @ V3 )
% 2.67/1.58 = ( ord_Least @ nat
% 2.67/1.58 @ ^ [D4: nat] : ( dist @ capacity @ c @ V @ D4 @ V3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_119_Graph_OisShortestPath__min__dist__def,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( isShortestPath @ Capacity )
% 2.67/1.58 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat,P: list @ ( product_prod @ nat @ nat ),V5: nat] :
% 2.67/1.58 ( ( isPath @ Capacity @ C2 @ U2 @ P @ V5 )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 2.67/1.58 = ( min_dist @ Capacity @ C2 @ U2 @ V5 ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_120_Graph_OisShortestPath__def,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( isShortestPath @ Capacity )
% 2.67/1.58 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat,P: list @ ( product_prod @ nat @ nat ),V5: nat] :
% 2.67/1.58 ( ( isPath @ Capacity @ C2 @ U2 @ P @ V5 )
% 2.67/1.58 & ! [P4: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ( ( isPath @ Capacity @ C2 @ U2 @ P4 @ V5 )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P4 ) ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_121_Graph_Omin__distI2,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,V3: nat,Q: nat > $o] :
% 2.67/1.58 ( ( connected @ Capacity @ C @ V @ V3 )
% 2.67/1.58 => ( ! [D6: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ V @ D6 @ V3 )
% 2.67/1.58 => ( ! [D7: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ V @ D7 @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ D6 @ D7 ) )
% 2.67/1.58 => ( Q @ D6 ) ) )
% 2.67/1.58 => ( Q @ ( min_dist @ Capacity @ C @ V @ V3 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_122_isShortestPath__alt,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ capacity @ c @ U @ P2 @ V )
% 2.67/1.58 = ( ( isSimplePath @ capacity @ c @ U @ P2 @ V )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 )
% 2.67/1.58 = ( min_dist @ capacity @ c @ U @ V ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_123_Graph_Odist__def,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( dist @ Capacity )
% 2.67/1.58 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,V5: nat,D4: nat,V6: nat] :
% 2.67/1.58 ? [P: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ( ( isPath @ Capacity @ C2 @ V5 @ P @ V6 )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 2.67/1.58 = D4 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_124_Graph_OisPath__distD,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isPath @ Capacity @ C @ U @ P2 @ V )
% 2.67/1.58 => ( dist @ Capacity @ C @ U @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ V ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_125_Graph_Omin__dist__is__dist,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,V3: nat] :
% 2.67/1.58 ( ( connected @ Capacity @ C @ V @ V3 )
% 2.67/1.58 => ( dist @ Capacity @ C @ V @ ( min_dist @ Capacity @ C @ V @ V3 ) @ V3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_126_Graph_Omin__dist__split_I1_J,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ Capacity @ C @ W @ D2 @ V )
% 2.67/1.58 => ( ( ( min_dist @ Capacity @ C @ U @ V )
% 2.67/1.58 = ( plus_plus @ nat @ D1 @ D2 ) )
% 2.67/1.58 => ( ( min_dist @ Capacity @ C @ U @ W )
% 2.67/1.58 = D1 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_127_isSPath__pathLE,axiom,
% 2.67/1.58 ! [S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 2.67/1.58 ( ( isPath @ capacity @ c @ S @ P2 @ T )
% 2.67/1.58 => ? [P6: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ capacity @ c @ S @ P6 @ T ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_128_shortestPath__is__simple,axiom,
% 2.67/1.58 ! [S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 2.67/1.58 ( ( isShortestPath @ capacity @ c @ S @ P2 @ T )
% 2.67/1.58 => ( isSimplePath @ capacity @ c @ S @ P2 @ T ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_129_Graph_OreachableNodes_Ocong,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( reachableNodes @ Capacity )
% 2.67/1.58 = ( reachableNodes @ Capacity ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_130_Graph_OisSimplePath_Ocong,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( isSimplePath @ Capacity )
% 2.67/1.58 = ( isSimplePath @ Capacity ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_131_Graph_OisSPath__pathLE,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 2.67/1.58 ( ( isPath @ Capacity @ C @ S @ P2 @ T )
% 2.67/1.58 => ? [P6: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ Capacity @ C @ S @ P6 @ T ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_132_Graph_OshortestPath__is__simple,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 2.67/1.58 ( ( isShortestPath @ Capacity @ C @ S @ P2 @ T )
% 2.67/1.58 => ( isSimplePath @ Capacity @ C @ S @ P2 @ T ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_133_Graph_OreachableNodes__def,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( reachableNodes @ Capacity )
% 2.67/1.58 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat] : ( collect @ nat @ ( connected @ Capacity @ C2 @ U2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_134_Graph_Omin__dist__def,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( min_dist @ Capacity )
% 2.67/1.58 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,V5: nat,V6: nat] :
% 2.67/1.58 ( ord_Least @ nat
% 2.67/1.58 @ ^ [D4: nat] : ( dist @ Capacity @ C2 @ V5 @ D4 @ V6 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_135_Graph_OisShortestPath__alt,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( isShortestPath @ Capacity )
% 2.67/1.58 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat,P: list @ ( product_prod @ nat @ nat ),V5: nat] :
% 2.67/1.58 ( ( isSimplePath @ Capacity @ C2 @ U2 @ P @ V5 )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 2.67/1.58 = ( min_dist @ Capacity @ C2 @ U2 @ V5 ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_136_Graph_OisPath_Ocong,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( isPath @ Capacity )
% 2.67/1.58 = ( isPath @ Capacity ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_137_Graph_Omin__dist_Ocong,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( min_dist @ Capacity )
% 2.67/1.58 = ( min_dist @ Capacity ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_138_Graph_Oconnected__refl,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat] : ( connected @ Capacity @ C @ V @ V ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_139_Graph_Oconnected_Ocong,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( connected @ Capacity )
% 2.67/1.58 = ( connected @ Capacity ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_140_Graph_Odist_Ocong,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( dist @ Capacity )
% 2.67/1.58 = ( dist @ Capacity ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_141_Graph_OisShortestPath_Ocong,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( isShortestPath @ Capacity )
% 2.67/1.58 = ( isShortestPath @ Capacity ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_142_Graph_Odist__trans,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ Capacity @ C @ W @ D2 @ V )
% 2.67/1.58 => ( dist @ Capacity @ C @ U @ ( plus_plus @ nat @ D1 @ D2 ) @ V ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_143_Graph_Oconnected__def,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( connected @ Capacity )
% 2.67/1.58 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,U2: nat,V5: nat] :
% 2.67/1.58 ? [P: list @ ( product_prod @ nat @ nat )] : ( isPath @ Capacity @ C2 @ U2 @ P @ V5 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_144_Graph_OshortestPath__is__path,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ Capacity @ C @ U @ P2 @ V )
% 2.67/1.58 => ( isPath @ Capacity @ C @ U @ P2 @ V ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_145_Graph_Oconnected__by__dist,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ( ( connected @ Capacity )
% 2.67/1.58 = ( ^ [C2: ( product_prod @ nat @ nat ) > Capacity,V5: nat,V6: nat] :
% 2.67/1.58 ? [D4: nat] : ( dist @ Capacity @ C2 @ V5 @ D4 @ V6 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_146_Graph_Oconnected__distI,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ V @ D @ V3 )
% 2.67/1.58 => ( connected @ Capacity @ C @ V @ V3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_147_Graph_Oobtain__shortest__path,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,V: nat] :
% 2.67/1.58 ( ( connected @ Capacity @ C @ U @ V )
% 2.67/1.58 => ~ ! [P3: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ~ ( isShortestPath @ Capacity @ C @ U @ P3 @ V ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_148_Graph_Omin__dist__less,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,Src: nat,V: nat,D: nat,D3: nat] :
% 2.67/1.58 ( ( connected @ Capacity @ C @ Src @ V )
% 2.67/1.58 => ( ( ( min_dist @ Capacity @ C @ Src @ V )
% 2.67/1.58 = D )
% 2.67/1.58 => ( ( ord_less @ nat @ D3 @ D )
% 2.67/1.58 => ? [V2: nat] :
% 2.67/1.58 ( ( connected @ Capacity @ C @ Src @ V2 )
% 2.67/1.58 & ( ( min_dist @ Capacity @ C @ Src @ V2 )
% 2.67/1.58 = D3 ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_149_Graph_Omin__dist__le,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,Src: nat,V: nat,D3: nat] :
% 2.67/1.58 ( ( connected @ Capacity @ C @ Src @ V )
% 2.67/1.58 => ( ( ord_less_eq @ nat @ D3 @ ( min_dist @ Capacity @ C @ Src @ V ) )
% 2.67/1.58 => ? [V2: nat] :
% 2.67/1.58 ( ( connected @ Capacity @ C @ Src @ V2 )
% 2.67/1.58 & ( ( min_dist @ Capacity @ C @ Src @ V2 )
% 2.67/1.58 = D3 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_150_Graph_Omin__distI__eq,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ V @ D @ V3 )
% 2.67/1.58 => ( ! [D5: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ V @ D5 @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ D @ D5 ) )
% 2.67/1.58 => ( ( min_dist @ Capacity @ C @ V @ V3 )
% 2.67/1.58 = D ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_151_Graph_Omin__dist__minD,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ V @ D @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( min_dist @ Capacity @ C @ V @ V3 ) @ D ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_152_Graph_Omin__dist__split_I2_J,axiom,
% 2.67/1.58 ! [Capacity: $tType] :
% 2.67/1.58 ( ( linordered_idom @ Capacity )
% 2.67/1.58 => ! [C: ( product_prod @ nat @ nat ) > Capacity,U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ Capacity @ C @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ Capacity @ C @ W @ D2 @ V )
% 2.67/1.58 => ( ( ( min_dist @ Capacity @ C @ U @ V )
% 2.67/1.58 = ( plus_plus @ nat @ D1 @ D2 ) )
% 2.67/1.58 => ( ( min_dist @ Capacity @ C @ W @ V )
% 2.67/1.58 = D2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_153__C1_Oprems_C_I3_J,axiom,
% 2.67/1.58 isPath @ a @ c2 @ ua @ p2_a @ t ).
% 2.67/1.58
% 2.67/1.58 thf(fact_154_ex__has__greatest__nat__lemma,axiom,
% 2.67/1.58 ! [A: $tType,P5: A > $o,K: A,F: A > nat,N: nat] :
% 2.67/1.58 ( ( P5 @ K )
% 2.67/1.58 => ( ! [X: A] :
% 2.67/1.58 ( ( P5 @ X )
% 2.67/1.58 => ? [Y2: A] :
% 2.67/1.58 ( ( P5 @ Y2 )
% 2.67/1.58 & ~ ( ord_less_eq @ nat @ ( F @ Y2 ) @ ( F @ X ) ) ) )
% 2.67/1.58 => ? [Y: A] :
% 2.67/1.58 ( ( P5 @ Y )
% 2.67/1.58 & ~ ( ord_less @ nat @ ( F @ Y ) @ ( plus_plus @ nat @ ( F @ K ) @ N ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_155_not__less__Least,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( wellorder @ A )
% 2.67/1.58 => ! [K: A,P5: A > $o] :
% 2.67/1.58 ( ( ord_less @ A @ K @ ( ord_Least @ A @ P5 ) )
% 2.67/1.58 => ~ ( P5 @ K ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_156_Least__le,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( wellorder @ A )
% 2.67/1.58 => ! [P5: A > $o,K: A] :
% 2.67/1.58 ( ( P5 @ K )
% 2.67/1.58 => ( ord_less_eq @ A @ ( ord_Least @ A @ P5 ) @ K ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_157_g_H_Oconnected__by__dist,axiom,
% 2.67/1.58 ! [V: nat,V3: nat] :
% 2.67/1.58 ( ( connected @ a @ c2 @ V @ V3 )
% 2.67/1.58 = ( ? [D4: nat] : ( dist @ a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_158_g_H_Omin__dist__is__dist,axiom,
% 2.67/1.58 ! [V: nat,V3: nat] :
% 2.67/1.58 ( ( connected @ a @ c2 @ V @ V3 )
% 2.67/1.58 => ( dist @ a @ c2 @ V @ ( min_dist @ a @ c2 @ V @ V3 ) @ V3 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_159_g_H_Oobtain__shortest__path,axiom,
% 2.67/1.58 ! [U: nat,V: nat] :
% 2.67/1.58 ( ( connected @ a @ c2 @ U @ V )
% 2.67/1.58 => ~ ! [P3: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ~ ( isShortestPath @ a @ c2 @ U @ P3 @ V ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_160_g_H_OshortestPath__is__simple,axiom,
% 2.67/1.58 ! [S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 2.67/1.58 ( ( isShortestPath @ a @ c2 @ S @ P2 @ T )
% 2.67/1.58 => ( isSimplePath @ a @ c2 @ S @ P2 @ T ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_161_g_H_OreachableNodes__def,axiom,
% 2.67/1.58 ! [U: nat] :
% 2.67/1.58 ( ( reachableNodes @ a @ c2 @ U )
% 2.67/1.58 = ( collect @ nat @ ( connected @ a @ c2 @ U ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_162_g_H_Omin__dist__less,axiom,
% 2.67/1.58 ! [Src: nat,V: nat,D: nat,D3: nat] :
% 2.67/1.58 ( ( connected @ a @ c2 @ Src @ V )
% 2.67/1.58 => ( ( ( min_dist @ a @ c2 @ Src @ V )
% 2.67/1.58 = D )
% 2.67/1.58 => ( ( ord_less @ nat @ D3 @ D )
% 2.67/1.58 => ? [V2: nat] :
% 2.67/1.58 ( ( connected @ a @ c2 @ Src @ V2 )
% 2.67/1.58 & ( ( min_dist @ a @ c2 @ Src @ V2 )
% 2.67/1.58 = D3 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_163_g_H_Omin__distI2,axiom,
% 2.67/1.58 ! [V: nat,V3: nat,Q: nat > $o] :
% 2.67/1.58 ( ( connected @ a @ c2 @ V @ V3 )
% 2.67/1.58 => ( ! [D6: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ V @ D6 @ V3 )
% 2.67/1.58 => ( ! [D7: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ V @ D7 @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ D6 @ D7 ) )
% 2.67/1.58 => ( Q @ D6 ) ) )
% 2.67/1.58 => ( Q @ ( min_dist @ a @ c2 @ V @ V3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_164_g_H_Omin__distI__eq,axiom,
% 2.67/1.58 ! [V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ V @ D @ V3 )
% 2.67/1.58 => ( ! [D5: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ V @ D5 @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ D @ D5 ) )
% 2.67/1.58 => ( ( min_dist @ a @ c2 @ V @ V3 )
% 2.67/1.58 = D ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_165_g_H_Omin__dist__le,axiom,
% 2.67/1.58 ! [Src: nat,V: nat,D3: nat] :
% 2.67/1.58 ( ( connected @ a @ c2 @ Src @ V )
% 2.67/1.58 => ( ( ord_less_eq @ nat @ D3 @ ( min_dist @ a @ c2 @ Src @ V ) )
% 2.67/1.58 => ? [V2: nat] :
% 2.67/1.58 ( ( connected @ a @ c2 @ Src @ V2 )
% 2.67/1.58 & ( ( min_dist @ a @ c2 @ Src @ V2 )
% 2.67/1.58 = D3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_166_g_H_Omin__dist__minD,axiom,
% 2.67/1.58 ! [V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ V @ D @ V3 )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( min_dist @ a @ c2 @ V @ V3 ) @ D ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_167_g_H_Omin__dist__split_I2_J,axiom,
% 2.67/1.58 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ a @ c2 @ W @ D2 @ V )
% 2.67/1.58 => ( ( ( min_dist @ a @ c2 @ U @ V )
% 2.67/1.58 = ( plus_plus @ nat @ D1 @ D2 ) )
% 2.67/1.58 => ( ( min_dist @ a @ c2 @ W @ V )
% 2.67/1.58 = D2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_168_g_H_Omin__dist__split_I1_J,axiom,
% 2.67/1.58 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ a @ c2 @ W @ D2 @ V )
% 2.67/1.58 => ( ( ( min_dist @ a @ c2 @ U @ V )
% 2.67/1.58 = ( plus_plus @ nat @ D1 @ D2 ) )
% 2.67/1.58 => ( ( min_dist @ a @ c2 @ U @ W )
% 2.67/1.58 = D1 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_169_g_H_Odist__trans,axiom,
% 2.67/1.58 ! [U: nat,D1: nat,W: nat,D2: nat,V: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ U @ D1 @ W )
% 2.67/1.58 => ( ( dist @ a @ c2 @ W @ D2 @ V )
% 2.67/1.58 => ( dist @ a @ c2 @ U @ ( plus_plus @ nat @ D1 @ D2 ) @ V ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_170_g_H_Oconnected__def,axiom,
% 2.67/1.58 ! [U: nat,V: nat] :
% 2.67/1.58 ( ( connected @ a @ c2 @ U @ V )
% 2.67/1.58 = ( ? [P: list @ ( product_prod @ nat @ nat )] : ( isPath @ a @ c2 @ U @ P @ V ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_171_g_H_OisSPath__pathLE,axiom,
% 2.67/1.58 ! [S: nat,P2: list @ ( product_prod @ nat @ nat ),T: nat] :
% 2.67/1.58 ( ( isPath @ a @ c2 @ S @ P2 @ T )
% 2.67/1.58 => ? [P6: list @ ( product_prod @ nat @ nat )] : ( isSimplePath @ a @ c2 @ S @ P6 @ T ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_172_g_H_OshortestPath__is__path,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ a @ c2 @ U @ P2 @ V )
% 2.67/1.58 => ( isPath @ a @ c2 @ U @ P2 @ V ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_173_g_H_OisShortestPath__alt,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ a @ c2 @ U @ P2 @ V )
% 2.67/1.58 = ( ( isSimplePath @ a @ c2 @ U @ P2 @ V )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 )
% 2.67/1.58 = ( min_dist @ a @ c2 @ U @ V ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_174_g_H_Omin__dist__def,axiom,
% 2.67/1.58 ! [V: nat,V3: nat] :
% 2.67/1.58 ( ( min_dist @ a @ c2 @ V @ V3 )
% 2.67/1.58 = ( ord_Least @ nat
% 2.67/1.58 @ ^ [D4: nat] : ( dist @ a @ c2 @ V @ D4 @ V3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_175_g_H_Odist__def,axiom,
% 2.67/1.58 ! [V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ V @ D @ V3 )
% 2.67/1.58 = ( ? [P: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ( ( isPath @ a @ c2 @ V @ P @ V3 )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P )
% 2.67/1.58 = D ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_176_g_H_OisPath__distD,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isPath @ a @ c2 @ U @ P2 @ V )
% 2.67/1.58 => ( dist @ a @ c2 @ U @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ V ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_177_g_H_OisShortestPath__min__dist__def,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ a @ c2 @ U @ P2 @ V )
% 2.67/1.58 = ( ( isPath @ a @ c2 @ U @ P2 @ V )
% 2.67/1.58 & ( ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 )
% 2.67/1.58 = ( min_dist @ a @ c2 @ U @ V ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_178_order__refl,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A] : ( ord_less_eq @ A @ X3 @ X3 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_179_g_H_OisShortestPath__def,axiom,
% 2.67/1.58 ! [U: nat,P2: list @ ( product_prod @ nat @ nat ),V: nat] :
% 2.67/1.58 ( ( isShortestPath @ a @ c2 @ U @ P2 @ V )
% 2.67/1.58 = ( ( isPath @ a @ c2 @ U @ P2 @ V )
% 2.67/1.58 & ! [P4: list @ ( product_prod @ nat @ nat )] :
% 2.67/1.58 ( ( isPath @ a @ c2 @ U @ P4 @ V )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P2 ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ P4 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_180_assms_I5_J,axiom,
% 2.67/1.58 isPath @ a @ c2 @ s @ p3 @ t ).
% 2.67/1.58
% 2.67/1.58 thf(fact_181__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062,axiom,
% 2.67/1.58 isPath @ a @ c2 @ u @ p2 @ t ).
% 2.67/1.58
% 2.67/1.58 thf(fact_182_g_H_Oconnected__distI,axiom,
% 2.67/1.58 ! [V: nat,D: nat,V3: nat] :
% 2.67/1.58 ( ( dist @ a @ c2 @ V @ D @ V3 )
% 2.67/1.58 => ( connected @ a @ c2 @ V @ V3 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_183_g_H_Oconnected__refl,axiom,
% 2.67/1.58 ! [V: nat] : ( connected @ a @ c2 @ V @ V ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_184_P2_H,axiom,
% 2.67/1.58 isPath @ a @ c2 @ ua @ p2_a @ t ).
% 2.67/1.58
% 2.67/1.58 thf(fact_185_le__funD,axiom,
% 2.67/1.58 ! [B3: $tType,A: $tType] :
% 2.67/1.58 ( ( ord @ B3 )
% 2.67/1.58 => ! [F: A > B3,G: A > B3,X3: A] :
% 2.67/1.58 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 2.67/1.58 => ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_186_le__funE,axiom,
% 2.67/1.58 ! [B3: $tType,A: $tType] :
% 2.67/1.58 ( ( ord @ B3 )
% 2.67/1.58 => ! [F: A > B3,G: A > B3,X3: A] :
% 2.67/1.58 ( ( ord_less_eq @ ( A > B3 ) @ F @ G )
% 2.67/1.58 => ( ord_less_eq @ B3 @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_187_le__funI,axiom,
% 2.67/1.58 ! [B3: $tType,A: $tType] :
% 2.67/1.58 ( ( ord @ B3 )
% 2.67/1.58 => ! [F: A > B3,G: A > B3] :
% 2.67/1.58 ( ! [X: A] : ( ord_less_eq @ B3 @ ( F @ X ) @ ( G @ X ) )
% 2.67/1.58 => ( ord_less_eq @ ( A > B3 ) @ F @ G ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_188_le__fun__def,axiom,
% 2.67/1.58 ! [B3: $tType,A: $tType] :
% 2.67/1.58 ( ( ord @ B3 )
% 2.67/1.58 => ( ( ord_less_eq @ ( A > B3 ) )
% 2.67/1.58 = ( ^ [F2: A > B3,G2: A > B3] :
% 2.67/1.58 ! [X2: A] : ( ord_less_eq @ B3 @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_189_order__subst1,axiom,
% 2.67/1.58 ! [A: $tType,B3: $tType] :
% 2.67/1.58 ( ( ( order @ B3 )
% 2.67/1.58 & ( order @ A ) )
% 2.67/1.58 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ ( F @ B ) )
% 2.67/1.58 => ( ( ord_less_eq @ B3 @ B @ C )
% 2.67/1.58 => ( ! [X: B3,Y: B3] :
% 2.67/1.58 ( ( ord_less_eq @ B3 @ X @ Y )
% 2.67/1.58 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y ) ) )
% 2.67/1.58 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_190_order__subst2,axiom,
% 2.67/1.58 ! [A: $tType,C4: $tType] :
% 2.67/1.58 ( ( ( order @ C4 )
% 2.67/1.58 & ( order @ A ) )
% 2.67/1.58 => ! [A2: A,B: A,F: A > C4,C: C4] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less_eq @ C4 @ ( F @ B ) @ C )
% 2.67/1.58 => ( ! [X: A,Y: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ X @ Y )
% 2.67/1.58 => ( ord_less_eq @ C4 @ ( F @ X ) @ ( F @ Y ) ) )
% 2.67/1.58 => ( ord_less_eq @ C4 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_191_ord__eq__le__subst,axiom,
% 2.67/1.58 ! [A: $tType,B3: $tType] :
% 2.67/1.58 ( ( ( ord @ B3 )
% 2.67/1.58 & ( ord @ A ) )
% 2.67/1.58 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 2.67/1.58 ( ( A2
% 2.67/1.58 = ( F @ B ) )
% 2.67/1.58 => ( ( ord_less_eq @ B3 @ B @ C )
% 2.67/1.58 => ( ! [X: B3,Y: B3] :
% 2.67/1.58 ( ( ord_less_eq @ B3 @ X @ Y )
% 2.67/1.58 => ( ord_less_eq @ A @ ( F @ X ) @ ( F @ Y ) ) )
% 2.67/1.58 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_192_ord__le__eq__subst,axiom,
% 2.67/1.58 ! [A: $tType,B3: $tType] :
% 2.67/1.58 ( ( ( ord @ B3 )
% 2.67/1.58 & ( ord @ A ) )
% 2.67/1.58 => ! [A2: A,B: A,F: A > B3,C: B3] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ( ( F @ B )
% 2.67/1.58 = C )
% 2.67/1.58 => ( ! [X: A,Y: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ X @ Y )
% 2.67/1.58 => ( ord_less_eq @ B3 @ ( F @ X ) @ ( F @ Y ) ) )
% 2.67/1.58 => ( ord_less_eq @ B3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_193_eq__iff,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.67/1.58 = ( ^ [X2: A,Y5: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ X2 @ Y5 )
% 2.67/1.58 & ( ord_less_eq @ A @ Y5 @ X2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_194_antisym,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.67/1.58 => ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.67/1.58 => ( X3 = Y3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_195_linear,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.67/1.58 | ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_196_eq__refl,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( X3 = Y3 )
% 2.67/1.58 => ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_197_le__cases,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ~ ( ord_less_eq @ A @ X3 @ Y3 )
% 2.67/1.58 => ( ord_less_eq @ A @ Y3 @ X3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_198_order_Otrans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less_eq @ A @ B @ C )
% 2.67/1.58 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_199_le__cases3,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.67/1.58 ( ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.67/1.58 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 2.67/1.58 => ( ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.67/1.58 => ~ ( ord_less_eq @ A @ X3 @ Z2 ) )
% 2.67/1.58 => ( ( ( ord_less_eq @ A @ X3 @ Z2 )
% 2.67/1.58 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 2.67/1.58 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 2.67/1.58 => ~ ( ord_less_eq @ A @ Y3 @ X3 ) )
% 2.67/1.58 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 2.67/1.58 => ~ ( ord_less_eq @ A @ Z2 @ X3 ) )
% 2.67/1.58 => ~ ( ( ord_less_eq @ A @ Z2 @ X3 )
% 2.67/1.58 => ~ ( ord_less_eq @ A @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_200_antisym__conv,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [Y3: A,X3: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ Y3 @ X3 )
% 2.67/1.58 => ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.67/1.58 = ( X3 = Y3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_201_order__class_Oorder_Oeq__iff,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.67/1.58 = ( ^ [A3: A,B2: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A3 @ B2 )
% 2.67/1.58 & ( ord_less_eq @ A @ B2 @ A3 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_202_ord__eq__le__trans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ord @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( A2 = B )
% 2.67/1.58 => ( ( ord_less_eq @ A @ B @ C )
% 2.67/1.58 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_203_ord__le__eq__trans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ord @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ( B = C )
% 2.67/1.58 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_204_order__class_Oorder_Oantisym,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A,B: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less_eq @ A @ B @ A2 )
% 2.67/1.58 => ( A2 = B ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_205_order__trans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.67/1.58 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 2.67/1.58 => ( ord_less_eq @ A @ X3 @ Z2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_206_dual__order_Orefl,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_207_linorder__wlog,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [P5: A > A > $o,A2: A,B: A] :
% 2.67/1.58 ( ! [A5: A,B5: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ A5 @ B5 )
% 2.67/1.58 => ( P5 @ A5 @ B5 ) )
% 2.67/1.58 => ( ! [A5: A,B5: A] :
% 2.67/1.58 ( ( P5 @ B5 @ A5 )
% 2.67/1.58 => ( P5 @ A5 @ B5 ) )
% 2.67/1.58 => ( P5 @ A2 @ B ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_208_dual__order_Otrans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [B: A,A2: A,C: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ B @ A2 )
% 2.67/1.58 => ( ( ord_less_eq @ A @ C @ B )
% 2.67/1.58 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_209_dual__order_Oeq__iff,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 2.67/1.58 = ( ^ [A3: A,B2: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ B2 @ A3 )
% 2.67/1.58 & ( ord_less_eq @ A @ A3 @ B2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_210_dual__order_Oantisym,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [B: A,A2: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ B @ A2 )
% 2.67/1.58 => ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( A2 = B ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_211_dual__order_Ostrict__implies__not__eq,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [B: A,A2: A] :
% 2.67/1.58 ( ( ord_less @ A @ B @ A2 )
% 2.67/1.58 => ( A2 != B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_212_order_Ostrict__implies__not__eq,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A,B: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( A2 != B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_213_not__less__iff__gr__or__eq,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ~ ( ord_less @ A @ X3 @ Y3 ) )
% 2.67/1.58 = ( ( ord_less @ A @ Y3 @ X3 )
% 2.67/1.58 | ( X3 = Y3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_214_dual__order_Ostrict__trans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [B: A,A2: A,C: A] :
% 2.67/1.58 ( ( ord_less @ A @ B @ A2 )
% 2.67/1.58 => ( ( ord_less @ A @ C @ B )
% 2.67/1.58 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_215_linorder__less__wlog,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [P5: A > A > $o,A2: A,B: A] :
% 2.67/1.58 ( ! [A5: A,B5: A] :
% 2.67/1.58 ( ( ord_less @ A @ A5 @ B5 )
% 2.67/1.58 => ( P5 @ A5 @ B5 ) )
% 2.67/1.58 => ( ! [A5: A] : ( P5 @ A5 @ A5 )
% 2.67/1.58 => ( ! [A5: A,B5: A] :
% 2.67/1.58 ( ( P5 @ B5 @ A5 )
% 2.67/1.58 => ( P5 @ A5 @ B5 ) )
% 2.67/1.58 => ( P5 @ A2 @ B ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_216_exists__least__iff,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( wellorder @ A )
% 2.67/1.58 => ( ( ^ [P7: A > $o] :
% 2.67/1.58 ? [X4: A] : ( P7 @ X4 ) )
% 2.67/1.58 = ( ^ [P8: A > $o] :
% 2.67/1.58 ? [N2: A] :
% 2.67/1.58 ( ( P8 @ N2 )
% 2.67/1.58 & ! [M2: A] :
% 2.67/1.58 ( ( ord_less @ A @ M2 @ N2 )
% 2.67/1.58 => ~ ( P8 @ M2 ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_217_less__imp__not__less,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ~ ( ord_less @ A @ Y3 @ X3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_218_order_Ostrict__trans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less @ A @ B @ C )
% 2.67/1.58 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_219_dual__order_Oirrefl,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A] :
% 2.67/1.58 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_220_linorder__cases,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ~ ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ( ( X3 != Y3 )
% 2.67/1.58 => ( ord_less @ A @ Y3 @ X3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_221_less__imp__triv,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A,P5: $o] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ( ( ord_less @ A @ Y3 @ X3 )
% 2.67/1.58 => P5 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_222_less__imp__not__eq2,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ( Y3 != X3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_223_antisym__conv3,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [Y3: A,X3: A] :
% 2.67/1.58 ( ~ ( ord_less @ A @ Y3 @ X3 )
% 2.67/1.58 => ( ( ~ ( ord_less @ A @ X3 @ Y3 ) )
% 2.67/1.58 = ( X3 = Y3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_224_less__induct,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( wellorder @ A )
% 2.67/1.58 => ! [P5: A > $o,A2: A] :
% 2.67/1.58 ( ! [X: A] :
% 2.67/1.58 ( ! [Y2: A] :
% 2.67/1.58 ( ( ord_less @ A @ Y2 @ X )
% 2.67/1.58 => ( P5 @ Y2 ) )
% 2.67/1.58 => ( P5 @ X ) )
% 2.67/1.58 => ( P5 @ A2 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_225_less__not__sym,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ~ ( ord_less @ A @ Y3 @ X3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_226_less__imp__not__eq,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ( X3 != Y3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_227_dual__order_Oasym,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [B: A,A2: A] :
% 2.67/1.58 ( ( ord_less @ A @ B @ A2 )
% 2.67/1.58 => ~ ( ord_less @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_228_ord__less__eq__trans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ord @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ( B = C )
% 2.67/1.58 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_229_ord__eq__less__trans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( ord @ A )
% 2.67/1.58 => ! [A2: A,B: A,C: A] :
% 2.67/1.58 ( ( A2 = B )
% 2.67/1.58 => ( ( ord_less @ A @ B @ C )
% 2.67/1.58 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_230_less__irrefl,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A] :
% 2.67/1.58 ~ ( ord_less @ A @ X3 @ X3 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_231_less__linear,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 | ( X3 = Y3 )
% 2.67/1.58 | ( ord_less @ A @ Y3 @ X3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_232_less__trans,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A,Z2: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ( ( ord_less @ A @ Y3 @ Z2 )
% 2.67/1.58 => ( ord_less @ A @ X3 @ Z2 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_233_less__asym_H,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [A2: A,B: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ~ ( ord_less @ A @ B @ A2 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_234_less__asym,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( preorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ~ ( ord_less @ A @ Y3 @ X3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_235_less__imp__neq,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ( X3 != Y3 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_236_dense,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( dense_order @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ? [Z3: A] :
% 2.67/1.58 ( ( ord_less @ A @ X3 @ Z3 )
% 2.67/1.58 & ( ord_less @ A @ Z3 @ Y3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_237_order_Oasym,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A,B: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ~ ( ord_less @ A @ B @ A2 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_238_neq__iff,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( X3 != Y3 )
% 2.67/1.58 = ( ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 | ( ord_less @ A @ Y3 @ X3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_239_neqE,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linorder @ A )
% 2.67/1.58 => ! [X3: A,Y3: A] :
% 2.67/1.58 ( ( X3 != Y3 )
% 2.67/1.58 => ( ~ ( ord_less @ A @ X3 @ Y3 )
% 2.67/1.58 => ( ord_less @ A @ Y3 @ X3 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_240_gt__ex,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( no_top @ A )
% 2.67/1.58 => ! [X3: A] :
% 2.67/1.58 ? [X_1: A] : ( ord_less @ A @ X3 @ X_1 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_241_lt__ex,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( no_bot @ A )
% 2.67/1.58 => ! [X3: A] :
% 2.67/1.58 ? [Y: A] : ( ord_less @ A @ Y @ X3 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_242_order__less__subst2,axiom,
% 2.67/1.58 ! [A: $tType,C4: $tType] :
% 2.67/1.58 ( ( ( order @ C4 )
% 2.67/1.58 & ( order @ A ) )
% 2.67/1.58 => ! [A2: A,B: A,F: A > C4,C: C4] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ( ord_less @ C4 @ ( F @ B ) @ C )
% 2.67/1.58 => ( ! [X: A,Y: A] :
% 2.67/1.58 ( ( ord_less @ A @ X @ Y )
% 2.67/1.58 => ( ord_less @ C4 @ ( F @ X ) @ ( F @ Y ) ) )
% 2.67/1.58 => ( ord_less @ C4 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_243_order__less__subst1,axiom,
% 2.67/1.58 ! [A: $tType,B3: $tType] :
% 2.67/1.58 ( ( ( order @ B3 )
% 2.67/1.58 & ( order @ A ) )
% 2.67/1.58 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ ( F @ B ) )
% 2.67/1.58 => ( ( ord_less @ B3 @ B @ C )
% 2.67/1.58 => ( ! [X: B3,Y: B3] :
% 2.67/1.58 ( ( ord_less @ B3 @ X @ Y )
% 2.67/1.58 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y ) ) )
% 2.67/1.58 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_244_ord__less__eq__subst,axiom,
% 2.67/1.58 ! [A: $tType,B3: $tType] :
% 2.67/1.58 ( ( ( ord @ B3 )
% 2.67/1.58 & ( ord @ A ) )
% 2.67/1.58 => ! [A2: A,B: A,F: A > B3,C: B3] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ( ( F @ B )
% 2.67/1.58 = C )
% 2.67/1.58 => ( ! [X: A,Y: A] :
% 2.67/1.58 ( ( ord_less @ A @ X @ Y )
% 2.67/1.58 => ( ord_less @ B3 @ ( F @ X ) @ ( F @ Y ) ) )
% 2.67/1.58 => ( ord_less @ B3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_245_ord__eq__less__subst,axiom,
% 2.67/1.58 ! [A: $tType,B3: $tType] :
% 2.67/1.58 ( ( ( ord @ B3 )
% 2.67/1.58 & ( ord @ A ) )
% 2.67/1.58 => ! [A2: A,F: B3 > A,B: B3,C: B3] :
% 2.67/1.58 ( ( A2
% 2.67/1.58 = ( F @ B ) )
% 2.67/1.58 => ( ( ord_less @ B3 @ B @ C )
% 2.67/1.58 => ( ! [X: B3,Y: B3] :
% 2.67/1.58 ( ( ord_less @ B3 @ X @ Y )
% 2.67/1.58 => ( ord_less @ A @ ( F @ X ) @ ( F @ Y ) ) )
% 2.67/1.58 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_246_ex__has__least__nat,axiom,
% 2.67/1.58 ! [A: $tType,P5: A > $o,K: A,M: A > nat] :
% 2.67/1.58 ( ( P5 @ K )
% 2.67/1.58 => ? [X: A] :
% 2.67/1.58 ( ( P5 @ X )
% 2.67/1.58 & ! [Y2: A] :
% 2.67/1.58 ( ( P5 @ Y2 )
% 2.67/1.58 => ( ord_less_eq @ nat @ ( M @ X ) @ ( M @ Y2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_247_LeastI2,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( wellorder @ A )
% 2.67/1.58 => ! [P5: A > $o,A2: A,Q: A > $o] :
% 2.67/1.58 ( ( P5 @ A2 )
% 2.67/1.58 => ( ! [X: A] :
% 2.67/1.58 ( ( P5 @ X )
% 2.67/1.58 => ( Q @ X ) )
% 2.67/1.58 => ( Q @ ( ord_Least @ A @ P5 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_248_LeastI__ex,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( wellorder @ A )
% 2.67/1.58 => ! [P5: A > $o] :
% 2.67/1.58 ( ? [X_12: A] : ( P5 @ X_12 )
% 2.67/1.58 => ( P5 @ ( ord_Least @ A @ P5 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_249_LeastI2__ex,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( wellorder @ A )
% 2.67/1.58 => ! [P5: A > $o,Q: A > $o] :
% 2.67/1.58 ( ? [X_12: A] : ( P5 @ X_12 )
% 2.67/1.58 => ( ! [X: A] :
% 2.67/1.58 ( ( P5 @ X )
% 2.67/1.58 => ( Q @ X ) )
% 2.67/1.58 => ( Q @ ( ord_Least @ A @ P5 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_250_LeastI,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( wellorder @ A )
% 2.67/1.58 => ! [P5: A > $o,K: A] :
% 2.67/1.58 ( ( P5 @ K )
% 2.67/1.58 => ( P5 @ ( ord_Least @ A @ P5 ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_251_order_Onot__eq__order__implies__strict,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A,B: A] :
% 2.67/1.58 ( ( A2 != B )
% 2.67/1.58 => ( ( ord_less_eq @ A @ A2 @ B )
% 2.67/1.58 => ( ord_less @ A @ A2 @ B ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_252_dual__order_Ostrict__implies__order,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [B: A,A2: A] :
% 2.67/1.58 ( ( ord_less @ A @ B @ A2 )
% 2.67/1.58 => ( ord_less_eq @ A @ B @ A2 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_253_dual__order_Ostrict__iff__order,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ( ( ord_less @ A )
% 2.67/1.58 = ( ^ [B2: A,A3: A] :
% 2.67/1.58 ( ( ord_less_eq @ A @ B2 @ A3 )
% 2.67/1.58 & ( A3 != B2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_254_dual__order_Oorder__iff__strict,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ( ( ord_less_eq @ A )
% 2.67/1.58 = ( ^ [B2: A,A3: A] :
% 2.67/1.58 ( ( ord_less @ A @ B2 @ A3 )
% 2.67/1.58 | ( A3 = B2 ) ) ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(fact_255_order_Ostrict__implies__order,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( order @ A )
% 2.67/1.58 => ! [A2: A,B: A] :
% 2.67/1.58 ( ( ord_less @ A @ A2 @ B )
% 2.67/1.58 => ( ord_less_eq @ A @ A2 @ B ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___HOL_Otype,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( type @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Orderings_Oord,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( ord @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Orderings_Oorder,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( order @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Ogroup__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( group_add @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Orderings_Olinorder,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( linorder @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Orderings_Opreorder,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( preorder @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Osemigroup__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( semigroup_add @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( comm_monoid_add @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( ab_semigroup_add @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Ocancel__semigroup__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( cancel_semigroup_add @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( ordere779506340up_add @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( ordere236663937imp_le @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( ordere223160158up_add @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(subcl_Rings_Olinordered__idom___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 2.67/1.58 ! [A: $tType] :
% 2.67/1.58 ( ( linordered_idom @ A )
% 2.67/1.58 => ( strict2144017051up_add @ A ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.67/1.58 ! [A6: $tType,A7: $tType] :
% 2.67/1.58 ( ( preorder @ A7 )
% 2.67/1.58 => ( preorder @ ( A6 > A7 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.67/1.58 ! [A6: $tType,A7: $tType] :
% 2.67/1.58 ( ( order @ A7 )
% 2.67/1.58 => ( order @ ( A6 > A7 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_fun___Orderings_Oord,axiom,
% 2.67/1.58 ! [A6: $tType,A7: $tType] :
% 2.67/1.58 ( ( ord @ A7 )
% 2.67/1.58 => ( ord @ ( A6 > A7 ) ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 2.67/1.58 strict2144017051up_add @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.67/1.58 ordere223160158up_add @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.67/1.58 ordere236663937imp_le @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.67/1.58 canoni770627133id_add @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.67/1.58 ordere779506340up_add @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.67/1.58 cancel_semigroup_add @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.67/1.58 ab_semigroup_add @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 2.67/1.58 comm_monoid_add @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.67/1.58 semigroup_add @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.67/1.58 wellorder @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 2.67/1.58 preorder @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.67/1.58 linorder @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 2.67/1.58 no_top @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 2.67/1.58 order @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 2.67/1.58 ord @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 2.67/1.58 size @ nat ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Set_Oset___Orderings_Opreorder_4,axiom,
% 2.67/1.58 ! [A6: $tType] : ( preorder @ ( set @ A6 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Set_Oset___Orderings_Oorder_5,axiom,
% 2.67/1.58 ! [A6: $tType] : ( order @ ( set @ A6 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Set_Oset___Orderings_Oord_6,axiom,
% 2.67/1.58 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_HOL_Obool___Orderings_Opreorder_7,axiom,
% 2.67/1.58 preorder @ $o ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder_8,axiom,
% 2.67/1.58 linorder @ $o ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_9,axiom,
% 2.67/1.58 order @ $o ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_HOL_Obool___Orderings_Oord_10,axiom,
% 2.67/1.58 ord @ $o ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_List_Olist___Nat_Osize_11,axiom,
% 2.67/1.58 ! [A6: $tType] : ( size @ ( list @ A6 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tcon_Product__Type_Oprod___Nat_Osize_12,axiom,
% 2.67/1.58 ! [A6: $tType,A7: $tType] : ( size @ ( product_prod @ A6 @ A7 ) ) ).
% 2.67/1.58
% 2.67/1.58 thf(tfree_0,hypothesis,
% 2.67/1.58 linordered_idom @ capacity ).
% 2.67/1.58
% 2.67/1.58 thf(tfree_1,hypothesis,
% 2.67/1.58 linordered_idom @ a ).
% 2.67/1.58
% 2.67/1.58 thf(conj_0,conjecture,
% 2.67/1.58 ord_less @ nat @ ( min_dist @ capacity @ c @ s @ t ) @ ( plus_plus @ nat @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p1a ) @ ( size_size @ ( list @ ( product_prod @ nat @ nat ) ) @ p2_a ) ) ).
% 2.67/1.58 ------------------------
% 2.84/1.60 % (7440)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/2Mi)
% 2.84/1.60 % (7441)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_7288 for (2999ds/2Mi)
% 2.84/1.60 % (7442)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_7288 for (2999ds/275Mi)
% 2.84/1.60 % (7443)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/18Mi)
% 2.84/1.60 % (7440)Instruction limit reached!
% 2.84/1.60 % (7440)------------------------------
% 2.84/1.60 % (7440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.60 % (7440)Termination reason: Unknown
% 2.84/1.60 % (7439)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_7288 for (2999ds/27Mi)
% 2.84/1.60 % (7440)Termination phase: shuffling
% 2.84/1.60
% 2.84/1.60 % (7440)Memory used [KB]: 1279
% 2.84/1.60 % (7440)Time elapsed: 0.002 s
% 2.84/1.60 % (7441)Instruction limit reached!
% 2.84/1.60 % (7441)------------------------------
% 2.84/1.60 % (7441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.60 % (7441)Termination reason: Unknown
% 2.84/1.60 % (7441)Termination phase: shuffling
% 2.84/1.60
% 2.84/1.60 % (7441)Memory used [KB]: 1407
% 2.84/1.60 % (7441)Time elapsed: 0.002 s
% 2.84/1.60 % (7441)Instructions burned: 3 (million)
% 2.84/1.60 % (7441)------------------------------
% 2.84/1.60 % (7441)------------------------------
% 2.84/1.60 % (7440)Instructions burned: 2 (million)
% 2.84/1.60 % (7440)------------------------------
% 2.84/1.60 % (7440)------------------------------
% 2.84/1.60 % (7438)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_7288 for (2999ds/4Mi)
% 2.84/1.60 % (7438)Instruction limit reached!
% 2.84/1.60 % (7438)------------------------------
% 2.84/1.60 % (7438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.60 % (7438)Termination reason: Unknown
% 2.84/1.60 % (7438)Termination phase: shuffling
% 2.84/1.60
% 2.84/1.60 % (7438)Memory used [KB]: 1407
% 2.84/1.60 % (7438)Time elapsed: 0.003 s
% 2.84/1.60 % (7438)Instructions burned: 5 (million)
% 2.84/1.60 % (7438)------------------------------
% 2.84/1.60 % (7438)------------------------------
% 2.84/1.60 % (7437)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/183Mi)
% 2.84/1.61 % (7443)Instruction limit reached!
% 2.84/1.61 % (7443)------------------------------
% 2.84/1.61 % (7443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.61 % (7443)Termination reason: Unknown
% 2.84/1.61 % (7443)Termination phase: shuffling
% 2.84/1.61
% 2.84/1.61 % (7443)Memory used [KB]: 1663
% 2.84/1.61 % (7443)Time elapsed: 0.007 s
% 2.84/1.61 % (7443)Instructions burned: 18 (million)
% 2.84/1.61 % (7443)------------------------------
% 2.84/1.61 % (7443)------------------------------
% 2.84/1.61 % (7439)Instruction limit reached!
% 2.84/1.61 % (7439)------------------------------
% 2.84/1.61 % (7439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.61 % (7439)Termination reason: Unknown
% 2.84/1.61 % (7439)Termination phase: Property scanning
% 2.84/1.61
% 2.84/1.61 % (7439)Memory used [KB]: 1791
% 2.84/1.61 % (7439)Time elapsed: 0.011 s
% 2.84/1.61 % (7439)Instructions burned: 29 (million)
% 2.84/1.61 % (7439)------------------------------
% 2.84/1.61 % (7439)------------------------------
% 2.84/1.61 % (7445)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_7288 for (2999ds/37Mi)
% 2.84/1.61 % (7446)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_7288 for (2999ds/15Mi)
% 2.84/1.61 % (7447)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_7288 for (2999ds/3Mi)
% 2.84/1.62 % (7447)Instruction limit reached!
% 2.84/1.62 % (7447)------------------------------
% 2.84/1.62 % (7447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.62 % (7447)Termination reason: Unknown
% 2.84/1.62 % (7447)Termination phase: shuffling
% 2.84/1.62
% 2.84/1.62 % (7447)Memory used [KB]: 1407
% 2.84/1.62 % (7447)Time elapsed: 0.002 s
% 2.84/1.62 % (7447)Instructions burned: 3 (million)
% 2.84/1.62 % (7447)------------------------------
% 2.84/1.62 % (7447)------------------------------
% 2.84/1.62 % (7446)Instruction limit reached!
% 2.84/1.62 % (7446)------------------------------
% 2.84/1.62 % (7446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.62 % (7446)Termination reason: Unknown
% 2.84/1.62 % (7446)Termination phase: shuffling
% 2.84/1.62
% 2.84/1.62 % (7446)Memory used [KB]: 1535
% 2.84/1.62 % (7446)Time elapsed: 0.006 s
% 2.84/1.62 % (7446)Instructions burned: 16 (million)
% 2.84/1.62 % (7446)------------------------------
% 2.84/1.62 % (7446)------------------------------
% 2.84/1.62 % (7444)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/3Mi)
% 2.84/1.62 % (7444)Instruction limit reached!
% 2.84/1.62 % (7444)------------------------------
% 2.84/1.62 % (7444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.62 % (7444)Termination reason: Unknown
% 2.84/1.62 % (7444)Termination phase: shuffling
% 2.84/1.62
% 2.84/1.62 % (7444)Memory used [KB]: 1407
% 2.84/1.62 % (7444)Time elapsed: 0.004 s
% 2.84/1.62 % (7448)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_7288 for (2999ds/1041Mi)
% 2.84/1.62 % (7444)Instructions burned: 3 (million)
% 2.84/1.62 % (7444)------------------------------
% 2.84/1.62 % (7444)------------------------------
% 2.84/1.62 % (7445)Instruction limit reached!
% 2.84/1.62 % (7445)------------------------------
% 2.84/1.62 % (7445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.62 % (7445)Termination reason: Unknown
% 2.84/1.62 % (7445)Termination phase: shuffling
% 2.84/1.62
% 2.84/1.62 % (7445)Memory used [KB]: 2046
% 2.84/1.62 % (7445)Time elapsed: 0.011 s
% 2.84/1.62 % (7445)Instructions burned: 37 (million)
% 2.84/1.62 % (7445)------------------------------
% 2.84/1.62 % (7445)------------------------------
% 2.84/1.63 % (7449)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/7Mi)
% 2.84/1.63 % (7450)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/16Mi)
% 2.84/1.63 % (7449)Instruction limit reached!
% 2.84/1.63 % (7449)------------------------------
% 2.84/1.63 % (7449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.63 % (7449)Termination reason: Unknown
% 2.84/1.63 % (7449)Termination phase: shuffling
% 2.84/1.63
% 2.84/1.63 % (7449)Memory used [KB]: 1407
% 2.84/1.63 % (7449)Time elapsed: 0.003 s
% 2.84/1.63 % (7449)Instructions burned: 7 (million)
% 2.84/1.63 % (7449)------------------------------
% 2.84/1.63 % (7449)------------------------------
% 2.84/1.63 % (7452)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_7288 for (2999ds/3Mi)
% 2.84/1.63 % (7450)Instruction limit reached!
% 2.84/1.63 % (7450)------------------------------
% 2.84/1.63 % (7450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.63 % (7450)Termination reason: Unknown
% 2.84/1.63 % (7450)Termination phase: shuffling
% 2.84/1.63
% 2.84/1.63 % (7450)Memory used [KB]: 1663
% 2.84/1.63 % (7450)Time elapsed: 0.006 s
% 2.84/1.63 % (7450)Instructions burned: 16 (million)
% 2.84/1.63 % (7450)------------------------------
% 2.84/1.63 % (7450)------------------------------
% 2.84/1.63 % (7452)Instruction limit reached!
% 2.84/1.63 % (7452)------------------------------
% 2.84/1.63 % (7452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.63 % (7452)Termination reason: Unknown
% 2.84/1.63 % (7452)Termination phase: shuffling
% 2.84/1.63
% 2.84/1.63 % (7452)Memory used [KB]: 1407
% 2.84/1.63 % (7452)Time elapsed: 0.002 s
% 2.84/1.63 % (7452)Instructions burned: 3 (million)
% 2.84/1.63 % (7452)------------------------------
% 2.84/1.63 % (7452)------------------------------
% 2.84/1.64 % (7451)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_7288 for (2999ds/3Mi)
% 2.84/1.64 % (7453)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/7Mi)
% 2.84/1.64 % (7451)Instruction limit reached!
% 2.84/1.64 % (7451)------------------------------
% 2.84/1.64 % (7451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.64 % (7451)Termination reason: Unknown
% 2.84/1.64 % (7451)Termination phase: shuffling
% 2.84/1.64
% 2.84/1.64 % (7451)Memory used [KB]: 1407
% 2.84/1.64 % (7451)Time elapsed: 0.003 s
% 2.84/1.64 % (7451)Instructions burned: 4 (million)
% 2.84/1.64 % (7451)------------------------------
% 2.84/1.64 % (7451)------------------------------
% 2.84/1.64 % (7453)Instruction limit reached!
% 2.84/1.64 % (7453)------------------------------
% 2.84/1.64 % (7453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.64 % (7453)Termination reason: Unknown
% 2.84/1.64 % (7453)Termination phase: shuffling
% 2.84/1.64
% 2.84/1.64 % (7453)Memory used [KB]: 1407
% 2.84/1.64 % (7453)Time elapsed: 0.003 s
% 2.84/1.64 % (7453)Instructions burned: 7 (million)
% 2.84/1.64 % (7453)------------------------------
% 2.84/1.64 % (7453)------------------------------
% 2.84/1.64 % (7454)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/3Mi)
% 2.84/1.64 % (7455)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/4Mi)
% 2.84/1.64 % (7454)Instruction limit reached!
% 2.84/1.64 % (7454)------------------------------
% 2.84/1.64 % (7454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.64 % (7454)Termination reason: Unknown
% 2.84/1.64 % (7454)Termination phase: shuffling
% 2.84/1.64
% 2.84/1.64 % (7454)Memory used [KB]: 1407
% 2.84/1.64 % (7454)Time elapsed: 0.002 s
% 2.84/1.64 % (7454)Instructions burned: 4 (million)
% 2.84/1.64 % (7454)------------------------------
% 2.84/1.64 % (7454)------------------------------
% 2.84/1.64 % (7455)Instruction limit reached!
% 2.84/1.64 % (7455)------------------------------
% 2.84/1.64 % (7455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.64 % (7455)Termination reason: Unknown
% 2.84/1.64 % (7455)Termination phase: shuffling
% 2.84/1.64
% 2.84/1.64 % (7455)Memory used [KB]: 1407
% 2.84/1.64 % (7455)Time elapsed: 0.003 s
% 2.84/1.64 % (7455)Instructions burned: 7 (million)
% 2.84/1.64 % (7455)------------------------------
% 2.84/1.64 % (7455)------------------------------
% 2.84/1.65 % (7457)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/710Mi)
% 2.84/1.65 % (7456)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/18Mi)
% 2.84/1.65 % (7458)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/6Mi)
% 2.84/1.65 % (7458)Instruction limit reached!
% 2.84/1.65 % (7458)------------------------------
% 2.84/1.65 % (7458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.65 % (7459)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_7288 for (2999ds/902Mi)
% 2.84/1.65 % (7458)Termination reason: Unknown
% 2.84/1.65 % (7458)Termination phase: shuffling
% 2.84/1.65
% 2.84/1.65 % (7458)Memory used [KB]: 1407
% 2.84/1.65 % (7458)Time elapsed: 0.003 s
% 2.84/1.65 % (7458)Instructions burned: 7 (million)
% 2.84/1.65 % (7458)------------------------------
% 2.84/1.65 % (7458)------------------------------
% 2.84/1.66 % (7456)Instruction limit reached!
% 2.84/1.66 % (7456)------------------------------
% 2.84/1.66 % (7456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.66 % (7456)Termination reason: Unknown
% 2.84/1.66 % (7456)Termination phase: shuffling
% 2.84/1.66
% 2.84/1.66 % (7456)Memory used [KB]: 1663
% 2.84/1.66 % (7456)Time elapsed: 0.008 s
% 2.84/1.66 % (7456)Instructions burned: 20 (million)
% 2.84/1.66 % (7456)------------------------------
% 2.84/1.66 % (7456)------------------------------
% 2.84/1.66 % (7460)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_7288 for (2999ds/21Mi)
% 2.84/1.66 % (7461)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/5Mi)
% 2.84/1.67 % (7461)Instruction limit reached!
% 2.84/1.67 % (7461)------------------------------
% 2.84/1.67 % (7461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.67 % (7461)Termination reason: Unknown
% 2.84/1.67 % (7461)Termination phase: shuffling
% 2.84/1.67
% 2.84/1.67 % (7461)Memory used [KB]: 1407
% 2.84/1.67 % (7461)Time elapsed: 0.003 s
% 2.84/1.67 % (7461)Instructions burned: 7 (million)
% 2.84/1.67 % (7461)------------------------------
% 2.84/1.67 % (7461)------------------------------
% 2.84/1.67 % (7460)Instruction limit reached!
% 2.84/1.67 % (7460)------------------------------
% 2.84/1.67 % (7460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.67 % (7460)Termination reason: Unknown
% 2.84/1.67 % (7460)Termination phase: shuffling
% 2.84/1.67
% 2.84/1.67 % (7460)Memory used [KB]: 1663
% 2.84/1.67 % (7460)Time elapsed: 0.008 s
% 2.84/1.67 % (7460)Instructions burned: 22 (million)
% 2.84/1.67 % (7460)------------------------------
% 2.84/1.67 % (7460)------------------------------
% 2.84/1.68 % (7462)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_7288 for (2999ds/6Mi)
% 2.84/1.68 % (7463)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7288 for (2999ds/377Mi)
% 2.84/1.68 % (7462)Instruction limit reached!
% 2.84/1.68 % (7462)------------------------------
% 2.84/1.68 % (7462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.68 % (7462)Termination reason: Unknown
% 2.84/1.68 % (7462)Termination phase: shuffling
% 2.84/1.68
% 2.84/1.68 % (7462)Memory used [KB]: 1407
% 2.84/1.68 % (7462)Time elapsed: 0.003 s
% 2.84/1.68 % (7462)Instructions burned: 8 (million)
% 2.84/1.68 % (7462)------------------------------
% 2.84/1.68 % (7462)------------------------------
% 2.84/1.68 % (7437)Instruction limit reached!
% 2.84/1.68 % (7437)------------------------------
% 2.84/1.68 % (7437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.68 % (7437)Termination reason: Unknown
% 2.84/1.68 % (7437)Termination phase: Saturation
% 2.84/1.68
% 2.84/1.68 % (7437)Memory used [KB]: 7164
% 2.84/1.68 % (7437)Time elapsed: 0.080 s
% 2.84/1.68 % (7437)Instructions burned: 184 (million)
% 2.84/1.68 % (7437)------------------------------
% 2.84/1.68 % (7437)------------------------------
% 2.84/1.68 % (7442)Instruction limit reached!
% 2.84/1.68 % (7442)------------------------------
% 2.84/1.68 % (7442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.68 % (7442)Termination reason: Unknown
% 2.84/1.68 % (7442)Termination phase: Saturation
% 2.84/1.68
% 2.84/1.68 % (7442)Memory used [KB]: 6908
% 2.84/1.68 % (7442)Time elapsed: 0.086 s
% 2.84/1.68 % (7442)Instructions burned: 277 (million)
% 2.84/1.68 % (7442)------------------------------
% 2.84/1.68 % (7442)------------------------------
% 2.84/1.69 % (7464)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_7288 for (2999ds/779Mi)
% 2.84/1.69 % (7465)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_7288 for (2998ds/19Mi)
% 2.84/1.69 % (7466)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7288 for (2998ds/879Mi)
% 2.84/1.70 % (7465)Instruction limit reached!
% 2.84/1.70 % (7465)------------------------------
% 2.84/1.70 % (7465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.70 % (7465)Termination reason: Unknown
% 2.84/1.70 % (7465)Termination phase: shuffling
% 2.84/1.70
% 2.84/1.70 % (7465)Memory used [KB]: 1791
% 2.84/1.70 % (7465)Time elapsed: 0.008 s
% 2.84/1.70 % (7465)Instructions burned: 21 (million)
% 2.84/1.70 % (7465)------------------------------
% 2.84/1.70 % (7465)------------------------------
% 2.84/1.71 % (7468)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7288 for (2998ds/17Mi)
% 2.84/1.72 % (7468)Instruction limit reached!
% 2.84/1.72 % (7468)------------------------------
% 2.84/1.72 % (7468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.72 % (7468)Termination reason: Unknown
% 2.84/1.72 % (7468)Termination phase: shuffling
% 2.84/1.72
% 2.84/1.72 % (7468)Memory used [KB]: 1663
% 2.84/1.72 % (7468)Time elapsed: 0.008 s
% 2.84/1.72 % (7468)Instructions burned: 18 (million)
% 2.84/1.72 % (7468)------------------------------
% 2.84/1.72 % (7468)------------------------------
% 2.84/1.73 % (7470)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7288 for (2998ds/3Mi)
% 2.84/1.73 % (7470)Instruction limit reached!
% 2.84/1.73 % (7470)------------------------------
% 2.84/1.73 % (7470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.73 % (7470)Termination reason: Unknown
% 2.84/1.73 % (7470)Termination phase: shuffling
% 2.84/1.73
% 2.84/1.73 % (7470)Memory used [KB]: 1407
% 2.84/1.73 % (7470)Time elapsed: 0.003 s
% 2.84/1.73 % (7470)Instructions burned: 4 (million)
% 2.84/1.73 % (7470)------------------------------
% 2.84/1.73 % (7470)------------------------------
% 2.84/1.74 % (7471)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7288 for (2998ds/30Mi)
% 2.84/1.75 % (7471)Instruction limit reached!
% 2.84/1.75 % (7471)------------------------------
% 2.84/1.75 % (7471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.75 % (7471)Termination reason: Unknown
% 2.84/1.75 % (7471)Termination phase: Property scanning
% 2.84/1.75
% 2.84/1.75 % (7471)Memory used [KB]: 1791
% 2.84/1.75 % (7471)Time elapsed: 0.012 s
% 2.84/1.75 % (7471)Instructions burned: 31 (million)
% 2.84/1.75 % (7471)------------------------------
% 2.84/1.75 % (7471)------------------------------
% 2.84/1.76 % (7479)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7288 for (2998ds/127Mi)
% 2.84/1.81 % (7463)Instruction limit reached!
% 2.84/1.81 % (7463)------------------------------
% 2.84/1.81 % (7463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.81 % (7463)Termination reason: Unknown
% 2.84/1.81 % (7463)Termination phase: Saturation
% 2.84/1.81
% 2.84/1.81 % (7463)Memory used [KB]: 7675
% 2.84/1.81 % (7463)Time elapsed: 0.135 s
% 2.84/1.81 % (7463)Instructions burned: 378 (million)
% 2.84/1.81 % (7463)------------------------------
% 2.84/1.81 % (7463)------------------------------
% 2.84/1.82 % (7492)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7288 for (2997ds/100Mi)
% 2.84/1.82 % (7479)Instruction limit reached!
% 2.84/1.82 % (7479)------------------------------
% 2.84/1.82 % (7479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.82 % (7479)Termination reason: Unknown
% 2.84/1.82 % (7479)Termination phase: Saturation
% 2.84/1.82
% 2.84/1.82 % (7479)Memory used [KB]: 6908
% 2.84/1.82 % (7479)Time elapsed: 0.067 s
% 2.84/1.82 % (7479)Instructions burned: 128 (million)
% 2.84/1.82 % (7479)------------------------------
% 2.84/1.82 % (7479)------------------------------
% 2.84/1.84 % (7497)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_7288 for (2997ds/3Mi)
% 2.84/1.84 % (7497)Instruction limit reached!
% 2.84/1.84 % (7497)------------------------------
% 2.84/1.84 % (7497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.84 % (7497)Termination reason: Unknown
% 2.84/1.84 % (7497)Termination phase: shuffling
% 2.84/1.84
% 2.84/1.84 % (7497)Memory used [KB]: 1407
% 2.84/1.84 % (7497)Time elapsed: 0.004 s
% 2.84/1.84 % (7497)Instructions burned: 4 (million)
% 2.84/1.84 % (7497)------------------------------
% 2.84/1.84 % (7497)------------------------------
% 2.84/1.85 % (7492)Instruction limit reached!
% 2.84/1.85 % (7492)------------------------------
% 2.84/1.85 % (7492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.85 % (7492)Termination reason: Unknown
% 2.84/1.85 % (7492)Termination phase: Saturation
% 2.84/1.85
% 2.84/1.85 % (7492)Memory used [KB]: 6780
% 2.84/1.85 % (7492)Time elapsed: 0.028 s
% 2.84/1.85 % (7492)Instructions burned: 100 (million)
% 2.84/1.85 % (7492)------------------------------
% 2.84/1.85 % (7492)------------------------------
% 2.84/1.86 % (7501)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_7288 for (2997ds/20Mi)
% 2.84/1.87 % (7501)Instruction limit reached!
% 2.84/1.87 % (7501)------------------------------
% 2.84/1.87 % (7501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.87 % (7501)Termination reason: Unknown
% 2.84/1.87 % (7501)Termination phase: shuffling
% 2.84/1.87
% 2.84/1.87 % (7501)Memory used [KB]: 1663
% 2.84/1.87 % (7501)Time elapsed: 0.008 s
% 2.84/1.87 % (7501)Instructions burned: 21 (million)
% 2.84/1.87 % (7501)------------------------------
% 2.84/1.87 % (7501)------------------------------
% 2.84/1.87 % (7502)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_7288 for (2997ds/86Mi)
% 2.84/1.87 % (7506)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_7288 for (2997ds/107Mi)
% 2.84/1.90 % (7457)Refutation not found, non-redundant clauses discarded% (7457)------------------------------
% 2.84/1.90 % (7457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.90 % (7457)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.84/1.90
% 2.84/1.90 % (7457)Memory used [KB]: 7803
% 2.84/1.90 % (7457)Time elapsed: 0.257 s
% 2.84/1.90 % (7457)Instructions burned: 672 (million)
% 2.84/1.90 % (7457)------------------------------
% 2.84/1.90 % (7457)------------------------------
% 2.84/1.91 % (7506)Instruction limit reached!
% 2.84/1.91 % (7506)------------------------------
% 2.84/1.91 % (7506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.91 % (7506)Termination reason: Unknown
% 2.84/1.91 % (7506)Termination phase: Saturation
% 2.84/1.91
% 2.84/1.91 % (7506)Memory used [KB]: 6780
% 2.84/1.91 % (7506)Time elapsed: 0.033 s
% 2.84/1.91 % (7506)Instructions burned: 108 (million)
% 2.84/1.91 % (7506)------------------------------
% 2.84/1.91 % (7506)------------------------------
% 2.84/1.91 % (7502)Instruction limit reached!
% 2.84/1.91 % (7502)------------------------------
% 2.84/1.91 % (7502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.91 % (7502)Termination reason: Unknown
% 2.84/1.91 % (7502)Termination phase: Saturation
% 2.84/1.91
% 2.84/1.91 % (7502)Memory used [KB]: 6652
% 2.84/1.91 % (7502)Time elapsed: 0.046 s
% 2.84/1.91 % (7502)Instructions burned: 87 (million)
% 2.84/1.91 % (7502)------------------------------
% 2.84/1.91 % (7502)------------------------------
% 2.84/1.92 % (7509)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_7288 for (2996ds/39Mi)
% 2.84/1.92 % (7510)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_7288 for (2996ds/448Mi)
% 2.84/1.93 % (7512)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_7288 for (2996ds/46Mi)
% 2.84/1.93 % (7509)Instruction limit reached!
% 2.84/1.93 % (7509)------------------------------
% 2.84/1.93 % (7509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.93 % (7509)Termination reason: Unknown
% 2.84/1.93 % (7509)Termination phase: shuffling
% 2.84/1.93
% 2.84/1.93 % (7509)Memory used [KB]: 2174
% 2.84/1.93 % (7509)Time elapsed: 0.018 s
% 2.84/1.93 % (7509)Instructions burned: 39 (million)
% 2.84/1.93 % (7509)------------------------------
% 2.84/1.93 % (7509)------------------------------
% 2.84/1.95 % (7514)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_7288 for (2996ds/98Mi)
% 2.84/1.95 % (7512)Instruction limit reached!
% 2.84/1.95 % (7512)------------------------------
% 2.84/1.95 % (7512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.95 % (7512)Termination reason: Unknown
% 2.84/1.95 % (7512)Termination phase: Preprocessing 2
% 2.84/1.95
% 2.84/1.95 % (7512)Memory used [KB]: 1791
% 2.84/1.95 % (7512)Time elapsed: 0.026 s
% 2.84/1.95 % (7512)Instructions burned: 46 (million)
% 2.84/1.95 % (7512)------------------------------
% 2.84/1.95 % (7512)------------------------------
% 2.84/1.97 % (7515)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_7288 for (2996ds/507Mi)
% 2.84/1.99 % (7514)Instruction limit reached!
% 2.84/1.99 % (7514)------------------------------
% 2.84/1.99 % (7514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.99 % (7514)Termination reason: Unknown
% 2.84/1.99 % (7514)Termination phase: Property scanning
% 2.84/1.99
% 2.84/1.99 % (7514)Memory used [KB]: 2174
% 2.84/1.99 % (7514)Time elapsed: 0.045 s
% 2.84/1.99 % (7514)Instructions burned: 98 (million)
% 2.84/1.99 % (7514)------------------------------
% 2.84/1.99 % (7514)------------------------------
% 2.84/2.00 % (7459)Instruction limit reached!
% 2.84/2.00 % (7459)------------------------------
% 2.84/2.00 % (7459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/2.00 % (7459)Termination reason: Unknown
% 2.84/2.00 % (7459)Termination phase: Saturation
% 2.84/2.00
% 2.84/2.00 % (7459)Memory used [KB]: 8315
% 2.84/2.00 % (7459)Time elapsed: 0.347 s
% 2.84/2.00 % (7459)Instructions burned: 902 (million)
% 2.84/2.00 % (7459)------------------------------
% 2.84/2.00 % (7459)------------------------------
% 2.84/2.02 % (7519)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7288 for (2995ds/39Mi)
% 2.84/2.02 % (7518)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_7288 for (2995ds/149Mi)
% 2.84/2.02 % (7464)Instruction limit reached!
% 2.84/2.02 % (7464)------------------------------
% 2.84/2.02 % (7464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/2.02 % (7464)Termination reason: Unknown
% 2.84/2.02 % (7464)Termination phase: Saturation
% 2.84/2.02
% 2.84/2.02 % (7464)Memory used [KB]: 8187
% 2.84/2.02 % (7464)Time elapsed: 0.333 s
% 2.84/2.02 % (7464)Instructions burned: 780 (million)
% 2.84/2.02 % (7464)------------------------------
% 2.84/2.02 % (7464)------------------------------
% 5.41/2.03 % (7448)Instruction limit reached!
% 5.41/2.03 % (7448)------------------------------
% 5.41/2.03 % (7448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.03 % (7448)Termination reason: Unknown
% 5.41/2.03 % (7448)Termination phase: Saturation
% 5.41/2.03
% 5.41/2.03 % (7448)Memory used [KB]: 9850
% 5.41/2.03 % (7448)Time elapsed: 0.407 s
% 5.41/2.03 % (7448)Instructions burned: 1041 (million)
% 5.41/2.03 % (7448)------------------------------
% 5.41/2.03 % (7448)------------------------------
% 5.41/2.03 % (7519)Instruction limit reached!
% 5.41/2.03 % (7519)------------------------------
% 5.41/2.03 % (7519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.03 % (7519)Termination reason: Unknown
% 5.41/2.03 % (7519)Termination phase: shuffling
% 5.41/2.03
% 5.41/2.03 % (7519)Memory used [KB]: 1918
% 5.41/2.03 % (7519)Time elapsed: 0.021 s
% 5.41/2.03 % (7519)Instructions burned: 39 (million)
% 5.41/2.03 % (7519)------------------------------
% 5.41/2.03 % (7519)------------------------------
% 5.41/2.04 % (7520)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_7288 for (2995ds/6Mi)
% 5.41/2.04 % (7520)Instruction limit reached!
% 5.41/2.04 % (7520)------------------------------
% 5.41/2.04 % (7520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.04 % (7520)Termination reason: Unknown
% 5.41/2.04 % (7520)Termination phase: shuffling
% 5.41/2.04
% 5.41/2.04 % (7520)Memory used [KB]: 1407
% 5.41/2.04 % (7520)Time elapsed: 0.005 s
% 5.41/2.04 % (7520)Instructions burned: 7 (million)
% 5.41/2.04 % (7520)------------------------------
% 5.41/2.04 % (7520)------------------------------
% 5.41/2.04 % (7521)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_7288 for (2995ds/1087Mi)
% 5.41/2.05 % (7523)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7288 for (2995ds/47Mi)
% 5.41/2.07 % (7525)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_7288 for (2995ds/44Mi)
% 5.41/2.07 % (7523)Instruction limit reached!
% 5.41/2.07 % (7523)------------------------------
% 5.41/2.07 % (7523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.07 % (7523)Termination reason: Unknown
% 5.41/2.07 % (7523)Termination phase: Preprocessing 3
% 5.41/2.07
% 5.41/2.07 % (7523)Memory used [KB]: 2174
% 5.41/2.07 % (7523)Time elapsed: 0.024 s
% 5.41/2.07 % (7523)Instructions burned: 47 (million)
% 5.41/2.07 % (7523)------------------------------
% 5.41/2.07 % (7523)------------------------------
% 5.41/2.09 % (7525)Instruction limit reached!
% 5.41/2.09 % (7525)------------------------------
% 5.41/2.09 % (7525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.09 % (7525)Termination reason: Unknown
% 5.41/2.09 % (7525)Termination phase: Property scanning
% 5.41/2.09
% 5.41/2.09 % (7525)Memory used [KB]: 2174
% 5.41/2.09 % (7525)Time elapsed: 0.020 s
% 5.41/2.09 % (7525)Instructions burned: 45 (million)
% 5.41/2.09 % (7525)------------------------------
% 5.41/2.09 % (7525)------------------------------
% 5.41/2.09 % (7518)Instruction limit reached!
% 5.41/2.09 % (7518)------------------------------
% 5.41/2.09 % (7518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.09 % (7518)Termination reason: Unknown
% 5.41/2.09 % (7518)Termination phase: Saturation
% 5.41/2.09
% 5.41/2.09 % (7518)Memory used [KB]: 7036
% 5.41/2.09 % (7518)Time elapsed: 0.101 s
% 5.41/2.09 % (7518)Instructions burned: 150 (million)
% 5.41/2.09 % (7518)------------------------------
% 5.41/2.09 % (7518)------------------------------
% 5.41/2.09 % (7466)Instruction limit reached!
% 5.41/2.09 % (7466)------------------------------
% 5.41/2.09 % (7466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.09 % (7466)Termination reason: Unknown
% 5.41/2.09 % (7466)Termination phase: Saturation
% 5.41/2.09
% 5.41/2.09 % (7466)Memory used [KB]: 8059
% 5.41/2.09 % (7466)Time elapsed: 0.397 s
% 5.41/2.09 % (7466)Instructions burned: 880 (million)
% 5.41/2.09 % (7466)------------------------------
% 5.41/2.09 % (7466)------------------------------
% 5.41/2.09 % (7528)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_7288 for (2995ds/432Mi)
% 5.41/2.10 % (7529)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7288 for (2995ds/62Mi)
% 5.41/2.10 % (7530)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_7288 for (2995ds/31Mi)
% 5.41/2.12 % (7531)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7288 for (2995ds/96Mi)
% 5.41/2.12 % (7530)Instruction limit reached!
% 5.41/2.12 % (7530)------------------------------
% 5.41/2.12 % (7530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.41/2.12 % (7530)Termination reason: Unknown
% 5.41/2.12 % (7530)Termination phase: Property scanning
% 5.41/2.12
% 5.41/2.12 % (7530)Memory used [KB]: 1791
% 5.41/2.12 % (7530)Time elapsed: 0.017 s
% 5.41/2.12 % (7530)Instructions burned: 33 (million)
% 5.41/2.12 % (7530)------------------------------
% 5.41/2.12 % (7530)------------------------------
% 6.29/2.13 % (7510)Instruction limit reached!
% 6.29/2.13 % (7510)------------------------------
% 6.29/2.13 % (7510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.13 % (7510)Termination reason: Unknown
% 6.29/2.13 % (7510)Termination phase: Saturation
% 6.29/2.13
% 6.29/2.13 % (7510)Memory used [KB]: 7931
% 6.29/2.13 % (7510)Time elapsed: 0.206 s
% 6.29/2.13 % (7510)Instructions burned: 448 (million)
% 6.29/2.13 % (7510)------------------------------
% 6.29/2.13 % (7510)------------------------------
% 6.29/2.13 % (7529)Instruction limit reached!
% 6.29/2.13 % (7529)------------------------------
% 6.29/2.13 % (7529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.13 % (7529)Termination reason: Unknown
% 6.29/2.13 % (7529)Termination phase: Property scanning
% 6.29/2.13
% 6.29/2.13 % (7529)Memory used [KB]: 2174
% 6.29/2.13 % (7529)Time elapsed: 0.030 s
% 6.29/2.13 % (7529)Instructions burned: 63 (million)
% 6.29/2.13 % (7529)------------------------------
% 6.29/2.13 % (7529)------------------------------
% 6.29/2.14 % (7535)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_7288 for (2994ds/71Mi)
% 6.29/2.14 % (7534)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_7288 for (2994ds/453Mi)
% 6.29/2.15 % (7537)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7288 for (2994ds/83Mi)
% 6.29/2.15 % (7515)Instruction limit reached!
% 6.29/2.15 % (7515)------------------------------
% 6.29/2.15 % (7515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.15 % (7515)Termination reason: Unknown
% 6.29/2.15 % (7515)Termination phase: Saturation
% 6.29/2.15
% 6.29/2.15 % (7515)Memory used [KB]: 7803
% 6.29/2.15 % (7515)Time elapsed: 0.184 s
% 6.29/2.15 % (7515)Instructions burned: 508 (million)
% 6.29/2.15 % (7515)------------------------------
% 6.29/2.15 % (7515)------------------------------
% 6.29/2.16 % (7531)Instruction limit reached!
% 6.29/2.16 % (7531)------------------------------
% 6.29/2.16 % (7531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.16 % (7531)Termination reason: Unknown
% 6.29/2.16 % (7531)Termination phase: Saturation
% 6.29/2.16
% 6.29/2.16 % (7531)Memory used [KB]: 6780
% 6.29/2.16 % (7531)Time elapsed: 0.047 s
% 6.29/2.16 % (7531)Instructions burned: 96 (million)
% 6.29/2.16 % (7531)------------------------------
% 6.29/2.16 % (7531)------------------------------
% 6.29/2.17 % (7535)Instruction limit reached!
% 6.29/2.17 % (7535)------------------------------
% 6.29/2.17 % (7535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.17 % (7535)Termination reason: Unknown
% 6.29/2.17 % (7535)Termination phase: Property scanning
% 6.29/2.17
% 6.29/2.17 % (7535)Memory used [KB]: 2174
% 6.29/2.17 % (7535)Time elapsed: 0.032 s
% 6.29/2.17 % (7535)Instructions burned: 71 (million)
% 6.29/2.17 % (7535)------------------------------
% 6.29/2.17 % (7535)------------------------------
% 6.29/2.17 % (7539)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7288 for (2994ds/11Mi)
% 6.29/2.17 % (7539)Instruction limit reached!
% 6.29/2.17 % (7539)------------------------------
% 6.29/2.17 % (7539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.17 % (7539)Termination reason: Unknown
% 6.29/2.17 % (7539)Termination phase: shuffling
% 6.29/2.17
% 6.29/2.17 % (7539)Memory used [KB]: 1535
% 6.29/2.17 % (7539)Time elapsed: 0.007 s
% 6.29/2.17 % (7539)Instructions burned: 11 (million)
% 6.29/2.17 % (7539)------------------------------
% 6.29/2.17 % (7539)------------------------------
% 6.29/2.18 % (7540)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_7288 for (2994ds/41Mi)
% 6.29/2.18 % (7542)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7288 for (2994ds/6Mi)
% 6.29/2.19 % (7542)Instruction limit reached!
% 6.29/2.19 % (7542)------------------------------
% 6.29/2.19 % (7542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.19 % (7542)Termination reason: Unknown
% 6.29/2.19 % (7542)Termination phase: shuffling
% 6.29/2.19
% 6.29/2.19 % (7542)Memory used [KB]: 1407
% 6.29/2.19 % (7542)Time elapsed: 0.005 s
% 6.29/2.19 % (7542)Instructions burned: 7 (million)
% 6.29/2.19 % (7542)------------------------------
% 6.29/2.19 % (7542)------------------------------
% 6.29/2.19 % (7537)Instruction limit reached!
% 6.29/2.19 % (7537)------------------------------
% 6.29/2.19 % (7537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.19 % (7537)Termination reason: Unknown
% 6.29/2.19 % (7537)Termination phase: Saturation
% 6.29/2.19
% 6.29/2.19 % (7537)Memory used [KB]: 6524
% 6.29/2.19 % (7537)Time elapsed: 0.041 s
% 6.29/2.19 % (7537)Instructions burned: 84 (million)
% 6.29/2.19 % (7537)------------------------------
% 6.29/2.19 % (7537)------------------------------
% 6.59/2.20 % (7540)Instruction limit reached!
% 6.59/2.20 % (7540)------------------------------
% 6.59/2.20 % (7540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.20 % (7540)Termination reason: Unknown
% 6.59/2.20 % (7540)Termination phase: Property scanning
% 6.59/2.20
% 6.59/2.20 % (7540)Memory used [KB]: 2174
% 6.59/2.20 % (7540)Time elapsed: 0.020 s
% 6.59/2.20 % (7540)Instructions burned: 41 (million)
% 6.59/2.20 % (7540)------------------------------
% 6.59/2.20 % (7540)------------------------------
% 6.59/2.20 % (7543)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_7288 for (2993ds/150Mi)
% 6.59/2.20 % (7544)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_7288 for (2993ds/343Mi)
% 6.59/2.21 % (7545)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_7288 for (2993ds/109Mi)
% 6.59/2.21 % (7546)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_7288 for (2993ds/253Mi)
% 6.59/2.26 % (7545)Instruction limit reached!
% 6.59/2.26 % (7545)------------------------------
% 6.59/2.26 % (7545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.26 % (7545)Termination reason: Unknown
% 6.59/2.26 % (7545)Termination phase: Saturation
% 6.59/2.26
% 6.59/2.26 % (7545)Memory used [KB]: 6908
% 6.59/2.26 % (7545)Time elapsed: 0.053 s
% 6.59/2.26 % (7545)Instructions burned: 109 (million)
% 6.59/2.26 % (7545)------------------------------
% 6.59/2.26 % (7545)------------------------------
% 6.59/2.27 % (7543)Instruction limit reached!
% 6.59/2.27 % (7543)------------------------------
% 6.59/2.27 % (7543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.27 % (7543)Termination reason: Unknown
% 6.59/2.27 % (7543)Termination phase: Saturation
% 6.59/2.27
% 6.59/2.27 % (7543)Memory used [KB]: 7036
% 6.59/2.27 % (7543)Time elapsed: 0.067 s
% 6.59/2.27 % (7543)Instructions burned: 151 (million)
% 6.59/2.27 % (7543)------------------------------
% 6.59/2.27 % (7543)------------------------------
% 6.59/2.27 % (7554)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_7288 for (2993ds/140Mi)
% 6.59/2.27 % (7528)Instruction limit reached!
% 6.59/2.27 % (7528)------------------------------
% 6.59/2.27 % (7528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.59/2.27 % (7528)Termination reason: Unknown
% 6.59/2.27 % (7528)Termination phase: Saturation
% 6.59/2.27
% 6.59/2.27 % (7528)Memory used [KB]: 4477
% 6.59/2.27 % (7528)Time elapsed: 0.209 s
% 6.59/2.27 % (7528)Instructions burned: 432 (million)
% 6.59/2.27 % (7528)------------------------------
% 6.59/2.27 % (7528)------------------------------
% 6.59/2.29 % (7555)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_7288 for (2993ds/614Mi)
% 6.97/2.30 % (7556)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_7288 for (2993ds/202Mi)
% 6.97/2.33 % (7544)Instruction limit reached!
% 6.97/2.33 % (7544)------------------------------
% 6.97/2.33 % (7544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.97/2.33 % (7544)Termination reason: Unknown
% 6.97/2.33 % (7544)Termination phase: Saturation
% 6.97/2.33
% 6.97/2.33 % (7544)Memory used [KB]: 7803
% 6.97/2.33 % (7544)Time elapsed: 0.126 s
% 6.97/2.33 % (7544)Instructions burned: 343 (million)
% 6.97/2.33 % (7544)------------------------------
% 6.97/2.33 % (7544)------------------------------
% 6.97/2.33 % (7546)Instruction limit reached!
% 6.97/2.33 % (7546)------------------------------
% 6.97/2.33 % (7546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.97/2.33 % (7546)Termination reason: Unknown
% 6.97/2.33 % (7546)Termination phase: Saturation
% 6.97/2.33
% 6.97/2.33 % (7546)Memory used [KB]: 7419
% 6.97/2.33 % (7546)Time elapsed: 0.118 s
% 6.97/2.33 % (7546)Instructions burned: 254 (million)
% 6.97/2.33 % (7546)------------------------------
% 6.97/2.33 % (7546)------------------------------
% 6.97/2.33 % (7534)Instruction limit reached!
% 6.97/2.33 % (7534)------------------------------
% 6.97/2.33 % (7534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.97/2.33 % (7534)Termination reason: Unknown
% 6.97/2.33 % (7534)Termination phase: Saturation
% 6.97/2.33
% 6.97/2.33 % (7534)Memory used [KB]: 7675
% 6.97/2.33 % (7534)Time elapsed: 0.197 s
% 6.97/2.33 % (7534)Instructions burned: 453 (million)
% 6.97/2.33 % (7534)------------------------------
% 6.97/2.33 % (7534)------------------------------
% 6.97/2.34 % (7563)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_7288 for (2992ds/339Mi)
% 6.97/2.35 % (7554)Instruction limit reached!
% 6.97/2.35 % (7554)------------------------------
% 6.97/2.35 % (7554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.97/2.35 % (7554)Termination reason: Unknown
% 6.97/2.35 % (7554)Termination phase: Saturation
% 6.97/2.35
% 6.97/2.35 % (7554)Memory used [KB]: 6780
% 6.97/2.35 % (7554)Time elapsed: 0.071 s
% 6.97/2.35 % (7554)Instructions burned: 142 (million)
% 6.97/2.35 % (7554)------------------------------
% 6.97/2.35 % (7554)------------------------------
% 6.97/2.35 % (7565)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_7288 for (2992ds/134Mi)
% 6.97/2.36 % (7566)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_7288 for (2992ds/298Mi)
% 6.97/2.36 % (7564)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_7288 for (2992ds/283Mi)
% 7.51/2.40 % (7556)Instruction limit reached!
% 7.51/2.40 % (7556)------------------------------
% 7.51/2.40 % (7556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.40 % (7556)Termination reason: Unknown
% 7.51/2.40 % (7556)Termination phase: Saturation
% 7.51/2.40
% 7.51/2.40 % (7556)Memory used [KB]: 7036
% 7.51/2.40 % (7556)Time elapsed: 0.120 s
% 7.51/2.40 % (7556)Instructions burned: 203 (million)
% 7.51/2.40 % (7556)------------------------------
% 7.51/2.40 % (7556)------------------------------
% 7.51/2.41 % (7565)Instruction limit reached!
% 7.51/2.41 % (7565)------------------------------
% 7.51/2.41 % (7565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.41 % (7565)Termination reason: Unknown
% 7.51/2.41 % (7565)Termination phase: Saturation
% 7.51/2.41
% 7.51/2.41 % (7565)Memory used [KB]: 6908
% 7.51/2.41 % (7565)Time elapsed: 0.065 s
% 7.51/2.41 % (7565)Instructions burned: 134 (million)
% 7.51/2.41 % (7565)------------------------------
% 7.51/2.41 % (7565)------------------------------
% 7.51/2.42 % (7573)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_7288 for (2991ds/192Mi)
% 7.51/2.42 % (7575)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_7288 for (2991ds/258Mi)
% 7.51/2.46 % (7566)Instruction limit reached!
% 7.51/2.46 % (7566)------------------------------
% 7.51/2.46 % (7566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.46 % (7566)Termination reason: Unknown
% 7.51/2.46 % (7566)Termination phase: Saturation
% 7.51/2.46
% 7.51/2.46 % (7566)Memory used [KB]: 8059
% 7.51/2.46 % (7566)Time elapsed: 0.105 s
% 7.51/2.46 % (7566)Instructions burned: 298 (million)
% 7.51/2.46 % (7566)------------------------------
% 7.51/2.46 % (7566)------------------------------
% 7.51/2.47 % (7563)Instruction limit reached!
% 7.51/2.47 % (7563)------------------------------
% 7.51/2.47 % (7563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.47 % (7563)Termination reason: Unknown
% 7.51/2.47 % (7563)Termination phase: Saturation
% 7.51/2.47
% 7.51/2.47 % (7563)Memory used [KB]: 7291
% 7.51/2.47 % (7563)Time elapsed: 0.134 s
% 7.51/2.47 % (7563)Instructions burned: 340 (million)
% 7.51/2.47 % (7563)------------------------------
% 7.51/2.47 % (7563)------------------------------
% 7.51/2.49 % (7580)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_7288 for (2991ds/231Mi)
% 7.51/2.49 % (7578)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_7288 for (2991ds/90Mi)
% 7.95/2.50 % (7564)Instruction limit reached!
% 7.95/2.50 % (7564)------------------------------
% 7.95/2.50 % (7564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.50 % (7564)Termination reason: Unknown
% 7.95/2.50 % (7564)Termination phase: Saturation
% 7.95/2.50
% 7.95/2.50 % (7564)Memory used [KB]: 7547
% 7.95/2.50 % (7564)Time elapsed: 0.165 s
% 7.95/2.50 % (7564)Instructions burned: 283 (million)
% 7.95/2.50 % (7564)------------------------------
% 7.95/2.50 % (7564)------------------------------
% 7.95/2.50 % (7521)Instruction limit reached!
% 7.95/2.50 % (7521)------------------------------
% 7.95/2.50 % (7521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.50 % (7521)Termination reason: Unknown
% 7.95/2.50 % (7521)Termination phase: Saturation
% 7.95/2.50
% 7.95/2.50 % (7521)Memory used [KB]: 8443
% 7.95/2.50 % (7521)Time elapsed: 0.480 s
% 7.95/2.50 % (7521)Instructions burned: 1089 (million)
% 7.95/2.50 % (7521)------------------------------
% 7.95/2.50 % (7521)------------------------------
% 7.95/2.51 % (7573)Instruction limit reached!
% 7.95/2.51 % (7573)------------------------------
% 7.95/2.51 % (7573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.51 % (7573)Termination reason: Unknown
% 7.95/2.51 % (7573)Termination phase: Saturation
% 7.95/2.51
% 7.95/2.51 % (7573)Memory used [KB]: 7803
% 7.95/2.51 % (7573)Time elapsed: 0.104 s
% 7.95/2.51 % (7573)Instructions burned: 192 (million)
% 7.95/2.51 % (7573)------------------------------
% 7.95/2.51 % (7573)------------------------------
% 7.95/2.51 % (7582)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_7288 for (2990ds/458Mi)
% 7.95/2.52 % (7583)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_7288 for (2990ds/31Mi)
% 7.95/2.53 % (7575)Instruction limit reached!
% 7.95/2.53 % (7575)------------------------------
% 7.95/2.53 % (7575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.53 % (7575)Termination reason: Unknown
% 7.95/2.53 % (7575)Termination phase: Saturation
% 7.95/2.53
% 7.95/2.53 % (7575)Memory used [KB]: 7419
% 7.95/2.53 % (7575)Time elapsed: 0.105 s
% 7.95/2.53 % (7575)Instructions burned: 259 (million)
% 7.95/2.53 % (7575)------------------------------
% 7.95/2.53 % (7575)------------------------------
% 7.95/2.53 % (7584)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_7288 for (2990ds/297Mi)
% 7.95/2.53 % (7583)Instruction limit reached!
% 7.95/2.53 % (7583)------------------------------
% 7.95/2.53 % (7583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.53 % (7583)Termination reason: Unknown
% 7.95/2.53 % (7583)Termination phase: Property scanning
% 7.95/2.53
% 7.95/2.53 % (7583)Memory used [KB]: 1791
% 7.95/2.53 % (7583)Time elapsed: 0.012 s
% 7.95/2.53 % (7583)Instructions burned: 31 (million)
% 7.95/2.53 % (7583)------------------------------
% 7.95/2.53 % (7583)------------------------------
% 7.95/2.54 % (7578)Instruction limit reached!
% 7.95/2.54 % (7578)------------------------------
% 7.95/2.54 % (7578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.54 % (7578)Termination reason: Unknown
% 7.95/2.54 % (7578)Termination phase: Saturation
% 7.95/2.54
% 7.95/2.54 % (7578)Memory used [KB]: 6780
% 7.95/2.54 % (7578)Time elapsed: 0.043 s
% 7.95/2.54 % (7578)Instructions burned: 90 (million)
% 7.95/2.54 % (7578)------------------------------
% 7.95/2.54 % (7578)------------------------------
% 7.95/2.54 % (7585)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_7288 for (2990ds/987Mi)
% 7.95/2.55 % (7586)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_7288 for (2990ds/182Mi)
% 7.95/2.56 % (7589)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_7288 for (2990ds/182Mi)
% 7.95/2.56 % (7555)Instruction limit reached!
% 7.95/2.56 % (7555)------------------------------
% 7.95/2.56 % (7555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.56 % (7555)Termination reason: Unknown
% 7.95/2.56 % (7555)Termination phase: Saturation
% 7.95/2.56
% 7.95/2.56 % (7555)Memory used [KB]: 8187
% 7.95/2.56 % (7555)Time elapsed: 0.279 s
% 7.95/2.56 % (7555)Instructions burned: 616 (million)
% 7.95/2.56 % (7555)------------------------------
% 7.95/2.56 % (7555)------------------------------
% 7.95/2.57 % (7591)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_7288 for (2990ds/154Mi)
% 7.95/2.59 % (7580)Instruction limit reached!
% 7.95/2.59 % (7580)------------------------------
% 7.95/2.59 % (7580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.95/2.59 % (7580)Termination reason: Unknown
% 7.95/2.59 % (7580)Termination phase: Saturation
% 7.95/2.59
% 7.95/2.59 % (7580)Memory used [KB]: 6908
% 7.95/2.59 % (7580)Time elapsed: 0.102 s
% 7.95/2.59 % (7580)Instructions burned: 231 (million)
% 7.95/2.59 % (7580)------------------------------
% 7.95/2.59 % (7580)------------------------------
% 9.25/2.60 % (7592)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_7288 for (2990ds/79Mi)
% 9.25/2.63 % (7591)Instruction limit reached!
% 9.25/2.63 % (7591)------------------------------
% 9.25/2.63 % (7591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.25/2.63 % (7591)Termination reason: Unknown
% 9.25/2.63 % (7591)Termination phase: Saturation
% 9.25/2.63
% 9.25/2.63 % (7591)Memory used [KB]: 2814
% 9.25/2.63 % (7591)Time elapsed: 0.058 s
% 9.25/2.63 % (7591)Instructions burned: 154 (million)
% 9.25/2.63 % (7591)------------------------------
% 9.25/2.63 % (7591)------------------------------
% 9.25/2.63 % (7586)Instruction limit reached!
% 9.25/2.63 % (7586)------------------------------
% 9.25/2.63 % (7586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.25/2.63 % (7586)Termination reason: Unknown
% 9.25/2.63 % (7586)Termination phase: Saturation
% 9.25/2.63
% 9.25/2.63 % (7586)Memory used [KB]: 7036
% 9.25/2.63 % (7586)Time elapsed: 0.091 s
% 9.25/2.63 % (7586)Instructions burned: 182 (million)
% 9.25/2.63 % (7586)------------------------------
% 9.25/2.63 % (7586)------------------------------
% 9.25/2.64 % (7589)Instruction limit reached!
% 9.25/2.64 % (7589)------------------------------
% 9.25/2.64 % (7589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.25/2.64 % (7589)Termination reason: Unknown
% 9.25/2.64 % (7589)Termination phase: Saturation
% 9.25/2.64
% 9.25/2.64 % (7589)Memory used [KB]: 7036
% 9.25/2.64 % (7589)Time elapsed: 0.102 s
% 9.25/2.64 % (7589)Instructions burned: 183 (million)
% 9.25/2.64 % (7589)------------------------------
% 9.25/2.64 % (7589)------------------------------
% 9.25/2.64 % (7592)Instruction limit reached!
% 9.25/2.64 % (7592)------------------------------
% 9.25/2.64 % (7592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.25/2.64 % (7592)Termination reason: Unknown
% 9.25/2.64 % (7592)Termination phase: Property scanning
% 9.25/2.64
% 9.25/2.64 % (7592)Memory used [KB]: 2174
% 9.25/2.64 % (7592)Time elapsed: 0.039 s
% 9.25/2.64 % (7592)Instructions burned: 79 (million)
% 9.25/2.64 % (7592)------------------------------
% 9.25/2.64 % (7592)------------------------------
% 9.25/2.64 % (7584)Instruction limit reached!
% 9.25/2.64 % (7584)------------------------------
% 9.25/2.64 % (7584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.25/2.64 % (7584)Termination reason: Unknown
% 9.25/2.64 % (7584)Termination phase: Saturation
% 9.25/2.64
% 9.25/2.64 % (7584)Memory used [KB]: 7419
% 9.25/2.64 % (7584)Time elapsed: 0.114 s
% 9.25/2.64 % (7584)Instructions burned: 300 (million)
% 9.25/2.64 % (7584)------------------------------
% 9.25/2.64 % (7584)------------------------------
% 9.25/2.65 % (7599)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_7288 for (2989ds/164Mi)
% 9.25/2.65 % (7596)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_7288 for (2989ds/114Mi)
% 9.25/2.66 % (7597)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_7288 for (2989ds/922Mi)
% 9.25/2.66 % (7598)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_7288 for (2989ds/182Mi)
% 9.25/2.66 % (7595)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_7288 for (2989ds/216Mi)
% 9.71/2.70 % (7599)Instruction limit reached!
% 9.71/2.70 % (7599)------------------------------
% 9.71/2.70 % (7599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/2.70 % (7599)Termination reason: Unknown
% 9.71/2.70 % (7599)Termination phase: Saturation
% 9.71/2.70
% 9.71/2.70 % (7599)Memory used [KB]: 2430
% 9.71/2.70 % (7599)Time elapsed: 0.048 s
% 9.71/2.70 % (7599)Instructions burned: 166 (million)
% 9.71/2.70 % (7599)------------------------------
% 9.71/2.70 % (7599)------------------------------
% 9.71/2.71 % (7596)Instruction limit reached!
% 9.71/2.71 % (7596)------------------------------
% 9.71/2.71 % (7596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/2.71 % (7596)Termination reason: Unknown
% 9.71/2.71 % (7596)Termination phase: Saturation
% 9.71/2.71
% 9.71/2.71 % (7596)Memory used [KB]: 6908
% 9.71/2.71 % (7596)Time elapsed: 0.057 s
% 9.71/2.71 % (7596)Instructions burned: 115 (million)
% 9.71/2.71 % (7596)------------------------------
% 9.71/2.71 % (7596)------------------------------
% 9.71/2.71 % (7604)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_7288 for (2988ds/50Mi)
% 9.71/2.72 % (7606)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_7288 for (2988ds/368Mi)
% 9.71/2.72 % (7604)Instruction limit reached!
% 9.71/2.72 % (7604)------------------------------
% 9.71/2.72 % (7604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/2.72 % (7604)Termination reason: Unknown
% 9.71/2.72 % (7604)Termination phase: Property scanning
% 9.71/2.72
% 9.71/2.72 % (7604)Memory used [KB]: 2174
% 9.71/2.72 % (7604)Time elapsed: 0.016 s
% 9.71/2.72 % (7604)Instructions burned: 52 (million)
% 9.71/2.72 % (7604)------------------------------
% 9.71/2.72 % (7604)------------------------------
% 9.71/2.73 % (7598)Instruction limit reached!
% 9.71/2.73 % (7598)------------------------------
% 9.71/2.73 % (7598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/2.73 % (7598)Termination reason: Unknown
% 9.71/2.73 % (7598)Termination phase: Saturation
% 9.71/2.73
% 9.71/2.73 % (7598)Memory used [KB]: 7291
% 9.71/2.73 % (7598)Time elapsed: 0.079 s
% 9.71/2.73 % (7598)Instructions burned: 184 (million)
% 9.71/2.73 % (7598)------------------------------
% 9.71/2.73 % (7598)------------------------------
% 9.71/2.74 % (7582)Instruction limit reached!
% 9.71/2.74 % (7582)------------------------------
% 9.71/2.74 % (7582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/2.74 % (7582)Termination reason: Unknown
% 9.71/2.74 % (7582)Termination phase: Saturation
% 9.71/2.74
% 9.71/2.74 % (7582)Memory used [KB]: 7675
% 9.71/2.74 % (7582)Time elapsed: 0.225 s
% 9.71/2.74 % (7582)Instructions burned: 459 (million)
% 9.71/2.74 % (7582)------------------------------
% 9.71/2.74 % (7582)------------------------------
% 9.71/2.74 % (7611)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_7288 for (2988ds/1021Mi)
% 9.71/2.74 % (7612)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_7288 for (2988ds/267Mi)
% 9.71/2.75 % (7613)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_7288 for (2988ds/204Mi)
% 9.71/2.76 % (7595)Instruction limit reached!
% 9.71/2.76 % (7595)------------------------------
% 9.71/2.76 % (7595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.71/2.76 % (7595)Termination reason: Unknown
% 9.71/2.76 % (7595)Termination phase: Saturation
% 9.71/2.76
% 9.71/2.76 % (7595)Memory used [KB]: 7419
% 9.71/2.76 % (7595)Time elapsed: 0.122 s
% 9.71/2.76 % (7595)Instructions burned: 217 (million)
% 9.71/2.76 % (7595)------------------------------
% 9.71/2.76 % (7595)------------------------------
% 9.71/2.78 % (7614)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_7288 for (2988ds/26Mi)
% 10.30/2.80 % (7614)Instruction limit reached!
% 10.30/2.80 % (7614)------------------------------
% 10.30/2.80 % (7614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.80 % (7614)Termination reason: Unknown
% 10.30/2.80 % (7614)Termination phase: shuffling
% 10.30/2.80
% 10.30/2.80 % (7614)Memory used [KB]: 1791
% 10.30/2.80 % (7614)Time elapsed: 0.014 s
% 10.30/2.80 % (7614)Instructions burned: 27 (million)
% 10.30/2.80 % (7614)------------------------------
% 10.30/2.80 % (7614)------------------------------
% 10.30/2.82 % (7616)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_7288 for (2987ds/53Mi)
% 10.30/2.84 % (7616)Instruction limit reached!
% 10.30/2.84 % (7616)------------------------------
% 10.30/2.84 % (7616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.84 % (7616)Termination reason: Unknown
% 10.30/2.84 % (7616)Termination phase: Property scanning
% 10.30/2.84
% 10.30/2.84 % (7616)Memory used [KB]: 2174
% 10.30/2.84 % (7616)Time elapsed: 0.019 s
% 10.30/2.84 % (7616)Instructions burned: 53 (million)
% 10.30/2.84 % (7616)------------------------------
% 10.30/2.84 % (7616)------------------------------
% 10.30/2.85 % (7613)Instruction limit reached!
% 10.30/2.85 % (7613)------------------------------
% 10.30/2.85 % (7613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.85 % (7613)Termination reason: Unknown
% 10.30/2.85 % (7613)Termination phase: Saturation
% 10.30/2.85
% 10.30/2.85 % (7613)Memory used [KB]: 7036
% 10.30/2.85 % (7613)Time elapsed: 0.125 s
% 10.30/2.85 % (7613)Instructions burned: 204 (million)
% 10.30/2.85 % (7613)------------------------------
% 10.30/2.85 % (7613)------------------------------
% 10.30/2.86 % (7612)Instruction limit reached!
% 10.30/2.86 % (7612)------------------------------
% 10.30/2.86 % (7612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.86 % (7612)Termination reason: Unknown
% 10.30/2.86 % (7612)Termination phase: Saturation
% 10.30/2.86
% 10.30/2.86 % (7612)Memory used [KB]: 7547
% 10.30/2.86 % (7612)Time elapsed: 0.137 s
% 10.30/2.86 % (7612)Instructions burned: 267 (million)
% 10.30/2.86 % (7612)------------------------------
% 10.30/2.86 % (7612)------------------------------
% 10.30/2.86 % (7622)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_7288 for (2987ds/4436Mi)
% 10.30/2.87 % (7623)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_7288 for (2987ds/1539Mi)
% 10.30/2.87 % (7624)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_7288 for (2987ds/408Mi)
% 10.60/2.90 % (7606)Instruction limit reached!
% 10.60/2.90 % (7606)------------------------------
% 10.60/2.90 % (7606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.60/2.90 % (7606)Termination reason: Unknown
% 10.60/2.90 % (7606)Termination phase: Saturation
% 10.60/2.90
% 10.60/2.90 % (7606)Memory used [KB]: 8315
% 10.60/2.90 % (7606)Time elapsed: 0.207 s
% 10.60/2.90 % (7606)Instructions burned: 368 (million)
% 10.60/2.90 % (7606)------------------------------
% 10.60/2.90 % (7606)------------------------------
% 10.60/2.92 % (7629)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_7288 for (2986ds/5205Mi)
% 10.60/3.02 % (7585)Instruction limit reached!
% 10.60/3.02 % (7585)------------------------------
% 10.60/3.02 % (7585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.60/3.02 % (7585)Termination reason: Unknown
% 10.60/3.02 % (7585)Termination phase: Saturation
% 10.60/3.02
% 10.60/3.02 % (7585)Memory used [KB]: 9722
% 10.60/3.02 % (7585)Time elapsed: 0.478 s
% 10.60/3.02 % (7585)Instructions burned: 988 (million)
% 10.60/3.02 % (7585)------------------------------
% 10.60/3.02 % (7585)------------------------------
% 12.02/3.03 % (7624)Instruction limit reached!
% 12.02/3.03 % (7624)------------------------------
% 12.02/3.03 % (7624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.03 % (7624)Termination reason: Unknown
% 12.02/3.03 % (7624)Termination phase: Saturation
% 12.02/3.03
% 12.02/3.03 % (7624)Memory used [KB]: 7931
% 12.02/3.03 % (7624)Time elapsed: 0.155 s
% 12.02/3.03 % (7624)Instructions burned: 410 (million)
% 12.02/3.03 % (7624)------------------------------
% 12.02/3.03 % (7624)------------------------------
% 12.02/3.04 % (7637)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_7288 for (2985ds/4350Mi)
% 12.02/3.04 % (7636)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_7288 for (2985ds/1913Mi)
% 12.02/3.09 % (7597)Instruction limit reached!
% 12.02/3.09 % (7597)------------------------------
% 12.02/3.09 % (7597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.02/3.09 % (7597)Termination reason: Unknown
% 12.02/3.09 % (7597)Termination phase: Saturation
% 12.02/3.09
% 12.02/3.09 % (7597)Memory used [KB]: 7803
% 12.02/3.09 % (7597)Time elapsed: 0.438 s
% 12.02/3.09 % (7597)Instructions burned: 923 (million)
% 12.02/3.09 % (7597)------------------------------
% 12.02/3.09 % (7597)------------------------------
% 12.02/3.11 % (7639)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_7288 for (2984ds/68Mi)
% 13.01/3.14 % (7639)Instruction limit reached!
% 13.01/3.14 % (7639)------------------------------
% 13.01/3.14 % (7639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.01/3.14 % (7639)Termination reason: Unknown
% 13.01/3.14 % (7639)Termination phase: shuffling
% 13.01/3.14
% 13.01/3.14 % (7639)Memory used [KB]: 2174
% 13.01/3.14 % (7639)Time elapsed: 0.030 s
% 13.01/3.14 % (7639)Instructions burned: 71 (million)
% 13.01/3.14 % (7639)------------------------------
% 13.01/3.14 % (7639)------------------------------
% 13.01/3.15 % (7640)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_7288 for (2984ds/358Mi)
% 13.34/3.22 % (7611)Instruction limit reached!
% 13.34/3.22 % (7611)------------------------------
% 13.34/3.22 % (7611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.22 % (7611)Termination reason: Unknown
% 13.34/3.22 % (7611)Termination phase: Saturation
% 13.34/3.22
% 13.34/3.22 % (7611)Memory used [KB]: 8571
% 13.34/3.22 % (7611)Time elapsed: 0.489 s
% 13.34/3.22 % (7611)Instructions burned: 1021 (million)
% 13.34/3.22 % (7611)------------------------------
% 13.34/3.22 % (7611)------------------------------
% 13.34/3.23 % (7643)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_7288 for (2983ds/31Mi)
% 13.34/3.25 % (7643)Instruction limit reached!
% 13.34/3.25 % (7643)------------------------------
% 13.34/3.25 % (7643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.34/3.25 % (7643)Termination reason: Unknown
% 13.34/3.25 % (7643)Termination phase: Property scanning
% 13.34/3.25
% 13.34/3.25 % (7643)Memory used [KB]: 1791
% 13.34/3.25 % (7643)Time elapsed: 0.018 s
% 13.34/3.25 % (7643)Instructions burned: 32 (million)
% 13.34/3.25 % (7643)------------------------------
% 13.34/3.25 % (7643)------------------------------
% 13.34/3.27 % (7644)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_7288 for (2983ds/279Mi)
% 13.68/3.31 % (7640)Instruction limit reached!
% 13.68/3.31 % (7640)------------------------------
% 13.68/3.31 % (7640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.31 % (7640)Termination reason: Unknown
% 13.68/3.31 % (7640)Termination phase: Saturation
% 13.68/3.31
% 13.68/3.31 % (7640)Memory used [KB]: 7419
% 13.68/3.31 % (7640)Time elapsed: 0.164 s
% 13.68/3.31 % (7640)Instructions burned: 359 (million)
% 13.68/3.31 % (7640)------------------------------
% 13.68/3.31 % (7640)------------------------------
% 13.68/3.33 % (7647)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_7288 for (2982ds/258Mi)
% 14.11/3.42 % (7644)Instruction limit reached!
% 14.11/3.42 % (7644)------------------------------
% 14.11/3.42 % (7644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.11/3.42 % (7644)Termination reason: Unknown
% 14.11/3.42 % (7644)Termination phase: Saturation
% 14.11/3.42
% 14.11/3.42 % (7644)Memory used [KB]: 7675
% 14.11/3.42 % (7644)Time elapsed: 0.153 s
% 14.11/3.42 % (7644)Instructions burned: 281 (million)
% 14.11/3.42 % (7644)------------------------------
% 14.11/3.42 % (7644)------------------------------
% 14.11/3.43 % (7651)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_7288 for (2981ds/26Mi)
% 14.11/3.44 % (7651)Instruction limit reached!
% 14.11/3.44 % (7651)------------------------------
% 14.11/3.44 % (7651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.11/3.44 % (7651)Termination reason: Unknown
% 14.11/3.44 % (7651)Termination phase: shuffling
% 14.11/3.44
% 14.11/3.44 % (7651)Memory used [KB]: 1791
% 14.11/3.44 % (7651)Time elapsed: 0.009 s
% 14.11/3.44 % (7651)Instructions burned: 27 (million)
% 14.11/3.44 % (7651)------------------------------
% 14.11/3.44 % (7651)------------------------------
% 14.11/3.45 % (7652)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_7288 for (2981ds/995Mi)
% 14.11/3.46 % (7647)Instruction limit reached!
% 14.11/3.46 % (7647)------------------------------
% 14.11/3.46 % (7647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.11/3.46 % (7647)Termination reason: Unknown
% 14.11/3.46 % (7647)Termination phase: Saturation
% 14.11/3.46
% 14.11/3.46 % (7647)Memory used [KB]: 7419
% 14.11/3.46 % (7647)Time elapsed: 0.131 s
% 14.11/3.46 % (7647)Instructions burned: 258 (million)
% 14.11/3.46 % (7647)------------------------------
% 14.11/3.46 % (7647)------------------------------
% 14.11/3.47 % (7653)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_7288 for (2981ds/373Mi)
% 14.97/3.60 % (7623)Instruction limit reached!
% 14.97/3.60 % (7623)------------------------------
% 14.97/3.60 % (7623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.97/3.60 % (7623)Termination reason: Unknown
% 14.97/3.60 % (7623)Termination phase: Saturation
% 14.97/3.60
% 14.97/3.60 % (7623)Memory used [KB]: 10618
% 14.97/3.60 % (7623)Time elapsed: 0.734 s
% 14.97/3.60 % (7623)Instructions burned: 1539 (million)
% 14.97/3.60 % (7623)------------------------------
% 14.97/3.60 % (7623)------------------------------
% 14.97/3.62 % (7653)Instruction limit reached!
% 14.97/3.62 % (7653)------------------------------
% 14.97/3.62 % (7653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.97/3.62 % (7653)Termination reason: Unknown
% 14.97/3.62 % (7653)Termination phase: Saturation
% 14.97/3.62
% 14.97/3.62 % (7653)Memory used [KB]: 8187
% 14.97/3.62 % (7653)Time elapsed: 0.152 s
% 14.97/3.62 % (7653)Instructions burned: 374 (million)
% 14.97/3.62 % (7653)------------------------------
% 14.97/3.62 % (7653)------------------------------
% 14.97/3.63 % (7657)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_7288 for (2979ds/253Mi)
% 14.97/3.64 % (7658)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_7288 for (2979ds/832Mi)
% 15.37/3.70 % (7657)Instruction limit reached!
% 15.37/3.70 % (7657)------------------------------
% 15.37/3.70 % (7657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.37/3.70 % (7657)Termination reason: Unknown
% 15.37/3.70 % (7657)Termination phase: Saturation
% 15.37/3.70
% 15.37/3.70 % (7657)Memory used [KB]: 7547
% 15.37/3.70 % (7657)Time elapsed: 0.074 s
% 15.37/3.70 % (7657)Instructions burned: 254 (million)
% 15.37/3.70 % (7657)------------------------------
% 15.37/3.70 % (7657)------------------------------
% 15.37/3.71 % (7660)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_7288 for (2978ds/668Mi)
% 15.65/3.89 % (7652)Instruction limit reached!
% 15.65/3.89 % (7652)------------------------------
% 15.65/3.89 % (7652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/3.89 % (7652)Termination reason: Unknown
% 15.65/3.89 % (7652)Termination phase: Saturation
% 15.65/3.89
% 15.65/3.89 % (7652)Memory used [KB]: 9594
% 15.65/3.89 % (7652)Time elapsed: 0.435 s
% 15.65/3.89 % (7652)Instructions burned: 996 (million)
% 15.65/3.89 % (7652)------------------------------
% 15.65/3.89 % (7652)------------------------------
% 16.29/3.91 % (7636)Instruction limit reached!
% 16.29/3.91 % (7636)------------------------------
% 16.29/3.91 % (7636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.91 % (7636)Termination reason: Unknown
% 16.29/3.91 % (7636)Termination phase: Saturation
% 16.29/3.91
% 16.29/3.91 % (7636)Memory used [KB]: 4477
% 16.29/3.91 % (7636)Time elapsed: 0.871 s
% 16.29/3.91 % (7636)Instructions burned: 1914 (million)
% 16.29/3.91 % (7636)------------------------------
% 16.29/3.91 % (7636)------------------------------
% 16.29/3.91 % (7663)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_7288 for (2976ds/40Mi)
% 16.29/3.92 % (7664)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_7288 for (2976ds/294Mi)
% 16.29/3.92 % (7663)Instruction limit reached!
% 16.29/3.92 % (7663)------------------------------
% 16.29/3.92 % (7663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.92 % (7663)Termination reason: Unknown
% 16.29/3.92 % (7663)Termination phase: Property scanning
% 16.29/3.92
% 16.29/3.92 % (7663)Memory used [KB]: 2174
% 16.29/3.92 % (7663)Time elapsed: 0.018 s
% 16.29/3.92 % (7663)Instructions burned: 41 (million)
% 16.29/3.92 % (7663)------------------------------
% 16.29/3.92 % (7663)------------------------------
% 16.29/3.94 % (7665)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_7288 for (2976ds/187Mi)
% 16.29/3.96 % (7660)Instruction limit reached!
% 16.29/3.96 % (7660)------------------------------
% 16.29/3.96 % (7660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.96 % (7660)Termination reason: Unknown
% 16.29/3.96 % (7660)Termination phase: Saturation
% 16.29/3.96
% 16.29/3.96 % (7660)Memory used [KB]: 14072
% 16.29/3.96 % (7660)Time elapsed: 0.256 s
% 16.29/3.96 % (7660)Instructions burned: 669 (million)
% 16.29/3.96 % (7660)------------------------------
% 16.29/3.96 % (7660)------------------------------
% 16.29/3.98 % (7666)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_7288 for (2976ds/371Mi)
% 16.29/4.01 % (7658)Instruction limit reached!
% 16.29/4.01 % (7658)------------------------------
% 16.29/4.01 % (7658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/4.01 % (7658)Termination reason: Unknown
% 16.29/4.01 % (7658)Termination phase: Saturation
% 16.29/4.01
% 16.29/4.01 % (7658)Memory used [KB]: 7803
% 16.29/4.01 % (7658)Time elapsed: 0.375 s
% 16.29/4.01 % (7658)Instructions burned: 833 (million)
% 16.29/4.01 % (7658)------------------------------
% 16.29/4.01 % (7658)------------------------------
% 19.32/4.03 % (7668)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_7288 for (2975ds/1827Mi)
% 19.32/4.03 % (7665)Instruction limit reached!
% 19.32/4.03 % (7665)------------------------------
% 19.32/4.03 % (7665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.32/4.03 % (7665)Termination reason: Unknown
% 19.32/4.03 % (7665)Termination phase: Saturation
% 19.32/4.03
% 19.32/4.03 % (7665)Memory used [KB]: 7291
% 19.32/4.03 % (7665)Time elapsed: 0.094 s
% 19.32/4.03 % (7665)Instructions burned: 187 (million)
% 19.32/4.03 % (7665)------------------------------
% 19.32/4.03 % (7665)------------------------------
% 19.32/4.04 % (7671)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_7288 for (2975ds/70Mi)
% 19.32/4.04 % (7664)Instruction limit reached!
% 19.32/4.04 % (7664)------------------------------
% 19.32/4.04 % (7664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.32/4.04 % (7664)Termination reason: Unknown
% 19.32/4.04 % (7664)Termination phase: Saturation
% 19.32/4.04
% 19.32/4.04 % (7664)Memory used [KB]: 7036
% 19.32/4.04 % (7664)Time elapsed: 0.124 s
% 19.32/4.04 % (7664)Instructions burned: 295 (million)
% 19.32/4.04 % (7664)------------------------------
% 19.32/4.04 % (7664)------------------------------
% 19.32/4.06 % (7673)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_7288 for (2975ds/316Mi)
% 19.32/4.07 % (7671)Instruction limit reached!
% 19.32/4.07 % (7671)------------------------------
% 19.32/4.07 % (7671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.32/4.07 % (7671)Termination reason: Unknown
% 19.32/4.07 % (7671)Termination phase: Preprocessing 3
% 19.32/4.07
% 19.32/4.07 % (7671)Memory used [KB]: 2174
% 19.32/4.07 % (7671)Time elapsed: 0.028 s
% 19.32/4.07 % (7671)Instructions burned: 71 (million)
% 19.32/4.07 % (7671)------------------------------
% 19.32/4.07 % (7671)------------------------------
% 19.32/4.08 % (7674)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_7288 for (2975ds/932Mi)
% 19.85/4.16 % (7666)Instruction limit reached!
% 19.85/4.16 % (7666)------------------------------
% 19.85/4.16 % (7666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.16 % (7666)Termination reason: Unknown
% 19.85/4.16 % (7666)Termination phase: Saturation
% 19.85/4.16
% 19.85/4.16 % (7666)Memory used [KB]: 8059
% 19.85/4.16 % (7666)Time elapsed: 0.184 s
% 19.85/4.16 % (7666)Instructions burned: 371 (million)
% 19.85/4.16 % (7666)------------------------------
% 19.85/4.16 % (7666)------------------------------
% 19.85/4.18 % (7679)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_7288 for (2974ds/4714Mi)
% 20.11/4.20 % (7673)Instruction limit reached!
% 20.11/4.20 % (7673)------------------------------
% 20.11/4.20 % (7673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.11/4.20 % (7673)Termination reason: Unknown
% 20.11/4.20 % (7673)Termination phase: Saturation
% 20.11/4.20
% 20.11/4.20 % (7673)Memory used [KB]: 7803
% 20.11/4.20 % (7673)Time elapsed: 0.144 s
% 20.11/4.20 % (7673)Instructions burned: 317 (million)
% 20.11/4.20 % (7673)------------------------------
% 20.11/4.20 % (7673)------------------------------
% 20.11/4.22 % (7680)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_7288 for (2973ds/8250Mi)
% 20.87/4.43 % (7674)Instruction limit reached!
% 20.87/4.43 % (7674)------------------------------
% 20.87/4.43 % (7674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.87/4.43 % (7674)Termination reason: Unknown
% 20.87/4.43 % (7674)Termination phase: Saturation
% 20.87/4.43
% 20.87/4.43 % (7674)Memory used [KB]: 9850
% 20.87/4.43 % (7674)Time elapsed: 0.351 s
% 20.87/4.43 % (7674)Instructions burned: 934 (million)
% 20.87/4.43 % (7674)------------------------------
% 20.87/4.43 % (7674)------------------------------
% 20.87/4.44 % (7683)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_7288 for (2971ds/770Mi)
% 20.87/4.47 % (7683)Refutation not found, incomplete strategy
% 20.87/4.47 % (7683)------------------------------
% 20.87/4.47 % (7683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.87/4.47 % (7683)Termination reason: Refutation not found, incomplete strategy
% 20.87/4.47
% 20.87/4.47
% 20.87/4.47 % (7683)Memory used [KB]: 6652
% 20.87/4.47 % (7683)Time elapsed: 0.054 s
% 20.87/4.47 % (7683)Instructions burned: 87 (million)
% 20.87/4.47 % (7683)------------------------------
% 20.87/4.47 % (7683)------------------------------
% 20.87/4.49 % (7684)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_7288 for (2971ds/794Mi)
% 22.47/4.84 % (7668)Instruction limit reached!
% 22.47/4.84 % (7668)------------------------------
% 22.47/4.84 % (7668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.47/4.84 % (7668)Termination reason: Unknown
% 22.47/4.84 % (7668)Termination phase: Saturation
% 22.47/4.84
% 22.47/4.84 % (7668)Memory used [KB]: 10746
% 22.47/4.84 % (7668)Time elapsed: 0.814 s
% 22.47/4.84 % (7668)Instructions burned: 1828 (million)
% 22.47/4.84 % (7668)------------------------------
% 22.47/4.84 % (7668)------------------------------
% 22.47/4.85 % (7684)Instruction limit reached!
% 22.47/4.85 % (7684)------------------------------
% 22.47/4.85 % (7684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.47/4.85 % (7684)Termination reason: Unknown
% 22.47/4.85 % (7684)Termination phase: Saturation
% 22.47/4.85
% 22.47/4.85 % (7684)Memory used [KB]: 6140
% 22.47/4.85 % (7684)Time elapsed: 0.381 s
% 22.47/4.85 % (7684)Instructions burned: 795 (million)
% 22.47/4.85 % (7684)------------------------------
% 22.47/4.85 % (7684)------------------------------
% 22.47/4.86 % (7688)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_7288 for (2967ds/464Mi)
% 22.47/4.86 % (7690)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_7288 for (2967ds/1376Mi)
% 23.98/4.96 % (7637)Instruction limit reached!
% 23.98/4.96 % (7637)------------------------------
% 23.98/4.96 % (7637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.98/4.96 % (7637)Termination reason: Unknown
% 23.98/4.96 % (7637)Termination phase: Saturation
% 23.98/4.96
% 23.98/4.96 % (7637)Memory used [KB]: 12153
% 23.98/4.96 % (7637)Time elapsed: 1.923 s
% 23.98/4.96 % (7637)Instructions burned: 4350 (million)
% 23.98/4.96 % (7637)------------------------------
% 23.98/4.96 % (7637)------------------------------
% 23.98/4.97 % (7692)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_7288 for (2966ds/906Mi)
% 23.98/4.99 % (7622)Instruction limit reached!
% 23.98/4.99 % (7622)------------------------------
% 23.98/4.99 % (7622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.98/4.99 % (7622)Termination reason: Unknown
% 23.98/4.99 % (7622)Termination phase: Saturation
% 23.98/4.99
% 23.98/4.99 % (7622)Memory used [KB]: 12025
% 23.98/4.99 % (7622)Time elapsed: 2.165 s
% 23.98/4.99 % (7622)Instructions burned: 4436 (million)
% 23.98/4.99 % (7622)------------------------------
% 23.98/4.99 % (7622)------------------------------
% 23.98/5.01 % (7693)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_7288 for (2966ds/434Mi)
% 26.33/5.10 % (7688)Instruction limit reached!
% 26.33/5.10 % (7688)------------------------------
% 26.33/5.10 % (7688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.33/5.10 % (7688)Termination reason: Unknown
% 26.33/5.10 % (7688)Termination phase: Saturation
% 26.33/5.10
% 26.33/5.10 % (7688)Memory used [KB]: 7675
% 26.33/5.10 % (7688)Time elapsed: 0.258 s
% 26.33/5.10 % (7688)Instructions burned: 464 (million)
% 26.33/5.10 % (7688)------------------------------
% 26.33/5.10 % (7688)------------------------------
% 26.33/5.11 % (7697)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_7288 for (2964ds/865Mi)
% 27.03/5.18 % (7629)Instruction limit reached!
% 27.03/5.18 % (7629)------------------------------
% 27.03/5.18 % (7629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.03/5.18 % (7629)Termination reason: Unknown
% 27.03/5.18 % (7629)Termination phase: Saturation
% 27.03/5.18
% 27.03/5.18 % (7629)Memory used [KB]: 15351
% 27.03/5.18 % (7629)Time elapsed: 2.247 s
% 27.03/5.18 % (7629)Instructions burned: 5206 (million)
% 27.03/5.18 % (7629)------------------------------
% 27.03/5.18 % (7629)------------------------------
% 27.03/5.20 % (7699)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_7288 for (2963ds/593Mi)
% 27.43/5.22 % (7693)Instruction limit reached!
% 27.43/5.22 % (7693)------------------------------
% 27.43/5.22 % (7693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.43/5.22 % (7693)Termination reason: Unknown
% 27.43/5.22 % (7693)Termination phase: Saturation
% 27.43/5.22
% 27.43/5.22 % (7693)Memory used [KB]: 7675
% 27.43/5.22 % (7693)Time elapsed: 0.232 s
% 27.43/5.22 % (7693)Instructions burned: 435 (million)
% 27.43/5.22 % (7693)------------------------------
% 27.43/5.22 % (7693)------------------------------
% 27.43/5.23 % (7701)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_7288 for (2963ds/443Mi)
% 28.27/5.42 % (7692)Instruction limit reached!
% 28.27/5.42 % (7692)------------------------------
% 28.27/5.42 % (7692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.27/5.42 % (7692)Termination reason: Unknown
% 28.27/5.42 % (7692)Termination phase: Saturation
% 28.27/5.42
% 28.27/5.42 % (7692)Memory used [KB]: 10746
% 28.27/5.42 % (7692)Time elapsed: 0.475 s
% 28.27/5.42 % (7692)Instructions burned: 906 (million)
% 28.27/5.42 % (7692)------------------------------
% 28.27/5.42 % (7692)------------------------------
% 28.27/5.43 % (7706)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_7288 for (2961ds/594Mi)
% 28.27/5.44 % (7697)Instruction limit reached!
% 28.27/5.44 % (7697)------------------------------
% 28.27/5.44 % (7697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.27/5.44 % (7697)Termination reason: Unknown
% 28.27/5.44 % (7697)Termination phase: Saturation
% 28.27/5.44
% 28.27/5.44 % (7697)Memory used [KB]: 9850
% 28.27/5.44 % (7697)Time elapsed: 0.326 s
% 28.27/5.44 % (7697)Instructions burned: 868 (million)
% 28.27/5.44 % (7697)------------------------------
% 28.27/5.44 % (7697)------------------------------
% 28.27/5.45 % (7709)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_7288 for (2961ds/327Mi)
% 28.27/5.45 % (7701)Instruction limit reached!
% 28.27/5.45 % (7701)------------------------------
% 28.27/5.45 % (7701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.27/5.45 % (7701)Termination reason: Unknown
% 28.27/5.45 % (7701)Termination phase: Saturation
% 28.27/5.45
% 28.27/5.45 % (7701)Memory used [KB]: 8059
% 28.27/5.45 % (7701)Time elapsed: 0.222 s
% 28.27/5.45 % (7701)Instructions burned: 444 (million)
% 28.27/5.45 % (7701)------------------------------
% 28.27/5.45 % (7701)------------------------------
% 28.27/5.47 % (7690)Instruction limit reached!
% 28.27/5.47 % (7690)------------------------------
% 28.27/5.47 % (7690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.27/5.47 % (7690)Termination reason: Unknown
% 28.27/5.47 % (7690)Termination phase: Saturation
% 28.27/5.47
% 28.27/5.47 % (7690)Memory used [KB]: 13048
% 28.27/5.47 % (7690)Time elapsed: 0.629 s
% 28.27/5.47 % (7690)Instructions burned: 1377 (million)
% 28.27/5.47 % (7690)------------------------------
% 28.27/5.47 % (7690)------------------------------
% 28.27/5.47 % (7710)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_7288 for (2961ds/5411Mi)
% 28.27/5.47 % (7699)Instruction limit reached!
% 28.27/5.47 % (7699)------------------------------
% 28.27/5.47 % (7699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.27/5.47 % (7699)Termination reason: Unknown
% 28.27/5.47 % (7699)Termination phase: Saturation
% 28.27/5.47
% 28.27/5.47 % (7699)Memory used [KB]: 9083
% 28.27/5.47 % (7699)Time elapsed: 0.279 s
% 28.27/5.47 % (7699)Instructions burned: 594 (million)
% 28.27/5.47 % (7699)------------------------------
% 28.27/5.47 % (7699)------------------------------
% 28.27/5.49 % (7713)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_7288 for (2961ds/96Mi)
% 28.27/5.49 % (7712)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_7288 for (2961ds/1762Mi)
% 29.44/5.52 % (7713)Instruction limit reached!
% 29.44/5.52 % (7713)------------------------------
% 29.44/5.52 % (7713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.52 % (7713)Termination reason: Unknown
% 29.44/5.52 % (7713)Termination phase: Property scanning
% 29.44/5.52
% 29.44/5.52 % (7713)Memory used [KB]: 2174
% 29.44/5.52 % (7713)Time elapsed: 0.028 s
% 29.44/5.52 % (7713)Instructions burned: 98 (million)
% 29.44/5.52 % (7713)------------------------------
% 29.44/5.52 % (7713)------------------------------
% 29.44/5.53 % (7716)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_7288 for (2960ds/503Mi)
% 29.44/5.58 % (7709)Instruction limit reached!
% 29.44/5.58 % (7709)------------------------------
% 29.44/5.58 % (7709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.58 % (7709)Termination reason: Unknown
% 29.44/5.58 % (7709)Termination phase: Saturation
% 29.44/5.58
% 29.44/5.58 % (7709)Memory used [KB]: 7803
% 29.44/5.58 % (7709)Time elapsed: 0.133 s
% 29.44/5.58 % (7709)Instructions burned: 327 (million)
% 29.44/5.58 % (7709)------------------------------
% 29.44/5.58 % (7709)------------------------------
% 29.44/5.59 % (7718)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_7288 for (2960ds/90Mi)
% 29.80/5.61 % (7718)Instruction limit reached!
% 29.80/5.61 % (7718)------------------------------
% 29.80/5.61 % (7718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.80/5.61 % (7718)Termination reason: Unknown
% 29.80/5.61 % (7718)Termination phase: Saturation
% 29.80/5.61
% 29.80/5.61 % (7718)Memory used [KB]: 6780
% 29.80/5.61 % (7718)Time elapsed: 0.027 s
% 29.80/5.61 % (7718)Instructions burned: 90 (million)
% 29.80/5.61 % (7718)------------------------------
% 29.80/5.61 % (7718)------------------------------
% 29.80/5.62 % (7719)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_7288 for (2959ds/593Mi)
% 29.80/5.65 % (7706)Instruction limit reached!
% 29.80/5.65 % (7706)------------------------------
% 29.80/5.65 % (7706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.80/5.65 % (7706)Termination reason: Unknown
% 29.80/5.65 % (7706)Termination phase: Saturation
% 29.80/5.65
% 29.80/5.65 % (7706)Memory used [KB]: 8315
% 29.80/5.65 % (7706)Time elapsed: 0.220 s
% 29.80/5.65 % (7706)Instructions burned: 595 (million)
% 29.80/5.65 % (7706)------------------------------
% 29.80/5.65 % (7706)------------------------------
% 29.80/5.66 % (7720)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_7288 for (2959ds/1512Mi)
% 29.80/5.68 % (7716)Instruction limit reached!
% 29.80/5.68 % (7716)------------------------------
% 29.80/5.68 % (7716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.80/5.68 % (7716)Termination reason: Unknown
% 29.80/5.68 % (7716)Termination phase: Saturation
% 29.80/5.68
% 29.80/5.68 % (7716)Memory used [KB]: 7547
% 29.80/5.68 % (7716)Time elapsed: 0.158 s
% 29.80/5.68 % (7716)Instructions burned: 503 (million)
% 29.80/5.68 % (7716)------------------------------
% 29.80/5.68 % (7716)------------------------------
% 29.80/5.69 % (7721)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_7288 for (2958ds/569Mi)
% 30.64/5.81 % (7719)Instruction limit reached!
% 30.64/5.81 % (7719)------------------------------
% 30.64/5.81 % (7719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.64/5.81 % (7719)Termination reason: Unknown
% 30.64/5.81 % (7719)Termination phase: Saturation
% 30.64/5.81
% 30.64/5.81 % (7719)Memory used [KB]: 8827
% 30.64/5.81 % (7719)Time elapsed: 0.191 s
% 30.64/5.81 % (7719)Instructions burned: 594 (million)
% 30.64/5.81 % (7719)------------------------------
% 30.64/5.81 % (7719)------------------------------
% 30.64/5.82 % (7769)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_7288 for (2957ds/501Mi)
% 30.64/5.84 % (7679)Instruction limit reached!
% 30.64/5.84 % (7679)------------------------------
% 30.64/5.84 % (7679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.64/5.84 % (7679)Termination reason: Unknown
% 30.64/5.84 % (7679)Termination phase: Saturation
% 30.64/5.84
% 30.64/5.84 % (7679)Memory used [KB]: 14072
% 30.64/5.84 % (7679)Time elapsed: 1.669 s
% 30.64/5.84 % (7679)Instructions burned: 4716 (million)
% 30.64/5.84 % (7679)------------------------------
% 30.64/5.84 % (7679)------------------------------
% 30.64/5.85 % (7780)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_7288 for (2957ds/562Mi)
% 30.64/5.86 % (7721)Instruction limit reached!
% 30.64/5.86 % (7721)------------------------------
% 30.64/5.86 % (7721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.64/5.86 % (7721)Termination reason: Unknown
% 30.64/5.86 % (7721)Termination phase: Saturation
% 30.64/5.86
% 30.64/5.86 % (7721)Memory used [KB]: 8571
% 30.64/5.86 % (7721)Time elapsed: 0.170 s
% 30.64/5.86 % (7721)Instructions burned: 570 (million)
% 30.64/5.86 % (7721)------------------------------
% 30.64/5.86 % (7721)------------------------------
% 30.64/5.87 % (7790)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_7288 for (2957ds/406Mi)
% 31.18/5.98 % (7769)Instruction limit reached!
% 31.18/5.98 % (7769)------------------------------
% 31.18/5.98 % (7769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/5.98 % (7769)Termination reason: Unknown
% 31.18/5.98 % (7769)Termination phase: Saturation
% 31.18/5.98
% 31.18/5.98 % (7769)Memory used [KB]: 8187
% 31.18/5.98 % (7769)Time elapsed: 0.156 s
% 31.18/5.98 % (7769)Instructions burned: 501 (million)
% 31.18/5.98 % (7769)------------------------------
% 31.18/5.98 % (7769)------------------------------
% 31.18/5.99 % (7838)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_7288 for (2956ds/582Mi)
% 31.18/6.00 % (7790)Refutation not found, non-redundant clauses discarded% (7790)------------------------------
% 31.18/6.00 % (7790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/6.00 % (7790)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.18/6.00
% 31.18/6.00 % (7790)Memory used [KB]: 7675
% 31.18/6.00 % (7790)Time elapsed: 0.125 s
% 31.18/6.00 % (7790)Instructions burned: 382 (million)
% 31.18/6.00 % (7790)------------------------------
% 31.18/6.00 % (7790)------------------------------
% 31.18/6.01 % (7851)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_7288 for (2955ds/456Mi)
% 31.18/6.01 % (7712)Instruction limit reached!
% 31.18/6.01 % (7712)------------------------------
% 31.18/6.01 % (7712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/6.01 % (7712)Termination reason: Unknown
% 31.18/6.01 % (7712)Termination phase: Saturation
% 31.18/6.01
% 31.18/6.01 % (7712)Memory used [KB]: 9978
% 31.18/6.01 % (7712)Time elapsed: 0.532 s
% 31.18/6.01 % (7712)Instructions burned: 1762 (million)
% 31.18/6.01 % (7712)------------------------------
% 31.18/6.01 % (7712)------------------------------
% 33.19/6.02 % (7855)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_7288 for (2955ds/393Mi)
% 33.19/6.02 % (7780)Instruction limit reached!
% 33.19/6.02 % (7780)------------------------------
% 33.19/6.02 % (7780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.19/6.02 % (7780)Termination reason: Unknown
% 33.19/6.02 % (7780)Termination phase: Saturation
% 33.19/6.02
% 33.19/6.02 % (7780)Memory used [KB]: 8571
% 33.19/6.02 % (7780)Time elapsed: 0.170 s
% 33.19/6.02 % (7780)Instructions burned: 565 (million)
% 33.19/6.02 % (7780)------------------------------
% 33.19/6.02 % (7780)------------------------------
% 33.19/6.03 % (7863)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_7288 for (2955ds/1335Mi)
% 33.60/6.13 % (7855)Instruction limit reached!
% 33.60/6.13 % (7855)------------------------------
% 33.60/6.13 % (7855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.60/6.13 % (7855)Termination reason: Unknown
% 33.60/6.13 % (7855)Termination phase: Saturation
% 33.60/6.13
% 33.60/6.13 % (7855)Memory used [KB]: 7547
% 33.60/6.13 % (7855)Time elapsed: 0.113 s
% 33.60/6.13 % (7855)Instructions burned: 393 (million)
% 33.60/6.13 % (7855)------------------------------
% 33.60/6.13 % (7855)------------------------------
% 33.60/6.14 % (7896)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_7288 for (2954ds/3373Mi)
% 33.60/6.15 % (7851)Instruction limit reached!
% 33.60/6.15 % (7851)------------------------------
% 33.60/6.15 % (7851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.60/6.15 % (7851)Termination reason: Unknown
% 33.60/6.15 % (7851)Termination phase: Saturation
% 33.60/6.15
% 33.60/6.15 % (7851)Memory used [KB]: 7931
% 33.60/6.15 % (7851)Time elapsed: 0.146 s
% 33.60/6.15 % (7851)Instructions burned: 456 (million)
% 33.60/6.15 % (7851)------------------------------
% 33.60/6.15 % (7851)------------------------------
% 33.60/6.15 % (7720)Instruction limit reached!
% 33.60/6.15 % (7720)------------------------------
% 33.60/6.15 % (7720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.60/6.15 % (7720)Termination reason: Unknown
% 33.60/6.15 % (7720)Termination phase: Saturation
% 33.60/6.15
% 33.60/6.15 % (7720)Memory used [KB]: 8187
% 33.60/6.15 % (7720)Time elapsed: 0.492 s
% 33.60/6.15 % (7720)Instructions burned: 1512 (million)
% 33.60/6.15 % (7720)------------------------------
% 33.60/6.15 % (7720)------------------------------
% 33.60/6.16 % (7903)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_7288 for (2954ds/474Mi)
% 33.60/6.16 % (7905)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_7288 for (2954ds/157Mi)
% 33.60/6.17 % (7838)Instruction limit reached!
% 33.60/6.17 % (7838)------------------------------
% 33.60/6.17 % (7838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.60/6.17 % (7838)Termination reason: Unknown
% 33.60/6.17 % (7838)Termination phase: Saturation
% 33.60/6.17
% 33.60/6.17 % (7838)Memory used [KB]: 8187
% 33.60/6.17 % (7838)Time elapsed: 0.184 s
% 33.60/6.17 % (7838)Instructions burned: 585 (million)
% 33.60/6.17 % (7838)------------------------------
% 33.60/6.17 % (7838)------------------------------
% 33.60/6.18 % (7908)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_7288 for (2954ds/590Mi)
% 34.18/6.21 % (7905)Instruction limit reached!
% 34.18/6.21 % (7905)------------------------------
% 34.18/6.21 % (7905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.18/6.21 % (7905)Termination reason: Unknown
% 34.18/6.21 % (7905)Termination phase: Saturation
% 34.18/6.21
% 34.18/6.21 % (7905)Memory used [KB]: 6908
% 34.18/6.21 % (7905)Time elapsed: 0.046 s
% 34.18/6.21 % (7905)Instructions burned: 157 (million)
% 34.18/6.21 % (7905)------------------------------
% 34.18/6.21 % (7905)------------------------------
% 34.18/6.22 % (7921)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_7288 for (2953ds/104Mi)
% 34.18/6.25 % (7921)Instruction limit reached!
% 34.18/6.25 % (7921)------------------------------
% 34.18/6.25 % (7921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.18/6.25 % (7921)Termination reason: Unknown
% 34.18/6.25 % (7921)Termination phase: Saturation
% 34.18/6.25
% 34.18/6.25 % (7921)Memory used [KB]: 2558
% 34.18/6.25 % (7921)Time elapsed: 0.032 s
% 34.18/6.25 % (7921)Instructions burned: 104 (million)
% 34.18/6.25 % (7921)------------------------------
% 34.18/6.25 % (7921)------------------------------
% 34.18/6.26 % (7937)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_7288 for (2953ds/414Mi)
% 34.48/6.30 % (7903)Instruction limit reached!
% 34.48/6.30 % (7903)------------------------------
% 34.48/6.30 % (7903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.48/6.30 % (7903)Termination reason: Unknown
% 34.48/6.30 % (7903)Termination phase: Saturation
% 34.48/6.30
% 34.48/6.30 % (7903)Memory used [KB]: 8315
% 34.48/6.30 % (7903)Time elapsed: 0.144 s
% 34.48/6.30 % (7903)Instructions burned: 474 (million)
% 34.48/6.30 % (7903)------------------------------
% 34.48/6.30 % (7903)------------------------------
% 34.48/6.31 % (7962)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_7288 for (2952ds/715Mi)
% 34.48/6.36 % (7908)Instruction limit reached!
% 34.48/6.36 % (7908)------------------------------
% 34.48/6.36 % (7908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.48/6.36 % (7908)Termination reason: Unknown
% 34.48/6.36 % (7908)Termination phase: Saturation
% 34.48/6.36
% 34.48/6.36 % (7908)Memory used [KB]: 7675
% 34.48/6.36 % (7908)Time elapsed: 0.178 s
% 34.48/6.36 % (7908)Instructions burned: 592 (million)
% 34.48/6.36 % (7908)------------------------------
% 34.48/6.36 % (7908)------------------------------
% 34.48/6.37 % (7967)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_7288 for (2952ds/961Mi)
% 34.48/6.38 % (7937)Instruction limit reached!
% 34.48/6.38 % (7937)------------------------------
% 34.48/6.38 % (7937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.48/6.38 % (7937)Termination reason: Unknown
% 34.48/6.38 % (7937)Termination phase: Saturation
% 34.48/6.38
% 34.48/6.38 % (7937)Memory used [KB]: 7547
% 34.48/6.38 % (7937)Time elapsed: 0.125 s
% 34.48/6.38 % (7937)Instructions burned: 414 (million)
% 34.48/6.38 % (7937)------------------------------
% 34.48/6.38 % (7937)------------------------------
% 34.48/6.39 % (7968)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_7288 for (2952ds/1213Mi)
% 35.15/6.45 % (7863)Instruction limit reached!
% 35.15/6.45 % (7863)------------------------------
% 35.15/6.45 % (7863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.15/6.45 % (7863)Termination reason: Unknown
% 35.15/6.45 % (7863)Termination phase: Saturation
% 35.15/6.45
% 35.15/6.45 % (7863)Memory used [KB]: 9210
% 35.15/6.45 % (7863)Time elapsed: 0.418 s
% 35.15/6.45 % (7863)Instructions burned: 1337 (million)
% 35.15/6.45 % (7863)------------------------------
% 35.15/6.45 % (7863)------------------------------
% 35.15/6.46 % (7969)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_7288 for (2951ds/1979Mi)
% 35.78/6.54 % (7962)Instruction limit reached!
% 35.78/6.54 % (7962)------------------------------
% 35.78/6.54 % (7962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.78/6.54 % (7962)Termination reason: Unknown
% 35.78/6.54 % (7962)Termination phase: Saturation
% 35.78/6.54
% 35.78/6.54 % (7962)Memory used [KB]: 4861
% 35.78/6.54 % (7962)Time elapsed: 0.225 s
% 35.78/6.54 % (7962)Instructions burned: 715 (million)
% 35.78/6.54 % (7962)------------------------------
% 35.78/6.54 % (7962)------------------------------
% 35.78/6.55 % (7970)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_7288 for (2950ds/481Mi)
% 36.20/6.66 % (7967)Instruction limit reached!
% 36.20/6.66 % (7967)------------------------------
% 36.20/6.66 % (7967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.20/6.66 % (7967)Termination reason: Unknown
% 36.20/6.66 % (7967)Termination phase: Saturation
% 36.20/6.66
% 36.20/6.66 % (7967)Memory used [KB]: 8187
% 36.20/6.66 % (7967)Time elapsed: 0.320 s
% 36.20/6.66 % (7967)Instructions burned: 961 (million)
% 36.20/6.66 % (7967)------------------------------
% 36.20/6.66 % (7967)------------------------------
% 36.20/6.67 % (7971)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_7288 for (2949ds/783Mi)
% 36.20/6.69 % (7970)Instruction limit reached!
% 36.20/6.69 % (7970)------------------------------
% 36.20/6.69 % (7970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.20/6.69 % (7970)Termination reason: Unknown
% 36.20/6.69 % (7970)Termination phase: Saturation
% 36.20/6.69
% 36.20/6.69 % (7970)Memory used [KB]: 8059
% 36.20/6.69 % (7970)Time elapsed: 0.172 s
% 36.20/6.69 % (7970)Instructions burned: 482 (million)
% 36.20/6.69 % (7970)------------------------------
% 36.20/6.69 % (7970)------------------------------
% 36.88/6.70 % (7972)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_7288 for (2948ds/432Mi)
% 36.88/6.78 % (7968)Instruction limit reached!
% 36.88/6.78 % (7968)------------------------------
% 36.88/6.78 % (7968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.88/6.78 % (7968)Termination reason: Unknown
% 36.88/6.78 % (7968)Termination phase: Saturation
% 36.88/6.78
% 36.88/6.78 % (7968)Memory used [KB]: 9083
% 36.88/6.78 % (7968)Time elapsed: 0.406 s
% 36.88/6.78 % (7968)Instructions burned: 1213 (million)
% 36.88/6.78 % (7968)------------------------------
% 36.88/6.78 % (7968)------------------------------
% 36.88/6.79 % (7973)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_7288 for (2948ds/1670Mi)
% 37.47/6.84 % (7972)Instruction limit reached!
% 37.47/6.84 % (7972)------------------------------
% 37.47/6.84 % (7972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.47/6.84 % (7972)Termination reason: Unknown
% 37.47/6.84 % (7972)Termination phase: Saturation
% 37.47/6.84
% 37.47/6.84 % (7972)Memory used [KB]: 7803
% 37.47/6.84 % (7972)Time elapsed: 0.164 s
% 37.47/6.84 % (7972)Instructions burned: 434 (million)
% 37.47/6.84 % (7972)------------------------------
% 37.47/6.84 % (7972)------------------------------
% 37.47/6.85 % (7974)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_7288 for (2947ds/90Mi)
% 37.47/6.88 % (7974)Instruction limit reached!
% 37.47/6.88 % (7974)------------------------------
% 37.47/6.88 % (7974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.47/6.88 % (7974)Termination reason: Unknown
% 37.47/6.88 % (7974)Termination phase: Saturation
% 37.47/6.88
% 37.47/6.88 % (7974)Memory used [KB]: 6780
% 37.47/6.88 % (7974)Time elapsed: 0.027 s
% 37.47/6.88 % (7974)Instructions burned: 90 (million)
% 37.47/6.88 % (7974)------------------------------
% 37.47/6.88 % (7974)------------------------------
% 37.47/6.89 % (7975)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_7288 for (2946ds/346Mi)
% 37.85/6.92 % (7971)Instruction limit reached!
% 37.85/6.92 % (7971)------------------------------
% 37.85/6.92 % (7971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.85/6.92 % (7971)Termination reason: Unknown
% 37.85/6.92 % (7971)Termination phase: Saturation
% 37.85/6.92
% 37.85/6.92 % (7971)Memory used [KB]: 9083
% 37.85/6.92 % (7971)Time elapsed: 0.266 s
% 37.85/6.92 % (7971)Instructions burned: 784 (million)
% 37.85/6.92 % (7971)------------------------------
% 37.85/6.92 % (7971)------------------------------
% 37.85/6.93 % (7976)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_7288 for (2946ds/401Mi)
% 37.85/6.99 % (7975)Instruction limit reached!
% 37.85/6.99 % (7975)------------------------------
% 37.85/6.99 % (7975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.85/6.99 % (7975)Termination reason: Unknown
% 37.85/6.99 % (7975)Termination phase: Saturation
% 37.85/6.99
% 37.85/6.99 % (7975)Memory used [KB]: 7803
% 37.85/6.99 % (7975)Time elapsed: 0.107 s
% 37.85/6.99 % (7975)Instructions burned: 346 (million)
% 37.85/6.99 % (7975)------------------------------
% 37.85/6.99 % (7975)------------------------------
% 37.85/7.00 % (7977)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_7288 for (2945ds/6454Mi)
% 40.27/7.05 % (7976)Instruction limit reached!
% 40.27/7.05 % (7976)------------------------------
% 40.27/7.05 % (7976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.27/7.05 % (7976)Termination reason: Unknown
% 40.27/7.05 % (7976)Termination phase: Saturation
% 40.27/7.05
% 40.27/7.05 % (7976)Memory used [KB]: 8955
% 40.27/7.05 % (7976)Time elapsed: 0.120 s
% 40.27/7.05 % (7976)Instructions burned: 401 (million)
% 40.27/7.05 % (7976)------------------------------
% 40.27/7.05 % (7976)------------------------------
% 40.27/7.06 % (7978)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_7288 for (2945ds/283Mi)
% 40.27/7.08 % (7969)Instruction limit reached!
% 40.27/7.08 % (7969)------------------------------
% 40.27/7.08 % (7969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.27/7.08 % (7969)Termination reason: Unknown
% 40.27/7.08 % (7969)Termination phase: Saturation
% 40.27/7.08
% 40.27/7.08 % (7969)Memory used [KB]: 8955
% 40.27/7.08 % (7969)Time elapsed: 0.644 s
% 40.27/7.08 % (7969)Instructions burned: 1979 (million)
% 40.27/7.08 % (7969)------------------------------
% 40.27/7.08 % (7969)------------------------------
% 40.27/7.09 % (7979)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_7288 for (2944ds/865Mi)
% 40.88/7.15 % (7978)Instruction limit reached!
% 40.88/7.15 % (7978)------------------------------
% 40.88/7.15 % (7978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.88/7.15 % (7978)Termination reason: Unknown
% 40.88/7.15 % (7978)Termination phase: Saturation
% 40.88/7.15
% 40.88/7.15 % (7978)Memory used [KB]: 7803
% 40.88/7.15 % (7978)Time elapsed: 0.092 s
% 40.88/7.15 % (7978)Instructions burned: 284 (million)
% 40.88/7.15 % (7978)------------------------------
% 40.88/7.15 % (7978)------------------------------
% 40.88/7.16 % (7980)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_7288 for (2944ds/4528Mi)
% 40.88/7.18 % (7896)Instruction limit reached!
% 40.88/7.18 % (7896)------------------------------
% 40.88/7.18 % (7896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.88/7.18 % (7896)Termination reason: Unknown
% 40.88/7.18 % (7896)Termination phase: Saturation
% 40.88/7.18
% 40.88/7.18 % (7896)Memory used [KB]: 12792
% 40.88/7.18 % (7896)Time elapsed: 1.044 s
% 40.88/7.18 % (7896)Instructions burned: 3375 (million)
% 40.88/7.18 % (7896)------------------------------
% 40.88/7.18 % (7896)------------------------------
% 40.88/7.19 % (7981)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_7288 for (2943ds/1001Mi)
% 41.36/7.20 % (7710)Instruction limit reached!
% 41.36/7.20 % (7710)------------------------------
% 41.36/7.20 % (7710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.36/7.20 % (7710)Termination reason: Unknown
% 41.36/7.20 % (7710)Termination phase: Saturation
% 41.36/7.20
% 41.36/7.20 % (7710)Memory used [KB]: 11129
% 41.36/7.20 % (7710)Time elapsed: 1.731 s
% 41.36/7.20 % (7710)Instructions burned: 5413 (million)
% 41.36/7.20 % (7710)------------------------------
% 41.36/7.20 % (7710)------------------------------
% 41.36/7.21 % (7982)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_7288 for (2943ds/102Mi)
% 41.36/7.22 % (7680)Instruction limit reached!
% 41.36/7.22 % (7680)------------------------------
% 41.36/7.22 % (7680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.36/7.22 % (7680)Termination reason: Unknown
% 41.36/7.22 % (7680)Termination phase: Saturation
% 41.36/7.22
% 41.36/7.22 % (7680)Memory used [KB]: 16886
% 41.36/7.22 % (7680)Time elapsed: 3.030 s
% 41.36/7.22 % (7680)Instructions burned: 8250 (million)
% 41.36/7.22 % (7680)------------------------------
% 41.36/7.22 % (7680)------------------------------
% 41.36/7.24 % (7983)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_7288 for (2943ds/952Mi)
% 41.36/7.24 % (7982)Instruction limit reached!
% 41.36/7.24 % (7982)------------------------------
% 41.36/7.24 % (7982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.36/7.24 % (7982)Termination reason: Unknown
% 41.36/7.24 % (7982)Termination phase: Saturation
% 41.36/7.24
% 41.36/7.24 % (7982)Memory used [KB]: 6780
% 41.36/7.24 % (7982)Time elapsed: 0.029 s
% 41.36/7.24 % (7982)Instructions burned: 105 (million)
% 41.36/7.24 % (7982)------------------------------
% 41.36/7.24 % (7982)------------------------------
% 41.36/7.25 % (7984)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_7288 for (2943ds/578Mi)
% 41.65/7.31 % (7973)Instruction limit reached!
% 41.65/7.31 % (7973)------------------------------
% 41.65/7.31 % (7973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.65/7.31 % (7973)Termination reason: Unknown
% 41.65/7.31 % (7973)Termination phase: Saturation
% 41.65/7.31
% 41.65/7.31 % (7973)Memory used [KB]: 9850
% 41.65/7.31 % (7973)Time elapsed: 0.545 s
% 41.65/7.31 % (7973)Instructions burned: 1672 (million)
% 41.65/7.31 % (7973)------------------------------
% 41.65/7.31 % (7973)------------------------------
% 41.65/7.32 % (7985)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_7288 for (2942ds/643Mi)
% 41.65/7.37 % (7979)Instruction limit reached!
% 41.65/7.37 % (7979)------------------------------
% 41.65/7.37 % (7979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.65/7.37 % (7979)Termination reason: Unknown
% 41.65/7.37 % (7979)Termination phase: Saturation
% 41.65/7.37
% 41.65/7.37 % (7979)Memory used [KB]: 8955
% 41.65/7.37 % (7979)Time elapsed: 0.284 s
% 41.65/7.37 % (7979)Instructions burned: 867 (million)
% 41.65/7.37 % (7979)------------------------------
% 41.65/7.37 % (7979)------------------------------
% 41.65/7.38 % (7986)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_7288 for (2942ds/865Mi)
% 42.06/7.42 % (7984)Instruction limit reached!
% 42.06/7.42 % (7984)------------------------------
% 42.06/7.42 % (7984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.06/7.42 % (7984)Termination reason: Unknown
% 42.06/7.42 % (7984)Termination phase: Saturation
% 42.06/7.42
% 42.06/7.42 % (7984)Memory used [KB]: 8571
% 42.06/7.42 % (7984)Time elapsed: 0.178 s
% 42.06/7.42 % (7984)Instructions burned: 580 (million)
% 42.06/7.42 % (7984)------------------------------
% 42.06/7.42 % (7984)------------------------------
% 42.06/7.43 % (7987)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_7288 for (2941ds/1174Mi)
% 42.35/7.51 % (7981)Instruction limit reached!
% 42.35/7.51 % (7981)------------------------------
% 42.35/7.51 % (7981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.35/7.51 % (7981)Termination reason: Unknown
% 42.35/7.51 % (7981)Termination phase: Saturation
% 42.35/7.51
% 42.35/7.51 % (7981)Memory used [KB]: 9210
% 42.35/7.51 % (7981)Time elapsed: 0.318 s
% 42.35/7.51 % (7981)Instructions burned: 1003 (million)
% 42.35/7.51 % (7981)------------------------------
% 42.35/7.51 % (7981)------------------------------
% 42.35/7.52 % (7985)Instruction limit reached!
% 42.35/7.52 % (7985)------------------------------
% 42.35/7.52 % (7985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.35/7.52 % (7985)Termination reason: Unknown
% 42.35/7.52 % (7985)Termination phase: Saturation
% 42.35/7.52
% 42.35/7.52 % (7985)Memory used [KB]: 9083
% 42.35/7.52 % (7985)Time elapsed: 0.201 s
% 42.35/7.52 % (7985)Instructions burned: 643 (million)
% 42.35/7.52 % (7985)------------------------------
% 42.35/7.52 % (7985)------------------------------
% 42.35/7.52 % (7988)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_7288 for (2940ds/644Mi)
% 42.35/7.53 % (7989)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_7288 for (2940ds/1201Mi)
% 42.35/7.54 % (7983)Instruction limit reached!
% 42.35/7.54 % (7983)------------------------------
% 42.35/7.54 % (7983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.35/7.54 % (7983)Termination reason: Unknown
% 42.35/7.54 % (7983)Termination phase: Saturation
% 42.35/7.54
% 42.35/7.54 % (7983)Memory used [KB]: 10234
% 42.35/7.54 % (7983)Time elapsed: 0.305 s
% 42.35/7.54 % (7983)Instructions burned: 953 (million)
% 42.35/7.54 % (7983)------------------------------
% 42.35/7.54 % (7983)------------------------------
% 42.35/7.55 % (7990)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_7288 for (2940ds/1046Mi)
% 43.30/7.65 % (7986)Instruction limit reached!
% 43.30/7.65 % (7986)------------------------------
% 43.30/7.65 % (7986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.30/7.65 % (7986)Termination reason: Unknown
% 43.30/7.65 % (7986)Termination phase: Saturation
% 43.30/7.65
% 43.30/7.65 % (7986)Memory used [KB]: 9210
% 43.30/7.65 % (7986)Time elapsed: 0.272 s
% 43.30/7.65 % (7986)Instructions burned: 865 (million)
% 43.30/7.65 % (7986)------------------------------
% 43.30/7.65 % (7986)------------------------------
% 43.30/7.66 % (7991)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_7288 for (2939ds/222Mi)
% 43.69/7.72 % (7988)Instruction limit reached!
% 43.69/7.72 % (7988)------------------------------
% 43.69/7.72 % (7988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.69/7.72 % (7988)Termination reason: Unknown
% 43.69/7.72 % (7988)Termination phase: Saturation
% 43.69/7.72
% 43.69/7.72 % (7988)Memory used [KB]: 9210
% 43.69/7.72 % (7988)Time elapsed: 0.202 s
% 43.69/7.72 % (7988)Instructions burned: 646 (million)
% 43.69/7.72 % (7988)------------------------------
% 43.69/7.72 % (7988)------------------------------
% 43.69/7.73 % (7991)Instruction limit reached!
% 43.69/7.73 % (7991)------------------------------
% 43.69/7.73 % (7991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.69/7.73 % (7991)Termination reason: Unknown
% 43.69/7.73 % (7991)Termination phase: Saturation
% 43.69/7.73
% 43.69/7.73 % (7991)Memory used [KB]: 7291
% 43.69/7.73 % (7991)Time elapsed: 0.064 s
% 43.69/7.73 % (7991)Instructions burned: 224 (million)
% 43.69/7.73 % (7991)------------------------------
% 43.69/7.73 % (7991)------------------------------
% 43.69/7.73 % (7992)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_7288 for (2938ds/68Mi)
% 43.69/7.74 % (7993)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_7288 for (2938ds/454Mi)
% 43.69/7.75 % (7992)Instruction limit reached!
% 43.69/7.75 % (7992)------------------------------
% 43.69/7.75 % (7992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.69/7.75 % (7992)Termination reason: Unknown
% 43.69/7.75 % (7992)Termination phase: Property scanning
% 43.69/7.75
% 43.69/7.75 % (7992)Memory used [KB]: 2174
% 43.69/7.75 % (7992)Time elapsed: 0.022 s
% 43.69/7.75 % (7992)Instructions burned: 68 (million)
% 43.69/7.75 % (7992)------------------------------
% 43.69/7.75 % (7992)------------------------------
% 43.69/7.76 % (7994)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_7288 for (2938ds/360Mi)
% 44.10/7.81 % (7987)Instruction limit reached!
% 44.10/7.81 % (7987)------------------------------
% 44.10/7.81 % (7987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.10/7.81 % (7987)Termination reason: Unknown
% 44.10/7.81 % (7987)Termination phase: Saturation
% 44.10/7.81
% 44.10/7.81 % (7987)Memory used [KB]: 9210
% 44.10/7.81 % (7987)Time elapsed: 0.380 s
% 44.10/7.81 % (7987)Instructions burned: 1175 (million)
% 44.10/7.81 % (7987)------------------------------
% 44.10/7.81 % (7987)------------------------------
% 44.10/7.82 % (7995)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_7288 for (2937ds/157Mi)
% 44.10/7.86 % (7995)Instruction limit reached!
% 44.10/7.86 % (7995)------------------------------
% 44.10/7.86 % (7995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.10/7.86 % (7995)Termination reason: Unknown
% 44.10/7.86 % (7995)Termination phase: Saturation
% 44.10/7.86
% 44.10/7.86 % (7995)Memory used [KB]: 6908
% 44.10/7.86 % (7995)Time elapsed: 0.044 s
% 44.10/7.86 % (7995)Instructions burned: 159 (million)
% 44.10/7.86 % (7995)------------------------------
% 44.10/7.86 % (7995)------------------------------
% 44.10/7.87 % (7994)Instruction limit reached!
% 44.10/7.87 % (7994)------------------------------
% 44.10/7.87 % (7994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.10/7.87 % (7994)Termination reason: Unknown
% 44.10/7.87 % (7994)Termination phase: Saturation
% 44.10/7.87
% 44.10/7.87 % (7994)Memory used [KB]: 8187
% 44.10/7.87 % (7994)Time elapsed: 0.107 s
% 44.10/7.87 % (7994)Instructions burned: 361 (million)
% 44.10/7.87 % (7994)------------------------------
% 44.10/7.87 % (7994)------------------------------
% 44.10/7.87 % (7990)Instruction limit reached!
% 44.10/7.87 % (7990)------------------------------
% 44.10/7.87 % (7990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.10/7.87 % (7990)Termination reason: Unknown
% 44.10/7.87 % (7990)Termination phase: Saturation
% 44.10/7.87
% 44.10/7.87 % (7990)Memory used [KB]: 9466
% 44.10/7.87 % (7990)Time elapsed: 0.320 s
% 44.10/7.87 % (7990)Instructions burned: 1046 (million)
% 44.10/7.87 % (7990)------------------------------
% 44.10/7.87 % (7990)------------------------------
% 44.10/7.87 % (7993)Instruction limit reached!
% 44.10/7.87 % (7993)------------------------------
% 44.10/7.87 % (7993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.10/7.87 % (7993)Termination reason: Unknown
% 44.10/7.87 % (7993)Termination phase: Saturation
% 44.10/7.87
% 44.10/7.87 % (7993)Memory used [KB]: 12792
% 44.10/7.87 % (7993)Time elapsed: 0.139 s
% 44.10/7.87 % (7993)Instructions burned: 455 (million)
% 44.10/7.87 % (7993)------------------------------
% 44.10/7.87 % (7993)------------------------------
% 44.10/7.87 % (7996)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_7288 for (2937ds/5061Mi)
% 44.10/7.88 % (7997)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_7288 for (2937ds/2401Mi)
% 44.10/7.88 % (7998)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_7288 for (2937ds/5798Mi)
% 44.10/7.88 % (7999)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_7288 for (2937ds/346Mi)
% 45.24/7.93 % (7989)Instruction limit reached!
% 45.24/7.93 % (7989)------------------------------
% 45.24/7.93 % (7989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.24/7.93 % (7989)Termination reason: Unknown
% 45.24/7.93 % (7989)Termination phase: Saturation
% 45.24/7.93
% 45.24/7.93 % (7989)Memory used [KB]: 8955
% 45.24/7.93 % (7989)Time elapsed: 0.400 s
% 45.24/7.93 % (7989)Instructions burned: 1201 (million)
% 45.24/7.93 % (7989)------------------------------
% 45.24/7.93 % (7989)------------------------------
% 45.24/7.94 % (8000)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_7288 for (2936ds/1321Mi)
% 45.24/7.99 % (7999)Instruction limit reached!
% 45.24/7.99 % (7999)------------------------------
% 45.24/7.99 % (7999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.24/7.99 % (7999)Termination reason: Unknown
% 45.24/7.99 % (7999)Termination phase: Saturation
% 45.24/7.99
% 45.24/7.99 % (7999)Memory used [KB]: 7803
% 45.24/7.99 % (7999)Time elapsed: 0.104 s
% 45.24/7.99 % (7999)Instructions burned: 348 (million)
% 45.24/7.99 % (7999)------------------------------
% 45.24/7.99 % (7999)------------------------------
% 45.24/8.00 % (8001)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_7288 for (2936ds/1312Mi)
% 49.22/8.34 % (8000)Instruction limit reached!
% 49.22/8.34 % (8000)------------------------------
% 49.22/8.34 % (8000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.22/8.34 % (8000)Termination reason: Unknown
% 49.22/8.34 % (8000)Termination phase: Saturation
% 49.22/8.34
% 49.22/8.34 % (8000)Memory used [KB]: 4861
% 49.22/8.34 % (8000)Time elapsed: 0.408 s
% 49.22/8.34 % (8000)Instructions burned: 1322 (million)
% 49.22/8.34 % (8000)------------------------------
% 49.22/8.34 % (8000)------------------------------
% 49.22/8.35 % (8002)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_7288 for (2932ds/672Mi)
% 49.22/8.39 % (8001)Instruction limit reached!
% 49.22/8.39 % (8001)------------------------------
% 49.22/8.39 % (8001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.22/8.39 % (8001)Termination reason: Unknown
% 49.22/8.39 % (8001)Termination phase: Saturation
% 49.22/8.39
% 49.22/8.39 % (8001)Memory used [KB]: 9722
% 49.22/8.39 % (8001)Time elapsed: 0.392 s
% 49.22/8.39 % (8001)Instructions burned: 1313 (million)
% 49.22/8.39 % (8001)------------------------------
% 49.22/8.39 % (8001)------------------------------
% 49.22/8.40 % (8003)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_7288 for (2931ds/1897Mi)
% 49.88/8.42 % (7980)Instruction limit reached!
% 49.88/8.42 % (7980)------------------------------
% 49.88/8.42 % (7980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.88/8.42 % (7980)Termination reason: Unknown
% 49.88/8.42 % (7980)Termination phase: Saturation
% 49.88/8.42
% 49.88/8.42 % (7980)Memory used [KB]: 5245
% 49.88/8.42 % (7980)Time elapsed: 1.267 s
% 49.88/8.42 % (7980)Instructions burned: 4529 (million)
% 49.88/8.42 % (7980)------------------------------
% 49.88/8.42 % (7980)------------------------------
% 49.88/8.43 % (8004)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_7288 for (2931ds/1202Mi)
% 50.32/8.56 % (8002)Instruction limit reached!
% 50.32/8.56 % (8002)------------------------------
% 50.32/8.56 % (8002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.32/8.56 % (8002)Termination reason: Unknown
% 50.32/8.56 % (8002)Termination phase: Saturation
% 50.32/8.56
% 50.32/8.56 % (8002)Memory used [KB]: 8315
% 50.32/8.56 % (8002)Time elapsed: 0.209 s
% 50.32/8.56 % (8002)Instructions burned: 673 (million)
% 50.32/8.56 % (8002)------------------------------
% 50.32/8.56 % (8002)------------------------------
% 50.32/8.57 % (8005)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_7288 for (2930ds/1493Mi)
% 50.94/8.62 % (7997)Instruction limit reached!
% 50.94/8.62 % (7997)------------------------------
% 50.94/8.62 % (7997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.94/8.62 % (7997)Termination reason: Unknown
% 50.94/8.62 % (7997)Termination phase: Saturation
% 50.94/8.62
% 50.94/8.62 % (7997)Memory used [KB]: 12281
% 50.94/8.62 % (7997)Time elapsed: 0.749 s
% 50.94/8.62 % (7997)Instructions burned: 2402 (million)
% 50.94/8.62 % (7997)------------------------------
% 50.94/8.62 % (7997)------------------------------
% 50.94/8.63 % (8006)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_7288 for (2929ds/7679Mi)
% 51.28/8.80 % (8004)Instruction limit reached!
% 51.28/8.80 % (8004)------------------------------
% 51.28/8.80 % (8004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.28/8.80 % (8004)Termination reason: Unknown
% 51.28/8.80 % (8004)Termination phase: Saturation
% 51.28/8.80
% 51.28/8.80 % (8004)Memory used [KB]: 5117
% 51.28/8.80 % (8004)Time elapsed: 0.365 s
% 51.28/8.80 % (8004)Instructions burned: 1205 (million)
% 51.28/8.80 % (8004)------------------------------
% 51.28/8.80 % (8004)------------------------------
% 51.58/8.81 % (8007)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_7288 for (2927ds/340Mi)
% 52.25/8.91 % (8007)Instruction limit reached!
% 52.25/8.91 % (8007)------------------------------
% 52.25/8.91 % (8007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.25/8.91 % (8007)Termination reason: Unknown
% 52.25/8.91 % (8007)Termination phase: Saturation
% 52.25/8.91
% 52.25/8.91 % (8007)Memory used [KB]: 8443
% 52.25/8.91 % (8007)Time elapsed: 0.107 s
% 52.25/8.91 % (8007)Instructions burned: 342 (million)
% 52.25/8.91 % (8007)------------------------------
% 52.25/8.91 % (8007)------------------------------
% 52.25/8.92 % (8008)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_7288 for (2926ds/3672Mi)
% 52.25/8.93 % (7977)Refutation not found, non-redundant clauses discarded% (7977)------------------------------
% 52.25/8.93 % (7977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.25/8.93 % (7977)Termination reason: Refutation not found, non-redundant clauses discarded
% 52.25/8.93
% 52.25/8.93 % (7977)Memory used [KB]: 11641
% 52.25/8.93 % (7977)Time elapsed: 1.922 s
% 52.25/8.93 % (7977)Instructions burned: 6319 (million)
% 52.25/8.93 % (7977)------------------------------
% 52.25/8.93 % (7977)------------------------------
% 52.25/8.94 % (8009)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_7288 for (2926ds/1535Mi)
% 52.25/8.99 % (8005)Instruction limit reached!
% 52.25/8.99 % (8005)------------------------------
% 52.25/8.99 % (8005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.25/8.99 % (8005)Termination reason: Unknown
% 52.25/8.99 % (8005)Termination phase: Saturation
% 52.25/8.99
% 52.25/8.99 % (8005)Memory used [KB]: 11513
% 52.25/8.99 % (8005)Time elapsed: 0.417 s
% 52.25/8.99 % (8005)Instructions burned: 1495 (million)
% 52.25/8.99 % (8005)------------------------------
% 52.25/8.99 % (8005)------------------------------
% 52.25/8.99 % (8003)Instruction limit reached!
% 52.25/8.99 % (8003)------------------------------
% 52.25/8.99 % (8003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.25/8.99 % (8003)Termination reason: Unknown
% 52.25/8.99 % (8003)Termination phase: Saturation
% 52.25/8.99
% 52.25/8.99 % (8003)Memory used [KB]: 9594
% 52.25/8.99 % (8003)Time elapsed: 0.595 s
% 52.25/8.99 % (8003)Instructions burned: 1899 (million)
% 52.25/8.99 % (8003)------------------------------
% 52.25/8.99 % (8003)------------------------------
% 52.25/9.00 % (8010)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_7288 for (2925ds/4637Mi)
% 52.25/9.00 % (8011)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_7288 for (2925ds/3174Mi)
% 56.24/9.38 % (8009)Instruction limit reached!
% 56.24/9.38 % (8009)------------------------------
% 56.24/9.38 % (8009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.24/9.38 % (8009)Termination reason: Unknown
% 56.24/9.38 % (8009)Termination phase: Saturation
% 56.24/9.38
% 56.24/9.38 % (8009)Memory used [KB]: 12153
% 56.24/9.38 % (8009)Time elapsed: 0.447 s
% 56.24/9.38 % (8009)Instructions burned: 1537 (million)
% 56.24/9.38 % (8009)------------------------------
% 56.24/9.38 % (8009)------------------------------
% 56.24/9.39 % (8012)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_7288 for (2921ds/307Mi)
% 56.94/9.45 % (7996)Instruction limit reached!
% 56.94/9.45 % (7996)------------------------------
% 56.94/9.45 % (7996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.94/9.45 % (7996)Termination reason: Unknown
% 56.94/9.45 % (7996)Termination phase: Saturation
% 56.94/9.45
% 56.94/9.45 % (7996)Memory used [KB]: 15223
% 56.94/9.45 % (7996)Time elapsed: 1.578 s
% 56.94/9.45 % (7996)Instructions burned: 5062 (million)
% 56.94/9.45 % (7996)------------------------------
% 56.94/9.45 % (7996)------------------------------
% 56.94/9.46 % (8013)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_7288 for (2921ds/3619Mi)
% 56.94/9.48 % (8012)Instruction limit reached!
% 56.94/9.48 % (8012)------------------------------
% 56.94/9.48 % (8012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.94/9.48 % (8012)Termination reason: Unknown
% 56.94/9.48 % (8012)Termination phase: Saturation
% 56.94/9.48
% 56.94/9.48 % (8012)Memory used [KB]: 7419
% 56.94/9.48 % (8012)Time elapsed: 0.090 s
% 56.94/9.48 % (8012)Instructions burned: 308 (million)
% 56.94/9.48 % (8012)------------------------------
% 56.94/9.48 % (8012)------------------------------
% 56.94/9.49 % (8014)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_7288 for (2920ds/2325Mi)
% 58.10/9.64 % (7998)Instruction limit reached!
% 58.10/9.64 % (7998)------------------------------
% 58.10/9.64 % (7998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.10/9.64 % (7998)Termination reason: Unknown
% 58.10/9.64 % (7998)Termination phase: Saturation
% 58.10/9.64
% 58.10/9.64 % (7998)Memory used [KB]: 13048
% 58.10/9.64 % (7998)Time elapsed: 1.761 s
% 58.10/9.64 % (7998)Instructions burned: 5798 (million)
% 58.10/9.64 % (7998)------------------------------
% 58.10/9.64 % (7998)------------------------------
% 58.10/9.65 % (8015)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_7288 for (2919ds/2341Mi)
% 59.38/10.00 % (8011)Instruction limit reached!
% 59.38/10.00 % (8011)------------------------------
% 59.38/10.00 % (8011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.38/10.00 % (8011)Termination reason: Unknown
% 59.38/10.00 % (8011)Termination phase: Saturation
% 59.38/10.00
% 59.38/10.00 % (8011)Memory used [KB]: 12920
% 59.38/10.00 % (8011)Time elapsed: 1.004 s
% 59.38/10.00 % (8011)Instructions burned: 3174 (million)
% 59.38/10.00 % (8011)------------------------------
% 59.38/10.00 % (8011)------------------------------
% 59.38/10.01 % (8016)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_7288 for (2915ds/7257Mi)
% 61.32/10.08 % (8008)Instruction limit reached!
% 61.32/10.08 % (8008)------------------------------
% 61.32/10.08 % (8008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.32/10.08 % (8008)Termination reason: Unknown
% 61.32/10.08 % (8008)Termination phase: Saturation
% 61.32/10.08
% 61.32/10.08 % (8008)Memory used [KB]: 12153
% 61.32/10.08 % (8008)Time elapsed: 1.158 s
% 61.32/10.08 % (8008)Instructions burned: 3673 (million)
% 61.32/10.08 % (8008)------------------------------
% 61.32/10.08 % (8008)------------------------------
% 61.32/10.09 % (8017)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_7288 for (2915ds/3710Mi)
% 62.28/10.24 % (8014)Instruction limit reached!
% 62.28/10.24 % (8014)------------------------------
% 62.28/10.24 % (8014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.28/10.24 % (8014)Termination reason: Unknown
% 62.28/10.24 % (8014)Termination phase: Saturation
% 62.28/10.24
% 62.28/10.24 % (8014)Memory used [KB]: 11001
% 62.28/10.24 % (8014)Time elapsed: 0.747 s
% 62.28/10.24 % (8014)Instructions burned: 2326 (million)
% 62.28/10.24 % (8014)------------------------------
% 62.28/10.24 % (8014)------------------------------
% 62.28/10.25 % (8018)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_7288 for (2913ds/326Mi)
% 62.72/10.35 % (8018)Instruction limit reached!
% 62.72/10.35 % (8018)------------------------------
% 62.72/10.35 % (8018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.72/10.35 % (8018)Termination reason: Unknown
% 62.72/10.35 % (8018)Termination phase: Saturation
% 62.72/10.35
% 62.72/10.35 % (8018)Memory used [KB]: 7675
% 62.72/10.35 % (8018)Time elapsed: 0.107 s
% 62.72/10.35 % (8018)Instructions burned: 328 (million)
% 62.72/10.35 % (8018)------------------------------
% 62.72/10.35 % (8018)------------------------------
% 62.72/10.36 % (8019)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_7288 for (2912ds/1100Mi)
% 62.72/10.39 % (8015)Instruction limit reached!
% 62.72/10.39 % (8015)------------------------------
% 62.72/10.39 % (8015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.72/10.39 % (8015)Termination reason: Unknown
% 62.72/10.39 % (8015)Termination phase: Saturation
% 62.72/10.39
% 62.72/10.39 % (8015)Memory used [KB]: 8315
% 62.72/10.39 % (8015)Time elapsed: 0.737 s
% 62.72/10.39 % (8015)Instructions burned: 2343 (million)
% 62.72/10.39 % (8015)------------------------------
% 62.72/10.39 % (8015)------------------------------
% 62.72/10.39 % (8020)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_7288 for (2911ds/406Mi)
% 63.25/10.48 % (8010)Instruction limit reached!
% 63.25/10.48 % (8010)------------------------------
% 63.25/10.48 % (8010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.25/10.48 % (8010)Termination reason: Unknown
% 63.25/10.48 % (8010)Termination phase: Saturation
% 63.25/10.48
% 63.25/10.48 % (8010)Memory used [KB]: 13176
% 63.25/10.48 % (8010)Time elapsed: 1.482 s
% 63.25/10.48 % (8010)Instructions burned: 4637 (million)
% 63.25/10.48 % (8010)------------------------------
% 63.25/10.48 % (8010)------------------------------
% 63.25/10.49 % (8021)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_7288 for (2911ds/1871Mi)
% 63.55/10.52 % (8020)Refutation not found, non-redundant clauses discarded% (8020)------------------------------
% 63.55/10.52 % (8020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.55/10.52 % (8020)Termination reason: Refutation not found, non-redundant clauses discarded
% 63.55/10.52
% 63.55/10.52 % (8020)Memory used [KB]: 7803
% 63.55/10.52 % (8020)Time elapsed: 0.124 s
% 63.55/10.52 % (8020)Instructions burned: 384 (million)
% 63.55/10.52 % (8020)------------------------------
% 63.55/10.52 % (8020)------------------------------
% 63.55/10.52 % (8013)Instruction limit reached!
% 63.55/10.52 % (8013)------------------------------
% 63.55/10.52 % (8013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.55/10.52 % (8013)Termination reason: Unknown
% 63.55/10.52 % (8013)Termination phase: Saturation
% 63.55/10.52
% 63.55/10.52 % (8013)Memory used [KB]: 11385
% 63.55/10.52 % (8013)Time elapsed: 1.063 s
% 63.55/10.52 % (8013)Instructions burned: 3621 (million)
% 63.55/10.52 % (8013)------------------------------
% 63.55/10.52 % (8013)------------------------------
% 63.55/10.53 % (8022)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_7288 for (2910ds/1194Mi)
% 63.55/10.53 % (8023)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_7288 for (2910ds/474Mi)
% 63.80/10.68 % (8023)Instruction limit reached!
% 63.80/10.68 % (8023)------------------------------
% 63.80/10.68 % (8023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.80/10.68 % (8023)Termination reason: Unknown
% 63.80/10.68 % (8023)Termination phase: Saturation
% 63.80/10.68
% 63.80/10.68 % (8023)Memory used [KB]: 8315
% 63.80/10.68 % (8023)Time elapsed: 0.148 s
% 63.80/10.68 % (8023)Instructions burned: 474 (million)
% 63.80/10.68 % (8023)------------------------------
% 63.80/10.68 % (8023)------------------------------
% 63.80/10.69 % (8024)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_7288 for (2909ds/3115Mi)
% 64.06/10.72 % (8019)Instruction limit reached!
% 64.06/10.72 % (8019)------------------------------
% 64.06/10.72 % (8019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.06/10.72 % (8019)Termination reason: Unknown
% 64.06/10.72 % (8019)Termination phase: Saturation
% 64.06/10.72
% 64.06/10.72 % (8019)Memory used [KB]: 9722
% 64.06/10.72 % (8019)Time elapsed: 0.356 s
% 64.06/10.72 % (8019)Instructions burned: 1100 (million)
% 64.06/10.72 % (8019)------------------------------
% 64.06/10.72 % (8019)------------------------------
% 64.06/10.73 % (8025)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_7288 for (2908ds/831Mi)
% 64.52/10.89 % (8006)Instruction limit reached!
% 64.52/10.89 % (8006)------------------------------
% 64.52/10.89 % (8006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.52/10.89 % (8006)Termination reason: Unknown
% 64.52/10.89 % (8006)Termination phase: Saturation
% 64.52/10.89
% 64.52/10.89 % (8006)Memory used [KB]: 21236
% 64.52/10.89 % (8006)Time elapsed: 2.254 s
% 64.52/10.89 % (8006)Instructions burned: 7679 (million)
% 64.52/10.89 % (8006)------------------------------
% 64.52/10.89 % (8006)------------------------------
% 64.64/10.90 % (8026)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_7288 for (2906ds/1188Mi)
% 64.64/10.91 % (8022)Instruction limit reached!
% 64.64/10.91 % (8022)------------------------------
% 64.64/10.91 % (8022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.64/10.91 % (8022)Termination reason: Unknown
% 64.64/10.91 % (8022)Termination phase: Saturation
% 64.64/10.91
% 64.64/10.91 % (8022)Memory used [KB]: 8699
% 64.64/10.91 % (8022)Time elapsed: 0.379 s
% 64.64/10.91 % (8022)Instructions burned: 1195 (million)
% 64.64/10.91 % (8022)------------------------------
% 64.64/10.91 % (8022)------------------------------
% 64.64/10.92 % (8027)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_7288 for (2906ds/2868Mi)
% 64.64/10.99 % (8025)Instruction limit reached!
% 64.64/10.99 % (8025)------------------------------
% 64.64/10.99 % (8025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.64/10.99 % (8025)Termination reason: Unknown
% 64.64/10.99 % (8025)Termination phase: Saturation
% 64.64/10.99
% 64.64/10.99 % (8025)Memory used [KB]: 8315
% 64.64/10.99 % (8025)Time elapsed: 0.263 s
% 64.64/10.99 % (8025)Instructions burned: 832 (million)
% 64.64/10.99 % (8025)------------------------------
% 64.64/10.99 % (8025)------------------------------
% 64.64/11.00 % (8028)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_7288 for (2905ds/1516Mi)
% 68.33/11.08 % (8021)Instruction limit reached!
% 68.33/11.08 % (8021)------------------------------
% 68.33/11.08 % (8021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.33/11.08 % (8021)Termination reason: Unknown
% 68.33/11.08 % (8021)Termination phase: Saturation
% 68.33/11.08
% 68.33/11.08 % (8021)Memory used [KB]: 11001
% 68.33/11.08 % (8021)Time elapsed: 0.597 s
% 68.33/11.08 % (8021)Instructions burned: 1874 (million)
% 68.33/11.08 % (8021)------------------------------
% 68.33/11.08 % (8021)------------------------------
% 68.33/11.09 % (8029)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_7288 for (2904ds/2321Mi)
% 69.48/11.26 % (8026)Instruction limit reached!
% 69.48/11.26 % (8026)------------------------------
% 69.48/11.26 % (8026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.48/11.26 % (8026)Termination reason: Unknown
% 69.48/11.26 % (8026)Termination phase: Saturation
% 69.48/11.26
% 69.48/11.26 % (8026)Memory used [KB]: 11001
% 69.48/11.26 % (8026)Time elapsed: 0.361 s
% 69.48/11.26 % (8026)Instructions burned: 1188 (million)
% 69.48/11.26 % (8026)------------------------------
% 69.48/11.26 % (8026)------------------------------
% 69.48/11.26 % (8017)Instruction limit reached!
% 69.48/11.26 % (8017)------------------------------
% 69.48/11.26 % (8017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.48/11.26 % (8017)Termination reason: Unknown
% 69.48/11.26 % (8017)Termination phase: Saturation
% 69.48/11.26
% 69.48/11.26 % (8017)Memory used [KB]: 18805
% 69.48/11.26 % (8017)Time elapsed: 1.172 s
% 69.48/11.26 % (8017)Instructions burned: 3710 (million)
% 69.48/11.26 % (8017)------------------------------
% 69.48/11.26 % (8017)------------------------------
% 69.48/11.27 % (8030)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_7288 for (2903ds/2812Mi)
% 69.48/11.27 % (8031)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_7288 for (2903ds/4604Mi)
% 70.44/11.45 % (8028)Instruction limit reached!
% 70.44/11.45 % (8028)------------------------------
% 70.44/11.45 % (8028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.44/11.45 % (8028)Termination reason: Unknown
% 70.44/11.45 % (8028)Termination phase: Saturation
% 70.44/11.45
% 70.44/11.45 % (8028)Memory used [KB]: 9466
% 70.44/11.45 % (8028)Time elapsed: 0.455 s
% 70.44/11.45 % (8028)Instructions burned: 1516 (million)
% 70.44/11.45 % (8028)------------------------------
% 70.44/11.45 % (8028)------------------------------
% 70.44/11.46 % (8032)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_7288 for (2901ds/2678Mi)
% 70.80/11.58 % (8024)Instruction limit reached!
% 70.80/11.58 % (8024)------------------------------
% 70.80/11.58 % (8024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.80/11.58 % (8024)Termination reason: Unknown
% 70.80/11.58 % (8024)Termination phase: Saturation
% 70.80/11.58
% 70.80/11.58 % (8024)Memory used [KB]: 13048
% 70.80/11.58 % (8024)Time elapsed: 0.893 s
% 70.80/11.58 % (8024)Instructions burned: 3115 (million)
% 70.80/11.58 % (8024)------------------------------
% 70.80/11.58 % (8024)------------------------------
% 70.80/11.59 % (8033)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_7288 for (2899ds/643Mi)
% 71.31/11.70 % (8027)Instruction limit reached!
% 71.31/11.70 % (8027)------------------------------
% 71.31/11.70 % (8027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.31/11.70 % (8027)Termination reason: Unknown
% 71.31/11.70 % (8027)Termination phase: Saturation
% 71.31/11.70
% 71.31/11.70 % (8027)Memory used [KB]: 13048
% 71.31/11.70 % (8027)Time elapsed: 0.785 s
% 71.31/11.70 % (8027)Instructions burned: 2868 (million)
% 71.31/11.70 % (8027)------------------------------
% 71.31/11.70 % (8027)------------------------------
% 71.31/11.71 % (8034)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_7288 for (2898ds/458Mi)
% 71.31/11.78 % (8029)Instruction limit reached!
% 71.31/11.78 % (8029)------------------------------
% 71.31/11.78 % (8029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.31/11.78 % (8029)Termination reason: Unknown
% 71.31/11.78 % (8029)Termination phase: Saturation
% 71.31/11.78
% 71.31/11.78 % (8029)Memory used [KB]: 11641
% 71.31/11.78 % (8029)Time elapsed: 0.688 s
% 71.31/11.78 % (8029)Instructions burned: 2322 (million)
% 71.31/11.78 % (8029)------------------------------
% 71.31/11.78 % (8029)------------------------------
% 71.31/11.79 % (8033)Instruction limit reached!
% 71.31/11.79 % (8033)------------------------------
% 71.31/11.79 % (8033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.31/11.79 % (8033)Termination reason: Unknown
% 71.31/11.79 % (8033)Termination phase: Saturation
% 71.31/11.79
% 71.31/11.79 % (8033)Memory used [KB]: 9083
% 71.31/11.79 % (8033)Time elapsed: 0.200 s
% 71.31/11.79 % (8033)Instructions burned: 645 (million)
% 71.31/11.79 % (8033)------------------------------
% 71.31/11.79 % (8033)------------------------------
% 71.31/11.79 % (8035)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_7288 for (2897ds/2546Mi)
% 72.32/11.80 % (8036)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_7288 for (2897ds/1432Mi)
% 72.32/11.85 % (8034)Instruction limit reached!
% 72.32/11.85 % (8034)------------------------------
% 72.32/11.85 % (8034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.32/11.85 % (8034)Termination reason: Unknown
% 72.32/11.85 % (8034)Termination phase: Saturation
% 72.32/11.85
% 72.32/11.85 % (8034)Memory used [KB]: 7931
% 72.32/11.85 % (8034)Time elapsed: 0.136 s
% 72.32/11.85 % (8034)Instructions burned: 458 (million)
% 72.32/11.85 % (8034)------------------------------
% 72.32/11.85 % (8034)------------------------------
% 72.32/11.86 % (8037)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_7288 for (2897ds/386Mi)
% 72.58/11.97 % (8037)Instruction limit reached!
% 72.58/11.97 % (8037)------------------------------
% 72.58/11.97 % (8037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.58/11.97 % (8037)Termination reason: Unknown
% 72.58/11.97 % (8037)Termination phase: Saturation
% 72.58/11.97
% 72.58/11.97 % (8037)Memory used [KB]: 8699
% 72.58/11.97 % (8037)Time elapsed: 0.117 s
% 72.58/11.97 % (8037)Instructions burned: 386 (million)
% 72.58/11.97 % (8037)------------------------------
% 72.58/11.97 % (8037)------------------------------
% 72.58/11.98 % (8038)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_7288 for (2896ds/360Mi)
% 75.37/12.09 % (8038)Instruction limit reached!
% 75.37/12.09 % (8038)------------------------------
% 75.37/12.09 % (8038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.37/12.09 % (8038)Termination reason: Unknown
% 75.37/12.09 % (8038)Termination phase: Saturation
% 75.37/12.09
% 75.37/12.09 % (8038)Memory used [KB]: 8059
% 75.37/12.09 % (8038)Time elapsed: 0.105 s
% 75.37/12.09 % (8038)Instructions burned: 361 (million)
% 75.37/12.09 % (8038)------------------------------
% 75.37/12.09 % (8038)------------------------------
% 75.37/12.09 % (8039)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_7288 for (2894ds/5446Mi)
% 76.07/12.13 % (8036)Instruction limit reached!
% 76.07/12.13 % (8036)------------------------------
% 76.07/12.13 % (8036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.07/12.13 % (8036)Termination reason: Unknown
% 76.07/12.13 % (8036)Termination phase: Saturation
% 76.07/12.13
% 76.07/12.13 % (8036)Memory used [KB]: 9210
% 76.07/12.13 % (8036)Time elapsed: 0.327 s
% 76.07/12.13 % (8036)Instructions burned: 1436 (million)
% 76.07/12.13 % (8036)------------------------------
% 76.07/12.13 % (8036)------------------------------
% 76.07/12.13 % (8016)Instruction limit reached!
% 76.07/12.13 % (8016)------------------------------
% 76.07/12.13 % (8016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.07/12.13 % (8016)Termination reason: Unknown
% 76.07/12.13 % (8016)Termination phase: Saturation
% 76.07/12.13
% 76.07/12.13 % (8016)Memory used [KB]: 18293
% 76.07/12.13 % (8016)Time elapsed: 2.117 s
% 76.07/12.13 % (8016)Instructions burned: 7259 (million)
% 76.07/12.13 % (8016)------------------------------
% 76.07/12.13 % (8016)------------------------------
% 76.07/12.14 % (8040)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_7288 for (2894ds/2573Mi)
% 76.07/12.14 % (8041)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_7288 for (2894ds/2655Mi)
% 76.07/12.16 % (8030)Instruction limit reached!
% 76.07/12.16 % (8030)------------------------------
% 76.07/12.16 % (8030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.07/12.16 % (8030)Termination reason: Unknown
% 76.07/12.16 % (8030)Termination phase: Saturation
% 76.07/12.16
% 76.07/12.16 % (8030)Memory used [KB]: 12792
% 76.07/12.16 % (8030)Time elapsed: 0.898 s
% 76.07/12.16 % (8030)Instructions burned: 2814 (million)
% 76.07/12.16 % (8030)------------------------------
% 76.07/12.16 % (8030)------------------------------
% 76.07/12.17 % (8042)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_7288 for (2894ds/2781Mi)
% 76.36/12.29 % (8032)Instruction limit reached!
% 76.36/12.29 % (8032)------------------------------
% 76.36/12.29 % (8032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.36/12.29 % (8032)Termination reason: Unknown
% 76.36/12.29 % (8032)Termination phase: Saturation
% 76.36/12.29
% 76.36/12.29 % (8032)Memory used [KB]: 10618
% 76.36/12.29 % (8032)Time elapsed: 0.831 s
% 76.36/12.29 % (8032)Instructions burned: 2679 (million)
% 76.36/12.29 % (8032)------------------------------
% 76.36/12.29 % (8032)------------------------------
% 76.68/12.30 % (8043)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_7288 for (2892ds/307Mi)
% 76.89/12.40 % (8043)Instruction limit reached!
% 76.89/12.40 % (8043)------------------------------
% 76.89/12.40 % (8043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.89/12.40 % (8043)Termination reason: Unknown
% 76.89/12.40 % (8043)Termination phase: Saturation
% 76.89/12.40
% 76.89/12.40 % (8043)Memory used [KB]: 7419
% 76.89/12.40 % (8043)Time elapsed: 0.095 s
% 76.89/12.40 % (8043)Instructions burned: 310 (million)
% 76.89/12.40 % (8043)------------------------------
% 76.89/12.40 % (8043)------------------------------
% 76.89/12.41 % (8044)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_7288 for (2891ds/1548Mi)
% 77.40/12.63 % (8035)Instruction limit reached!
% 77.40/12.63 % (8035)------------------------------
% 77.40/12.63 % (8035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.40/12.63 % (8035)Termination reason: Unknown
% 77.40/12.63 % (8035)Termination phase: Saturation
% 77.40/12.63
% 77.40/12.63 % (8035)Memory used [KB]: 11001
% 77.40/12.63 % (8035)Time elapsed: 0.842 s
% 77.40/12.63 % (8035)Instructions burned: 2547 (million)
% 77.40/12.63 % (8035)------------------------------
% 77.40/12.63 % (8035)------------------------------
% 77.40/12.64 % (8045)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_7288 for (2889ds/5214Mi)
% 77.40/12.67 % (8031)Instruction limit reached!
% 77.40/12.67 % (8031)------------------------------
% 77.40/12.67 % (8031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.40/12.67 % (8031)Termination reason: Unknown
% 77.40/12.67 % (8031)Termination phase: Saturation
% 77.40/12.67
% 77.40/12.67 % (8031)Memory used [KB]: 12920
% 77.40/12.67 % (8031)Time elapsed: 1.398 s
% 77.40/12.67 % (8031)Instructions burned: 4606 (million)
% 77.40/12.67 % (8031)------------------------------
% 77.40/12.67 % (8031)------------------------------
% 77.40/12.68 % (8046)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_7288 for (2889ds/3201Mi)
% 77.52/12.89 % (8044)Instruction limit reached!
% 77.52/12.89 % (8044)------------------------------
% 77.52/12.89 % (8044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.52/12.89 % (8044)Termination reason: Unknown
% 77.52/12.89 % (8044)Termination phase: Saturation
% 77.52/12.89
% 77.52/12.89 % (8044)Memory used [KB]: 9978
% 77.52/12.89 % (8044)Time elapsed: 0.481 s
% 77.52/12.89 % (8044)Instructions burned: 1549 (million)
% 77.52/12.89 % (8044)------------------------------
% 77.52/12.89 % (8044)------------------------------
% 77.52/12.89 % (8040)Instruction limit reached!
% 77.52/12.89 % (8040)------------------------------
% 77.52/12.89 % (8040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.52/12.89 % (8040)Termination reason: Unknown
% 77.52/12.89 % (8040)Termination phase: Saturation
% 77.52/12.89
% 77.52/12.89 % (8040)Memory used [KB]: 12281
% 77.52/12.89 % (8040)Time elapsed: 0.753 s
% 77.52/12.89 % (8040)Instructions burned: 2576 (million)
% 77.52/12.89 % (8040)------------------------------
% 77.52/12.89 % (8040)------------------------------
% 78.78/12.90 % (8047)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_7288 for (2886ds/454Mi)
% 78.78/12.90 % (8048)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_7288 for (2886ds/3049Mi)
% 78.78/12.93 % (8041)Instruction limit reached!
% 78.78/12.93 % (8041)------------------------------
% 78.78/12.93 % (8041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.78/12.93 % (8041)Termination reason: Unknown
% 78.78/12.93 % (8041)Termination phase: Saturation
% 78.78/12.93
% 78.78/12.93 % (8041)Memory used [KB]: 10874
% 78.78/12.93 % (8041)Time elapsed: 0.789 s
% 78.78/12.93 % (8041)Instructions burned: 2657 (million)
% 78.78/12.93 % (8041)------------------------------
% 78.78/12.93 % (8041)------------------------------
% 78.78/12.94 % (8050)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_7288 for (2886ds/7311Mi)
% 82.38/13.03 % (8047)Instruction limit reached!
% 82.38/13.03 % (8047)------------------------------
% 82.38/13.03 % (8047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.38/13.03 % (8047)Termination reason: Unknown
% 82.38/13.03 % (8047)Termination phase: Saturation
% 82.38/13.03
% 82.38/13.03 % (8047)Memory used [KB]: 13432
% 82.38/13.03 % (8047)Time elapsed: 0.139 s
% 82.38/13.03 % (8047)Instructions burned: 455 (million)
% 82.38/13.03 % (8047)------------------------------
% 82.38/13.03 % (8047)------------------------------
% 82.38/13.04 % (8051)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_7288 for (2885ds/6804Mi)
% 82.38/13.06 % (8042)Instruction limit reached!
% 82.38/13.06 % (8042)------------------------------
% 82.38/13.06 % (8042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.38/13.06 % (8042)Termination reason: Unknown
% 82.38/13.06 % (8042)Termination phase: Saturation
% 82.38/13.06
% 82.38/13.06 % (8042)Memory used [KB]: 5117
% 82.38/13.06 % (8042)Time elapsed: 0.887 s
% 82.38/13.06 % (8042)Instructions burned: 2782 (million)
% 82.38/13.06 % (8042)------------------------------
% 82.38/13.06 % (8042)------------------------------
% 82.38/13.07 % (8052)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_7288 for (2885ds/1683Mi)
% 85.36/13.61 % (8052)Instruction limit reached!
% 85.36/13.61 % (8052)------------------------------
% 85.36/13.61 % (8052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.36/13.61 % (8052)Termination reason: Unknown
% 85.36/13.61 % (8052)Termination phase: Saturation
% 85.36/13.61
% 85.36/13.61 % (8052)Memory used [KB]: 10490
% 85.36/13.61 % (8052)Time elapsed: 0.544 s
% 85.36/13.61 % (8052)Instructions burned: 1683 (million)
% 85.36/13.61 % (8052)------------------------------
% 85.36/13.61 % (8052)------------------------------
% 85.36/13.62 % (8053)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_7288 for (2879ds/4688Mi)
% 85.36/13.66 % (8046)Instruction limit reached!
% 85.36/13.66 % (8046)------------------------------
% 85.36/13.66 % (8046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.36/13.66 % (8046)Termination reason: Unknown
% 85.36/13.66 % (8046)Termination phase: Saturation
% 85.36/13.66
% 85.36/13.66 % (8046)Memory used [KB]: 13304
% 85.36/13.66 % (8046)Time elapsed: 0.981 s
% 85.36/13.66 % (8046)Instructions burned: 3201 (million)
% 85.36/13.66 % (8046)------------------------------
% 85.36/13.66 % (8046)------------------------------
% 85.36/13.67 % (8054)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_7288 for (2879ds/2207Mi)
% 86.79/13.86 % (8048)Instruction limit reached!
% 86.79/13.86 % (8048)------------------------------
% 86.79/13.86 % (8048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.79/13.86 % (8048)Termination reason: Unknown
% 86.79/13.86 % (8048)Termination phase: Saturation
% 86.79/13.86
% 86.79/13.86 % (8048)Memory used [KB]: 9466
% 86.79/13.86 % (8048)Time elapsed: 0.960 s
% 86.79/13.86 % (8048)Instructions burned: 3052 (million)
% 86.79/13.86 % (8048)------------------------------
% 86.79/13.86 % (8048)------------------------------
% 86.79/13.87 % (8039)Instruction limit reached!
% 86.79/13.87 % (8039)------------------------------
% 86.79/13.87 % (8039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.79/13.87 % (8039)Termination reason: Unknown
% 86.79/13.87 % (8039)Termination phase: Saturation
% 86.79/13.87
% 86.79/13.87 % (8039)Memory used [KB]: 17526
% 86.79/13.87 % (8039)Time elapsed: 1.774 s
% 86.79/13.87 % (8039)Instructions burned: 5448 (million)
% 86.79/13.87 % (8039)------------------------------
% 86.79/13.87 % (8039)------------------------------
% 86.79/13.87 % (8055)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_7288 for (2877ds/8216Mi)
% 86.79/13.88 % (8056)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_7288 for (2877ds/430Mi)
% 87.15/14.01 % (8056)Instruction limit reached!
% 87.15/14.01 % (8056)------------------------------
% 87.15/14.01 % (8056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.15/14.01 % (8056)Termination reason: Unknown
% 87.15/14.01 % (8056)Termination phase: Saturation
% 87.15/14.01
% 87.15/14.01 % (8056)Memory used [KB]: 7803
% 87.15/14.01 % (8056)Time elapsed: 0.128 s
% 87.15/14.01 % (8056)Instructions burned: 431 (million)
% 87.15/14.01 % (8056)------------------------------
% 87.15/14.01 % (8056)------------------------------
% 87.15/14.02 % (8058)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_7288 for (2875ds/2012Mi)
% 90.47/14.24 % (8045)Instruction limit reached!
% 90.47/14.24 % (8045)------------------------------
% 90.47/14.24 % (8045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.47/14.24 % (8045)Termination reason: Unknown
% 90.47/14.24 % (8045)Termination phase: Saturation
% 90.47/14.24
% 90.47/14.24 % (8045)Memory used [KB]: 16119
% 90.47/14.24 % (8045)Time elapsed: 1.602 s
% 90.47/14.24 % (8045)Instructions burned: 5214 (million)
% 90.47/14.24 % (8045)------------------------------
% 90.47/14.24 % (8045)------------------------------
% 90.47/14.25 % (8105)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_7288 for (2873ds/631Mi)
% 91.02/14.38 % (8054)Instruction limit reached!
% 91.02/14.38 % (8054)------------------------------
% 91.02/14.38 % (8054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.02/14.38 % (8054)Termination reason: Unknown
% 91.02/14.38 % (8054)Termination phase: Saturation
% 91.02/14.38
% 91.02/14.38 % (8054)Memory used [KB]: 10746
% 91.02/14.38 % (8054)Time elapsed: 0.708 s
% 91.02/14.38 % (8054)Instructions burned: 2209 (million)
% 91.02/14.38 % (8054)------------------------------
% 91.02/14.38 % (8054)------------------------------
% 91.02/14.39 % (8162)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_7288 for (2872ds/8785Mi)
% 91.52/14.45 % (8105)Instruction limit reached!
% 91.52/14.45 % (8105)------------------------------
% 91.52/14.45 % (8105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.52/14.45 % (8105)Termination reason: Unknown
% 91.52/14.45 % (8105)Termination phase: Saturation
% 91.52/14.45
% 91.52/14.45 % (8105)Memory used [KB]: 8955
% 91.52/14.45 % (8105)Time elapsed: 0.199 s
% 91.52/14.45 % (8105)Instructions burned: 632 (million)
% 91.52/14.45 % (8105)------------------------------
% 91.52/14.45 % (8105)------------------------------
% 91.52/14.46 % (8188)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_7288 for (2871ds/739Mi)
% 92.52/14.63 % (8058)Instruction limit reached!
% 92.52/14.63 % (8058)------------------------------
% 92.52/14.63 % (8058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.52/14.63 % (8058)Termination reason: Unknown
% 92.52/14.63 % (8058)Termination phase: Saturation
% 92.52/14.63
% 92.52/14.63 % (8058)Memory used [KB]: 19957
% 92.52/14.63 % (8058)Time elapsed: 0.617 s
% 92.52/14.63 % (8058)Instructions burned: 2013 (million)
% 92.52/14.63 % (8058)------------------------------
% 92.52/14.63 % (8058)------------------------------
% 92.52/14.64 % (8256)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_7288 for (2869ds/5473Mi)
% 92.52/14.70 % (8188)Instruction limit reached!
% 92.52/14.70 % (8188)------------------------------
% 92.52/14.70 % (8188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.52/14.70 % (8188)Termination reason: Unknown
% 92.52/14.70 % (8188)Termination phase: Saturation
% 92.52/14.70
% 92.52/14.70 % (8188)Memory used [KB]: 8443
% 92.52/14.70 % (8188)Time elapsed: 0.235 s
% 92.52/14.70 % (8188)Instructions burned: 741 (million)
% 92.52/14.70 % (8188)------------------------------
% 92.52/14.70 % (8188)------------------------------
% 93.79/14.71 % (8284)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_7288 for (2868ds/43570Mi)
% 96.50/15.07 % (8051)Instruction limit reached!
% 96.50/15.07 % (8051)------------------------------
% 96.50/15.07 % (8051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.50/15.07 % (8051)Termination reason: Unknown
% 96.50/15.07 % (8051)Termination phase: Saturation
% 96.50/15.07
% 96.50/15.07 % (8051)Memory used [KB]: 11257
% 96.50/15.07 % (8051)Time elapsed: 2.023 s
% 96.50/15.07 % (8051)Instructions burned: 6807 (million)
% 96.50/15.07 % (8051)------------------------------
% 96.50/15.07 % (8051)------------------------------
% 96.50/15.08 % (8430)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_7288 for (2865ds/8382Mi)
% 96.50/15.12 % (8053)Instruction limit reached!
% 96.50/15.12 % (8053)------------------------------
% 96.50/15.12 % (8053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.50/15.12 % (8053)Termination reason: Unknown
% 96.50/15.12 % (8053)Termination phase: Saturation
% 96.50/15.12
% 96.50/15.12 % (8053)Memory used [KB]: 6780
% 96.50/15.12 % (8053)Time elapsed: 1.494 s
% 96.50/15.12 % (8053)Instructions burned: 4690 (million)
% 96.50/15.12 % (8053)------------------------------
% 96.50/15.12 % (8053)------------------------------
% 96.50/15.13 % (8455)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_7288 for (2864ds/407Mi)
% 97.46/15.20 % (8050)Instruction limit reached!
% 97.46/15.20 % (8050)------------------------------
% 97.46/15.20 % (8050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.46/15.20 % (8050)Termination reason: Unknown
% 97.46/15.20 % (8050)Termination phase: Saturation
% 97.46/15.20
% 97.46/15.20 % (8050)Memory used [KB]: 18166
% 97.46/15.20 % (8050)Time elapsed: 2.265 s
% 97.46/15.20 % (8050)Instructions burned: 7311 (million)
% 97.46/15.20 % (8050)------------------------------
% 97.46/15.20 % (8050)------------------------------
% 97.46/15.21 % (8483)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_7288 for (2863ds/2971Mi)
% 97.46/15.26 % (8455)Instruction limit reached!
% 97.46/15.26 % (8455)------------------------------
% 97.46/15.26 % (8455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.46/15.26 % (8455)Termination reason: Unknown
% 97.46/15.26 % (8455)Termination phase: Saturation
% 97.46/15.26
% 97.46/15.26 % (8455)Memory used [KB]: 8315
% 97.46/15.26 % (8455)Time elapsed: 0.135 s
% 97.46/15.26 % (8455)Instructions burned: 407 (million)
% 97.46/15.26 % (8455)------------------------------
% 97.46/15.26 % (8455)------------------------------
% 97.46/15.27 % (8515)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_7288 for (2863ds/9822Mi)
% 103.44/16.05 % (8483)Instruction limit reached!
% 103.44/16.05 % (8483)------------------------------
% 103.44/16.05 % (8483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.44/16.05 % (8483)Termination reason: Unknown
% 103.44/16.05 % (8483)Termination phase: Saturation
% 103.44/16.05
% 103.44/16.05 % (8483)Memory used [KB]: 12792
% 103.44/16.05 % (8483)Time elapsed: 0.834 s
% 103.44/16.05 % (8483)Instructions burned: 2972 (million)
% 103.44/16.05 % (8483)------------------------------
% 103.44/16.05 % (8483)------------------------------
% 103.44/16.06 % (8649)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_7288 for (2855ds/8425Mi)
% 104.56/16.23 % (8055)Instruction limit reached!
% 104.56/16.23 % (8055)------------------------------
% 104.56/16.23 % (8055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.56/16.23 % (8055)Termination reason: Unknown
% 104.56/16.23 % (8055)Termination phase: Saturation
% 104.56/16.23
% 104.56/16.23 % (8055)Memory used [KB]: 9850
% 104.56/16.23 % (8055)Time elapsed: 2.367 s
% 104.56/16.23 % (8055)Instructions burned: 8216 (million)
% 104.56/16.23 % (8055)------------------------------
% 104.56/16.23 % (8055)------------------------------
% 104.56/16.24 % (8650)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_7288 for (2853ds/3107Mi)
% 105.10/16.36 % (8256)Instruction limit reached!
% 105.10/16.36 % (8256)------------------------------
% 105.10/16.36 % (8256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.10/16.36 % (8256)Termination reason: Unknown
% 105.10/16.36 % (8256)Termination phase: Saturation
% 105.10/16.36
% 105.10/16.36 % (8256)Memory used [KB]: 13944
% 105.10/16.36 % (8256)Time elapsed: 1.721 s
% 105.10/16.36 % (8256)Instructions burned: 5473 (million)
% 105.10/16.36 % (8256)------------------------------
% 105.10/16.36 % (8256)------------------------------
% 105.10/16.37 % (8651)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_7288 for (2852ds/7967Mi)
% 111.19/17.17 % (8162)Instruction limit reached!
% 111.19/17.17 % (8162)------------------------------
% 111.19/17.17 % (8162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.19/17.17 % (8162)Termination reason: Unknown
% 111.19/17.17 % (8162)Termination phase: Saturation
% 111.19/17.17
% 111.19/17.17 % (8162)Memory used [KB]: 16630
% 111.19/17.17 % (8162)Time elapsed: 2.788 s
% 111.19/17.17 % (8162)Instructions burned: 8787 (million)
% 111.19/17.17 % (8162)------------------------------
% 111.19/17.17 % (8162)------------------------------
% 111.19/17.18 % (8652)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_7288 for (2844ds/3629Mi)
% 111.67/17.20 % (8650)Instruction limit reached!
% 111.67/17.20 % (8650)------------------------------
% 111.67/17.20 % (8650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.67/17.20 % (8650)Termination reason: Unknown
% 111.67/17.20 % (8650)Termination phase: Saturation
% 111.67/17.20
% 111.67/17.20 % (8650)Memory used [KB]: 11257
% 111.67/17.20 % (8650)Time elapsed: 0.959 s
% 111.67/17.20 % (8650)Instructions burned: 3108 (million)
% 111.67/17.20 % (8650)------------------------------
% 111.67/17.20 % (8650)------------------------------
% 111.67/17.21 % (8653)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_7288 for (2843ds/939Mi)
% 113.20/17.53 % (8653)Instruction limit reached!
% 113.20/17.53 % (8653)------------------------------
% 113.20/17.53 % (8653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.20/17.53 % (8653)Termination reason: Unknown
% 113.20/17.53 % (8653)Termination phase: Saturation
% 113.20/17.53
% 113.20/17.53 % (8653)Memory used [KB]: 9083
% 113.20/17.53 % (8653)Time elapsed: 0.320 s
% 113.20/17.53 % (8653)Instructions burned: 941 (million)
% 113.20/17.53 % (8653)------------------------------
% 113.20/17.53 % (8653)------------------------------
% 113.20/17.54 % (8654)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_7288 for (2840ds/1188Mi)
% 114.53/17.71 % (8430)Instruction limit reached!
% 114.53/17.71 % (8430)------------------------------
% 114.53/17.71 % (8430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.53/17.71 % (8430)Termination reason: Unknown
% 114.53/17.71 % (8430)Termination phase: Saturation
% 114.53/17.71
% 114.53/17.71 % (8430)Memory used [KB]: 20852
% 114.53/17.71 % (8430)Time elapsed: 2.632 s
% 114.53/17.71 % (8430)Instructions burned: 8384 (million)
% 114.53/17.71 % (8430)------------------------------
% 114.53/17.71 % (8430)------------------------------
% 114.53/17.72 % (8655)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_7288 for (2838ds/3205Mi)
% 115.35/17.90 % (8654)Instruction limit reached!
% 115.35/17.90 % (8654)------------------------------
% 115.35/17.90 % (8654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.35/17.90 % (8654)Termination reason: Unknown
% 115.35/17.90 % (8654)Termination phase: Saturation
% 115.35/17.90
% 115.35/17.90 % (8654)Memory used [KB]: 10874
% 115.35/17.90 % (8654)Time elapsed: 0.364 s
% 115.35/17.90 % (8654)Instructions burned: 1190 (million)
% 115.35/17.90 % (8654)------------------------------
% 115.35/17.90 % (8654)------------------------------
% 115.35/17.91 % (8657)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_7288 for (2836ds/865Mi)
% 118.20/18.19 % (8657)Instruction limit reached!
% 118.20/18.19 % (8657)------------------------------
% 118.20/18.19 % (8657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.20/18.19 % (8657)Termination reason: Unknown
% 118.20/18.19 % (8657)Termination phase: Saturation
% 118.20/18.19
% 118.20/18.19 % (8657)Memory used [KB]: 9210
% 118.20/18.19 % (8657)Time elapsed: 0.280 s
% 118.20/18.19 % (8657)Instructions burned: 867 (million)
% 118.20/18.19 % (8657)------------------------------
% 118.20/18.19 % (8657)------------------------------
% 118.73/18.20 % (8658)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_7288 for (2833ds/7469Mi)
% 119.33/18.31 % (8652)Instruction limit reached!
% 119.33/18.31 % (8652)------------------------------
% 119.33/18.31 % (8652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.33/18.31 % (8652)Termination reason: Unknown
% 119.33/18.31 % (8652)Termination phase: Saturation
% 119.33/18.31
% 119.33/18.31 % (8652)Memory used [KB]: 12409
% 119.33/18.31 % (8652)Time elapsed: 1.150 s
% 119.33/18.31 % (8652)Instructions burned: 3629 (million)
% 119.33/18.31 % (8652)------------------------------
% 119.33/18.31 % (8652)------------------------------
% 119.33/18.32 % (8659)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_7288 for (2832ds/4165Mi)
% 119.33/18.36 % (8515)Instruction limit reached!
% 119.33/18.36 % (8515)------------------------------
% 119.33/18.36 % (8515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.33/18.36 % (8515)Termination reason: Unknown
% 119.33/18.36 % (8515)Termination phase: Saturation
% 119.33/18.36
% 119.33/18.36 % (8515)Memory used [KB]: 17526
% 119.33/18.36 % (8515)Time elapsed: 3.110 s
% 119.33/18.36 % (8515)Instructions burned: 9825 (million)
% 119.33/18.36 % (8515)------------------------------
% 119.33/18.36 % (8515)------------------------------
% 119.33/18.37 % (8660)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_7288 for (2832ds/13468Mi)
% 120.23/18.58 % (8651)Instruction limit reached!
% 120.23/18.58 % (8651)------------------------------
% 120.23/18.58 % (8651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.23/18.58 % (8651)Termination reason: Unknown
% 120.23/18.58 % (8651)Termination phase: Saturation
% 120.23/18.58
% 120.23/18.58 % (8651)Memory used [KB]: 12920
% 120.23/18.58 % (8651)Time elapsed: 2.207 s
% 120.23/18.58 % (8651)Instructions burned: 7967 (million)
% 120.23/18.58 % (8651)------------------------------
% 120.23/18.58 % (8651)------------------------------
% 120.23/18.59 % (8661)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_7288 for (2830ds/2635Mi)
% 120.63/18.61 % (8649)Instruction limit reached!
% 120.63/18.61 % (8649)------------------------------
% 120.63/18.61 % (8649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.63/18.61 % (8649)Termination reason: Unknown
% 120.63/18.61 % (8649)Termination phase: Saturation
% 120.63/18.61
% 120.63/18.61 % (8649)Memory used [KB]: 16502
% 120.63/18.61 % (8649)Time elapsed: 2.556 s
% 120.63/18.61 % (8649)Instructions burned: 8428 (million)
% 120.63/18.61 % (8649)------------------------------
% 120.63/18.61 % (8649)------------------------------
% 120.63/18.62 % (8662)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_7288 for (2829ds/631Mi)
% 120.86/18.71 % (8655)Instruction limit reached!
% 120.86/18.71 % (8655)------------------------------
% 120.86/18.71 % (8655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.86/18.71 % (8655)Termination reason: Unknown
% 120.86/18.71 % (8655)Termination phase: Saturation
% 120.86/18.71
% 120.86/18.71 % (8655)Memory used [KB]: 14328
% 120.86/18.71 % (8655)Time elapsed: 0.990 s
% 120.86/18.71 % (8655)Instructions burned: 3205 (million)
% 120.86/18.71 % (8655)------------------------------
% 120.86/18.71 % (8655)------------------------------
% 120.86/18.72 % (8663)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_7288 for (2828ds/15557Mi)
% 120.96/18.81 % (8662)Instruction limit reached!
% 120.96/18.81 % (8662)------------------------------
% 120.96/18.81 % (8662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.96/18.81 % (8662)Termination reason: Unknown
% 120.96/18.81 % (8662)Termination phase: Saturation
% 120.96/18.81
% 120.96/18.81 % (8662)Memory used [KB]: 9083
% 120.96/18.81 % (8662)Time elapsed: 0.191 s
% 120.96/18.81 % (8662)Instructions burned: 631 (million)
% 120.96/18.81 % (8662)------------------------------
% 120.96/18.81 % (8662)------------------------------
% 120.96/18.82 % (8664)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_7288 for (2827ds/2142Mi)
% 127.14/19.43 % (8661)Instruction limit reached!
% 127.14/19.43 % (8661)------------------------------
% 127.14/19.43 % (8661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.14/19.43 % (8661)Termination reason: Unknown
% 127.14/19.43 % (8661)Termination phase: Saturation
% 127.14/19.43
% 127.14/19.43 % (8661)Memory used [KB]: 11641
% 127.14/19.43 % (8661)Time elapsed: 0.844 s
% 127.14/19.43 % (8661)Instructions burned: 2636 (million)
% 127.14/19.43 % (8661)------------------------------
% 127.14/19.43 % (8661)------------------------------
% 127.14/19.44 % (8665)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_7288 for (2821ds/5624Mi)
% 127.81/19.50 % (8664)Instruction limit reached!
% 127.81/19.50 % (8664)------------------------------
% 127.81/19.50 % (8664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.81/19.50 % (8664)Termination reason: Unknown
% 127.81/19.50 % (8664)Termination phase: Saturation
% 127.81/19.50
% 127.81/19.50 % (8664)Memory used [KB]: 8699
% 127.81/19.50 % (8664)Time elapsed: 0.700 s
% 127.81/19.50 % (8664)Instructions burned: 2143 (million)
% 127.81/19.50 % (8664)------------------------------
% 127.81/19.50 % (8664)------------------------------
% 127.81/19.51 % (8666)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_7288 for (2820ds/1665Mi)
% 128.30/19.61 % (8659)Instruction limit reached!
% 128.30/19.61 % (8659)------------------------------
% 128.30/19.61 % (8659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 128.30/19.61 % (8659)Termination reason: Unknown
% 128.30/19.61 % (8659)Termination phase: Saturation
% 128.30/19.61
% 128.30/19.61 % (8659)Memory used [KB]: 15223
% 128.30/19.61 % (8659)Time elapsed: 1.292 s
% 128.30/19.61 % (8659)Instructions burned: 4166 (million)
% 128.30/19.61 % (8659)------------------------------
% 128.30/19.61 % (8659)------------------------------
% 128.30/19.62 % (8667)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_7288 for (2819ds/64912Mi)
% 131.51/20.04 % (8666)Instruction limit reached!
% 131.51/20.04 % (8666)------------------------------
% 131.51/20.04 % (8666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 131.51/20.04 % (8666)Termination reason: Unknown
% 131.51/20.04 % (8666)Termination phase: Saturation
% 131.51/20.04
% 131.51/20.04 % (8666)Memory used [KB]: 9850
% 131.51/20.04 % (8666)Time elapsed: 0.527 s
% 131.51/20.04 % (8666)Instructions burned: 1665 (million)
% 131.51/20.04 % (8666)------------------------------
% 131.51/20.04 % (8666)------------------------------
% 131.51/20.05 % (8668)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_7288 for (2815ds/7801Mi)
% 134.42/20.55 % (8658)Instruction limit reached!
% 134.42/20.55 % (8658)------------------------------
% 134.42/20.55 % (8658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 134.42/20.55 % (8658)Termination reason: Unknown
% 134.42/20.55 % (8658)Termination phase: Saturation
% 134.42/20.55
% 134.42/20.55 % (8658)Memory used [KB]: 12025
% 134.42/20.55 % (8658)Time elapsed: 2.348 s
% 134.42/20.55 % (8658)Instructions burned: 7471 (million)
% 134.42/20.55 % (8658)------------------------------
% 134.42/20.55 % (8658)------------------------------
% 134.42/20.56 % (8669)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_7288 for (2810ds/15194Mi)
% 139.77/21.22 % (8665)Instruction limit reached!
% 139.77/21.22 % (8665)------------------------------
% 139.77/21.22 % (8665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.77/21.22 % (8665)Termination reason: Unknown
% 139.77/21.22 % (8665)Termination phase: Saturation
% 139.77/21.22
% 139.77/21.22 % (8665)Memory used [KB]: 11513
% 139.77/21.22 % (8665)Time elapsed: 1.782 s
% 139.77/21.22 % (8665)Instructions burned: 5627 (million)
% 139.77/21.22 % (8665)------------------------------
% 139.77/21.22 % (8665)------------------------------
% 139.77/21.23 % (8670)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on DTF2THF_7288 for (2803ds/6753Mi)
% 147.50/22.33 % (8668)Instruction limit reached!
% 147.50/22.33 % (8668)------------------------------
% 147.50/22.33 % (8668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.50/22.33 % (8668)Termination reason: Unknown
% 147.50/22.33 % (8668)Termination phase: Saturation
% 147.50/22.33
% 147.50/22.33 % (8668)Memory used [KB]: 14711
% 147.50/22.33 % (8668)Time elapsed: 2.286 s
% 147.50/22.33 % (8668)Instructions burned: 7801 (million)
% 147.50/22.33 % (8668)------------------------------
% 147.50/22.33 % (8668)------------------------------
% 147.50/22.34 % (8671)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_7288 for (2792ds/1003Mi)
% 148.75/22.52 % (8660)Instruction limit reached!
% 148.75/22.52 % (8660)------------------------------
% 148.75/22.52 % (8660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.75/22.52 % (8660)Termination reason: Unknown
% 148.75/22.52 % (8660)Termination phase: Saturation
% 148.75/22.52
% 148.75/22.52 % (8660)Memory used [KB]: 16247
% 148.75/22.52 % (8660)Time elapsed: 4.152 s
% 148.75/22.52 % (8660)Instructions burned: 13469 (million)
% 148.75/22.52 % (8660)------------------------------
% 148.75/22.52 % (8660)------------------------------
% 148.75/22.53 % (8672)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_7288 for (2790ds/13018Mi)
% 149.30/22.65 % (8671)Instruction limit reached!
% 149.30/22.65 % (8671)------------------------------
% 149.30/22.65 % (8671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 149.30/22.65 % (8671)Termination reason: Unknown
% 149.30/22.65 % (8671)Termination phase: Saturation
% 149.30/22.65
% 149.30/22.65 % (8671)Memory used [KB]: 9083
% 149.30/22.65 % (8671)Time elapsed: 0.307 s
% 149.30/22.65 % (8671)Instructions burned: 1004 (million)
% 149.30/22.65 % (8671)------------------------------
% 149.30/22.65 % (8671)------------------------------
% 149.30/22.66 % (8673)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_7288 for (2789ds/1267Mi)
% 152.59/23.04 % (8673)Instruction limit reached!
% 152.59/23.04 % (8673)------------------------------
% 152.59/23.04 % (8673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 152.59/23.04 % (8673)Termination reason: Unknown
% 152.59/23.04 % (8673)Termination phase: Saturation
% 152.59/23.04
% 152.59/23.04 % (8673)Memory used [KB]: 9083
% 152.59/23.04 % (8673)Time elapsed: 0.382 s
% 152.59/23.04 % (8673)Instructions burned: 1269 (million)
% 152.59/23.04 % (8673)------------------------------
% 152.59/23.04 % (8673)------------------------------
% 152.59/23.05 % (8674)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on DTF2THF_7288 for (2785ds/2570Mi)
% 153.70/23.22 % (8663)Instruction limit reached!
% 153.70/23.22 % (8663)------------------------------
% 153.70/23.22 % (8663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.70/23.22 % (8663)Termination reason: Unknown
% 153.70/23.22 % (8663)Termination phase: Saturation
% 153.70/23.22
% 153.70/23.22 % (8663)Memory used [KB]: 31726
% 153.70/23.22 % (8663)Time elapsed: 4.502 s
% 153.70/23.22 % (8663)Instructions burned: 15559 (million)
% 153.70/23.22 % (8663)------------------------------
% 153.70/23.22 % (8663)------------------------------
% 153.70/23.23 % (8675)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_7288 for (2783ds/13163Mi)
% 154.23/23.40 % (8670)Instruction limit reached!
% 154.23/23.40 % (8670)------------------------------
% 154.23/23.40 % (8670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.23/23.40 % (8670)Termination reason: Unknown
% 154.23/23.40 % (8670)Termination phase: Saturation
% 154.23/23.40
% 154.23/23.40 % (8670)Memory used [KB]: 11001
% 154.23/23.40 % (8670)Time elapsed: 2.166 s
% 154.23/23.40 % (8670)Instructions burned: 6754 (million)
% 154.23/23.40 % (8670)------------------------------
% 154.23/23.40 % (8670)------------------------------
% 152.56/23.41 % (8676)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_7288 for (2781ds/5087Mi)
% 155.94/23.78 % (8674)Instruction limit reached!
% 155.94/23.78 % (8674)------------------------------
% 155.94/23.78 % (8674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.94/23.78 % (8674)Termination reason: Unknown
% 155.94/23.78 % (8674)Termination phase: Saturation
% 155.94/23.78
% 155.94/23.78 % (8674)Memory used [KB]: 10490
% 155.94/23.78 % (8674)Time elapsed: 0.734 s
% 155.94/23.78 % (8674)Instructions burned: 2571 (million)
% 155.94/23.78 % (8674)------------------------------
% 155.94/23.78 % (8674)------------------------------
% 155.94/23.79 % (8677)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_7288 for (2778ds/10380Mi)
% 166.63/25.09 % (8676)Instruction limit reached!
% 166.63/25.09 % (8676)------------------------------
% 166.63/25.09 % (8676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 166.63/25.09 % (8676)Termination reason: Unknown
% 166.63/25.09 % (8676)Termination phase: Saturation
% 166.63/25.09
% 166.63/25.09 % (8676)Memory used [KB]: 13304
% 166.63/25.09 % (8676)Time elapsed: 1.687 s
% 166.63/25.09 % (8676)Instructions burned: 5088 (million)
% 166.63/25.09 % (8676)------------------------------
% 166.63/25.09 % (8676)------------------------------
% 166.63/25.10 % (8678)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_7288 for (2764ds/4218Mi)
% 167.33/25.13 % (8669)Instruction limit reached!
% 167.33/25.13 % (8669)------------------------------
% 167.33/25.13 % (8669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 167.33/25.13 % (8669)Termination reason: Unknown
% 167.33/25.13 % (8669)Termination phase: Saturation
% 167.33/25.13
% 167.33/25.13 % (8669)Memory used [KB]: 15607
% 167.33/25.13 % (8669)Time elapsed: 4.573 s
% 167.33/25.13 % (8669)Instructions burned: 15196 (million)
% 167.33/25.13 % (8669)------------------------------
% 167.33/25.13 % (8669)------------------------------
% 167.33/25.14 % (8679)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_7288 for (2764ds/3971Mi)
% 175.60/26.31 % (8679)Instruction limit reached!
% 175.60/26.31 % (8679)------------------------------
% 175.60/26.31 % (8679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 175.60/26.31 % (8679)Termination reason: Unknown
% 175.60/26.31 % (8679)Termination phase: Saturation
% 175.60/26.31
% 175.60/26.31 % (8679)Memory used [KB]: 10618
% 175.60/26.31 % (8679)Time elapsed: 1.166 s
% 175.60/26.31 % (8679)Instructions burned: 3971 (million)
% 175.60/26.31 % (8679)------------------------------
% 175.60/26.31 % (8679)------------------------------
% 175.60/26.32 % (8680)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_7288 for (2752ds/14014Mi)
% 175.60/26.38 % (8678)Instruction limit reached!
% 175.60/26.38 % (8678)------------------------------
% 175.60/26.38 % (8678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 175.60/26.38 % (8678)Termination reason: Unknown
% 175.60/26.38 % (8678)Termination phase: Saturation
% 175.60/26.38
% 175.60/26.38 % (8678)Memory used [KB]: 12281
% 175.60/26.38 % (8678)Time elapsed: 1.274 s
% 175.60/26.38 % (8678)Instructions burned: 4218 (million)
% 175.60/26.38 % (8678)------------------------------
% 175.60/26.38 % (8678)------------------------------
% 175.60/26.39 % (8681)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_7288 for (2752ds/8517Mi)
% 177.21/26.61 % (8672)Instruction limit reached!
% 177.21/26.61 % (8672)------------------------------
% 177.21/26.61 % (8672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 177.21/26.61 % (8672)Termination reason: Unknown
% 177.21/26.61 % (8672)Termination phase: Saturation
% 177.21/26.61
% 177.21/26.61 % (8672)Memory used [KB]: 37099
% 177.21/26.61 % (8672)Time elapsed: 4.080 s
% 177.21/26.61 % (8672)Instructions burned: 13019 (million)
% 177.21/26.61 % (8672)------------------------------
% 177.21/26.61 % (8672)------------------------------
% 177.21/26.62 % (8682)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_7288 for (2749ds/10148Mi)
% 178.42/26.91 % (8677)Instruction limit reached!
% 178.42/26.91 % (8677)------------------------------
% 178.42/26.91 % (8677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 178.42/26.91 % (8677)Termination reason: Unknown
% 178.42/26.91 % (8677)Termination phase: Saturation
% 178.42/26.91
% 178.42/26.91 % (8677)Memory used [KB]: 11769
% 178.42/26.91 % (8677)Time elapsed: 3.120 s
% 178.42/26.91 % (8677)Instructions burned: 10380 (million)
% 178.42/26.91 % (8677)------------------------------
% 178.42/26.91 % (8677)------------------------------
% 178.42/26.92 % (8683)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_7288 for (2746ds/9078Mi)
% 182.60/27.34 % (8675)Instruction limit reached!
% 182.60/27.34 % (8675)------------------------------
% 182.60/27.34 % (8675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 182.60/27.34 % (8675)Termination reason: Unknown
% 182.60/27.34 % (8675)Termination phase: Saturation
% 182.60/27.34
% 182.60/27.34 % (8675)Memory used [KB]: 21748
% 182.60/27.34 % (8675)Time elapsed: 4.106 s
% 182.60/27.34 % (8675)Instructions burned: 13164 (million)
% 182.60/27.34 % (8675)------------------------------
% 182.60/27.34 % (8675)------------------------------
% 182.60/27.35 % (8684)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_7288 for (2742ds/16164Mi)
% 190.32/28.42 % (8284)Instruction limit reached!
% 190.32/28.42 % (8284)------------------------------
% 190.32/28.42 % (8284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 190.32/28.42 % (8284)Termination reason: Unknown
% 190.32/28.42 % (8284)Termination phase: Saturation
% 190.32/28.42
% 190.32/28.42 % (8284)Memory used [KB]: 28656
% 190.32/28.42 % (8284)Time elapsed: 13.711 s
% 190.32/28.42 % (8284)Instructions burned: 43572 (million)
% 190.32/28.42 % (8284)------------------------------
% 190.32/28.42 % (8284)------------------------------
% 190.32/28.43 % (8685)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_7288 for (2731ds/6102Mi)
% 193.37/29.00 % (8681)Instruction limit reached!
% 193.37/29.00 % (8681)------------------------------
% 193.37/29.00 % (8681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 193.37/29.00 % (8681)Termination reason: Unknown
% 193.37/29.00 % (8681)Termination phase: Saturation
% 193.37/29.00
% 193.37/29.00 % (8681)Memory used [KB]: 21748
% 193.37/29.00 % (8681)Time elapsed: 2.614 s
% 193.37/29.00 % (8681)Instructions burned: 8517 (million)
% 193.37/29.00 % (8681)------------------------------
% 193.37/29.00 % (8681)------------------------------
% 193.37/29.01 % (8687)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on DTF2THF_7288 for (2725ds/10308Mi)
% 198.15/29.68 % (8683)Instruction limit reached!
% 198.15/29.68 % (8683)------------------------------
% 198.15/29.68 % (8683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 198.15/29.68 % (8683)Termination reason: Unknown
% 198.15/29.68 % (8683)Termination phase: Saturation
% 198.15/29.68
% 198.15/29.68 % (8683)Memory used [KB]: 20340
% 198.15/29.68 % (8683)Time elapsed: 2.758 s
% 198.15/29.68 % (8683)Instructions burned: 9079 (million)
% 198.15/29.68 % (8683)------------------------------
% 198.15/29.68 % (8683)------------------------------
% 198.15/29.69 % (8915)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on DTF2THF_7288 for (2719ds/4041Mi)
% 198.74/29.78 % (8682)Instruction limit reached!
% 198.74/29.78 % (8682)------------------------------
% 198.74/29.78 % (8682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 198.74/29.78 % (8682)Termination reason: Unknown
% 198.74/29.78 % (8682)Termination phase: Saturation
% 198.74/29.78
% 198.74/29.78 % (8682)Memory used [KB]: 17654
% 198.74/29.78 % (8682)Time elapsed: 3.156 s
% 198.74/29.78 % (8682)Instructions burned: 10149 (million)
% 198.74/29.78 % (8682)------------------------------
% 198.74/29.78 % (8682)------------------------------
% 198.74/29.79 % (8960)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=6901:si=on:rtra=on_0 on DTF2THF_7288 for (2718ds/6901Mi)
% 203.66/30.32 % (8685)Refutation not found, non-redundant clauses discarded% (8685)------------------------------
% 203.66/30.32 % (8685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 203.66/30.32 % (8685)Termination reason: Refutation not found, non-redundant clauses discarded
% 203.66/30.32
% 203.66/30.32 % (8685)Memory used [KB]: 13176
% 203.66/30.32 % (8685)Time elapsed: 1.895 s
% 203.66/30.32 % (8685)Instructions burned: 6015 (million)
% 203.66/30.32 % (8685)------------------------------
% 203.66/30.32 % (8685)------------------------------
% 203.66/30.33 % (9197)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_7288 for (2712ds/5576Mi)
% 207.30/30.91 % (8680)Instruction limit reached!
% 207.30/30.91 % (8680)------------------------------
% 207.30/30.91 % (8680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 207.30/30.91 % (8680)Termination reason: Unknown
% 207.30/30.91 % (8680)Termination phase: Saturation
% 207.30/30.91
% 207.30/30.91 % (8680)Memory used [KB]: 19445
% 207.30/30.91 % (8680)Time elapsed: 4.598 s
% 207.30/30.91 % (8680)Instructions burned: 14014 (million)
% 207.30/30.91 % (8680)------------------------------
% 207.30/30.91 % (8680)------------------------------
% 207.30/30.93 % (9275)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_7288 for (2706ds/2014Mi)
% 207.30/31.02 % (8915)Instruction limit reached!
% 207.30/31.02 % (8915)------------------------------
% 207.30/31.02 % (8915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 207.30/31.02 % (8915)Termination reason: Unknown
% 207.30/31.02 % (8915)Termination phase: Saturation
% 207.30/31.02
% 207.30/31.02 % (8915)Memory used [KB]: 12281
% 207.30/31.02 % (8915)Time elapsed: 1.335 s
% 207.30/31.02 % (8915)Instructions burned: 4042 (million)
% 207.30/31.02 % (8915)------------------------------
% 207.30/31.02 % (8915)------------------------------
% 208.73/31.04 % (9276)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=5115:si=on:rtra=on_0 on DTF2THF_7288 for (2705ds/5115Mi)
% 211.60/31.54 % (9275)Instruction limit reached!
% 211.60/31.54 % (9275)------------------------------
% 211.60/31.54 % (9275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 211.60/31.54 % (9275)Termination reason: Unknown
% 211.60/31.54 % (9275)Termination phase: Saturation
% 211.60/31.54
% 211.60/31.54 % (9275)Memory used [KB]: 16758
% 211.60/31.54 % (9275)Time elapsed: 0.641 s
% 211.60/31.54 % (9275)Instructions burned: 2015 (million)
% 211.60/31.54 % (9275)------------------------------
% 211.60/31.54 % (9275)------------------------------
% 211.60/31.55 % (9277)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on DTF2THF_7288 for (2700ds/13001Mi)
% 213.66/31.96 % (8960)Instruction limit reached!
% 213.66/31.96 % (8960)------------------------------
% 213.66/31.96 % (8960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 213.66/31.96 % (8960)Termination reason: Unknown
% 213.66/31.96 % (8960)Termination phase: Saturation
% 213.66/31.96
% 213.66/31.96 % (8960)Memory used [KB]: 15991
% 213.66/31.96 % (8960)Time elapsed: 2.177 s
% 213.66/31.96 % (8960)Instructions burned: 6901 (million)
% 213.66/31.96 % (8960)------------------------------
% 213.66/31.96 % (8960)------------------------------
% 213.66/31.97 % (9278)dis+10_1:2_aac=none:acc=on:atotf=0.1:au=on:fde=none:ins=1:ixr=off:nwc=5.0:i=11105:si=on:rtra=on_0 on DTF2THF_7288 for (2696ds/11105Mi)
% 215.73/32.08 % (8684)Instruction limit reached!
% 215.73/32.08 % (8684)------------------------------
% 215.73/32.08 % (8684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 215.73/32.08 % (8684)Termination reason: Unknown
% 215.73/32.08 % (8684)Termination phase: Saturation
% 215.73/32.08
% 215.73/32.08 % (8684)Memory used [KB]: 14839
% 215.73/32.08 % (8684)Time elapsed: 4.730 s
% 215.73/32.08 % (8684)Instructions burned: 16165 (million)
% 215.73/32.08 % (8684)------------------------------
% 215.73/32.08 % (8684)------------------------------
% 215.73/32.09 % (9279)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=13832:si=on:rtra=on_0 on DTF2THF_7288 for (2695ds/13832Mi)
% 215.73/32.12 % (9197)Instruction limit reached!
% 215.73/32.12 % (9197)------------------------------
% 215.73/32.12 % (9197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 215.73/32.12 % (9197)Termination reason: Unknown
% 215.73/32.12 % (9197)Termination phase: Saturation
% 215.73/32.12
% 215.73/32.12 % (9197)Memory used [KB]: 14583
% 215.73/32.12 % (9197)Time elapsed: 1.813 s
% 215.73/32.12 % (9197)Instructions burned: 5577 (million)
% 215.73/32.12 % (9197)------------------------------
% 215.73/32.12 % (9197)------------------------------
% 216.43/32.13 % (9280)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=32887:si=on:rtra=on_0 on DTF2THF_7288 for (2694ds/32887Mi)
% 217.29/32.32 % (8687)Instruction limit reached!
% 217.29/32.32 % (8687)------------------------------
% 217.29/32.32 % (8687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 217.29/32.32 % (8687)Termination reason: Unknown
% 217.29/32.32 % (8687)Termination phase: Saturation
% 217.29/32.32
% 217.29/32.32 % (8687)Memory used [KB]: 14328
% 217.29/32.32 % (8687)Time elapsed: 3.312 s
% 217.29/32.32 % (8687)Instructions burned: 10309 (million)
% 217.29/32.32 % (8687)------------------------------
% 217.29/32.32 % (8687)------------------------------
% 217.29/32.33 % (9281)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on DTF2THF_7288 for (2692ds/3362Mi)
% 218.54/32.63 % (9276)Instruction limit reached!
% 218.54/32.63 % (9276)------------------------------
% 218.54/32.63 % (9276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 218.54/32.63 % (9276)Termination reason: Unknown
% 218.54/32.63 % (9276)Termination phase: Saturation
% 218.54/32.63
% 218.54/32.63 % (9276)Memory used [KB]: 21620
% 218.54/32.63 % (9276)Time elapsed: 1.592 s
% 218.54/32.63 % (9276)Instructions burned: 5115 (million)
% 218.54/32.63 % (9276)------------------------------
% 218.54/32.63 % (9276)------------------------------
% 218.54/32.64 % (9282)ott+1002_1:1_au=on:cnfonf=lazy_simp:nwc=5.0:sgt=5:ss=axioms:st=1.5:i=24965:si=on:rtra=on_0 on DTF2THF_7288 for (2689ds/24965Mi)
% 224.71/33.38 % (9281)Instruction limit reached!
% 224.71/33.38 % (9281)------------------------------
% 224.71/33.38 % (9281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 224.71/33.38 % (9281)Termination reason: Unknown
% 224.71/33.38 % (9281)Termination phase: Saturation
% 224.71/33.38
% 224.71/33.38 % (9281)Memory used [KB]: 14072
% 224.71/33.38 % (9281)Time elapsed: 1.046 s
% 224.71/33.38 % (9281)Instructions burned: 3364 (million)
% 224.71/33.38 % (9281)------------------------------
% 224.71/33.38 % (9281)------------------------------
% 224.71/33.39 % (9283)lrs+1010_2:1_amm=off:avsq=on:c=on:cbe=off:e2e=on:fsr=off:ins=3:s2a=on:s2at=-1.0:i=15705:si=on:rtra=on_0 on DTF2THF_7288 for (2682ds/15705Mi)
% 236.83/35.12 % (9277)Instruction limit reached!
% 236.83/35.12 % (9277)------------------------------
% 236.83/35.12 % (9277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 236.83/35.12 % (9277)Termination reason: Unknown
% 236.83/35.12 % (9277)Termination phase: Saturation
% 236.83/35.12
% 236.83/35.12 % (9277)Memory used [KB]: 18166
% 236.83/35.12 % (9277)Time elapsed: 3.572 s
% 236.83/35.12 % (9277)Instructions burned: 13003 (million)
% 236.83/35.12 % (9277)------------------------------
% 236.83/35.12 % (9277)------------------------------
% 237.55/35.13 % (9284)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1536:si=on:rtra=on_0 on DTF2THF_7288 for (2664ds/1536Mi)
% 238.59/35.39 % (9278)Instruction limit reached!
% 238.59/35.39 % (9278)------------------------------
% 238.59/35.39 % (9278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 238.59/35.39 % (9278)Termination reason: Unknown
% 238.59/35.39 % (9278)Termination phase: Saturation
% 238.59/35.39
% 238.59/35.39 % (9278)Memory used [KB]: 31982
% 238.59/35.39 % (9278)Time elapsed: 3.414 s
% 238.59/35.39 % (9278)Instructions burned: 11105 (million)
% 238.59/35.39 % (9278)------------------------------
% 238.59/35.39 % (9278)------------------------------
% 239.20/35.40 % (9285)dis+10_1:1_fde=none:kws=precedence:piset=not:prag=on:slsq=on:slsqc=1:sp=unary_frequency:i=23684:si=on:rtra=on_0 on DTF2THF_7288 for (2661ds/23684Mi)
% 240.20/35.61 % (9284)Instruction limit reached!
% 240.20/35.61 % (9284)------------------------------
% 240.20/35.61 % (9284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 240.20/35.61 % (9284)Termination reason: Unknown
% 240.20/35.61 % (9284)Termination phase: Saturation
% 240.20/35.61
% 240.20/35.61 % (9284)Memory used [KB]: 9338
% 240.20/35.61 % (9284)Time elapsed: 0.478 s
% 240.20/35.61 % (9284)Instructions burned: 1538 (million)
% 240.20/35.61 % (9284)------------------------------
% 240.20/35.61 % (9284)------------------------------
% 240.20/35.62 % (9286)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=4925:si=on:rtra=on_0 on DTF2THF_7288 for (2659ds/4925Mi)
% 241.67/35.85 % (9280)First to succeed.
% 241.67/35.85 % (9280)Refutation found. Thanks to Tanya!
% 241.67/35.85 % SZS status Theorem for DTF2THF_7288
% 241.67/35.85 % SZS output start Proof for DTF2THF_7288
% 241.67/35.85 thf(type_def_5, type, nat: $tType).
% 241.67/35.85 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 241.67/35.85 thf(type_def_8, type, list: ($tType) > $tType).
% 241.67/35.85 thf(type_def_9, type, set: ($tType) > $tType).
% 241.67/35.85 thf(type_def_10, type, capacity: $tType).
% 241.67/35.85 thf(type_def_11, type, a: $tType).
% 241.67/35.85 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 241.67/35.85 thf(func_def_1, type, list: ($tType) > $tType).
% 241.67/35.85 thf(func_def_2, type, capacity: $tType).
% 241.67/35.85 thf(func_def_3, type, set: ($tType) > $tType).
% 241.67/35.85 thf(func_def_4, type, nat: $tType).
% 241.67/35.85 thf(func_def_5, type, a: $tType).
% 241.67/35.85 thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_7, type, size: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_9, type, order: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_10, type, group_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_11, type, no_bot: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_12, type, no_top: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_13, type, linorder: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_14, type, preorder: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_15, type, wellorder: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_16, type, semigroup_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_17, type, dense_order: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_18, type, linordered_idom: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_19, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_20, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_21, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_22, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_23, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_24, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_25, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_26, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 241.67/35.85 thf(func_def_27, type, connected: !>[X0: $tType]:((product_prod @ nat @ nat > X0) > nat > nat > $o)).
% 241.67/35.85 thf(func_def_28, type, dist: !>[X0: $tType]:((product_prod @ nat @ nat > X0) > nat > nat > nat > $o)).
% 241.67/35.85 thf(func_def_29, type, isPath: !>[X0: $tType]:((product_prod @ nat @ nat > X0) > nat > list @ product_prod @ nat @ nat > nat > $o)).
% 241.67/35.85 thf(func_def_30, type, isShortestPath: !>[X0: $tType]:((product_prod @ nat @ nat > X0) > nat > list @ product_prod @ nat @ nat > nat > $o)).
% 241.67/35.85 thf(func_def_31, type, isSimplePath: !>[X0: $tType]:((product_prod @ nat @ nat > X0) > nat > list @ product_prod @ nat @ nat > nat > $o)).
% 241.67/35.85 thf(func_def_32, type, min_dist: !>[X0: $tType]:((product_prod @ nat @ nat > X0) > nat > nat > nat)).
% 241.67/35.85 thf(func_def_33, type, reachableNodes: !>[X0: $tType]:((product_prod @ nat @ nat > X0) > nat > set @ nat)).
% 241.67/35.85 thf(func_def_34, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 241.67/35.85 thf(func_def_35, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 241.67/35.85 thf(func_def_36, type, ord_Least: !>[X0: $tType]:((X0 > $o) > X0)).
% 241.67/35.85 thf(func_def_37, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 241.67/35.85 thf(func_def_38, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 241.67/35.85 thf(func_def_39, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 241.67/35.85 thf(func_def_40, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 241.67/35.85 thf(func_def_41, type, c: product_prod @ nat @ nat > capacity).
% 241.67/35.85 thf(func_def_42, type, c2: product_prod @ nat @ nat > a).
% 241.67/35.85 thf(func_def_43, type, p: list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_44, type, p1: list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_45, type, p1a: list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_46, type, p2: list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_47, type, p2_a: list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_48, type, p3: list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_49, type, s: nat).
% 241.67/35.85 thf(func_def_50, type, t: nat).
% 241.67/35.85 thf(func_def_51, type, u: nat).
% 241.67/35.85 thf(func_def_52, type, ua: nat).
% 241.67/35.85 thf(func_def_53, type, v: nat).
% 241.67/35.85 thf(func_def_54, type, va: nat).
% 241.67/35.85 thf(func_def_71, type, sK0: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 241.67/35.85 thf(func_def_72, type, sK1: !>[X0: $tType]:(nat > (X0 > nat) > X0 > (X0 > $o) > X0)).
% 241.67/35.85 thf(func_def_73, type, sK2: nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_74, type, sK3: nat > nat > nat).
% 241.67/35.85 thf(func_def_75, type, sK4: (nat > nat) > nat).
% 241.67/35.85 thf(func_def_76, type, sK5: (nat > nat) > nat).
% 241.67/35.85 thf(func_def_77, type, sK6: (nat > $o) > nat).
% 241.67/35.85 thf(func_def_78, type, sK7: nat > nat > nat > nat).
% 241.67/35.85 thf(func_def_79, type, sK8: (nat > $o) > nat > nat > nat).
% 241.67/35.85 thf(func_def_80, type, sK9: (nat > $o) > nat).
% 241.67/35.85 thf(func_def_81, type, sK10: (nat > $o) > nat > nat > nat).
% 241.67/35.85 thf(func_def_82, type, sK11: !>[X0: $tType]:((nat > $o) > nat > nat > (product_prod @ nat @ nat > X0) > nat)).
% 241.67/35.85 thf(func_def_83, type, sK12: nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_84, type, sK13: !>[X0: $tType]:(nat > nat > (product_prod @ nat @ nat > X0) > list @ product_prod @ nat @ nat)).
% 241.67/35.85 thf(func_def_85, type, sK14: nat > nat > nat > nat).
% 241.67/35.85 thf(func_def_86, type, sK15: (nat > nat) > nat).
% 241.67/35.85 thf(func_def_87, type, sK16: (nat > nat) > nat).
% 241.67/35.85 thf(func_def_88, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 241.67/35.85 thf(func_def_89, type, sK18: nat > nat > nat).
% 241.67/35.85 thf(func_def_90, type, sK19: !>[X0: $tType]:(nat > nat > (product_prod @ nat @ nat > X0) > nat)).
% 241.67/35.85 thf(func_def_91, type, sK20: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 241.67/35.85 thf(func_def_92, type, sK21: !>[X0: $tType]:(nat > nat > (product_prod @ nat @ nat > X0) > nat)).
% 241.67/35.85 thf(func_def_93, type, sK22: nat > nat > nat).
% 241.67/35.85 thf(func_def_94, type, sK23: nat > nat > nat).
% 241.67/35.85 thf(func_def_95, type, sK24: nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_96, type, sK25: !>[X0: $tType]:(nat > nat > nat > (product_prod @ nat @ nat > X0) > nat)).
% 241.67/35.85 thf(func_def_97, type, sK26: !>[X0: $tType]:(nat > nat > (product_prod @ nat @ nat > X0) > list @ product_prod @ nat @ nat)).
% 241.67/35.85 thf(func_def_98, type, sK27: nat > nat > nat).
% 241.67/35.85 thf(func_def_99, type, sK28: nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_101, type, sK30: nat > nat > nat).
% 241.67/35.85 thf(func_def_102, type, sK31: nat > nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_103, type, sK32: list @ product_prod @ nat @ nat > nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_104, type, sK33: nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_105, type, sK34: nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_106, type, sK35: nat > nat > nat).
% 241.67/35.85 thf(func_def_107, type, sK36: nat > nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_108, type, sK37: list @ product_prod @ nat @ nat > nat > nat > list @ product_prod @ nat @ nat).
% 241.67/35.85 thf(func_def_109, type, ph38: !>[X0: $tType]:(X0)).
% 241.67/35.85 thf(f10645,plain,(
% 241.67/35.85 $false),
% 241.67/35.85 inference(avatar_sat_refutation,[status(thm)],[f7480,f10554,f10638])).
% 241.67/35.85 thf(f10638,plain,(
% 241.67/35.85 ~spl29_3),
% 241.67/35.85 inference(avatar_contradiction_clause,[status(thm)],[f10637])).
% 241.67/35.85 thf(f10637,plain,(
% 241.67/35.85 $false | ~spl29_3),
% 241.67/35.85 inference(subsumption_resolution,[status(thm)],[f10608,f1194])).
% 241.67/35.85 thf(f1194,plain,(
% 241.67/35.85 ((ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))) != $true)),
% 241.67/35.85 inference(cnf_transformation,[status(thm)],[f890])).
% 241.67/35.85 thf(f890,plain,(
% 241.67/35.85 ((ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))) != $true)),
% 241.67/35.85 inference(flattening,[status(thm)],[f365])).
% 241.67/35.85 thf(f365,plain,(
% 241.67/35.85 ~((ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))) = $true)),
% 241.67/35.85 inference(fool_elimination,[status(thm)],[f364])).
% 241.67/35.85 thf(f364,plain,(
% 241.67/35.85 ~(ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a)))),
% 241.67/35.85 inference(rectify,[status(thm)],[f302])).
% 241.67/35.85 thf(f302,negated_conjecture,(
% 241.67/35.85 ~(ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a)))),
% 241.67/35.85 inference(negated_conjecture,[status(cth)],[f301])).
% 241.67/35.85 thf(f301,conjecture,(
% 241.67/35.85 (ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a)))),
% 241.67/35.85 file('/export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2THF_7288.p',conj_0)).
% 241.67/35.85 thf(f10608,plain,(
% 241.67/35.85 ((ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))) = $true) | ~spl29_3),
% 241.67/35.85 inference(backward_demodulation,[status(thm)],[f9107,f1520])).
% 241.67/35.85 thf(f1520,plain,(
% 241.67/35.85 ((min_dist @ capacity @ c @ ua @ t) = (size_size @ list @ product_prod @ nat @ nat @ p2_a)) | ~spl29_3),
% 241.67/35.85 inference(avatar_component_clause,[status(thm)],[f1518])).
% 241.67/35.85 thf(f1518,definition,(
% 241.67/35.85 spl29_3 <=> ((min_dist @ capacity @ c @ ua @ t) = (size_size @ list @ product_prod @ nat @ nat @ p2_a))),
% 241.67/35.85 introduced(definition,[new_symbols(naming,[spl29_3])],[avatar_definition])).
% 241.67/35.85 thf(f9107,plain,(
% 241.67/35.85 ($true = (ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (min_dist @ capacity @ c @ ua @ t))))),
% 241.67/35.85 inference(superposition,[status(thm)],[f1550,f1215])).
% 241.67/35.85 thf(f1215,plain,(
% 241.67/35.85 ((min_dist @ capacity @ c @ s @ t) = (plus_plus @ nat @ (min_dist @ capacity @ c @ s @ ua) @ (min_dist @ capacity @ c @ ua @ t)))),
% 241.67/35.85 inference(cnf_transformation,[status(thm)],[f1])).
% 241.67/35.85 thf(f1,axiom,(
% 241.67/35.85 ((min_dist @ capacity @ c @ s @ t) = (plus_plus @ nat @ (min_dist @ capacity @ c @ s @ ua) @ (min_dist @ capacity @ c @ ua @ t)))),
% 241.67/35.85 file('/export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2THF_7288.p',fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062)).
% 241.67/35.85 thf(f1550,plain,(
% 241.67/35.85 ( ! [X0 : nat] : (((ord_less @ nat @ (plus_plus @ nat @ (min_dist @ capacity @ c @ s @ ua) @ X0) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ X0)) = $true)) )),
% 241.67/35.85 inference(trivial_inequality_removal,[status(thm)],[f1548])).
% 241.67/35.85 thf(f1548,plain,(
% 241.67/35.85 ( ! [X0 : nat] : (((ord_less @ nat @ (plus_plus @ nat @ (min_dist @ capacity @ c @ s @ ua) @ X0) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ X0)) = $true) | ($true != $true)) )),
% 241.67/35.85 inference(superposition,[status(thm)],[f1188,f1187])).
% 241.67/35.85 thf(f1187,plain,(
% 241.67/35.85 ((ord_less @ nat @ (min_dist @ capacity @ c @ s @ ua) @ (size_size @ list @ product_prod @ nat @ nat @ p1a)) = $true)),
% 241.67/35.85 inference(cnf_transformation,[status(thm)],[f555])).
% 241.67/35.85 thf(f555,plain,(
% 241.67/35.85 ((ord_less @ nat @ (min_dist @ capacity @ c @ s @ ua) @ (size_size @ list @ product_prod @ nat @ nat @ p1a)) = $true)),
% 241.67/35.85 inference(fool_elimination,[status(thm)],[f554])).
% 241.67/35.85 thf(f554,plain,(
% 241.67/35.85 (ord_less @ nat @ (min_dist @ capacity @ c @ s @ ua) @ (size_size @ list @ product_prod @ nat @ nat @ p1a))),
% 241.67/35.85 inference(rectify,[status(thm)],[f2])).
% 241.67/35.85 thf(f2,axiom,(
% 241.67/35.85 (ord_less @ nat @ (min_dist @ capacity @ c @ s @ ua) @ (size_size @ list @ product_prod @ nat @ nat @ p1a))),
% 241.67/35.85 file('/export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2THF_7288.p',fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062)).
% 241.67/35.85 thf(f1188,plain,(
% 241.67/35.85 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != (ord_less @ nat @ X0 @ X1)) | ($true = (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X2)))) )),
% 241.67/35.85 inference(cnf_transformation,[status(thm)],[f969])).
% 241.67/35.85 thf(f969,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X2))) | ($true != (ord_less @ nat @ X0 @ X1)))),
% 241.67/35.85 inference(ennf_transformation,[status(thm)],[f785])).
% 241.67/35.85 thf(f785,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (ord_less @ nat @ X0 @ X1)) => ($true = (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X2))))),
% 241.67/35.85 inference(fool_elimination,[status(thm)],[f784])).
% 241.67/35.85 thf(f784,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X2)))),
% 241.67/35.85 inference(rectify,[status(thm)],[f113])).
% 241.67/35.85 thf(f113,axiom,(
% 241.67/35.85 ! [X27 : nat,X28 : nat,X2 : nat] : ((ord_less @ nat @ X27 @ X28) => (ord_less @ nat @ (plus_plus @ nat @ X27 @ X2) @ (plus_plus @ nat @ X28 @ X2)))),
% 241.67/35.85 file('/export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2THF_7288.p',fact_112_add__less__mono1)).
% 241.67/35.85 thf(f10554,plain,(
% 241.67/35.85 ~spl29_4),
% 241.67/35.85 inference(avatar_contradiction_clause,[status(thm)],[f10553])).
% 241.67/35.85 thf(f10553,plain,(
% 241.67/35.85 $false | ~spl29_4),
% 241.67/35.85 inference(subsumption_resolution,[status(thm)],[f10552,f1194])).
% 241.67/35.85 thf(f10552,plain,(
% 241.67/35.85 ((ord_less @ nat @ (min_dist @ capacity @ c @ s @ t) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))) = $true) | ~spl29_4),
% 241.67/35.85 inference(forward_demodulation,[status(thm)],[f10525,f1215])).
% 241.67/35.85 thf(f10525,plain,(
% 241.67/35.85 ($true = (ord_less @ nat @ (plus_plus @ nat @ (min_dist @ capacity @ c @ s @ ua) @ (min_dist @ capacity @ c @ ua @ t)) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a)))) | ~spl29_4),
% 241.67/35.85 inference(trivial_inequality_removal,[status(thm)],[f10506])).
% 241.67/35.85 thf(f10506,plain,(
% 241.67/35.85 ($true != $true) | ($true = (ord_less @ nat @ (plus_plus @ nat @ (min_dist @ capacity @ c @ s @ ua) @ (min_dist @ capacity @ c @ ua @ t)) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a)))) | ~spl29_4),
% 241.67/35.85 inference(superposition,[status(thm)],[f1578,f1524])).
% 241.67/35.85 thf(f1524,plain,(
% 241.67/35.85 ($true = (ord_less @ nat @ (min_dist @ capacity @ c @ ua @ t) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))) | ~spl29_4),
% 241.67/35.85 inference(avatar_component_clause,[status(thm)],[f1522])).
% 241.67/35.85 thf(f1522,definition,(
% 241.67/35.85 spl29_4 <=> ($true = (ord_less @ nat @ (min_dist @ capacity @ c @ ua @ t) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a)))),
% 241.67/35.85 introduced(definition,[new_symbols(naming,[spl29_4])],[avatar_definition])).
% 241.67/35.85 thf(f1578,plain,(
% 241.67/35.85 ( ! [X0 : nat,X1 : nat] : (($true != (ord_less @ nat @ X0 @ X1)) | ($true = (ord_less @ nat @ (plus_plus @ nat @ (min_dist @ capacity @ c @ s @ ua) @ X0) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ X1)))) )),
% 241.67/35.85 inference(trivial_inequality_removal,[status(thm)],[f1576])).
% 241.67/35.85 thf(f1576,plain,(
% 241.67/35.85 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ (plus_plus @ nat @ (min_dist @ capacity @ c @ s @ ua) @ X0) @ (plus_plus @ nat @ (size_size @ list @ product_prod @ nat @ nat @ p1a) @ X1))) | ($true != (ord_less @ nat @ X0 @ X1)) | ($true != $true)) )),
% 241.67/35.85 inference(superposition,[status(thm)],[f1231,f1187])).
% 241.67/35.85 thf(f1231,plain,(
% 241.67/35.85 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != (ord_less @ nat @ X0 @ X1)) | ((ord_less @ nat @ X2 @ X3) != $true) | ($true = (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X3)))) )),
% 241.67/35.85 inference(cnf_transformation,[status(thm)],[f973])).
% 241.67/35.85 thf(f973,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true != (ord_less @ nat @ X0 @ X1)) | ((ord_less @ nat @ X2 @ X3) != $true) | ($true = (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X3))))),
% 241.67/35.85 inference(flattening,[status(thm)],[f972])).
% 241.67/35.85 thf(f972,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true = (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X3))) | ((ord_less @ nat @ X2 @ X3) != $true)) | ($true != (ord_less @ nat @ X0 @ X1)))),
% 241.67/35.85 inference(ennf_transformation,[status(thm)],[f709])).
% 241.67/35.85 thf(f709,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = (ord_less @ nat @ X0 @ X1)) => (((ord_less @ nat @ X2 @ X3) = $true) => ($true = (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X3)))))),
% 241.67/35.85 inference(fool_elimination,[status(thm)],[f708])).
% 241.67/35.85 thf(f708,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((ord_less @ nat @ X0 @ X1) => ((ord_less @ nat @ X2 @ X3) => (ord_less @ nat @ (plus_plus @ nat @ X0 @ X2) @ (plus_plus @ nat @ X1 @ X3))))),
% 241.67/35.85 inference(rectify,[status(thm)],[f116])).
% 241.67/35.85 thf(f116,axiom,(
% 241.67/35.85 ! [X27 : nat,X28 : nat,X2 : nat,X42 : nat] : ((ord_less @ nat @ X27 @ X28) => ((ord_less @ nat @ X2 @ X42) => (ord_less @ nat @ (plus_plus @ nat @ X27 @ X2) @ (plus_plus @ nat @ X28 @ X42))))),
% 241.67/35.85 file('/export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2THF_7288.p',fact_115_add__less__mono)).
% 241.67/35.85 thf(f7480,plain,(
% 241.67/35.85 spl29_4 | spl29_3),
% 241.67/35.85 inference(avatar_split_clause,[status(thm)],[f3992,f1518,f1522])).
% 241.67/35.85 thf(f3992,plain,(
% 241.67/35.85 ($true = (ord_less @ nat @ (min_dist @ capacity @ c @ ua @ t) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))) | ((min_dist @ capacity @ c @ ua @ t) = (size_size @ list @ product_prod @ nat @ nat @ p2_a))),
% 241.67/35.85 inference(trivial_inequality_removal,[status(thm)],[f3984])).
% 241.67/35.85 thf(f3984,plain,(
% 241.67/35.85 ($true = (ord_less @ nat @ (min_dist @ capacity @ c @ ua @ t) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))) | ((min_dist @ capacity @ c @ ua @ t) = (size_size @ list @ product_prod @ nat @ nat @ p2_a)) | ($true != $true)),
% 241.67/35.85 inference(superposition,[status(thm)],[f1166,f1138])).
% 241.67/35.85 thf(f1138,plain,(
% 241.67/35.85 ((ord_less_eq @ nat @ (min_dist @ capacity @ c @ ua @ t) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a)) = $true)),
% 241.67/35.85 inference(cnf_transformation,[status(thm)],[f465])).
% 241.67/35.85 thf(f465,plain,(
% 241.67/35.85 ((ord_less_eq @ nat @ (min_dist @ capacity @ c @ ua @ t) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a)) = $true)),
% 241.67/35.85 inference(fool_elimination,[status(thm)],[f464])).
% 241.67/35.85 thf(f464,plain,(
% 241.67/35.85 (ord_less_eq @ nat @ (min_dist @ capacity @ c @ ua @ t) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))),
% 241.67/35.85 inference(rectify,[status(thm)],[f3])).
% 241.67/35.85 thf(f3,axiom,(
% 241.67/35.85 (ord_less_eq @ nat @ (min_dist @ capacity @ c @ ua @ t) @ (size_size @ list @ product_prod @ nat @ nat @ p2_a))),
% 241.67/35.85 file('/export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2THF_7288.p',fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062)).
% 241.67/35.85 thf(f1166,plain,(
% 241.67/35.85 ( ! [X0 : nat,X1 : nat] : (($true != (ord_less_eq @ nat @ X0 @ X1)) | (X0 = X1) | ($true = (ord_less @ nat @ X0 @ X1))) )),
% 241.67/35.85 inference(cnf_transformation,[status(thm)],[f1026])).
% 241.67/35.85 thf(f1026,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != (ord_less_eq @ nat @ X0 @ X1)) | ($true = (ord_less @ nat @ X0 @ X1)))),
% 241.67/35.85 inference(flattening,[status(thm)],[f1025])).
% 241.67/35.85 thf(f1025,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat] : ((($true = (ord_less @ nat @ X0 @ X1)) | (X0 = X1)) | ($true != (ord_less_eq @ nat @ X0 @ X1)))),
% 241.67/35.85 inference(ennf_transformation,[status(thm)],[f697])).
% 241.67/35.85 thf(f697,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat] : (($true = (ord_less_eq @ nat @ X0 @ X1)) => ((X0 != X1) => ($true = (ord_less @ nat @ X0 @ X1))))),
% 241.67/35.85 inference(fool_elimination,[status(thm)],[f696])).
% 241.67/35.85 thf(f696,plain,(
% 241.67/35.85 ! [X0 : nat,X1 : nat] : ((ord_less_eq @ nat @ X0 @ X1) => ((X0 != X1) => (ord_less @ nat @ X0 @ X1)))),
% 241.67/35.85 inference(rectify,[status(thm)],[f58])).
% 241.67/35.85 thf(f58,axiom,(
% 241.67/35.85 ! [X3 : nat,X4 : nat] : ((ord_less_eq @ nat @ X3 @ X4) => ((X3 != X4) => (ord_less @ nat @ X3 @ X4)))),
% 241.67/35.85 file('/export/starexec/sandbox2/tmp/tmp.TlDsJuhsAT/DTF2THF_7288.p',fact_57_le__neq__implies__less)).
% 241.67/35.85 % SZS output end Proof for DTF2THF_7288
% 241.67/35.85 % (9280)------------------------------
% 241.67/35.85 % (9280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 241.67/35.85 % (9280)Termination reason: Refutation
% 241.67/35.85
% 241.67/35.85 % (9280)Memory used [KB]: 12537
% 241.67/35.85 % (9280)Time elapsed: 3.741 s
% 241.67/35.85 % (9280)Instructions burned: 14120 (million)
% 241.67/35.85 % (9280)------------------------------
% 241.67/35.85 % (9280)------------------------------
% 241.67/35.85 % (7431)Success in time 34.277 s
%------------------------------------------------------------------------------